Merge pull request #29309 from varun-jaiswal17:fix_dll_mismatch

Fix ONNXRuntime dll path mismatch #29309

**1. C2664 build error in `net_impl_backend.cpp`**
`EnableProfiling()` expects `const wchar_t*` on Windows (`ORTCHAR_T`), but was passed `const char*`. 

Fixed by converting to `std::wstring`, as suggested in #29278 

---

**2. Wrong ORT DLL loaded at runtime (`modules/dnn/CMakeLists.txt`)**
With `DOWNLOAD_ONNXRUNTIME=ON`, the DLL glob only searched `bin/` but the downloaded package places DLLs in `lib/`. This left the build tree with no ORT DLL, causing Windows to fall back to the stale `System32\onnxruntime.dll` (1.17.1), crashing against the ORT 1.25.1 API. 

Fixed by adding `lib/` as fallback and staging DLLs into the build bin directory at configure time.

Closes : #29278 

### Pull Request Readiness Checklist

See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request

- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [x] The feature is well documented and sample code can be built with the project CMake

.github/workflows/4.x.yml

@@ -1,14 +0,0 @@
-name: 4.x
-
-on:
-  schedule:
-    - cron: '0 3 * * *'
-  workflow_dispatch:
-
-jobs:
-  CodeQL:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-CodeQL.yaml@main
-    with:
-      target_branch: '4.x'
-      workflow_branch: main
-

.github/workflows/5.x.yml

@@ -0,0 +1,13 @@
+name: 5.x
+
+on:
+  schedule:
+    - cron: '0 3 * * *'
+  workflow_dispatch:
+
+jobs:
+  CodeQL:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-CodeQL.yaml@main
+    with:
+      target_branch: '5.x'
+      workflow_branch: main

.github/workflows/PR-4.x.yaml

@@ -1,58 +0,0 @@
-name: PR:4.x
-
-on:
-  pull_request:
-    branches:
-      - 4.x
-
-jobs:
-
-  Linux:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-Linux.yaml@main
-    with:
-      workflow_branch: main
-
-  Linux-no-HAL:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-Linux-NoHAL.yaml@main
-
-  Windows:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-Windows.yaml@main
-    with:
-      workflow_branch: main
-
-  Ubuntu2404-ARM64:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-ARM64.yaml@main
-
-  Ubuntu2404-ARM64-Debug:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-ARM64-Debug.yaml@main
-
-  Ubuntu2004-x64-OpenVINO:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-U20-OpenVINO.yaml@main
-
-  Ubuntu2004-x64-CUDA:
-    if: "${{ contains(github.event.pull_request.labels.*.name, 'category: dnn') }} || ${{ contains(github.event.pull_request.labels.*.name, 'category: dnn (onnx)') }}"
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-U20-Cuda.yaml@main
-
-  macOS-ARM64:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-macOS-ARM64.yaml@main
-
-  macOS-x64:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-macOS-x86_64.yaml@main
-
-  macOS-ARM64-Vulkan:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-macOS-ARM64-Vulkan.yaml@main
-
-  iOS:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-iOS.yaml@main
-
-  Android-SDK:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-4.x-Android-SDK.yaml@main
-
-  TIM-VX:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-timvx-backend-tests-4.x.yml@main
-
-  docs:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-docs.yaml@main
-
-  Linux-RISC-V-Clang:
-    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-4.x-RISCV.yaml@main

.github/workflows/PR-5.x.yaml

@@ -0,0 +1,62 @@
+name: PR:5.x
+
+on:
+  pull_request:
+    branches:
+      - 5.x
+
+jobs:
+  Linux:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-Linux.yaml@main
+    with:
+      workflow_branch: 'main'
+
+  Linux-no-HAL:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-Linux-NoHAL.yaml@main
+
+  Windows:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-Windows.yaml@main
+    with:
+      workflow_branch: main
+
+  Ubuntu2404-ARM64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-ARM64.yaml@main
+
+  Ubuntu2404-ARM64-Debug:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-ARM64-Debug.yaml@main
+
+  Ubuntu2004-x64-OpenVINO:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-U20-OpenVINO.yaml@main
+
+  Ubuntu2004-x64-CUDA:
+    if: "${{ contains(github.event.pull_request.labels.*.name, 'category: dnn') }} || ${{ contains(github.event.pull_request.labels.*.name, 'category: dnn (onnx)') }}"
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-U20-Cuda.yaml@main
+
+# Vulkan configuration disabled as Vulkan backend for DNN does not support int/int64 for now
+# Details: https://github.com/opencv/opencv/issues/25110
+#  Windows10-x64-Vulkan:
+#    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-W10-Vulkan.yaml@main
+
+  macOS-ARM64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-macOS-ARM64.yaml@main
+
+#  macOS-ARM64-Vulkan:
+#    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-macOS-ARM64-Vulkan.yaml@main
+
+  macOS-x64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-macOS-x86_64.yaml@main
+
+  iOS:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-iOS.yaml@main
+
+  Android:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-Android.yaml@main
+
+  TIM-VX:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-timvx-backend-tests-4.x.yml@main
+
+  docs:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-docs.yaml@main
+
+  Linux-RISC-V-Clang:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-RISCV.yaml@main

3rdparty/clapack/CMakeLists.txt

@@ -0,0 +1,49 @@
+# ----------------------------------------------------------------------------
+#  CMake file for opencv_lapack. See root CMakeLists.txt
+#
+# ----------------------------------------------------------------------------
+project(clapack)
+
+# TODO: extract it from sources somehow
+set(CLAPACK_VERSION "3.9.0" PARENT_SCOPE)
+
+include_directories("${CMAKE_CURRENT_SOURCE_DIR}/include")
+
+# The .cpp files:
+file(GLOB lapack_srcs src/*.c)
+file(GLOB runtime_srcs runtime/*.c)
+file(GLOB lib_hdrs include/*.h)
+
+# ----------------------------------------------------------------------------------
+# 				Define the library target:
+# ----------------------------------------------------------------------------------
+
+set(the_target "libclapack")
+
+add_library(${the_target} STATIC ${lapack_srcs} ${runtime_srcs} ${lib_hdrs})
+
+ocv_warnings_disable(CMAKE_C_FLAGS -Wno-parentheses -Wno-uninitialized -Wno-array-bounds
+    -Wno-implicit-function-declaration -Wno-unused -Wunused-parameter -Wstringop-truncation
+    -Wtautological-negation-compare) # gcc/clang warnings
+ocv_warnings_disable(CMAKE_C_FLAGS /wd4244 /wd4554 /wd4723 /wd4819) # visual studio warnings
+
+set_target_properties(${the_target}
+  PROPERTIES OUTPUT_NAME ${the_target}
+  DEBUG_POSTFIX "${OPENCV_DEBUG_POSTFIX}"
+  COMPILE_PDB_NAME ${the_target}
+  COMPILE_PDB_NAME_DEBUG "${the_target}${OPENCV_DEBUG_POSTFIX}"
+  ARCHIVE_OUTPUT_DIRECTORY ${3P_LIBRARY_OUTPUT_PATH}
+  )
+
+set(CLAPACK_INCLUDE_DIR "${CMAKE_CURRENT_SOURCE_DIR}/include" PARENT_SCOPE)
+set(CLAPACK_LIBRARIES ${the_target} PARENT_SCOPE)
+
+if(ENABLE_SOLUTION_FOLDERS)
+  set_target_properties(${the_target} PROPERTIES FOLDER "3rdparty")
+endif()
+
+if(NOT BUILD_SHARED_LIBS)
+  ocv_install_target(${the_target} EXPORT OpenCVModules ARCHIVE DESTINATION ${OPENCV_3P_LIB_INSTALL_PATH} COMPONENT dev)
+endif()
+
+ocv_install_3rdparty_licenses(clapack lapack_LICENSE)

3rdparty/clapack/include/cblas.h

@@ -0,0 +1,102 @@
+#ifndef __CBLAS_H__
+#define __CBLAS_H__
+
+/* most of the stuff is in lapacke.h */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+typedef struct lapack_complex
+{
+    float r, i;
+} lapack_complex;
+
+typedef struct lapack_doublecomplex
+{
+    double r, i;
+} lapack_doublecomplex;
+
+typedef enum {CblasRowMajor=101, CblasColMajor=102} CBLAS_LAYOUT;
+typedef enum {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113} CBLAS_TRANSPOSE;
+
+void cblas_xerbla(const CBLAS_LAYOUT layout, int info,
+                  const char *rout, const char *form, ...);
+
+void cblas_sgemm(CBLAS_LAYOUT layout, CBLAS_TRANSPOSE TransA,
+                 CBLAS_TRANSPOSE TransB, const int M, const int N,
+                 const int K, const float alpha, const float *A,
+                 const int lda, const float *B, const int ldb,
+                 const float beta, float *C, const int ldc);
+
+void cblas_dgemm(CBLAS_LAYOUT layout, CBLAS_TRANSPOSE TransA,
+              CBLAS_TRANSPOSE TransB, const int M, const int N,
+              const int K, const double alpha, const double *A,
+              const int lda, const double *B, const int ldb,
+              const double beta, double *C, const int ldc);
+
+void cblas_cgemm(CBLAS_LAYOUT layout, CBLAS_TRANSPOSE TransA,
+               CBLAS_TRANSPOSE TransB, const int M, const int N,
+               const int K, const void *alpha, const void *A,
+               const int lda, const void *B, const int ldb,
+               const void *beta, void *C, const int ldc);
+
+void cblas_zgemm(CBLAS_LAYOUT layout, CBLAS_TRANSPOSE TransA,
+                CBLAS_TRANSPOSE TransB, const int M, const int N,
+                const int K, const void *alpha, const void *A,
+                const int lda, const void *B, const int ldb,
+                const void *beta, void *C, const int ldc);
+
+int xerbla_(char *, int *);
+int lsame_(char *, char *);
+double slamch_(char* cmach);
+double slamc3_(float *a, float *b);
+double dlamch_(char* cmach);
+double dlamc3_(double *a, double *b);
+
+int dgels_(char *trans, int *m, int *n, int *nrhs, double *a,
+	int *lda, double *b, int *ldb, double *work, int *lwork, int *info);
+
+int dgesv_(int *n, int *nrhs, double *a, int *lda, int *ipiv,
+	double *b, int *ldb, int *info);
+
+int dgetrf_(int *m, int *n, double *a, int *lda, int *ipiv,
+	int *info);
+
+int dposv_(char *uplo, int *n, int *nrhs, double *a, int *
+	lda, double *b, int *ldb, int *info);
+
+int dpotrf_(char *uplo, int *n, double *a, int *lda, int *
+	info);
+
+int sgels_(char *trans, int *m, int *n, int *nrhs, float *a,
+	int *lda, float *b, int *ldb, float *work, int *lwork, int *info);
+
+int sgeev_(char *jobvl, char *jobvr, int *n, float *a, int *
+	lda, float *wr, float *wi, float *vl, int *ldvl, float *vr, int *
+	ldvr, float *work, int *lwork, int *info);
+
+int sgeqrf_(int *m, int *n, float *a, int *lda, float *tau,
+	float *work, int *lwork, int *info);
+
+int sgesv_(int *n, int *nrhs, float *a, int *lda, int *ipiv,
+	float *b, int *ldb, int *info);
+
+int sgetrf_(int *m, int *n, float *a, int *lda, int *ipiv,
+	int *info);
+
+int sposv_(char *uplo, int *n, int *nrhs, float *a, int *
+	lda, float *b, int *ldb, int *info);
+
+int spotrf_(char *uplo, int *n, float *a, int *lda, int *
+	info);
+
+int sgesdd_(char *jobz, int *m, int *n, float *a, int *lda,
+	float *s, float *u, int *ldu, float *vt, int *ldvt, float *work,
+	int *lwork, int *iwork, int *info);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* __CBLAS_H__ */

3rdparty/clapack/include/f2c.h

@@ -0,0 +1,129 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef __F2C_H__
+#define __F2C_H__
+
+#include <assert.h>
+#include <math.h>
+#include <ctype.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+
+#include "cblas.h"
+#include "lapack.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#undef complex
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef lapack_complex complex;
+typedef lapack_doublecomplex doublecomplex;
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+#ifndef abs
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#endif
+#define dabs(x) (double)abs(x)
+#ifndef min
+#define min(a,b) ((a) <= (b) ? (a) : (b))
+#endif
+#ifndef max
+#define max(a,b) ((a) >= (b) ? (a) : (b))
+#endif
+#define dmin(a,b) (double)min(a,b)
+#define dmax(a,b) (double)max(a,b)
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+static __inline double r_lg10(float *x)
+{
+    return 0.43429448190325182765*log(*x);
+}
+
+static __inline double d_lg10(double *x)
+{
+    return 0.43429448190325182765*log(*x);
+}
+
+static __inline double d_sign(double *a, double *b)
+{
+    double x = fabs(*a);
+    return *b >= 0 ? x : -x;
+}
+
+static __inline double r_sign(float *a, float *b)
+{
+    double x = fabs((double)*a);
+    return *b >= 0 ? x : -x;
+}
+
+static __inline int i_nint(float *x)
+{
+    return (int)(*x >= 0 ? floor(*x + .5) : -floor(.5 - *x));
+}
+
+int pow_ii(int *ap, int *bp);
+double pow_di(double *ap, int *bp);
+static __inline double pow_ri(float *ap, int *bp)
+{
+    double apd = *ap;
+    return pow_di(&apd, bp);
+}
+static __inline double pow_dd(double *ap, double *bp)
+{
+    return pow(*ap, *bp);
+}
+
+static __inline void d_cnjg(doublecomplex *r, doublecomplex *z)
+{
+	double zi = z->i;
+	r->r = z->r;
+	r->i = -zi;
+}
+
+static __inline void r_cnjg(complex *r, complex *z)
+{
+	float zi = z->i;
+	r->r = z->r;
+	r->i = -zi;
+}
+
+static __inline int s_copy(char *a, char *b, int maxlen)
+{
+    strncpy(a, b, maxlen);
+    a[maxlen] = '\0';
+    return 0;
+}
+
+int s_cat(char *lp, char **rpp, int* rnp, int *np);
+int s_cmp(char *a0, char *b0);
+static __inline int i_len(char* s)
+{
+    return (int)strlen(s);
+}
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

3rdparty/clapack/include/lapack.h

@@ -0,0 +1,386 @@
+// this is auto-generated header for Lapack subset
+#ifndef __CLAPACK_H__
+#define __CLAPACK_H__
+
+#include "cblas.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+int cgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, lapack_complex *alpha, lapack_complex *a, int *lda, lapack_complex *b, int *ldb,
+	lapack_complex *beta, lapack_complex *c__, int *ldc);
+
+int daxpy_(int *n, double *da, double *dx, int *incx, double
+	*dy, int *incy);
+
+int dbdsdc_(char *uplo, char *compq, int *n, double *d__,
+	double *e, double *u, int *ldu, double *vt, int *ldvt, double *q, int
+	*iq, double *work, int *iwork, int *info);
+
+int dbdsqr_(char *uplo, int *n, int *ncvt, int *nru, int *
+	ncc, double *d__, double *e, double *vt, int *ldvt, double *u, int *
+	ldu, double *c__, int *ldc, double *work, int *info);
+
+int dcombssq_(double *v1, double *v2);
+
+int dcopy_(int *n, double *dx, int *incx, double *dy, int *
+	incy);
+
+double ddot_(int *n, double *dx, int *incx, double *dy, int *incy);
+
+int dgebak_(char *job, char *side, int *n, int *ilo, int *
+	ihi, double *scale, int *m, double *v, int *ldv, int *info);
+
+int dgebal_(char *job, int *n, double *a, int *lda, int *ilo,
+	 int *ihi, double *scale, int *info);
+
+int dgebd2_(int *m, int *n, double *a, int *lda, double *d__,
+	 double *e, double *tauq, double *taup, double *work, int *info);
+
+int dgebrd_(int *m, int *n, double *a, int *lda, double *d__,
+	 double *e, double *tauq, double *taup, double *work, int *lwork, int
+	*info);
+
+int dgeev_(char *jobvl, char *jobvr, int *n, double *a, int *
+	lda, double *wr, double *wi, double *vl, int *ldvl, double *vr, int *
+	ldvr, double *work, int *lwork, int *info);
+
+int dgehd2_(int *n, int *ilo, int *ihi, double *a, int *lda,
+	double *tau, double *work, int *info);
+
+int dgehrd_(int *n, int *ilo, int *ihi, double *a, int *lda,
+	double *tau, double *work, int *lwork, int *info);
+
+int dgelq2_(int *m, int *n, double *a, int *lda, double *tau,
+	 double *work, int *info);
+
+int dgelqf_(int *m, int *n, double *a, int *lda, double *tau,
+	 double *work, int *lwork, int *info);
+
+int dgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, double *alpha, double *a, int *lda, double *b, int *ldb, double *
+	beta, double *c__, int *ldc);
+
+int dgemv_(char *trans, int *m, int *n, double *alpha,
+	double *a, int *lda, double *x, int *incx, double *beta, double *y,
+	int *incy);
+
+int dgeqr2_(int *m, int *n, double *a, int *lda, double *tau,
+	 double *work, int *info);
+
+int dgeqrf_(int *m, int *n, double *a, int *lda, double *tau,
+	 double *work, int *lwork, int *info);
+
+int dger_(int *m, int *n, double *alpha, double *x, int *
+	incx, double *y, int *incy, double *a, int *lda);
+
+int dgesdd_(char *jobz, int *m, int *n, double *a, int *lda,
+	double *s, double *u, int *ldu, double *vt, int *ldvt, double *work,
+	int *lwork, int *iwork, int *info);
+
+int dhseqr_(char *job, char *compz, int *n, int *ilo, int *
+	ihi, double *h__, int *ldh, double *wr, double *wi, double *z__, int *
+	ldz, double *work, int *lwork, int *info);
+
+int disnan_(double *din);
+
+// "small" is a macro defined in Windows headers: https://stackoverflow.com/a/27794577
+#ifdef small
+#undef small
+#endif
+
+int dlabad_(double *small, double *large);
+
+int dlabrd_(int *m, int *n, int *nb, double *a, int *lda,
+	double *d__, double *e, double *tauq, double *taup, double *x, int *
+	ldx, double *y, int *ldy);
+
+int dlacpy_(char *uplo, int *m, int *n, double *a, int *lda,
+	double *b, int *ldb);
+
+int dladiv1_(double *a, double *b, double *c__, double *d__,
+	double *p, double *q);
+
+double dladiv2_(double *a, double *b, double *c__, double *d__, double *r__,
+	double *t);
+
+int dladiv_(double *a, double *b, double *c__, double *d__,
+	double *p, double *q);
+
+int dlaed6_(int *kniter, int *orgati, double *rho, double *
+	d__, double *z__, double *finit, double *tau, int *info);
+
+int dlaexc_(int *wantq, int *n, double *t, int *ldt, double *
+	q, int *ldq, int *j1, int *n1, int *n2, double *work, int *info);
+
+int dlahqr_(int *wantt, int *wantz, int *n, int *ilo, int *
+	ihi, double *h__, int *ldh, double *wr, double *wi, int *iloz, int *
+	ihiz, double *z__, int *ldz, int *info);
+
+int dlahr2_(int *n, int *k, int *nb, double *a, int *lda,
+	double *tau, double *t, int *ldt, double *y, int *ldy);
+
+int dlaisnan_(double *din1, double *din2);
+
+int dlaln2_(int *ltrans, int *na, int *nw, double *smin,
+	double *ca, double *a, int *lda, double *d1, double *d2, double *b,
+	int *ldb, double *wr, double *wi, double *x, int *ldx, double *scale,
+	double *xnorm, int *info);
+
+int dlamrg_(int *n1, int *n2, double *a, int *dtrd1, int *
+	dtrd2, int *index);
+
+double dlange_(char *norm, int *m, int *n, double *a, int *lda, double *work);
+
+double dlanst_(char *norm, int *n, double *d__, double *e);
+
+int dlanv2_(double *a, double *b, double *c__, double *d__,
+	double *rt1r, double *rt1i, double *rt2r, double *rt2i, double *cs,
+	double *sn);
+
+double dlapy2_(double *x, double *y);
+
+int dlaqr0_(int *wantt, int *wantz, int *n, int *ilo, int *
+	ihi, double *h__, int *ldh, double *wr, double *wi, int *iloz, int *
+	ihiz, double *z__, int *ldz, double *work, int *lwork, int *info);
+
+int dlaqr1_(int *n, double *h__, int *ldh, double *sr1,
+	double *si1, double *sr2, double *si2, double *v);
+
+int dlaqr2_(int *wantt, int *wantz, int *n, int *ktop, int *
+	kbot, int *nw, double *h__, int *ldh, int *iloz, int *ihiz, double *
+	z__, int *ldz, int *ns, int *nd, double *sr, double *si, double *v,
+	int *ldv, int *nh, double *t, int *ldt, int *nv, double *wv, int *
+	ldwv, double *work, int *lwork);
+
+int dlaqr3_(int *wantt, int *wantz, int *n, int *ktop, int *
+	kbot, int *nw, double *h__, int *ldh, int *iloz, int *ihiz, double *
+	z__, int *ldz, int *ns, int *nd, double *sr, double *si, double *v,
+	int *ldv, int *nh, double *t, int *ldt, int *nv, double *wv, int *
+	ldwv, double *work, int *lwork);
+
+int dlaqr4_(int *wantt, int *wantz, int *n, int *ilo, int *
+	ihi, double *h__, int *ldh, double *wr, double *wi, int *iloz, int *
+	ihiz, double *z__, int *ldz, double *work, int *lwork, int *info);
+
+int dlaqr5_(int *wantt, int *wantz, int *kacc22, int *n, int
+	*ktop, int *kbot, int *nshfts, double *sr, double *si, double *h__,
+	int *ldh, int *iloz, int *ihiz, double *z__, int *ldz, double *v, int
+	*ldv, double *u, int *ldu, int *nv, double *wv, int *ldwv, int *nh,
+	double *wh, int *ldwh);
+
+int dlarf_(char *side, int *m, int *n, double *v, int *incv,
+	double *tau, double *c__, int *ldc, double *work);
+
+int dlarfb_(char *side, char *trans, char *direct, char *
+	storev, int *m, int *n, int *k, double *v, int *ldv, double *t, int *
+	ldt, double *c__, int *ldc, double *work, int *ldwork);
+
+int dlarfg_(int *n, double *alpha, double *x, int *incx,
+	double *tau);
+
+int dlarft_(char *direct, char *storev, int *n, int *k,
+	double *v, int *ldv, double *tau, double *t, int *ldt);
+
+int dlarfx_(char *side, int *m, int *n, double *v, double *
+	tau, double *c__, int *ldc, double *work);
+
+int dlartg_(double *f, double *g, double *cs, double *sn,
+	double *r__);
+
+int dlas2_(double *f, double *g, double *h__, double *ssmin,
+	double *ssmax);
+
+int dlascl_(char *type__, int *kl, int *ku, double *cfrom,
+	double *cto, int *m, int *n, double *a, int *lda, int *info);
+
+int dlasd0_(int *n, int *sqre, double *d__, double *e,
+	double *u, int *ldu, double *vt, int *ldvt, int *smlsiz, int *iwork,
+	double *work, int *info);
+
+int dlasd1_(int *nl, int *nr, int *sqre, double *d__, double
+	*alpha, double *beta, double *u, int *ldu, double *vt, int *ldvt, int
+	*idxq, int *iwork, double *work, int *info);
+
+int dlasd2_(int *nl, int *nr, int *sqre, int *k, double *d__,
+	 double *z__, double *alpha, double *beta, double *u, int *ldu,
+	double *vt, int *ldvt, double *dsigma, double *u2, int *ldu2, double *
+	vt2, int *ldvt2, int *idxp, int *idx, int *idxc, int *idxq, int *
+	coltyp, int *info);
+
+int dlasd3_(int *nl, int *nr, int *sqre, int *k, double *d__,
+	 double *q, int *ldq, double *dsigma, double *u, int *ldu, double *u2,
+	 int *ldu2, double *vt, int *ldvt, double *vt2, int *ldvt2, int *idxc,
+	 int *ctot, double *z__, int *info);
+
+int dlasd4_(int *n, int *i__, double *d__, double *z__,
+	double *delta, double *rho, double *sigma, double *work, int *info);
+
+int dlasd5_(int *i__, double *d__, double *z__, double *
+	delta, double *rho, double *dsigma, double *work);
+
+int dlasd6_(int *icompq, int *nl, int *nr, int *sqre, double
+	*d__, double *vf, double *vl, double *alpha, double *beta, int *idxq,
+	int *perm, int *givptr, int *givcol, int *ldgcol, double *givnum, int
+	*ldgnum, double *poles, double *difl, double *difr, double *z__, int *
+	k, double *c__, double *s, double *work, int *iwork, int *info);
+
+int dlasd7_(int *icompq, int *nl, int *nr, int *sqre, int *k,
+	 double *d__, double *z__, double *zw, double *vf, double *vfw,
+	double *vl, double *vlw, double *alpha, double *beta, double *dsigma,
+	int *idx, int *idxp, int *idxq, int *perm, int *givptr, int *givcol,
+	int *ldgcol, double *givnum, int *ldgnum, double *c__, double *s, int
+	*info);
+
+int dlasd8_(int *icompq, int *k, double *d__, double *z__,
+	double *vf, double *vl, double *difl, double *difr, int *lddifr,
+	double *dsigma, double *work, int *info);
+
+int dlasda_(int *icompq, int *smlsiz, int *n, int *sqre,
+	double *d__, double *e, double *u, int *ldu, double *vt, int *k,
+	double *difl, double *difr, double *z__, double *poles, int *givptr,
+	int *givcol, int *ldgcol, int *perm, double *givnum, double *c__,
+	double *s, double *work, int *iwork, int *info);
+
+int dlasdq_(char *uplo, int *sqre, int *n, int *ncvt, int *
+	nru, int *ncc, double *d__, double *e, double *vt, int *ldvt, double *
+	u, int *ldu, double *c__, int *ldc, double *work, int *info);
+
+int dlasdt_(int *n, int *lvl, int *nd, int *inode, int *
+	ndiml, int *ndimr, int *msub);
+
+int dlaset_(char *uplo, int *m, int *n, double *alpha,
+	double *beta, double *a, int *lda);
+
+int dlasq1_(int *n, double *d__, double *e, double *work,
+	int *info);
+
+int dlasq2_(int *n, double *z__, int *info);
+
+int dlasq3_(int *i0, int *n0, double *z__, int *pp, double *
+	dmin__, double *sigma, double *desig, double *qmax, int *nfail, int *
+	iter, int *ndiv, int *ieee, int *ttype, double *dmin1, double *dmin2,
+	double *dn, double *dn1, double *dn2, double *g, double *tau);
+
+int dlasq4_(int *i0, int *n0, double *z__, int *pp, int *
+	n0in, double *dmin__, double *dmin1, double *dmin2, double *dn,
+	double *dn1, double *dn2, double *tau, int *ttype, double *g);
+
+int dlasq5_(int *i0, int *n0, double *z__, int *pp, double *
+	tau, double *sigma, double *dmin__, double *dmin1, double *dmin2,
+	double *dn, double *dnm1, double *dnm2, int *ieee, double *eps);
+
+int dlasq6_(int *i0, int *n0, double *z__, int *pp, double *
+	dmin__, double *dmin1, double *dmin2, double *dn, double *dnm1,
+	double *dnm2);
+
+int dlasr_(char *side, char *pivot, char *direct, int *m,
+	int *n, double *c__, double *s, double *a, int *lda);
+
+int dlasrt_(char *id, int *n, double *d__, int *info);
+
+int dlassq_(int *n, double *x, int *incx, double *scale,
+	double *sumsq);
+
+int dlasv2_(double *f, double *g, double *h__, double *ssmin,
+	 double *ssmax, double *snr, double *csr, double *snl, double *csl);
+
+int dlasy2_(int *ltranl, int *ltranr, int *isgn, int *n1,
+	int *n2, double *tl, int *ldtl, double *tr, int *ldtr, double *b, int
+	*ldb, double *scale, double *x, int *ldx, double *xnorm, int *info);
+
+double dnrm2_(int *n, double *x, int *incx);
+
+int dorg2r_(int *m, int *n, int *k, double *a, int *lda,
+	double *tau, double *work, int *info);
+
+int dorgbr_(char *vect, int *m, int *n, int *k, double *a,
+	int *lda, double *tau, double *work, int *lwork, int *info);
+
+int dorghr_(int *n, int *ilo, int *ihi, double *a, int *lda,
+	double *tau, double *work, int *lwork, int *info);
+
+int dorgl2_(int *m, int *n, int *k, double *a, int *lda,
+	double *tau, double *work, int *info);
+
+int dorglq_(int *m, int *n, int *k, double *a, int *lda,
+	double *tau, double *work, int *lwork, int *info);
+
+int dorgqr_(int *m, int *n, int *k, double *a, int *lda,
+	double *tau, double *work, int *lwork, int *info);
+
+int dorm2r_(char *side, char *trans, int *m, int *n, int *k,
+	double *a, int *lda, double *tau, double *c__, int *ldc, double *work,
+	 int *info);
+
+int dormbr_(char *vect, char *side, char *trans, int *m, int
+	*n, int *k, double *a, int *lda, double *tau, double *c__, int *ldc,
+	double *work, int *lwork, int *info);
+
+int dormhr_(char *side, char *trans, int *m, int *n, int *
+	ilo, int *ihi, double *a, int *lda, double *tau, double *c__, int *
+	ldc, double *work, int *lwork, int *info);
+
+int dorml2_(char *side, char *trans, int *m, int *n, int *k,
+	double *a, int *lda, double *tau, double *c__, int *ldc, double *work,
+	 int *info);
+
+int dormlq_(char *side, char *trans, int *m, int *n, int *k,
+	double *a, int *lda, double *tau, double *c__, int *ldc, double *work,
+	 int *lwork, int *info);
+
+int dormqr_(char *side, char *trans, int *m, int *n, int *k,
+	double *a, int *lda, double *tau, double *c__, int *ldc, double *work,
+	 int *lwork, int *info);
+
+int drot_(int *n, double *dx, int *incx, double *dy, int *
+	incy, double *c__, double *s);
+
+int dscal_(int *n, double *da, double *dx, int *incx);
+
+int dswap_(int *n, double *dx, int *incx, double *dy, int *
+	incy);
+
+int dtrevc3_(char *side, char *howmny, int *select, int *n,
+	double *t, int *ldt, double *vl, int *ldvl, double *vr, int *ldvr,
+	int *mm, int *m, double *work, int *lwork, int *info);
+
+int dtrexc_(char *compq, int *n, double *t, int *ldt, double
+	*q, int *ldq, int *ifst, int *ilst, double *work, int *info);
+
+int dtrmm_(char *side, char *uplo, char *transa, char *diag,
+	int *m, int *n, double *alpha, double *a, int *lda, double *b, int *
+	ldb);
+
+int dtrmv_(char *uplo, char *trans, char *diag, int *n,
+	double *a, int *lda, double *x, int *incx);
+
+int idamax_(int *n, double *dx, int *incx);
+
+int ieeeck_(int *ispec, float *zero, float *one);
+
+int iladlc_(int *m, int *n, double *a, int *lda);
+
+int iladlr_(int *m, int *n, double *a, int *lda);
+
+int ilaenv_(int *ispec, char *name__, char *opts, int *n1, int *n2, int *n3,
+	int *n4);
+
+int iparmq_(int *ispec, char *name__, char *opts, int *n, int *ilo, int *ihi,
+	int *lwork);
+
+int sgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, float *alpha, float *a, int *lda, float *b, int *ldb, float *beta,
+	float *c__, int *ldc);
+
+int zgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, lapack_doublecomplex *alpha, lapack_doublecomplex *a, int *lda, lapack_doublecomplex *b,
+	 int *ldb, lapack_doublecomplex *beta, lapack_doublecomplex *c__, int *ldc);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

3rdparty/clapack/lapack_LICENSE

@@ -0,0 +1,48 @@
+Copyright (c) 1992-2017 The University of Tennessee and The University
+                        of Tennessee Research Foundation.  All rights
+                        reserved.
+Copyright (c) 2000-2017 The University of California Berkeley. All
+                        rights reserved.
+Copyright (c) 2006-2017 The University of Colorado Denver.  All rights
+                        reserved.
+
+$COPYRIGHT$
+
+Additional copyrights may follow
+
+$HEADER$
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+- Redistributions of source code must retain the above copyright
+  notice, this list of conditions and the following disclaimer.
+
+- Redistributions in binary form must reproduce the above copyright
+  notice, this list of conditions and the following disclaimer listed
+  in this license in the documentation and/or other materials
+  provided with the distribution.
+
+- Neither the name of the copyright holders nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+The copyright holders provide no reassurances that the source code
+provided does not infringe any patent, copyright, or any other
+intellectual property rights of third parties.  The copyright holders
+disclaim any liability to any recipient for claims brought against
+recipient by any third party for infringement of that parties
+intellectual property rights.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

3rdparty/clapack/make_clapack.py

@@ -0,0 +1,272 @@
+appdoc = """
+    This is generator of CLapack subset.
+    The usage:
+
+    1. Make sure you have the special version of f2c installed.
+       Grab it from https://github.com/vpisarev/f2c/tree/for_lapack.
+    2. Download fresh version of Lapack from
+       https://github.com/Reference-LAPACK/lapack.
+       You may choose some specific version or the latest snapshot.
+    3. If necessary, edit "roots" and "banlist" variables in this script, specify the needed and unneeded functions
+    4. From within a working directory run
+
+       $ python3 <opencv_root>/3rdparty/clapack/make_clapack.py <lapack_root>
+       or
+       $ F2C=<path_to_custom_f2c> python3 <opencv_root>/3rdparty/clapack/make_clapack.py <lapack_root>
+
+       it will generate "new_clapack" directory with "include" and "src" subdirectories.
+    5. erase opencv/3rdparty/clapack/src and replace it with new_clapack/src.
+    6. copy new_clapack/include/lapack.h to opencv/3rdparty/clapack/include.
+    7. optionally, edit opencv/3rdparty/clapack/CMakeLists.txt and update CLAPACK_VERSION as needed.
+
+    This is it. Now build it and enjoy.
+"""
+
+import glob, re, os, shutil, subprocess, sys
+
+roots = ["cgemm_", "dgemm_", "sgemm_", "zgemm_",
+         "dgeev_", "dgesdd_", 
+         #"dsyevr_",
+         #"dgesv_", "dgetrf_", "dposv_", "dpotrf_", "dgels_", "dgeqrf_",
+         #"sgesv_", "sgetrf_", "sposv_", "spotrf_", "sgels_", "sgeqrf_"
+         ]
+banlist = ["slamch_", "slamc3_", "dlamch_", "dlamc3_", "lsame_", "xerbla_"]
+
+if len(sys.argv) < 2:
+    print(appdoc)
+    sys.exit(0)
+
+lapack_root = sys.argv[1]
+dst_path = "."
+
+def error(msg):
+    print ("error: " + msg)
+    sys.exit(0)
+
+def file2fun(fname):
+    return (os.path.basename(fname)[:-2]).upper()
+
+def print_graph(m):
+    for (k, neighbors) in sorted(m.items()):
+        print (k + " : " + ", ".join(sorted(list(neighbors))))
+
+blas_path = os.path.join(lapack_root, "BLAS/SRC")
+lapack_path = os.path.join(lapack_root, "SRC")
+
+roots = [f[:-1].upper() for f in roots]
+banlist = [f[:-1].upper() for f in banlist]
+
+def fun2file(func):
+    filename = func.lower() + ".f"
+    blas_loc = blas_path + "/" + filename
+    lapack_loc = lapack_path + "/" + filename
+    if os.path.exists(blas_loc):
+        return blas_loc
+    elif os.path.exists(lapack_loc):
+        return lapack_loc
+    else:
+        error("neither %s nor %s exist" % (blas_loc, lapack_loc))
+
+all_files = glob.glob(blas_path + "/*.f") + glob.glob(lapack_path + "/*.f")
+all_funcs = [file2fun(fname) for fname in all_files]
+all_funcs_set = set(all_funcs).difference(set(banlist))
+all_funcs = sorted(list(all_funcs_set))
+
+func_deps = {}
+
+#print all_funcs
+
+words_regexp = re.compile(r'\w+')
+
+def scan_deps(func):
+    global func_deps
+    if func in func_deps:
+        return
+    func_deps[func] = set([]) # to avoid possibly infinite recursion
+    f = open(fun2file(func), 'rt')
+    deps = []
+    external_mode = False
+    for l in f.readlines():
+        if l.startswith('*'):
+            continue
+        l = l.strip().upper()
+        if l.startswith('EXTERNAL '):
+            external_mode = True
+        elif l.startswith('$') and external_mode:
+            pass
+        else:
+            external_mode = False
+        if not external_mode:
+            continue
+        for w in words_regexp.findall(l):
+            if w in all_funcs_set:
+                deps.append(w)
+    f.close()
+    # remove func from its dependencies
+    deps = set(deps).difference(set([func]))
+    func_deps[func] = deps
+    for d in deps:
+        scan_deps(d)
+
+for r in roots:
+    scan_deps(r)
+
+selected_funcs = sorted(func_deps.keys())
+print ("total files before amalgamation: %d" % len(selected_funcs))
+
+inv_deps = {}
+for func in selected_funcs:
+    inv_deps[func] = set([])
+
+for (func, deps) in func_deps.items():
+    for d in deps:
+        inv_deps[d] = inv_deps[d].union(set([func]))
+
+#print_graph(inv_deps)
+
+func_home = {}
+for func in selected_funcs:
+    func_home[func] = func
+
+def get_home0(func, func0):
+    used_by = inv_deps[func]
+    if len(used_by) == 1:
+        p = list(used_by)[0]
+        if p != func and p != func0:
+            return get_home0(p, func0)
+        return func
+    return func
+
+# try to merge some files
+for func in selected_funcs:
+    func_home[func] = get_home0(func, func)
+
+# try to merge some files even more
+for iters in range(100):
+    homes_changed = False
+    for (func, used_by) in inv_deps.items():
+        p0 = func_home[func]
+        n = len(used_by)
+        if n == 1:
+            p = list(used_by)[0]
+            p1 = func_home[p]
+            if p1 != p0:
+                func_home[func] = p1
+                homes_changed = True
+            continue
+        elif n > 1:
+            phomes = set([])
+            for p in used_by:
+                phomes.add(func_home[p])
+            if len(phomes) == 1:
+                p1 = list(phomes)[0]
+                if p1 != p0:
+                    func_home[func] = p1
+                    homes_changed = True
+    if not homes_changed:
+        break
+
+res_files = {}
+for (func, h) in func_home.items():
+    elems = res_files.get(h, set([]))
+    elems.add(func)
+    res_files[h] = elems
+
+print ("total files after amalgamation: %d" % len(res_files))
+#print_graph(res_files)
+
+outdir = os.path.join(dst_path, "new_clapack")
+outdir_src = os.path.join(outdir, "src")
+outdir_inc = os.path.join(outdir, "include")
+
+shutil.rmtree(outdir, ignore_errors=True)
+try:
+    os.makedirs(outdir_src)
+except os.error:
+    pass
+try:
+    os.makedirs(outdir_inc)
+except os.error:
+    pass
+
+f2c_appname = os.getenv("F2C", default="f2c")
+print ("f2c used: %s" % f2c_appname)
+
+f2c_getver_cmd = f2c_appname + " -v"
+
+verstr = subprocess.check_output(f2c_getver_cmd.split(' ')).decode("utf-8")
+if "for_lapack" not in verstr:
+    error("invalid version of f2c\n" + appdoc)
+
+f2c_flags = "-ctypes -localconst -no-proto"
+f2c_cmd0 = f2c_appname + " " + f2c_flags
+f2c_cmd1 = f2c_appname + " -hdr none " + f2c_flags
+
+lapack_protos = {}
+extract_fn_regexp = re.compile(r'.+?(\w+)\s*\(')
+
+def extract_proto(func, csrc):
+    global lapack_protos
+    cname = func.lower() + "_"
+    cfname = func.lower() + ".c"
+    regexp_str = r'\n(?:/\* Subroutine \*/\s*)?\w+\s+\w+\s*\((?:.|\n)+?\)[\s\n]*\{'
+    proto_regexp = re.compile(regexp_str)
+    ps = proto_regexp.findall(csrc)
+    for p in ps:
+        n = p.find("*/")
+        if n < 0:
+            n = 0
+        else:
+            n += 2
+        p = p[n:-1].strip() + ";"
+        fns = extract_fn_regexp.findall(p)
+        if len(fns) != 1:
+            error("prototype of function (%s) when analyzing %s cannot be parsed" % (p, cfname))
+        fn = fns[0]
+        if fn not in lapack_protos:
+            p = re.sub(r'\bcomplex\b', 'lapack_complex', p)
+            p = re.sub(r'\bdoublecomplex\b', 'lapack_doublecomplex', p)
+            lapack_protos[fn] = p
+
+for (filename, funcs) in sorted(res_files.items()):
+    out = ""
+    f2c_cmd = f2c_cmd0
+    for func in sorted(list(funcs)):
+        ffilename = fun2file(func)
+        print ("running " + f2c_cmd + " on " + ffilename +  " ...")
+        ffile = open(ffilename, 'rt')
+        delta_out = subprocess.check_output(f2c_cmd.split(' '), stdin=ffile).decode("utf-8")
+        # remove trailing whitespaces
+        delta_out = '\n'.join([l.rstrip() for l in delta_out.split('\n')])
+        extract_proto(func, delta_out)
+        out += delta_out
+        ffile.close()
+        f2c_cmd = f2c_cmd1
+    outname = os.path.join(outdir_src, filename.lower() + ".c")
+    outfile = open(outname, 'wt')
+    outfile.write(out)
+    outfile.close()
+
+proto_hdr = """// this is auto-generated header for Lapack subset
+#ifndef __CLAPACK_H__
+#define __CLAPACK_H__
+
+#include "cblas.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+%s
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
+""" % "\n\n".join([p for (n, p) in sorted(lapack_protos.items())])
+
+proto_hdr_fname = os.path.join(outdir_inc, "lapack.h")
+f = open(proto_hdr_fname, 'wt')
+f.write(proto_hdr)
+f.close()

3rdparty/clapack/runtime/cblas_wrap.c

@@ -0,0 +1,289 @@
+#include "f2c.h"
+#include <stdarg.h>
+
+void cblas_cgemm(const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE TransA,
+                 const CBLAS_TRANSPOSE TransB, const int M, const int N,
+                 const int K, const void *alpha, const void  *A,
+                 const int lda, const void  *B, const int ldb,
+                 const void *beta, void  *C, const int ldc)
+{
+   char TA, TB;
+
+   if( layout == CblasColMajor )
+   {
+      if(TransA == CblasTrans) TA='T';
+      else if ( TransA == CblasConjTrans ) TA='C';
+      else if ( TransA == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_cgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+
+      if(TransB == CblasTrans) TB='T';
+      else if ( TransB == CblasConjTrans ) TB='C';
+      else if ( TransB == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 3, "cblas_cgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      cgemm_(&TA, &TB, (int*)&M, (int*)&N, (int*)&K, (complex*)alpha, (complex*)A, (int*)&lda,
+             (complex*)B, (int*)&ldb, (complex*)beta, (complex*)C, (int*)&ldc);
+   }
+   else if (layout == CblasRowMajor)
+   {
+      if(TransA == CblasTrans) TB='T';
+      else if ( TransA == CblasConjTrans ) TB='C';
+      else if ( TransA == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_cgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+      if(TransB == CblasTrans) TA='T';
+      else if ( TransB == CblasConjTrans ) TA='C';
+      else if ( TransB == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_cgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      cgemm_(&TA, &TB, (int*)&N, (int*)&M, (int*)&K, (complex*)alpha, (complex*)B, (int*)&ldb,
+             (complex*)A, (int*)&lda, (complex*)beta, (complex*)C, (int*)&ldc);
+   }
+   else cblas_xerbla(layout, 1, "cblas_cgemm", "Illegal layout setting, %d\n", layout);
+}
+
+void cblas_dgemm(const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE TransA,
+                 const CBLAS_TRANSPOSE TransB, const int M, const int N,
+                 const int K, const double alpha, const double *A,
+                 const int lda, const double  *B, const int ldb,
+                 const double beta, double  *C, const int ldc)
+{
+   char TA, TB;
+
+   if( layout == CblasColMajor )
+   {
+      if(TransA == CblasTrans) TA='T';
+      else if ( TransA == CblasConjTrans ) TA='C';
+      else if ( TransA == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_dgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+
+      if(TransB == CblasTrans) TB='T';
+      else if ( TransB == CblasConjTrans ) TB='C';
+      else if ( TransB == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 3, "cblas_dgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      dgemm_(&TA, &TB, (int*)&M, (int*)&N, (int*)&K, (double*)&alpha, (double*)A, (int*)&lda,
+             (double*)B, (int*)&ldb, (double*)&beta, (double*)C, (int*)&ldc);
+   }
+   else if (layout == CblasRowMajor)
+   {
+      if(TransA == CblasTrans) TB='T';
+      else if ( TransA == CblasConjTrans ) TB='C';
+      else if ( TransA == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_dgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+      if(TransB == CblasTrans) TA='T';
+      else if ( TransB == CblasConjTrans ) TA='C';
+      else if ( TransB == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_dgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      dgemm_(&TA, &TB, (int*)&N, (int*)&M, (int*)&K, (double*)&alpha, (double*)B, (int*)&ldb,
+             (double*)A, (int*)&lda, (double*)&beta, (double*)C, (int*)&ldc);
+   }
+   else cblas_xerbla(layout, 1, "cblas_dgemm", "Illegal layout setting, %d\n", layout);
+}
+
+
+void cblas_sgemm(const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE TransA,
+                 const CBLAS_TRANSPOSE TransB, const int M, const int N,
+                 const int K, const float alpha, const float  *A,
+                 const int lda, const float  *B, const int ldb,
+                 const float beta, float  *C, const int ldc)
+{
+   char TA, TB;
+
+   if( layout == CblasColMajor )
+   {
+      if(TransA == CblasTrans) TA='T';
+      else if ( TransA == CblasConjTrans ) TA='C';
+      else if ( TransA == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_sgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+
+      if(TransB == CblasTrans) TB='T';
+      else if ( TransB == CblasConjTrans ) TB='C';
+      else if ( TransB == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 3, "cblas_sgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      sgemm_(&TA, &TB, (int*)&M, (int*)&N, (int*)&K, (float*)&alpha, (float*)A, (int*)&lda,
+             (float*)B, (int*)&ldb, (float*)&beta, (float*)C, (int*)&ldc);
+   }
+   else if (layout == CblasRowMajor)
+   {
+      if(TransA == CblasTrans) TB='T';
+      else if ( TransA == CblasConjTrans ) TB='C';
+      else if ( TransA == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_sgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+      if(TransB == CblasTrans) TA='T';
+      else if ( TransB == CblasConjTrans ) TA='C';
+      else if ( TransB == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_sgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      sgemm_(&TA, &TB, (int*)&N, (int*)&M, (int*)&K, (float*)&alpha, (float*)B, (int*)&ldb,
+             (float*)A, (int*)&lda, (float*)&beta, (float*)C, (int*)&ldc);
+   }
+   else cblas_xerbla(layout, 1, "cblas_sgemm", "Illegal layout setting, %d\n", layout);
+}
+
+void cblas_zgemm(const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE TransA,
+                 const CBLAS_TRANSPOSE TransB, const int M, const int N,
+                 const int K, const void *alpha, const void  *A,
+                 const int lda, const void  *B, const int ldb,
+                 const void *beta, void  *C, const int ldc)
+{
+   char TA, TB;
+
+   if( layout == CblasColMajor )
+   {
+      if(TransA == CblasTrans) TA='T';
+      else if ( TransA == CblasConjTrans ) TA='C';
+      else if ( TransA == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_zgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+
+      if(TransB == CblasTrans) TB='T';
+      else if ( TransB == CblasConjTrans ) TB='C';
+      else if ( TransB == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 3, "cblas_zgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      zgemm_(&TA, &TB, (int*)&M, (int*)&N, (int*)&K, (doublecomplex*)alpha, (doublecomplex*)A, (int*)&lda,
+             (doublecomplex*)B, (int*)&ldb, (doublecomplex*)beta, (doublecomplex*)C, (int*)&ldc);
+   }
+   else if (layout == CblasRowMajor)
+   {
+      if(TransA == CblasTrans) TB='T';
+      else if ( TransA == CblasConjTrans ) TB='C';
+      else if ( TransA == CblasNoTrans )   TB='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_zgemm", "Illegal TransA setting, %d\n", TransA);
+         return;
+      }
+      if(TransB == CblasTrans) TA='T';
+      else if ( TransB == CblasConjTrans ) TA='C';
+      else if ( TransB == CblasNoTrans )   TA='N';
+      else
+      {
+         cblas_xerbla(layout, 2, "cblas_zgemm", "Illegal TransB setting, %d\n", TransB);
+         return;
+      }
+
+      zgemm_(&TA, &TB, (int*)&N, (int*)&M, (int*)&K, (doublecomplex*)alpha, (doublecomplex*)B, (int*)&ldb,
+             (doublecomplex*)A, (int*)&lda, (doublecomplex*)beta, (doublecomplex*)C, (int*)&ldc);
+   }
+   else cblas_xerbla(layout, 1, "cblas_zgemm", "Illegal layout setting, %d\n", layout);
+}
+
+void cblas_xerbla(const CBLAS_LAYOUT layout, int info, const char *rout, const char *form, ...)
+{
+   extern int RowMajorStrg;
+   char empty[1] = "";
+   va_list argptr;
+
+   va_start(argptr, form);
+
+   if (layout == CblasRowMajor)
+   {
+      if (strstr(rout,"gemm") != 0)
+      {
+         if      (info == 5 ) info =  4;
+         else if (info == 4 ) info =  5;
+         else if (info == 11) info =  9;
+         else if (info == 9 ) info = 11;
+      }
+      else if (strstr(rout,"symm") != 0 || strstr(rout,"hemm") != 0)
+      {
+         if      (info == 5 ) info =  4;
+         else if (info == 4 ) info =  5;
+      }
+      else if (strstr(rout,"trmm") != 0 || strstr(rout,"trsm") != 0)
+      {
+         if      (info == 7 ) info =  6;
+         else if (info == 6 ) info =  7;
+      }
+      else if (strstr(rout,"gemv") != 0)
+      {
+         if      (info == 4)  info = 3;
+         else if (info == 3)  info = 4;
+      }
+      else if (strstr(rout,"gbmv") != 0)
+      {
+         if      (info == 4)  info = 3;
+         else if (info == 3)  info = 4;
+         else if (info == 6)  info = 5;
+         else if (info == 5)  info = 6;
+      }
+      else if (strstr(rout,"ger") != 0)
+      {
+         if      (info == 3) info = 2;
+         else if (info == 2) info = 3;
+         else if (info == 8) info = 6;
+         else if (info == 6) info = 8;
+      }
+      else if ( (strstr(rout,"her2") != 0 || strstr(rout,"hpr2") != 0)
+                 && strstr(rout,"her2k") == 0 )
+      {
+         if      (info == 8) info = 6;
+         else if (info == 6) info = 8;
+      }
+   }
+   if (info)
+      fprintf(stderr, "Parameter %d to routine %s was incorrect\n", info, rout);
+   vfprintf(stderr, form, argptr);
+   va_end(argptr);
+   if (info && !info)
+      xerbla_(empty, &info); /* Force link of our F77 error handler */
+   exit(-1);
+}

3rdparty/clapack/runtime/dlamch_custom.c

@@ -0,0 +1,72 @@
+#include "f2c.h"
+#include <float.h>
+#include <stdio.h>
+
+/* *********************************************************************** */
+
+double dlamc3_(double *a, double *b)
+{
+    /*  -- LAPACK auxiliary routine (version 3.1) -- */
+    /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+    /*     November 2006 */
+
+    /*     .. Scalar Arguments .. */
+    /*     .. */
+
+    /*  Purpose */
+    /*  ======= */
+
+    /*  DLAMC3  is intended to force  A  and  B  to be stored prior to doing */
+    /*  the addition of  A  and  B ,  for use in situations where optimizers */
+    /*  might hold one of these in a register. */
+
+    /*  Arguments */
+    /*  ========= */
+
+    /*  A       (input) DOUBLE PRECISION */
+    /*  B       (input) DOUBLE PRECISION */
+    /*          The values A and B. */
+
+    /* ===================================================================== */
+
+    /*     .. Executable Statements .. */
+
+    double ret_val = *a + *b;
+
+    return ret_val;
+
+    /*     End of DLAMC3 */
+
+} /* dlamc3_ */
+
+
+/* simpler version of dlamch for the case of IEEE754-compliant FPU module by Piotr Luszczek S.
+   taken from http://www.mail-archive.com/numpy-discussion@lists.sourceforge.net/msg02448.html */
+
+#ifndef DBL_DIGITS
+#define DBL_DIGITS 53
+#endif
+
+static const unsigned char lapack_dlamch_tab0[] =
+{
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 4, 5, 6, 7, 0, 8, 9, 0, 10, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 4, 5, 6, 7, 0, 8, 9,
+    0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
+};
+
+const double lapack_dlamch_tab1[] =
+{
+    0, FLT_RADIX, DBL_EPSILON, DBL_MAX_EXP, DBL_MIN_EXP, DBL_DIGITS, DBL_MAX,
+    DBL_EPSILON*FLT_RADIX, 1, DBL_MIN*(1 + DBL_EPSILON), DBL_MIN
+};
+
+double dlamch_(char* cmach)
+{
+    return lapack_dlamch_tab1[lapack_dlamch_tab0[(unsigned char)cmach[0]]];
+}

3rdparty/clapack/runtime/lapack_stubs.c

@@ -0,0 +1,96 @@
+#include "f2c.h"
+
+static const int CLAPACK_NOT_IMPLEMENTED = -1024;
+
+int sgesdd_(char *jobz, int *m, int *n, float *a, int *lda,
+	float *s, float *u, int *ldu, float *vt, int *ldvt, float *work,
+	int *lwork, int *iwork, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int dgels_(char *trans, int *m, int *n, int *nrhs, double *a,
+	int *lda, double *b, int *ldb, double *work, int *lwork, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int dgesv_(int *n, int *nrhs, double *a, int *lda, int *ipiv,
+	double *b, int *ldb, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int dgetrf_(int *m, int *n, double *a, int *lda, int *ipiv,
+	int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int dposv_(char *uplo, int *n, int *nrhs, double *a, int *
+	lda, double *b, int *ldb, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int dpotrf_(char *uplo, int *n, double *a, int *lda, int *
+	info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int sgels_(char *trans, int *m, int *n, int *nrhs, float *a,
+	int *lda, float *b, int *ldb, float *work, int *lwork, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int sgeev_(char *jobvl, char *jobvr, int *n, float *a, int *
+	lda, float *wr, float *wi, float *vl, int *ldvl, float *vr, int *
+	ldvr, float *work, int *lwork, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int sgeqrf_(int *m, int *n, float *a, int *lda, float *tau,
+	float *work, int *lwork, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int sgesv_(int *n, int *nrhs, float *a, int *lda, int *ipiv,
+	float *b, int *ldb, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}        
+
+int sgetrf_(int *m, int *n, float *a, int *lda, int *ipiv,
+	int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}
+
+int sposv_(char *uplo, int *n, int *nrhs, float *a, int *
+	lda, float *b, int *ldb, int *info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}        
+
+int spotrf_(char *uplo, int *n, float *a, int *lda, int *
+	info)
+{
+    *info = CLAPACK_NOT_IMPLEMENTED;
+    return 0;
+}

3rdparty/clapack/runtime/lsame_custom.c

@@ -0,0 +1,25 @@
+#include "f2c.h"
+
+static const unsigned char lapack_toupper_tab[] =
+{
+    0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
+    24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45,
+    46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,
+    68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
+    90, 91, 92, 93, 94, 95, 96, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
+    80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 123, 124, 125, 126, 127, 128, 129, 130, 131,
+    132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149,
+    150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,
+    168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185,
+    186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203,
+    204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221,
+    222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239,
+    240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255
+};
+
+#define lapack_toupper(c) ((char)lapack_toupper_tab[(unsigned char)(c)])
+
+int lsame_(char *ca, char *cb)
+{
+    return lapack_toupper(ca[0]) == lapack_toupper(cb[0]);
+}

3rdparty/clapack/runtime/pow_di.c

@@ -0,0 +1,27 @@
+#include "f2c.h"
+
+double pow_di(double *ap, int *bp)
+{
+    double p = 1;
+    double x = *ap;
+    int n = *bp;
+
+    if(n != 0)
+    {
+        if(n < 0)
+        {
+            n = -n;
+            x = 1/x;
+        }
+        unsigned u = (unsigned)n;
+        for(;;)
+        {
+            if((u & 1) != 0)
+                p *= x;
+            if((u >>= 1) == 0)
+                break;
+            x *= x;
+        }
+    }
+    return p;
+}

3rdparty/clapack/runtime/pow_ii.c

@@ -0,0 +1,25 @@
+#include "f2c.h"
+
+int pow_ii(int *ap, int *bp)
+{
+    int p;
+    int x = *ap;
+    int n = *bp;
+
+    if (n <= 0) {
+        if (n == 0 || x == 1)
+            return 1;
+        return x != -1 ? 0 : (n & 1) ? -1 : 1;
+    }
+    unsigned u = (unsigned)n;
+    for(p = 1; ; )
+    {
+        if(u & 01)
+            p *= x;
+        if(u >>= 1)
+            x *= x;
+        else
+            break;
+    }
+    return p;
+}

3rdparty/clapack/runtime/s_cat.c

@@ -0,0 +1,22 @@
+/* Unless compiled with -DNO_OVERWRITE, this variant of s_cat allows the
+ * target of a concatenation to appear on its right-hand side (contrary
+ * to the Fortran 77 Standard, but in accordance with Fortran 90).
+ */
+
+#include "f2c.h"
+
+int s_cat(char *lp, char **rpp, int* rnp, int *np)
+{
+    int i, L = 0;
+    int n = *np;
+
+    for(i = 0; i < n; i++) {
+        int ni = rnp[i];
+        if(ni > 0) {
+            memcpy(lp + L, rpp[i], ni);
+            L += ni;
+        }
+    }
+    lp[L] = '\0';
+    return 0;
+}

3rdparty/clapack/runtime/s_cmp.c

@@ -0,0 +1,40 @@
+#include "f2c.h"
+
+/* compare two strings */
+int s_cmp(char *a0, char *b0)
+{
+    int la = (int)strlen(a0);
+    int lb = (int)strlen(b0);
+    unsigned char *a, *aend, *b, *bend;
+    a = (unsigned char *)a0;
+    b = (unsigned char *)b0;
+    aend = a + la;
+    bend = b + lb;
+
+    if(la <= lb)
+    	{
+    	while(a < aend)
+    		if(*a != *b)
+    			return( *a - *b );
+    		else
+    			{ ++a; ++b; }
+
+    	while(b < bend)
+    		if(*b != ' ')
+    			return( ' ' - *b );
+    		else	++b;
+    	}
+    else
+    	{
+    	while(b < bend)
+    		if(*a == *b)
+    			{ ++a; ++b; }
+    		else
+    			return( *a - *b );
+    	while(a < aend)
+    		if(*a != ' ')
+    			return(*a - ' ');
+    		else	++a;
+    	}
+    return(0);
+}

3rdparty/clapack/runtime/slamch_custom.c

@@ -0,0 +1,71 @@
+#include "f2c.h"
+#include <float.h>
+#include <stdio.h>
+
+/* *********************************************************************** */
+
+double slamc3_(float *a, float *b)
+{
+    /*  -- LAPACK auxiliary routine (version 3.1) -- */
+    /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+    /*     November 2006 */
+
+    /*     .. Scalar Arguments .. */
+    /*     .. */
+
+    /*  Purpose */
+    /*  ======= */
+
+    /*  SLAMC3  is intended to force  A  and  B  to be stored prior to doing */
+    /*  the addition of  A  and  B ,  for use in situations where optimizers */
+    /*  might hold one of these in a register. */
+
+    /*  Arguments */
+    /*  ========= */
+
+    /*  A       (input) REAL */
+    /*  B       (input) REAL */
+    /*          The values A and B. */
+
+    /* ===================================================================== */
+
+    /*     .. Executable Statements .. */
+
+    float ret_val = *a + *b;
+
+    return ret_val;
+
+    /*     End of SLAMC3 */
+
+} /* slamc3_ */
+
+/* simpler version of slamch for the case of IEEE754-compliant FPU module by Piotr Luszczek S.
+ taken from http://www.mail-archive.com/numpy-discussion@lists.sourceforge.net/msg02448.html */
+
+#ifndef FLT_DIGITS
+#define FLT_DIGITS 24
+#endif
+
+static const unsigned char lapack_slamch_tab0[] =
+{
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 4, 5, 6, 7, 0, 8, 9, 0, 10, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 4, 5, 6, 7, 0, 8, 9,
+    0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
+};
+
+const double lapack_slamch_tab1[] =
+{
+    0, FLT_RADIX, FLT_EPSILON, FLT_MAX_EXP, FLT_MIN_EXP, FLT_DIGITS, FLT_MAX,
+    FLT_EPSILON*FLT_RADIX, 1, FLT_MIN*(1 + FLT_EPSILON), FLT_MIN
+};
+
+double slamch_(char* cmach)
+{
+    return lapack_slamch_tab1[lapack_slamch_tab0[(unsigned char)cmach[0]]];
+}

3rdparty/clapack/runtime/xerbla_custom.c

@@ -0,0 +1,19 @@
+/* xerbla.f -- translated by f2c (version 20061008).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Subroutine */ int xerbla_(char *srname, int *info)
+{
+    printf("** On entry to %s, parameter number %2i had an illegal value\n", srname, *info);
+    return 0;
+} /* xerbla_ */

3rdparty/clapack/src/cgemm.c

@@ -0,0 +1,752 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b CGEMM
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+//
+//      .. Scalar Arguments ..
+//      COMPLEX ALPHA,BETA
+//      INTEGER K,LDA,LDB,LDC,M,N
+//      CHARACTER TRANSA,TRANSB
+//      ..
+//      .. Array Arguments ..
+//      COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> CGEMM  performs one of the matrix-matrix operations
+//>
+//>    C := alpha*op( A )*op( B ) + beta*C,
+//>
+//> where  op( X ) is one of
+//>
+//>    op( X ) = X   or   op( X ) = X**T   or   op( X ) = X**H,
+//>
+//> alpha and beta are scalars, and A, B and C are matrices, with op( A )
+//> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] TRANSA
+//> \verbatim
+//>          TRANSA is CHARACTER*1
+//>           On entry, TRANSA specifies the form of op( A ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSA = 'N' or 'n',  op( A ) = A.
+//>
+//>              TRANSA = 'T' or 't',  op( A ) = A**T.
+//>
+//>              TRANSA = 'C' or 'c',  op( A ) = A**H.
+//> \endverbatim
+//>
+//> \param[in] TRANSB
+//> \verbatim
+//>          TRANSB is CHARACTER*1
+//>           On entry, TRANSB specifies the form of op( B ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSB = 'N' or 'n',  op( B ) = B.
+//>
+//>              TRANSB = 'T' or 't',  op( B ) = B**T.
+//>
+//>              TRANSB = 'C' or 'c',  op( B ) = B**H.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>           On entry,  M  specifies  the number  of rows  of the  matrix
+//>           op( A )  and of the  matrix  C.  M  must  be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry,  N  specifies the number  of columns of the matrix
+//>           op( B ) and the number of columns of the matrix C. N must be
+//>           at least zero.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>           On entry,  K  specifies  the number of columns of the matrix
+//>           op( A ) and the number of rows of the matrix op( B ). K must
+//>           be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is COMPLEX
+//>           On entry, ALPHA specifies the scalar alpha.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is COMPLEX array, dimension ( LDA, ka ), where ka is
+//>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
+//>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
+//>           part of the array  A  must contain the matrix  A,  otherwise
+//>           the leading  k by m  part of the array  A  must contain  the
+//>           matrix A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
+//>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
+//>           least  max( 1, k ).
+//> \endverbatim
+//>
+//> \param[in] B
+//> \verbatim
+//>          B is COMPLEX array, dimension ( LDB, kb ), where kb is
+//>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
+//>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
+//>           part of the array  B  must contain the matrix  B,  otherwise
+//>           the leading  n by k  part of the array  B  must contain  the
+//>           matrix B.
+//> \endverbatim
+//>
+//> \param[in] LDB
+//> \verbatim
+//>          LDB is INTEGER
+//>           On entry, LDB specifies the first dimension of B as declared
+//>           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
+//>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
+//>           least  max( 1, n ).
+//> \endverbatim
+//>
+//> \param[in] BETA
+//> \verbatim
+//>          BETA is COMPLEX
+//>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
+//>           supplied as zero then C need not be set on input.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is COMPLEX array, dimension ( LDC, N )
+//>           Before entry, the leading  m by n  part of the array  C must
+//>           contain the matrix  C,  except when  beta  is zero, in which
+//>           case C need not be set on entry.
+//>           On exit, the array  C  is overwritten by the  m by n  matrix
+//>           ( alpha*op( A )*op( B ) + beta*C ).
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>           On entry, LDC specifies the first dimension of C as declared
+//>           in  the  calling  (sub)  program.   LDC  must  be  at  least
+//>           max( 1, m ).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup complex_blas_level3
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 3 Blas routine.
+//>
+//>  -- Written on 8-February-1989.
+//>     Jack Dongarra, Argonne National Laboratory.
+//>     Iain Duff, AERE Harwell.
+//>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
+//>     Sven Hammarling, Numerical Algorithms Group Ltd.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int cgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, complex *alpha, complex *a, int *lda, complex *b, int *ldb,
+	complex *beta, complex *c__, int *ldc)
+{
+    // Table of constant values
+    complex c_b1 = {1.f,0.f};
+    complex c_b2 = {0.f,0.f};
+
+    // System generated locals
+    int a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
+	    i__3, i__4, i__5, i__6;
+    complex q__1, q__2, q__3, q__4;
+
+    // Local variables
+    int i__, j, l, info;
+    int nota, notb;
+    complex temp;
+    int conja, conjb;
+    int ncola;
+    extern int lsame_(char *, char *);
+    int nrowa, nrowb;
+    extern /* Subroutine */ int xerbla_(char *, int *);
+
+    //
+    // -- Reference BLAS level3 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Parameters ..
+    //    ..
+    //
+    //    Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
+    //    conjugated or transposed, set  CONJA and CONJB  as true if  A  and
+    //    B  respectively are to be  transposed but  not conjugated  and set
+    //    NROWA, NCOLA and  NROWB  as the number of rows and  columns  of  A
+    //    and the number of rows of  B  respectively.
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+
+    // Function Body
+    nota = lsame_(transa, "N");
+    notb = lsame_(transb, "N");
+    conja = lsame_(transa, "C");
+    conjb = lsame_(transb, "C");
+    if (nota) {
+	nrowa = *m;
+	ncola = *k;
+    } else {
+	nrowa = *k;
+	ncola = *m;
+    }
+    if (notb) {
+	nrowb = *k;
+    } else {
+	nrowb = *n;
+    }
+    //
+    //    Test the input parameters.
+    //
+    info = 0;
+    if (! nota && ! conja && ! lsame_(transa, "T")) {
+	info = 1;
+    } else if (! notb && ! conjb && ! lsame_(transb, "T")) {
+	info = 2;
+    } else if (*m < 0) {
+	info = 3;
+    } else if (*n < 0) {
+	info = 4;
+    } else if (*k < 0) {
+	info = 5;
+    } else if (*lda < max(1,nrowa)) {
+	info = 8;
+    } else if (*ldb < max(1,nrowb)) {
+	info = 10;
+    } else if (*ldc < max(1,*m)) {
+	info = 13;
+    }
+    if (info != 0) {
+	xerbla_("CGEMM ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*m == 0 || *n == 0 || (alpha->r == 0.f && alpha->i == 0.f || *k == 0)
+	    && (beta->r == 1.f && beta->i == 0.f)) {
+	return 0;
+    }
+    //
+    //    And when  alpha.eq.zero.
+    //
+    if (alpha->r == 0.f && alpha->i == 0.f) {
+	if (beta->r == 0.f && beta->i == 0.f) {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * c_dim1;
+		    c__[i__3].r = 0.f, c__[i__3].i = 0.f;
+// L10:
+		}
+// L20:
+	    }
+	} else {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * c_dim1;
+		    i__4 = i__ + j * c_dim1;
+		    q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i,
+			    q__1.i = beta->r * c__[i__4].i + beta->i * c__[
+			    i__4].r;
+		    c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+// L30:
+		}
+// L40:
+	    }
+	}
+	return 0;
+    }
+    //
+    //    Start the operations.
+    //
+    if (notb) {
+	if (nota) {
+	    //
+	    //          Form  C := alpha*A*B + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (beta->r == 0.f && beta->i == 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			c__[i__3].r = 0.f, c__[i__3].i = 0.f;
+// L50:
+		    }
+		} else if (beta->r != 1.f || beta->i != 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			i__4 = i__ + j * c_dim1;
+			q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__1.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+// L60:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    i__3 = l + j * b_dim1;
+		    q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
+			    q__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3]
+			    .r;
+		    temp.r = q__1.r, temp.i = q__1.i;
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			i__4 = i__ + j * c_dim1;
+			i__5 = i__ + j * c_dim1;
+			i__6 = i__ + l * a_dim1;
+			q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
+				q__2.i = temp.r * a[i__6].i + temp.i * a[i__6]
+				.r;
+			q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5].i +
+				q__2.i;
+			c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
+// L70:
+		    }
+// L80:
+		}
+// L90:
+	    }
+	} else if (conja) {
+	    //
+	    //          Form  C := alpha*A**H*B + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0.f, temp.i = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			r_cnjg(&q__3, &a[l + i__ * a_dim1]);
+			i__4 = l + j * b_dim1;
+			q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i,
+				q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4]
+				.r;
+			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
+			temp.r = q__1.r, temp.i = q__1.i;
+// L100:
+		    }
+		    if (beta->r == 0.f && beta->i == 0.f) {
+			i__3 = i__ + j * c_dim1;
+			q__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			q__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    }
+// L110:
+		}
+// L120:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0.f, temp.i = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			i__4 = l + i__ * a_dim1;
+			i__5 = l + j * b_dim1;
+			q__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
+				.i, q__2.i = a[i__4].r * b[i__5].i + a[i__4]
+				.i * b[i__5].r;
+			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
+			temp.r = q__1.r, temp.i = q__1.i;
+// L130:
+		    }
+		    if (beta->r == 0.f && beta->i == 0.f) {
+			i__3 = i__ + j * c_dim1;
+			q__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			q__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    }
+// L140:
+		}
+// L150:
+	    }
+	}
+    } else if (nota) {
+	if (conjb) {
+	    //
+	    //          Form  C := alpha*A*B**H + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (beta->r == 0.f && beta->i == 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			c__[i__3].r = 0.f, c__[i__3].i = 0.f;
+// L160:
+		    }
+		} else if (beta->r != 1.f || beta->i != 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			i__4 = i__ + j * c_dim1;
+			q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__1.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+// L170:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    r_cnjg(&q__2, &b[j + l * b_dim1]);
+		    q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i =
+			    alpha->r * q__2.i + alpha->i * q__2.r;
+		    temp.r = q__1.r, temp.i = q__1.i;
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			i__4 = i__ + j * c_dim1;
+			i__5 = i__ + j * c_dim1;
+			i__6 = i__ + l * a_dim1;
+			q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
+				q__2.i = temp.r * a[i__6].i + temp.i * a[i__6]
+				.r;
+			q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5].i +
+				q__2.i;
+			c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
+// L180:
+		    }
+// L190:
+		}
+// L200:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (beta->r == 0.f && beta->i == 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			c__[i__3].r = 0.f, c__[i__3].i = 0.f;
+// L210:
+		    }
+		} else if (beta->r != 1.f || beta->i != 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			i__4 = i__ + j * c_dim1;
+			q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__1.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+// L220:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    i__3 = j + l * b_dim1;
+		    q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
+			    q__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3]
+			    .r;
+		    temp.r = q__1.r, temp.i = q__1.i;
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			i__4 = i__ + j * c_dim1;
+			i__5 = i__ + j * c_dim1;
+			i__6 = i__ + l * a_dim1;
+			q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
+				q__2.i = temp.r * a[i__6].i + temp.i * a[i__6]
+				.r;
+			q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5].i +
+				q__2.i;
+			c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
+// L230:
+		    }
+// L240:
+		}
+// L250:
+	    }
+	}
+    } else if (conja) {
+	if (conjb) {
+	    //
+	    //          Form  C := alpha*A**H*B**H + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0.f, temp.i = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			r_cnjg(&q__3, &a[l + i__ * a_dim1]);
+			r_cnjg(&q__4, &b[j + l * b_dim1]);
+			q__2.r = q__3.r * q__4.r - q__3.i * q__4.i, q__2.i =
+				q__3.r * q__4.i + q__3.i * q__4.r;
+			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
+			temp.r = q__1.r, temp.i = q__1.i;
+// L260:
+		    }
+		    if (beta->r == 0.f && beta->i == 0.f) {
+			i__3 = i__ + j * c_dim1;
+			q__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			q__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    }
+// L270:
+		}
+// L280:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**H*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0.f, temp.i = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			r_cnjg(&q__3, &a[l + i__ * a_dim1]);
+			i__4 = j + l * b_dim1;
+			q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i,
+				q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4]
+				.r;
+			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
+			temp.r = q__1.r, temp.i = q__1.i;
+// L290:
+		    }
+		    if (beta->r == 0.f && beta->i == 0.f) {
+			i__3 = i__ + j * c_dim1;
+			q__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			q__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    }
+// L300:
+		}
+// L310:
+	    }
+	}
+    } else {
+	if (conjb) {
+	    //
+	    //          Form  C := alpha*A**T*B**H + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0.f, temp.i = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			i__4 = l + i__ * a_dim1;
+			r_cnjg(&q__3, &b[j + l * b_dim1]);
+			q__2.r = a[i__4].r * q__3.r - a[i__4].i * q__3.i,
+				q__2.i = a[i__4].r * q__3.i + a[i__4].i *
+				q__3.r;
+			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
+			temp.r = q__1.r, temp.i = q__1.i;
+// L320:
+		    }
+		    if (beta->r == 0.f && beta->i == 0.f) {
+			i__3 = i__ + j * c_dim1;
+			q__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			q__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    }
+// L330:
+		}
+// L340:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0.f, temp.i = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			i__4 = l + i__ * a_dim1;
+			i__5 = j + l * b_dim1;
+			q__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
+				.i, q__2.i = a[i__4].r * b[i__5].i + a[i__4]
+				.i * b[i__5].r;
+			q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
+			temp.r = q__1.r, temp.i = q__1.i;
+// L350:
+		    }
+		    if (beta->r == 0.f && beta->i == 0.f) {
+			i__3 = i__ + j * c_dim1;
+			q__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			q__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				q__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, q__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
+			c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+		    }
+// L360:
+		}
+// L370:
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of CGEMM .
+    //
+} // cgemm_
+

3rdparty/clapack/src/dcopy.c

@@ -0,0 +1,171 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DCOPY
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
+//
+//      .. Scalar Arguments ..
+//      INTEGER INCX,INCY,N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION DX(*),DY(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//>    DCOPY copies a vector, x, to a vector, y.
+//>    uses unrolled loops for increments equal to 1.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>         number of elements in input vector(s)
+//> \endverbatim
+//>
+//> \param[in] DX
+//> \verbatim
+//>          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>         storage spacing between elements of DX
+//> \endverbatim
+//>
+//> \param[out] DY
+//> \verbatim
+//>          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
+//> \endverbatim
+//>
+//> \param[in] INCY
+//> \verbatim
+//>          INCY is INTEGER
+//>         storage spacing between elements of DY
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2017
+//
+//> \ingroup double_blas_level1
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>     jack dongarra, linpack, 3/11/78.
+//>     modified 12/3/93, array(1) declarations changed to array(*)
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dcopy_(int *n, double *dx, int *incx, double *dy, int *
+	incy)
+{
+    // System generated locals
+    int i__1;
+
+    // Local variables
+    int i__, m, ix, iy, mp1;
+
+    //
+    // -- Reference BLAS level1 routine (version 3.8.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    // Parameter adjustments
+    --dy;
+    --dx;
+
+    // Function Body
+    if (*n <= 0) {
+	return 0;
+    }
+    if (*incx == 1 && *incy == 1) {
+	//
+	//       code for both increments equal to 1
+	//
+	//
+	//       clean-up loop
+	//
+	m = *n % 7;
+	if (m != 0) {
+	    i__1 = m;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		dy[i__] = dx[i__];
+	    }
+	    if (*n < 7) {
+		return 0;
+	    }
+	}
+	mp1 = m + 1;
+	i__1 = *n;
+	for (i__ = mp1; i__ <= i__1; i__ += 7) {
+	    dy[i__] = dx[i__];
+	    dy[i__ + 1] = dx[i__ + 1];
+	    dy[i__ + 2] = dx[i__ + 2];
+	    dy[i__ + 3] = dx[i__ + 3];
+	    dy[i__ + 4] = dx[i__ + 4];
+	    dy[i__ + 5] = dx[i__ + 5];
+	    dy[i__ + 6] = dx[i__ + 6];
+	}
+    } else {
+	//
+	//       code for unequal increments or equal increments
+	//         not equal to 1
+	//
+	ix = 1;
+	iy = 1;
+	if (*incx < 0) {
+	    ix = (-(*n) + 1) * *incx + 1;
+	}
+	if (*incy < 0) {
+	    iy = (-(*n) + 1) * *incy + 1;
+	}
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    dy[iy] = dx[ix];
+	    ix += *incx;
+	    iy += *incy;
+	}
+    }
+    return 0;
+} // dcopy_
+

3rdparty/clapack/src/ddot.c

@@ -0,0 +1,172 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DDOT
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
+//
+//      .. Scalar Arguments ..
+//      INTEGER INCX,INCY,N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION DX(*),DY(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//>    DDOT forms the dot product of two vectors.
+//>    uses unrolled loops for increments equal to one.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>         number of elements in input vector(s)
+//> \endverbatim
+//>
+//> \param[in] DX
+//> \verbatim
+//>          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>         storage spacing between elements of DX
+//> \endverbatim
+//>
+//> \param[in] DY
+//> \verbatim
+//>          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
+//> \endverbatim
+//>
+//> \param[in] INCY
+//> \verbatim
+//>          INCY is INTEGER
+//>         storage spacing between elements of DY
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2017
+//
+//> \ingroup double_blas_level1
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>     jack dongarra, linpack, 3/11/78.
+//>     modified 12/3/93, array(1) declarations changed to array(*)
+//> \endverbatim
+//>
+// =====================================================================
+double ddot_(int *n, double *dx, int *incx, double *dy, int *incy)
+{
+    // System generated locals
+    int i__1;
+    double ret_val;
+
+    // Local variables
+    int i__, m, ix, iy, mp1;
+    double dtemp;
+
+    //
+    // -- Reference BLAS level1 routine (version 3.8.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    // Parameter adjustments
+    --dy;
+    --dx;
+
+    // Function Body
+    ret_val = 0.;
+    dtemp = 0.;
+    if (*n <= 0) {
+	return ret_val;
+    }
+    if (*incx == 1 && *incy == 1) {
+	//
+	//       code for both increments equal to 1
+	//
+	//
+	//       clean-up loop
+	//
+	m = *n % 5;
+	if (m != 0) {
+	    i__1 = m;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		dtemp += dx[i__] * dy[i__];
+	    }
+	    if (*n < 5) {
+		ret_val = dtemp;
+		return ret_val;
+	    }
+	}
+	mp1 = m + 1;
+	i__1 = *n;
+	for (i__ = mp1; i__ <= i__1; i__ += 5) {
+	    dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] +
+		    dx[i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] +
+		    dx[i__ + 4] * dy[i__ + 4];
+	}
+    } else {
+	//
+	//       code for unequal increments or equal increments
+	//         not equal to 1
+	//
+	ix = 1;
+	iy = 1;
+	if (*incx < 0) {
+	    ix = (-(*n) + 1) * *incx + 1;
+	}
+	if (*incy < 0) {
+	    iy = (-(*n) + 1) * *incy + 1;
+	}
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    dtemp += dx[ix] * dy[iy];
+	    ix += *incx;
+	    iy += *incy;
+	}
+    }
+    ret_val = dtemp;
+    return ret_val;
+} // ddot_
+

3rdparty/clapack/src/dgemm.c

@@ -0,0 +1,444 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DGEMM
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION ALPHA,BETA
+//      INTEGER K,LDA,LDB,LDC,M,N
+//      CHARACTER TRANSA,TRANSB
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DGEMM  performs one of the matrix-matrix operations
+//>
+//>    C := alpha*op( A )*op( B ) + beta*C,
+//>
+//> where  op( X ) is one of
+//>
+//>    op( X ) = X   or   op( X ) = X**T,
+//>
+//> alpha and beta are scalars, and A, B and C are matrices, with op( A )
+//> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] TRANSA
+//> \verbatim
+//>          TRANSA is CHARACTER*1
+//>           On entry, TRANSA specifies the form of op( A ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSA = 'N' or 'n',  op( A ) = A.
+//>
+//>              TRANSA = 'T' or 't',  op( A ) = A**T.
+//>
+//>              TRANSA = 'C' or 'c',  op( A ) = A**T.
+//> \endverbatim
+//>
+//> \param[in] TRANSB
+//> \verbatim
+//>          TRANSB is CHARACTER*1
+//>           On entry, TRANSB specifies the form of op( B ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSB = 'N' or 'n',  op( B ) = B.
+//>
+//>              TRANSB = 'T' or 't',  op( B ) = B**T.
+//>
+//>              TRANSB = 'C' or 'c',  op( B ) = B**T.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>           On entry,  M  specifies  the number  of rows  of the  matrix
+//>           op( A )  and of the  matrix  C.  M  must  be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry,  N  specifies the number  of columns of the matrix
+//>           op( B ) and the number of columns of the matrix C. N must be
+//>           at least zero.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>           On entry,  K  specifies  the number of columns of the matrix
+//>           op( A ) and the number of rows of the matrix op( B ). K must
+//>           be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is DOUBLE PRECISION.
+//>           On entry, ALPHA specifies the scalar alpha.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
+//>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
+//>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
+//>           part of the array  A  must contain the matrix  A,  otherwise
+//>           the leading  k by m  part of the array  A  must contain  the
+//>           matrix A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
+//>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
+//>           least  max( 1, k ).
+//> \endverbatim
+//>
+//> \param[in] B
+//> \verbatim
+//>          B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is
+//>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
+//>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
+//>           part of the array  B  must contain the matrix  B,  otherwise
+//>           the leading  n by k  part of the array  B  must contain  the
+//>           matrix B.
+//> \endverbatim
+//>
+//> \param[in] LDB
+//> \verbatim
+//>          LDB is INTEGER
+//>           On entry, LDB specifies the first dimension of B as declared
+//>           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
+//>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
+//>           least  max( 1, n ).
+//> \endverbatim
+//>
+//> \param[in] BETA
+//> \verbatim
+//>          BETA is DOUBLE PRECISION.
+//>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
+//>           supplied as zero then C need not be set on input.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is DOUBLE PRECISION array, dimension ( LDC, N )
+//>           Before entry, the leading  m by n  part of the array  C must
+//>           contain the matrix  C,  except when  beta  is zero, in which
+//>           case C need not be set on entry.
+//>           On exit, the array  C  is overwritten by the  m by n  matrix
+//>           ( alpha*op( A )*op( B ) + beta*C ).
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>           On entry, LDC specifies the first dimension of C as declared
+//>           in  the  calling  (sub)  program.   LDC  must  be  at  least
+//>           max( 1, m ).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup double_blas_level3
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 3 Blas routine.
+//>
+//>  -- Written on 8-February-1989.
+//>     Jack Dongarra, Argonne National Laboratory.
+//>     Iain Duff, AERE Harwell.
+//>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
+//>     Sven Hammarling, Numerical Algorithms Group Ltd.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, double *alpha, double *a, int *lda, double *b, int *ldb, double *
+	beta, double *c__, int *ldc)
+{
+    // System generated locals
+    int a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
+	    i__3;
+
+    // Local variables
+    int i__, j, l, info;
+    int nota, notb;
+    double temp;
+    int ncola;
+    extern int lsame_(char *, char *);
+    int nrowa, nrowb;
+    extern /* Subroutine */ int xerbla_(char *, int *);
+
+    //
+    // -- Reference BLAS level3 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Parameters ..
+    //    ..
+    //
+    //    Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
+    //    transposed and set  NROWA, NCOLA and  NROWB  as the number of rows
+    //    and  columns of  A  and the  number of  rows  of  B  respectively.
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+
+    // Function Body
+    nota = lsame_(transa, "N");
+    notb = lsame_(transb, "N");
+    if (nota) {
+	nrowa = *m;
+	ncola = *k;
+    } else {
+	nrowa = *k;
+	ncola = *m;
+    }
+    if (notb) {
+	nrowb = *k;
+    } else {
+	nrowb = *n;
+    }
+    //
+    //    Test the input parameters.
+    //
+    info = 0;
+    if (! nota && ! lsame_(transa, "C") && ! lsame_(transa, "T")) {
+	info = 1;
+    } else if (! notb && ! lsame_(transb, "C") && ! lsame_(transb, "T")) {
+	info = 2;
+    } else if (*m < 0) {
+	info = 3;
+    } else if (*n < 0) {
+	info = 4;
+    } else if (*k < 0) {
+	info = 5;
+    } else if (*lda < max(1,nrowa)) {
+	info = 8;
+    } else if (*ldb < max(1,nrowb)) {
+	info = 10;
+    } else if (*ldc < max(1,*m)) {
+	info = 13;
+    }
+    if (info != 0) {
+	xerbla_("DGEMM ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
+	return 0;
+    }
+    //
+    //    And if  alpha.eq.zero.
+    //
+    if (*alpha == 0.) {
+	if (*beta == 0.) {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    c__[i__ + j * c_dim1] = 0.;
+// L10:
+		}
+// L20:
+	    }
+	} else {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
+// L30:
+		}
+// L40:
+	    }
+	}
+	return 0;
+    }
+    //
+    //    Start the operations.
+    //
+    if (notb) {
+	if (nota) {
+	    //
+	    //          Form  C := alpha*A*B + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (*beta == 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = 0.;
+// L50:
+		    }
+		} else if (*beta != 1.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
+// L60:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    temp = *alpha * b[l + j * b_dim1];
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1];
+// L70:
+		    }
+// L80:
+		}
+// L90:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			temp += a[l + i__ * a_dim1] * b[l + j * b_dim1];
+// L100:
+		    }
+		    if (*beta == 0.) {
+			c__[i__ + j * c_dim1] = *alpha * temp;
+		    } else {
+			c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
+				i__ + j * c_dim1];
+		    }
+// L110:
+		}
+// L120:
+	    }
+	}
+    } else {
+	if (nota) {
+	    //
+	    //          Form  C := alpha*A*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (*beta == 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = 0.;
+// L130:
+		    }
+		} else if (*beta != 1.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
+// L140:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    temp = *alpha * b[j + l * b_dim1];
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1];
+// L150:
+		    }
+// L160:
+		}
+// L170:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			temp += a[l + i__ * a_dim1] * b[j + l * b_dim1];
+// L180:
+		    }
+		    if (*beta == 0.) {
+			c__[i__ + j * c_dim1] = *alpha * temp;
+		    } else {
+			c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
+				i__ + j * c_dim1];
+		    }
+// L190:
+		}
+// L200:
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of DGEMM .
+    //
+} // dgemm_
+

3rdparty/clapack/src/dgemv.c

@@ -0,0 +1,370 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DGEMV
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION ALPHA,BETA
+//      INTEGER INCX,INCY,LDA,M,N
+//      CHARACTER TRANS
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DGEMV  performs one of the matrix-vector operations
+//>
+//>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
+//>
+//> where alpha and beta are scalars, x and y are vectors and A is an
+//> m by n matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] TRANS
+//> \verbatim
+//>          TRANS is CHARACTER*1
+//>           On entry, TRANS specifies the operation to be performed as
+//>           follows:
+//>
+//>              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
+//>
+//>              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
+//>
+//>              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>           On entry, M specifies the number of rows of the matrix A.
+//>           M must be at least zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry, N specifies the number of columns of the matrix A.
+//>           N must be at least zero.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is DOUBLE PRECISION.
+//>           On entry, ALPHA specifies the scalar alpha.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension ( LDA, N )
+//>           Before entry, the leading m by n part of the array A must
+//>           contain the matrix of coefficients.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program. LDA must be at least
+//>           max( 1, m ).
+//> \endverbatim
+//>
+//> \param[in] X
+//> \verbatim
+//>          X is DOUBLE PRECISION array, dimension at least
+//>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
+//>           and at least
+//>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
+//>           Before entry, the incremented array X must contain the
+//>           vector x.
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>           On entry, INCX specifies the increment for the elements of
+//>           X. INCX must not be zero.
+//> \endverbatim
+//>
+//> \param[in] BETA
+//> \verbatim
+//>          BETA is DOUBLE PRECISION.
+//>           On entry, BETA specifies the scalar beta. When BETA is
+//>           supplied as zero then Y need not be set on input.
+//> \endverbatim
+//>
+//> \param[in,out] Y
+//> \verbatim
+//>          Y is DOUBLE PRECISION array, dimension at least
+//>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
+//>           and at least
+//>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
+//>           Before entry with BETA non-zero, the incremented array Y
+//>           must contain the vector y. On exit, Y is overwritten by the
+//>           updated vector y.
+//> \endverbatim
+//>
+//> \param[in] INCY
+//> \verbatim
+//>          INCY is INTEGER
+//>           On entry, INCY specifies the increment for the elements of
+//>           Y. INCY must not be zero.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup double_blas_level2
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 2 Blas routine.
+//>  The vector and matrix arguments are not referenced when N = 0, or M = 0
+//>
+//>  -- Written on 22-October-1986.
+//>     Jack Dongarra, Argonne National Lab.
+//>     Jeremy Du Croz, Nag Central Office.
+//>     Sven Hammarling, Nag Central Office.
+//>     Richard Hanson, Sandia National Labs.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dgemv_(char *trans, int *m, int *n, double *alpha,
+	double *a, int *lda, double *x, int *incx, double *beta, double *y,
+	int *incy)
+{
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2;
+
+    // Local variables
+    int i__, j, ix, iy, jx, jy, kx, ky, info;
+    double temp;
+    int lenx, leny;
+    extern int lsame_(char *, char *);
+    extern /* Subroutine */ int xerbla_(char *, int *);
+
+    //
+    // -- Reference BLAS level2 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //
+    //    Test the input parameters.
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --x;
+    --y;
+
+    // Function Body
+    info = 0;
+    if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C"))
+	    {
+	info = 1;
+    } else if (*m < 0) {
+	info = 2;
+    } else if (*n < 0) {
+	info = 3;
+    } else if (*lda < max(1,*m)) {
+	info = 6;
+    } else if (*incx == 0) {
+	info = 8;
+    } else if (*incy == 0) {
+	info = 11;
+    }
+    if (info != 0) {
+	xerbla_("DGEMV ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
+	return 0;
+    }
+    //
+    //    Set  LENX  and  LENY, the lengths of the vectors x and y, and set
+    //    up the start points in  X  and  Y.
+    //
+    if (lsame_(trans, "N")) {
+	lenx = *n;
+	leny = *m;
+    } else {
+	lenx = *m;
+	leny = *n;
+    }
+    if (*incx > 0) {
+	kx = 1;
+    } else {
+	kx = 1 - (lenx - 1) * *incx;
+    }
+    if (*incy > 0) {
+	ky = 1;
+    } else {
+	ky = 1 - (leny - 1) * *incy;
+    }
+    //
+    //    Start the operations. In this version the elements of A are
+    //    accessed sequentially with one pass through A.
+    //
+    //    First form  y := beta*y.
+    //
+    if (*beta != 1.) {
+	if (*incy == 1) {
+	    if (*beta == 0.) {
+		i__1 = leny;
+		for (i__ = 1; i__ <= i__1; ++i__) {
+		    y[i__] = 0.;
+// L10:
+		}
+	    } else {
+		i__1 = leny;
+		for (i__ = 1; i__ <= i__1; ++i__) {
+		    y[i__] = *beta * y[i__];
+// L20:
+		}
+	    }
+	} else {
+	    iy = ky;
+	    if (*beta == 0.) {
+		i__1 = leny;
+		for (i__ = 1; i__ <= i__1; ++i__) {
+		    y[iy] = 0.;
+		    iy += *incy;
+// L30:
+		}
+	    } else {
+		i__1 = leny;
+		for (i__ = 1; i__ <= i__1; ++i__) {
+		    y[iy] = *beta * y[iy];
+		    iy += *incy;
+// L40:
+		}
+	    }
+	}
+    }
+    if (*alpha == 0.) {
+	return 0;
+    }
+    if (lsame_(trans, "N")) {
+	//
+	//       Form  y := alpha*A*x + y.
+	//
+	jx = kx;
+	if (*incy == 1) {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		temp = *alpha * x[jx];
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    y[i__] += temp * a[i__ + j * a_dim1];
+// L50:
+		}
+		jx += *incx;
+// L60:
+	    }
+	} else {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		temp = *alpha * x[jx];
+		iy = ky;
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    y[iy] += temp * a[i__ + j * a_dim1];
+		    iy += *incy;
+// L70:
+		}
+		jx += *incx;
+// L80:
+	    }
+	}
+    } else {
+	//
+	//       Form  y := alpha*A**T*x + y.
+	//
+	jy = ky;
+	if (*incx == 1) {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		temp = 0.;
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp += a[i__ + j * a_dim1] * x[i__];
+// L90:
+		}
+		y[jy] += *alpha * temp;
+		jy += *incy;
+// L100:
+	    }
+	} else {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		temp = 0.;
+		ix = kx;
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp += a[i__ + j * a_dim1] * x[ix];
+		    ix += *incx;
+// L110:
+		}
+		y[jy] += *alpha * temp;
+		jy += *incy;
+// L120:
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of DGEMV .
+    //
+} // dgemv_
+

3rdparty/clapack/src/disnan.c

@@ -0,0 +1,186 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DISNAN tests input for NaN.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DISNAN + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/disnan.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/disnan.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/disnan.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      LOGICAL FUNCTION DISNAN( DIN )
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION, INTENT(IN) :: DIN
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DISNAN returns .TRUE. if its argument is NaN, and .FALSE.
+//> otherwise.  To be replaced by the Fortran 2003 intrinsic in the
+//> future.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] DIN
+//> \verbatim
+//>          DIN is DOUBLE PRECISION
+//>          Input to test for NaN.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date June 2017
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+int disnan_(double *din)
+{
+    // System generated locals
+    int ret_val;
+
+    // Local variables
+    extern int dlaisnan_(double *, double *);
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.1) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    June 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    // .. External Functions ..
+    // ..
+    // .. Executable Statements ..
+    ret_val = dlaisnan_(din, din);
+    return ret_val;
+} // disnan_
+
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+//> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLAISNAN + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaisnan.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaisnan.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaisnan.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION, INTENT(IN) :: DIN1, DIN2
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> This routine is not for general use.  It exists solely to avoid
+//> over-optimization in DISNAN.
+//>
+//> DLAISNAN checks for NaNs by comparing its two arguments for
+//> inequality.  NaN is the only floating-point value where NaN != NaN
+//> returns .TRUE.  To check for NaNs, pass the same variable as both
+//> arguments.
+//>
+//> A compiler must assume that the two arguments are
+//> not the same variable, and the test will not be optimized away.
+//> Interprocedural or whole-program optimization may delete this
+//> test.  The ISNAN functions will be replaced by the correct
+//> Fortran 03 intrinsic once the intrinsic is widely available.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] DIN1
+//> \verbatim
+//>          DIN1 is DOUBLE PRECISION
+//> \endverbatim
+//>
+//> \param[in] DIN2
+//> \verbatim
+//>          DIN2 is DOUBLE PRECISION
+//>          Two numbers to compare for inequality.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date June 2017
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+int dlaisnan_(double *din1, double *din2)
+{
+    // System generated locals
+    int ret_val;
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.1) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    June 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    // .. Executable Statements ..
+    ret_val = *din1 != *din2;
+    return ret_val;
+} // dlaisnan_
+

3rdparty/clapack/src/dlacpy.c

@@ -0,0 +1,184 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLACPY copies all or part of one two-dimensional array to another.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLACPY + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlacpy.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlacpy.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlacpy.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          UPLO
+//      INTEGER            LDA, LDB, M, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLACPY copies all or part of a two-dimensional matrix A to another
+//> matrix B.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] UPLO
+//> \verbatim
+//>          UPLO is CHARACTER*1
+//>          Specifies the part of the matrix A to be copied to B.
+//>          = 'U':      Upper triangular part
+//>          = 'L':      Lower triangular part
+//>          Otherwise:  All of the matrix A
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix A.  M >= 0.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix A.  N >= 0.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          The m by n matrix A.  If UPLO = 'U', only the upper triangle
+//>          or trapezoid is accessed; if UPLO = 'L', only the lower
+//>          triangle or trapezoid is accessed.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A.  LDA >= max(1,M).
+//> \endverbatim
+//>
+//> \param[out] B
+//> \verbatim
+//>          B is DOUBLE PRECISION array, dimension (LDB,N)
+//>          On exit, B = A in the locations specified by UPLO.
+//> \endverbatim
+//>
+//> \param[in] LDB
+//> \verbatim
+//>          LDB is INTEGER
+//>          The leading dimension of the array B.  LDB >= max(1,M).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dlacpy_(char *uplo, int *m, int *n, double *a, int *lda,
+	double *b, int *ldb)
+{
+    // System generated locals
+    int a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
+
+    // Local variables
+    int i__, j;
+    extern int lsame_(char *, char *);
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+
+    // Function Body
+    if (lsame_(uplo, "U")) {
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = min(j,*m);
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		b[i__ + j * b_dim1] = a[i__ + j * a_dim1];
+// L10:
+	    }
+// L20:
+	}
+    } else if (lsame_(uplo, "L")) {
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = j; i__ <= i__2; ++i__) {
+		b[i__ + j * b_dim1] = a[i__ + j * a_dim1];
+// L30:
+	    }
+// L40:
+	}
+    } else {
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		b[i__ + j * b_dim1] = a[i__ + j * a_dim1];
+// L50:
+	    }
+// L60:
+	}
+    }
+    return 0;
+    //
+    //    End of DLACPY
+    //
+} // dlacpy_
+

3rdparty/clapack/src/dlange.c

@@ -0,0 +1,367 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DCOMBSSQ adds two scaled sum of squares quantities.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DCOMBSSQ( V1, V2 )
+//
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   V1( 2 ), V2( 2 )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DCOMBSSQ adds two scaled sum of squares quantities, V1 := V1 + V2.
+//> That is,
+//>
+//>    V1_scale**2 * V1_sumsq := V1_scale**2 * V1_sumsq
+//>                            + V2_scale**2 * V2_sumsq
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in,out] V1
+//> \verbatim
+//>          V1 is DOUBLE PRECISION array, dimension (2).
+//>          The first scaled sum.
+//>          V1(1) = V1_scale, V1(2) = V1_sumsq.
+//> \endverbatim
+//>
+//> \param[in] V2
+//> \verbatim
+//>          V2 is DOUBLE PRECISION array, dimension (2).
+//>          The second scaled sum.
+//>          V2(1) = V2_scale, V2(2) = V2_sumsq.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2018
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dcombssq_(double *v1, double *v2)
+{
+    // System generated locals
+    double d__1;
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2018
+    //
+    //    .. Array Arguments ..
+    //    ..
+    //
+    //=====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    // Parameter adjustments
+    --v2;
+    --v1;
+
+    // Function Body
+    if (v1[1] >= v2[1]) {
+	if (v1[1] != 0.) {
+	    // Computing 2nd power
+	    d__1 = v2[1] / v1[1];
+	    v1[2] += d__1 * d__1 * v2[2];
+	}
+    } else {
+	// Computing 2nd power
+	d__1 = v1[1] / v2[1];
+	v1[2] = v2[2] + d__1 * d__1 * v1[2];
+	v1[1] = v2[1];
+    }
+    return 0;
+    //
+    //    End of DCOMBSSQ
+    //
+} // dcombssq_
+
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+//> \brief \b DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLANGE + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlange.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlange.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlange.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          NORM
+//      INTEGER            LDA, M, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * ), WORK( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLANGE  returns the value of the one norm,  or the Frobenius norm, or
+//> the  infinity norm,  or the  element of  largest absolute value  of a
+//> real matrix A.
+//> \endverbatim
+//>
+//> \return DLANGE
+//> \verbatim
+//>
+//>    DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
+//>             (
+//>             ( norm1(A),         NORM = '1', 'O' or 'o'
+//>             (
+//>             ( normI(A),         NORM = 'I' or 'i'
+//>             (
+//>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
+//>
+//> where  norm1  denotes the  one norm of a matrix (maximum column sum),
+//> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
+//> normF  denotes the  Frobenius norm of a matrix (square root of sum of
+//> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] NORM
+//> \verbatim
+//>          NORM is CHARACTER*1
+//>          Specifies the value to be returned in DLANGE as described
+//>          above.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix A.  M >= 0.  When M = 0,
+//>          DLANGE is set to zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix A.  N >= 0.  When N = 0,
+//>          DLANGE is set to zero.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          The m by n matrix A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A.  LDA >= max(M,1).
+//> \endverbatim
+//>
+//> \param[out] WORK
+//> \verbatim
+//>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
+//>          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
+//>          referenced.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup doubleGEauxiliary
+//
+// =====================================================================
+double dlange_(char *norm, int *m, int *n, double *a, int *lda, double *work)
+{
+    // Table of constant values
+    int c__1 = 1;
+
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2;
+    double ret_val, d__1;
+
+    // Local variables
+    extern /* Subroutine */ int dcombssq_(double *, double *);
+    int i__, j;
+    double sum, ssq[2], temp;
+    extern int lsame_(char *, char *);
+    double value;
+    extern int disnan_(double *);
+    extern /* Subroutine */ int dlassq_(int *, double *, int *, double *,
+	    double *);
+    double colssq[2];
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    //=====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Local Arrays ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --work;
+
+    // Function Body
+    if (min(*m,*n) == 0) {
+	value = 0.;
+    } else if (lsame_(norm, "M")) {
+	//
+	//       Find max(abs(A(i,j))).
+	//
+	value = 0.;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		temp = (d__1 = a[i__ + j * a_dim1], abs(d__1));
+		if (value < temp || disnan_(&temp)) {
+		    value = temp;
+		}
+// L10:
+	    }
+// L20:
+	}
+    } else if (lsame_(norm, "O") || *(unsigned char *)norm == '1') {
+	//
+	//       Find norm1(A).
+	//
+	value = 0.;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    sum = 0.;
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		sum += (d__1 = a[i__ + j * a_dim1], abs(d__1));
+// L30:
+	    }
+	    if (value < sum || disnan_(&sum)) {
+		value = sum;
+	    }
+// L40:
+	}
+    } else if (lsame_(norm, "I")) {
+	//
+	//       Find normI(A).
+	//
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    work[i__] = 0.;
+// L50:
+	}
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1));
+// L60:
+	    }
+// L70:
+	}
+	value = 0.;
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    temp = work[i__];
+	    if (value < temp || disnan_(&temp)) {
+		value = temp;
+	    }
+// L80:
+	}
+    } else if (lsame_(norm, "F") || lsame_(norm, "E")) {
+	//
+	//       Find normF(A).
+	//       SSQ(1) is scale
+	//       SSQ(2) is sum-of-squares
+	//       For better accuracy, sum each column separately.
+	//
+	ssq[0] = 0.;
+	ssq[1] = 1.;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    colssq[0] = 0.;
+	    colssq[1] = 1.;
+	    dlassq_(m, &a[j * a_dim1 + 1], &c__1, colssq, &colssq[1]);
+	    dcombssq_(ssq, colssq);
+// L90:
+	}
+	value = ssq[0] * sqrt(ssq[1]);
+    }
+    ret_val = value;
+    return ret_val;
+    //
+    //    End of DLANGE
+    //
+} // dlange_
+

3rdparty/clapack/src/dlapy2.c

@@ -0,0 +1,125 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLAPY2 returns sqrt(x2+y2).
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLAPY2 + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapy2.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapy2.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapy2.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      DOUBLE PRECISION FUNCTION DLAPY2( X, Y )
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION   X, Y
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary
+//> overflow.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] X
+//> \verbatim
+//>          X is DOUBLE PRECISION
+//> \endverbatim
+//>
+//> \param[in] Y
+//> \verbatim
+//>          Y is DOUBLE PRECISION
+//>          X and Y specify the values x and y.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date June 2017
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+double dlapy2_(double *x, double *y)
+{
+    // System generated locals
+    double ret_val, d__1;
+
+    // Local variables
+    int x_is_nan__, y_is_nan__;
+    double w, z__, xabs, yabs;
+    extern int disnan_(double *);
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.1) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    June 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    x_is_nan__ = disnan_(x);
+    y_is_nan__ = disnan_(y);
+    if (x_is_nan__) {
+	ret_val = *x;
+    }
+    if (y_is_nan__) {
+	ret_val = *y;
+    }
+    if (! (x_is_nan__ || y_is_nan__)) {
+	xabs = abs(*x);
+	yabs = abs(*y);
+	w = max(xabs,yabs);
+	z__ = min(xabs,yabs);
+	if (z__ == 0.) {
+	    ret_val = w;
+	} else {
+	    // Computing 2nd power
+	    d__1 = z__ / w;
+	    ret_val = w * sqrt(d__1 * d__1 + 1.);
+	}
+    }
+    return ret_val;
+    //
+    //    End of DLAPY2
+    //
+} // dlapy2_
+

3rdparty/clapack/src/dlarf.c

@@ -0,0 +1,768 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DGER
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION ALPHA
+//      INTEGER INCX,INCY,LDA,M,N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DGER   performs the rank 1 operation
+//>
+//>    A := alpha*x*y**T + A,
+//>
+//> where alpha is a scalar, x is an m element vector, y is an n element
+//> vector and A is an m by n matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>           On entry, M specifies the number of rows of the matrix A.
+//>           M must be at least zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry, N specifies the number of columns of the matrix A.
+//>           N must be at least zero.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is DOUBLE PRECISION.
+//>           On entry, ALPHA specifies the scalar alpha.
+//> \endverbatim
+//>
+//> \param[in] X
+//> \verbatim
+//>          X is DOUBLE PRECISION array, dimension at least
+//>           ( 1 + ( m - 1 )*abs( INCX ) ).
+//>           Before entry, the incremented array X must contain the m
+//>           element vector x.
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>           On entry, INCX specifies the increment for the elements of
+//>           X. INCX must not be zero.
+//> \endverbatim
+//>
+//> \param[in] Y
+//> \verbatim
+//>          Y is DOUBLE PRECISION array, dimension at least
+//>           ( 1 + ( n - 1 )*abs( INCY ) ).
+//>           Before entry, the incremented array Y must contain the n
+//>           element vector y.
+//> \endverbatim
+//>
+//> \param[in] INCY
+//> \verbatim
+//>          INCY is INTEGER
+//>           On entry, INCY specifies the increment for the elements of
+//>           Y. INCY must not be zero.
+//> \endverbatim
+//>
+//> \param[in,out] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension ( LDA, N )
+//>           Before entry, the leading m by n part of the array A must
+//>           contain the matrix of coefficients. On exit, A is
+//>           overwritten by the updated matrix.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program. LDA must be at least
+//>           max( 1, m ).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup double_blas_level2
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 2 Blas routine.
+//>
+//>  -- Written on 22-October-1986.
+//>     Jack Dongarra, Argonne National Lab.
+//>     Jeremy Du Croz, Nag Central Office.
+//>     Sven Hammarling, Nag Central Office.
+//>     Richard Hanson, Sandia National Labs.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dger_(int *m, int *n, double *alpha, double *x, int *
+	incx, double *y, int *incy, double *a, int *lda)
+{
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2;
+
+    // Local variables
+    int i__, j, ix, jy, kx, info;
+    double temp;
+    extern /* Subroutine */ int xerbla_(char *, int *);
+
+    //
+    // -- Reference BLAS level2 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //
+    //    Test the input parameters.
+    //
+    // Parameter adjustments
+    --x;
+    --y;
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+
+    // Function Body
+    info = 0;
+    if (*m < 0) {
+	info = 1;
+    } else if (*n < 0) {
+	info = 2;
+    } else if (*incx == 0) {
+	info = 5;
+    } else if (*incy == 0) {
+	info = 7;
+    } else if (*lda < max(1,*m)) {
+	info = 9;
+    }
+    if (info != 0) {
+	xerbla_("DGER  ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*m == 0 || *n == 0 || *alpha == 0.) {
+	return 0;
+    }
+    //
+    //    Start the operations. In this version the elements of A are
+    //    accessed sequentially with one pass through A.
+    //
+    if (*incy > 0) {
+	jy = 1;
+    } else {
+	jy = 1 - (*n - 1) * *incy;
+    }
+    if (*incx == 1) {
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    if (y[jy] != 0.) {
+		temp = *alpha * y[jy];
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    a[i__ + j * a_dim1] += x[i__] * temp;
+// L10:
+		}
+	    }
+	    jy += *incy;
+// L20:
+	}
+    } else {
+	if (*incx > 0) {
+	    kx = 1;
+	} else {
+	    kx = 1 - (*m - 1) * *incx;
+	}
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    if (y[jy] != 0.) {
+		temp = *alpha * y[jy];
+		ix = kx;
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    a[i__ + j * a_dim1] += x[ix] * temp;
+		    ix += *incx;
+// L30:
+		}
+	    }
+	    jy += *incy;
+// L40:
+	}
+    }
+    return 0;
+    //
+    //    End of DGER  .
+    //
+} // dger_
+
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+//> \brief \b DLARF applies an elementary reflector to a general rectangular matrix.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLARF + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarf.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarf.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarf.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          SIDE
+//      INTEGER            INCV, LDC, M, N
+//      DOUBLE PRECISION   TAU
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLARF applies a real elementary reflector H to a real m by n matrix
+//> C, from either the left or the right. H is represented in the form
+//>
+//>       H = I - tau * v * v**T
+//>
+//> where tau is a real scalar and v is a real vector.
+//>
+//> If tau = 0, then H is taken to be the unit matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] SIDE
+//> \verbatim
+//>          SIDE is CHARACTER*1
+//>          = 'L': form  H * C
+//>          = 'R': form  C * H
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix C.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix C.
+//> \endverbatim
+//>
+//> \param[in] V
+//> \verbatim
+//>          V is DOUBLE PRECISION array, dimension
+//>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
+//>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
+//>          The vector v in the representation of H. V is not used if
+//>          TAU = 0.
+//> \endverbatim
+//>
+//> \param[in] INCV
+//> \verbatim
+//>          INCV is INTEGER
+//>          The increment between elements of v. INCV <> 0.
+//> \endverbatim
+//>
+//> \param[in] TAU
+//> \verbatim
+//>          TAU is DOUBLE PRECISION
+//>          The value tau in the representation of H.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is DOUBLE PRECISION array, dimension (LDC,N)
+//>          On entry, the m by n matrix C.
+//>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
+//>          or C * H if SIDE = 'R'.
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>          The leading dimension of the array C. LDC >= max(1,M).
+//> \endverbatim
+//>
+//> \param[out] WORK
+//> \verbatim
+//>          WORK is DOUBLE PRECISION array, dimension
+//>                         (N) if SIDE = 'L'
+//>                      or (M) if SIDE = 'R'
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup doubleOTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dlarf_(char *side, int *m, int *n, double *v, int *incv,
+	double *tau, double *c__, int *ldc, double *work)
+{
+    // Table of constant values
+    double c_b4 = 1.;
+    double c_b5 = 0.;
+    int c__1 = 1;
+
+    // System generated locals
+    int c_dim1, c_offset;
+    double d__1;
+
+    // Local variables
+    int i__;
+    int applyleft;
+    extern /* Subroutine */ int dger_(int *, int *, double *, double *, int *,
+	     double *, int *, double *, int *);
+    extern int lsame_(char *, char *);
+    extern /* Subroutine */ int dgemv_(char *, int *, int *, double *, double
+	    *, int *, double *, int *, double *, double *, int *);
+    int lastc, lastv;
+    extern int iladlc_(int *, int *, double *, int *), iladlr_(int *, int *,
+	    double *, int *);
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    // Parameter adjustments
+    --v;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+    --work;
+
+    // Function Body
+    applyleft = lsame_(side, "L");
+    lastv = 0;
+    lastc = 0;
+    if (*tau != 0.) {
+	//    Set up variables for scanning V.  LASTV begins pointing to the end
+	//    of V.
+	if (applyleft) {
+	    lastv = *m;
+	} else {
+	    lastv = *n;
+	}
+	if (*incv > 0) {
+	    i__ = (lastv - 1) * *incv + 1;
+	} else {
+	    i__ = 1;
+	}
+	//    Look for the last non-zero row in V.
+	while(lastv > 0 && v[i__] == 0.) {
+	    --lastv;
+	    i__ -= *incv;
+	}
+	if (applyleft) {
+	    //    Scan for the last non-zero column in C(1:lastv,:).
+	    lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
+	} else {
+	    //    Scan for the last non-zero row in C(:,1:lastv).
+	    lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
+	}
+    }
+    //    Note that lastc.eq.0 renders the BLAS operations null; no special
+    //    case is needed at this level.
+    if (applyleft) {
+	//
+	//       Form  H * C
+	//
+	if (lastv > 0) {
+	    //
+	    //          w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
+	    //
+	    dgemv_("Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, &
+		    v[1], incv, &c_b5, &work[1], &c__1);
+	    //
+	    //          C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
+	    //
+	    d__1 = -(*tau);
+	    dger_(&lastv, &lastc, &d__1, &v[1], incv, &work[1], &c__1, &c__[
+		    c_offset], ldc);
+	}
+    } else {
+	//
+	//       Form  C * H
+	//
+	if (lastv > 0) {
+	    //
+	    //          w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
+	    //
+	    dgemv_("No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc,
+		     &v[1], incv, &c_b5, &work[1], &c__1);
+	    //
+	    //          C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
+	    //
+	    d__1 = -(*tau);
+	    dger_(&lastc, &lastv, &d__1, &work[1], &c__1, &v[1], incv, &c__[
+		    c_offset], ldc);
+	}
+    }
+    return 0;
+    //
+    //    End of DLARF
+    //
+} // dlarf_
+
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+//> \brief \b ILADLC scans a matrix for its last non-zero column.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download ILADLC + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iladlc.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iladlc.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iladlc.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      INTEGER FUNCTION ILADLC( M, N, A, LDA )
+//
+//      .. Scalar Arguments ..
+//      INTEGER            M, N, LDA
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> ILADLC scans A for its last non-zero column.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix A.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix A.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          The m by n matrix A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A. LDA >= max(1,M).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+int iladlc_(int *m, int *n, double *a, int *lda)
+{
+    // System generated locals
+    int a_dim1, a_offset, ret_val, i__1;
+
+    // Local variables
+    int i__;
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Quick test for the common case where one corner is non-zero.
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+
+    // Function Body
+    if (*n == 0) {
+	ret_val = *n;
+    } else if (a[*n * a_dim1 + 1] != 0. || a[*m + *n * a_dim1] != 0.) {
+	ret_val = *n;
+    } else {
+	//    Now scan each column from the end, returning with the first non-zero.
+	for (ret_val = *n; ret_val >= 1; --ret_val) {
+	    i__1 = *m;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		if (a[i__ + ret_val * a_dim1] != 0.) {
+		    return ret_val;
+		}
+	    }
+	}
+    }
+    return ret_val;
+} // iladlc_
+
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+//> \brief \b ILADLR scans a matrix for its last non-zero row.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download ILADLR + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iladlr.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iladlr.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iladlr.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      INTEGER FUNCTION ILADLR( M, N, A, LDA )
+//
+//      .. Scalar Arguments ..
+//      INTEGER            M, N, LDA
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> ILADLR scans A for its last non-zero row.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix A.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix A.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          The m by n matrix A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A. LDA >= max(1,M).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+int iladlr_(int *m, int *n, double *a, int *lda)
+{
+    // System generated locals
+    int a_dim1, a_offset, ret_val, i__1;
+
+    // Local variables
+    int i__, j;
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Quick test for the common case where one corner is non-zero.
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+
+    // Function Body
+    if (*m == 0) {
+	ret_val = *m;
+    } else if (a[*m + a_dim1] != 0. || a[*m + *n * a_dim1] != 0.) {
+	ret_val = *m;
+    } else {
+	//    Scan up each column tracking the last zero row seen.
+	ret_val = 0;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__ = *m;
+	    while(a[max(i__,1) + j * a_dim1] == 0. && i__ >= 1) {
+		--i__;
+	    }
+	    ret_val = max(ret_val,i__);
+	}
+    }
+    return ret_val;
+} // iladlr_
+

3rdparty/clapack/src/dlarfb.c

@@ -0,0 +1,824 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLARFB + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfb.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfb.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfb.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
+//                         T, LDT, C, LDC, WORK, LDWORK )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          DIRECT, SIDE, STOREV, TRANS
+//      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ),
+//     $                   WORK( LDWORK, * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLARFB applies a real block reflector H or its transpose H**T to a
+//> real m by n matrix C, from either the left or the right.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] SIDE
+//> \verbatim
+//>          SIDE is CHARACTER*1
+//>          = 'L': apply H or H**T from the Left
+//>          = 'R': apply H or H**T from the Right
+//> \endverbatim
+//>
+//> \param[in] TRANS
+//> \verbatim
+//>          TRANS is CHARACTER*1
+//>          = 'N': apply H (No transpose)
+//>          = 'T': apply H**T (Transpose)
+//> \endverbatim
+//>
+//> \param[in] DIRECT
+//> \verbatim
+//>          DIRECT is CHARACTER*1
+//>          Indicates how H is formed from a product of elementary
+//>          reflectors
+//>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
+//>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
+//> \endverbatim
+//>
+//> \param[in] STOREV
+//> \verbatim
+//>          STOREV is CHARACTER*1
+//>          Indicates how the vectors which define the elementary
+//>          reflectors are stored:
+//>          = 'C': Columnwise
+//>          = 'R': Rowwise
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix C.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix C.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>          The order of the matrix T (= the number of elementary
+//>          reflectors whose product defines the block reflector).
+//>          If SIDE = 'L', M >= K >= 0;
+//>          if SIDE = 'R', N >= K >= 0.
+//> \endverbatim
+//>
+//> \param[in] V
+//> \verbatim
+//>          V is DOUBLE PRECISION array, dimension
+//>                                (LDV,K) if STOREV = 'C'
+//>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
+//>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
+//>          The matrix V. See Further Details.
+//> \endverbatim
+//>
+//> \param[in] LDV
+//> \verbatim
+//>          LDV is INTEGER
+//>          The leading dimension of the array V.
+//>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
+//>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
+//>          if STOREV = 'R', LDV >= K.
+//> \endverbatim
+//>
+//> \param[in] T
+//> \verbatim
+//>          T is DOUBLE PRECISION array, dimension (LDT,K)
+//>          The triangular k by k matrix T in the representation of the
+//>          block reflector.
+//> \endverbatim
+//>
+//> \param[in] LDT
+//> \verbatim
+//>          LDT is INTEGER
+//>          The leading dimension of the array T. LDT >= K.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is DOUBLE PRECISION array, dimension (LDC,N)
+//>          On entry, the m by n matrix C.
+//>          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>          The leading dimension of the array C. LDC >= max(1,M).
+//> \endverbatim
+//>
+//> \param[out] WORK
+//> \verbatim
+//>          WORK is DOUBLE PRECISION array, dimension (LDWORK,K)
+//> \endverbatim
+//>
+//> \param[in] LDWORK
+//> \verbatim
+//>          LDWORK is INTEGER
+//>          The leading dimension of the array WORK.
+//>          If SIDE = 'L', LDWORK >= max(1,N);
+//>          if SIDE = 'R', LDWORK >= max(1,M).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date June 2013
+//
+//> \ingroup doubleOTHERauxiliary
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  The shape of the matrix V and the storage of the vectors which define
+//>  the H(i) is best illustrated by the following example with n = 5 and
+//>  k = 3. The elements equal to 1 are not stored; the corresponding
+//>  array elements are modified but restored on exit. The rest of the
+//>  array is not used.
+//>
+//>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
+//>
+//>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
+//>                   ( v1  1    )                     (     1 v2 v2 v2 )
+//>                   ( v1 v2  1 )                     (        1 v3 v3 )
+//>                   ( v1 v2 v3 )
+//>                   ( v1 v2 v3 )
+//>
+//>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
+//>
+//>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
+//>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
+//>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
+//>                   (     1 v3 )
+//>                   (        1 )
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char *
+	storev, int *m, int *n, int *k, double *v, int *ldv, double *t, int *
+	ldt, double *c__, int *ldc, double *work, int *ldwork)
+{
+    // Table of constant values
+    int c__1 = 1;
+    double c_b14 = 1.;
+    double c_b25 = -1.;
+
+    // System generated locals
+    int c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
+	    work_offset, i__1, i__2;
+
+    // Local variables
+    int i__, j;
+    extern /* Subroutine */ int dgemm_(char *, char *, int *, int *, int *,
+	    double *, double *, int *, double *, int *, double *, double *,
+	    int *);
+    extern int lsame_(char *, char *);
+    extern /* Subroutine */ int dcopy_(int *, double *, int *, double *, int *
+	    ), dtrmm_(char *, char *, char *, char *, int *, int *, double *,
+	    double *, int *, double *, int *);
+    char transt[1+1]={'\0'};
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    June 2013
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Quick return if possible
+    //
+    // Parameter adjustments
+    v_dim1 = *ldv;
+    v_offset = 1 + v_dim1;
+    v -= v_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1;
+    t -= t_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+    work_dim1 = *ldwork;
+    work_offset = 1 + work_dim1;
+    work -= work_offset;
+
+    // Function Body
+    if (*m <= 0 || *n <= 0) {
+	return 0;
+    }
+    if (lsame_(trans, "N")) {
+	*(unsigned char *)transt = 'T';
+    } else {
+	*(unsigned char *)transt = 'N';
+    }
+    if (lsame_(storev, "C")) {
+	if (lsame_(direct, "F")) {
+	    //
+	    //          Let  V =  ( V1 )    (first K rows)
+	    //                    ( V2 )
+	    //          where  V1  is unit lower triangular.
+	    //
+	    if (lsame_(side, "L")) {
+		//
+		//             Form  H * C  or  H**T * C  where  C = ( C1 )
+		//                                                   ( C2 )
+		//
+		//             W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
+		//
+		//             W := C1**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
+			     &c__1);
+// L10:
+		}
+		//
+		//             W := W * V1
+		//
+		dtrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b14,
+			 &v[v_offset], ldv, &work[work_offset], ldwork);
+		if (*m > *k) {
+		    //
+		    //                W := W + C2**T * V2
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("Transpose", "No transpose", n, k, &i__1, &c_b14, &
+			    c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1],
+			    ldv, &c_b14, &work[work_offset], ldwork);
+		}
+		//
+		//             W := W * T**T  or  W * T
+		//
+		dtrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - V * W**T
+		//
+		if (*m > *k) {
+		    //
+		    //                C2 := C2 - V2 * W**T
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("No transpose", "Transpose", &i__1, n, k, &c_b25, &
+			    v[*k + 1 + v_dim1], ldv, &work[work_offset],
+			    ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc);
+		}
+		//
+		//             W := W * V1**T
+		//
+		dtrmm_("Right", "Lower", "Transpose", "Unit", n, k, &c_b14, &
+			v[v_offset], ldv, &work[work_offset], ldwork);
+		//
+		//             C1 := C1 - W**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *n;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
+// L20:
+		    }
+// L30:
+		}
+	    } else if (lsame_(side, "R")) {
+		//
+		//             Form  C * H  or  C * H**T  where  C = ( C1  C2 )
+		//
+		//             W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
+		//
+		//             W := C1
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
+			    work_dim1 + 1], &c__1);
+// L40:
+		}
+		//
+		//             W := W * V1
+		//
+		dtrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b14,
+			 &v[v_offset], ldv, &work[work_offset], ldwork);
+		if (*n > *k) {
+		    //
+		    //                W := W + C2 * V2
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "No transpose", m, k, &i__1, &
+			    c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k +
+			    1 + v_dim1], ldv, &c_b14, &work[work_offset],
+			    ldwork);
+		}
+		//
+		//             W := W * T  or  W * T**T
+		//
+		dtrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - W * V**T
+		//
+		if (*n > *k) {
+		    //
+		    //                C2 := C2 - W * V2**T
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "Transpose", m, &i__1, k, &c_b25, &
+			    work[work_offset], ldwork, &v[*k + 1 + v_dim1],
+			    ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc);
+		}
+		//
+		//             W := W * V1**T
+		//
+		dtrmm_("Right", "Lower", "Transpose", "Unit", m, k, &c_b14, &
+			v[v_offset], ldv, &work[work_offset], ldwork);
+		//
+		//             C1 := C1 - W
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
+// L50:
+		    }
+// L60:
+		}
+	    }
+	} else {
+	    //
+	    //          Let  V =  ( V1 )
+	    //                    ( V2 )    (last K rows)
+	    //          where  V2  is unit upper triangular.
+	    //
+	    if (lsame_(side, "L")) {
+		//
+		//             Form  H * C  or  H**T * C  where  C = ( C1 )
+		//                                                   ( C2 )
+		//
+		//             W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
+		//
+		//             W := C2**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
+			    work_dim1 + 1], &c__1);
+// L70:
+		}
+		//
+		//             W := W * V2
+		//
+		dtrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b14,
+			 &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset],
+			ldwork);
+		if (*m > *k) {
+		    //
+		    //                W := W + C1**T * V1
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("Transpose", "No transpose", n, k, &i__1, &c_b14, &
+			    c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, &
+			    work[work_offset], ldwork);
+		}
+		//
+		//             W := W * T**T  or  W * T
+		//
+		dtrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - V * W**T
+		//
+		if (*m > *k) {
+		    //
+		    //                C1 := C1 - V1 * W**T
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("No transpose", "Transpose", &i__1, n, k, &c_b25, &
+			    v[v_offset], ldv, &work[work_offset], ldwork, &
+			    c_b14, &c__[c_offset], ldc);
+		}
+		//
+		//             W := W * V2**T
+		//
+		dtrmm_("Right", "Upper", "Transpose", "Unit", n, k, &c_b14, &
+			v[*m - *k + 1 + v_dim1], ldv, &work[work_offset],
+			ldwork);
+		//
+		//             C2 := C2 - W**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *n;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j *
+				work_dim1];
+// L80:
+		    }
+// L90:
+		}
+	    } else if (lsame_(side, "R")) {
+		//
+		//             Form  C * H  or  C * H**T  where  C = ( C1  C2 )
+		//
+		//             W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
+		//
+		//             W := C2
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
+			    j * work_dim1 + 1], &c__1);
+// L100:
+		}
+		//
+		//             W := W * V2
+		//
+		dtrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b14,
+			 &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset],
+			ldwork);
+		if (*n > *k) {
+		    //
+		    //                W := W + C1 * V1
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "No transpose", m, k, &i__1, &
+			    c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
+			    c_b14, &work[work_offset], ldwork);
+		}
+		//
+		//             W := W * T  or  W * T**T
+		//
+		dtrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - W * V**T
+		//
+		if (*n > *k) {
+		    //
+		    //                C1 := C1 - W * V1**T
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "Transpose", m, &i__1, k, &c_b25, &
+			    work[work_offset], ldwork, &v[v_offset], ldv, &
+			    c_b14, &c__[c_offset], ldc);
+		}
+		//
+		//             W := W * V2**T
+		//
+		dtrmm_("Right", "Upper", "Transpose", "Unit", m, k, &c_b14, &
+			v[*n - *k + 1 + v_dim1], ldv, &work[work_offset],
+			ldwork);
+		//
+		//             C2 := C2 - W
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j *
+				work_dim1];
+// L110:
+		    }
+// L120:
+		}
+	    }
+	}
+    } else if (lsame_(storev, "R")) {
+	if (lsame_(direct, "F")) {
+	    //
+	    //          Let  V =  ( V1  V2 )    (V1: first K columns)
+	    //          where  V1  is unit upper triangular.
+	    //
+	    if (lsame_(side, "L")) {
+		//
+		//             Form  H * C  or  H**T * C  where  C = ( C1 )
+		//                                                   ( C2 )
+		//
+		//             W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
+		//
+		//             W := C1**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
+			     &c__1);
+// L130:
+		}
+		//
+		//             W := W * V1**T
+		//
+		dtrmm_("Right", "Upper", "Transpose", "Unit", n, k, &c_b14, &
+			v[v_offset], ldv, &work[work_offset], ldwork);
+		if (*m > *k) {
+		    //
+		    //                W := W + C2**T * V2**T
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("Transpose", "Transpose", n, k, &i__1, &c_b14, &
+			    c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 +
+			    1], ldv, &c_b14, &work[work_offset], ldwork);
+		}
+		//
+		//             W := W * T**T  or  W * T
+		//
+		dtrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - V**T * W**T
+		//
+		if (*m > *k) {
+		    //
+		    //                C2 := C2 - V2**T * W**T
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("Transpose", "Transpose", &i__1, n, k, &c_b25, &v[(
+			    *k + 1) * v_dim1 + 1], ldv, &work[work_offset],
+			    ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc);
+		}
+		//
+		//             W := W * V1
+		//
+		dtrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b14,
+			 &v[v_offset], ldv, &work[work_offset], ldwork);
+		//
+		//             C1 := C1 - W**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *n;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
+// L140:
+		    }
+// L150:
+		}
+	    } else if (lsame_(side, "R")) {
+		//
+		//             Form  C * H  or  C * H**T  where  C = ( C1  C2 )
+		//
+		//             W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
+		//
+		//             W := C1
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
+			    work_dim1 + 1], &c__1);
+// L160:
+		}
+		//
+		//             W := W * V1**T
+		//
+		dtrmm_("Right", "Upper", "Transpose", "Unit", m, k, &c_b14, &
+			v[v_offset], ldv, &work[work_offset], ldwork);
+		if (*n > *k) {
+		    //
+		    //                W := W + C2 * V2**T
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "Transpose", m, k, &i__1, &c_b14, &
+			    c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) *
+			    v_dim1 + 1], ldv, &c_b14, &work[work_offset],
+			    ldwork);
+		}
+		//
+		//             W := W * T  or  W * T**T
+		//
+		dtrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - W * V
+		//
+		if (*n > *k) {
+		    //
+		    //                C2 := C2 - W * V2
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "No transpose", m, &i__1, k, &
+			    c_b25, &work[work_offset], ldwork, &v[(*k + 1) *
+			    v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1
+			    + 1], ldc);
+		}
+		//
+		//             W := W * V1
+		//
+		dtrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b14,
+			 &v[v_offset], ldv, &work[work_offset], ldwork);
+		//
+		//             C1 := C1 - W
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
+// L170:
+		    }
+// L180:
+		}
+	    }
+	} else {
+	    //
+	    //          Let  V =  ( V1  V2 )    (V2: last K columns)
+	    //          where  V2  is unit lower triangular.
+	    //
+	    if (lsame_(side, "L")) {
+		//
+		//             Form  H * C  or  H**T * C  where  C = ( C1 )
+		//                                                   ( C2 )
+		//
+		//             W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
+		//
+		//             W := C2**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
+			    work_dim1 + 1], &c__1);
+// L190:
+		}
+		//
+		//             W := W * V2**T
+		//
+		dtrmm_("Right", "Lower", "Transpose", "Unit", n, k, &c_b14, &
+			v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset]
+			, ldwork);
+		if (*m > *k) {
+		    //
+		    //                W := W + C1**T * V1**T
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("Transpose", "Transpose", n, k, &i__1, &c_b14, &
+			    c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, &
+			    work[work_offset], ldwork);
+		}
+		//
+		//             W := W * T**T  or  W * T
+		//
+		dtrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - V**T * W**T
+		//
+		if (*m > *k) {
+		    //
+		    //                C1 := C1 - V1**T * W**T
+		    //
+		    i__1 = *m - *k;
+		    dgemm_("Transpose", "Transpose", &i__1, n, k, &c_b25, &v[
+			    v_offset], ldv, &work[work_offset], ldwork, &
+			    c_b14, &c__[c_offset], ldc);
+		}
+		//
+		//             W := W * V2
+		//
+		dtrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b14,
+			 &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
+			work_offset], ldwork);
+		//
+		//             C2 := C2 - W**T
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *n;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j *
+				work_dim1];
+// L200:
+		    }
+// L210:
+		}
+	    } else if (lsame_(side, "R")) {
+		//
+		//             Form  C * H  or  C * H'  where  C = ( C1  C2 )
+		//
+		//             W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
+		//
+		//             W := C2
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
+			    j * work_dim1 + 1], &c__1);
+// L220:
+		}
+		//
+		//             W := W * V2**T
+		//
+		dtrmm_("Right", "Lower", "Transpose", "Unit", m, k, &c_b14, &
+			v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset]
+			, ldwork);
+		if (*n > *k) {
+		    //
+		    //                W := W + C1 * V1**T
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "Transpose", m, k, &i__1, &c_b14, &
+			    c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, &
+			    work[work_offset], ldwork);
+		}
+		//
+		//             W := W * T  or  W * T**T
+		//
+		dtrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b14, &t[
+			t_offset], ldt, &work[work_offset], ldwork);
+		//
+		//             C := C - W * V
+		//
+		if (*n > *k) {
+		    //
+		    //                C1 := C1 - W * V1
+		    //
+		    i__1 = *n - *k;
+		    dgemm_("No transpose", "No transpose", m, &i__1, k, &
+			    c_b25, &work[work_offset], ldwork, &v[v_offset],
+			    ldv, &c_b14, &c__[c_offset], ldc);
+		}
+		//
+		//             W := W * V2
+		//
+		dtrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b14,
+			 &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
+			work_offset], ldwork);
+		//
+		//             C1 := C1 - W
+		//
+		i__1 = *k;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j *
+				work_dim1];
+// L230:
+		    }
+// L240:
+		}
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of DLARFB
+    //
+} // dlarfb_
+

3rdparty/clapack/src/dlarfg.c

@@ -0,0 +1,216 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLARFG generates an elementary reflector (Householder matrix).
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLARFG + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
+//
+//      .. Scalar Arguments ..
+//      INTEGER            INCX, N
+//      DOUBLE PRECISION   ALPHA, TAU
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   X( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLARFG generates a real elementary reflector H of order n, such
+//> that
+//>
+//>       H * ( alpha ) = ( beta ),   H**T * H = I.
+//>           (   x   )   (   0  )
+//>
+//> where alpha and beta are scalars, and x is an (n-1)-element real
+//> vector. H is represented in the form
+//>
+//>       H = I - tau * ( 1 ) * ( 1 v**T ) ,
+//>                     ( v )
+//>
+//> where tau is a real scalar and v is a real (n-1)-element
+//> vector.
+//>
+//> If the elements of x are all zero, then tau = 0 and H is taken to be
+//> the unit matrix.
+//>
+//> Otherwise  1 <= tau <= 2.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The order of the elementary reflector.
+//> \endverbatim
+//>
+//> \param[in,out] ALPHA
+//> \verbatim
+//>          ALPHA is DOUBLE PRECISION
+//>          On entry, the value alpha.
+//>          On exit, it is overwritten with the value beta.
+//> \endverbatim
+//>
+//> \param[in,out] X
+//> \verbatim
+//>          X is DOUBLE PRECISION array, dimension
+//>                         (1+(N-2)*abs(INCX))
+//>          On entry, the vector x.
+//>          On exit, it is overwritten with the vector v.
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>          The increment between elements of X. INCX > 0.
+//> \endverbatim
+//>
+//> \param[out] TAU
+//> \verbatim
+//>          TAU is DOUBLE PRECISION
+//>          The value tau.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2017
+//
+//> \ingroup doubleOTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dlarfg_(int *n, double *alpha, double *x, int *incx,
+	double *tau)
+{
+    // System generated locals
+    int i__1;
+    double d__1;
+
+    // Local variables
+    int j, knt;
+    double beta;
+    extern double dnrm2_(int *, double *, int *);
+    extern /* Subroutine */ int dscal_(int *, double *, double *, int *);
+    double xnorm;
+    extern double dlapy2_(double *, double *), dlamch_(char *);
+    double safmin, rsafmn;
+
+    //
+    // -- LAPACK auxiliary routine (version 3.8.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    // Parameter adjustments
+    --x;
+
+    // Function Body
+    if (*n <= 1) {
+	*tau = 0.;
+	return 0;
+    }
+    i__1 = *n - 1;
+    xnorm = dnrm2_(&i__1, &x[1], incx);
+    if (xnorm == 0.) {
+	//
+	//       H  =  I
+	//
+	*tau = 0.;
+    } else {
+	//
+	//       general case
+	//
+	d__1 = dlapy2_(alpha, &xnorm);
+	beta = -d_sign(&d__1, alpha);
+	safmin = dlamch_("S") / dlamch_("E");
+	knt = 0;
+	if (abs(beta) < safmin) {
+	    //
+	    //          XNORM, BETA may be inaccurate; scale X and recompute them
+	    //
+	    rsafmn = 1. / safmin;
+L10:
+	    ++knt;
+	    i__1 = *n - 1;
+	    dscal_(&i__1, &rsafmn, &x[1], incx);
+	    beta *= rsafmn;
+	    *alpha *= rsafmn;
+	    if (abs(beta) < safmin && knt < 20) {
+		goto L10;
+	    }
+	    //
+	    //          New BETA is at most 1, at least SAFMIN
+	    //
+	    i__1 = *n - 1;
+	    xnorm = dnrm2_(&i__1, &x[1], incx);
+	    d__1 = dlapy2_(alpha, &xnorm);
+	    beta = -d_sign(&d__1, alpha);
+	}
+	*tau = (beta - *alpha) / beta;
+	i__1 = *n - 1;
+	d__1 = 1. / (*alpha - beta);
+	dscal_(&i__1, &d__1, &x[1], incx);
+	//
+	//       If ALPHA is subnormal, it may lose relative accuracy
+	//
+	i__1 = knt;
+	for (j = 1; j <= i__1; ++j) {
+	    beta *= safmin;
+// L20:
+	}
+	*alpha = beta;
+    }
+    return 0;
+    //
+    //    End of DLARFG
+    //
+} // dlarfg_
+

3rdparty/clapack/src/dlarft.c

@@ -0,0 +1,389 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLARFT + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarft.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarft.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarft.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          DIRECT, STOREV
+//      INTEGER            K, LDT, LDV, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   T( LDT, * ), TAU( * ), V( LDV, * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLARFT forms the triangular factor T of a real block reflector H
+//> of order n, which is defined as a product of k elementary reflectors.
+//>
+//> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
+//>
+//> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
+//>
+//> If STOREV = 'C', the vector which defines the elementary reflector
+//> H(i) is stored in the i-th column of the array V, and
+//>
+//>    H  =  I - V * T * V**T
+//>
+//> If STOREV = 'R', the vector which defines the elementary reflector
+//> H(i) is stored in the i-th row of the array V, and
+//>
+//>    H  =  I - V**T * T * V
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] DIRECT
+//> \verbatim
+//>          DIRECT is CHARACTER*1
+//>          Specifies the order in which the elementary reflectors are
+//>          multiplied to form the block reflector:
+//>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
+//>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
+//> \endverbatim
+//>
+//> \param[in] STOREV
+//> \verbatim
+//>          STOREV is CHARACTER*1
+//>          Specifies how the vectors which define the elementary
+//>          reflectors are stored (see also Further Details):
+//>          = 'C': columnwise
+//>          = 'R': rowwise
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The order of the block reflector H. N >= 0.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>          The order of the triangular factor T (= the number of
+//>          elementary reflectors). K >= 1.
+//> \endverbatim
+//>
+//> \param[in] V
+//> \verbatim
+//>          V is DOUBLE PRECISION array, dimension
+//>                               (LDV,K) if STOREV = 'C'
+//>                               (LDV,N) if STOREV = 'R'
+//>          The matrix V. See further details.
+//> \endverbatim
+//>
+//> \param[in] LDV
+//> \verbatim
+//>          LDV is INTEGER
+//>          The leading dimension of the array V.
+//>          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
+//> \endverbatim
+//>
+//> \param[in] TAU
+//> \verbatim
+//>          TAU is DOUBLE PRECISION array, dimension (K)
+//>          TAU(i) must contain the scalar factor of the elementary
+//>          reflector H(i).
+//> \endverbatim
+//>
+//> \param[out] T
+//> \verbatim
+//>          T is DOUBLE PRECISION array, dimension (LDT,K)
+//>          The k by k triangular factor T of the block reflector.
+//>          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
+//>          lower triangular. The rest of the array is not used.
+//> \endverbatim
+//>
+//> \param[in] LDT
+//> \verbatim
+//>          LDT is INTEGER
+//>          The leading dimension of the array T. LDT >= K.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup doubleOTHERauxiliary
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  The shape of the matrix V and the storage of the vectors which define
+//>  the H(i) is best illustrated by the following example with n = 5 and
+//>  k = 3. The elements equal to 1 are not stored.
+//>
+//>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
+//>
+//>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
+//>                   ( v1  1    )                     (     1 v2 v2 v2 )
+//>                   ( v1 v2  1 )                     (        1 v3 v3 )
+//>                   ( v1 v2 v3 )
+//>                   ( v1 v2 v3 )
+//>
+//>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
+//>
+//>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
+//>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
+//>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
+//>                   (     1 v3 )
+//>                   (        1 )
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dlarft_(char *direct, char *storev, int *n, int *k,
+	double *v, int *ldv, double *tau, double *t, int *ldt)
+{
+    // Table of constant values
+    int c__1 = 1;
+    double c_b7 = 1.;
+
+    // System generated locals
+    int t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
+    double d__1;
+
+    // Local variables
+    int i__, j, prevlastv;
+    extern int lsame_(char *, char *);
+    extern /* Subroutine */ int dgemv_(char *, int *, int *, double *, double
+	    *, int *, double *, int *, double *, double *, int *);
+    int lastv;
+    extern /* Subroutine */ int dtrmv_(char *, char *, char *, int *, double *
+	    , int *, double *, int *);
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Quick return if possible
+    //
+    // Parameter adjustments
+    v_dim1 = *ldv;
+    v_offset = 1 + v_dim1;
+    v -= v_offset;
+    --tau;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1;
+    t -= t_offset;
+
+    // Function Body
+    if (*n == 0) {
+	return 0;
+    }
+    if (lsame_(direct, "F")) {
+	prevlastv = *n;
+	i__1 = *k;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    prevlastv = max(i__,prevlastv);
+	    if (tau[i__] == 0.) {
+		//
+		//             H(i)  =  I
+		//
+		i__2 = i__;
+		for (j = 1; j <= i__2; ++j) {
+		    t[j + i__ * t_dim1] = 0.;
+		}
+	    } else {
+		//
+		//             general case
+		//
+		if (lsame_(storev, "C")) {
+		    //                Skip any trailing zeros.
+		    i__2 = i__ + 1;
+		    for (lastv = *n; lastv >= i__2; --lastv) {
+			if (v[lastv + i__ * v_dim1] != 0.) {
+			    break;
+			}
+		    }
+		    i__2 = i__ - 1;
+		    for (j = 1; j <= i__2; ++j) {
+			t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1];
+		    }
+		    j = min(lastv,prevlastv);
+		    //
+		    //                T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
+		    //
+		    i__2 = j - i__;
+		    i__3 = i__ - 1;
+		    d__1 = -tau[i__];
+		    dgemv_("Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 +
+			    v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, &
+			    c_b7, &t[i__ * t_dim1 + 1], &c__1);
+		} else {
+		    //                Skip any trailing zeros.
+		    i__2 = i__ + 1;
+		    for (lastv = *n; lastv >= i__2; --lastv) {
+			if (v[i__ + lastv * v_dim1] != 0.) {
+			    break;
+			}
+		    }
+		    i__2 = i__ - 1;
+		    for (j = 1; j <= i__2; ++j) {
+			t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1];
+		    }
+		    j = min(lastv,prevlastv);
+		    //
+		    //                T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T
+		    //
+		    i__2 = i__ - 1;
+		    i__3 = j - i__;
+		    d__1 = -tau[i__];
+		    dgemv_("No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) *
+			     v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1],
+			    ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1);
+		}
+		//
+		//             T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
+		//
+		i__2 = i__ - 1;
+		dtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
+			t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
+		t[i__ + i__ * t_dim1] = tau[i__];
+		if (i__ > 1) {
+		    prevlastv = max(prevlastv,lastv);
+		} else {
+		    prevlastv = lastv;
+		}
+	    }
+	}
+    } else {
+	prevlastv = 1;
+	for (i__ = *k; i__ >= 1; --i__) {
+	    if (tau[i__] == 0.) {
+		//
+		//             H(i)  =  I
+		//
+		i__1 = *k;
+		for (j = i__; j <= i__1; ++j) {
+		    t[j + i__ * t_dim1] = 0.;
+		}
+	    } else {
+		//
+		//             general case
+		//
+		if (i__ < *k) {
+		    if (lsame_(storev, "C")) {
+			//                   Skip any leading zeros.
+			i__1 = i__ - 1;
+			for (lastv = 1; lastv <= i__1; ++lastv) {
+			    if (v[lastv + i__ * v_dim1] != 0.) {
+				break;
+			    }
+			}
+			i__1 = *k;
+			for (j = i__ + 1; j <= i__1; ++j) {
+			    t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__
+				    + j * v_dim1];
+			}
+			j = max(lastv,prevlastv);
+			//
+			//                   T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)
+			//
+			i__1 = *n - *k + i__ - j;
+			i__2 = *k - i__;
+			d__1 = -tau[i__];
+			dgemv_("Transpose", &i__1, &i__2, &d__1, &v[j + (i__
+				+ 1) * v_dim1], ldv, &v[j + i__ * v_dim1], &
+				c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], &
+				c__1);
+		    } else {
+			//                   Skip any leading zeros.
+			i__1 = i__ - 1;
+			for (lastv = 1; lastv <= i__1; ++lastv) {
+			    if (v[i__ + lastv * v_dim1] != 0.) {
+				break;
+			    }
+			}
+			i__1 = *k;
+			for (j = i__ + 1; j <= i__1; ++j) {
+			    t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k
+				    + i__) * v_dim1];
+			}
+			j = max(lastv,prevlastv);
+			//
+			//                   T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T
+			//
+			i__1 = *k - i__;
+			i__2 = *n - *k + i__ - j;
+			d__1 = -tau[i__];
+			dgemv_("No transpose", &i__1, &i__2, &d__1, &v[i__ +
+				1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
+				ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1)
+				;
+		    }
+		    //
+		    //                T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
+		    //
+		    i__1 = *k - i__;
+		    dtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+			    + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
+			     t_dim1], &c__1);
+		    if (i__ > 1) {
+			prevlastv = min(prevlastv,lastv);
+		    } else {
+			prevlastv = lastv;
+		    }
+		}
+		t[i__ + i__ * t_dim1] = tau[i__];
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of DLARFT
+    //
+} // dlarft_
+

3rdparty/clapack/src/dlartg.c

@@ -0,0 +1,236 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLARTG generates a plane rotation with real cosine and real sine.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLARTG + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlartg.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlartg.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlartg.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLARTG( F, G, CS, SN, R )
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION   CS, F, G, R, SN
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLARTG generate a plane rotation so that
+//>
+//>    [  CS  SN  ]  .  [ F ]  =  [ R ]   where CS**2 + SN**2 = 1.
+//>    [ -SN  CS  ]     [ G ]     [ 0 ]
+//>
+//> This is a slower, more accurate version of the BLAS1 routine DROTG,
+//> with the following other differences:
+//>    F and G are unchanged on return.
+//>    If G=0, then CS=1 and SN=0.
+//>    If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any
+//>       floating point operations (saves work in DBDSQR when
+//>       there are zeros on the diagonal).
+//>
+//> If F exceeds G in magnitude, CS will be positive.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] F
+//> \verbatim
+//>          F is DOUBLE PRECISION
+//>          The first component of vector to be rotated.
+//> \endverbatim
+//>
+//> \param[in] G
+//> \verbatim
+//>          G is DOUBLE PRECISION
+//>          The second component of vector to be rotated.
+//> \endverbatim
+//>
+//> \param[out] CS
+//> \verbatim
+//>          CS is DOUBLE PRECISION
+//>          The cosine of the rotation.
+//> \endverbatim
+//>
+//> \param[out] SN
+//> \verbatim
+//>          SN is DOUBLE PRECISION
+//>          The sine of the rotation.
+//> \endverbatim
+//>
+//> \param[out] R
+//> \verbatim
+//>          R is DOUBLE PRECISION
+//>          The nonzero component of the rotated vector.
+//>
+//>  This version has a few statements commented out for thread safety
+//>  (machine parameters are computed on each entry). 10 feb 03, SJH.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dlartg_(double *f, double *g, double *cs, double *sn,
+	double *r__)
+{
+    // System generated locals
+    int i__1;
+    double d__1, d__2;
+
+    // Local variables
+    int i__;
+    double f1, g1, eps, scale;
+    int count;
+    double safmn2, safmx2;
+    extern double dlamch_(char *);
+    double safmin;
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    LOGICAL            FIRST
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Save statement ..
+    //    SAVE               FIRST, SAFMX2, SAFMIN, SAFMN2
+    //    ..
+    //    .. Data statements ..
+    //    DATA               FIRST / .TRUE. /
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    IF( FIRST ) THEN
+    safmin = dlamch_("S");
+    eps = dlamch_("E");
+    d__1 = dlamch_("B");
+    i__1 = (int) (log(safmin / eps) / log(dlamch_("B")) / 2.);
+    safmn2 = pow_di(&d__1, &i__1);
+    safmx2 = 1. / safmn2;
+    //       FIRST = .FALSE.
+    //    END IF
+    if (*g == 0.) {
+	*cs = 1.;
+	*sn = 0.;
+	*r__ = *f;
+    } else if (*f == 0.) {
+	*cs = 0.;
+	*sn = 1.;
+	*r__ = *g;
+    } else {
+	f1 = *f;
+	g1 = *g;
+	// Computing MAX
+	d__1 = abs(f1), d__2 = abs(g1);
+	scale = max(d__1,d__2);
+	if (scale >= safmx2) {
+	    count = 0;
+L10:
+	    ++count;
+	    f1 *= safmn2;
+	    g1 *= safmn2;
+	    // Computing MAX
+	    d__1 = abs(f1), d__2 = abs(g1);
+	    scale = max(d__1,d__2);
+	    if (scale >= safmx2) {
+		goto L10;
+	    }
+	    // Computing 2nd power
+	    d__1 = f1;
+	    // Computing 2nd power
+	    d__2 = g1;
+	    *r__ = sqrt(d__1 * d__1 + d__2 * d__2);
+	    *cs = f1 / *r__;
+	    *sn = g1 / *r__;
+	    i__1 = count;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		*r__ *= safmx2;
+// L20:
+	    }
+	} else if (scale <= safmn2) {
+	    count = 0;
+L30:
+	    ++count;
+	    f1 *= safmx2;
+	    g1 *= safmx2;
+	    // Computing MAX
+	    d__1 = abs(f1), d__2 = abs(g1);
+	    scale = max(d__1,d__2);
+	    if (scale <= safmn2) {
+		goto L30;
+	    }
+	    // Computing 2nd power
+	    d__1 = f1;
+	    // Computing 2nd power
+	    d__2 = g1;
+	    *r__ = sqrt(d__1 * d__1 + d__2 * d__2);
+	    *cs = f1 / *r__;
+	    *sn = g1 / *r__;
+	    i__1 = count;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		*r__ *= safmn2;
+// L40:
+	    }
+	} else {
+	    // Computing 2nd power
+	    d__1 = f1;
+	    // Computing 2nd power
+	    d__2 = g1;
+	    *r__ = sqrt(d__1 * d__1 + d__2 * d__2);
+	    *cs = f1 / *r__;
+	    *sn = g1 / *r__;
+	}
+	if (abs(*f) > abs(*g) && *cs < 0.) {
+	    *cs = -(*cs);
+	    *sn = -(*sn);
+	    *r__ = -(*r__);
+	}
+    }
+    return 0;
+    //
+    //    End of DLARTG
+    //
+} // dlartg_
+

3rdparty/clapack/src/dlascl.c

@@ -0,0 +1,413 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLASCL + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlascl.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlascl.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlascl.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          TYPE
+//      INTEGER            INFO, KL, KU, LDA, M, N
+//      DOUBLE PRECISION   CFROM, CTO
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLASCL multiplies the M by N real matrix A by the real scalar
+//> CTO/CFROM.  This is done without over/underflow as long as the final
+//> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
+//> A may be full, upper triangular, lower triangular, upper Hessenberg,
+//> or banded.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] TYPE
+//> \verbatim
+//>          TYPE is CHARACTER*1
+//>          TYPE indices the storage type of the input matrix.
+//>          = 'G':  A is a full matrix.
+//>          = 'L':  A is a lower triangular matrix.
+//>          = 'U':  A is an upper triangular matrix.
+//>          = 'H':  A is an upper Hessenberg matrix.
+//>          = 'B':  A is a symmetric band matrix with lower bandwidth KL
+//>                  and upper bandwidth KU and with the only the lower
+//>                  half stored.
+//>          = 'Q':  A is a symmetric band matrix with lower bandwidth KL
+//>                  and upper bandwidth KU and with the only the upper
+//>                  half stored.
+//>          = 'Z':  A is a band matrix with lower bandwidth KL and upper
+//>                  bandwidth KU. See DGBTRF for storage details.
+//> \endverbatim
+//>
+//> \param[in] KL
+//> \verbatim
+//>          KL is INTEGER
+//>          The lower bandwidth of A.  Referenced only if TYPE = 'B',
+//>          'Q' or 'Z'.
+//> \endverbatim
+//>
+//> \param[in] KU
+//> \verbatim
+//>          KU is INTEGER
+//>          The upper bandwidth of A.  Referenced only if TYPE = 'B',
+//>          'Q' or 'Z'.
+//> \endverbatim
+//>
+//> \param[in] CFROM
+//> \verbatim
+//>          CFROM is DOUBLE PRECISION
+//> \endverbatim
+//>
+//> \param[in] CTO
+//> \verbatim
+//>          CTO is DOUBLE PRECISION
+//>
+//>          The matrix A is multiplied by CTO/CFROM. A(I,J) is computed
+//>          without over/underflow if the final result CTO*A(I,J)/CFROM
+//>          can be represented without over/underflow.  CFROM must be
+//>          nonzero.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix A.  M >= 0.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix A.  N >= 0.
+//> \endverbatim
+//>
+//> \param[in,out] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          The matrix to be multiplied by CTO/CFROM.  See TYPE for the
+//>          storage type.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A.
+//>          If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M);
+//>             TYPE = 'B', LDA >= KL+1;
+//>             TYPE = 'Q', LDA >= KU+1;
+//>             TYPE = 'Z', LDA >= 2*KL+KU+1.
+//> \endverbatim
+//>
+//> \param[out] INFO
+//> \verbatim
+//>          INFO is INTEGER
+//>          0  - successful exit
+//>          <0 - if INFO = -i, the i-th argument had an illegal value.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date June 2016
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dlascl_(char *type__, int *kl, int *ku, double *cfrom,
+	double *cto, int *m, int *n, double *a, int *lda, int *info)
+{
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+
+    // Local variables
+    int i__, j, k1, k2, k3, k4;
+    double mul, cto1;
+    int done;
+    double ctoc;
+    extern int lsame_(char *, char *);
+    int itype;
+    double cfrom1;
+    extern double dlamch_(char *);
+    double cfromc;
+    extern int disnan_(double *);
+    extern /* Subroutine */ int xerbla_(char *, int *);
+    double bignum, smlnum;
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    June 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Test the input arguments
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+
+    // Function Body
+    *info = 0;
+    if (lsame_(type__, "G")) {
+	itype = 0;
+    } else if (lsame_(type__, "L")) {
+	itype = 1;
+    } else if (lsame_(type__, "U")) {
+	itype = 2;
+    } else if (lsame_(type__, "H")) {
+	itype = 3;
+    } else if (lsame_(type__, "B")) {
+	itype = 4;
+    } else if (lsame_(type__, "Q")) {
+	itype = 5;
+    } else if (lsame_(type__, "Z")) {
+	itype = 6;
+    } else {
+	itype = -1;
+    }
+    if (itype == -1) {
+	*info = -1;
+    } else if (*cfrom == 0. || disnan_(cfrom)) {
+	*info = -4;
+    } else if (disnan_(cto)) {
+	*info = -5;
+    } else if (*m < 0) {
+	*info = -6;
+    } else if (*n < 0 || itype == 4 && *n != *m || itype == 5 && *n != *m) {
+	*info = -7;
+    } else if (itype <= 3 && *lda < max(1,*m)) {
+	*info = -9;
+    } else if (itype >= 4) {
+	// Computing MAX
+	i__1 = *m - 1;
+	if (*kl < 0 || *kl > max(i__1,0)) {
+	    *info = -2;
+	} else /* if(complicated condition) */ {
+	    // Computing MAX
+	    i__1 = *n - 1;
+	    if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) &&
+		    *kl != *ku) {
+		*info = -3;
+	    } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < *
+		    ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) {
+		*info = -9;
+	    }
+	}
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DLASCL", &i__1);
+	return 0;
+    }
+    //
+    //    Quick return if possible
+    //
+    if (*n == 0 || *m == 0) {
+	return 0;
+    }
+    //
+    //    Get machine parameters
+    //
+    smlnum = dlamch_("S");
+    bignum = 1. / smlnum;
+    cfromc = *cfrom;
+    ctoc = *cto;
+L10:
+    cfrom1 = cfromc * smlnum;
+    if (cfrom1 == cfromc) {
+	//       CFROMC is an inf.  Multiply by a correctly signed zero for
+	//       finite CTOC, or a NaN if CTOC is infinite.
+	mul = ctoc / cfromc;
+	done = TRUE_;
+	cto1 = ctoc;
+    } else {
+	cto1 = ctoc / bignum;
+	if (cto1 == ctoc) {
+	    //          CTOC is either 0 or an inf.  In both cases, CTOC itself
+	    //          serves as the correct multiplication factor.
+	    mul = ctoc;
+	    done = TRUE_;
+	    cfromc = 1.;
+	} else if (abs(cfrom1) > abs(ctoc) && ctoc != 0.) {
+	    mul = smlnum;
+	    done = FALSE_;
+	    cfromc = cfrom1;
+	} else if (abs(cto1) > abs(cfromc)) {
+	    mul = bignum;
+	    done = FALSE_;
+	    ctoc = cto1;
+	} else {
+	    mul = ctoc / cfromc;
+	    done = TRUE_;
+	}
+    }
+    if (itype == 0) {
+	//
+	//       Full matrix
+	//
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] *= mul;
+// L20:
+	    }
+// L30:
+	}
+    } else if (itype == 1) {
+	//
+	//       Lower triangular matrix
+	//
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = j; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] *= mul;
+// L40:
+	    }
+// L50:
+	}
+    } else if (itype == 2) {
+	//
+	//       Upper triangular matrix
+	//
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = min(j,*m);
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] *= mul;
+// L60:
+	    }
+// L70:
+	}
+    } else if (itype == 3) {
+	//
+	//       Upper Hessenberg matrix
+	//
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    // Computing MIN
+	    i__3 = j + 1;
+	    i__2 = min(i__3,*m);
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] *= mul;
+// L80:
+	    }
+// L90:
+	}
+    } else if (itype == 4) {
+	//
+	//       Lower half of a symmetric band matrix
+	//
+	k3 = *kl + 1;
+	k4 = *n + 1;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    // Computing MIN
+	    i__3 = k3, i__4 = k4 - j;
+	    i__2 = min(i__3,i__4);
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] *= mul;
+// L100:
+	    }
+// L110:
+	}
+    } else if (itype == 5) {
+	//
+	//       Upper half of a symmetric band matrix
+	//
+	k1 = *ku + 2;
+	k3 = *ku + 1;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    // Computing MAX
+	    i__2 = k1 - j;
+	    i__3 = k3;
+	    for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
+		a[i__ + j * a_dim1] *= mul;
+// L120:
+	    }
+// L130:
+	}
+    } else if (itype == 6) {
+	//
+	//       Band matrix
+	//
+	k1 = *kl + *ku + 2;
+	k2 = *kl + 1;
+	k3 = (*kl << 1) + *ku + 1;
+	k4 = *kl + *ku + 1 + *m;
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    // Computing MAX
+	    i__3 = k1 - j;
+	    // Computing MIN
+	    i__4 = k3, i__5 = k4 - j;
+	    i__2 = min(i__4,i__5);
+	    for (i__ = max(i__3,k2); i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] *= mul;
+// L140:
+	    }
+// L150:
+	}
+    }
+    if (! done) {
+	goto L10;
+    }
+    return 0;
+    //
+    //    End of DLASCL
+    //
+} // dlascl_
+

3rdparty/clapack/src/dlaset.c

@@ -0,0 +1,209 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLASET + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaset.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaset.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaset.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          UPLO
+//      INTEGER            LDA, M, N
+//      DOUBLE PRECISION   ALPHA, BETA
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLASET initializes an m-by-n matrix A to BETA on the diagonal and
+//> ALPHA on the offdiagonals.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] UPLO
+//> \verbatim
+//>          UPLO is CHARACTER*1
+//>          Specifies the part of the matrix A to be set.
+//>          = 'U':      Upper triangular part is set; the strictly lower
+//>                      triangular part of A is not changed.
+//>          = 'L':      Lower triangular part is set; the strictly upper
+//>                      triangular part of A is not changed.
+//>          Otherwise:  All of the matrix A is set.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix A.  M >= 0.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix A.  N >= 0.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is DOUBLE PRECISION
+//>          The constant to which the offdiagonal elements are to be set.
+//> \endverbatim
+//>
+//> \param[in] BETA
+//> \verbatim
+//>          BETA is DOUBLE PRECISION
+//>          The constant to which the diagonal elements are to be set.
+//> \endverbatim
+//>
+//> \param[out] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          On exit, the leading m-by-n submatrix of A is set as follows:
+//>
+//>          if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n,
+//>          if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n,
+//>          otherwise,     A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j,
+//>
+//>          and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n).
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A.  LDA >= max(1,M).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dlaset_(char *uplo, int *m, int *n, double *alpha,
+	double *beta, double *a, int *lda)
+{
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2, i__3;
+
+    // Local variables
+    int i__, j;
+    extern int lsame_(char *, char *);
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    //=====================================================================
+    //
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+
+    // Function Body
+    if (lsame_(uplo, "U")) {
+	//
+	//       Set the strictly upper triangular or trapezoidal part of the
+	//       array to ALPHA.
+	//
+	i__1 = *n;
+	for (j = 2; j <= i__1; ++j) {
+	    // Computing MIN
+	    i__3 = j - 1;
+	    i__2 = min(i__3,*m);
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] = *alpha;
+// L10:
+	    }
+// L20:
+	}
+    } else if (lsame_(uplo, "L")) {
+	//
+	//       Set the strictly lower triangular or trapezoidal part of the
+	//       array to ALPHA.
+	//
+	i__1 = min(*m,*n);
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = j + 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] = *alpha;
+// L30:
+	    }
+// L40:
+	}
+    } else {
+	//
+	//       Set the leading m-by-n submatrix to ALPHA.
+	//
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] = *alpha;
+// L50:
+	    }
+// L60:
+	}
+    }
+    //
+    //    Set the first min(M,N) diagonal elements to BETA.
+    //
+    i__1 = min(*m,*n);
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	a[i__ + i__ * a_dim1] = *beta;
+// L70:
+    }
+    return 0;
+    //
+    //    End of DLASET
+    //
+} // dlaset_
+

3rdparty/clapack/src/dlassq.c

@@ -0,0 +1,172 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DLASSQ updates a sum of squares represented in scaled form.
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DLASSQ + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlassq.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlassq.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlassq.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
+//
+//      .. Scalar Arguments ..
+//      INTEGER            INCX, N
+//      DOUBLE PRECISION   SCALE, SUMSQ
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   X( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DLASSQ  returns the values  scl  and  smsq  such that
+//>
+//>    ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
+//>
+//> where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
+//> assumed to be non-negative and  scl  returns the value
+//>
+//>    scl = max( scale, abs( x( i ) ) ).
+//>
+//> scale and sumsq must be supplied in SCALE and SUMSQ and
+//> scl and smsq are overwritten on SCALE and SUMSQ respectively.
+//>
+//> The routine makes only one pass through the vector x.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of elements to be used from the vector X.
+//> \endverbatim
+//>
+//> \param[in] X
+//> \verbatim
+//>          X is DOUBLE PRECISION array, dimension (1+(N-1)*INCX)
+//>          The vector for which a scaled sum of squares is computed.
+//>             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>          The increment between successive values of the vector X.
+//>          INCX > 0.
+//> \endverbatim
+//>
+//> \param[in,out] SCALE
+//> \verbatim
+//>          SCALE is DOUBLE PRECISION
+//>          On entry, the value  scale  in the equation above.
+//>          On exit, SCALE is overwritten with  scl , the scaling factor
+//>          for the sum of squares.
+//> \endverbatim
+//>
+//> \param[in,out] SUMSQ
+//> \verbatim
+//>          SUMSQ is DOUBLE PRECISION
+//>          On entry, the value  sumsq  in the equation above.
+//>          On exit, SUMSQ is overwritten with  smsq , the basic sum of
+//>          squares from which  scl  has been factored out.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup OTHERauxiliary
+//
+// =====================================================================
+/* Subroutine */ int dlassq_(int *n, double *x, int *incx, double *scale,
+	double *sumsq)
+{
+    // System generated locals
+    int i__1, i__2;
+    double d__1;
+
+    // Local variables
+    int ix;
+    double absxi;
+    extern int disnan_(double *);
+
+    //
+    // -- LAPACK auxiliary routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    //=====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    // Parameter adjustments
+    --x;
+
+    // Function Body
+    if (*n > 0) {
+	i__1 = (*n - 1) * *incx + 1;
+	i__2 = *incx;
+	for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
+	    absxi = (d__1 = x[ix], abs(d__1));
+	    if (absxi > 0. || disnan_(&absxi)) {
+		if (*scale < absxi) {
+		    // Computing 2nd power
+		    d__1 = *scale / absxi;
+		    *sumsq = *sumsq * (d__1 * d__1) + 1;
+		    *scale = absxi;
+		} else {
+		    // Computing 2nd power
+		    d__1 = absxi / *scale;
+		    *sumsq += d__1 * d__1;
+		}
+	    }
+// L10:
+	}
+    }
+    return 0;
+    //
+    //    End of DLASSQ
+    //
+} // dlassq_
+

3rdparty/clapack/src/dnrm2.c

@@ -0,0 +1,149 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DNRM2
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
+//
+//      .. Scalar Arguments ..
+//      INTEGER INCX,N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION X(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DNRM2 returns the euclidean norm of a vector via the function
+//> name, so that
+//>
+//>    DNRM2 := sqrt( x'*x )
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>         number of elements in input vector(s)
+//> \endverbatim
+//>
+//> \param[in] X
+//> \verbatim
+//>          X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>         storage spacing between elements of DX
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2017
+//
+//> \ingroup double_blas_level1
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  -- This version written on 25-October-1982.
+//>     Modified on 14-October-1993 to inline the call to DLASSQ.
+//>     Sven Hammarling, Nag Ltd.
+//> \endverbatim
+//>
+// =====================================================================
+double dnrm2_(int *n, double *x, int *incx)
+{
+    // System generated locals
+    int i__1, i__2;
+    double ret_val, d__1;
+
+    // Local variables
+    int ix;
+    double ssq, norm, scale, absxi;
+
+    //
+    // -- Reference BLAS level1 routine (version 3.8.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    // Parameter adjustments
+    --x;
+
+    // Function Body
+    if (*n < 1 || *incx < 1) {
+	norm = 0.;
+    } else if (*n == 1) {
+	norm = abs(x[1]);
+    } else {
+	scale = 0.;
+	ssq = 1.;
+	//       The following loop is equivalent to this call to the LAPACK
+	//       auxiliary routine:
+	//       CALL DLASSQ( N, X, INCX, SCALE, SSQ )
+	//
+	i__1 = (*n - 1) * *incx + 1;
+	i__2 = *incx;
+	for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
+	    if (x[ix] != 0.) {
+		absxi = (d__1 = x[ix], abs(d__1));
+		if (scale < absxi) {
+		    // Computing 2nd power
+		    d__1 = scale / absxi;
+		    ssq = ssq * (d__1 * d__1) + 1.;
+		    scale = absxi;
+		} else {
+		    // Computing 2nd power
+		    d__1 = absxi / scale;
+		    ssq += d__1 * d__1;
+		}
+	    }
+// L10:
+	}
+	norm = scale * sqrt(ssq);
+    }
+    ret_val = norm;
+    return ret_val;
+    //
+    //    End of DNRM2.
+    //
+} // dnrm2_
+

3rdparty/clapack/src/dorgqr.c

@@ -0,0 +1,571 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DORG2R + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorg2r.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorg2r.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorg2r.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
+//
+//      .. Scalar Arguments ..
+//      INTEGER            INFO, K, LDA, M, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DORG2R generates an m by n real matrix Q with orthonormal columns,
+//> which is defined as the first n columns of a product of k elementary
+//> reflectors of order m
+//>
+//>       Q  =  H(1) H(2) . . . H(k)
+//>
+//> as returned by DGEQRF.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix Q. M >= 0.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix Q. M >= N >= 0.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>          The number of elementary reflectors whose product defines the
+//>          matrix Q. N >= K >= 0.
+//> \endverbatim
+//>
+//> \param[in,out] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          On entry, the i-th column must contain the vector which
+//>          defines the elementary reflector H(i), for i = 1,2,...,k, as
+//>          returned by DGEQRF in the first k columns of its array
+//>          argument A.
+//>          On exit, the m-by-n matrix Q.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The first dimension of the array A. LDA >= max(1,M).
+//> \endverbatim
+//>
+//> \param[in] TAU
+//> \verbatim
+//>          TAU is DOUBLE PRECISION array, dimension (K)
+//>          TAU(i) must contain the scalar factor of the elementary
+//>          reflector H(i), as returned by DGEQRF.
+//> \endverbatim
+//>
+//> \param[out] WORK
+//> \verbatim
+//>          WORK is DOUBLE PRECISION array, dimension (N)
+//> \endverbatim
+//>
+//> \param[out] INFO
+//> \verbatim
+//>          INFO is INTEGER
+//>          = 0: successful exit
+//>          < 0: if INFO = -i, the i-th argument has an illegal value
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup doubleOTHERcomputational
+//
+// =====================================================================
+/* Subroutine */ int dorg2r_(int *m, int *n, int *k, double *a, int *lda,
+	double *tau, double *work, int *info)
+{
+    // Table of constant values
+    int c__1 = 1;
+
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2;
+    double d__1;
+
+    // Local variables
+    int i__, j, l;
+    extern /* Subroutine */ int dscal_(int *, double *, double *, int *),
+	    dlarf_(char *, int *, int *, double *, int *, double *, double *,
+	    int *, double *), xerbla_(char *, int *);
+
+    //
+    // -- LAPACK computational routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Test the input arguments
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    // Function Body
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0 || *n > *m) {
+	*info = -2;
+    } else if (*k < 0 || *k > *n) {
+	*info = -3;
+    } else if (*lda < max(1,*m)) {
+	*info = -5;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DORG2R", &i__1);
+	return 0;
+    }
+    //
+    //    Quick return if possible
+    //
+    if (*n <= 0) {
+	return 0;
+    }
+    //
+    //    Initialise columns k+1:n to columns of the unit matrix
+    //
+    i__1 = *n;
+    for (j = *k + 1; j <= i__1; ++j) {
+	i__2 = *m;
+	for (l = 1; l <= i__2; ++l) {
+	    a[l + j * a_dim1] = 0.;
+// L10:
+	}
+	a[j + j * a_dim1] = 1.;
+// L20:
+    }
+    for (i__ = *k; i__ >= 1; --i__) {
+	//
+	//       Apply H(i) to A(i:m,i:n) from the left
+	//
+	if (i__ < *n) {
+	    a[i__ + i__ * a_dim1] = 1.;
+	    i__1 = *m - i__ + 1;
+	    i__2 = *n - i__;
+	    dlarf_("Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[
+		    i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
+	}
+	if (i__ < *m) {
+	    i__1 = *m - i__;
+	    d__1 = -tau[i__];
+	    dscal_(&i__1, &d__1, &a[i__ + 1 + i__ * a_dim1], &c__1);
+	}
+	a[i__ + i__ * a_dim1] = 1. - tau[i__];
+	//
+	//       Set A(1:i-1,i) to zero
+	//
+	i__1 = i__ - 1;
+	for (l = 1; l <= i__1; ++l) {
+	    a[l + i__ * a_dim1] = 0.;
+// L30:
+	}
+// L40:
+    }
+    return 0;
+    //
+    //    End of DORG2R
+    //
+} // dorg2r_
+
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+//> \brief \b DORGQR
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DORGQR + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgqr.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgqr.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgqr.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
+//
+//      .. Scalar Arguments ..
+//      INTEGER            INFO, K, LDA, LWORK, M, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DORGQR generates an M-by-N real matrix Q with orthonormal columns,
+//> which is defined as the first N columns of a product of K elementary
+//> reflectors of order M
+//>
+//>       Q  =  H(1) H(2) . . . H(k)
+//>
+//> as returned by DGEQRF.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix Q. M >= 0.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix Q. M >= N >= 0.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>          The number of elementary reflectors whose product defines the
+//>          matrix Q. N >= K >= 0.
+//> \endverbatim
+//>
+//> \param[in,out] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,N)
+//>          On entry, the i-th column must contain the vector which
+//>          defines the elementary reflector H(i), for i = 1,2,...,k, as
+//>          returned by DGEQRF in the first k columns of its array
+//>          argument A.
+//>          On exit, the M-by-N matrix Q.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The first dimension of the array A. LDA >= max(1,M).
+//> \endverbatim
+//>
+//> \param[in] TAU
+//> \verbatim
+//>          TAU is DOUBLE PRECISION array, dimension (K)
+//>          TAU(i) must contain the scalar factor of the elementary
+//>          reflector H(i), as returned by DGEQRF.
+//> \endverbatim
+//>
+//> \param[out] WORK
+//> \verbatim
+//>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+//>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+//> \endverbatim
+//>
+//> \param[in] LWORK
+//> \verbatim
+//>          LWORK is INTEGER
+//>          The dimension of the array WORK. LWORK >= max(1,N).
+//>          For optimum performance LWORK >= N*NB, where NB is the
+//>          optimal blocksize.
+//>
+//>          If LWORK = -1, then a workspace query is assumed; the routine
+//>          only calculates the optimal size of the WORK array, returns
+//>          this value as the first entry of the WORK array, and no error
+//>          message related to LWORK is issued by XERBLA.
+//> \endverbatim
+//>
+//> \param[out] INFO
+//> \verbatim
+//>          INFO is INTEGER
+//>          = 0:  successful exit
+//>          < 0:  if INFO = -i, the i-th argument has an illegal value
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup doubleOTHERcomputational
+//
+// =====================================================================
+/* Subroutine */ int dorgqr_(int *m, int *n, int *k, double *a, int *lda,
+	double *tau, double *work, int *lwork, int *info)
+{
+    // Table of constant values
+    int c__1 = 1;
+    int c_n1 = -1;
+    int c__3 = 3;
+    int c__2 = 2;
+
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2, i__3;
+
+    // Local variables
+    int i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
+    extern /* Subroutine */ int dorg2r_(int *, int *, int *, double *, int *,
+	    double *, double *, int *), dlarfb_(char *, char *, char *, char *
+	    , int *, int *, int *, double *, int *, double *, int *, double *,
+	     int *, double *, int *), dlarft_(char *, char *, int *, int *,
+	    double *, int *, double *, double *, int *), xerbla_(char *, int *
+	    );
+    extern int ilaenv_(int *, char *, char *, int *, int *, int *, int *);
+    int ldwork, lwkopt;
+    int lquery;
+
+    //
+    // -- LAPACK computational routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Test the input arguments
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    // Function Body
+    *info = 0;
+    nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1);
+    lwkopt = max(1,*n) * nb;
+    work[1] = (double) lwkopt;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0 || *n > *m) {
+	*info = -2;
+    } else if (*k < 0 || *k > *n) {
+	*info = -3;
+    } else if (*lda < max(1,*m)) {
+	*info = -5;
+    } else if (*lwork < max(1,*n) && ! lquery) {
+	*info = -8;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DORGQR", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+    //
+    //    Quick return if possible
+    //
+    if (*n <= 0) {
+	work[1] = 1.;
+	return 0;
+    }
+    nbmin = 2;
+    nx = 0;
+    iws = *n;
+    if (nb > 1 && nb < *k) {
+	//
+	//       Determine when to cross over from blocked to unblocked code.
+	//
+	// Computing MAX
+	i__1 = 0, i__2 = ilaenv_(&c__3, "DORGQR", " ", m, n, k, &c_n1);
+	nx = max(i__1,i__2);
+	if (nx < *k) {
+	    //
+	    //          Determine if workspace is large enough for blocked code.
+	    //
+	    ldwork = *n;
+	    iws = ldwork * nb;
+	    if (*lwork < iws) {
+		//
+		//             Not enough workspace to use optimal NB:  reduce NB and
+		//             determine the minimum value of NB.
+		//
+		nb = *lwork / ldwork;
+		// Computing MAX
+		i__1 = 2, i__2 = ilaenv_(&c__2, "DORGQR", " ", m, n, k, &c_n1)
+			;
+		nbmin = max(i__1,i__2);
+	    }
+	}
+    }
+    if (nb >= nbmin && nb < *k && nx < *k) {
+	//
+	//       Use blocked code after the last block.
+	//       The first kk columns are handled by the block method.
+	//
+	ki = (*k - nx - 1) / nb * nb;
+	// Computing MIN
+	i__1 = *k, i__2 = ki + nb;
+	kk = min(i__1,i__2);
+	//
+	//       Set A(1:kk,kk+1:n) to zero.
+	//
+	i__1 = *n;
+	for (j = kk + 1; j <= i__1; ++j) {
+	    i__2 = kk;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		a[i__ + j * a_dim1] = 0.;
+// L10:
+	    }
+// L20:
+	}
+    } else {
+	kk = 0;
+    }
+    //
+    //    Use unblocked code for the last or only block.
+    //
+    if (kk < *n) {
+	i__1 = *m - kk;
+	i__2 = *n - kk;
+	i__3 = *k - kk;
+	dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
+		tau[kk + 1], &work[1], &iinfo);
+    }
+    if (kk > 0) {
+	//
+	//       Use blocked code
+	//
+	i__1 = -nb;
+	for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
+	    // Computing MIN
+	    i__2 = nb, i__3 = *k - i__ + 1;
+	    ib = min(i__2,i__3);
+	    if (i__ + ib <= *n) {
+		//
+		//             Form the triangular factor of the block reflector
+		//             H = H(i) H(i+1) . . . H(i+ib-1)
+		//
+		i__2 = *m - i__ + 1;
+		dlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
+			a_dim1], lda, &tau[i__], &work[1], &ldwork);
+		//
+		//             Apply H to A(i:m,i+ib:n) from the left
+		//
+		i__2 = *m - i__ + 1;
+		i__3 = *n - i__ - ib + 1;
+		dlarfb_("Left", "No transpose", "Forward", "Columnwise", &
+			i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
+			1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
+			work[ib + 1], &ldwork);
+	    }
+	    //
+	    //          Apply H to rows i:m of current block
+	    //
+	    i__2 = *m - i__ + 1;
+	    dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
+		    work[1], &iinfo);
+	    //
+	    //          Set rows 1:i-1 of current block to zero
+	    //
+	    i__2 = i__ + ib - 1;
+	    for (j = i__; j <= i__2; ++j) {
+		i__3 = i__ - 1;
+		for (l = 1; l <= i__3; ++l) {
+		    a[l + j * a_dim1] = 0.;
+// L30:
+		}
+// L40:
+	    }
+// L50:
+	}
+    }
+    work[1] = (double) iws;
+    return 0;
+    //
+    //    End of DORGQR
+    //
+} // dorgqr_
+

3rdparty/clapack/src/dormqr.c

@@ -0,0 +1,684 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DORM2R + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorm2r.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorm2r.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorm2r.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
+//                         WORK, INFO )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          SIDE, TRANS
+//      INTEGER            INFO, K, LDA, LDC, M, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DORM2R overwrites the general real m by n matrix C with
+//>
+//>       Q * C  if SIDE = 'L' and TRANS = 'N', or
+//>
+//>       Q**T* C  if SIDE = 'L' and TRANS = 'T', or
+//>
+//>       C * Q  if SIDE = 'R' and TRANS = 'N', or
+//>
+//>       C * Q**T if SIDE = 'R' and TRANS = 'T',
+//>
+//> where Q is a real orthogonal matrix defined as the product of k
+//> elementary reflectors
+//>
+//>       Q = H(1) H(2) . . . H(k)
+//>
+//> as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n
+//> if SIDE = 'R'.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] SIDE
+//> \verbatim
+//>          SIDE is CHARACTER*1
+//>          = 'L': apply Q or Q**T from the Left
+//>          = 'R': apply Q or Q**T from the Right
+//> \endverbatim
+//>
+//> \param[in] TRANS
+//> \verbatim
+//>          TRANS is CHARACTER*1
+//>          = 'N': apply Q  (No transpose)
+//>          = 'T': apply Q**T (Transpose)
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix C. M >= 0.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix C. N >= 0.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>          The number of elementary reflectors whose product defines
+//>          the matrix Q.
+//>          If SIDE = 'L', M >= K >= 0;
+//>          if SIDE = 'R', N >= K >= 0.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,K)
+//>          The i-th column must contain the vector which defines the
+//>          elementary reflector H(i), for i = 1,2,...,k, as returned by
+//>          DGEQRF in the first k columns of its array argument A.
+//>          A is modified by the routine but restored on exit.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A.
+//>          If SIDE = 'L', LDA >= max(1,M);
+//>          if SIDE = 'R', LDA >= max(1,N).
+//> \endverbatim
+//>
+//> \param[in] TAU
+//> \verbatim
+//>          TAU is DOUBLE PRECISION array, dimension (K)
+//>          TAU(i) must contain the scalar factor of the elementary
+//>          reflector H(i), as returned by DGEQRF.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is DOUBLE PRECISION array, dimension (LDC,N)
+//>          On entry, the m by n matrix C.
+//>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>          The leading dimension of the array C. LDC >= max(1,M).
+//> \endverbatim
+//>
+//> \param[out] WORK
+//> \verbatim
+//>          WORK is DOUBLE PRECISION array, dimension
+//>                                   (N) if SIDE = 'L',
+//>                                   (M) if SIDE = 'R'
+//> \endverbatim
+//>
+//> \param[out] INFO
+//> \verbatim
+//>          INFO is INTEGER
+//>          = 0: successful exit
+//>          < 0: if INFO = -i, the i-th argument had an illegal value
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup doubleOTHERcomputational
+//
+// =====================================================================
+/* Subroutine */ int dorm2r_(char *side, char *trans, int *m, int *n, int *k,
+	double *a, int *lda, double *tau, double *c__, int *ldc, double *work,
+	 int *info)
+{
+    // Table of constant values
+    int c__1 = 1;
+
+    // System generated locals
+    int a_dim1, a_offset, c_dim1, c_offset, i__1, i__2;
+
+    // Local variables
+    int i__, i1, i2, i3, ic, jc, mi, ni, nq;
+    double aii;
+    int left;
+    extern /* Subroutine */ int dlarf_(char *, int *, int *, double *, int *,
+	    double *, double *, int *, double *);
+    extern int lsame_(char *, char *);
+    extern /* Subroutine */ int xerbla_(char *, int *);
+    int notran;
+
+    //
+    // -- LAPACK computational routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Test the input arguments
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --tau;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+    --work;
+
+    // Function Body
+    *info = 0;
+    left = lsame_(side, "L");
+    notran = lsame_(trans, "N");
+    //
+    //    NQ is the order of Q
+    //
+    if (left) {
+	nq = *m;
+    } else {
+	nq = *n;
+    }
+    if (! left && ! lsame_(side, "R")) {
+	*info = -1;
+    } else if (! notran && ! lsame_(trans, "T")) {
+	*info = -2;
+    } else if (*m < 0) {
+	*info = -3;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*k < 0 || *k > nq) {
+	*info = -5;
+    } else if (*lda < max(1,nq)) {
+	*info = -7;
+    } else if (*ldc < max(1,*m)) {
+	*info = -10;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DORM2R", &i__1);
+	return 0;
+    }
+    //
+    //    Quick return if possible
+    //
+    if (*m == 0 || *n == 0 || *k == 0) {
+	return 0;
+    }
+    if (left && ! notran || ! left && notran) {
+	i1 = 1;
+	i2 = *k;
+	i3 = 1;
+    } else {
+	i1 = *k;
+	i2 = 1;
+	i3 = -1;
+    }
+    if (left) {
+	ni = *n;
+	jc = 1;
+    } else {
+	mi = *m;
+	ic = 1;
+    }
+    i__1 = i2;
+    i__2 = i3;
+    for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+	if (left) {
+	    //
+	    //          H(i) is applied to C(i:m,1:n)
+	    //
+	    mi = *m - i__ + 1;
+	    ic = i__;
+	} else {
+	    //
+	    //          H(i) is applied to C(1:m,i:n)
+	    //
+	    ni = *n - i__ + 1;
+	    jc = i__;
+	}
+	//
+	//       Apply H(i)
+	//
+	aii = a[i__ + i__ * a_dim1];
+	a[i__ + i__ * a_dim1] = 1.;
+	dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], &c__[
+		ic + jc * c_dim1], ldc, &work[1]);
+	a[i__ + i__ * a_dim1] = aii;
+// L10:
+    }
+    return 0;
+    //
+    //    End of DORM2R
+    //
+} // dorm2r_
+
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+//> \brief \b DORMQR
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+//> \htmlonly
+//> Download DORMQR + dependencies
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormqr.f">
+//> [TGZ]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormqr.f">
+//> [ZIP]</a>
+//> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormqr.f">
+//> [TXT]</a>
+//> \endhtmlonly
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
+//                         WORK, LWORK, INFO )
+//
+//      .. Scalar Arguments ..
+//      CHARACTER          SIDE, TRANS
+//      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DORMQR overwrites the general real M-by-N matrix C with
+//>
+//>                 SIDE = 'L'     SIDE = 'R'
+//> TRANS = 'N':      Q * C          C * Q
+//> TRANS = 'T':      Q**T * C       C * Q**T
+//>
+//> where Q is a real orthogonal matrix defined as the product of k
+//> elementary reflectors
+//>
+//>       Q = H(1) H(2) . . . H(k)
+//>
+//> as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
+//> if SIDE = 'R'.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] SIDE
+//> \verbatim
+//>          SIDE is CHARACTER*1
+//>          = 'L': apply Q or Q**T from the Left;
+//>          = 'R': apply Q or Q**T from the Right.
+//> \endverbatim
+//>
+//> \param[in] TRANS
+//> \verbatim
+//>          TRANS is CHARACTER*1
+//>          = 'N':  No transpose, apply Q;
+//>          = 'T':  Transpose, apply Q**T.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>          The number of rows of the matrix C. M >= 0.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>          The number of columns of the matrix C. N >= 0.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>          The number of elementary reflectors whose product defines
+//>          the matrix Q.
+//>          If SIDE = 'L', M >= K >= 0;
+//>          if SIDE = 'R', N >= K >= 0.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension (LDA,K)
+//>          The i-th column must contain the vector which defines the
+//>          elementary reflector H(i), for i = 1,2,...,k, as returned by
+//>          DGEQRF in the first k columns of its array argument A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>          The leading dimension of the array A.
+//>          If SIDE = 'L', LDA >= max(1,M);
+//>          if SIDE = 'R', LDA >= max(1,N).
+//> \endverbatim
+//>
+//> \param[in] TAU
+//> \verbatim
+//>          TAU is DOUBLE PRECISION array, dimension (K)
+//>          TAU(i) must contain the scalar factor of the elementary
+//>          reflector H(i), as returned by DGEQRF.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is DOUBLE PRECISION array, dimension (LDC,N)
+//>          On entry, the M-by-N matrix C.
+//>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>          The leading dimension of the array C. LDC >= max(1,M).
+//> \endverbatim
+//>
+//> \param[out] WORK
+//> \verbatim
+//>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+//>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+//> \endverbatim
+//>
+//> \param[in] LWORK
+//> \verbatim
+//>          LWORK is INTEGER
+//>          The dimension of the array WORK.
+//>          If SIDE = 'L', LWORK >= max(1,N);
+//>          if SIDE = 'R', LWORK >= max(1,M).
+//>          For good performance, LWORK should generally be larger.
+//>
+//>          If LWORK = -1, then a workspace query is assumed; the routine
+//>          only calculates the optimal size of the WORK array, returns
+//>          this value as the first entry of the WORK array, and no error
+//>          message related to LWORK is issued by XERBLA.
+//> \endverbatim
+//>
+//> \param[out] INFO
+//> \verbatim
+//>          INFO is INTEGER
+//>          = 0:  successful exit
+//>          < 0:  if INFO = -i, the i-th argument had an illegal value
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup doubleOTHERcomputational
+//
+// =====================================================================
+/* Subroutine */ int dormqr_(char *side, char *trans, int *m, int *n, int *k,
+	double *a, int *lda, double *tau, double *c__, int *ldc, double *work,
+	 int *lwork, int *info)
+{
+    // Table of constant values
+    int c__1 = 1;
+    int c_n1 = -1;
+    int c__2 = 2;
+    int c__65 = 65;
+
+    // System generated locals
+    address a__1[2];
+    int a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, i__5;
+    char ch__1[2+1]={'\0'};
+
+    // Local variables
+    int i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt;
+    int left;
+    extern int lsame_(char *, char *);
+    int nbmin, iinfo;
+    extern /* Subroutine */ int dorm2r_(char *, char *, int *, int *, int *,
+	    double *, int *, double *, double *, int *, double *, int *),
+	    dlarfb_(char *, char *, char *, char *, int *, int *, int *,
+	    double *, int *, double *, int *, double *, int *, double *, int *
+	    ), dlarft_(char *, char *, int *, int *, double *, int *, double *
+	    , double *, int *), xerbla_(char *, int *);
+    extern int ilaenv_(int *, char *, char *, int *, int *, int *, int *);
+    int notran;
+    int ldwork, lwkopt;
+    int lquery;
+
+    //
+    // -- LAPACK computational routine (version 3.7.0) --
+    // -- LAPACK is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Executable Statements ..
+    //
+    //    Test the input arguments
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --tau;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+    --work;
+
+    // Function Body
+    *info = 0;
+    left = lsame_(side, "L");
+    notran = lsame_(trans, "N");
+    lquery = *lwork == -1;
+    //
+    //    NQ is the order of Q and NW is the minimum dimension of WORK
+    //
+    if (left) {
+	nq = *m;
+	nw = *n;
+    } else {
+	nq = *n;
+	nw = *m;
+    }
+    if (! left && ! lsame_(side, "R")) {
+	*info = -1;
+    } else if (! notran && ! lsame_(trans, "T")) {
+	*info = -2;
+    } else if (*m < 0) {
+	*info = -3;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*k < 0 || *k > nq) {
+	*info = -5;
+    } else if (*lda < max(1,nq)) {
+	*info = -7;
+    } else if (*ldc < max(1,*m)) {
+	*info = -10;
+    } else if (*lwork < max(1,nw) && ! lquery) {
+	*info = -12;
+    }
+    if (*info == 0) {
+	//
+	//       Compute the workspace requirements
+	//
+	// Computing MIN
+	// Writing concatenation
+	i__3[0] = 1, a__1[0] = side;
+	i__3[1] = 1, a__1[1] = trans;
+	s_cat(ch__1, a__1, i__3, &c__2);
+	i__1 = 64, i__2 = ilaenv_(&c__1, "DORMQR", ch__1, m, n, k, &c_n1);
+	nb = min(i__1,i__2);
+	lwkopt = max(1,nw) * nb + 4160;
+	work[1] = (double) lwkopt;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DORMQR", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+    //
+    //    Quick return if possible
+    //
+    if (*m == 0 || *n == 0 || *k == 0) {
+	work[1] = 1.;
+	return 0;
+    }
+    nbmin = 2;
+    ldwork = nw;
+    if (nb > 1 && nb < *k) {
+	if (*lwork < nw * nb + 4160) {
+	    nb = (*lwork - 4160) / ldwork;
+	    // Computing MAX
+	    // Writing concatenation
+	    i__3[0] = 1, a__1[0] = side;
+	    i__3[1] = 1, a__1[1] = trans;
+	    s_cat(ch__1, a__1, i__3, &c__2);
+	    i__1 = 2, i__2 = ilaenv_(&c__2, "DORMQR", ch__1, m, n, k, &c_n1);
+	    nbmin = max(i__1,i__2);
+	}
+    }
+    if (nb < nbmin || nb >= *k) {
+	//
+	//       Use unblocked code
+	//
+	dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
+		c_offset], ldc, &work[1], &iinfo);
+    } else {
+	//
+	//       Use blocked code
+	//
+	iwt = nw * nb + 1;
+	if (left && ! notran || ! left && notran) {
+	    i1 = 1;
+	    i2 = *k;
+	    i3 = nb;
+	} else {
+	    i1 = (*k - 1) / nb * nb + 1;
+	    i2 = 1;
+	    i3 = -nb;
+	}
+	if (left) {
+	    ni = *n;
+	    jc = 1;
+	} else {
+	    mi = *m;
+	    ic = 1;
+	}
+	i__1 = i2;
+	i__2 = i3;
+	for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+	    // Computing MIN
+	    i__4 = nb, i__5 = *k - i__ + 1;
+	    ib = min(i__4,i__5);
+	    //
+	    //          Form the triangular factor of the block reflector
+	    //          H = H(i) H(i+1) . . . H(i+ib-1)
+	    //
+	    i__4 = nq - i__ + 1;
+	    dlarft_("Forward", "Columnwise", &i__4, &ib, &a[i__ + i__ *
+		    a_dim1], lda, &tau[i__], &work[iwt], &c__65);
+	    if (left) {
+		//
+		//             H or H**T is applied to C(i:m,1:n)
+		//
+		mi = *m - i__ + 1;
+		ic = i__;
+	    } else {
+		//
+		//             H or H**T is applied to C(1:m,i:n)
+		//
+		ni = *n - i__ + 1;
+		jc = i__;
+	    }
+	    //
+	    //          Apply H or H**T
+	    //
+	    dlarfb_(side, trans, "Forward", "Columnwise", &mi, &ni, &ib, &a[
+		    i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic +
+		    jc * c_dim1], ldc, &work[1], &ldwork);
+// L10:
+	}
+    }
+    work[1] = (double) lwkopt;
+    return 0;
+    //
+    //    End of DORMQR
+    //
+} // dormqr_
+

3rdparty/clapack/src/drot.c

@@ -0,0 +1,164 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DROT
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION C,S
+//      INTEGER INCX,INCY,N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION DX(*),DY(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//>    DROT applies a plane rotation.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>         number of elements in input vector(s)
+//> \endverbatim
+//>
+//> \param[in,out] DX
+//> \verbatim
+//>          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>         storage spacing between elements of DX
+//> \endverbatim
+//>
+//> \param[in,out] DY
+//> \verbatim
+//>          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
+//> \endverbatim
+//>
+//> \param[in] INCY
+//> \verbatim
+//>          INCY is INTEGER
+//>         storage spacing between elements of DY
+//> \endverbatim
+//>
+//> \param[in] C
+//> \verbatim
+//>          C is DOUBLE PRECISION
+//> \endverbatim
+//>
+//> \param[in] S
+//> \verbatim
+//>          S is DOUBLE PRECISION
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2017
+//
+//> \ingroup double_blas_level1
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>     jack dongarra, linpack, 3/11/78.
+//>     modified 12/3/93, array(1) declarations changed to array(*)
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int drot_(int *n, double *dx, int *incx, double *dy, int *
+	incy, double *c__, double *s)
+{
+    // System generated locals
+    int i__1;
+
+    // Local variables
+    int i__, ix, iy;
+    double dtemp;
+
+    //
+    // -- Reference BLAS level1 routine (version 3.8.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Local Scalars ..
+    //    ..
+    // Parameter adjustments
+    --dy;
+    --dx;
+
+    // Function Body
+    if (*n <= 0) {
+	return 0;
+    }
+    if (*incx == 1 && *incy == 1) {
+	//
+	//      code for both increments equal to 1
+	//
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    dtemp = *c__ * dx[i__] + *s * dy[i__];
+	    dy[i__] = *c__ * dy[i__] - *s * dx[i__];
+	    dx[i__] = dtemp;
+	}
+    } else {
+	//
+	//      code for unequal increments or equal increments not equal
+	//        to 1
+	//
+	ix = 1;
+	iy = 1;
+	if (*incx < 0) {
+	    ix = (-(*n) + 1) * *incx + 1;
+	}
+	if (*incy < 0) {
+	    iy = (-(*n) + 1) * *incy + 1;
+	}
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    dtemp = *c__ * dx[ix] + *s * dy[iy];
+	    dy[iy] = *c__ * dy[iy] - *s * dx[ix];
+	    dx[ix] = dtemp;
+	    ix += *incx;
+	    iy += *incy;
+	}
+    }
+    return 0;
+} // drot_
+

3rdparty/clapack/src/dscal.c

@@ -0,0 +1,155 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DSCAL
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DSCAL(N,DA,DX,INCX)
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION DA
+//      INTEGER INCX,N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION DX(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//>    DSCAL scales a vector by a constant.
+//>    uses unrolled loops for increment equal to 1.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>         number of elements in input vector(s)
+//> \endverbatim
+//>
+//> \param[in] DA
+//> \verbatim
+//>          DA is DOUBLE PRECISION
+//>           On entry, DA specifies the scalar alpha.
+//> \endverbatim
+//>
+//> \param[in,out] DX
+//> \verbatim
+//>          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>         storage spacing between elements of DX
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2017
+//
+//> \ingroup double_blas_level1
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>     jack dongarra, linpack, 3/11/78.
+//>     modified 3/93 to return if incx .le. 0.
+//>     modified 12/3/93, array(1) declarations changed to array(*)
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dscal_(int *n, double *da, double *dx, int *incx)
+{
+    // System generated locals
+    int i__1, i__2;
+
+    // Local variables
+    int i__, m, mp1, nincx;
+
+    //
+    // -- Reference BLAS level1 routine (version 3.8.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    // Parameter adjustments
+    --dx;
+
+    // Function Body
+    if (*n <= 0 || *incx <= 0) {
+	return 0;
+    }
+    if (*incx == 1) {
+	//
+	//       code for increment equal to 1
+	//
+	//
+	//       clean-up loop
+	//
+	m = *n % 5;
+	if (m != 0) {
+	    i__1 = m;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		dx[i__] = *da * dx[i__];
+	    }
+	    if (*n < 5) {
+		return 0;
+	    }
+	}
+	mp1 = m + 1;
+	i__1 = *n;
+	for (i__ = mp1; i__ <= i__1; i__ += 5) {
+	    dx[i__] = *da * dx[i__];
+	    dx[i__ + 1] = *da * dx[i__ + 1];
+	    dx[i__ + 2] = *da * dx[i__ + 2];
+	    dx[i__ + 3] = *da * dx[i__ + 3];
+	    dx[i__ + 4] = *da * dx[i__ + 4];
+	}
+    } else {
+	//
+	//       code for increment not equal to 1
+	//
+	nincx = *n * *incx;
+	i__1 = nincx;
+	i__2 = *incx;
+	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+	    dx[i__] = *da * dx[i__];
+	}
+    }
+    return 0;
+} // dscal_
+

3rdparty/clapack/src/dswap.c

@@ -0,0 +1,178 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DSWAP
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DSWAP(N,DX,INCX,DY,INCY)
+//
+//      .. Scalar Arguments ..
+//      INTEGER INCX,INCY,N
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION DX(*),DY(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//>    DSWAP interchanges two vectors.
+//>    uses unrolled loops for increments equal to 1.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>         number of elements in input vector(s)
+//> \endverbatim
+//>
+//> \param[in,out] DX
+//> \verbatim
+//>          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>         storage spacing between elements of DX
+//> \endverbatim
+//>
+//> \param[in,out] DY
+//> \verbatim
+//>          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
+//> \endverbatim
+//>
+//> \param[in] INCY
+//> \verbatim
+//>          INCY is INTEGER
+//>         storage spacing between elements of DY
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date November 2017
+//
+//> \ingroup double_blas_level1
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>     jack dongarra, linpack, 3/11/78.
+//>     modified 12/3/93, array(1) declarations changed to array(*)
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dswap_(int *n, double *dx, int *incx, double *dy, int *
+	incy)
+{
+    // System generated locals
+    int i__1;
+
+    // Local variables
+    int i__, m, ix, iy, mp1;
+    double dtemp;
+
+    //
+    // -- Reference BLAS level1 routine (version 3.8.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    November 2017
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    // Parameter adjustments
+    --dy;
+    --dx;
+
+    // Function Body
+    if (*n <= 0) {
+	return 0;
+    }
+    if (*incx == 1 && *incy == 1) {
+	//
+	//      code for both increments equal to 1
+	//
+	//
+	//      clean-up loop
+	//
+	m = *n % 3;
+	if (m != 0) {
+	    i__1 = m;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		dtemp = dx[i__];
+		dx[i__] = dy[i__];
+		dy[i__] = dtemp;
+	    }
+	    if (*n < 3) {
+		return 0;
+	    }
+	}
+	mp1 = m + 1;
+	i__1 = *n;
+	for (i__ = mp1; i__ <= i__1; i__ += 3) {
+	    dtemp = dx[i__];
+	    dx[i__] = dy[i__];
+	    dy[i__] = dtemp;
+	    dtemp = dx[i__ + 1];
+	    dx[i__ + 1] = dy[i__ + 1];
+	    dy[i__ + 1] = dtemp;
+	    dtemp = dx[i__ + 2];
+	    dx[i__ + 2] = dy[i__ + 2];
+	    dy[i__ + 2] = dtemp;
+	}
+    } else {
+	//
+	//      code for unequal increments or equal increments not equal
+	//        to 1
+	//
+	ix = 1;
+	iy = 1;
+	if (*incx < 0) {
+	    ix = (-(*n) + 1) * *incx + 1;
+	}
+	if (*incy < 0) {
+	    iy = (-(*n) + 1) * *incy + 1;
+	}
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    dtemp = dx[ix];
+	    dx[ix] = dy[iy];
+	    dy[iy] = dtemp;
+	    ix += *incx;
+	    iy += *incy;
+	}
+    }
+    return 0;
+} // dswap_
+

3rdparty/clapack/src/dtrmm.c

@@ -0,0 +1,509 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DTRMM
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
+//
+//      .. Scalar Arguments ..
+//      DOUBLE PRECISION ALPHA
+//      INTEGER LDA,LDB,M,N
+//      CHARACTER DIAG,SIDE,TRANSA,UPLO
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION A(LDA,*),B(LDB,*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DTRMM  performs one of the matrix-matrix operations
+//>
+//>    B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
+//>
+//> where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
+//> non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
+//>
+//>    op( A ) = A   or   op( A ) = A**T.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] SIDE
+//> \verbatim
+//>          SIDE is CHARACTER*1
+//>           On entry,  SIDE specifies whether  op( A ) multiplies B from
+//>           the left or right as follows:
+//>
+//>              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
+//>
+//>              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
+//> \endverbatim
+//>
+//> \param[in] UPLO
+//> \verbatim
+//>          UPLO is CHARACTER*1
+//>           On entry, UPLO specifies whether the matrix A is an upper or
+//>           lower triangular matrix as follows:
+//>
+//>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
+//>
+//>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
+//> \endverbatim
+//>
+//> \param[in] TRANSA
+//> \verbatim
+//>          TRANSA is CHARACTER*1
+//>           On entry, TRANSA specifies the form of op( A ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSA = 'N' or 'n'   op( A ) = A.
+//>
+//>              TRANSA = 'T' or 't'   op( A ) = A**T.
+//>
+//>              TRANSA = 'C' or 'c'   op( A ) = A**T.
+//> \endverbatim
+//>
+//> \param[in] DIAG
+//> \verbatim
+//>          DIAG is CHARACTER*1
+//>           On entry, DIAG specifies whether or not A is unit triangular
+//>           as follows:
+//>
+//>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
+//>
+//>              DIAG = 'N' or 'n'   A is not assumed to be unit
+//>                                  triangular.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>           On entry, M specifies the number of rows of B. M must be at
+//>           least zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry, N specifies the number of columns of B.  N must be
+//>           at least zero.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is DOUBLE PRECISION.
+//>           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
+//>           zero then  A is not referenced and  B need not be set before
+//>           entry.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>           A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m
+//>           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
+//>           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
+//>           upper triangular part of the array  A must contain the upper
+//>           triangular matrix  and the strictly lower triangular part of
+//>           A is not referenced.
+//>           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
+//>           lower triangular part of the array  A must contain the lower
+//>           triangular matrix  and the strictly upper triangular part of
+//>           A is not referenced.
+//>           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
+//>           A  are not referenced either,  but are assumed to be  unity.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
+//>           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
+//>           then LDA must be at least max( 1, n ).
+//> \endverbatim
+//>
+//> \param[in,out] B
+//> \verbatim
+//>          B is DOUBLE PRECISION array, dimension ( LDB, N )
+//>           Before entry,  the leading  m by n part of the array  B must
+//>           contain the matrix  B,  and  on exit  is overwritten  by the
+//>           transformed matrix.
+//> \endverbatim
+//>
+//> \param[in] LDB
+//> \verbatim
+//>          LDB is INTEGER
+//>           On entry, LDB specifies the first dimension of B as declared
+//>           in  the  calling  (sub)  program.   LDB  must  be  at  least
+//>           max( 1, m ).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup double_blas_level3
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 3 Blas routine.
+//>
+//>  -- Written on 8-February-1989.
+//>     Jack Dongarra, Argonne National Laboratory.
+//>     Iain Duff, AERE Harwell.
+//>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
+//>     Sven Hammarling, Numerical Algorithms Group Ltd.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag,
+	int *m, int *n, double *alpha, double *a, int *lda, double *b, int *
+	ldb)
+{
+    // System generated locals
+    int a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
+
+    // Local variables
+    int i__, j, k, info;
+    double temp;
+    int lside;
+    extern int lsame_(char *, char *);
+    int nrowa;
+    int upper;
+    extern /* Subroutine */ int xerbla_(char *, int *);
+    int nounit;
+
+    //
+    // -- Reference BLAS level3 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Parameters ..
+    //    ..
+    //
+    //    Test the input parameters.
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+
+    // Function Body
+    lside = lsame_(side, "L");
+    if (lside) {
+	nrowa = *m;
+    } else {
+	nrowa = *n;
+    }
+    nounit = lsame_(diag, "N");
+    upper = lsame_(uplo, "U");
+    info = 0;
+    if (! lside && ! lsame_(side, "R")) {
+	info = 1;
+    } else if (! upper && ! lsame_(uplo, "L")) {
+	info = 2;
+    } else if (! lsame_(transa, "N") && ! lsame_(transa, "T") && ! lsame_(
+	    transa, "C")) {
+	info = 3;
+    } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) {
+	info = 4;
+    } else if (*m < 0) {
+	info = 5;
+    } else if (*n < 0) {
+	info = 6;
+    } else if (*lda < max(1,nrowa)) {
+	info = 9;
+    } else if (*ldb < max(1,*m)) {
+	info = 11;
+    }
+    if (info != 0) {
+	xerbla_("DTRMM ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*m == 0 || *n == 0) {
+	return 0;
+    }
+    //
+    //    And when  alpha.eq.zero.
+    //
+    if (*alpha == 0.) {
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = *m;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		b[i__ + j * b_dim1] = 0.;
+// L10:
+	    }
+// L20:
+	}
+	return 0;
+    }
+    //
+    //    Start the operations.
+    //
+    if (lside) {
+	if (lsame_(transa, "N")) {
+	    //
+	    //          Form  B := alpha*A*B.
+	    //
+	    if (upper) {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *m;
+		    for (k = 1; k <= i__2; ++k) {
+			if (b[k + j * b_dim1] != 0.) {
+			    temp = *alpha * b[k + j * b_dim1];
+			    i__3 = k - 1;
+			    for (i__ = 1; i__ <= i__3; ++i__) {
+				b[i__ + j * b_dim1] += temp * a[i__ + k *
+					a_dim1];
+// L30:
+			    }
+			    if (nounit) {
+				temp *= a[k + k * a_dim1];
+			    }
+			    b[k + j * b_dim1] = temp;
+			}
+// L40:
+		    }
+// L50:
+		}
+	    } else {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    for (k = *m; k >= 1; --k) {
+			if (b[k + j * b_dim1] != 0.) {
+			    temp = *alpha * b[k + j * b_dim1];
+			    b[k + j * b_dim1] = temp;
+			    if (nounit) {
+				b[k + j * b_dim1] *= a[k + k * a_dim1];
+			    }
+			    i__2 = *m;
+			    for (i__ = k + 1; i__ <= i__2; ++i__) {
+				b[i__ + j * b_dim1] += temp * a[i__ + k *
+					a_dim1];
+// L60:
+			    }
+			}
+// L70:
+		    }
+// L80:
+		}
+	    }
+	} else {
+	    //
+	    //          Form  B := alpha*A**T*B.
+	    //
+	    if (upper) {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    for (i__ = *m; i__ >= 1; --i__) {
+			temp = b[i__ + j * b_dim1];
+			if (nounit) {
+			    temp *= a[i__ + i__ * a_dim1];
+			}
+			i__2 = i__ - 1;
+			for (k = 1; k <= i__2; ++k) {
+			    temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
+// L90:
+			}
+			b[i__ + j * b_dim1] = *alpha * temp;
+// L100:
+		    }
+// L110:
+		}
+	    } else {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			temp = b[i__ + j * b_dim1];
+			if (nounit) {
+			    temp *= a[i__ + i__ * a_dim1];
+			}
+			i__3 = *m;
+			for (k = i__ + 1; k <= i__3; ++k) {
+			    temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
+// L120:
+			}
+			b[i__ + j * b_dim1] = *alpha * temp;
+// L130:
+		    }
+// L140:
+		}
+	    }
+	}
+    } else {
+	if (lsame_(transa, "N")) {
+	    //
+	    //          Form  B := alpha*B*A.
+	    //
+	    if (upper) {
+		for (j = *n; j >= 1; --j) {
+		    temp = *alpha;
+		    if (nounit) {
+			temp *= a[j + j * a_dim1];
+		    }
+		    i__1 = *m;
+		    for (i__ = 1; i__ <= i__1; ++i__) {
+			b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
+// L150:
+		    }
+		    i__1 = j - 1;
+		    for (k = 1; k <= i__1; ++k) {
+			if (a[k + j * a_dim1] != 0.) {
+			    temp = *alpha * a[k + j * a_dim1];
+			    i__2 = *m;
+			    for (i__ = 1; i__ <= i__2; ++i__) {
+				b[i__ + j * b_dim1] += temp * b[i__ + k *
+					b_dim1];
+// L160:
+			    }
+			}
+// L170:
+		    }
+// L180:
+		}
+	    } else {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    temp = *alpha;
+		    if (nounit) {
+			temp *= a[j + j * a_dim1];
+		    }
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
+// L190:
+		    }
+		    i__2 = *n;
+		    for (k = j + 1; k <= i__2; ++k) {
+			if (a[k + j * a_dim1] != 0.) {
+			    temp = *alpha * a[k + j * a_dim1];
+			    i__3 = *m;
+			    for (i__ = 1; i__ <= i__3; ++i__) {
+				b[i__ + j * b_dim1] += temp * b[i__ + k *
+					b_dim1];
+// L200:
+			    }
+			}
+// L210:
+		    }
+// L220:
+		}
+	    }
+	} else {
+	    //
+	    //          Form  B := alpha*B*A**T.
+	    //
+	    if (upper) {
+		i__1 = *n;
+		for (k = 1; k <= i__1; ++k) {
+		    i__2 = k - 1;
+		    for (j = 1; j <= i__2; ++j) {
+			if (a[j + k * a_dim1] != 0.) {
+			    temp = *alpha * a[j + k * a_dim1];
+			    i__3 = *m;
+			    for (i__ = 1; i__ <= i__3; ++i__) {
+				b[i__ + j * b_dim1] += temp * b[i__ + k *
+					b_dim1];
+// L230:
+			    }
+			}
+// L240:
+		    }
+		    temp = *alpha;
+		    if (nounit) {
+			temp *= a[k + k * a_dim1];
+		    }
+		    if (temp != 1.) {
+			i__2 = *m;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
+// L250:
+			}
+		    }
+// L260:
+		}
+	    } else {
+		for (k = *n; k >= 1; --k) {
+		    i__1 = *n;
+		    for (j = k + 1; j <= i__1; ++j) {
+			if (a[j + k * a_dim1] != 0.) {
+			    temp = *alpha * a[j + k * a_dim1];
+			    i__2 = *m;
+			    for (i__ = 1; i__ <= i__2; ++i__) {
+				b[i__ + j * b_dim1] += temp * b[i__ + k *
+					b_dim1];
+// L270:
+			    }
+			}
+// L280:
+		    }
+		    temp = *alpha;
+		    if (nounit) {
+			temp *= a[k + k * a_dim1];
+		    }
+		    if (temp != 1.) {
+			i__1 = *m;
+			for (i__ = 1; i__ <= i__1; ++i__) {
+			    b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
+// L290:
+			}
+		    }
+// L300:
+		}
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of DTRMM .
+    //
+} // dtrmm_
+

3rdparty/clapack/src/dtrmv.c

@@ -0,0 +1,396 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b DTRMV
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
+//
+//      .. Scalar Arguments ..
+//      INTEGER INCX,LDA,N
+//      CHARACTER DIAG,TRANS,UPLO
+//      ..
+//      .. Array Arguments ..
+//      DOUBLE PRECISION A(LDA,*),X(*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> DTRMV  performs one of the matrix-vector operations
+//>
+//>    x := A*x,   or   x := A**T*x,
+//>
+//> where x is an n element vector and  A is an n by n unit, or non-unit,
+//> upper or lower triangular matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] UPLO
+//> \verbatim
+//>          UPLO is CHARACTER*1
+//>           On entry, UPLO specifies whether the matrix is an upper or
+//>           lower triangular matrix as follows:
+//>
+//>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
+//>
+//>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
+//> \endverbatim
+//>
+//> \param[in] TRANS
+//> \verbatim
+//>          TRANS is CHARACTER*1
+//>           On entry, TRANS specifies the operation to be performed as
+//>           follows:
+//>
+//>              TRANS = 'N' or 'n'   x := A*x.
+//>
+//>              TRANS = 'T' or 't'   x := A**T*x.
+//>
+//>              TRANS = 'C' or 'c'   x := A**T*x.
+//> \endverbatim
+//>
+//> \param[in] DIAG
+//> \verbatim
+//>          DIAG is CHARACTER*1
+//>           On entry, DIAG specifies whether or not A is unit
+//>           triangular as follows:
+//>
+//>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
+//>
+//>              DIAG = 'N' or 'n'   A is not assumed to be unit
+//>                                  triangular.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry, N specifies the order of the matrix A.
+//>           N must be at least zero.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is DOUBLE PRECISION array, dimension ( LDA, N )
+//>           Before entry with  UPLO = 'U' or 'u', the leading n by n
+//>           upper triangular part of the array A must contain the upper
+//>           triangular matrix and the strictly lower triangular part of
+//>           A is not referenced.
+//>           Before entry with UPLO = 'L' or 'l', the leading n by n
+//>           lower triangular part of the array A must contain the lower
+//>           triangular matrix and the strictly upper triangular part of
+//>           A is not referenced.
+//>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
+//>           A are not referenced either, but are assumed to be unity.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program. LDA must be at least
+//>           max( 1, n ).
+//> \endverbatim
+//>
+//> \param[in,out] X
+//> \verbatim
+//>          X is DOUBLE PRECISION array, dimension at least
+//>           ( 1 + ( n - 1 )*abs( INCX ) ).
+//>           Before entry, the incremented array X must contain the n
+//>           element vector x. On exit, X is overwritten with the
+//>           transformed vector x.
+//> \endverbatim
+//>
+//> \param[in] INCX
+//> \verbatim
+//>          INCX is INTEGER
+//>           On entry, INCX specifies the increment for the elements of
+//>           X. INCX must not be zero.
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup double_blas_level2
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 2 Blas routine.
+//>  The vector and matrix arguments are not referenced when N = 0, or M = 0
+//>
+//>  -- Written on 22-October-1986.
+//>     Jack Dongarra, Argonne National Lab.
+//>     Jeremy Du Croz, Nag Central Office.
+//>     Sven Hammarling, Nag Central Office.
+//>     Richard Hanson, Sandia National Labs.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, int *n,
+	double *a, int *lda, double *x, int *incx)
+{
+    // System generated locals
+    int a_dim1, a_offset, i__1, i__2;
+
+    // Local variables
+    int i__, j, ix, jx, kx, info;
+    double temp;
+    extern int lsame_(char *, char *);
+    extern /* Subroutine */ int xerbla_(char *, int *);
+    int nounit;
+
+    //
+    // -- Reference BLAS level2 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. Parameters ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //
+    //    Test the input parameters.
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --x;
+
+    // Function Body
+    info = 0;
+    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
+	info = 1;
+    } else if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans,
+	     "C")) {
+	info = 2;
+    } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) {
+	info = 3;
+    } else if (*n < 0) {
+	info = 4;
+    } else if (*lda < max(1,*n)) {
+	info = 6;
+    } else if (*incx == 0) {
+	info = 8;
+    }
+    if (info != 0) {
+	xerbla_("DTRMV ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*n == 0) {
+	return 0;
+    }
+    nounit = lsame_(diag, "N");
+    //
+    //    Set up the start point in X if the increment is not unity. This
+    //    will be  ( N - 1 )*INCX  too small for descending loops.
+    //
+    if (*incx <= 0) {
+	kx = 1 - (*n - 1) * *incx;
+    } else if (*incx != 1) {
+	kx = 1;
+    }
+    //
+    //    Start the operations. In this version the elements of A are
+    //    accessed sequentially with one pass through A.
+    //
+    if (lsame_(trans, "N")) {
+	//
+	//       Form  x := A*x.
+	//
+	if (lsame_(uplo, "U")) {
+	    if (*incx == 1) {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    if (x[j] != 0.) {
+			temp = x[j];
+			i__2 = j - 1;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    x[i__] += temp * a[i__ + j * a_dim1];
+// L10:
+			}
+			if (nounit) {
+			    x[j] *= a[j + j * a_dim1];
+			}
+		    }
+// L20:
+		}
+	    } else {
+		jx = kx;
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    if (x[jx] != 0.) {
+			temp = x[jx];
+			ix = kx;
+			i__2 = j - 1;
+			for (i__ = 1; i__ <= i__2; ++i__) {
+			    x[ix] += temp * a[i__ + j * a_dim1];
+			    ix += *incx;
+// L30:
+			}
+			if (nounit) {
+			    x[jx] *= a[j + j * a_dim1];
+			}
+		    }
+		    jx += *incx;
+// L40:
+		}
+	    }
+	} else {
+	    if (*incx == 1) {
+		for (j = *n; j >= 1; --j) {
+		    if (x[j] != 0.) {
+			temp = x[j];
+			i__1 = j + 1;
+			for (i__ = *n; i__ >= i__1; --i__) {
+			    x[i__] += temp * a[i__ + j * a_dim1];
+// L50:
+			}
+			if (nounit) {
+			    x[j] *= a[j + j * a_dim1];
+			}
+		    }
+// L60:
+		}
+	    } else {
+		kx += (*n - 1) * *incx;
+		jx = kx;
+		for (j = *n; j >= 1; --j) {
+		    if (x[jx] != 0.) {
+			temp = x[jx];
+			ix = kx;
+			i__1 = j + 1;
+			for (i__ = *n; i__ >= i__1; --i__) {
+			    x[ix] += temp * a[i__ + j * a_dim1];
+			    ix -= *incx;
+// L70:
+			}
+			if (nounit) {
+			    x[jx] *= a[j + j * a_dim1];
+			}
+		    }
+		    jx -= *incx;
+// L80:
+		}
+	    }
+	}
+    } else {
+	//
+	//       Form  x := A**T*x.
+	//
+	if (lsame_(uplo, "U")) {
+	    if (*incx == 1) {
+		for (j = *n; j >= 1; --j) {
+		    temp = x[j];
+		    if (nounit) {
+			temp *= a[j + j * a_dim1];
+		    }
+		    for (i__ = j - 1; i__ >= 1; --i__) {
+			temp += a[i__ + j * a_dim1] * x[i__];
+// L90:
+		    }
+		    x[j] = temp;
+// L100:
+		}
+	    } else {
+		jx = kx + (*n - 1) * *incx;
+		for (j = *n; j >= 1; --j) {
+		    temp = x[jx];
+		    ix = jx;
+		    if (nounit) {
+			temp *= a[j + j * a_dim1];
+		    }
+		    for (i__ = j - 1; i__ >= 1; --i__) {
+			ix -= *incx;
+			temp += a[i__ + j * a_dim1] * x[ix];
+// L110:
+		    }
+		    x[jx] = temp;
+		    jx -= *incx;
+// L120:
+		}
+	    }
+	} else {
+	    if (*incx == 1) {
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    temp = x[j];
+		    if (nounit) {
+			temp *= a[j + j * a_dim1];
+		    }
+		    i__2 = *n;
+		    for (i__ = j + 1; i__ <= i__2; ++i__) {
+			temp += a[i__ + j * a_dim1] * x[i__];
+// L130:
+		    }
+		    x[j] = temp;
+// L140:
+		}
+	    } else {
+		jx = kx;
+		i__1 = *n;
+		for (j = 1; j <= i__1; ++j) {
+		    temp = x[jx];
+		    ix = jx;
+		    if (nounit) {
+			temp *= a[j + j * a_dim1];
+		    }
+		    i__2 = *n;
+		    for (i__ = j + 1; i__ <= i__2; ++i__) {
+			ix += *incx;
+			temp += a[i__ + j * a_dim1] * x[ix];
+// L150:
+		    }
+		    x[jx] = temp;
+		    jx += *incx;
+// L160:
+		}
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of DTRMV .
+    //
+} // dtrmv_
+

3rdparty/clapack/src/sgemm.c

@@ -0,0 +1,444 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b SGEMM
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+//
+//      .. Scalar Arguments ..
+//      REAL ALPHA,BETA
+//      INTEGER K,LDA,LDB,LDC,M,N
+//      CHARACTER TRANSA,TRANSB
+//      ..
+//      .. Array Arguments ..
+//      REAL A(LDA,*),B(LDB,*),C(LDC,*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> SGEMM  performs one of the matrix-matrix operations
+//>
+//>    C := alpha*op( A )*op( B ) + beta*C,
+//>
+//> where  op( X ) is one of
+//>
+//>    op( X ) = X   or   op( X ) = X**T,
+//>
+//> alpha and beta are scalars, and A, B and C are matrices, with op( A )
+//> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] TRANSA
+//> \verbatim
+//>          TRANSA is CHARACTER*1
+//>           On entry, TRANSA specifies the form of op( A ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSA = 'N' or 'n',  op( A ) = A.
+//>
+//>              TRANSA = 'T' or 't',  op( A ) = A**T.
+//>
+//>              TRANSA = 'C' or 'c',  op( A ) = A**T.
+//> \endverbatim
+//>
+//> \param[in] TRANSB
+//> \verbatim
+//>          TRANSB is CHARACTER*1
+//>           On entry, TRANSB specifies the form of op( B ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSB = 'N' or 'n',  op( B ) = B.
+//>
+//>              TRANSB = 'T' or 't',  op( B ) = B**T.
+//>
+//>              TRANSB = 'C' or 'c',  op( B ) = B**T.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>           On entry,  M  specifies  the number  of rows  of the  matrix
+//>           op( A )  and of the  matrix  C.  M  must  be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry,  N  specifies the number  of columns of the matrix
+//>           op( B ) and the number of columns of the matrix C. N must be
+//>           at least zero.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>           On entry,  K  specifies  the number of columns of the matrix
+//>           op( A ) and the number of rows of the matrix op( B ). K must
+//>           be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is REAL
+//>           On entry, ALPHA specifies the scalar alpha.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is REAL array, dimension ( LDA, ka ), where ka is
+//>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
+//>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
+//>           part of the array  A  must contain the matrix  A,  otherwise
+//>           the leading  k by m  part of the array  A  must contain  the
+//>           matrix A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
+//>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
+//>           least  max( 1, k ).
+//> \endverbatim
+//>
+//> \param[in] B
+//> \verbatim
+//>          B is REAL array, dimension ( LDB, kb ), where kb is
+//>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
+//>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
+//>           part of the array  B  must contain the matrix  B,  otherwise
+//>           the leading  n by k  part of the array  B  must contain  the
+//>           matrix B.
+//> \endverbatim
+//>
+//> \param[in] LDB
+//> \verbatim
+//>          LDB is INTEGER
+//>           On entry, LDB specifies the first dimension of B as declared
+//>           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
+//>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
+//>           least  max( 1, n ).
+//> \endverbatim
+//>
+//> \param[in] BETA
+//> \verbatim
+//>          BETA is REAL
+//>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
+//>           supplied as zero then C need not be set on input.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is REAL array, dimension ( LDC, N )
+//>           Before entry, the leading  m by n  part of the array  C must
+//>           contain the matrix  C,  except when  beta  is zero, in which
+//>           case C need not be set on entry.
+//>           On exit, the array  C  is overwritten by the  m by n  matrix
+//>           ( alpha*op( A )*op( B ) + beta*C ).
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>           On entry, LDC specifies the first dimension of C as declared
+//>           in  the  calling  (sub)  program.   LDC  must  be  at  least
+//>           max( 1, m ).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup single_blas_level3
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 3 Blas routine.
+//>
+//>  -- Written on 8-February-1989.
+//>     Jack Dongarra, Argonne National Laboratory.
+//>     Iain Duff, AERE Harwell.
+//>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
+//>     Sven Hammarling, Numerical Algorithms Group Ltd.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int sgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, float *alpha, float *a, int *lda, float *b, int *ldb, float *beta,
+	float *c__, int *ldc)
+{
+    // System generated locals
+    int a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
+	    i__3;
+
+    // Local variables
+    int i__, j, l, info;
+    int nota, notb;
+    float temp;
+    int ncola;
+    extern int lsame_(char *, char *);
+    int nrowa, nrowb;
+    extern /* Subroutine */ int xerbla_(char *, int *);
+
+    //
+    // -- Reference BLAS level3 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Parameters ..
+    //    ..
+    //
+    //    Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
+    //    transposed and set  NROWA, NCOLA and  NROWB  as the number of rows
+    //    and  columns of  A  and the  number of  rows  of  B  respectively.
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+
+    // Function Body
+    nota = lsame_(transa, "N");
+    notb = lsame_(transb, "N");
+    if (nota) {
+	nrowa = *m;
+	ncola = *k;
+    } else {
+	nrowa = *k;
+	ncola = *m;
+    }
+    if (notb) {
+	nrowb = *k;
+    } else {
+	nrowb = *n;
+    }
+    //
+    //    Test the input parameters.
+    //
+    info = 0;
+    if (! nota && ! lsame_(transa, "C") && ! lsame_(transa, "T")) {
+	info = 1;
+    } else if (! notb && ! lsame_(transb, "C") && ! lsame_(transb, "T")) {
+	info = 2;
+    } else if (*m < 0) {
+	info = 3;
+    } else if (*n < 0) {
+	info = 4;
+    } else if (*k < 0) {
+	info = 5;
+    } else if (*lda < max(1,nrowa)) {
+	info = 8;
+    } else if (*ldb < max(1,nrowb)) {
+	info = 10;
+    } else if (*ldc < max(1,*m)) {
+	info = 13;
+    }
+    if (info != 0) {
+	xerbla_("SGEMM ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*m == 0 || *n == 0 || (*alpha == 0.f || *k == 0) && *beta == 1.f) {
+	return 0;
+    }
+    //
+    //    And if  alpha.eq.zero.
+    //
+    if (*alpha == 0.f) {
+	if (*beta == 0.f) {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    c__[i__ + j * c_dim1] = 0.f;
+// L10:
+		}
+// L20:
+	    }
+	} else {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
+// L30:
+		}
+// L40:
+	    }
+	}
+	return 0;
+    }
+    //
+    //    Start the operations.
+    //
+    if (notb) {
+	if (nota) {
+	    //
+	    //          Form  C := alpha*A*B + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (*beta == 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = 0.f;
+// L50:
+		    }
+		} else if (*beta != 1.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
+// L60:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    temp = *alpha * b[l + j * b_dim1];
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1];
+// L70:
+		    }
+// L80:
+		}
+// L90:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			temp += a[l + i__ * a_dim1] * b[l + j * b_dim1];
+// L100:
+		    }
+		    if (*beta == 0.f) {
+			c__[i__ + j * c_dim1] = *alpha * temp;
+		    } else {
+			c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
+				i__ + j * c_dim1];
+		    }
+// L110:
+		}
+// L120:
+	    }
+	}
+    } else {
+	if (nota) {
+	    //
+	    //          Form  C := alpha*A*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (*beta == 0.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = 0.f;
+// L130:
+		    }
+		} else if (*beta != 1.f) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
+// L140:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    temp = *alpha * b[j + l * b_dim1];
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1];
+// L150:
+		    }
+// L160:
+		}
+// L170:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp = 0.f;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			temp += a[l + i__ * a_dim1] * b[j + l * b_dim1];
+// L180:
+		    }
+		    if (*beta == 0.f) {
+			c__[i__ + j * c_dim1] = *alpha * temp;
+		    } else {
+			c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
+				i__ + j * c_dim1];
+		    }
+// L190:
+		}
+// L200:
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of SGEMM .
+    //
+} // sgemm_
+

3rdparty/clapack/src/zgemm.c

@@ -0,0 +1,752 @@
+/*  -- translated by f2c (version 20201020 (for_lapack)). -- */
+
+#include "f2c.h"
+
+//> \brief \b ZGEMM
+//
+// =========== DOCUMENTATION ===========
+//
+// Online html documentation available at
+//           http://www.netlib.org/lapack/explore-html/
+//
+// Definition:
+// ===========
+//
+//      SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+//
+//      .. Scalar Arguments ..
+//      COMPLEX*16 ALPHA,BETA
+//      INTEGER K,LDA,LDB,LDC,M,N
+//      CHARACTER TRANSA,TRANSB
+//      ..
+//      .. Array Arguments ..
+//      COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
+//      ..
+//
+//
+//> \par Purpose:
+// =============
+//>
+//> \verbatim
+//>
+//> ZGEMM  performs one of the matrix-matrix operations
+//>
+//>    C := alpha*op( A )*op( B ) + beta*C,
+//>
+//> where  op( X ) is one of
+//>
+//>    op( X ) = X   or   op( X ) = X**T   or   op( X ) = X**H,
+//>
+//> alpha and beta are scalars, and A, B and C are matrices, with op( A )
+//> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
+//> \endverbatim
+//
+// Arguments:
+// ==========
+//
+//> \param[in] TRANSA
+//> \verbatim
+//>          TRANSA is CHARACTER*1
+//>           On entry, TRANSA specifies the form of op( A ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSA = 'N' or 'n',  op( A ) = A.
+//>
+//>              TRANSA = 'T' or 't',  op( A ) = A**T.
+//>
+//>              TRANSA = 'C' or 'c',  op( A ) = A**H.
+//> \endverbatim
+//>
+//> \param[in] TRANSB
+//> \verbatim
+//>          TRANSB is CHARACTER*1
+//>           On entry, TRANSB specifies the form of op( B ) to be used in
+//>           the matrix multiplication as follows:
+//>
+//>              TRANSB = 'N' or 'n',  op( B ) = B.
+//>
+//>              TRANSB = 'T' or 't',  op( B ) = B**T.
+//>
+//>              TRANSB = 'C' or 'c',  op( B ) = B**H.
+//> \endverbatim
+//>
+//> \param[in] M
+//> \verbatim
+//>          M is INTEGER
+//>           On entry,  M  specifies  the number  of rows  of the  matrix
+//>           op( A )  and of the  matrix  C.  M  must  be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] N
+//> \verbatim
+//>          N is INTEGER
+//>           On entry,  N  specifies the number  of columns of the matrix
+//>           op( B ) and the number of columns of the matrix C. N must be
+//>           at least zero.
+//> \endverbatim
+//>
+//> \param[in] K
+//> \verbatim
+//>          K is INTEGER
+//>           On entry,  K  specifies  the number of columns of the matrix
+//>           op( A ) and the number of rows of the matrix op( B ). K must
+//>           be at least  zero.
+//> \endverbatim
+//>
+//> \param[in] ALPHA
+//> \verbatim
+//>          ALPHA is COMPLEX*16
+//>           On entry, ALPHA specifies the scalar alpha.
+//> \endverbatim
+//>
+//> \param[in] A
+//> \verbatim
+//>          A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
+//>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
+//>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
+//>           part of the array  A  must contain the matrix  A,  otherwise
+//>           the leading  k by m  part of the array  A  must contain  the
+//>           matrix A.
+//> \endverbatim
+//>
+//> \param[in] LDA
+//> \verbatim
+//>          LDA is INTEGER
+//>           On entry, LDA specifies the first dimension of A as declared
+//>           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
+//>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
+//>           least  max( 1, k ).
+//> \endverbatim
+//>
+//> \param[in] B
+//> \verbatim
+//>          B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is
+//>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
+//>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
+//>           part of the array  B  must contain the matrix  B,  otherwise
+//>           the leading  n by k  part of the array  B  must contain  the
+//>           matrix B.
+//> \endverbatim
+//>
+//> \param[in] LDB
+//> \verbatim
+//>          LDB is INTEGER
+//>           On entry, LDB specifies the first dimension of B as declared
+//>           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
+//>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
+//>           least  max( 1, n ).
+//> \endverbatim
+//>
+//> \param[in] BETA
+//> \verbatim
+//>          BETA is COMPLEX*16
+//>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
+//>           supplied as zero then C need not be set on input.
+//> \endverbatim
+//>
+//> \param[in,out] C
+//> \verbatim
+//>          C is COMPLEX*16 array, dimension ( LDC, N )
+//>           Before entry, the leading  m by n  part of the array  C must
+//>           contain the matrix  C,  except when  beta  is zero, in which
+//>           case C need not be set on entry.
+//>           On exit, the array  C  is overwritten by the  m by n  matrix
+//>           ( alpha*op( A )*op( B ) + beta*C ).
+//> \endverbatim
+//>
+//> \param[in] LDC
+//> \verbatim
+//>          LDC is INTEGER
+//>           On entry, LDC specifies the first dimension of C as declared
+//>           in  the  calling  (sub)  program.   LDC  must  be  at  least
+//>           max( 1, m ).
+//> \endverbatim
+//
+// Authors:
+// ========
+//
+//> \author Univ. of Tennessee
+//> \author Univ. of California Berkeley
+//> \author Univ. of Colorado Denver
+//> \author NAG Ltd.
+//
+//> \date December 2016
+//
+//> \ingroup complex16_blas_level3
+//
+//> \par Further Details:
+// =====================
+//>
+//> \verbatim
+//>
+//>  Level 3 Blas routine.
+//>
+//>  -- Written on 8-February-1989.
+//>     Jack Dongarra, Argonne National Laboratory.
+//>     Iain Duff, AERE Harwell.
+//>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
+//>     Sven Hammarling, Numerical Algorithms Group Ltd.
+//> \endverbatim
+//>
+// =====================================================================
+/* Subroutine */ int zgemm_(char *transa, char *transb, int *m, int *n, int *
+	k, doublecomplex *alpha, doublecomplex *a, int *lda, doublecomplex *b,
+	 int *ldb, doublecomplex *beta, doublecomplex *c__, int *ldc)
+{
+    // Table of constant values
+    doublecomplex c_b1 = {1.,0.};
+    doublecomplex c_b2 = {0.,0.};
+
+    // System generated locals
+    int a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
+	    i__3, i__4, i__5, i__6;
+    doublecomplex z__1, z__2, z__3, z__4;
+
+    // Local variables
+    int i__, j, l, info;
+    int nota, notb;
+    doublecomplex temp;
+    int conja, conjb;
+    int ncola;
+    extern int lsame_(char *, char *);
+    int nrowa, nrowb;
+    extern /* Subroutine */ int xerbla_(char *, int *);
+
+    //
+    // -- Reference BLAS level3 routine (version 3.7.0) --
+    // -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
+    // -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+    //    December 2016
+    //
+    //    .. Scalar Arguments ..
+    //    ..
+    //    .. Array Arguments ..
+    //    ..
+    //
+    // =====================================================================
+    //
+    //    .. External Functions ..
+    //    ..
+    //    .. External Subroutines ..
+    //    ..
+    //    .. Intrinsic Functions ..
+    //    ..
+    //    .. Local Scalars ..
+    //    ..
+    //    .. Parameters ..
+    //    ..
+    //
+    //    Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
+    //    conjugated or transposed, set  CONJA and CONJB  as true if  A  and
+    //    B  respectively are to be  transposed but  not conjugated  and set
+    //    NROWA, NCOLA and  NROWB  as the number of rows and  columns  of  A
+    //    and the number of rows of  B  respectively.
+    //
+    // Parameter adjustments
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+
+    // Function Body
+    nota = lsame_(transa, "N");
+    notb = lsame_(transb, "N");
+    conja = lsame_(transa, "C");
+    conjb = lsame_(transb, "C");
+    if (nota) {
+	nrowa = *m;
+	ncola = *k;
+    } else {
+	nrowa = *k;
+	ncola = *m;
+    }
+    if (notb) {
+	nrowb = *k;
+    } else {
+	nrowb = *n;
+    }
+    //
+    //    Test the input parameters.
+    //
+    info = 0;
+    if (! nota && ! conja && ! lsame_(transa, "T")) {
+	info = 1;
+    } else if (! notb && ! conjb && ! lsame_(transb, "T")) {
+	info = 2;
+    } else if (*m < 0) {
+	info = 3;
+    } else if (*n < 0) {
+	info = 4;
+    } else if (*k < 0) {
+	info = 5;
+    } else if (*lda < max(1,nrowa)) {
+	info = 8;
+    } else if (*ldb < max(1,nrowb)) {
+	info = 10;
+    } else if (*ldc < max(1,*m)) {
+	info = 13;
+    }
+    if (info != 0) {
+	xerbla_("ZGEMM ", &info);
+	return 0;
+    }
+    //
+    //    Quick return if possible.
+    //
+    if (*m == 0 || *n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) &&
+	     (beta->r == 1. && beta->i == 0.)) {
+	return 0;
+    }
+    //
+    //    And when  alpha.eq.zero.
+    //
+    if (alpha->r == 0. && alpha->i == 0.) {
+	if (beta->r == 0. && beta->i == 0.) {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * c_dim1;
+		    c__[i__3].r = 0., c__[i__3].i = 0.;
+// L10:
+		}
+// L20:
+	    }
+	} else {
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * c_dim1;
+		    i__4 = i__ + j * c_dim1;
+		    z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i,
+			    z__1.i = beta->r * c__[i__4].i + beta->i * c__[
+			    i__4].r;
+		    c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+// L30:
+		}
+// L40:
+	    }
+	}
+	return 0;
+    }
+    //
+    //    Start the operations.
+    //
+    if (notb) {
+	if (nota) {
+	    //
+	    //          Form  C := alpha*A*B + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (beta->r == 0. && beta->i == 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			c__[i__3].r = 0., c__[i__3].i = 0.;
+// L50:
+		    }
+		} else if (beta->r != 1. || beta->i != 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			i__4 = i__ + j * c_dim1;
+			z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__1.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+// L60:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    i__3 = l + j * b_dim1;
+		    z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
+			    z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3]
+			    .r;
+		    temp.r = z__1.r, temp.i = z__1.i;
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			i__4 = i__ + j * c_dim1;
+			i__5 = i__ + j * c_dim1;
+			i__6 = i__ + l * a_dim1;
+			z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
+				z__2.i = temp.r * a[i__6].i + temp.i * a[i__6]
+				.r;
+			z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i +
+				z__2.i;
+			c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
+// L70:
+		    }
+// L80:
+		}
+// L90:
+	    }
+	} else if (conja) {
+	    //
+	    //          Form  C := alpha*A**H*B + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0., temp.i = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			d_cnjg(&z__3, &a[l + i__ * a_dim1]);
+			i__4 = l + j * b_dim1;
+			z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i,
+				z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4]
+				.r;
+			z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
+			temp.r = z__1.r, temp.i = z__1.i;
+// L100:
+		    }
+		    if (beta->r == 0. && beta->i == 0.) {
+			i__3 = i__ + j * c_dim1;
+			z__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			z__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    }
+// L110:
+		}
+// L120:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0., temp.i = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			i__4 = l + i__ * a_dim1;
+			i__5 = l + j * b_dim1;
+			z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
+				.i, z__2.i = a[i__4].r * b[i__5].i + a[i__4]
+				.i * b[i__5].r;
+			z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
+			temp.r = z__1.r, temp.i = z__1.i;
+// L130:
+		    }
+		    if (beta->r == 0. && beta->i == 0.) {
+			i__3 = i__ + j * c_dim1;
+			z__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			z__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    }
+// L140:
+		}
+// L150:
+	    }
+	}
+    } else if (nota) {
+	if (conjb) {
+	    //
+	    //          Form  C := alpha*A*B**H + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (beta->r == 0. && beta->i == 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			c__[i__3].r = 0., c__[i__3].i = 0.;
+// L160:
+		    }
+		} else if (beta->r != 1. || beta->i != 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			i__4 = i__ + j * c_dim1;
+			z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__1.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+// L170:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    d_cnjg(&z__2, &b[j + l * b_dim1]);
+		    z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i =
+			    alpha->r * z__2.i + alpha->i * z__2.r;
+		    temp.r = z__1.r, temp.i = z__1.i;
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			i__4 = i__ + j * c_dim1;
+			i__5 = i__ + j * c_dim1;
+			i__6 = i__ + l * a_dim1;
+			z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
+				z__2.i = temp.r * a[i__6].i + temp.i * a[i__6]
+				.r;
+			z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i +
+				z__2.i;
+			c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
+// L180:
+		    }
+// L190:
+		}
+// L200:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		if (beta->r == 0. && beta->i == 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			c__[i__3].r = 0., c__[i__3].i = 0.;
+// L210:
+		    }
+		} else if (beta->r != 1. || beta->i != 0.) {
+		    i__2 = *m;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = i__ + j * c_dim1;
+			i__4 = i__ + j * c_dim1;
+			z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__1.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+// L220:
+		    }
+		}
+		i__2 = *k;
+		for (l = 1; l <= i__2; ++l) {
+		    i__3 = j + l * b_dim1;
+		    z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
+			    z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3]
+			    .r;
+		    temp.r = z__1.r, temp.i = z__1.i;
+		    i__3 = *m;
+		    for (i__ = 1; i__ <= i__3; ++i__) {
+			i__4 = i__ + j * c_dim1;
+			i__5 = i__ + j * c_dim1;
+			i__6 = i__ + l * a_dim1;
+			z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
+				z__2.i = temp.r * a[i__6].i + temp.i * a[i__6]
+				.r;
+			z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i +
+				z__2.i;
+			c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
+// L230:
+		    }
+// L240:
+		}
+// L250:
+	    }
+	}
+    } else if (conja) {
+	if (conjb) {
+	    //
+	    //          Form  C := alpha*A**H*B**H + beta*C.
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0., temp.i = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			d_cnjg(&z__3, &a[l + i__ * a_dim1]);
+			d_cnjg(&z__4, &b[j + l * b_dim1]);
+			z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i =
+				z__3.r * z__4.i + z__3.i * z__4.r;
+			z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
+			temp.r = z__1.r, temp.i = z__1.i;
+// L260:
+		    }
+		    if (beta->r == 0. && beta->i == 0.) {
+			i__3 = i__ + j * c_dim1;
+			z__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			z__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    }
+// L270:
+		}
+// L280:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**H*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0., temp.i = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			d_cnjg(&z__3, &a[l + i__ * a_dim1]);
+			i__4 = j + l * b_dim1;
+			z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i,
+				z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4]
+				.r;
+			z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
+			temp.r = z__1.r, temp.i = z__1.i;
+// L290:
+		    }
+		    if (beta->r == 0. && beta->i == 0.) {
+			i__3 = i__ + j * c_dim1;
+			z__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			z__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    }
+// L300:
+		}
+// L310:
+	    }
+	}
+    } else {
+	if (conjb) {
+	    //
+	    //          Form  C := alpha*A**T*B**H + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0., temp.i = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			i__4 = l + i__ * a_dim1;
+			d_cnjg(&z__3, &b[j + l * b_dim1]);
+			z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i,
+				z__2.i = a[i__4].r * z__3.i + a[i__4].i *
+				z__3.r;
+			z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
+			temp.r = z__1.r, temp.i = z__1.i;
+// L320:
+		    }
+		    if (beta->r == 0. && beta->i == 0.) {
+			i__3 = i__ + j * c_dim1;
+			z__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			z__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    }
+// L330:
+		}
+// L340:
+	    }
+	} else {
+	    //
+	    //          Form  C := alpha*A**T*B**T + beta*C
+	    //
+	    i__1 = *n;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    temp.r = 0., temp.i = 0.;
+		    i__3 = *k;
+		    for (l = 1; l <= i__3; ++l) {
+			i__4 = l + i__ * a_dim1;
+			i__5 = j + l * b_dim1;
+			z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
+				.i, z__2.i = a[i__4].r * b[i__5].i + a[i__4]
+				.i * b[i__5].r;
+			z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
+			temp.r = z__1.r, temp.i = z__1.i;
+// L350:
+		    }
+		    if (beta->r == 0. && beta->i == 0.) {
+			i__3 = i__ + j * c_dim1;
+			z__1.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__1.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    } else {
+			i__3 = i__ + j * c_dim1;
+			z__2.r = alpha->r * temp.r - alpha->i * temp.i,
+				z__2.i = alpha->r * temp.i + alpha->i *
+				temp.r;
+			i__4 = i__ + j * c_dim1;
+			z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
+				.i, z__3.i = beta->r * c__[i__4].i + beta->i *
+				 c__[i__4].r;
+			z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+			c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+		    }
+// L360:
+		}
+// L370:
+	    }
+	}
+    }
+    return 0;
+    //
+    //    End of ZGEMM .
+    //
+} // zgemm_
+

3rdparty/ffmpeg/ffmpeg.cmake

@@ -1,9 +1,9 @@
-# Binaries branch name: ffmpeg/4.x_20251226
-# Binaries were created for OpenCV: cff7581175d2abfc6aef2e4f04f482e258b5c864
-ocv_update(FFMPEG_BINARIES_COMMIT "d82ad9a54a7b42a1648a9cae8fed5c2f20ea396c")
-ocv_update(FFMPEG_FILE_HASH_BIN32 "47730de2286110b0d1250ff9cf50ce56")
-ocv_update(FFMPEG_FILE_HASH_BIN64 "3248b4663ffef770cdb54ec8b9d16a28")
-ocv_update(FFMPEG_FILE_HASH_CMAKE "8862c87496e2e8c375965e1277dee1c7")
+# Binaries branch name: ffmpeg/5.x_20260602
+# Binaries were created for OpenCV: a0a660fcb1e58a295e6caa6aee64ed4d369b0181
+ocv_update(FFMPEG_BINARIES_COMMIT "06dc20cad65dc7fcf784f70c95d46750520889a7")
+ocv_update(FFMPEG_FILE_HASH_BIN32 "9cef7a78b6f7ec8cf1a3935c058cfac5")
+ocv_update(FFMPEG_FILE_HASH_BIN64 "a821a1135251859655090c795af05789")
+ocv_update(FFMPEG_FILE_HASH_CMAKE "e09efc33312d1173be8a9446f3b088fe")
 
 function(download_win_ffmpeg script_var)
   set(${script_var} "" PARENT_SCOPE)

3rdparty/harfbuzz/CMakeLists.txt

@@ -0,0 +1,70 @@
+# ----------------------------------------------------------------------------
+#  CMake file for the bundled HarfBuzz text-shaping library. See root CMakeLists.txt
+#
+#  OpenCV vendors a minimal subset of HarfBuzz (core + HB_HAS_RASTER) as a
+#  normal static library: each .cc is a separate translation unit. The subset
+#  is produced by hb_extract.py (see that script to update HarfBuzz).
+# ----------------------------------------------------------------------------
+project(${HARFBUZZ_LIBRARY} CXX)
+
+ocv_include_directories("${CMAKE_CURRENT_SOURCE_DIR}/src")
+
+# Every .cc copied by hb_extract.py is a real translation unit (the script
+# never copies non-TU .cc files), so a plain recursive glob is exactly right.
+file(GLOB_RECURSE lib_srcs src/*.cc)
+file(GLOB_RECURSE lib_hdrs src/*.h src/*.hh)
+
+# HarfBuzz is built with HB_TINY for minimum footprint. Because we request the
+# software rasterizer (HB_HAS_RASTER, defined below), HB_TINY does NOT disable
+# the draw/paint/color APIs nor CFF (PostScript/.otf
+# outlines) -- see hb-config.hh: HB_NO_DRAW/COLOR/PAINT and the TINY->HB_NO_CFF
+# rule only trigger when no HB_HAS_* backend is requested. So CFF (CJK/Indic),
+# COLR/CPAL color and our rasterizer all survive HB_TINY.
+#
+# Two features HB_TINY (via HB_LEAN) would otherwise drop are restored through
+# HarfBuzz's config-override hook (hb-opencv-config.hh): thread-safety (HB_NO_MT)
+# and variable fonts (HB_NO_VAR). No platform backends (CoreText/DirectWrite/...).
+
+add_library(${HARFBUZZ_LIBRARY} STATIC ${OPENCV_3RDPARTY_EXCLUDE_FROM_ALL} ${lib_srcs} ${lib_hdrs})
+
+target_compile_definitions(${HARFBUZZ_LIBRARY} PRIVATE
+    HB_TINY
+    HB_HAS_RASTER   # request the software rasterizer: keeps draw/paint/color + CFF under HB_TINY
+    "HB_CONFIG_OVERRIDE_H=\"hb-opencv-config.hh\"")
+
+set_target_properties(${HARFBUZZ_LIBRARY} PROPERTIES
+  CXX_STANDARD 17
+  CXX_STANDARD_REQUIRED ON
+)
+
+ocv_warnings_disable(CMAKE_CXX_FLAGS
+    -Wunused-variable -Wunused-function -Wunused-parameter
+    -Wunused-but-set-variable    # clang15/gcc
+    -Wshadow
+    -Wmissing-declarations       # gcc
+    -Wmissing-prototypes         # clang
+    -Wimplicit-fallthrough
+    -Wextra-semi                 # clang
+    -Wdeprecated-copy            # gcc/clang
+    -Wsuggest-override
+    -Wcast-function-type
+    -Wclass-memaccess            # gcc
+    -Wexpansion-to-defined
+)
+ocv_warnings_disable(CMAKE_CXX_FLAGS /wd4244 /wd4267 /wd4127 /wd4146 /wd4456 /wd4459) # MSVC
+
+set_target_properties(${HARFBUZZ_LIBRARY}
+  PROPERTIES OUTPUT_NAME ${HARFBUZZ_LIBRARY}
+  DEBUG_POSTFIX "${OPENCV_DEBUG_POSTFIX}"
+  COMPILE_PDB_NAME ${HARFBUZZ_LIBRARY}
+  COMPILE_PDB_NAME_DEBUG "${HARFBUZZ_LIBRARY}${OPENCV_DEBUG_POSTFIX}"
+  ARCHIVE_OUTPUT_DIRECTORY ${3P_LIBRARY_OUTPUT_PATH}
+  )
+
+if(ENABLE_SOLUTION_FOLDERS)
+  set_target_properties(${HARFBUZZ_LIBRARY} PROPERTIES FOLDER "3rdparty")
+endif()
+
+if(NOT BUILD_SHARED_LIBS)
+  ocv_install_target(${HARFBUZZ_LIBRARY} EXPORT OpenCVModules ARCHIVE DESTINATION ${OPENCV_3P_LIB_INSTALL_PATH} COMPONENT dev OPTIONAL)
+endif()

3rdparty/harfbuzz/COPYING

@@ -0,0 +1,42 @@
+HarfBuzz is licensed under the so-called "Old MIT" license.  Details follow.
+For parts of HarfBuzz that are licensed under different licenses see individual
+files names COPYING in subdirectories where applicable.
+
+Copyright © 2010-2022  Google, Inc.
+Copyright © 2015-2020  Ebrahim Byagowi
+Copyright © 2019,2020  Facebook, Inc.
+Copyright © 2012,2015  Mozilla Foundation
+Copyright © 2011  Codethink Limited
+Copyright © 2008,2010  Nokia Corporation and/or its subsidiary(-ies)
+Copyright © 2009  Keith Stribley
+Copyright © 2011  Martin Hosken and SIL International
+Copyright © 2007  Chris Wilson
+Copyright © 2005,2006,2020,2021,2022,2023  Behdad Esfahbod
+Copyright © 2004,2007,2008,2009,2010,2013,2021,2022,2023  Red Hat, Inc.
+Copyright © 1998-2005  David Turner and Werner Lemberg
+Copyright © 2016  Igalia S.L.
+Copyright © 2022  Matthias Clasen
+Copyright © 2018,2021  Khaled Hosny
+Copyright © 2018,2019,2020  Adobe, Inc
+Copyright © 2013-2015  Alexei Podtelezhnikov
+
+For full copyright notices consult the individual files in the package.
+
+
+Permission is hereby granted, without written agreement and without
+license or royalty fees, to use, copy, modify, and distribute this
+software and its documentation for any purpose, provided that the
+above copyright notice and the following two paragraphs appear in
+all copies of this software.
+
+IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+DAMAGE.
+
+THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.

3rdparty/harfbuzz/README.md

@@ -0,0 +1,220 @@
+# HarfBuzz
+
+<div align="center">
+
+<p><img src="HarfBuzz.png" alt="HarfBuzz Logo" width="256"/></p>
+
+[![Linux CI Status](https://github.com/harfbuzz/harfbuzz/actions/workflows/linux.yml/badge.svg)](https://github.com/harfbuzz/harfbuzz/actions/workflows/linux.yml)
+[![macoOS CI Status](https://github.com/harfbuzz/harfbuzz/actions/workflows/macos.yml/badge.svg)](https://github.com/harfbuzz/harfbuzz/actions/workflows/macos.yml)
+[![Windows CI Status](https://github.com/harfbuzz/harfbuzz/actions/workflows/msvc.yml/badge.svg)](https://github.com/harfbuzz/harfbuzz/actions/workflows/msvc.yml)
+[![OSS-Fuzz Status](https://oss-fuzz-build-logs.storage.googleapis.com/badges/harfbuzz.svg)](https://oss-fuzz-build-logs.storage.googleapis.com/index.html#harfbuzz)
+[![Coverity Scan Build Status](https://scan.coverity.com/projects/15166/badge.svg)](https://scan.coverity.com/projects/harfbuzz)
+[![Packaging status](https://repology.org/badge/tiny-repos/harfbuzz.svg)](https://repology.org/project/harfbuzz/versions)
+[![OpenSSF Scorecard](https://api.securityscorecards.dev/projects/github.com/harfbuzz/harfbuzz/badge)](https://securityscorecards.dev/viewer/?uri=github.com/harfbuzz/harfbuzz)
+
+</div>
+
+HarfBuzz started as a text shaping engine but has grown into a
+full font platform — the `ffmpeg` of text shaping.  It primarily
+supports [OpenType][1], but also [Apple Advanced Typography][2].
+
+HarfBuzz shapes the majority of text on modern screens.
+
+HarfBuzz is optimized for robustness, correctness, and performance
+— in that order. Achieve all.
+
+**[Try it live at harfbuzz-world.cc](https://harfbuzz-world.cc/)** — an interactive playground for shaping, subsetting, rasterization, vector output, and GPU rendering, all running in your browser.
+
+Here is a quick map of its components:
+
+### Core libraries
+
+| Library | Description |
+|---------|-------------|
+| **libharfbuzz** | Text shaping, draw API, paint API. Highly configurable (see [CONFIG.md](CONFIG.md)). Optional integration backends compiled in: hb-ft (FreeType), hb-coretext (macOS), hb-uniscribe (Windows), hb-directwrite (Windows), hb-gdi (Windows), hb-glib, hb-graphite2. |
+| **libharfbuzz-subset** | Font subsetting and variable-font instancing. |
+
+### Auxiliary libraries
+
+| Library | Description |
+|---------|-------------|
+| **libharfbuzz-icu** | ICU Unicode integration. |
+| **libharfbuzz-cairo** | Cairo rendering integration. |
+| **libharfbuzz-gobject** | GObject/GI bindings. |
+
+### Experimental libraries
+
+| Library | Description |
+|---------|-------------|
+| **libharfbuzz-raster** | Glyph rasterization to bitmaps, including color fonts. Uses hb-draw and hb-paint. |
+| **libharfbuzz-vector** | Glyph output to vector formats (currently SVG), including color fonts. Uses hb-draw and hb-paint. |
+| **libharfbuzz-gpu** | Encodes glyph outlines for GPU rasterization (Slug algorithm). Provides shader sources in GLSL, WGSL, MSL, and HLSL. [Live demo.](https://harfbuzz.github.io/hb-gpu-demo/) |
+
+Notable missing feature: font hinting (including autohinting)
+is not implemented.  For hinted rasterization, use FreeType or
+Skrifa.
+
+For simplified builds, amalgamated sources are available:
+`harfbuzz.cc` (just libharfbuzz), `harfbuzz-subset.cc` (just
+libharfbuzz-subset), or `harfbuzz-world.cc` (everything, driven
+by a custom `hb-features.h`).  For a live in-browser playground
+plus a worked example of the world.cc single-file build, see
+[harfbuzz-world.cc][26].
+
+### Command-line tools
+
+| Tool | Description |
+|------|-------------|
+| **hb-shape** | Shape text and display glyph output. |
+| **hb-view** | Render shaped text to an image. |
+| **hb-subset** | Subset and optimize fonts. |
+| **hb-info** | Display font metadata. |
+| **hb-raster** | Render glyphs to bitmap images. |
+| **hb-vector** | Render glyphs to vector formats (SVG). |
+| **hb-gpu** | Interactive GPU text rendering. |
+
+The canonical source tree and bug trackers are available on [github][4].
+Both development and user support discussion around HarfBuzz happen on
+[github][4] as well.
+
+For license information, see [COPYING](COPYING).
+
+## API stability
+
+The API that comes with `hb.h` will not change incompatibly. Other, peripheral,
+headers are more likely to go through minor modifications, but again, we do our
+best to never change API in an incompatible way. We will never break the ABI.
+
+The API and ABI are stable even across major version number jumps. In fact,
+current HarfBuzz is API/ABI compatible all the way back to the 0.9.x series.
+If one day we need to break the API/ABI, that would be called a new library.
+
+As such, we bump the major version number only when we add major new features,
+the minor version when there is new API, and the micro version when there
+are bug fixes.
+
+## Documentation
+
+For user manual as well as API documentation, check: https://harfbuzz.github.io
+
+## Download
+
+Tarball releases and Win32/Win64 binary bundles are available on the
+[github releases][3] page.
+
+## Development
+
+For build information, see [BUILD.md](BUILD.md).
+
+For custom configurations, see [CONFIG.md](CONFIG.md).
+
+For testing and profiling, see [TESTING.md](TESTING.md).
+
+For using with Python, see [README.python.md](README.python.md). There is also [uharfbuzz](https://github.com/harfbuzz/uharfbuzz).
+
+For cross-compiling to Windows from Linux or macOS, see [README.mingw.md](README.mingw.md).
+
+To report bugs or submit patches please use [github][4] issues and pull-requests.
+
+### Developer documents
+
+To get a better idea of where HarfBuzz stands in the text rendering stack you
+may want to read [State of Text Rendering 2024][6].
+Here are a few presentation slides about HarfBuzz over the years:
+
+- 2026 – [HarfBuzz at 20!][25]
+- 2016 – [Ten Years of HarfBuzz][20]
+- 2014 – [Unicode, OpenType, and HarfBuzz: Closing the Circle][7]
+- 2012 – [HarfBuzz, The Free and Open Text Shaping Engine][8]
+- 2009 – [HarfBuzz: the Free and Open Shaping Engine][9]
+
+More presentations and papers are available on [behdad][11]'s website.
+In particular, the following _studies_ are relevant to HarfBuzz development:
+
+- 2025 – [AAT layout caches][24]
+- 2025 – [OpenType Layout lookup caches][23]
+- 2025 – [Introducing HarfRust][22]
+- 2025 – [Subsetting][21]
+- 2025 – [Caching][12]
+- 2025 – [`hb-decycler`][13]
+- 2022 – [`hb-iter`][14]
+- 2022 – [A C library written in C++][15]
+- 2022 – [The case of the slow `hb-ft` `>h_advance` function][18]
+- 2022 – [PackTab: A static integer table packer][16]
+- 2020 – [HarfBuzz OT+AAT "Unishaper"][19]
+- 2014 – [Building the Indic Shaper][17]
+- 2012 – [Memory Consumption][10]
+
+
+## Name
+
+HarfBuzz /hærfˈbɒːz/
+
+From Persian حرف (*Harf*: letter) and باز (*Buzz*: open).
+Transliteration of the Persian calque for *OpenType*.
+
+As a noun: *The* Open Source *text shaping* engine.
+
+As an adjective: Insincerely talkative; glib. A nod to the
+GNOME project where HarfBuzz originates from.
+
+The logo shows حرف‌باز in the IranNastaliq font, on a Damascus
+steel background.
+
+> Background: Originally there was this font format called TrueType. People and
+> companies started calling their type engines all things ending in Type:
+> FreeType, CoolType, ClearType, etc. And then came OpenType, which is the
+> successor of TrueType. So, for my OpenType implementation, I decided to stick
+> with the concept but use the Persian translation. Which is fitting given that
+> Persian is written in the Arabic script, and OpenType is an extension of
+> TrueType that adds support for complex script rendering, and HarfBuzz is an
+> implementation of OpenType text shaping.
+
+## Users
+
+HarfBuzz is used in Android, Chrome, ChromeOS, Firefox, Flutter, GNOME, GTK+, KDE,
+Qt, LibreOffice, OpenJDK, XeTeX, Adobe Photoshop, Illustrator, InDesign,
+Microsoft Edge, Amazon Kindle, PlayStation, Godot Engine, Unreal Engine,
+Figma, Canva, QuarkXPress, Scribus, smart TVs,
+car displays, and many other places.
+
+<p align="center">
+  <a href="https://xkcd.com/2347/" rel="nofollow">
+    <img src="xkcd.png" width="256" alt="xkcd-derived image">
+  </a>
+</p>
+
+## Distribution
+
+<details>
+  <summary>Packaging status of HarfBuzz</summary>
+
+[![Packaging status](https://repology.org/badge/vertical-allrepos/harfbuzz.svg?header=harfbuzz)](https://repology.org/project/harfbuzz/versions)
+
+</details>
+
+[1]: https://docs.microsoft.com/en-us/typography/opentype/spec/
+[2]: https://developer.apple.com/fonts/TrueType-Reference-Manual/RM06/Chap6AATIntro.html
+[3]: https://github.com/harfbuzz/harfbuzz/releases
+[4]: https://github.com/harfbuzz/harfbuzz
+[6]: https://behdad.org/text2024
+[7]: https://docs.google.com/presentation/d/1x97pfbB1gbD53Yhz6-_yBUozQMVJ_5yMqqR_D-R7b7I/preview
+[8]: https://docs.google.com/presentation/d/1ySTZaXP5XKFg0OpmHZM00v5b17GSr3ojnzJekl4U8qI/preview
+[9]: https://behdad.org/doc/harfbuzz2009-slides.pdf
+[10]: https://docs.google.com/document/d/12jfNpQJzeVIAxoUSpk7KziyINAa1msbGliyXqguS86M/preview
+[11]: https://behdad.org/
+[12]: https://docs.google.com/document/d/1_VgObf6Je0J8byMLsi7HCQHnKo2emGnx_ib_sHo-bt4/preview
+[13]: https://docs.google.com/document/d/1Y-u08l9YhObRVObETZt1k8f_5lQdOix9TRH3zEXaoAw/preview
+[14]: https://docs.google.com/document/d/1o-xvxCbgMe9JYFHLVnPjk01ZY_8Cj0vB9-KTI1d0nyk/preview
+[15]: https://docs.google.com/document/d/18hI56KJpvXtwWbc9QSaz9zzhJwIMnrJ-zkAaKS-W-8k/preview
+[16]: https://docs.google.com/document/d/1Xq3owVt61HVkJqbLFHl73il6pcTy6PdPJJ7bSouQiQw/preview
+[17]: https://docs.google.com/document/d/1wMPwVNBvsIriamcyBO5aNs7Cdr8lmbwLJ8GmZBAswF4/preview
+[18]: https://docs.google.com/document/d/1wskYbA-czBt57oH9gEuGf3sWbTx7bfOiEIcDs36-heo/preview
+[19]: https://prezi.com/view/THNPJGFVDUCWoM20syev/
+[20]: https://behdad.org/doc/harfbuzz10years-slides.pdf
+[21]: https://docs.google.com/document/d/1_vZrt97OorJ0jA1YzJ29LRcGr3YGrNJANdOABjVZGEs/preview
+[22]: https://docs.google.com/document/d/1aH_waagdEM5UhslQxCeFEb82ECBhPlZjy5_MwLNLBYo/preview
+[23]: https://docs.google.com/document/d/1hRd5oYQJLrt0JuwWhEJWi7wh_9rbaIJkX6IR9DW7rZQ/preview
+[24]: https://docs.google.com/document/d/1a3K6fHjsiWW36vSzwJwCwEBOgznunKs80PSpBbpfHiA/preview
+[25]: https://docs.google.com/presentation/d/1o9Exz1c-Lr-dJjA8dcBn_Vl_Y37cupmFzmclMjBE_Bc/view
+[26]: https://harfbuzz-world.cc/

3rdparty/harfbuzz/hb_extract.py

@@ -0,0 +1,386 @@
+#!/usr/bin/env python3
+"""
+hb_extract.py -- copy the minimal subset of HarfBuzz sources used by OpenCV.
+
+OpenCV vendors HarfBuzz as a normal static library: every .cc is a separate
+translation unit (no unity / amalgamation build). This script reproduces the
+exact src/ tree that OpenCV ships, from a pristine HarfBuzz checkout.
+
+It does three things beyond a naive copy, all to keep the vendored tree small
+and buildable with OpenCV's configuration (HB_TINY + HB_HAS_RASTER, see
+CMakeLists.txt):
+
+  1. Copies the translation units that upstream `harfbuzz-world.cc` would
+     compile for the requested HB_HAS_* sections -- EXCEPT the ones that build
+     to an empty object under our config (see EMPTY_TUS). It never emits
+     `harfbuzz-world.cc` itself (we compile each .cc directly), and never
+     copies non-TU .cc files found under src/OT|graph (only real TUs from the
+     parsed world.cc lists are copied), so CMake's file(GLOB_RECURSE src/*.cc)
+     picks up exactly the right set.
+
+  2. Prunes headers down to the set actually reachable by #include from the
+     copied TUs (+ the public headers OpenCV includes). This automatically
+     drops the large amount of HarfBuzz src/ that we never compile -- GPU and
+     WASM backends, the subset/repacker graph, platform backends (CoreText/
+     DirectWrite/GDI/Uniscribe/Graphite2/GObject/Cairo), the vector-paint
+     backend, and headers used only by the skipped empty TUs -- without a
+     hardcoded blocklist.
+
+  3. Generates `hb-opencv-config.hh`, the config-override header CMakeLists.txt
+     points HB_CONFIG_OVERRIDE_H at. It re-enables thread-safety (HB_NO_MT) and
+     variable fonts (HB_NO_VAR) that HB_TINY would otherwise switch off. (It
+     does NOT generate upstream's hb-features.h: nothing we compile includes
+     it.)
+
+Usage (to refresh this very directory, just point it at a harfbuzz checkout):
+  python hb_extract.py path/to/harfbuzz
+
+  The defaults already produce the OpenCV subset: output '.', features
+  HB_HAS_RASTER, and it also copies README.md + COPYING. Override only if needed:
+    -o DIR              output root (default '.')
+    -f FLAGS            comma-separated HB_HAS_* (default HB_HAS_RASTER)
+    -a FILES            extra files (default README.md,COPYING)
+    --list-flags        print available HB_HAS_* flags and exit
+
+-a paths are relative to the harfbuzz repo root (parent of src/):
+  -a README.md            -> copied to   <out>/README.md
+  -a COPYING              -> copied to   <out>/COPYING
+  -a src/hb-raster.h      -> copied to   <out>/src/hb-raster.h
+"""
+
+import argparse
+import posixpath
+import re
+import shutil
+import sys
+from pathlib import Path
+
+
+# Translation units that compile to an EMPTY object (libtool: "has no symbols")
+# under OpenCV's HarfBuzz configuration (HB_TINY + HB_HAS_RASTER => AAT, legacy
+# fallback shaping, math, meta, name, buffer (de)serialize/verify and the style
+# API are all compiled out). They contribute nothing, so we do not vendor them.
+# Re-derive this list (from the libtool warnings of a clean libharfbuzz build)
+# if the HarfBuzz configuration in CMakeLists.txt changes.
+EMPTY_TUS = {
+    "hb-aat-layout.cc",
+    "hb-aat-map.cc",
+    "hb-buffer-serialize.cc",
+    "hb-buffer-verify.cc",
+    "hb-fallback-shape.cc",
+    "hb-ot-math.cc",
+    "hb-ot-meta.cc",
+    "hb-ot-name.cc",
+    "hb-raster.cc",
+    "hb-style.cc",
+}
+
+# Public headers OpenCV's text engine (drawing_text.cpp) includes directly.
+# Used together with the copied TUs as the roots of the header-reachability
+# prune.
+SEED_PUBLIC_HEADERS = ("hb.h", "hb-ot.h", "hb-raster.h")
+
+# Generated config-override header. CMakeLists.txt builds HarfBuzz with HB_TINY
+# and HB_CONFIG_OVERRIDE_H="hb-opencv-config.hh"; this file is included by
+# hb-config.hh after HB_TINY/HB_LEAN expand (so the #undef takes effect) but
+# before the option-closure derives dependent macros.
+OPENCV_CONFIG_HH = '''\
+/*
+ * OpenCV-specific HarfBuzz configuration override.  GENERATED by hb_extract.py.
+ *
+ * HarfBuzz is built with HB_TINY (see 3rdparty/harfbuzz/CMakeLists.txt) for the
+ * smallest possible footprint. HB_TINY pulls in HB_LEAN + HB_MINI, which would
+ * disable two features that OpenCV's text engine relies on. We restore them
+ * here.
+ *
+ * This file is included by hb-config.hh via HB_CONFIG_OVERRIDE_H, i.e. AFTER
+ * HB_TINY/HB_LEAN/HB_MINI have expanded their macros (so the #undef below takes
+ * effect) but BEFORE the "closure of options" derives dependent macros (e.g.
+ * HB_NO_VAR_COMPOSITES from HB_NO_VAR). That ordering is what makes a plain
+ * #undef sufficient.
+ *
+ *   HB_NO_MT  - keep thread-safety. hb_font_t instances live inside cv::FontFace
+ *               objects, NOT in the thread_local FontRenderEngine, so a single
+ *               FontFace (and its hb_font_t) can be shared across threads; its
+ *               reference counting must stay atomic.
+ *
+ *   HB_NO_VAR - keep variable-font support: the 'wght' axis used for synthetic
+ *               weights and named-instance/axis queries (hb_font_set_variations,
+ *               hb_ot_var_*). Variable fonts are a primary reason OpenCV adopted
+ *               HarfBuzz, so this must remain enabled.
+ */
+
+#undef HB_NO_MT
+#undef HB_NO_VAR
+'''
+
+OPENCV_CONFIG_NAME = "hb-opencv-config.hh"
+
+
+def parse_world_cc(path):
+    """Return (core_files, sections) parsed from harfbuzz-world.cc.
+
+    core_files -- list of .cc paths (relative to src/) in the unconditional
+                  "Core library" section.
+    sections   -- dict HB_HAS_XXX -> list of .cc paths from that #ifdef block.
+    """
+    lines = path.read_text(encoding="utf-8").splitlines()
+    include_re = re.compile(r'^\s*#include\s+"([^"]+\.cc)"')
+
+    core_files = []
+    sections = {}
+
+    STATE_PREAMBLE, STATE_CORE, STATE_IFDEF = "preamble", "core", "ifdef"
+    state = STATE_PREAMBLE
+    current_flag = None
+    ifdef_depth = 0
+
+    for line in lines:
+        if state == STATE_PREAMBLE:
+            if "/* Core library." in line:
+                state = STATE_CORE
+
+        elif state == STATE_CORE:
+            m = include_re.match(line)
+            if m:
+                core_files.append(m.group(1))
+            else:
+                m = re.match(r"^\s*#ifdef\s+(HB_HAS_\w+)", line)
+                if m:
+                    current_flag = m.group(1)
+                    sections[current_flag] = []
+                    state = STATE_IFDEF
+                    ifdef_depth = 1
+
+        elif state == STATE_IFDEF:
+            if re.match(r"^\s*#if", line):
+                ifdef_depth += 1
+            elif re.match(r"^\s*#endif", line):
+                ifdef_depth -= 1
+                if ifdef_depth == 0:
+                    state = STATE_CORE
+                    current_flag = None
+            else:
+                m = include_re.match(line)
+                if m and current_flag is not None:
+                    sections[current_flag].append(m.group(1))
+
+    return core_files, sections
+
+
+def copy_files(file_list, src_dir, out_src_dir, label=""):
+    skipped = []
+    for rel in file_list:
+        if Path(rel).name in EMPTY_TUS:
+            skipped.append(rel)
+            continue
+        src = src_dir / rel
+        dst = out_src_dir / rel
+        dst.parent.mkdir(parents=True, exist_ok=True)
+        if not src.exists():
+            print(f"  [WARN] not found: {src}", file=sys.stderr)
+            continue
+        shutil.copy2(src, dst)
+        print(f"  [{label or 'core'}] src/{rel}")
+    for rel in skipped:
+        print(f"  [skip-empty] src/{rel}")
+
+
+def copy_headers(src_dir, out_src_dir, public_h=True):
+    """Copy all candidate headers: src/*.hh, src/*.h (public API), and *.h/*.hh
+    from src/OT/** and src/graph/**. The unreferenced ones are removed later by
+    prune_unreferenced_headers().
+
+    NOTE: .cc files under OT/ and graph/ are intentionally NOT copied here --
+    the only ones we need are real translation units, copied via the parsed
+    world.cc lists. Copying e.g. src/graph/test-classdef-graph.cc would make
+    CMake's file(GLOB_RECURSE src/*.cc) try to compile a non-TU file.
+    """
+    count = 0
+
+    def _copy(p):
+        nonlocal count
+        dst = out_src_dir / p.relative_to(src_dir)
+        dst.parent.mkdir(parents=True, exist_ok=True)
+        shutil.copy2(p, dst)
+        count += 1
+
+    for hdr in src_dir.glob("*.hh"):
+        _copy(hdr)
+
+    for subdir in ("OT", "graph"):
+        d = src_dir / subdir
+        if not d.exists():
+            continue
+        for hdr in d.rglob("*"):
+            if hdr.is_file() and hdr.suffix in (".h", ".hh"):
+                _copy(hdr)
+
+    if public_h:
+        for hdr in src_dir.glob("*.h"):
+            _copy(hdr)
+
+    return count
+
+
+def prune_unreferenced_headers(out_src_dir):
+    """Delete every header not reachable by #include from the copied TUs and the
+    public seed headers, then drop any directory left empty.
+
+    HarfBuzz's amalgamated src/ ships many headers we never compile (GPU/WASM
+    backends, subset/repacker graph, platform backends, vector-paint, and the
+    headers used only by the empty TUs we skip). Reachability removes them all
+    without a hardcoded list. The edge regex also treats any quoted "...h"/
+    "...hh" literal as an include, which covers the `#include HB_STRING_ARRAY_LIST`
+    macro-indirection trick (e.g. hb-ot-cff1-std-str.hh, hb-ot-post-macroman.hh).
+    """
+    files = {p.relative_to(out_src_dir).as_posix()
+             for p in out_src_dir.rglob("*") if p.is_file()}
+    headers = {f for f in files if f.endswith((".h", ".hh"))}
+    edge_re = re.compile(r'#\s*include\s+["<]([^">]+)[">]|"([^"]+\.hh?)"')
+
+    def resolve(inc, including):
+        for cand in (posixpath.normpath(posixpath.join(posixpath.dirname(including), inc)),
+                     posixpath.normpath(inc)):
+            if cand in files:
+                return cand
+        return None
+
+    seeds = {f for f in files if f.endswith(".cc")}
+    seeds |= {h for h in SEED_PUBLIC_HEADERS if h in files}
+
+    seen, stack = set(), list(seeds)
+    while stack:
+        cur = stack.pop()
+        if cur in seen:
+            continue
+        seen.add(cur)
+        try:
+            txt = (out_src_dir / cur).read_text(encoding="utf-8", errors="ignore")
+        except OSError:
+            continue
+        for m in edge_re.finditer(txt):
+            inc = m.group(1) or m.group(2)
+            r = resolve(inc, cur)
+            if r and r not in seen:
+                stack.append(r)
+
+    needed = {f for f in seen if f.endswith((".h", ".hh"))}
+    for h in sorted(headers - needed):
+        (out_src_dir / h).unlink()
+        print(f"  [prune] src/{h}")
+
+    # remove directories left empty by pruning (deepest first)
+    for d in sorted((p for p in out_src_dir.rglob("*") if p.is_dir()),
+                    key=lambda p: len(p.parts), reverse=True):
+        try:
+            d.rmdir()
+        except OSError:
+            pass
+
+    return len(headers - needed), len(needed)
+
+
+def write_opencv_config_h(out_src_dir):
+    """Generate hb-opencv-config.hh (the HB_CONFIG_OVERRIDE_H header)."""
+    (out_src_dir / OPENCV_CONFIG_NAME).write_text(OPENCV_CONFIG_HH, encoding="utf-8")
+    print(f"  [gen] src/{OPENCV_CONFIG_NAME}")
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description="Copy the OpenCV subset of HarfBuzz sources.",
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+        epilog="""
+examples:
+  python hb_extract.py ~/work/harfbuzz -o . -f HB_HAS_RASTER -a README.md,COPYING
+  python hb_extract.py ~/work/harfbuzz --list-flags
+        """,
+    )
+    parser.add_argument("harfbuzz_dir", metavar="harfbuzz-dir",
+                        help="path to the harfbuzz repo root (contains src/)")
+    parser.add_argument("-o", "--output", metavar="DIR", default=".",
+                        help="output root directory; sources go into DIR/src/ "
+                             "(default: current directory)")
+    parser.add_argument("-f", "--features", metavar="FLAGS", default="HB_HAS_RASTER",
+                        help="comma-separated HB_HAS_* flags (default: HB_HAS_RASTER)")
+    parser.add_argument("-a", "--add", metavar="FILES", default="README.md,COPYING",
+                        help="comma-separated files relative to the harfbuzz repo "
+                             "root (default: README.md,COPYING)")
+    parser.add_argument("--no-public-headers", action="store_true",
+                        help="skip copying public src/*.h API headers "
+                             "(OT/, graph/, *.hh are always copied)")
+    parser.add_argument("--list-flags", action="store_true",
+                        help="list available HB_HAS_* flags and exit")
+    args = parser.parse_args()
+
+    repo_dir = Path(args.harfbuzz_dir).resolve()
+    world_cc_path = repo_dir / "src" / "harfbuzz-world.cc"
+    if not world_cc_path.exists():
+        print(f"error: {world_cc_path} not found", file=sys.stderr)
+        sys.exit(1)
+
+    src_dir = world_cc_path.parent
+    core_files, sections = parse_world_cc(world_cc_path)
+
+    if args.list_flags:
+        for flag, files in sorted(sections.items()):
+            print(f"  {flag:<22}  ({len(files)} .cc files)")
+        return
+
+    enabled_flags = [f.strip() for f in args.features.split(",") if f.strip()]
+    extra_files = [f.strip() for f in args.add.split(",") if f.strip()]
+
+    out_dir = Path(args.output).resolve()
+    out_src_dir = out_dir / "src"
+
+    # Start from a clean src/ so removed-upstream files do not linger.
+    if out_src_dir.exists():
+        shutil.rmtree(out_src_dir)
+    out_src_dir.mkdir(parents=True, exist_ok=True)
+
+    print(f"\nsource : {repo_dir}")
+    print(f"output : {out_dir}")
+    print(f"flags  : {enabled_flags}\n")
+
+    print("core:")
+    copy_files(core_files, src_dir, out_src_dir)
+
+    for flag in enabled_flags:
+        flag_files = sections.get(flag)
+        if not flag_files:
+            print(f"\n[{flag}]: no .cc files (flag not found in harfbuzz-world.cc)")
+            continue
+        print(f"\n[{flag}]:")
+        copy_files(flag_files, src_dir, out_src_dir, label=flag)
+
+    if extra_files:
+        print("\nextra:")
+        for rel in extra_files:
+            src = repo_dir / rel
+            dst = out_dir / rel
+            dst.parent.mkdir(parents=True, exist_ok=True)
+            if not src.exists():
+                print(f"  [WARN] not found: {src}", file=sys.stderr)
+                continue
+            shutil.copy2(src, dst)
+            print(f"  [add] {rel}")
+
+    n = copy_headers(src_dir, out_src_dir,
+                     public_h=not args.no_public_headers)
+    print(f"\nheaders: {n} files copied")
+
+    print("\nprune (unreferenced headers):")
+    removed, kept = prune_unreferenced_headers(out_src_dir)
+    print(f"  removed {removed}, kept {kept}")
+
+    print("\ngenerated:")
+    write_opencv_config_h(out_src_dir)
+
+    all_cc = sorted(out_src_dir.rglob("*.cc"))
+    all_h = list(out_src_dir.rglob("*.h")) + list(out_src_dir.rglob("*.hh"))
+    print(f"\ndone: {len(all_cc)} .cc  |  {len(all_h)} headers  ->  {out_dir}")
+
+
+if __name__ == "__main__":
+    main()

3rdparty/harfbuzz/src/OT/Color/CPAL/CPAL.hh

@@ -0,0 +1,367 @@
+/*
+ * Copyright © 2016  Google, Inc.
+ * Copyright © 2018  Ebrahim Byagowi
+ *
+ *  This is part of HarfBuzz, a text shaping library.
+ *
+ * Permission is hereby granted, without written agreement and without
+ * license or royalty fees, to use, copy, modify, and distribute this
+ * software and its documentation for any purpose, provided that the
+ * above copyright notice and the following two paragraphs appear in
+ * all copies of this software.
+ *
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+ * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+ * DAMAGE.
+ *
+ * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+ * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+ * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ * Google Author(s): Sascha Brawer
+ */
+
+#ifndef OT_COLOR_CPAL_CPAL_HH
+#define OT_COLOR_CPAL_CPAL_HH
+
+#include "../../../hb-open-type.hh"
+#include "../../../hb-ot-color.h"
+#include "../../../hb-ot-name.h"
+
+
+/*
+ * CPAL -- Color Palette
+ * https://docs.microsoft.com/en-us/typography/opentype/spec/cpal
+ */
+#define HB_OT_TAG_CPAL HB_TAG('C','P','A','L')
+
+namespace OT {
+
+
+struct CPALV1Tail
+{
+  friend struct CPAL;
+
+  private:
+  hb_ot_color_palette_flags_t get_palette_flags (const void *base,
+						 unsigned int palette_index,
+						 unsigned int palette_count) const
+  {
+    if (!paletteFlagsZ) return HB_OT_COLOR_PALETTE_FLAG_DEFAULT;
+    return (hb_ot_color_palette_flags_t) (uint32_t)
+	   (base+paletteFlagsZ).as_array (palette_count)[palette_index];
+  }
+
+  hb_ot_name_id_t get_palette_name_id (const void *base,
+				       unsigned int palette_index,
+				       unsigned int palette_count) const
+  {
+    if (!paletteLabelsZ) return HB_OT_NAME_ID_INVALID;
+    return (base+paletteLabelsZ).as_array (palette_count)[palette_index];
+  }
+
+  hb_ot_name_id_t get_color_name_id (const void *base,
+				     unsigned int color_index,
+				     unsigned int color_count) const
+  {
+    if (!colorLabelsZ) return HB_OT_NAME_ID_INVALID;
+    return (base+colorLabelsZ).as_array (color_count)[color_index];
+  }
+
+  public:
+  void collect_name_ids (const void *base,
+                         unsigned palette_count,
+                         unsigned color_count,
+                         const hb_map_t *color_index_map,
+                         hb_set_t *nameids_to_retain /* OUT */) const
+  {
+    if (paletteLabelsZ)
+    {
+      + (base+paletteLabelsZ).as_array (palette_count)
+      | hb_sink (nameids_to_retain)
+      ;
+    }
+
+    if (colorLabelsZ)
+    {
+      const hb_array_t<const NameID> colorLabels = (base+colorLabelsZ).as_array (color_count);
+      for (unsigned i = 0; i < color_count; i++)
+      {
+        if (!color_index_map->has (i)) continue;
+        nameids_to_retain->add (colorLabels[i]);
+      }
+    }
+  }
+
+  bool serialize (hb_serialize_context_t *c,
+                  unsigned palette_count,
+                  unsigned color_count,
+                  const void *base,
+                  const hb_map_t *color_index_map) const
+  {
+    TRACE_SERIALIZE (this);
+    auto *out = c->allocate_size<CPALV1Tail> (static_size);
+    if (unlikely (!out)) return_trace (false);
+
+    out->paletteFlagsZ = 0;
+    if (paletteFlagsZ)
+      out->paletteFlagsZ.serialize_copy (c, paletteFlagsZ, base, 0, hb_serialize_context_t::Head, palette_count);
+
+    out->paletteLabelsZ = 0;
+    if (paletteLabelsZ)
+      out->paletteLabelsZ.serialize_copy (c, paletteLabelsZ, base, 0, hb_serialize_context_t::Head, palette_count);
+
+    const hb_array_t<const NameID> colorLabels = (base+colorLabelsZ).as_array (color_count);
+    if (colorLabelsZ)
+    {
+      c->push ();
+      for (unsigned i = 0; i < color_count; i++)
+      {
+        if (!color_index_map->has (i)) continue;
+        if (!c->copy<NameID> (colorLabels[i]))
+        {
+          c->pop_discard ();
+          return_trace (false);
+        }
+      }
+      c->add_link (out->colorLabelsZ, c->pop_pack ());
+    }
+    return_trace (true);
+  }
+
+  bool sanitize (hb_sanitize_context_t *c,
+		 const void *base,
+		 unsigned int palette_count,
+		 unsigned int color_count) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+		  (!paletteFlagsZ  || (base+paletteFlagsZ).sanitize (c, palette_count)) &&
+		  (!paletteLabelsZ || (base+paletteLabelsZ).sanitize (c, palette_count)) &&
+		  (!colorLabelsZ   || (base+colorLabelsZ).sanitize (c, color_count)));
+  }
+
+  protected:
+  // TODO(garretrieger): these offsets can hold nulls so we should not be using non-null offsets
+  //                     here. Currently they are needed since UnsizedArrayOf doesn't define null_size
+  NNOffset32To<UnsizedArrayOf<HBUINT32>>
+		paletteFlagsZ;		/* Offset from the beginning of CPAL table to
+					 * the Palette Type Array. Set to 0 if no array
+					 * is provided. */
+  NNOffset32To<UnsizedArrayOf<NameID>>
+		paletteLabelsZ;		/* Offset from the beginning of CPAL table to
+					 * the palette labels array. Set to 0 if no
+					 * array is provided. */
+  NNOffset32To<UnsizedArrayOf<NameID>>
+		colorLabelsZ;		/* Offset from the beginning of CPAL table to
+					 * the color labels array. Set to 0
+					 * if no array is provided. */
+  public:
+  DEFINE_SIZE_STATIC (12);
+};
+
+typedef HBUINT32 BGRAColor;
+
+struct CPAL
+{
+  static constexpr hb_tag_t tableTag = HB_OT_TAG_CPAL;
+
+  bool has_data () const { return numPalettes; }
+
+  size_t get_size () const
+  { return min_size + numPalettes * sizeof (colorRecordIndicesZ[0]); }
+
+  unsigned int get_palette_count () const { return numPalettes; }
+  unsigned int   get_color_count () const { return numColors; }
+
+  hb_ot_color_palette_flags_t get_palette_flags (unsigned int palette_index) const
+  { return v1 ().get_palette_flags (this, palette_index, numPalettes); }
+
+  hb_ot_name_id_t get_palette_name_id (unsigned int palette_index) const
+  { return v1 ().get_palette_name_id (this, palette_index, numPalettes); }
+
+  hb_ot_name_id_t get_color_name_id (unsigned int color_index) const
+  { return v1 ().get_color_name_id (this, color_index, numColors); }
+
+  hb_array_t<const BGRAColor> get_palette_colors (unsigned int palette_index) const
+  {
+    if (unlikely (palette_index >= numPalettes))
+      return hb_array_t<const BGRAColor> ();
+    unsigned int start_index = colorRecordIndicesZ[palette_index];
+    hb_array_t<const BGRAColor> all_colors ((this+colorRecordsZ).arrayZ, numColorRecords);
+    return all_colors.sub_array (start_index, numColors);
+  }
+  unsigned int get_palette_colors (unsigned int  palette_index,
+				   unsigned int  start_offset,
+				   unsigned int *color_count, /* IN/OUT.  May be NULL. */
+				   hb_color_t   *colors       /* OUT.     May be NULL. */) const
+  {
+    if (unlikely (palette_index >= numPalettes))
+    {
+      if (color_count) *color_count = 0;
+      return 0;
+    }
+    unsigned int start_index = colorRecordIndicesZ[palette_index];
+    hb_array_t<const BGRAColor> all_colors ((this+colorRecordsZ).arrayZ, numColorRecords);
+    hb_array_t<const BGRAColor> palette_colors = all_colors.sub_array (start_index,
+								       numColors);
+    if (color_count)
+    {
+      + palette_colors.sub_array (start_offset, color_count)
+      | hb_sink (hb_array (colors, *color_count))
+      ;
+    }
+    return numColors;
+  }
+
+  void collect_name_ids (const hb_map_t *color_index_map,
+                         hb_set_t *nameids_to_retain /* OUT */) const
+  {
+    if (version == 1)
+    {
+      hb_barrier ();
+      v1 ().collect_name_ids (this, numPalettes, numColors, color_index_map, nameids_to_retain);
+    }
+  }
+
+  private:
+  const CPALV1Tail& v1 () const
+  {
+    if (version == 0) return Null (CPALV1Tail);
+    hb_barrier ();
+    return StructAfter<CPALV1Tail> (*this);
+  }
+
+  public:
+  bool serialize (hb_serialize_context_t *c,
+                  const hb_array_t<const HBUINT16> &color_record_indices,
+                  const hb_array_t<const BGRAColor> &color_records,
+                  const hb_vector_t<unsigned>& first_color_index_for_layer,
+                  const hb_map_t& first_color_to_layer_index,
+                  const hb_set_t &retained_color_indices) const
+  {
+    TRACE_SERIALIZE (this);
+
+    // TODO(grieger): limit total final size.
+
+    for (const auto idx : color_record_indices)
+    {
+      hb_codepoint_t layer_index = first_color_to_layer_index[idx];
+
+      HBUINT16 new_idx;
+      new_idx = layer_index * retained_color_indices.get_population ();
+      if (!c->copy<HBUINT16> (new_idx)) return_trace (false);
+    }
+
+    c->push ();
+    for (unsigned first_color_index : first_color_index_for_layer)
+    {
+      for (hb_codepoint_t color_index : retained_color_indices)
+      {
+        if (!c->copy<BGRAColor> (color_records[first_color_index + color_index]))
+        {
+          c->pop_discard ();
+          return_trace (false);
+        }
+      }
+    }
+
+    c->add_link (colorRecordsZ, c->pop_pack ());
+    return_trace (true);
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    if (!numPalettes) return_trace (false);
+
+    const hb_map_t *color_index_map = &c->plan->colr_palettes;
+    if (color_index_map->is_empty ()) return_trace (false);
+
+    hb_set_t retained_color_indices;
+    for (const auto _ : color_index_map->keys ())
+    {
+      if (_ == 0xFFFF) continue;
+      retained_color_indices.add (_);
+    }
+    if (retained_color_indices.is_empty ()) return_trace (false);
+
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+
+
+    out->version = version;
+    out->numColors = retained_color_indices.get_population ();
+    out->numPalettes = numPalettes;
+
+    hb_vector_t<unsigned> first_color_index_for_layer;
+    hb_map_t first_color_to_layer_index;
+
+    const hb_array_t<const HBUINT16> colorRecordIndices = colorRecordIndicesZ.as_array (numPalettes);
+    for (const auto first_color_record_idx : colorRecordIndices)
+    {
+      if (first_color_to_layer_index.has (first_color_record_idx)) continue;
+
+      first_color_index_for_layer.push (first_color_record_idx);
+      if (unlikely (!c->serializer->propagate_error (first_color_index_for_layer))) return_trace (false);
+      first_color_to_layer_index.set (first_color_record_idx,
+                                      first_color_index_for_layer.length - 1);
+    }
+
+    out->numColorRecords = first_color_index_for_layer.length
+                           * retained_color_indices.get_population ();
+
+    const hb_array_t<const BGRAColor> color_records = (this+colorRecordsZ).as_array (numColorRecords);
+    if (!out->serialize (c->serializer,
+                         colorRecordIndices,
+                         color_records,
+                         first_color_index_for_layer,
+                         first_color_to_layer_index,
+                         retained_color_indices))
+      return_trace (false);
+
+    if (version == 1)
+    {
+      hb_barrier ();
+      return_trace (v1 ().serialize (c->serializer, numPalettes, numColors, this, color_index_map));
+    }
+
+    return_trace (true);
+  }
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+		  hb_barrier () &&
+		  (this+colorRecordsZ).sanitize (c, numColorRecords) &&
+		  colorRecordIndicesZ.sanitize (c, numPalettes) &&
+		  (version == 0 || v1 ().sanitize (c, this, numPalettes, numColors)));
+  }
+
+  protected:
+  HBUINT16	version;		/* Table version number */
+  /* Version 0 */
+  HBUINT16	numColors;		/* Number of colors in each palette. */
+  HBUINT16	numPalettes;		/* Number of palettes in the table. */
+  HBUINT16	numColorRecords;	/* Total number of color records, combined for
+					 * all palettes. */
+  NNOffset32To<UnsizedArrayOf<BGRAColor>>
+		colorRecordsZ;		/* Offset from the beginning of CPAL table to
+					 * the first ColorRecord. */
+  UnsizedArrayOf<HBUINT16>
+		colorRecordIndicesZ;	/* Index of each palette’s first color record in
+					 * the combined color record array. */
+/*CPALV1Tail	v1;*/
+  public:
+  DEFINE_SIZE_ARRAY (12, colorRecordIndicesZ);
+};
+
+} /* namespace OT */
+
+
+#endif /* OT_COLOR_CPAL_CPAL_HH */

3rdparty/harfbuzz/src/OT/Color/sbix/sbix.hh

@@ -0,0 +1,449 @@
+/*
+ * Copyright © 2018  Ebrahim Byagowi
+ * Copyright © 2020  Google, Inc.
+ *
+ *  This is part of HarfBuzz, a text shaping library.
+ *
+ * Permission is hereby granted, without written agreement and without
+ * license or royalty fees, to use, copy, modify, and distribute this
+ * software and its documentation for any purpose, provided that the
+ * above copyright notice and the following two paragraphs appear in
+ * all copies of this software.
+ *
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+ * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+ * DAMAGE.
+ *
+ * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+ * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+ * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ * Google Author(s): Calder Kitagawa
+ */
+
+#ifndef OT_COLOR_SBIX_SBIX_HH
+#define OT_COLOR_SBIX_SBIX_HH
+
+#include "../../../hb-open-type.hh"
+#include "../../../hb-paint.hh"
+
+/*
+ * sbix -- Standard Bitmap Graphics
+ * https://docs.microsoft.com/en-us/typography/opentype/spec/sbix
+ * https://developer.apple.com/fonts/TrueType-Reference-Manual/RM06/Chap6sbix.html
+ */
+#define HB_OT_TAG_sbix HB_TAG('s','b','i','x')
+
+
+namespace OT {
+
+
+struct SBIXGlyph
+{
+  SBIXGlyph* copy (hb_serialize_context_t *c, unsigned int data_length) const
+  {
+    TRACE_SERIALIZE (this);
+    SBIXGlyph* new_glyph = c->start_embed<SBIXGlyph> ();
+    if (unlikely (!c->extend_min (new_glyph))) return_trace (nullptr);
+
+    new_glyph->xOffset = xOffset;
+    new_glyph->yOffset = yOffset;
+    new_glyph->graphicType = graphicType;
+    data.copy (c, data_length);
+    return_trace (new_glyph);
+  }
+
+  HBINT16	xOffset;	/* The horizontal (x-axis) offset from the left
+				 * edge of the graphic to the glyph’s origin.
+				 * That is, the x-coordinate of the point on the
+				 * baseline at the left edge of the glyph. */
+  HBINT16	yOffset;	/* The vertical (y-axis) offset from the bottom
+				 * edge of the graphic to the glyph’s origin.
+				 * That is, the y-coordinate of the point on the
+				 * baseline at the left edge of the glyph. */
+  Tag		graphicType;	/* Indicates the format of the embedded graphic
+				 * data: one of 'jpg ', 'png ' or 'tiff', or the
+				 * special format 'dupe'. */
+  UnsizedArrayOf<HBUINT8>
+		data;		/* The actual embedded graphic data. The total
+				 * length is inferred from sequential entries in
+				 * the glyphDataOffsets array and the fixed size
+				 * (8 bytes) of the preceding fields. */
+  public:
+  DEFINE_SIZE_ARRAY (8, data);
+};
+
+struct SBIXStrike
+{
+  static size_t get_size (unsigned num_glyphs)
+  { return min_size + num_glyphs * HBUINT32::static_size; }
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+		  imageOffsetsZ.sanitize_shallow (c, c->get_num_glyphs () + 1));
+  }
+
+  hb_blob_t *get_glyph_blob (unsigned int  glyph_id,
+			     hb_blob_t    *sbix_blob,
+			     hb_tag_t      file_type,
+			     int          *x_offset,
+			     int          *y_offset,
+			     unsigned int  num_glyphs,
+			     unsigned int *strike_ppem) const
+  {
+    if (unlikely (!ppem)) return hb_blob_get_empty (); /* To get Null() object out of the way. */
+
+    unsigned int retry_count = 8;
+    unsigned int sbix_len = sbix_blob->length;
+    unsigned int strike_offset = (const char *) this - (const char *) sbix_blob->data;
+    assert (strike_offset < sbix_len);
+
+  retry:
+    if (unlikely (glyph_id >= num_glyphs ||
+		  imageOffsetsZ[glyph_id + 1] <= imageOffsetsZ[glyph_id] ||
+		  imageOffsetsZ[glyph_id + 1] - imageOffsetsZ[glyph_id] <= SBIXGlyph::min_size ||
+		  (unsigned int) imageOffsetsZ[glyph_id + 1] > sbix_len - strike_offset))
+      return hb_blob_get_empty ();
+
+    unsigned int glyph_offset = strike_offset + (unsigned int) imageOffsetsZ[glyph_id] + SBIXGlyph::min_size;
+    unsigned int glyph_length = imageOffsetsZ[glyph_id + 1] - imageOffsetsZ[glyph_id] - SBIXGlyph::min_size;
+
+    const SBIXGlyph *glyph = &(this+imageOffsetsZ[glyph_id]);
+
+    if (glyph->graphicType == HB_TAG ('d','u','p','e'))
+    {
+      if (glyph_length >= 2)
+      {
+	glyph_id = *((HBUINT16 *) &glyph->data);
+	if (retry_count--)
+	  goto retry;
+      }
+      return hb_blob_get_empty ();
+    }
+
+    if (unlikely (file_type != glyph->graphicType))
+      return hb_blob_get_empty ();
+
+    if (strike_ppem) *strike_ppem = ppem;
+    if (x_offset) *x_offset = glyph->xOffset;
+    if (y_offset) *y_offset = glyph->yOffset;
+    return hb_blob_create_sub_blob (sbix_blob, glyph_offset, glyph_length);
+  }
+
+  bool subset (hb_subset_context_t *c, unsigned int available_len) const
+  {
+    TRACE_SUBSET (this);
+    unsigned int num_output_glyphs = c->plan->num_output_glyphs ();
+
+    auto* out = c->serializer->start_embed<SBIXStrike> ();
+    auto snap = c->serializer->snapshot ();
+    if (unlikely (!c->serializer->extend (out, num_output_glyphs + 1))) return_trace (false);
+    out->ppem = ppem;
+    out->resolution = resolution;
+    HBUINT32 head;
+    head = get_size (num_output_glyphs + 1);
+
+    bool has_glyphs = false;
+    for (unsigned new_gid = 0; new_gid < num_output_glyphs; new_gid++)
+    {
+      hb_codepoint_t old_gid;
+      if (!c->plan->old_gid_for_new_gid (new_gid, &old_gid) ||
+	  unlikely (imageOffsetsZ[old_gid].is_null () ||
+		    imageOffsetsZ[old_gid + 1].is_null () ||
+		    imageOffsetsZ[old_gid + 1] <= imageOffsetsZ[old_gid] ||
+		    imageOffsetsZ[old_gid + 1] - imageOffsetsZ[old_gid] <= SBIXGlyph::min_size) ||
+		    (unsigned int) imageOffsetsZ[old_gid + 1] > available_len)
+      {
+	out->imageOffsetsZ[new_gid] = head;
+	continue;
+      }
+      has_glyphs = true;
+      unsigned int delta = imageOffsetsZ[old_gid + 1] - imageOffsetsZ[old_gid];
+      unsigned int glyph_data_length = delta - SBIXGlyph::min_size;
+      if (!(this+imageOffsetsZ[old_gid]).copy (c->serializer, glyph_data_length))
+	return_trace (false);
+      out->imageOffsetsZ[new_gid] = head;
+      head += delta;
+    }
+    if (has_glyphs)
+      out->imageOffsetsZ[num_output_glyphs] = head;
+    else
+      c->serializer->revert (snap);
+    return_trace (has_glyphs);
+  }
+
+  public:
+  HBUINT16	ppem;		/* The PPEM size for which this strike was designed. */
+  HBUINT16	resolution;	/* The device pixel density (in PPI) for which this
+				 * strike was designed. (E.g., 96 PPI, 192 PPI.) */
+  protected:
+  UnsizedArrayOf<Offset32To<SBIXGlyph>>
+		imageOffsetsZ;	/* Offset from the beginning of the strike data header
+				 * to bitmap data for an individual glyph ID. */
+  public:
+  DEFINE_SIZE_ARRAY (4, imageOffsetsZ);
+};
+
+struct sbix
+{
+  static constexpr hb_tag_t tableTag = HB_OT_TAG_sbix;
+
+  bool has_data () const { return version; }
+
+  const SBIXStrike &get_strike (unsigned int i) const { return this+strikes[i]; }
+
+  struct accelerator_t
+  {
+    accelerator_t (hb_face_t *face)
+    {
+      table = hb_sanitize_context_t ().reference_table<sbix> (face);
+      num_glyphs = face->get_num_glyphs ();
+    }
+    ~accelerator_t () { table.destroy (); }
+
+    bool has_data () const { return table->has_data (); }
+
+    bool get_extents (hb_font_t          *font,
+		      hb_codepoint_t      glyph,
+		      hb_glyph_extents_t *extents,
+		      bool                scale = true) const
+    {
+      /* We only support PNG right now, and following function checks type. */
+      return get_png_extents (font, glyph, extents, scale);
+    }
+
+    hb_blob_t *reference_png (hb_font_t      *font,
+			      hb_codepoint_t  glyph_id,
+			      int            *x_offset,
+			      int            *y_offset,
+			      unsigned int   *available_ppem) const
+    {
+      return choose_strike (font).get_glyph_blob (glyph_id, table.get_blob (),
+						  HB_TAG ('p','n','g',' '),
+						  x_offset, y_offset,
+						  num_glyphs, available_ppem);
+    }
+
+    bool paint_glyph (hb_font_t *font, hb_codepoint_t glyph, hb_paint_funcs_t *funcs, void *data) const
+    {
+      if (!has_data ())
+        return false;
+
+      int x_offset = 0, y_offset = 0;
+      unsigned int strike_ppem = 0;
+      hb_glyph_extents_t extents;
+      hb_glyph_extents_t pixel_extents;
+
+      if (!font->get_glyph_extents (glyph, &extents, false))
+        return false;
+
+      if (unlikely (!get_extents (font, glyph, &pixel_extents, false)))
+        return false;
+
+      hb_blob_t *blob = reference_png (font, glyph, &x_offset, &y_offset, &strike_ppem);
+      if (hb_blob_is_immutable (blob))
+        return false;
+
+      bool ret = funcs->image (data,
+			       blob,
+			       pixel_extents.width, -pixel_extents.height,
+			       HB_PAINT_IMAGE_FORMAT_PNG,
+			       0.f,
+			       &extents);
+
+      hb_blob_destroy (blob);
+
+      return ret;
+    }
+
+    private:
+
+    const SBIXStrike &choose_strike (hb_font_t *font) const
+    {
+      unsigned count = table->strikes.len;
+      if (unlikely (!count))
+	return Null (SBIXStrike);
+
+      unsigned int requested_ppem = hb_max (font->x_ppem, font->y_ppem);
+      if (!requested_ppem)
+	requested_ppem = 1<<30; /* Choose largest strike. */
+      /* TODO Add DPI sensitivity as well? */
+      unsigned int best_i = 0;
+      unsigned int best_ppem = table->get_strike (0).ppem;
+
+      for (unsigned int i = 1; i < count; i++)
+      {
+	unsigned int ppem = (table->get_strike (i)).ppem;
+	if ((requested_ppem <= ppem && ppem < best_ppem) ||
+	    (requested_ppem > best_ppem && ppem > best_ppem))
+	{
+	  best_i = i;
+	  best_ppem = ppem;
+	}
+      }
+
+      return table->get_strike (best_i);
+    }
+
+    struct PNGHeader
+    {
+      HBUINT8	signature[8];
+      struct
+      {
+	struct
+	{
+	  HBUINT32	length;
+	  Tag		type;
+	}		header;
+	HBUINT32	width;
+	HBUINT32	height;
+	HBUINT8		bitDepth;
+	HBUINT8		colorType;
+	HBUINT8		compressionMethod;
+	HBUINT8		filterMethod;
+	HBUINT8		interlaceMethod;
+      } IHDR;
+
+      public:
+      DEFINE_SIZE_STATIC (29);
+    };
+
+    bool get_png_extents (hb_font_t          *font,
+			  hb_codepoint_t      glyph,
+			  hb_glyph_extents_t *extents,
+			  bool                scale = true) const
+    {
+      /* Following code is safe to call even without data.
+       * But faster to short-circuit. */
+      if (!has_data ())
+	return false;
+
+      int x_offset = 0, y_offset = 0;
+      unsigned int strike_ppem = 0;
+      hb_blob_t *blob = reference_png (font, glyph, &x_offset, &y_offset, &strike_ppem);
+
+      const PNGHeader &png = *blob->as<PNGHeader>();
+
+      if (png.IHDR.height >= 65536 || png.IHDR.width >= 65536)
+      {
+	hb_blob_destroy (blob);
+	return false;
+      }
+
+      extents->x_bearing = x_offset;
+      extents->y_bearing = png.IHDR.height + y_offset;
+      extents->width     = png.IHDR.width;
+      extents->height    = -1 * png.IHDR.height;
+
+      /* Convert to font units. */
+      if (strike_ppem && scale)
+      {
+	float scale = font->face->get_upem () / (float) strike_ppem;
+	extents->x_bearing = roundf (extents->x_bearing * scale);
+	extents->y_bearing = roundf (extents->y_bearing * scale);
+	extents->width = roundf (extents->width * scale);
+	extents->height = roundf (extents->height * scale);
+      }
+
+      if (scale)
+	font->scale_glyph_extents (extents);
+
+      hb_blob_destroy (blob);
+
+      return strike_ppem;
+    }
+
+    private:
+    hb_blob_ptr_t<sbix> table;
+
+    unsigned int num_glyphs;
+  };
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (likely (c->check_struct (this) &&
+			  hb_barrier () &&
+			  version >= 1 &&
+			  strikes.sanitize (c, this)));
+  }
+
+  bool
+  add_strike (hb_subset_context_t *c, unsigned i) const
+  {
+    if (strikes[i].is_null () || c->source_blob->length < (unsigned) strikes[i])
+      return false;
+
+    return (this+strikes[i]).subset (c, c->source_blob->length - (unsigned) strikes[i]);
+  }
+
+  bool serialize_strike_offsets (hb_subset_context_t *c) const
+  {
+    TRACE_SERIALIZE (this);
+
+    auto *out = c->serializer->start_embed<Array32OfOffset32To<SBIXStrike>> ();
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+
+    hb_vector_t<Offset32To<SBIXStrike>*> new_strikes;
+    hb_vector_t<hb_serialize_context_t::objidx_t> objidxs;
+    for (int i = strikes.len - 1; i >= 0; --i)
+    {
+      auto* o = out->serialize_append (c->serializer);
+      if (unlikely (!o)) return_trace (false);
+      *o = 0;
+      auto snap = c->serializer->snapshot ();
+      c->serializer->push ();
+      bool ret = add_strike (c, i);
+      if (!ret)
+      {
+	c->serializer->pop_discard ();
+	out->pop ();
+	c->serializer->revert (snap);
+      }
+      else
+      {
+	objidxs.push (c->serializer->pop_pack ());
+	new_strikes.push (o);
+      }
+    }
+    for (unsigned int i = 0; i < new_strikes.length; ++i)
+      c->serializer->add_link (*new_strikes[i], objidxs[new_strikes.length - 1 - i]);
+
+    return_trace (true);
+  }
+
+  bool subset (hb_subset_context_t* c) const
+  {
+    TRACE_SUBSET (this);
+
+    if (unlikely (!c->serializer->embed (this->version))) return_trace (false);
+    if (unlikely (!c->serializer->embed (this->flags))) return_trace (false);
+
+    return_trace (serialize_strike_offsets (c));
+  }
+
+  protected:
+  HBUINT16	version;	/* Table version number — set to 1 */
+  HBUINT16	flags;		/* Bit 0: Set to 1. Bit 1: Draw outlines.
+				 * Bits 2 to 15: reserved (set to 0). */
+  Array32OfOffset32To<SBIXStrike>
+		strikes;	/* Offsets from the beginning of the 'sbix'
+				 * table to data for each individual bitmap strike. */
+  public:
+  DEFINE_SIZE_ARRAY (8, strikes);
+};
+
+struct sbix_accelerator_t : sbix::accelerator_t {
+  sbix_accelerator_t (hb_face_t *face) : sbix::accelerator_t (face) {}
+};
+
+
+} /* namespace OT */
+
+#endif /* OT_COLOR_SBIX_SBIX_HH */

3rdparty/harfbuzz/src/OT/Color/svg/svg.hh

@@ -0,0 +1,829 @@
+/*
+ * Copyright © 2018  Ebrahim Byagowi
+ *
+ *  This is part of HarfBuzz, a text shaping library.
+ *
+ * Permission is hereby granted, without written agreement and without
+ * license or royalty fees, to use, copy, modify, and distribute this
+ * software and its documentation for any purpose, provided that the
+ * above copyright notice and the following two paragraphs appear in
+ * all copies of this software.
+ *
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+ * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+ * DAMAGE.
+ *
+ * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+ * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+ * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ */
+
+#ifndef OT_COLOR_SVG_SVG_HH
+#define OT_COLOR_SVG_SVG_HH
+
+#include "../../../hb-open-type.hh"
+#include "../../../hb-blob.hh"
+#include "../../../hb-limits.hh"
+#include "../../../hb-map.hh"
+#include "../../../hb-paint.hh"
+#include "../../../hb-zlib.hh"
+#include <ctype.h>
+#include <string.h>
+
+/*
+ * SVG -- SVG (Scalable Vector Graphics)
+ * https://docs.microsoft.com/en-us/typography/opentype/spec/svg
+ */
+
+#define HB_OT_TAG_SVG HB_TAG('S','V','G',' ')
+
+
+namespace OT {
+
+static inline hb_blob_t *
+hb_ot_svg_reference_normalized_blob (hb_blob_t *image,
+                                     const char **svg,
+                                     unsigned *len)
+{
+  hb_blob_t *blob = hb_blob_reference (image);
+  unsigned data_len = 0;
+  const char *data = hb_blob_get_data (blob, &data_len);
+
+  if (!data || !data_len)
+    goto fail;
+
+  if (hb_blob_is_gzip (data, data_len))
+  {
+    uint32_t expected_size = 0;
+    if (hb_gzip_get_uncompressed_size (data, data_len, &expected_size) &&
+        unlikely ((size_t) expected_size > (size_t) HB_SVG_MAX_DOCUMENT_SIZE))
+      goto fail;
+
+    hb_blob_t *uncompressed = hb_blob_decompress_gzip (blob,
+                                                       HB_SVG_MAX_DOCUMENT_SIZE);
+    if (!uncompressed)
+      goto fail;
+
+    hb_blob_destroy (blob);
+    blob = uncompressed;
+    data = hb_blob_get_data (blob, &data_len);
+    if (!data || !data_len)
+      goto fail;
+  }
+
+  if (unlikely ((size_t) data_len > (size_t) HB_SVG_MAX_DOCUMENT_SIZE))
+    goto fail;
+
+  if (svg) *svg = data;
+  if (len) *len = data_len;
+  return blob;
+
+fail:
+  hb_blob_destroy (blob);
+  if (svg) *svg = nullptr;
+  if (len) *len = 0;
+  return nullptr;
+}
+
+struct SVGDocumentIndexEntry
+{
+  int cmp (hb_codepoint_t g) const
+  { return g < startGlyphID ? -1 : g > endGlyphID ? 1 : 0; }
+
+  hb_codepoint_t get_start_glyph () const
+  { return startGlyphID; }
+
+  hb_codepoint_t get_end_glyph () const
+  { return endGlyphID; }
+
+  hb_blob_t *reference_blob (hb_blob_t *svg_blob, unsigned int index_offset) const
+  {
+    return hb_blob_create_sub_blob (svg_blob,
+				    index_offset + (unsigned int) svgDoc,
+				    svgDocLength);
+  }
+
+  bool sanitize (hb_sanitize_context_t *c, const void *base) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+		  hb_barrier () &&
+		  svgDoc.sanitize (c, base, svgDocLength));
+  }
+
+  protected:
+  HBUINT16	startGlyphID;	/* The first glyph ID in the range described by
+				 * this index entry. */
+  HBUINT16	endGlyphID;	/* The last glyph ID in the range described by
+				 * this index entry. Must be >= startGlyphID. */
+  NNOffset32To<UnsizedArrayOf<HBUINT8>>
+		svgDoc;		/* Offset from the beginning of the SVG Document Index
+				 * to an SVG document. Must be non-zero. */
+  HBUINT32	svgDocLength;	/* Length of the SVG document.
+				 * Must be non-zero. */
+  public:
+  DEFINE_SIZE_STATIC (12);
+};
+
+struct SVG
+{
+  static constexpr hb_tag_t tableTag = HB_OT_TAG_SVG;
+
+  struct svg_id_span_t
+  {
+    const char *p;
+    unsigned len;
+
+    bool operator == (const svg_id_span_t &o) const
+    {
+      return len == o.len && !memcmp (p, o.p, len);
+    }
+
+    uint32_t hash () const
+    {
+      uint32_t h = hb_hash (len);
+      for (unsigned i = 0; i < len; i++)
+        h = h * 33u + (unsigned char) p[i];
+      return h;
+    }
+  };
+
+  struct svg_defs_entry_t
+  {
+    svg_id_span_t id;
+    unsigned start;
+    unsigned end;
+  };
+
+  struct svg_doc_cache_t
+  {
+    hb_blob_t *blob = nullptr;
+    const char *svg = nullptr;
+    unsigned len = 0;
+    hb_vector_t<svg_defs_entry_t> defs_entries;
+    hb_codepoint_t start_glyph = HB_CODEPOINT_INVALID;
+    hb_codepoint_t end_glyph = HB_CODEPOINT_INVALID;
+    hb_vector_t<hb_pair_t<uint32_t, uint32_t>> glyph_spans;
+    hb_hashmap_t<svg_id_span_t, hb_pair_t<uint32_t, uint32_t>> id_spans;
+  };
+
+  bool has_data () const { return svgDocEntries; }
+
+  struct accelerator_t
+  {
+    accelerator_t (hb_face_t *face);
+    ~accelerator_t ();
+
+    hb_blob_t *reference_blob_for_glyph (hb_codepoint_t glyph_id) const
+    {
+      return table->get_glyph_entry (glyph_id).reference_blob (table.get_blob (),
+							       table->svgDocEntries);
+    }
+
+    unsigned get_document_count () const
+    { return table->get_document_count (); }
+
+    bool get_glyph_document_index (hb_codepoint_t glyph_id, unsigned *index) const
+    { return table->get_glyph_document_index (glyph_id, index); }
+
+    bool get_document_glyph_range (unsigned index,
+                                   hb_codepoint_t *start_glyph,
+                                   hb_codepoint_t *end_glyph) const
+    { return table->get_document_glyph_range (index, start_glyph, end_glyph); }
+
+    bool has_data () const { return table->has_data (); }
+
+    const svg_doc_cache_t *
+    get_or_create_doc_cache (hb_blob_t *image,
+                             const char *svg,
+                             unsigned len,
+                             unsigned doc_index,
+                             hb_codepoint_t start_glyph,
+                             hb_codepoint_t end_glyph) const;
+
+    const char *
+    doc_cache_get_svg (const svg_doc_cache_t *doc,
+                       unsigned *len) const;
+
+    const hb_vector_t<svg_defs_entry_t> *
+    doc_cache_get_defs_entries (const svg_doc_cache_t *doc) const;
+
+    bool
+    doc_cache_get_glyph_span (const svg_doc_cache_t *doc,
+                              hb_codepoint_t glyph,
+                              unsigned *start,
+                              unsigned *end) const;
+
+    bool
+    doc_cache_find_id_span (const svg_doc_cache_t *doc,
+                            svg_id_span_t id,
+                            unsigned *start,
+                            unsigned *end) const;
+
+    bool
+    doc_cache_find_id_cstr (const svg_doc_cache_t *doc,
+                            const char *id,
+                            unsigned *start,
+                            unsigned *end) const;
+
+    bool paint_glyph (hb_font_t *font HB_UNUSED, hb_codepoint_t glyph, hb_paint_funcs_t *funcs, void *data) const
+    {
+      if (!has_data ())
+        return false;
+
+      hb_blob_t *blob = reference_blob_for_glyph (glyph);
+
+      if (blob == hb_blob_get_empty ())
+        return false;
+
+      bool ret = funcs->image (data,
+			       blob,
+			       0, 0,
+			       HB_PAINT_IMAGE_FORMAT_SVG,
+			       0.f,
+			       nullptr);
+
+      hb_blob_destroy (blob);
+
+      return ret;
+    }
+
+    private:
+    svg_doc_cache_t *
+    make_doc_cache (hb_blob_t *image,
+                    const char *svg,
+                    unsigned len,
+                    hb_codepoint_t start_glyph,
+                    hb_codepoint_t end_glyph) const;
+
+    static void destroy_doc_cache (svg_doc_cache_t *doc);
+
+    hb_blob_ptr_t<SVG> table;
+    mutable hb_vector_t<hb_atomic_t<svg_doc_cache_t *>> doc_caches;
+    public:
+    DEFINE_SIZE_STATIC (sizeof (hb_blob_ptr_t<SVG>) +
+                        sizeof (hb_vector_t<hb_atomic_t<svg_doc_cache_t *>>));
+  };
+
+  const SVGDocumentIndexEntry &get_glyph_entry (hb_codepoint_t glyph_id) const
+  { return (this+svgDocEntries).bsearch (glyph_id); }
+
+  unsigned get_document_count () const
+  {
+    if (!has_data ())
+      return 0;
+    return (this + svgDocEntries).len;
+  }
+
+  bool get_glyph_document_index (hb_codepoint_t glyph_id, unsigned *index) const
+  {
+    if (!has_data ())
+      return false;
+    return (this + svgDocEntries).bfind (glyph_id, index);
+  }
+
+  bool get_document_glyph_range (unsigned index,
+                                 hb_codepoint_t *start_glyph,
+                                 hb_codepoint_t *end_glyph) const
+  {
+    if (!has_data ())
+      return false;
+
+    const auto &entries = this + svgDocEntries;
+    if (index >= entries.len)
+      return false;
+
+    const auto &entry = entries.arrayZ[index];
+    if (start_glyph) *start_glyph = entry.get_start_glyph ();
+    if (end_glyph) *end_glyph = entry.get_end_glyph ();
+    return true;
+  }
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (likely (c->check_struct (this) &&
+			  (this+svgDocEntries).sanitize_shallow (c)));
+  }
+
+  protected:
+  HBUINT16	version;	/* Table version (starting at 0). */
+  Offset32To<SortedArray16Of<SVGDocumentIndexEntry>>
+		svgDocEntries;	/* Offset (relative to the start of the SVG table) to the
+				 * SVG Documents Index. Must be non-zero. */
+				/* Array of SVG Document Index Entries. */
+  HBUINT32	reserved;	/* Set to 0. */
+  public:
+  DEFINE_SIZE_STATIC (10);
+};
+
+namespace _hb_svg_cache_impl {
+
+struct glyph_entry_t
+{
+  hb_codepoint_t glyph;
+  uint32_t start;
+  uint32_t end;
+};
+
+struct id_entry_t
+{
+  SVG::svg_id_span_t id;
+  uint32_t start;
+  uint32_t end;
+};
+
+struct open_elem_t
+{
+  unsigned start;
+  SVG::svg_id_span_t id;
+  bool in_defs_content;
+  bool is_defs;
+};
+
+static const unsigned MAX_DEPTH = 128;
+
+static inline int
+find_substr (const char *s,
+             unsigned n,
+             unsigned from,
+             const char *needle,
+             unsigned needle_len)
+{
+  if (!needle_len || from >= n || needle_len > n)
+    return -1;
+  for (unsigned i = from; i + needle_len <= n; i++)
+    if (s[i] == needle[0] && !memcmp (s + i, needle, needle_len))
+      return (int) i;
+  return -1;
+}
+
+static inline bool
+parse_id_in_start_tag (const char *svg,
+                       unsigned tag_start,
+                       unsigned tag_end,
+                       SVG::svg_id_span_t *id)
+{
+  unsigned p = tag_start;
+  while (p + 4 <= tag_end)
+  {
+    if (!memcmp (svg + p, "id=\"", 4))
+    {
+      unsigned b = p + 4;
+      unsigned e = b;
+      while (e < tag_end && svg[e] != '"') e++;
+      if (e <= tag_end && e > b)
+      {
+        *id = {svg + b, e - b};
+        return true;
+      }
+    }
+    if (!memcmp (svg + p, "id='", 4))
+    {
+      unsigned b = p + 4;
+      unsigned e = b;
+      while (e < tag_end && svg[e] != '\'') e++;
+      if (e <= tag_end && e > b)
+      {
+        *id = {svg + b, e - b};
+        return true;
+      }
+    }
+    p++;
+  }
+  return false;
+}
+
+static inline bool
+parse_glyph_id_span (const SVG::svg_id_span_t &id,
+                     hb_codepoint_t *glyph)
+{
+  if (id.len <= 5 || memcmp (id.p, "glyph", 5))
+    return false;
+
+  hb_codepoint_t gid = 0;
+  for (unsigned i = 5; i < id.len; i++)
+  {
+    unsigned char c = (unsigned char) id.p[i];
+    if (c < '0' || c > '9')
+      return false;
+    hb_codepoint_t digit = (hb_codepoint_t) (c - '0');
+    if (unlikely (gid > HB_CODEPOINT_INVALID / 10 ||
+                  (gid == HB_CODEPOINT_INVALID / 10 &&
+                   digit > HB_CODEPOINT_INVALID % 10)))
+      return false;
+    gid = (hb_codepoint_t) (gid * 10 + digit);
+  }
+
+  *glyph = gid;
+  return true;
+}
+
+static inline bool
+parse_cache_entries_linear (const char *svg,
+                            unsigned len,
+                            hb_vector_t<SVG::svg_defs_entry_t> *defs_entries,
+                            hb_vector_t<glyph_entry_t> *glyph_spans,
+                            hb_vector_t<id_entry_t> *id_entries)
+{
+  open_elem_t stack[MAX_DEPTH] = {};
+  unsigned depth = 0;
+  if (unlikely (!defs_entries->alloc (256) ||
+                !glyph_spans->alloc (256) ||
+                !id_entries->alloc (256)))
+    return false;
+
+  unsigned defs_depth = 0;
+  unsigned i = 0;
+  while (i < len)
+  {
+    if (svg[i] != '<')
+    {
+      i++;
+      continue;
+    }
+
+    if (i + 4 <= len && !memcmp (svg + i, "<!--", 4))
+    {
+      int cend = find_substr (svg, len, i + 4, "-->", 3);
+      if (cend < 0) return false;
+      i = (unsigned) cend + 3;
+      continue;
+    }
+    if (i + 9 <= len && !memcmp (svg + i, "<![CDATA[", 9))
+    {
+      int cend = find_substr (svg, len, i + 9, "]]>", 3);
+      if (cend < 0) return false;
+      i = (unsigned) cend + 3;
+      continue;
+    }
+
+    bool closing = (i + 1 < len && svg[i + 1] == '/');
+    bool special = (i + 1 < len && (svg[i + 1] == '!' || svg[i + 1] == '?'));
+
+    unsigned gt = i + 1;
+    char quote = 0;
+    while (gt < len)
+    {
+      char c = svg[gt];
+      if (quote)
+      {
+        if (c == quote) quote = 0;
+      }
+      else
+      {
+        if (c == '"' || c == '\'')
+          quote = c;
+        else if (c == '>')
+          break;
+      }
+      gt++;
+    }
+    if (gt >= len)
+      return false;
+
+    if (special)
+    {
+      i = gt + 1;
+      continue;
+    }
+
+    unsigned p = i + (closing ? 2 : 1);
+    while (p < gt && isspace ((unsigned char) svg[p])) p++;
+    const char *name = svg + p;
+    unsigned name_len = 0;
+    while (p + name_len < gt)
+    {
+      unsigned char c = (unsigned char) name[name_len];
+      if (!(isalnum (c) || c == '_' || c == '-' || c == ':'))
+        break;
+      name_len++;
+    }
+    bool is_defs = (name_len == 4 && !memcmp (name, "defs", 4));
+
+    if (closing)
+    {
+      if (!depth)
+      {
+        i = gt + 1;
+        continue;
+      }
+
+      open_elem_t e = stack[--depth];
+      unsigned end = gt + 1;
+
+      if (e.id.len)
+      {
+        if (unlikely (!id_entries->push_or_fail (id_entry_t {e.id, (uint32_t) e.start, (uint32_t) end})))
+          return false;
+
+        if (e.in_defs_content)
+        {
+          if (unlikely (!defs_entries->push_or_fail ()))
+            return false;
+          auto &slot = defs_entries->tail ();
+          slot.id = e.id;
+          slot.start = e.start;
+          slot.end = end;
+        }
+
+        hb_codepoint_t gid;
+        if (parse_glyph_id_span (e.id, &gid))
+        {
+          if (unlikely (!glyph_spans->push_or_fail (glyph_entry_t {gid, (uint32_t) e.start, (uint32_t) end})))
+            return false;
+        }
+      }
+
+      if (e.is_defs && defs_depth)
+        defs_depth--;
+
+      i = end;
+      continue;
+    }
+
+    SVG::svg_id_span_t id = {};
+    parse_id_in_start_tag (svg, i, gt, &id);
+
+    unsigned r = gt;
+    while (r > i && isspace ((unsigned char) svg[r - 1])) r--;
+    bool self_closing = (r > i && svg[r - 1] == '/');
+
+    open_elem_t e = {};
+    e.start = i;
+    e.id = id;
+    e.in_defs_content = defs_depth > 0;
+    e.is_defs = is_defs;
+
+    if (self_closing)
+    {
+      unsigned end = gt + 1;
+      if (e.id.len)
+      {
+        if (unlikely (!id_entries->push_or_fail (id_entry_t {e.id, (uint32_t) e.start, (uint32_t) end})))
+          return false;
+
+        if (e.in_defs_content)
+        {
+          if (unlikely (!defs_entries->push_or_fail ()))
+            return false;
+          auto &slot = defs_entries->tail ();
+          slot.id = e.id;
+          slot.start = e.start;
+          slot.end = end;
+        }
+
+        hb_codepoint_t gid;
+        if (parse_glyph_id_span (e.id, &gid))
+        {
+          if (unlikely (!glyph_spans->push_or_fail (glyph_entry_t {gid, (uint32_t) e.start, (uint32_t) end})))
+            return false;
+        }
+      }
+    }
+    else
+    {
+      if (unlikely (depth >= MAX_DEPTH))
+        return false;
+      stack[depth++] = e;
+      if (is_defs)
+        defs_depth++;
+    }
+
+    i = gt + 1;
+  }
+
+  return true;
+}
+
+} /* namespace _hb_svg_cache_impl */
+
+inline
+SVG::accelerator_t::accelerator_t (hb_face_t *face)
+{
+  table = hb_sanitize_context_t ().reference_table<SVG> (face);
+  doc_caches.init ();
+  unsigned doc_count = table->get_document_count ();
+  if (doc_count && unlikely (!doc_caches.resize (doc_count)))
+    doc_caches.clear ();
+  for (unsigned i = 0; i < doc_caches.length; i++)
+    doc_caches.arrayZ[i].set_relaxed (nullptr);
+}
+
+inline
+SVG::accelerator_t::~accelerator_t ()
+{
+  for (unsigned i = 0; i < doc_caches.length; i++)
+    destroy_doc_cache (doc_caches.arrayZ[i].get_relaxed ());
+  doc_caches.fini ();
+  table.destroy ();
+}
+
+inline void
+SVG::accelerator_t::destroy_doc_cache (svg_doc_cache_t *doc)
+{
+  if (!doc)
+    return;
+  doc->glyph_spans.fini ();
+  doc->defs_entries.fini ();
+  doc->id_spans.fini ();
+  hb_blob_destroy (doc->blob);
+  hb_free (doc);
+}
+
+inline SVG::svg_doc_cache_t *
+SVG::accelerator_t::make_doc_cache (hb_blob_t *image,
+                                    const char *svg,
+                                    unsigned len,
+                                    hb_codepoint_t start_glyph,
+                                    hb_codepoint_t end_glyph) const
+{
+  static const uint32_t INVALID_SPAN = 0xFFFFFFFFu;
+
+  auto *doc = (svg_doc_cache_t *) hb_malloc (sizeof (svg_doc_cache_t));
+  if (!doc)
+    return nullptr;
+
+  doc->blob = nullptr;
+  doc->svg = nullptr;
+  doc->len = 0;
+  doc->defs_entries.init ();
+  doc->start_glyph = HB_CODEPOINT_INVALID;
+  doc->end_glyph = HB_CODEPOINT_INVALID;
+  doc->glyph_spans.init ();
+  doc->id_spans.init ();
+
+  doc->blob = hb_blob_reference (image);
+  doc->svg = svg;
+  doc->len = len;
+  doc->start_glyph = start_glyph;
+  doc->end_glyph = end_glyph;
+
+  if (unlikely (start_glyph == HB_CODEPOINT_INVALID || end_glyph < start_glyph))
+  {
+    destroy_doc_cache (doc);
+    return nullptr;
+  }
+
+  unsigned glyph_count = end_glyph - start_glyph + 1;
+  if (!doc->glyph_spans.resize ((int) glyph_count))
+  {
+    destroy_doc_cache (doc);
+    return nullptr;
+  }
+  for (unsigned i = 0; i < glyph_count; i++)
+    doc->glyph_spans.arrayZ[i] = hb_pair_t<uint32_t, uint32_t> (INVALID_SPAN, INVALID_SPAN);
+
+  hb_vector_t<_hb_svg_cache_impl::glyph_entry_t> glyph_spans;
+  glyph_spans.init ();
+  hb_vector_t<_hb_svg_cache_impl::id_entry_t> id_entries;
+  id_entries.init ();
+  if (!_hb_svg_cache_impl::parse_cache_entries_linear (svg, len,
+                                                       &doc->defs_entries,
+                                                       &glyph_spans,
+                                                       &id_entries))
+  {
+    id_entries.fini ();
+    glyph_spans.fini ();
+    destroy_doc_cache (doc);
+    return nullptr;
+  }
+
+  for (unsigned i = 0; i < glyph_spans.length; i++)
+  {
+    const auto &span = glyph_spans.arrayZ[i];
+    if (unlikely (span.glyph < start_glyph || span.glyph > end_glyph))
+      continue;
+    doc->glyph_spans.arrayZ[span.glyph - start_glyph] = hb_pair_t<uint32_t, uint32_t> (span.start, span.end);
+  }
+
+  for (unsigned i = 0; i < id_entries.length; i++)
+  {
+    const auto &e = id_entries.arrayZ[i];
+    hb_pair_t<uint32_t, uint32_t> *out = nullptr;
+    if (doc->id_spans.has (e.id, &out))
+      continue;
+    if (unlikely (!doc->id_spans.set (e.id, hb_pair_t<uint32_t, uint32_t> (e.start, e.end))))
+    {
+      id_entries.fini ();
+      glyph_spans.fini ();
+      destroy_doc_cache (doc);
+      return nullptr;
+    }
+  }
+
+  id_entries.fini ();
+  glyph_spans.fini ();
+  return doc;
+}
+
+inline const SVG::svg_doc_cache_t *
+SVG::accelerator_t::get_or_create_doc_cache (hb_blob_t *image,
+                                              const char *svg,
+                                              unsigned len,
+                                              unsigned doc_index,
+                                              hb_codepoint_t start_glyph,
+                                              hb_codepoint_t end_glyph) const
+{
+  if (doc_index >= doc_caches.length)
+    return nullptr;
+
+  auto &slot = doc_caches.arrayZ[doc_index];
+  auto *doc = slot.get_acquire ();
+  if (doc)
+    return doc;
+
+  auto *fresh = make_doc_cache (image, svg, len, start_glyph, end_glyph);
+  if (!fresh)
+    return nullptr;
+
+  auto *expected = (svg_doc_cache_t *) nullptr;
+  if (slot.cmpexch (expected, fresh))
+    return fresh;
+
+  destroy_doc_cache (fresh);
+  return expected;
+}
+
+inline const char *
+SVG::accelerator_t::doc_cache_get_svg (const svg_doc_cache_t *doc,
+                                       unsigned *len) const
+{
+  if (!doc)
+  {
+    if (len) *len = 0;
+    return nullptr;
+  }
+  if (len) *len = doc->len;
+  return doc->svg;
+}
+
+inline const hb_vector_t<SVG::svg_defs_entry_t> *
+SVG::accelerator_t::doc_cache_get_defs_entries (const svg_doc_cache_t *doc) const
+{
+  return doc ? &doc->defs_entries : nullptr;
+}
+
+inline bool
+SVG::accelerator_t::doc_cache_get_glyph_span (const svg_doc_cache_t *doc,
+                                              hb_codepoint_t glyph,
+                                              unsigned *start,
+                                              unsigned *end) const
+{
+  static const uint32_t INVALID_SPAN = 0xFFFFFFFFu;
+  if (!doc || doc->start_glyph == HB_CODEPOINT_INVALID ||
+      glyph < doc->start_glyph || glyph > doc->end_glyph)
+    return false;
+
+  const auto &span = doc->glyph_spans.arrayZ[glyph - doc->start_glyph];
+  if (span.first == INVALID_SPAN)
+    return false;
+  if (unlikely (span.first > span.second || span.second > doc->len))
+    return false;
+
+  if (start) *start = span.first;
+  if (end) *end = span.second;
+  return true;
+}
+
+inline bool
+SVG::accelerator_t::doc_cache_find_id_span (const svg_doc_cache_t *doc,
+                                            svg_id_span_t id,
+                                            unsigned *start,
+                                            unsigned *end) const
+{
+  if (!doc || !id.p || !id.len)
+    return false;
+  hb_pair_t<uint32_t, uint32_t> *span = nullptr;
+  if (!doc->id_spans.has (id, &span))
+    return false;
+  if (unlikely (span->first > span->second || span->second > doc->len))
+    return false;
+  if (start) *start = span->first;
+  if (end) *end = span->second;
+  return true;
+}
+
+inline bool
+SVG::accelerator_t::doc_cache_find_id_cstr (const svg_doc_cache_t *doc,
+                                            const char *id,
+                                            unsigned *start,
+                                            unsigned *end) const
+{
+  if (!id) return false;
+  svg_id_span_t key = {id, (unsigned) strlen (id)};
+  return doc_cache_find_id_span (doc, key, start, end);
+}
+
+struct SVG_accelerator_t : SVG::accelerator_t {
+  SVG_accelerator_t (hb_face_t *face) : SVG::accelerator_t (face) {}
+};
+
+} /* namespace OT */
+
+
+#endif /* OT_COLOR_SVG_SVG_HH */

3rdparty/harfbuzz/src/OT/Layout/Common/Coverage.hh

@@ -0,0 +1,394 @@
+/*
+ * Copyright © 2007,2008,2009  Red Hat, Inc.
+ * Copyright © 2010,2012  Google, Inc.
+ *
+ *  This is part of HarfBuzz, a text shaping library.
+ *
+ * Permission is hereby granted, without written agreement and without
+ * license or royalty fees, to use, copy, modify, and distribute this
+ * software and its documentation for any purpose, provided that the
+ * above copyright notice and the following two paragraphs appear in
+ * all copies of this software.
+ *
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+ * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+ * DAMAGE.
+ *
+ * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+ * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+ * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ * Red Hat Author(s): Behdad Esfahbod
+ * Google Author(s): Behdad Esfahbod, Garret Rieger
+ */
+
+#ifndef OT_LAYOUT_COMMON_COVERAGE_HH
+#define OT_LAYOUT_COMMON_COVERAGE_HH
+
+#include "../types.hh"
+#include "CoverageFormat1.hh"
+#include "CoverageFormat2.hh"
+
+namespace OT {
+namespace Layout {
+namespace Common {
+
+template<typename Iterator>
+static inline void Coverage_serialize (hb_serialize_context_t *c,
+                                       Iterator it);
+
+struct Coverage
+{
+
+  protected:
+  union {
+  struct { HBUINT16 v; }        format;         /* Format identifier */
+  CoverageFormat1_3<SmallTypes> format1;
+  CoverageFormat2_4<SmallTypes> format2;
+#ifndef HB_NO_BEYOND_64K
+  CoverageFormat1_3<MediumTypes>format3;
+  CoverageFormat2_4<MediumTypes>format4;
+#endif
+  } u;
+  public:
+  DEFINE_SIZE_UNION (2, format.v);
+
+#ifndef HB_OPTIMIZE_SIZE
+  HB_ALWAYS_INLINE
+#endif
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    if (!u.format.v.sanitize (c)) return_trace (false);
+    hb_barrier ();
+    switch (u.format.v)
+    {
+    case 1: return_trace (u.format1.sanitize (c));
+    case 2: return_trace (u.format2.sanitize (c));
+#ifndef HB_NO_BEYOND_64K
+    case 3: return_trace (u.format3.sanitize (c));
+    case 4: return_trace (u.format4.sanitize (c));
+#endif
+    default:return_trace (true);
+    }
+  }
+
+  /* Has interface. */
+  unsigned operator [] (hb_codepoint_t k) const { return get (k); }
+  bool has (hb_codepoint_t k) const { return (*this)[k] != NOT_COVERED; }
+  /* Predicate. */
+  bool operator () (hb_codepoint_t k) const { return has (k); }
+
+  unsigned int get (hb_codepoint_t k) const { return get_coverage (k); }
+  unsigned int get_coverage (hb_codepoint_t glyph_id) const
+  {
+    switch (u.format.v) {
+    case 1: return u.format1.get_coverage (glyph_id);
+    case 2: return u.format2.get_coverage (glyph_id);
+#ifndef HB_NO_BEYOND_64K
+    case 3: return u.format3.get_coverage (glyph_id);
+    case 4: return u.format4.get_coverage (glyph_id);
+#endif
+    default:return NOT_COVERED;
+    }
+  }
+  unsigned int get_coverage (hb_codepoint_t glyph_id,
+			     hb_ot_layout_mapping_cache_t *cache) const
+  {
+    unsigned coverage;
+    if (cache && cache->get (glyph_id, &coverage)) return coverage < cache->MAX_VALUE ? coverage : NOT_COVERED;
+    coverage = get_coverage (glyph_id);
+    if (cache) {
+      if (coverage == NOT_COVERED)
+	cache->set_unchecked (glyph_id, cache->MAX_VALUE);
+      else if (likely (coverage < cache->MAX_VALUE))
+	cache->set_unchecked (glyph_id, coverage);
+    }
+    return coverage;
+  }
+
+  unsigned int get_coverage_binary (hb_codepoint_t glyph_id,
+				    hb_ot_layout_binary_cache_t *cache) const
+  {
+    unsigned coverage;
+    if (cache && cache->get (glyph_id, &coverage)) return coverage < cache->MAX_VALUE ? coverage : NOT_COVERED;
+    coverage = get_coverage (glyph_id);
+    if (cache) {
+      if (coverage == NOT_COVERED)
+	cache->set_unchecked (glyph_id, cache->MAX_VALUE);
+      else
+	cache->set_unchecked (glyph_id, 0);
+    }
+    return coverage;
+  }
+
+  unsigned get_population () const
+  {
+    switch (u.format.v) {
+    case 1: return u.format1.get_population ();
+    case 2: return u.format2.get_population ();
+#ifndef HB_NO_BEYOND_64K
+    case 3: return u.format3.get_population ();
+    case 4: return u.format4.get_population ();
+#endif
+    default:return NOT_COVERED;
+    }
+  }
+
+  template <typename Iterator,
+      hb_requires (hb_is_sorted_source_of (Iterator, hb_codepoint_t))>
+  bool serialize (hb_serialize_context_t *c, Iterator glyphs)
+  {
+    TRACE_SERIALIZE (this);
+    if (unlikely (!c->extend_min (this))) return_trace (false);
+
+    unsigned count = hb_len (glyphs);
+    unsigned num_ranges = 0;
+    hb_codepoint_t last = (hb_codepoint_t) -2;
+    hb_codepoint_t max = 0;
+    bool unsorted = false;
+    for (auto g: glyphs)
+    {
+      if (last != (hb_codepoint_t) -2 && g < last)
+	unsorted = true;
+      if (last + 1 != g)
+	num_ranges++;
+      last = g;
+      if (g > max) max = g;
+    }
+    u.format.v = !unsorted && count <= num_ranges * 3 ? 1 : 2;
+
+#ifndef HB_NO_BEYOND_64K
+    if (max > 0xFFFFu)
+      u.format.v += 2;
+    if (unlikely (max > 0xFFFFFFu))
+#else
+    if (unlikely (max > 0xFFFFu))
+#endif
+    {
+      c->check_success (false, HB_SERIALIZE_ERROR_INT_OVERFLOW);
+      return_trace (false);
+    }
+
+    switch (u.format.v)
+    {
+    case 1: return_trace (u.format1.serialize (c, glyphs));
+    case 2: return_trace (u.format2.serialize (c, glyphs));
+#ifndef HB_NO_BEYOND_64K
+    case 3: return_trace (u.format3.serialize (c, glyphs));
+    case 4: return_trace (u.format4.serialize (c, glyphs));
+#endif
+    default:return_trace (false);
+    }
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    auto it =
+    + iter ()
+    | hb_take (c->plan->source->get_num_glyphs ())
+    | hb_map_retains_sorting (c->plan->glyph_map_gsub)
+    | hb_filter ([] (hb_codepoint_t glyph) { return glyph != HB_MAP_VALUE_INVALID; })
+    ;
+
+    // Cache the iterator result as it will be iterated multiple times
+    // by the serialize code below.
+    hb_sorted_vector_t<hb_codepoint_t> glyphs (it);
+    Coverage_serialize (c->serializer, glyphs.iter ());
+    return_trace (bool (glyphs));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    switch (u.format.v)
+    {
+    case 1: return u.format1.intersects (glyphs);
+    case 2: return u.format2.intersects (glyphs);
+#ifndef HB_NO_BEYOND_64K
+    case 3: return u.format3.intersects (glyphs);
+    case 4: return u.format4.intersects (glyphs);
+#endif
+    default:return false;
+    }
+  }
+  bool intersects_coverage (const hb_set_t *glyphs, unsigned int index) const
+  {
+    switch (u.format.v)
+    {
+    case 1: return u.format1.intersects_coverage (glyphs, index);
+    case 2: return u.format2.intersects_coverage (glyphs, index);
+#ifndef HB_NO_BEYOND_64K
+    case 3: return u.format3.intersects_coverage (glyphs, index);
+    case 4: return u.format4.intersects_coverage (glyphs, index);
+#endif
+    default:return false;
+    }
+  }
+
+  unsigned cost () const
+  {
+    switch (u.format.v) {
+    case 1: hb_barrier (); return u.format1.cost ();
+    case 2: hb_barrier (); return u.format2.cost ();
+#ifndef HB_NO_BEYOND_64K
+    case 3: hb_barrier (); return u.format3.cost ();
+    case 4: hb_barrier (); return u.format4.cost ();
+#endif
+    default:return 0u;
+    }
+  }
+
+  /* Might return false if array looks unsorted.
+   * Used for faster rejection of corrupt data. */
+  template <typename set_t>
+  bool collect_coverage (set_t *glyphs) const
+  {
+    switch (u.format.v)
+    {
+    case 1: return u.format1.collect_coverage (glyphs);
+    case 2: return u.format2.collect_coverage (glyphs);
+#ifndef HB_NO_BEYOND_64K
+    case 3: return u.format3.collect_coverage (glyphs);
+    case 4: return u.format4.collect_coverage (glyphs);
+#endif
+    default:return false;
+    }
+  }
+
+  template <typename IterableOut,
+	    hb_requires (hb_is_sink_of (IterableOut, hb_codepoint_t))>
+  void intersect_set (const hb_set_t &glyphs, IterableOut&& intersect_glyphs) const
+  {
+    switch (u.format.v)
+    {
+    case 1: return u.format1.intersect_set (glyphs, intersect_glyphs);
+    case 2: return u.format2.intersect_set (glyphs, intersect_glyphs);
+#ifndef HB_NO_BEYOND_64K
+    case 3: return u.format3.intersect_set (glyphs, intersect_glyphs);
+    case 4: return u.format4.intersect_set (glyphs, intersect_glyphs);
+#endif
+    default:return ;
+    }
+  }
+
+  struct iter_t : hb_iter_with_fallback_t<iter_t, hb_codepoint_t>
+  {
+    static constexpr bool is_sorted_iterator = true;
+    iter_t (const Coverage &c_ = Null (Coverage))
+    {
+      hb_memset (this, 0, sizeof (*this));
+      format = c_.u.format.v;
+      switch (format)
+      {
+      case 1: u.format1.init (c_.u.format1); return;
+      case 2: u.format2.init (c_.u.format2); return;
+#ifndef HB_NO_BEYOND_64K
+      case 3: u.format3.init (c_.u.format3); return;
+      case 4: u.format4.init (c_.u.format4); return;
+#endif
+      default:                               return;
+      }
+    }
+    bool __more__ () const
+    {
+      switch (format)
+      {
+      case 1: return u.format1.__more__ ();
+      case 2: return u.format2.__more__ ();
+#ifndef HB_NO_BEYOND_64K
+      case 3: return u.format3.__more__ ();
+      case 4: return u.format4.__more__ ();
+#endif
+      default:return false;
+      }
+    }
+    void __next__ ()
+    {
+      switch (format)
+      {
+      case 1: u.format1.__next__ (); break;
+      case 2: u.format2.__next__ (); break;
+#ifndef HB_NO_BEYOND_64K
+      case 3: u.format3.__next__ (); break;
+      case 4: u.format4.__next__ (); break;
+#endif
+      default:                   break;
+      }
+    }
+    typedef hb_codepoint_t __item_t__;
+    __item_t__ __item__ () const { return get_glyph (); }
+
+    hb_codepoint_t get_glyph () const
+    {
+      switch (format)
+      {
+      case 1: return u.format1.get_glyph ();
+      case 2: return u.format2.get_glyph ();
+#ifndef HB_NO_BEYOND_64K
+      case 3: return u.format3.get_glyph ();
+      case 4: return u.format4.get_glyph ();
+#endif
+      default:return 0;
+      }
+    }
+    bool operator != (const iter_t& o) const
+    {
+      if (unlikely (format != o.format)) return true;
+      switch (format)
+      {
+      case 1: return u.format1 != o.u.format1;
+      case 2: return u.format2 != o.u.format2;
+#ifndef HB_NO_BEYOND_64K
+      case 3: return u.format3 != o.u.format3;
+      case 4: return u.format4 != o.u.format4;
+#endif
+      default:return false;
+      }
+    }
+    iter_t __end__ () const
+    {
+      iter_t it;
+      it.format = format;
+      switch (format)
+      {
+      case 1: it.u.format1 = u.format1.__end__ (); break;
+      case 2: it.u.format2 = u.format2.__end__ (); break;
+#ifndef HB_NO_BEYOND_64K
+      case 3: it.u.format3 = u.format3.__end__ (); break;
+      case 4: it.u.format4 = u.format4.__end__ (); break;
+#endif
+      default: break;
+      }
+      return it;
+    }
+
+    private:
+    unsigned int format;
+    union {
+#ifndef HB_NO_BEYOND_64K
+    CoverageFormat2_4<MediumTypes>::iter_t      format4; /* Put this one first since it's larger; helps shut up compiler. */
+    CoverageFormat1_3<MediumTypes>::iter_t      format3;
+#endif
+    CoverageFormat2_4<SmallTypes>::iter_t       format2; /* Put this one first since it's larger; helps shut up compiler. */
+    CoverageFormat1_3<SmallTypes>::iter_t       format1;
+    } u;
+  };
+  iter_t iter () const { return iter_t (*this); }
+};
+
+template<typename Iterator>
+static inline void
+Coverage_serialize (hb_serialize_context_t *c,
+                    Iterator it)
+{ c->start_embed<Coverage> ()->serialize (c, it); }
+
+}
+}
+}
+
+#endif  // #ifndef OT_LAYOUT_COMMON_COVERAGE_HH

3rdparty/harfbuzz/src/OT/Layout/Common/CoverageFormat1.hh

@@ -0,0 +1,135 @@
+/*
+ * Copyright © 2007,2008,2009  Red Hat, Inc.
+ * Copyright © 2010,2012  Google, Inc.
+ *
+ *  This is part of HarfBuzz, a text shaping library.
+ *
+ * Permission is hereby granted, without written agreement and without
+ * license or royalty fees, to use, copy, modify, and distribute this
+ * software and its documentation for any purpose, provided that the
+ * above copyright notice and the following two paragraphs appear in
+ * all copies of this software.
+ *
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+ * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+ * DAMAGE.
+ *
+ * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+ * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+ * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ * Red Hat Author(s): Behdad Esfahbod
+ * Google Author(s): Behdad Esfahbod, Garret Rieger
+ */
+
+
+#ifndef OT_LAYOUT_COMMON_COVERAGEFORMAT1_HH
+#define OT_LAYOUT_COMMON_COVERAGEFORMAT1_HH
+
+namespace OT {
+namespace Layout {
+namespace Common {
+
+#define NOT_COVERED             ((unsigned int) -1)
+
+template <typename Types>
+struct CoverageFormat1_3
+{
+  friend struct Coverage;
+
+  public:
+  HBUINT16      coverageFormat; /* Format identifier--format = 1 */
+  SortedArray16Of<typename Types::HBGlyphID>
+                glyphArray;     /* Array of GlyphIDs--in numerical order */
+
+  DEFINE_SIZE_ARRAY (4, glyphArray);
+
+  private:
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (glyphArray.sanitize (c));
+  }
+
+  unsigned int get_coverage (hb_codepoint_t glyph_id) const
+  {
+    unsigned int i;
+    glyphArray.bfind (glyph_id, &i, HB_NOT_FOUND_STORE, NOT_COVERED);
+    return i;
+  }
+
+  unsigned get_population () const
+  {
+    return glyphArray.len;
+  }
+
+  template <typename Iterator,
+      hb_requires (hb_is_sorted_source_of (Iterator, hb_codepoint_t))>
+  bool serialize (hb_serialize_context_t *c, Iterator glyphs)
+  {
+    TRACE_SERIALIZE (this);
+    return_trace (glyphArray.serialize (c, glyphs));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    if (glyphArray.len > glyphs->get_population () * hb_bit_storage ((unsigned) glyphArray.len))
+    {
+      for (auto g : *glyphs)
+        if (get_coverage (g) != NOT_COVERED)
+	  return true;
+      return false;
+    }
+
+    for (const auto& g : glyphArray.as_array ())
+      if (glyphs->has (g))
+        return true;
+    return false;
+  }
+  bool intersects_coverage (const hb_set_t *glyphs, unsigned int index) const
+  { return glyphs->has (glyphArray[index]); }
+
+  template <typename IterableOut,
+	    hb_requires (hb_is_sink_of (IterableOut, hb_codepoint_t))>
+  void intersect_set (const hb_set_t &glyphs, IterableOut&& intersect_glyphs) const
+  {
+    unsigned count = glyphArray.len;
+    for (unsigned i = 0; i < count; i++)
+      if (glyphs.has (glyphArray[i]))
+        intersect_glyphs << glyphArray[i];
+  }
+
+  unsigned cost () const { return hb_bit_storage ((unsigned) glyphArray.len); /* bsearch cost */ }
+
+  template <typename set_t>
+  bool collect_coverage (set_t *glyphs) const
+  { return glyphs->add_sorted_array (glyphArray.as_array ()); }
+
+  public:
+  /* Older compilers need this to be public. */
+  struct iter_t
+  {
+    void init (const struct CoverageFormat1_3 &c_) { c = &c_; i = 0; }
+    bool __more__ () const { return i < c->glyphArray.len; }
+    void __next__ () { i++; }
+    hb_codepoint_t get_glyph () const { return c->glyphArray[i]; }
+    bool operator != (const iter_t& o) const
+    { return i != o.i; }
+    iter_t __end__ () const { iter_t it; it.init (*c); it.i = c->glyphArray.len; return it; }
+
+    private:
+    const struct CoverageFormat1_3 *c;
+    unsigned int i;
+  };
+  private:
+};
+
+}
+}
+}
+
+#endif  // #ifndef OT_LAYOUT_COMMON_COVERAGEFORMAT1_HH

3rdparty/harfbuzz/src/OT/Layout/Common/CoverageFormat2.hh

@@ -0,0 +1,241 @@
+/*
+ * Copyright © 2007,2008,2009  Red Hat, Inc.
+ * Copyright © 2010,2012  Google, Inc.
+ *
+ *  This is part of HarfBuzz, a text shaping library.
+ *
+ * Permission is hereby granted, without written agreement and without
+ * license or royalty fees, to use, copy, modify, and distribute this
+ * software and its documentation for any purpose, provided that the
+ * above copyright notice and the following two paragraphs appear in
+ * all copies of this software.
+ *
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+ * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+ * DAMAGE.
+ *
+ * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+ * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+ * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ * Red Hat Author(s): Behdad Esfahbod
+ * Google Author(s): Behdad Esfahbod, Garret Rieger
+ */
+
+#ifndef OT_LAYOUT_COMMON_COVERAGEFORMAT2_HH
+#define OT_LAYOUT_COMMON_COVERAGEFORMAT2_HH
+
+#include "RangeRecord.hh"
+
+namespace OT {
+namespace Layout {
+namespace Common {
+
+template <typename Types>
+struct CoverageFormat2_4
+{
+  friend struct Coverage;
+
+  public:
+  HBUINT16      coverageFormat; /* Format identifier--format = 2 */
+  SortedArray16Of<RangeRecord<Types>>
+                rangeRecord;    /* Array of glyph ranges--ordered by
+                                 * Start GlyphID. rangeCount entries
+                                 * long */
+  public:
+  DEFINE_SIZE_ARRAY (4, rangeRecord);
+
+  private:
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (rangeRecord.sanitize (c));
+  }
+
+  unsigned int get_coverage (hb_codepoint_t glyph_id) const
+  {
+    const RangeRecord<Types> &range = rangeRecord.bsearch (glyph_id);
+    return likely (range.first <= range.last)
+         ? (unsigned int) range.value + (glyph_id - range.first)
+         : NOT_COVERED;
+  }
+
+  unsigned get_population () const
+  {
+    typename Types::large_int ret = 0;
+    for (const auto &r : rangeRecord)
+      ret += r.get_population ();
+    return ret > UINT_MAX ? UINT_MAX : (unsigned) ret;
+  }
+
+  template <typename Iterator,
+      hb_requires (hb_is_sorted_source_of (Iterator, hb_codepoint_t))>
+  bool serialize (hb_serialize_context_t *c, Iterator glyphs)
+  {
+    TRACE_SERIALIZE (this);
+    if (unlikely (!c->extend_min (this))) return_trace (false);
+
+    unsigned num_ranges = 0;
+    hb_codepoint_t last = (hb_codepoint_t) -2;
+    for (auto g: glyphs)
+    {
+      if (last + 1 != g)
+        num_ranges++;
+      last = g;
+    }
+
+    if (unlikely (!rangeRecord.serialize (c, num_ranges))) return_trace (false);
+    if (!num_ranges) return_trace (true);
+
+    unsigned count = 0;
+    unsigned range = (unsigned) -1;
+    last = (hb_codepoint_t) -2;
+    unsigned unsorted = false;
+    for (auto g: glyphs)
+    {
+      if (last + 1 != g)
+      {
+	if (unlikely (last != (hb_codepoint_t) -2 && last + 1 > g))
+	  unsorted = true;
+
+        range++;
+        rangeRecord.arrayZ[range].first = g;
+        rangeRecord.arrayZ[range].value = count;
+      }
+      rangeRecord.arrayZ[range].last = g;
+      last = g;
+      count++;
+    }
+
+    if (unlikely (unsorted))
+      rangeRecord.as_array ().qsort (RangeRecord<Types>::cmp_range);
+
+    return_trace (true);
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    if (rangeRecord.len > glyphs->get_population () * hb_bit_storage ((unsigned) rangeRecord.len))
+    {
+      for (auto g : *glyphs)
+        if (get_coverage (g) != NOT_COVERED)
+	  return true;
+      return false;
+    }
+
+    return hb_any (+ hb_iter (rangeRecord)
+                   | hb_map ([glyphs] (const RangeRecord<Types> &range) { return range.intersects (*glyphs); }));
+  }
+  bool intersects_coverage (const hb_set_t *glyphs, unsigned int index) const
+  {
+    auto *range = rangeRecord.as_array ().bsearch (index);
+    if (range)
+      return range->intersects (*glyphs);
+    return false;
+  }
+
+  template <typename IterableOut,
+	    hb_requires (hb_is_sink_of (IterableOut, hb_codepoint_t))>
+  void intersect_set (const hb_set_t &glyphs, IterableOut&& intersect_glyphs) const
+  {
+    /* Break out of loop for overlapping, broken, tables,
+     * to avoid fuzzer timouts. */
+    hb_codepoint_t last = 0;
+    for (const auto& range : rangeRecord)
+    {
+      if (unlikely (range.first < last))
+        break;
+      last = range.last;
+      for (hb_codepoint_t g = range.first - 1;
+	   glyphs.next (&g) && g <= last;)
+	intersect_glyphs << g;
+    }
+  }
+
+  unsigned cost () const { return hb_bit_storage ((unsigned) rangeRecord.len); /* bsearch cost */ }
+
+  template <typename set_t>
+  bool collect_coverage (set_t *glyphs) const
+  {
+    for (const auto& range: rangeRecord)
+      if (unlikely (!range.collect_coverage (glyphs)))
+        return false;
+    return true;
+  }
+
+  public:
+  /* Older compilers need this to be public. */
+  struct iter_t
+  {
+    void init (const CoverageFormat2_4 &c_)
+    {
+      c = &c_;
+      coverage = 0;
+      i = 0;
+      j = c->rangeRecord.len ? c->rangeRecord[0].first : 0;
+      if (unlikely (c->rangeRecord[0].first > c->rangeRecord[0].last))
+      {
+        /* Broken table. Skip. */
+        i = c->rangeRecord.len;
+        j = 0;
+      }
+    }
+    bool __more__ () const { return i < c->rangeRecord.len; }
+    void __next__ ()
+    {
+      if (j >= c->rangeRecord[i].last)
+      {
+        i++;
+        if (__more__ ())
+        {
+          unsigned int old = coverage;
+          j = c->rangeRecord.arrayZ[i].first;
+          coverage = c->rangeRecord.arrayZ[i].value;
+          if (unlikely (coverage != old + 1))
+          {
+            /* Broken table. Skip. Important to avoid DoS.
+             * Also, our callers depend on coverage being
+             * consecutive and monotonically increasing,
+             * ie. iota(). */
+           i = c->rangeRecord.len;
+           j = 0;
+           return;
+          }
+        }
+        else
+          j = 0;
+        return;
+      }
+      coverage++;
+      j++;
+    }
+    hb_codepoint_t get_glyph () const { return j; }
+    bool operator != (const iter_t& o) const
+    { return i != o.i || j != o.j; }
+    iter_t __end__ () const
+    {
+      iter_t it;
+      it.init (*c);
+      it.i = c->rangeRecord.len;
+      it.j = 0;
+      return it;
+    }
+
+    private:
+    const struct CoverageFormat2_4 *c;
+    unsigned int i, coverage;
+    hb_codepoint_t j;
+  };
+  private:
+};
+
+}
+}
+}
+
+#endif  // #ifndef OT_LAYOUT_COMMON_COVERAGEFORMAT2_HH

3rdparty/harfbuzz/src/OT/Layout/Common/RangeRecord.hh

@@ -0,0 +1,97 @@
+/*
+ * Copyright © 2007,2008,2009  Red Hat, Inc.
+ * Copyright © 2010,2012  Google, Inc.
+ *
+ *  This is part of HarfBuzz, a text shaping library.
+ *
+ * Permission is hereby granted, without written agreement and without
+ * license or royalty fees, to use, copy, modify, and distribute this
+ * software and its documentation for any purpose, provided that the
+ * above copyright notice and the following two paragraphs appear in
+ * all copies of this software.
+ *
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
+ * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
+ * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+ * DAMAGE.
+ *
+ * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
+ * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
+ * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ * Red Hat Author(s): Behdad Esfahbod
+ * Google Author(s): Behdad Esfahbod, Garret Rieger
+ */
+
+#ifndef OT_LAYOUT_COMMON_RANGERECORD_HH
+#define OT_LAYOUT_COMMON_RANGERECORD_HH
+
+namespace OT {
+namespace Layout {
+namespace Common {
+
+template <typename Types>
+struct RangeRecord
+{
+  typename Types::HBGlyphID     first;          /* First GlyphID in the range */
+  typename Types::HBGlyphID     last;           /* Last GlyphID in the range */
+  HBUINT16                      value;          /* Value */
+
+  DEFINE_SIZE_STATIC (2 + 2 * Types::size);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this));
+  }
+
+  int cmp (hb_codepoint_t g) const
+  { return g < first ? -1 : g <= last ? 0 : +1; }
+
+  HB_INTERNAL static int cmp_range (const void *pa, const void *pb) {
+    const RangeRecord *a = (const RangeRecord *) pa;
+    const RangeRecord *b = (const RangeRecord *) pb;
+    if (a->first < b->first) return -1;
+    if (a->first > b->first) return +1;
+    if (a->last < b->last) return -1;
+    if (a->last > b->last) return +1;
+    if (a->value < b->value) return -1;
+    if (a->value > b->value) return +1;
+    return 0;
+  }
+
+  unsigned get_population () const
+  {
+    if (unlikely (last < first)) return 0;
+    return (last - first + 1);
+  }
+
+  bool intersects (const hb_set_t &glyphs) const
+  { return glyphs.intersects (first, last); }
+
+  template <typename set_t>
+  bool collect_coverage (set_t *glyphs) const
+  { return glyphs->add_range (first, last); }
+};
+
+}
+}
+}
+
+// TODO(garretrieger): This was previously implemented using
+//    DECLARE_NULL_NAMESPACE_BYTES_TEMPLATE1 (OT, RangeRecord, 9);
+//    but that only works when there is only a single namespace level.
+//    The macro should probably be fixed so it can work in this situation.
+extern HB_INTERNAL const unsigned char _hb_Null_OT_RangeRecord[9];
+template <typename Spec>
+struct Null<OT::Layout::Common::RangeRecord<Spec>> {
+  static OT::Layout::Common::RangeRecord<Spec> const & get_null () {
+    return *reinterpret_cast<const OT::Layout::Common::RangeRecord<Spec> *> (_hb_Null_OT_RangeRecord);
+  }
+};
+
+
+#endif  // #ifndef OT_LAYOUT_COMMON_RANGERECORD_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/Anchor.hh

@@ -0,0 +1,84 @@
+#ifndef OT_LAYOUT_GPOS_ANCHOR_HH
+#define OT_LAYOUT_GPOS_ANCHOR_HH
+
+#include "AnchorFormat1.hh"
+#include "AnchorFormat2.hh"
+#include "AnchorFormat3.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct Anchor
+{
+  protected:
+  union {
+  struct { HBUINT16 v; } format;        /* Format identifier */
+  AnchorFormat1         format1;
+  AnchorFormat2         format2;
+  AnchorFormat3         format3;
+  } u;
+  public:
+  DEFINE_SIZE_UNION (2, format.v);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    if (!u.format.v.sanitize (c)) return_trace (false);
+    hb_barrier ();
+    switch (u.format.v) {
+    case 1: return_trace (u.format1.sanitize (c));
+    case 2: return_trace (u.format2.sanitize (c));
+    case 3: return_trace (u.format3.sanitize (c));
+    default:return_trace (true);
+    }
+  }
+
+  void get_anchor (hb_ot_apply_context_t *c, hb_codepoint_t glyph_id,
+                   float *x, float *y) const
+  {
+    *x = *y = 0;
+    switch (u.format.v) {
+    case 1: u.format1.get_anchor (c, glyph_id, x, y); return;
+    case 2: u.format2.get_anchor (c, glyph_id, x, y); return;
+    case 3: u.format3.get_anchor (c, glyph_id, x, y); return;
+    default:                                          return;
+    }
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    switch (u.format.v) {
+    case 1: return_trace (bool (reinterpret_cast<Anchor *> (u.format1.copy (c->serializer))));
+    case 2:
+      if (c->plan->flags & HB_SUBSET_FLAGS_NO_HINTING)
+      {
+        // AnchorFormat 2 just containins extra hinting information, so
+        // if hints are being dropped convert to format 1.
+        return_trace (bool (reinterpret_cast<Anchor *> (u.format1.copy (c->serializer))));
+      }
+      return_trace (bool (reinterpret_cast<Anchor *> (u.format2.copy (c->serializer))));
+    case 3: return_trace (u.format3.subset (c));
+    default:return_trace (false);
+    }
+  }
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    switch (u.format.v) {
+    case 1: case 2:
+      return;
+    case 3:
+      u.format3.collect_variation_indices (c);
+      return;
+    default: return;
+    }
+  }
+};
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_ANCHOR_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/AnchorFormat1.hh

@@ -0,0 +1,46 @@
+#ifndef OT_LAYOUT_GPOS_ANCHORFORMAT1_HH
+#define OT_LAYOUT_GPOS_ANCHORFORMAT1_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct AnchorFormat1
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  FWORD         xCoordinate;            /* Horizontal value--in design units */
+  FWORD         yCoordinate;            /* Vertical value--in design units */
+  public:
+  DEFINE_SIZE_STATIC (6);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this));
+  }
+
+  void get_anchor (hb_ot_apply_context_t *c, hb_codepoint_t glyph_id HB_UNUSED,
+                   float *x, float *y) const
+  {
+    hb_font_t *font = c->font;
+    *x = font->em_fscale_x (xCoordinate);
+    *y = font->em_fscale_y (yCoordinate);
+  }
+
+  AnchorFormat1* copy (hb_serialize_context_t *c) const
+  {
+    TRACE_SERIALIZE (this);
+    AnchorFormat1* out = c->embed<AnchorFormat1> (this);
+    if (!out) return_trace (out);
+    out->format = 1;
+    return_trace (out);
+  }
+};
+
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_ANCHORFORMAT1_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/AnchorFormat2.hh

@@ -0,0 +1,58 @@
+#ifndef OT_LAYOUT_GPOS_ANCHORFORMAT2_HH
+#define OT_LAYOUT_GPOS_ANCHORFORMAT2_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct AnchorFormat2
+{
+
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 2 */
+  FWORD         xCoordinate;            /* Horizontal value--in design units */
+  FWORD         yCoordinate;            /* Vertical value--in design units */
+  HBUINT16      anchorPoint;            /* Index to glyph contour point */
+  public:
+  DEFINE_SIZE_STATIC (8);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this));
+  }
+
+  void get_anchor (hb_ot_apply_context_t *c, hb_codepoint_t glyph_id,
+                   float *x, float *y) const
+  {
+    hb_font_t *font = c->font;
+
+#ifdef HB_NO_HINTING
+    *x = font->em_fscale_x (xCoordinate);
+    *y = font->em_fscale_y (yCoordinate);
+    return;
+#endif
+
+    unsigned int x_ppem = font->x_ppem;
+    unsigned int y_ppem = font->y_ppem;
+    hb_position_t cx = 0, cy = 0;
+    bool ret;
+
+    ret = (x_ppem || y_ppem) &&
+          font->get_glyph_contour_point_for_origin (glyph_id, anchorPoint, HB_DIRECTION_LTR, &cx, &cy);
+    *x = ret && x_ppem ? cx : font->em_fscale_x (xCoordinate);
+    *y = ret && y_ppem ? cy : font->em_fscale_y (yCoordinate);
+  }
+
+  AnchorFormat2* copy (hb_serialize_context_t *c) const
+  {
+    TRACE_SERIALIZE (this);
+    return_trace (c->embed<AnchorFormat2> (this));
+  }
+};
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_ANCHORFORMAT2_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/AnchorFormat3.hh

@@ -0,0 +1,123 @@
+#ifndef OT_LAYOUT_GPOS_ANCHORFORMAT3_HH
+#define OT_LAYOUT_GPOS_ANCHORFORMAT3_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct AnchorFormat3
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 3 */
+  FWORD         xCoordinate;            /* Horizontal value--in design units */
+  FWORD         yCoordinate;            /* Vertical value--in design units */
+  Offset16To<Device>
+                xDeviceTable;           /* Offset to Device table for X
+                                         * coordinate-- from beginning of
+                                         * Anchor table (may be NULL) */
+  Offset16To<Device>
+                yDeviceTable;           /* Offset to Device table for Y
+                                         * coordinate-- from beginning of
+                                         * Anchor table (may be NULL) */
+  public:
+  DEFINE_SIZE_STATIC (10);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    if (unlikely (!c->check_struct (this))) return_trace (false);
+
+    return_trace (xDeviceTable.sanitize (c, this) && yDeviceTable.sanitize (c, this));
+  }
+
+  void get_anchor (hb_ot_apply_context_t *c, hb_codepoint_t glyph_id HB_UNUSED,
+                   float *x, float *y) const
+  {
+    hb_font_t *font = c->font;
+    *x = font->em_fscale_x (xCoordinate);
+    *y = font->em_fscale_y (yCoordinate);
+
+    if ((font->x_ppem || font->has_nonzero_coords) && xDeviceTable.sanitize (&c->sanitizer, this))
+    {
+      hb_barrier ();
+      *x += (this+xDeviceTable).get_x_delta (font, c->var_store, c->var_store_cache);
+    }
+    if ((font->y_ppem || font->has_nonzero_coords) && yDeviceTable.sanitize (&c->sanitizer, this))
+    {
+      hb_barrier ();
+      *y += (this+yDeviceTable).get_y_delta (font, c->var_store, c->var_store_cache);
+    }
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->embed (format))) return_trace (false);
+    if (unlikely (!c->serializer->embed (xCoordinate))) return_trace (false);
+    if (unlikely (!c->serializer->embed (yCoordinate))) return_trace (false);
+
+    unsigned x_varidx = xDeviceTable ? (this+xDeviceTable).get_variation_index () : HB_OT_LAYOUT_NO_VARIATIONS_INDEX;
+    if (x_varidx != HB_OT_LAYOUT_NO_VARIATIONS_INDEX)
+    {
+      hb_pair_t<unsigned, int> *new_varidx_delta;
+      if (!c->plan->layout_variation_idx_delta_map.has (x_varidx, &new_varidx_delta))
+        return_trace (false);
+
+      x_varidx = hb_first (*new_varidx_delta);
+      int delta = hb_second (*new_varidx_delta);
+      if (delta != 0)
+      {
+        if (!c->serializer->check_assign (out->xCoordinate, xCoordinate + delta,
+                                          HB_SERIALIZE_ERROR_INT_OVERFLOW))
+          return_trace (false);
+      }
+    }
+
+    unsigned y_varidx = yDeviceTable ? (this+yDeviceTable).get_variation_index () : HB_OT_LAYOUT_NO_VARIATIONS_INDEX;
+    if (y_varidx != HB_OT_LAYOUT_NO_VARIATIONS_INDEX)
+    {
+      hb_pair_t<unsigned, int> *new_varidx_delta;
+      if (!c->plan->layout_variation_idx_delta_map.has (y_varidx, &new_varidx_delta))
+        return_trace (false);
+
+      y_varidx = hb_first (*new_varidx_delta);
+      int delta = hb_second (*new_varidx_delta);
+      if (delta != 0)
+      {
+        if (!c->serializer->check_assign (out->yCoordinate, yCoordinate + delta,
+                                          HB_SERIALIZE_ERROR_INT_OVERFLOW))
+          return_trace (false);
+      }
+    }
+
+
+    bool no_downgrade = (!xDeviceTable.is_null () && !(this+xDeviceTable).is_variation_device ()) ||
+                        x_varidx != HB_OT_LAYOUT_NO_VARIATIONS_INDEX ||
+                        y_varidx != HB_OT_LAYOUT_NO_VARIATIONS_INDEX ||
+                        (!yDeviceTable.is_null () && !(this+yDeviceTable).is_variation_device ());
+
+    if (!no_downgrade)
+      return_trace (c->serializer->check_assign (out->format, 1, HB_SERIALIZE_ERROR_INT_OVERFLOW));
+
+    if (!c->serializer->embed (xDeviceTable)) return_trace (false);
+    if (!c->serializer->embed (yDeviceTable)) return_trace (false);
+
+    out->xDeviceTable.serialize_copy (c->serializer, xDeviceTable, this, 0, hb_serialize_context_t::Head, &c->plan->layout_variation_idx_delta_map);
+    out->yDeviceTable.serialize_copy (c->serializer, yDeviceTable, this, 0, hb_serialize_context_t::Head, &c->plan->layout_variation_idx_delta_map);
+    return_trace (out);
+  }
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    (this+xDeviceTable).collect_variation_indices (c);
+    (this+yDeviceTable).collect_variation_indices (c);
+  }
+};
+
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_ANCHORFORMAT3_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/AnchorMatrix.hh

@@ -0,0 +1,94 @@
+#ifndef OT_LAYOUT_GPOS_ANCHORMATRIX_HH
+#define OT_LAYOUT_GPOS_ANCHORMATRIX_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct AnchorMatrix
+{
+  HBUINT16      rows;                   /* Number of rows */
+  UnsizedArrayOf<Offset16To<Anchor, AnchorMatrix>>
+                matrixZ;                /* Matrix of offsets to Anchor tables--
+                                         * from beginning of AnchorMatrix table */
+  public:
+  DEFINE_SIZE_ARRAY (2, matrixZ);
+
+  bool sanitize (hb_sanitize_context_t *c, unsigned int cols) const
+  {
+    TRACE_SANITIZE (this);
+    if (!c->check_struct (this)) return_trace (false);
+    hb_barrier ();
+    if (unlikely (hb_unsigned_mul_overflows (rows, cols))) return_trace (false);
+    unsigned int count = rows * cols;
+    if (!c->check_array (matrixZ.arrayZ, count)) return_trace (false);
+
+    if (c->lazy_some_gpos)
+      return_trace (true);
+
+    hb_barrier ();
+    for (unsigned int i = 0; i < count; i++)
+      if (!matrixZ[i].sanitize (c, this)) return_trace (false);
+    return_trace (true);
+  }
+
+  const Anchor& get_anchor (hb_ot_apply_context_t *c,
+			    unsigned int row, unsigned int col,
+			    unsigned int cols, bool *found) const
+  {
+    *found = false;
+    if (unlikely (row >= rows || col >= cols)) return Null (Anchor);
+    auto &offset = matrixZ[row * cols + col];
+    if (unlikely (!offset.sanitize (&c->sanitizer, this))) return Null (Anchor);
+    hb_barrier ();
+    *found = !offset.is_null ();
+    return this+offset;
+  }
+
+  template <typename Iterator,
+            hb_requires (hb_is_iterator (Iterator))>
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c,
+                                  Iterator index_iter) const
+  {
+    for (unsigned i : index_iter)
+      (this+matrixZ[i]).collect_variation_indices (c);
+  }
+
+  template <typename Iterator,
+      hb_requires (hb_is_iterator (Iterator))>
+  bool subset (hb_subset_context_t *c,
+               unsigned             num_rows,
+               Iterator             index_iter) const
+  {
+    TRACE_SUBSET (this);
+
+    auto *out = c->serializer->start_embed (this);
+
+    if (!index_iter) return_trace (false);
+    if (unlikely (!c->serializer->extend_min (out)))  return_trace (false);
+
+    out->rows = num_rows;
+    for (const unsigned i : index_iter)
+    {
+      auto *offset = c->serializer->embed (matrixZ[i]);
+      if (!offset) return_trace (false);
+      offset->serialize_subset (c, matrixZ[i], this);
+    }
+
+    return_trace (true);
+  }
+
+  bool offset_is_null (unsigned row, unsigned col, unsigned num_cols) const
+  {
+    if (unlikely (row >= rows || col >= num_cols)) return true;
+    auto &offset = matrixZ[row * num_cols + col];
+    return offset.is_null ();
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_ANCHORMATRIX_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/ChainContextPos.hh

@@ -0,0 +1,14 @@
+#ifndef OT_LAYOUT_GPOS_CHAINCONTEXTPOS_HH
+#define OT_LAYOUT_GPOS_CHAINCONTEXTPOS_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct ChainContextPos : ChainContext {};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_CHAINCONTEXTPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/Common.hh

@@ -0,0 +1,33 @@
+#ifndef OT_LAYOUT_GPOS_COMMON_HH
+#define OT_LAYOUT_GPOS_COMMON_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+enum attach_type_t {
+  ATTACH_TYPE_NONE      = 0X00,
+
+  /* Each attachment should be either a mark or a cursive; can't be both. */
+  ATTACH_TYPE_MARK      = 0X01,
+  ATTACH_TYPE_CURSIVE   = 0X02,
+};
+
+/* buffer **position** var allocations */
+#define attach_chain() var.i16[0] /* glyph to which this attaches to, relative to current glyphs; negative for going back, positive for forward. */
+#define attach_type() var.u8[2] /* attachment type */
+/* Note! if attach_chain() is zero, the value of attach_type() is irrelevant. */
+
+template<typename Iterator, typename SrcLookup>
+static void SinglePos_serialize (hb_serialize_context_t *c,
+                                 const SrcLookup *src,
+                                 Iterator it,
+                                 const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map,
+                                 unsigned new_format);
+
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_COMMON_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/ContextPos.hh

@@ -0,0 +1,14 @@
+#ifndef OT_LAYOUT_GPOS_CONTEXTPOS_HH
+#define OT_LAYOUT_GPOS_CONTEXTPOS_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct ContextPos : Context {};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_CONTEXTPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/CursivePos.hh

@@ -0,0 +1,35 @@
+#ifndef OT_LAYOUT_GPOS_CURSIVEPOS_HH
+#define OT_LAYOUT_GPOS_CURSIVEPOS_HH
+
+#include "CursivePosFormat1.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct CursivePos
+{
+  protected:
+  union {
+  struct { HBUINT16 v; } format;        /* Format identifier */
+  CursivePosFormat1     format1;
+  } u;
+
+  public:
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  {
+    if (unlikely (!c->may_dispatch (this, &u.format.v))) return c->no_dispatch_return_value ();
+    TRACE_DISPATCH (this, u.format.v);
+    switch (u.format.v) {
+    case 1: return_trace (c->dispatch (u.format1, std::forward<Ts> (ds)...));
+    default:return_trace (c->default_return_value ());
+    }
+  }
+};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_CURSIVEPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/CursivePosFormat1.hh

@@ -0,0 +1,332 @@
+#ifndef OT_LAYOUT_GPOS_CURSIVEPOSFORMAT1_HH
+#define OT_LAYOUT_GPOS_CURSIVEPOSFORMAT1_HH
+
+#include "Anchor.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct EntryExitRecord
+{
+  friend struct CursivePosFormat1;
+
+  bool sanitize (hb_sanitize_context_t *c, const struct CursivePosFormat1 *base) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (entryAnchor.sanitize (c, base) && exitAnchor.sanitize (c, base));
+  }
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c,
+                                  const struct CursivePosFormat1 *src_base) const
+  {
+    (src_base+entryAnchor).collect_variation_indices (c);
+    (src_base+exitAnchor).collect_variation_indices (c);
+  }
+
+  bool subset (hb_subset_context_t *c,
+	       const struct CursivePosFormat1 *src_base) const
+  {
+    TRACE_SERIALIZE (this);
+    auto *out = c->serializer->embed (this);
+    if (unlikely (!out)) return_trace (false);
+
+    bool ret = false;
+    ret |= out->entryAnchor.serialize_subset (c, entryAnchor, src_base);
+    ret |= out->exitAnchor.serialize_subset (c, exitAnchor, src_base);
+    return_trace (ret);
+  }
+
+  protected:
+  Offset16To<Anchor, struct CursivePosFormat1>
+                entryAnchor;            /* Offset to EntryAnchor table--from
+                                         * beginning of CursivePos
+                                         * subtable--may be NULL */
+  Offset16To<Anchor, struct CursivePosFormat1>
+                exitAnchor;             /* Offset to ExitAnchor table--from
+                                         * beginning of CursivePos
+                                         * subtable--may be NULL */
+  public:
+  DEFINE_SIZE_STATIC (4);
+};
+
+static inline void
+reverse_cursive_minor_offset (hb_glyph_position_t *pos,
+                              unsigned int len,
+                              unsigned int i,
+                              hb_direction_t direction,
+                              unsigned int new_parent)
+{
+  int chain = pos[i].attach_chain(), type = pos[i].attach_type();
+  if (likely (!chain || 0 == (type & ATTACH_TYPE_CURSIVE)))
+    return;
+
+  pos[i].attach_chain() = 0;
+
+  unsigned int j = (int) i + chain;
+
+  if (unlikely (j >= len))
+    return;
+
+  /* Stop if we see new parent in the chain. */
+  if (j == new_parent)
+    return;
+
+  int16_t reversed_chain = -chain;
+  /* The old edge was cleared above; if the reversed distance truncates,
+   * keep it detached instead of storing a poisoned chain.
+   */
+  if (unlikely (reversed_chain != -chain))
+    return;
+
+  reverse_cursive_minor_offset (pos, len, j, direction, new_parent);
+
+  if (HB_DIRECTION_IS_HORIZONTAL (direction))
+    pos[j].y_offset = -pos[i].y_offset;
+  else
+    pos[j].x_offset = -pos[i].x_offset;
+
+  pos[j].attach_chain() = reversed_chain;
+  pos[j].attach_type() = type;
+}
+
+
+struct CursivePosFormat1
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  Offset16To<Coverage>
+                coverage;               /* Offset to Coverage table--from
+                                         * beginning of subtable */
+  Array16Of<EntryExitRecord>
+                entryExitRecord;        /* Array of EntryExit records--in
+                                         * Coverage Index order */
+  public:
+  DEFINE_SIZE_ARRAY (6, entryExitRecord);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    if (unlikely (!coverage.sanitize (c, this)))
+      return_trace (false);
+
+    if (c->lazy_some_gpos)
+      return_trace (entryExitRecord.sanitize_shallow (c));
+    else
+      return_trace (entryExitRecord.sanitize (c, this));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  { return (this+coverage).intersects (glyphs); }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    + hb_zip (this+coverage, entryExitRecord)
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    | hb_apply ([&] (const EntryExitRecord& record) { record.collect_variation_indices (c, this); })
+    ;
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  { if (unlikely (!(this+coverage).collect_coverage (c->input))) return; }
+
+  const Coverage &get_coverage () const { return this+coverage; }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+
+    const EntryExitRecord &this_record = entryExitRecord[(this+coverage).get_coverage  (buffer->cur().codepoint)];
+    if (!this_record.entryAnchor ||
+	unlikely (!this_record.entryAnchor.sanitize (&c->sanitizer, this))) return_trace (false);
+    hb_barrier ();
+
+    auto &skippy_iter = c->iter_input;
+    skippy_iter.reset_fast (buffer->idx);
+    unsigned unsafe_from;
+    if (unlikely (!skippy_iter.prev (&unsafe_from)))
+    {
+      buffer->unsafe_to_concat_from_outbuffer (unsafe_from, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    const EntryExitRecord &prev_record = entryExitRecord[(this+coverage).get_coverage  (buffer->info[skippy_iter.idx].codepoint)];
+    if (!prev_record.exitAnchor ||
+	unlikely (!prev_record.exitAnchor.sanitize (&c->sanitizer, this)))
+    {
+      buffer->unsafe_to_concat_from_outbuffer (skippy_iter.idx, buffer->idx + 1);
+      return_trace (false);
+    }
+    hb_barrier ();
+
+    unsigned int i = skippy_iter.idx;
+    unsigned int j = buffer->idx;
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "cursive attaching glyph at %u to glyph at %u",
+			  i, j);
+    }
+
+    buffer->unsafe_to_break (i, j + 1);
+    float entry_x, entry_y, exit_x, exit_y;
+    (this+prev_record.exitAnchor).get_anchor (c, buffer->info[i].codepoint, &exit_x, &exit_y);
+    (this+this_record.entryAnchor).get_anchor (c, buffer->info[j].codepoint, &entry_x, &entry_y);
+
+    hb_glyph_position_t *pos = buffer->pos;
+
+    hb_position_t d;
+    /* Main-direction adjustment */
+    switch (c->direction) {
+      case HB_DIRECTION_LTR:
+        pos[i].x_advance  = roundf (exit_x) + pos[i].x_offset;
+
+        d = roundf (entry_x) + pos[j].x_offset;
+        pos[j].x_advance -= d;
+        pos[j].x_offset  -= d;
+        break;
+      case HB_DIRECTION_RTL:
+        d = roundf (exit_x) + pos[i].x_offset;
+        pos[i].x_advance -= d;
+        pos[i].x_offset  -= d;
+
+        pos[j].x_advance  = roundf (entry_x) + pos[j].x_offset;
+        break;
+      case HB_DIRECTION_TTB:
+        pos[i].y_advance  = roundf (exit_y) + pos[i].y_offset;
+
+        d = roundf (entry_y) + pos[j].y_offset;
+        pos[j].y_advance -= d;
+        pos[j].y_offset  -= d;
+        break;
+      case HB_DIRECTION_BTT:
+        d = roundf (exit_y) + pos[i].y_offset;
+        pos[i].y_advance -= d;
+        pos[i].y_offset  -= d;
+
+        pos[j].y_advance  = roundf (entry_y);
+        break;
+      case HB_DIRECTION_INVALID:
+      default:
+        break;
+    }
+
+    /* Cross-direction adjustment */
+
+    /* We attach child to parent (think graph theory and rooted trees whereas
+     * the root stays on baseline and each node aligns itself against its
+     * parent.
+     *
+     * Optimize things for the case of RightToLeft, as that's most common in
+     * Arabic. */
+    unsigned int child  = i;
+    unsigned int parent = j;
+    hb_position_t x_offset = roundf (entry_x - exit_x);
+    hb_position_t y_offset = roundf (entry_y - exit_y);
+    if  (!(c->lookup_props & LookupFlag::RightToLeft))
+    {
+      unsigned int k = child;
+      child = parent;
+      parent = k;
+      x_offset = -x_offset;
+      y_offset = -y_offset;
+    }
+
+    /* If child was already connected to someone else, walk through its old
+     * chain and reverse the link direction, such that the whole tree of its
+     * previous connection now attaches to new parent.  Watch out for case
+     * where new parent is on the path from old chain...
+     */
+    reverse_cursive_minor_offset (pos, buffer->len, child, c->direction, parent);
+
+    pos[child].attach_chain() = (int) parent - (int) child;
+    if (pos[child].attach_chain() != (int) parent - (int) child)
+    {
+      pos[child].attach_chain() = 0;
+      goto overflow;
+    }
+    pos[child].attach_type() = ATTACH_TYPE_CURSIVE;
+    buffer->scratch_flags |= HB_BUFFER_SCRATCH_FLAG_HAS_GPOS_ATTACHMENT;
+    if (likely (HB_DIRECTION_IS_HORIZONTAL (c->direction)))
+      pos[child].y_offset = y_offset;
+    else
+      pos[child].x_offset = x_offset;
+
+    /* If parent was attached to child, separate them.
+     * https://github.com/harfbuzz/harfbuzz/issues/2469
+     */
+    if (unlikely (pos[parent].attach_chain() == -pos[child].attach_chain()))
+    {
+      pos[parent].attach_chain() = 0;
+      if (likely (HB_DIRECTION_IS_HORIZONTAL (c->direction)))
+	pos[parent].y_offset = 0;
+      else
+	pos[parent].x_offset = 0;
+    }
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "cursive attached glyph at %u to glyph at %u",
+			  i, j);
+    }
+
+  overflow:
+    buffer->idx++;
+    return_trace (true);
+  }
+
+  template <typename Iterator,
+            hb_requires (hb_is_iterator (Iterator))>
+  void serialize (hb_subset_context_t *c,
+                  Iterator it,
+                  const struct CursivePosFormat1 *src_base)
+  {
+    if (unlikely (!c->serializer->extend_min ((*this)))) return;
+    this->format = 1;
+    this->entryExitRecord.len = it.len ();
+
+    for (const EntryExitRecord& entry_record : + it
+                                               | hb_map (hb_second))
+      entry_record.subset (c, src_base);
+
+    auto glyphs =
+    + it
+    | hb_map_retains_sorting (hb_first)
+    ;
+
+    coverage.serialize_serialize (c->serializer, glyphs);
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    auto *out = c->serializer->start_embed (*this);
+
+    auto it =
+    + hb_zip (this+coverage, entryExitRecord)
+    | hb_filter (glyphset, hb_first)
+    | hb_map_retains_sorting ([&] (hb_pair_t<hb_codepoint_t, const EntryExitRecord&> p) -> hb_pair_t<hb_codepoint_t, const EntryExitRecord&>
+                              { return hb_pair (glyph_map[p.first], p.second);})
+    ;
+
+    bool ret = bool (it);
+    out->serialize (c, it, this);
+    return_trace (ret);
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_CURSIVEPOSFORMAT1_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/ExtensionPos.hh

@@ -0,0 +1,17 @@
+#ifndef OT_LAYOUT_GPOS_EXTENSIONPOS_HH
+#define OT_LAYOUT_GPOS_EXTENSIONPOS_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct ExtensionPos : Extension<ExtensionPos>
+{
+  typedef struct PosLookupSubTable SubTable;
+};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_EXTENSIONPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/GPOS.hh

@@ -0,0 +1,206 @@
+#ifndef OT_LAYOUT_GPOS_GPOS_HH
+#define OT_LAYOUT_GPOS_GPOS_HH
+
+#include "../../../hb-ot-layout-common.hh"
+#include "../../../hb-ot-layout-gsubgpos.hh"
+#include "Common.hh"
+#include "PosLookup.hh"
+
+namespace OT {
+
+using Layout::GPOS_impl::PosLookup;
+
+namespace Layout {
+
+static void
+propagate_attachment_offsets (hb_glyph_position_t *pos,
+                              unsigned int len,
+                              unsigned int i,
+                              hb_direction_t direction,
+                              unsigned nesting_level = HB_MAX_NESTING_LEVEL);
+
+/*
+ * GPOS -- Glyph Positioning
+ * https://docs.microsoft.com/en-us/typography/opentype/spec/gpos
+ */
+
+struct GPOS : GSUBGPOS
+{
+  static constexpr hb_tag_t tableTag = HB_OT_TAG_GPOS;
+
+  using Lookup = PosLookup;
+
+  const PosLookup& get_lookup (unsigned int i) const
+  { return static_cast<const PosLookup &> (GSUBGPOS::get_lookup (i)); }
+
+  static inline void position_start (hb_font_t *font, hb_buffer_t *buffer);
+  static inline void position_finish_advances (hb_font_t *font, hb_buffer_t *buffer);
+  static inline void position_finish_offsets (hb_font_t *font, hb_buffer_t *buffer);
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    hb_subset_layout_context_t l (c, tableTag);
+    return GSUBGPOS::subset<PosLookup> (&l);
+  }
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (GSUBGPOS::sanitize<PosLookup> (c));
+  }
+
+  HB_INTERNAL bool is_blocklisted (hb_blob_t *blob,
+                                   hb_face_t *face) const;
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    for (unsigned i = 0; i < GSUBGPOS::get_lookup_count (); i++)
+    {
+      if (!c->gpos_lookups->has (i)) continue;
+      const PosLookup &l = get_lookup (i);
+      l.dispatch (c);
+    }
+  }
+
+  void closure_lookups (hb_face_t      *face,
+                        const hb_set_t *glyphs,
+                        hb_set_t       *lookup_indexes /* IN/OUT */) const
+  { GSUBGPOS::closure_lookups<PosLookup> (face, glyphs, lookup_indexes); }
+
+  typedef GSUBGPOS::accelerator_t<GPOS> accelerator_t;
+};
+
+
+static void
+propagate_attachment_offsets (hb_glyph_position_t *pos,
+                              unsigned int len,
+                              unsigned int i,
+                              hb_direction_t direction,
+                              unsigned nesting_level)
+{
+  /* Adjusts offsets of attached glyphs (both cursive and mark) to accumulate
+   * offset of glyph they are attached to. */
+  int chain = pos[i].attach_chain();
+  int type = pos[i].attach_type();
+
+  pos[i].attach_chain() = 0;
+
+  unsigned int j = (int) i + chain;
+
+  if (unlikely (j >= len))
+    return;
+
+  if (unlikely (!nesting_level))
+    return;
+
+  if (pos[j].attach_chain())
+    propagate_attachment_offsets (pos, len, j, direction, nesting_level - 1);
+
+  assert (!!(type & GPOS_impl::ATTACH_TYPE_MARK) ^ !!(type & GPOS_impl::ATTACH_TYPE_CURSIVE));
+
+  if (type & GPOS_impl::ATTACH_TYPE_CURSIVE)
+  {
+    if (HB_DIRECTION_IS_HORIZONTAL (direction))
+      pos[i].y_offset += pos[j].y_offset;
+    else
+      pos[i].x_offset += pos[j].x_offset;
+  }
+  else /*if (type & GPOS_impl::ATTACH_TYPE_MARK)*/
+  {
+    pos[i].x_offset += pos[j].x_offset;
+    pos[i].y_offset += pos[j].y_offset;
+
+    // i is the position of the mark; j is the base.
+    if (j < i)
+    {
+      /* This is the common case: mark follows base.
+       * And currently the only way in OpenType. */
+      if (HB_DIRECTION_IS_FORWARD (direction))
+	for (unsigned int k = j; k < i; k++) {
+	  pos[i].x_offset -= pos[k].x_advance;
+	  pos[i].y_offset -= pos[k].y_advance;
+	}
+      else
+	for (unsigned int k = j + 1; k < i + 1; k++) {
+	  pos[i].x_offset += pos[k].x_advance;
+	  pos[i].y_offset += pos[k].y_advance;
+	}
+    }
+    else // j > i
+    {
+      /* This can happen with `kerx`: a mark attaching
+       * to a base after it in the logical order. */
+      if (HB_DIRECTION_IS_FORWARD (direction))
+	for (unsigned int k = i; k < j; k++) {
+	  pos[i].x_offset += pos[k].x_advance;
+	  pos[i].y_offset += pos[k].y_advance;
+	}
+      else
+	for (unsigned int k = i + 1; k < j + 1; k++) {
+	  pos[i].x_offset -= pos[k].x_advance;
+	  pos[i].y_offset -= pos[k].y_advance;
+	}
+    }
+  }
+}
+
+void
+GPOS::position_start (hb_font_t *font HB_UNUSED, hb_buffer_t *buffer)
+{
+  unsigned int count = buffer->len;
+  for (unsigned int i = 0; i < count; i++)
+    buffer->pos[i].attach_chain() = buffer->pos[i].attach_type() = 0;
+}
+
+void
+GPOS::position_finish_advances (hb_font_t *font HB_UNUSED, hb_buffer_t *buffer HB_UNUSED)
+{
+  //_hb_buffer_assert_gsubgpos_vars (buffer);
+}
+
+void
+GPOS::position_finish_offsets (hb_font_t *font, hb_buffer_t *buffer)
+{
+  _hb_buffer_assert_gsubgpos_vars (buffer);
+
+  unsigned int len;
+  hb_glyph_position_t *pos = hb_buffer_get_glyph_positions (buffer, &len);
+  hb_direction_t direction = buffer->props.direction;
+
+  /* Handle attachments */
+  if (buffer->scratch_flags & HB_BUFFER_SCRATCH_FLAG_HAS_GPOS_ATTACHMENT)
+  {
+    auto *pos = buffer->pos;
+    // https://github.com/harfbuzz/harfbuzz/issues/5514
+    if (HB_DIRECTION_IS_FORWARD (direction))
+    {
+      for (unsigned i = 0; i < len; i++)
+	if (pos[i].attach_chain())
+	  propagate_attachment_offsets (pos, len, i, direction);
+    } else {
+      for (unsigned i = len; i-- > 0; )
+	if (pos[i].attach_chain())
+	  propagate_attachment_offsets (pos, len, i, direction);
+    }
+  }
+
+  if (unlikely (font->slant_xy) &&
+      HB_DIRECTION_IS_HORIZONTAL (direction))
+  {
+    /* Slanting shaping results is only supported for horizontal text,
+     * as it gets weird otherwise. */
+    for (unsigned i = 0; i < len; i++)
+      if (unlikely (pos[i].y_offset))
+        pos[i].x_offset += roundf (font->slant_xy * pos[i].y_offset);
+  }
+}
+
+}
+
+struct GPOS_accelerator_t : Layout::GPOS::accelerator_t {
+  GPOS_accelerator_t (hb_face_t *face) : Layout::GPOS::accelerator_t (face) {}
+};
+
+}
+
+#endif  /* OT_LAYOUT_GPOS_GPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/LigatureArray.hh

@@ -0,0 +1,68 @@
+#ifndef OT_LAYOUT_GPOS_LIGATUREARRAY_HH
+#define OT_LAYOUT_GPOS_LIGATUREARRAY_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+
+typedef AnchorMatrix LigatureAttach;    /* component-major--
+                                         * in order of writing direction--,
+                                         * mark-minor--
+                                         * ordered by class--zero-based. */
+
+/* Array of LigatureAttach tables ordered by LigatureCoverage Index */
+struct LigatureArray : List16OfOffset16To<LigatureAttach>
+{
+  template <typename Iterator,
+            hb_requires (hb_is_iterator (Iterator))>
+  bool subset (hb_subset_context_t *c,
+               Iterator             coverage,
+               unsigned             class_count,
+               const hb_map_t      *klass_mapping,
+               hb_sorted_vector_t<hb_codepoint_t> &new_coverage /* OUT */) const
+  {
+    TRACE_SUBSET (this);
+    const hb_map_t &glyph_map = c->plan->glyph_map_gsub;
+
+    auto *out = c->serializer->start_embed (this);
+    if (unlikely (!c->serializer->extend_min (out)))  return_trace (false);
+
+    bool ret = false;
+    for (const auto _ : + hb_zip (coverage, *this)
+                        | hb_filter (glyph_map, hb_first))
+    {
+      const LigatureAttach& src = (this + _.second);
+      bool non_empty = + hb_range (src.rows * class_count)
+                       | hb_filter ([=] (unsigned index) { return klass_mapping->has (index % class_count); })
+                       | hb_map ([&] (const unsigned index) { return !src.offset_is_null (index / class_count, index % class_count, class_count); })
+                       | hb_any;
+
+      if (!non_empty) continue;
+
+      auto *matrix = out->serialize_append (c->serializer);
+      if (unlikely (!matrix)) return_trace (false);
+
+      auto indexes =
+          + hb_range (src.rows * class_count)
+          | hb_filter ([=] (unsigned index) { return klass_mapping->has (index % class_count); })
+          ;
+      ret |= matrix->serialize_subset (c,
+				       _.second,
+				       this,
+				       src.rows,
+				       indexes);
+
+      hb_codepoint_t new_gid = glyph_map.get (_.first);
+      new_coverage.push (new_gid);
+    }
+    return_trace (ret);
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_LIGATUREARRAY_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkArray.hh

@@ -0,0 +1,134 @@
+#ifndef OT_LAYOUT_GPOS_MARKARRAY_HH
+#define OT_LAYOUT_GPOS_MARKARRAY_HH
+
+#include "AnchorMatrix.hh"
+#include "MarkRecord.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct MarkArray : Array16Of<MarkRecord>        /* Array of MarkRecords--in Coverage order */
+{
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (Array16Of<MarkRecord>::sanitize (c, this));
+  }
+
+  bool apply (hb_ot_apply_context_t *c,
+              unsigned int mark_index, unsigned int glyph_index,
+              const AnchorMatrix &anchors, unsigned int class_count,
+              unsigned int glyph_pos) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+    const MarkRecord &record = Array16Of<MarkRecord>::operator[](mark_index);
+    unsigned int mark_class = record.klass;
+
+    const Anchor& mark_anchor = this + record.markAnchor;
+    bool found;
+    const Anchor& glyph_anchor = anchors.get_anchor (c, glyph_index, mark_class, class_count, &found);
+    /* If this subtable doesn't have an anchor for this base and this class,
+     * return false such that the subsequent subtables have a chance at it. */
+    if (unlikely (!found)) return_trace (false);
+
+    float mark_x, mark_y, base_x, base_y;
+
+    buffer->unsafe_to_break (glyph_pos, buffer->idx + 1);
+    mark_anchor.get_anchor (c, buffer->cur().codepoint, &mark_x, &mark_y);
+    glyph_anchor.get_anchor (c, buffer->info[glyph_pos].codepoint, &base_x, &base_y);
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "attaching mark glyph at %u to glyph at %u",
+			  c->buffer->idx, glyph_pos);
+    }
+
+    hb_glyph_position_t &o = buffer->cur_pos();
+    o.attach_chain() = (int) glyph_pos - (int) buffer->idx;
+    if (o.attach_chain() != (int) glyph_pos - (int) buffer->idx)
+    {
+      o.attach_chain() = 0;
+      goto overflow;
+    }
+    o.attach_type() = ATTACH_TYPE_MARK;
+    o.x_offset = roundf (base_x - mark_x);
+    o.y_offset = roundf (base_y - mark_y);
+    buffer->scratch_flags |= HB_BUFFER_SCRATCH_FLAG_HAS_GPOS_ATTACHMENT;
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "attached mark glyph at %u to glyph at %u",
+			  c->buffer->idx, glyph_pos);
+    }
+
+  overflow:
+    buffer->idx++;
+    return_trace (true);
+  }
+
+  template <typename Iterator,
+      hb_requires (hb_is_iterator (Iterator))>
+  bool subset (hb_subset_context_t *c,
+               Iterator             coverage,
+               const hb_map_t      *klass_mapping) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+
+    auto* out = c->serializer->start_embed (this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+
+    auto mark_iter =
+    + hb_zip (coverage, this->iter ())
+    | hb_filter (glyphset, hb_first)
+    | hb_map (hb_second)
+    ;
+
+    bool ret = false;
+    unsigned new_length = 0;
+    for (const auto& mark_record : mark_iter) {
+      ret |= mark_record.subset (c, this, klass_mapping);
+      new_length++;
+    }
+
+    if (unlikely (!c->serializer->check_assign (out->len, new_length,
+                                                HB_SERIALIZE_ERROR_ARRAY_OVERFLOW)))
+      return_trace (false);
+
+    return_trace (ret);
+  }
+};
+
+HB_INTERNAL inline
+void Markclass_closure_and_remap_indexes (const Coverage  &mark_coverage,
+                                          const MarkArray &mark_array,
+                                          const hb_set_t  &glyphset,
+                                          hb_map_t*        klass_mapping /* INOUT */)
+{
+  hb_set_t orig_classes;
+
+  + hb_zip (mark_coverage, mark_array)
+  | hb_filter (glyphset, hb_first)
+  | hb_map (hb_second)
+  | hb_map (&MarkRecord::get_class)
+  | hb_sink (orig_classes)
+  ;
+
+  unsigned idx = 0;
+  for (auto klass : orig_classes.iter ())
+  {
+    if (klass_mapping->has (klass)) continue;
+    klass_mapping->set (klass, idx);
+    idx++;
+  }
+}
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKARRAY_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkBasePos.hh

@@ -0,0 +1,41 @@
+#ifndef OT_LAYOUT_GPOS_MARKBASEPOS_HH
+#define OT_LAYOUT_GPOS_MARKBASEPOS_HH
+
+#include "MarkBasePosFormat1.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct MarkBasePos
+{
+  protected:
+  union {
+  struct { HBUINT16 v; }		format;         /* Format identifier */
+  MarkBasePosFormat1_2<SmallTypes>	format1;
+#ifndef HB_NO_BEYOND_64K
+  MarkBasePosFormat1_2<MediumTypes>	format2;
+#endif
+  } u;
+
+  public:
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  {
+    if (unlikely (!c->may_dispatch (this, &u.format.v))) return c->no_dispatch_return_value ();
+    TRACE_DISPATCH (this, u.format.v);
+    switch (u.format.v) {
+    case 1: return_trace (c->dispatch (u.format1, std::forward<Ts> (ds)...));
+#ifndef HB_NO_BEYOND_64K
+    case 2: return_trace (c->dispatch (u.format2, std::forward<Ts> (ds)...));
+#endif
+    default:return_trace (c->default_return_value ());
+    }
+  }
+};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKBASEPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkBasePosFormat1.hh

@@ -0,0 +1,250 @@
+#ifndef OT_LAYOUT_GPOS_MARKBASEPOSFORMAT1_HH
+#define OT_LAYOUT_GPOS_MARKBASEPOSFORMAT1_HH
+
+#include "MarkArray.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+typedef AnchorMatrix BaseArray;         /* base-major--
+                                         * in order of BaseCoverage Index--,
+                                         * mark-minor--
+                                         * ordered by class--zero-based. */
+
+template <typename Types>
+struct MarkBasePosFormat1_2
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  typename Types::template OffsetTo<Coverage>
+                markCoverage;           /* Offset to MarkCoverage table--from
+                                         * beginning of MarkBasePos subtable */
+  typename Types::template OffsetTo<Coverage>
+                baseCoverage;           /* Offset to BaseCoverage table--from
+                                         * beginning of MarkBasePos subtable */
+  HBUINT16      classCount;             /* Number of classes defined for marks */
+  typename Types::template OffsetTo<MarkArray>
+                markArray;              /* Offset to MarkArray table--from
+                                         * beginning of MarkBasePos subtable */
+  typename Types::template OffsetTo<BaseArray>
+                baseArray;              /* Offset to BaseArray table--from
+                                         * beginning of MarkBasePos subtable */
+
+  public:
+  DEFINE_SIZE_STATIC (4 + 4 * Types::size);
+
+    bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+                  markCoverage.sanitize (c, this) &&
+                  baseCoverage.sanitize (c, this) &&
+                  markArray.sanitize (c, this) &&
+                  baseArray.sanitize (c, this, (unsigned int) classCount));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    return (this+markCoverage).intersects (glyphs) &&
+           (this+baseCoverage).intersects (glyphs);
+  }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    + hb_zip (this+markCoverage, this+markArray)
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    | hb_apply ([&] (const MarkRecord& record) { record.collect_variation_indices (c, &(this+markArray)); })
+    ;
+
+    hb_map_t klass_mapping;
+    Markclass_closure_and_remap_indexes (this+markCoverage, this+markArray, *c->glyph_set, &klass_mapping);
+
+    unsigned basecount = (this+baseArray).rows;
+    auto base_iter =
+    + hb_zip (this+baseCoverage, hb_range (basecount))
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    ;
+
+    hb_sorted_vector_t<unsigned> base_indexes;
+    for (const unsigned row : base_iter)
+    {
+      + hb_range ((unsigned) classCount)
+      | hb_filter (klass_mapping)
+      | hb_map ([&] (const unsigned col) { return row * (unsigned) classCount + col; })
+      | hb_sink (base_indexes)
+      ;
+    }
+    (this+baseArray).collect_variation_indices (c, base_indexes.iter ());
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  {
+    if (unlikely (!(this+markCoverage).collect_coverage (c->input))) return;
+    if (unlikely (!(this+baseCoverage).collect_coverage (c->input))) return;
+  }
+
+  const Coverage &get_coverage () const { return this+markCoverage; }
+
+  static inline bool accept (hb_buffer_t *buffer, unsigned idx)
+  {
+    /* We only want to attach to the first of a MultipleSubst sequence.
+     * https://github.com/harfbuzz/harfbuzz/issues/740
+     * Reject others...
+     * ...but stop if we find a mark in the MultipleSubst sequence:
+     * https://github.com/harfbuzz/harfbuzz/issues/1020 */
+    return !_hb_glyph_info_multiplied (&buffer->info[idx]) ||
+	   0 == _hb_glyph_info_get_lig_comp (&buffer->info[idx]) ||
+	   (idx == 0 ||
+	    _hb_glyph_info_is_mark (&buffer->info[idx - 1]) ||
+	    !_hb_glyph_info_multiplied (&buffer->info[idx - 1]) ||
+	    _hb_glyph_info_get_lig_id (&buffer->info[idx]) !=
+	    _hb_glyph_info_get_lig_id (&buffer->info[idx - 1]) ||
+	    _hb_glyph_info_get_lig_comp (&buffer->info[idx]) !=
+	    _hb_glyph_info_get_lig_comp (&buffer->info[idx - 1]) + 1
+	    );
+  }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+    unsigned int mark_index = (this+markCoverage).get_coverage  (buffer->cur().codepoint);
+    if (likely (mark_index == NOT_COVERED)) return_trace (false);
+
+    /* Now we search backwards for a non-mark glyph.
+     * We don't use skippy_iter.prev() to avoid O(n^2) behavior. */
+
+    auto &skippy_iter = c->iter_input;
+    skippy_iter.set_lookup_props (LookupFlag::IgnoreMarks);
+
+    if (c->last_base_until > buffer->idx)
+    {
+      c->last_base_until = 0;
+      c->last_base = -1;
+    }
+    unsigned j;
+    for (j = buffer->idx; j > c->last_base_until; j--)
+    {
+      auto match = skippy_iter.match (buffer->info[j - 1]);
+      if (match == skippy_iter.MATCH)
+      {
+        // https://github.com/harfbuzz/harfbuzz/issues/4124
+	if (!accept (buffer, j - 1) &&
+	    NOT_COVERED == (this+baseCoverage).get_coverage  (buffer->info[j - 1].codepoint))
+	  match = skippy_iter.SKIP;
+      }
+      if (match == skippy_iter.MATCH)
+      {
+	c->last_base = (signed) j - 1;
+	break;
+      }
+    }
+    c->last_base_until = buffer->idx;
+    if (c->last_base == -1)
+    {
+      buffer->unsafe_to_concat_from_outbuffer (0, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    unsigned idx = (unsigned) c->last_base;
+
+    /* Checking that matched glyph is actually a base glyph by GDEF is too strong; disabled */
+    //if (!_hb_glyph_info_is_base_glyph (&buffer->info[idx])) { return_trace (false); }
+
+    unsigned int base_index = (this+baseCoverage).get_coverage  (buffer->info[idx].codepoint);
+    if (base_index == NOT_COVERED)
+    {
+      buffer->unsafe_to_concat_from_outbuffer (idx, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    return_trace ((this+markArray).apply (c, mark_index, base_index, this+baseArray, classCount, idx));
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+    out->format = format;
+
+    hb_map_t klass_mapping;
+    Markclass_closure_and_remap_indexes (this+markCoverage, this+markArray, glyphset, &klass_mapping);
+
+    if (!klass_mapping.get_population ()) return_trace (false);
+    out->classCount = klass_mapping.get_population ();
+
+    auto mark_iter =
+    + hb_zip (this+markCoverage, this+markArray)
+    | hb_filter (glyphset, hb_first)
+    ;
+
+    hb_sorted_vector_t<hb_codepoint_t> new_coverage;
+    + mark_iter
+    | hb_map (hb_first)
+    | hb_map (glyph_map)
+    | hb_sink (new_coverage)
+    ;
+
+    if (!out->markCoverage.serialize_serialize (c->serializer, new_coverage.iter ()))
+      return_trace (false);
+
+    if (unlikely (!out->markArray.serialize_subset (c, markArray, this,
+						    (this+markCoverage).iter (),
+						    &klass_mapping)))
+      return_trace (false);
+
+    unsigned basecount = (this+baseArray).rows;
+    auto base_iter =
+    + hb_zip (this+baseCoverage, hb_range (basecount))
+    | hb_filter (glyphset, hb_first)
+    ;
+
+    new_coverage.reset ();
+    hb_sorted_vector_t<unsigned> base_indexes;
+    auto &base_array = (this+baseArray);
+    for (const auto _ : + base_iter)
+    {
+      unsigned row = _.second;
+      bool non_empty = + hb_range ((unsigned) classCount)
+                       | hb_filter (klass_mapping)
+                       | hb_map ([&] (const unsigned col) { return !base_array.offset_is_null (row, col, (unsigned) classCount); })
+                       | hb_any
+                       ;
+
+      if (!non_empty) continue;
+      
+      hb_codepoint_t new_g = glyph_map.get ( _.first);
+      new_coverage.push (new_g);
+
+      + hb_range ((unsigned) classCount)
+      | hb_filter (klass_mapping)
+      | hb_map ([&] (const unsigned col) { return row * (unsigned) classCount + col; })
+      | hb_sink (base_indexes)
+      ;
+    }
+
+    if (!new_coverage) return_trace (false);
+    if (!out->baseCoverage.serialize_serialize (c->serializer, new_coverage.iter ()))
+      return_trace (false);
+
+    return_trace (out->baseArray.serialize_subset (c, baseArray, this,
+						   new_coverage.length,
+						   base_indexes.iter ()));
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKBASEPOSFORMAT1_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkLigPos.hh

@@ -0,0 +1,41 @@
+#ifndef OT_LAYOUT_GPOS_MARKLIGPOS_HH
+#define OT_LAYOUT_GPOS_MARKLIGPOS_HH
+
+#include "MarkLigPosFormat1.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct MarkLigPos
+{
+  protected:
+  union {
+  struct { HBUINT16 v; }		format;         /* Format identifier */
+  MarkLigPosFormat1_2<SmallTypes>	format1;
+#ifndef HB_NO_BEYOND_64K
+  MarkLigPosFormat1_2<MediumTypes>	format2;
+#endif
+  } u;
+
+  public:
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  {
+    if (unlikely (!c->may_dispatch (this, &u.format.v))) return c->no_dispatch_return_value ();
+    TRACE_DISPATCH (this, u.format.v);
+    switch (u.format.v) {
+    case 1: return_trace (c->dispatch (u.format1, std::forward<Ts> (ds)...));
+#ifndef HB_NO_BEYOND_64K
+    case 2: return_trace (c->dispatch (u.format2, std::forward<Ts> (ds)...));
+#endif
+    default:return_trace (c->default_return_value ());
+    }
+  }
+};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKLIGPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkLigPosFormat1.hh

@@ -0,0 +1,218 @@
+#ifndef OT_LAYOUT_GPOS_MARKLIGPOSFORMAT1_HH
+#define OT_LAYOUT_GPOS_MARKLIGPOSFORMAT1_HH
+
+#include "LigatureArray.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+
+template <typename Types>
+struct MarkLigPosFormat1_2
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  typename Types::template OffsetTo<Coverage>
+                markCoverage;           /* Offset to Mark Coverage table--from
+                                         * beginning of MarkLigPos subtable */
+  typename Types::template OffsetTo<Coverage>
+                ligatureCoverage;       /* Offset to Ligature Coverage
+                                         * table--from beginning of MarkLigPos
+                                         * subtable */
+  HBUINT16      classCount;             /* Number of defined mark classes */
+  typename Types::template OffsetTo<MarkArray>
+                markArray;              /* Offset to MarkArray table--from
+                                         * beginning of MarkLigPos subtable */
+  typename Types::template OffsetTo<LigatureArray>
+                ligatureArray;          /* Offset to LigatureArray table--from
+                                         * beginning of MarkLigPos subtable */
+  public:
+  DEFINE_SIZE_STATIC (4 + 4 * Types::size);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+                  markCoverage.sanitize (c, this) &&
+                  ligatureCoverage.sanitize (c, this) &&
+                  markArray.sanitize (c, this) &&
+                  ligatureArray.sanitize (c, this, (unsigned int) classCount));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    return (this+markCoverage).intersects (glyphs) &&
+           (this+ligatureCoverage).intersects (glyphs);
+  }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    + hb_zip (this+markCoverage, this+markArray)
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    | hb_apply ([&] (const MarkRecord& record) { record.collect_variation_indices (c, &(this+markArray)); })
+    ;
+
+    hb_map_t klass_mapping;
+    Markclass_closure_and_remap_indexes (this+markCoverage, this+markArray, *c->glyph_set, &klass_mapping);
+
+    unsigned ligcount = (this+ligatureArray).len;
+    auto lig_iter =
+    + hb_zip (this+ligatureCoverage, hb_range (ligcount))
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    ;
+
+    const LigatureArray& lig_array = this+ligatureArray;
+    for (const unsigned i : lig_iter)
+    {
+      hb_sorted_vector_t<unsigned> lig_indexes;
+      unsigned row_count = lig_array[i].rows;
+      for (unsigned row : + hb_range (row_count))
+      {
+        + hb_range ((unsigned) classCount)
+        | hb_filter (klass_mapping)
+        | hb_map ([&] (const unsigned col) { return row * (unsigned) classCount + col; })
+        | hb_sink (lig_indexes)
+        ;
+      }
+
+      lig_array[i].collect_variation_indices (c, lig_indexes.iter ());
+    }
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  {
+    if (unlikely (!(this+markCoverage).collect_coverage (c->input))) return;
+    if (unlikely (!(this+ligatureCoverage).collect_coverage (c->input))) return;
+  }
+
+  const Coverage &get_coverage () const { return this+markCoverage; }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+    unsigned int mark_index = (this+markCoverage).get_coverage  (buffer->cur().codepoint);
+    if (likely (mark_index == NOT_COVERED)) return_trace (false);
+
+    /* Now we search backwards for a non-mark glyph */
+
+    auto &skippy_iter = c->iter_input;
+    skippy_iter.set_lookup_props (LookupFlag::IgnoreMarks);
+
+    if (c->last_base_until > buffer->idx)
+    {
+      c->last_base_until = 0;
+      c->last_base = -1;
+    }
+    unsigned j;
+    for (j = buffer->idx; j > c->last_base_until; j--)
+    {
+      auto match = skippy_iter.match (buffer->info[j - 1]);
+      if (match == skippy_iter.MATCH)
+      {
+	c->last_base = (signed) j - 1;
+	break;
+      }
+    }
+    c->last_base_until = buffer->idx;
+    if (c->last_base == -1)
+    {
+      buffer->unsafe_to_concat_from_outbuffer (0, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    unsigned idx = (unsigned) c->last_base;
+
+    /* Checking that matched glyph is actually a ligature by GDEF is too strong; disabled */
+    //if (!_hb_glyph_info_is_ligature (&buffer->info[idx])) { return_trace (false); }
+
+    unsigned int lig_index = (this+ligatureCoverage).get_coverage  (buffer->info[idx].codepoint);
+    if (lig_index == NOT_COVERED)
+    {
+      buffer->unsafe_to_concat_from_outbuffer (idx, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    const LigatureArray& lig_array = this+ligatureArray;
+    const LigatureAttach& lig_attach = lig_array[lig_index];
+
+    /* Find component to attach to */
+    unsigned int comp_count = lig_attach.rows;
+    if (unlikely (!comp_count))
+    {
+      buffer->unsafe_to_concat_from_outbuffer (idx, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    /* We must now check whether the ligature ID of the current mark glyph
+     * is identical to the ligature ID of the found ligature.  If yes, we
+     * can directly use the component index.  If not, we attach the mark
+     * glyph to the last component of the ligature. */
+    unsigned int comp_index;
+    unsigned int lig_id = _hb_glyph_info_get_lig_id (&buffer->info[idx]);
+    unsigned int mark_id = _hb_glyph_info_get_lig_id (&buffer->cur());
+    unsigned int mark_comp = _hb_glyph_info_get_lig_comp (&buffer->cur());
+    if (lig_id && lig_id == mark_id && mark_comp > 0)
+      comp_index = hb_min (comp_count, _hb_glyph_info_get_lig_comp (&buffer->cur())) - 1;
+    else
+      comp_index = comp_count - 1;
+
+    return_trace ((this+markArray).apply (c, mark_index, comp_index, lig_attach, classCount, idx));
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = c->plan->glyph_map_gsub;
+
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+    out->format = format;
+
+    hb_map_t klass_mapping;
+    Markclass_closure_and_remap_indexes (this+markCoverage, this+markArray, glyphset, &klass_mapping);
+
+    if (!klass_mapping.get_population ()) return_trace (false);
+    out->classCount = klass_mapping.get_population ();
+
+    auto mark_iter =
+    + hb_zip (this+markCoverage, this+markArray)
+    | hb_filter (glyphset, hb_first)
+    ;
+
+    auto new_mark_coverage =
+    + mark_iter
+    | hb_map_retains_sorting (hb_first)
+    | hb_map_retains_sorting (glyph_map)
+    ;
+
+    if (!out->markCoverage.serialize_serialize (c->serializer, new_mark_coverage))
+      return_trace (false);
+
+    if (unlikely (!out->markArray.serialize_subset (c, markArray, this,
+						    (this+markCoverage).iter (),
+						    &klass_mapping)))
+      return_trace (false);
+
+    hb_sorted_vector_t<hb_codepoint_t> new_lig_coverage;
+    if (!out->ligatureArray.serialize_subset (c, ligatureArray, this,
+					      hb_iter (this+ligatureCoverage),
+					      classCount, &klass_mapping, new_lig_coverage))
+      return_trace (false);
+
+    return_trace (out->ligatureCoverage.serialize_serialize (c->serializer, new_lig_coverage.iter ()));
+  }
+
+};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKLIGPOSFORMAT1_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkMarkPos.hh

@@ -0,0 +1,42 @@
+#ifndef OT_LAYOUT_GPOS_MARKMARKPOS_HH
+#define OT_LAYOUT_GPOS_MARKMARKPOS_HH
+
+#include "MarkMarkPosFormat1.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct MarkMarkPos
+{
+  protected:
+  union {
+  struct { HBUINT16 v; }		format;         /* Format identifier */
+  MarkMarkPosFormat1_2<SmallTypes>	format1;
+#ifndef HB_NO_BEYOND_64K
+  MarkMarkPosFormat1_2<MediumTypes>	format2;
+#endif
+  } u;
+
+  public:
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  {
+    if (unlikely (!c->may_dispatch (this, &u.format.v))) return c->no_dispatch_return_value ();
+    TRACE_DISPATCH (this, u.format.v);
+    switch (u.format.v) {
+    case 1: return_trace (c->dispatch (u.format1, std::forward<Ts> (ds)...));
+#ifndef HB_NO_BEYOND_64K
+    case 2: return_trace (c->dispatch (u.format2, std::forward<Ts> (ds)...));
+#endif
+    default:return_trace (c->default_return_value ());
+    }
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKMARKPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkMarkPosFormat1.hh

@@ -0,0 +1,239 @@
+#ifndef OT_LAYOUT_GPOS_MARKMARKPOSFORMAT1_HH
+#define OT_LAYOUT_GPOS_MARKMARKPOSFORMAT1_HH
+
+#include "MarkMarkPosFormat1.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+typedef AnchorMatrix Mark2Array;        /* mark2-major--
+                                         * in order of Mark2Coverage Index--,
+                                         * mark1-minor--
+                                         * ordered by class--zero-based. */
+
+template <typename Types>
+struct MarkMarkPosFormat1_2
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  typename Types::template OffsetTo<Coverage>
+                mark1Coverage;          /* Offset to Combining Mark1 Coverage
+                                         * table--from beginning of MarkMarkPos
+                                         * subtable */
+  typename Types::template OffsetTo<Coverage>
+                mark2Coverage;          /* Offset to Combining Mark2 Coverage
+                                         * table--from beginning of MarkMarkPos
+                                         * subtable */
+  HBUINT16      classCount;             /* Number of defined mark classes */
+  typename Types::template OffsetTo<MarkArray>
+                mark1Array;             /* Offset to Mark1Array table--from
+                                         * beginning of MarkMarkPos subtable */
+  typename Types::template OffsetTo<Mark2Array>
+                mark2Array;             /* Offset to Mark2Array table--from
+                                         * beginning of MarkMarkPos subtable */
+  public:
+  DEFINE_SIZE_STATIC (4 + 4 * Types::size);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+                  mark1Coverage.sanitize (c, this) &&
+                  mark2Coverage.sanitize (c, this) &&
+                  mark1Array.sanitize (c, this) &&
+		  hb_barrier () &&
+                  mark2Array.sanitize (c, this, (unsigned int) classCount));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    return (this+mark1Coverage).intersects (glyphs) &&
+           (this+mark2Coverage).intersects (glyphs);
+  }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    + hb_zip (this+mark1Coverage, this+mark1Array)
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    | hb_apply ([&] (const MarkRecord& record) { record.collect_variation_indices (c, &(this+mark1Array)); })
+    ;
+
+    hb_map_t klass_mapping;
+    Markclass_closure_and_remap_indexes (this+mark1Coverage, this+mark1Array, *c->glyph_set, &klass_mapping);
+
+    unsigned mark2_count = (this+mark2Array).rows;
+    auto mark2_iter =
+    + hb_zip (this+mark2Coverage, hb_range (mark2_count))
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    ;
+
+    hb_sorted_vector_t<unsigned> mark2_indexes;
+    for (const unsigned row : mark2_iter)
+    {
+      + hb_range ((unsigned) classCount)
+      | hb_filter (klass_mapping)
+      | hb_map ([&] (const unsigned col) { return row * (unsigned) classCount + col; })
+      | hb_sink (mark2_indexes)
+      ;
+    }
+    (this+mark2Array).collect_variation_indices (c, mark2_indexes.iter ());
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  {
+    if (unlikely (!(this+mark1Coverage).collect_coverage (c->input))) return;
+    if (unlikely (!(this+mark2Coverage).collect_coverage (c->input))) return;
+  }
+
+  const Coverage &get_coverage () const { return this+mark1Coverage; }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+    unsigned int mark1_index = (this+mark1Coverage).get_coverage  (buffer->cur().codepoint);
+    if (likely (mark1_index == NOT_COVERED)) return_trace (false);
+
+    /* now we search backwards for a suitable mark glyph until a non-mark glyph */
+    auto &skippy_iter = c->iter_input;
+    skippy_iter.reset_fast (buffer->idx);
+    skippy_iter.set_lookup_props (c->lookup_props & ~(uint32_t)LookupFlag::IgnoreFlags);
+    unsigned unsafe_from;
+    if (unlikely (!skippy_iter.prev (&unsafe_from)))
+    {
+      buffer->unsafe_to_concat_from_outbuffer (unsafe_from, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    if (likely (!_hb_glyph_info_is_mark (&buffer->info[skippy_iter.idx])))
+    {
+      buffer->unsafe_to_concat_from_outbuffer (skippy_iter.idx, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    unsigned int j = skippy_iter.idx;
+
+    unsigned int id1 = _hb_glyph_info_get_lig_id (&buffer->cur());
+    unsigned int id2 = _hb_glyph_info_get_lig_id (&buffer->info[j]);
+    unsigned int comp1 = _hb_glyph_info_get_lig_comp (&buffer->cur());
+    unsigned int comp2 = _hb_glyph_info_get_lig_comp (&buffer->info[j]);
+
+    if (likely (id1 == id2))
+    {
+      if (id1 == 0) /* Marks belonging to the same base. */
+        goto good;
+      else if (comp1 == comp2) /* Marks belonging to the same ligature component. */
+        goto good;
+    }
+    else
+    {
+      /* If ligature ids don't match, it may be the case that one of the marks
+       * itself is a ligature.  In which case match. */
+      if ((id1 > 0 && !comp1) || (id2 > 0 && !comp2))
+        goto good;
+    }
+
+    /* Didn't match. */
+    buffer->unsafe_to_concat_from_outbuffer (skippy_iter.idx, buffer->idx + 1);
+    return_trace (false);
+
+    good:
+    unsigned int mark2_index = (this+mark2Coverage).get_coverage  (buffer->info[j].codepoint);
+    if (mark2_index == NOT_COVERED)
+    {
+      buffer->unsafe_to_concat_from_outbuffer (skippy_iter.idx, buffer->idx + 1);
+      return_trace (false);
+    }
+
+    return_trace ((this+mark1Array).apply (c, mark1_index, mark2_index, this+mark2Array, classCount, j));
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+    out->format = format;
+
+    hb_map_t klass_mapping;
+    Markclass_closure_and_remap_indexes (this+mark1Coverage, this+mark1Array, glyphset, &klass_mapping);
+
+    if (!klass_mapping.get_population ()) return_trace (false);
+    out->classCount = klass_mapping.get_population ();
+
+    auto mark1_iter =
+    + hb_zip (this+mark1Coverage, this+mark1Array)
+    | hb_filter (glyphset, hb_first)
+    ;
+
+    hb_sorted_vector_t<hb_codepoint_t> new_coverage;
+    + mark1_iter
+    | hb_map (hb_first)
+    | hb_map (glyph_map)
+    | hb_sink (new_coverage)
+    ;
+
+    if (!out->mark1Coverage.serialize_serialize (c->serializer, new_coverage.iter ()))
+      return_trace (false);
+
+    if (unlikely (!out->mark1Array.serialize_subset (c, mark1Array, this,
+						     (this+mark1Coverage).iter (),
+						     &klass_mapping)))
+      return_trace (false);
+
+    unsigned mark2count = (this+mark2Array).rows;
+    auto mark2_iter =
+    + hb_zip (this+mark2Coverage, hb_range (mark2count))
+    | hb_filter (glyphset, hb_first)
+    ;
+
+    new_coverage.reset ();
+    hb_sorted_vector_t<unsigned> mark2_indexes;
+    auto &mark2_array = (this+mark2Array);
+    for (const auto _ : + mark2_iter)
+    {
+      unsigned row = _.second;
+
+      bool non_empty = + hb_range ((unsigned) classCount)
+                       | hb_filter (klass_mapping)
+                       | hb_map ([&] (const unsigned col) { return !mark2_array.offset_is_null (row, col, (unsigned) classCount); })
+                       | hb_any
+                       ;
+
+      if (!non_empty) continue;
+
+      hb_codepoint_t new_g = glyph_map.get ( _.first);
+      new_coverage.push (new_g);
+
+      + hb_range ((unsigned) classCount)
+      | hb_filter (klass_mapping)
+      | hb_map ([&] (const unsigned col) { return row * (unsigned) classCount + col; })
+      | hb_sink (mark2_indexes)
+      ;
+    }
+
+    if (!new_coverage) return_trace (false);
+    if (!out->mark2Coverage.serialize_serialize (c->serializer, new_coverage.iter ()))
+      return_trace (false);
+
+    return_trace (out->mark2Array.serialize_subset (c, mark2Array, this,
+						    mark2_iter.len (),
+						    mark2_indexes.iter ()));
+
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKMARKPOSFORMAT1_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/MarkRecord.hh

@@ -0,0 +1,51 @@
+#ifndef OT_LAYOUT_GPOS_MARKRECORD_HH
+#define OT_LAYOUT_GPOS_MARKRECORD_HH
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct MarkRecord
+{
+  friend struct MarkArray;
+
+  public:
+  HBUINT16      klass;                  /* Class defined for this mark */
+  Offset16To<Anchor>
+                markAnchor;             /* Offset to Anchor table--from
+                                         * beginning of MarkArray table */
+  public:
+  DEFINE_SIZE_STATIC (4);
+
+  unsigned get_class () const { return (unsigned) klass; }
+  bool sanitize (hb_sanitize_context_t *c, const void *base) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) && markAnchor.sanitize (c, base));
+  }
+
+  bool subset (hb_subset_context_t    *c,
+	       const void             *src_base,
+	       const hb_map_t         *klass_mapping) const
+  {
+    TRACE_SUBSET (this);
+    auto *out = c->serializer->embed (this);
+    if (unlikely (!out)) return_trace (false);
+
+    out->klass = klass_mapping->get (klass);
+    return_trace (out->markAnchor.serialize_subset (c, markAnchor, src_base));
+  }
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c,
+                                  const void *src_base) const
+  {
+    (src_base+markAnchor).collect_variation_indices (c);
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_MARKRECORD_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/PairPos.hh

@@ -0,0 +1,46 @@
+#ifndef OT_LAYOUT_GPOS_PAIRPOS_HH
+#define OT_LAYOUT_GPOS_PAIRPOS_HH
+
+#include "PairPosFormat1.hh"
+#include "PairPosFormat2.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct PairPos
+{
+  protected:
+  union {
+  struct { HBUINT16 v; }	format;         /* Format identifier */
+  PairPosFormat1_3<SmallTypes>	format1;
+  PairPosFormat2_4<SmallTypes>	format2;
+#ifndef HB_NO_BEYOND_64K
+  PairPosFormat1_3<MediumTypes>	format3;
+  PairPosFormat2_4<MediumTypes>	format4;
+#endif
+  } u;
+
+  public:
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  {
+    if (unlikely (!c->may_dispatch (this, &u.format.v))) return c->no_dispatch_return_value ();
+    TRACE_DISPATCH (this, u.format.v);
+    switch (u.format.v) {
+    case 1: return_trace (c->dispatch (u.format1, std::forward<Ts> (ds)...));
+    case 2: return_trace (c->dispatch (u.format2, std::forward<Ts> (ds)...));
+#ifndef HB_NO_BEYOND_64K
+    case 3: return_trace (c->dispatch (u.format3, std::forward<Ts> (ds)...));
+    case 4: return_trace (c->dispatch (u.format4, std::forward<Ts> (ds)...));
+#endif
+    default:return_trace (c->default_return_value ());
+    }
+  }
+};
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_PAIRPOS_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/PairPosFormat1.hh

@@ -0,0 +1,254 @@
+#ifndef OT_LAYOUT_GPOS_PAIRPOSFORMAT1_HH
+#define OT_LAYOUT_GPOS_PAIRPOSFORMAT1_HH
+
+#include "PairSet.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+
+template <typename Types>
+struct PairPosFormat1_3
+{
+  using PairSet = GPOS_impl::PairSet<Types>;
+  using PairValueRecord = GPOS_impl::PairValueRecord<Types>;
+
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  typename Types::template OffsetTo<Coverage>
+                coverage;               /* Offset to Coverage table--from
+                                         * beginning of subtable */
+  ValueFormat   valueFormat[2];         /* [0] Defines the types of data in
+                                         * ValueRecord1--for the first glyph
+                                         * in the pair--may be zero (0) */
+                                        /* [1] Defines the types of data in
+                                         * ValueRecord2--for the second glyph
+                                         * in the pair--may be zero (0) */
+  Array16Of<typename Types::template OffsetTo<PairSet>>
+                pairSet;                /* Array of PairSet tables
+                                         * ordered by Coverage Index */
+  public:
+  DEFINE_SIZE_ARRAY (8 + Types::size, pairSet);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+
+    if (!c->check_struct (this)) return_trace (false);
+    hb_barrier ();
+
+    unsigned int len1 = valueFormat[0].get_len ();
+    unsigned int len2 = valueFormat[1].get_len ();
+    typename PairSet::sanitize_closure_t closure =
+    {
+      valueFormat,
+      len1,
+      PairSet::get_size (len1, len2)
+    };
+
+    return_trace (coverage.sanitize (c, this) && pairSet.sanitize (c, this, &closure));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    auto &cov = this+coverage;
+
+    if (pairSet.len > glyphs->get_population () * hb_bit_storage ((unsigned) pairSet.len))
+    {
+      for (hb_codepoint_t g : glyphs->iter())
+      {
+	unsigned i = cov.get_coverage (g);
+	if ((this+pairSet[i]).intersects (glyphs, valueFormat))
+	  return true;
+      }
+      return false;
+    }
+
+    return
+    + hb_zip (cov, pairSet)
+    | hb_filter (*glyphs, hb_first)
+    | hb_map (hb_second)
+    | hb_map ([glyphs, this] (const typename Types::template OffsetTo<PairSet> &_)
+              { return (this+_).intersects (glyphs, valueFormat); })
+    | hb_any
+    ;
+  }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    if ((!valueFormat[0].has_device ()) && (!valueFormat[1].has_device ())) return;
+
+    auto it =
+    + hb_zip (this+coverage, pairSet)
+    | hb_filter (c->glyph_set, hb_first)
+    | hb_map (hb_second)
+    ;
+
+    if (!it) return;
+    + it
+    | hb_map (hb_add (this))
+    | hb_apply ([&] (const PairSet& _) { _.collect_variation_indices (c, valueFormat); })
+    ;
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  {
+    if (unlikely (!(this+coverage).collect_coverage (c->input))) return;
+    unsigned int count = pairSet.len;
+    for (unsigned int i = 0; i < count; i++)
+      (this+pairSet[i]).collect_glyphs (c, valueFormat);
+  }
+
+  const Coverage &get_coverage () const { return this+coverage; }
+
+  struct external_cache_t
+  {
+    hb_ot_layout_mapping_cache_t coverage;
+  };
+  void *external_cache_create () const
+  {
+    external_cache_t *cache = (external_cache_t *) hb_malloc (sizeof (external_cache_t));
+    if (likely (cache))
+    {
+      cache->coverage.clear ();
+    }
+    return cache;
+  }
+
+  bool apply (hb_ot_apply_context_t *c, void *external_cache) const
+  {
+    TRACE_APPLY (this);
+
+    hb_buffer_t *buffer = c->buffer;
+
+#ifndef HB_NO_OT_LAYOUT_LOOKUP_CACHE
+    external_cache_t *cache = (external_cache_t *) external_cache;
+    unsigned int index = (this+coverage).get_coverage  (buffer->cur().codepoint, cache ? &cache->coverage : nullptr);
+#else
+    unsigned int index = (this+coverage).get_coverage  (buffer->cur().codepoint);
+#endif
+    if (index == NOT_COVERED) return_trace (false);
+
+    auto &skippy_iter = c->iter_input;
+    skippy_iter.reset_fast (buffer->idx);
+    unsigned unsafe_to;
+    if (unlikely (!skippy_iter.next (&unsafe_to)))
+    {
+      buffer->unsafe_to_concat (buffer->idx, unsafe_to);
+      return_trace (false);
+    }
+
+    return_trace ((this+pairSet[index]).apply (c, valueFormat, skippy_iter.idx));
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+    out->format = format;
+
+    hb_pair_t<unsigned, unsigned> newFormats = hb_pair (valueFormat[0], valueFormat[1]);
+
+    if (c->plan->normalized_coords)
+    {
+      /* all device flags will be dropped when full instancing, no need to strip
+       * hints, also do not strip emtpy cause we don't compute the new default
+       * value during stripping */
+      newFormats = compute_effective_value_formats (glyphset, false, false, &c->plan->layout_variation_idx_delta_map);
+    }
+    /* do not strip hints for VF */
+    else if (c->plan->flags & HB_SUBSET_FLAGS_NO_HINTING)
+    {
+      hb_blob_t* blob = hb_face_reference_table (c->plan->source, HB_TAG ('f','v','a','r'));
+      bool has_fvar = (blob != hb_blob_get_empty ());
+      hb_blob_destroy (blob);
+
+      bool strip = !has_fvar;
+      /* special case: strip hints when a VF has no GDEF varstore after
+       * subsetting*/
+      if (has_fvar && !c->plan->has_gdef_varstore)
+        strip = true;
+      newFormats = compute_effective_value_formats (glyphset, strip, true);
+    }
+
+    out->valueFormat[0] = newFormats.first;
+    out->valueFormat[1] = newFormats.second;
+
+    hb_sorted_vector_t<hb_codepoint_t> new_coverage;
+
+    + hb_zip (this+coverage, pairSet)
+    | hb_filter (glyphset, hb_first)
+    | hb_filter ([this, c, out] (const typename Types::template OffsetTo<PairSet>& _)
+                 {
+                   auto snap = c->serializer->snapshot ();
+                   auto *o = out->pairSet.serialize_append (c->serializer);
+                   if (unlikely (!o)) return false;
+                   bool ret = o->serialize_subset (c, _, this, valueFormat, out->valueFormat);
+                   if (!ret)
+                   {
+                     out->pairSet.pop ();
+                     c->serializer->revert (snap);
+                   }
+                   return ret;
+                 },
+                 hb_second)
+    | hb_map (hb_first)
+    | hb_map (glyph_map)
+    | hb_sink (new_coverage)
+    ;
+
+    out->coverage.serialize_serialize (c->serializer, new_coverage.iter ());
+
+    return_trace (bool (new_coverage));
+  }
+
+
+  hb_pair_t<unsigned, unsigned> compute_effective_value_formats (const hb_set_t& glyphset,
+                                                                 bool strip_hints, bool strip_empty,
+                                                                 const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *varidx_delta_map = nullptr) const
+  {
+    unsigned record_size = PairSet::get_size (valueFormat);
+
+    unsigned format1 = 0;
+    unsigned format2 = 0;
+    for (const auto & _ :
+	  + hb_zip (this+coverage, pairSet)
+	  | hb_filter (glyphset, hb_first)
+	  | hb_map (hb_second)
+	)
+    {
+      const PairSet& set = (this + _);
+      const PairValueRecord *record = &set.firstPairValueRecord;
+
+      unsigned count = set.len;
+      for (unsigned i = 0; i < count; i++)
+      {
+        if (record->intersects (glyphset))
+        {
+          format1 = format1 | valueFormat[0].get_effective_format (record->get_values_1 (), strip_hints, strip_empty, &set, varidx_delta_map);
+          format2 = format2 | valueFormat[1].get_effective_format (record->get_values_2 (valueFormat[0]), strip_hints, strip_empty, &set, varidx_delta_map);
+        }
+        record = &StructAtOffset<const PairValueRecord> (record, record_size);
+      }
+
+      if (format1 == valueFormat[0] && format2 == valueFormat[1])
+        break;
+    }
+
+    return hb_pair (format1, format2);
+  }
+};
+
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_PAIRPOSFORMAT1_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/PairPosFormat2.hh

@@ -0,0 +1,389 @@
+#ifndef OT_LAYOUT_GPOS_PAIRPOSFORMAT2_HH
+#define OT_LAYOUT_GPOS_PAIRPOSFORMAT2_HH
+
+#include "ValueFormat.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+template <typename Types>
+struct PairPosFormat2_4 : ValueBase
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 2 */
+  typename Types::template OffsetTo<Coverage>
+                coverage;               /* Offset to Coverage table--from
+                                         * beginning of subtable */
+  ValueFormat   valueFormat1;           /* ValueRecord definition--for the
+                                         * first glyph of the pair--may be zero
+                                         * (0) */
+  ValueFormat   valueFormat2;           /* ValueRecord definition--for the
+                                         * second glyph of the pair--may be
+                                         * zero (0) */
+  typename Types::template OffsetTo<ClassDef>
+                classDef1;              /* Offset to ClassDef table--from
+                                         * beginning of PairPos subtable--for
+                                         * the first glyph of the pair */
+  typename Types::template OffsetTo<ClassDef>
+                classDef2;              /* Offset to ClassDef table--from
+                                         * beginning of PairPos subtable--for
+                                         * the second glyph of the pair */
+  HBUINT16      class1Count;            /* Number of classes in ClassDef1
+                                         * table--includes Class0 */
+  HBUINT16      class2Count;            /* Number of classes in ClassDef2
+                                         * table--includes Class0 */
+  ValueRecord   values;                 /* Matrix of value pairs:
+                                         * class1-major, class2-minor,
+                                         * Each entry has value1 and value2 */
+  public:
+  DEFINE_SIZE_ARRAY (10 + 3 * Types::size, values);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    if (!(c->check_struct (this)
+       && coverage.sanitize (c, this)
+       && classDef1.sanitize (c, this)
+       && classDef2.sanitize (c, this))) return_trace (false);
+
+    unsigned int len1 = valueFormat1.get_len ();
+    unsigned int len2 = valueFormat2.get_len ();
+    unsigned int stride = HBUINT16::static_size * (len1 + len2);
+    unsigned int count = (unsigned int) class1Count * (unsigned int) class2Count;
+    return_trace (c->check_range ((const void *) values,
+                                  count,
+                                  stride) &&
+		  (c->lazy_some_gpos ||
+		   (valueFormat1.sanitize_values_stride_unsafe (c, this, &values[0], count, stride) &&
+		    valueFormat2.sanitize_values_stride_unsafe (c, this, &values[len1], count, stride))));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    return (this+coverage).intersects (glyphs) &&
+           (this+classDef2).intersects (glyphs);
+  }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    if (!intersects (c->glyph_set)) return;
+    if ((!valueFormat1.has_device ()) && (!valueFormat2.has_device ())) return;
+
+    hb_set_t klass1_glyphs, klass2_glyphs;
+    if (!(this+classDef1).collect_coverage (&klass1_glyphs)) return;
+    if (!(this+classDef2).collect_coverage (&klass2_glyphs)) return;
+
+    hb_set_t class1_set, class2_set;
+    for (const unsigned cp : + c->glyph_set->iter () | hb_filter (this + coverage))
+    {
+      if (!klass1_glyphs.has (cp)) class1_set.add (0);
+      else
+      {
+        unsigned klass1 = (this+classDef1).get (cp);
+        class1_set.add (klass1);
+      }
+    }
+
+    class2_set.add (0);
+    for (const unsigned cp : + c->glyph_set->iter () | hb_filter (klass2_glyphs))
+    {
+      unsigned klass2 = (this+classDef2).get (cp);
+      class2_set.add (klass2);
+    }
+
+    if (class1_set.is_empty ()
+        || class2_set.is_empty ()
+        || (class2_set.get_population() == 1 && class2_set.has(0)))
+      return;
+
+    unsigned len1 = valueFormat1.get_len ();
+    unsigned len2 = valueFormat2.get_len ();
+    const hb_array_t<const Value> values_array = values.as_array ((unsigned)class1Count * (unsigned) class2Count * (len1 + len2));
+    for (const unsigned class1_idx : class1_set.iter ())
+    {
+      for (const unsigned class2_idx : class2_set.iter ())
+      {
+        unsigned start_offset = (class1_idx * (unsigned) class2Count + class2_idx) * (len1 + len2);
+        if (valueFormat1.has_device ())
+          valueFormat1.collect_variation_indices (c, this, values_array.sub_array (start_offset, len1));
+
+        if (valueFormat2.has_device ())
+          valueFormat2.collect_variation_indices (c, this, values_array.sub_array (start_offset+len1, len2));
+      }
+    }
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  {
+    if (unlikely (!(this+coverage).collect_coverage (c->input))) return;
+    if (unlikely (!(this+classDef2).collect_coverage (c->input))) return;
+  }
+
+  const Coverage &get_coverage () const { return this+coverage; }
+
+  struct external_cache_t
+  {
+    hb_ot_layout_mapping_cache_t coverage;
+    hb_ot_layout_mapping_cache_t first;
+    hb_ot_layout_mapping_cache_t second;
+  };
+  void *external_cache_create () const
+  {
+    external_cache_t *cache = (external_cache_t *) hb_malloc (sizeof (external_cache_t));
+    if (likely (cache))
+    {
+      cache->coverage.clear ();
+      cache->first.clear ();
+      cache->second.clear ();
+    }
+    return cache;
+  }
+
+  bool apply (hb_ot_apply_context_t *c, void *external_cache) const
+  {
+    TRACE_APPLY (this);
+
+    hb_buffer_t *buffer = c->buffer;
+
+#ifndef HB_NO_OT_LAYOUT_LOOKUP_CACHE
+    external_cache_t *cache = (external_cache_t *) external_cache;
+    unsigned int index = (this+coverage).get_coverage  (buffer->cur().codepoint, cache ? &cache->coverage : nullptr);
+#else
+    unsigned int index = (this+coverage).get_coverage  (buffer->cur().codepoint);
+#endif
+    if (index == NOT_COVERED) return_trace (false);
+
+    auto &skippy_iter = c->iter_input;
+    skippy_iter.reset_fast (buffer->idx);
+    unsigned unsafe_to;
+    if (unlikely (!skippy_iter.next (&unsafe_to)))
+    {
+      buffer->unsafe_to_concat (buffer->idx, unsafe_to);
+      return_trace (false);
+    }
+
+#ifndef HB_NO_OT_LAYOUT_LOOKUP_CACHE
+    unsigned int klass1 = (this+classDef1).get_class (buffer->cur().codepoint, cache ? &cache->first : nullptr);
+    unsigned int klass2 = (this+classDef2).get_class (buffer->info[skippy_iter.idx].codepoint, cache ? &cache->second : nullptr);
+#else
+    unsigned int klass1 = (this+classDef1).get_class (buffer->cur().codepoint);
+    unsigned int klass2 = (this+classDef2).get_class (buffer->info[skippy_iter.idx].codepoint);
+#endif
+    if (unlikely (klass1 >= class1Count || klass2 >= class2Count))
+    {
+      buffer->unsafe_to_concat (buffer->idx, skippy_iter.idx + 1);
+      return_trace (false);
+    }
+
+    unsigned int len1 = valueFormat1.get_len ();
+    unsigned int len2 = valueFormat2.get_len ();
+    unsigned int record_len = len1 + len2;
+
+    const Value *v = &values[record_len * (klass1 * class2Count + klass2)];
+
+    bool applied_first = false, applied_second = false;
+
+
+    /* Isolate simple kerning and apply it half to each side.
+     * Results in better cursor positioning / underline drawing.
+     *
+     * Disabled, because causes issues... :-(
+     * https://github.com/harfbuzz/harfbuzz/issues/3408
+     * https://github.com/harfbuzz/harfbuzz/pull/3235#issuecomment-1029814978
+     */
+#ifndef HB_SPLIT_KERN
+    if (false)
+#endif
+    {
+      if (!len2)
+      {
+        const hb_direction_t dir = buffer->props.direction;
+        const bool horizontal = HB_DIRECTION_IS_HORIZONTAL (dir);
+        const bool backward = HB_DIRECTION_IS_BACKWARD (dir);
+        unsigned mask = horizontal ? ValueFormat::xAdvance : ValueFormat::yAdvance;
+        if (backward)
+          mask |= mask >> 2; /* Add eg. xPlacement in RTL. */
+        /* Add Devices. */
+        mask |= mask << 4;
+
+        if (valueFormat1 & ~mask)
+          goto bail;
+
+        /* Is simple kern. Apply value on an empty position slot,
+         * then split it between sides. */
+
+        hb_glyph_position_t pos{};
+        if (valueFormat1.apply_value (c, this, v, pos))
+        {
+          hb_position_t *src  = &pos.x_advance;
+          hb_position_t *dst1 = &buffer->cur_pos().x_advance;
+          hb_position_t *dst2 = &buffer->pos[skippy_iter.idx].x_advance;
+          unsigned i = horizontal ? 0 : 1;
+
+          hb_position_t kern  = src[i];
+          hb_position_t kern1 = kern >> 1;
+          hb_position_t kern2 = kern - kern1;
+
+          if (!backward)
+          {
+            dst1[i] += kern1;
+            dst2[i] += kern2;
+            dst2[i + 2] += kern2;
+          }
+          else
+          {
+            dst1[i] += kern1;
+            dst1[i + 2] += src[i + 2] - kern2;
+            dst2[i] += kern2;
+          }
+
+          applied_first = applied_second = kern != 0;
+          goto success;
+        }
+        goto boring;
+      }
+    }
+    bail:
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "try kerning glyphs at %u,%u",
+			  c->buffer->idx, skippy_iter.idx);
+    }
+
+    applied_first = len1 && valueFormat1.apply_value (c, this, v, buffer->cur_pos());
+    applied_second = len2 && valueFormat2.apply_value (c, this, v + len1, buffer->pos[skippy_iter.idx]);
+
+    if (applied_first || applied_second)
+      if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+      {
+	c->buffer->message (c->font,
+			    "kerned glyphs at %u,%u",
+			    c->buffer->idx, skippy_iter.idx);
+      }
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "tried kerning glyphs at %u,%u",
+			  c->buffer->idx, skippy_iter.idx);
+    }
+
+    success:
+    if (applied_first || applied_second)
+      buffer->unsafe_to_break (buffer->idx, skippy_iter.idx + 1);
+    else
+    boring:
+      buffer->unsafe_to_concat (buffer->idx, skippy_iter.idx + 1);
+
+    if (len2)
+    {
+      skippy_iter.idx++;
+      // https://github.com/harfbuzz/harfbuzz/issues/3824
+      // https://github.com/harfbuzz/harfbuzz/issues/3888#issuecomment-1326781116
+      buffer->unsafe_to_break (buffer->idx, skippy_iter.idx + 1);
+    }
+
+    buffer->idx = skippy_iter.idx;
+
+    return_trace (true);
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+    out->format = format;
+
+    hb_map_t klass1_map;
+    out->classDef1.serialize_subset (c, classDef1, this, &klass1_map, true, true, &(this + coverage));
+    out->class1Count = klass1_map.get_population ();
+
+    hb_map_t klass2_map;
+    out->classDef2.serialize_subset (c, classDef2, this, &klass2_map, true, false);
+    out->class2Count = klass2_map.get_population ();
+
+    unsigned len1 = valueFormat1.get_len ();
+    unsigned len2 = valueFormat2.get_len ();
+
+    hb_pair_t<unsigned, unsigned> newFormats = hb_pair (valueFormat1, valueFormat2);
+
+    if (c->plan->normalized_coords)
+    {
+      /* in case of full instancing, all var device flags will be dropped so no
+       * need to strip hints here */
+      newFormats = compute_effective_value_formats (klass1_map, klass2_map, false, false, &c->plan->layout_variation_idx_delta_map);
+    }
+    /* do not strip hints for VF */
+    else if (c->plan->flags & HB_SUBSET_FLAGS_NO_HINTING)
+    {
+      hb_blob_t* blob = hb_face_reference_table (c->plan->source, HB_TAG ('f','v','a','r'));
+      bool has_fvar = (blob != hb_blob_get_empty ());
+      hb_blob_destroy (blob);
+
+      bool strip = !has_fvar;
+      /* special case: strip hints when a VF has no GDEF varstore after
+       * subsetting*/
+      if (has_fvar && !c->plan->has_gdef_varstore)
+        strip = true;
+      newFormats = compute_effective_value_formats (klass1_map, klass2_map, strip, true);
+    }
+
+    out->valueFormat1 = newFormats.first;
+    out->valueFormat2 = newFormats.second;
+
+    unsigned total_len = len1 + len2;
+    hb_vector_t<unsigned> class2_idxs (+ hb_range ((unsigned) class2Count) | hb_filter (klass2_map));
+    for (unsigned class1_idx : + hb_range ((unsigned) class1Count) | hb_filter (klass1_map))
+    {
+      for (unsigned class2_idx : class2_idxs)
+      {
+        unsigned idx = (class1_idx * (unsigned) class2Count + class2_idx) * total_len;
+        valueFormat1.copy_values (c->serializer, out->valueFormat1, this, &values[idx], &c->plan->layout_variation_idx_delta_map);
+        valueFormat2.copy_values (c->serializer, out->valueFormat2, this, &values[idx + len1], &c->plan->layout_variation_idx_delta_map);
+      }
+    }
+
+    bool ret = out->coverage.serialize_subset(c, coverage, this);
+    return_trace (out->class1Count && out->class2Count && ret);
+  }
+
+
+  hb_pair_t<unsigned, unsigned> compute_effective_value_formats (const hb_map_t& klass1_map,
+                                                                 const hb_map_t& klass2_map,
+                                                                 bool strip_hints, bool strip_empty,
+                                                                 const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *varidx_delta_map = nullptr) const
+  {
+    unsigned len1 = valueFormat1.get_len ();
+    unsigned len2 = valueFormat2.get_len ();
+    unsigned record_size = len1 + len2;
+
+    unsigned format1 = 0;
+    unsigned format2 = 0;
+
+    for (unsigned class1_idx : + hb_range ((unsigned) class1Count) | hb_filter (klass1_map))
+    {
+      for (unsigned class2_idx : + hb_range ((unsigned) class2Count) | hb_filter (klass2_map))
+      {
+        unsigned idx = (class1_idx * (unsigned) class2Count + class2_idx) * record_size;
+        format1 = format1 | valueFormat1.get_effective_format (&values[idx], strip_hints, strip_empty, this, varidx_delta_map);
+        format2 = format2 | valueFormat2.get_effective_format (&values[idx + len1], strip_hints, strip_empty, this, varidx_delta_map);
+      }
+
+      if (format1 == valueFormat1 && format2 == valueFormat2)
+        break;
+    }
+
+    return hb_pair (format1, format2);
+  }
+};
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_PAIRPOSFORMAT2_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/PairSet.hh

@@ -0,0 +1,210 @@
+#ifndef OT_LAYOUT_GPOS_PAIRSET_HH
+#define OT_LAYOUT_GPOS_PAIRSET_HH
+
+#include "PairValueRecord.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+
+template <typename Types>
+struct PairSet : ValueBase
+{
+  template <typename Types2>
+  friend struct PairPosFormat1_3;
+
+  using PairValueRecord = GPOS_impl::PairValueRecord<Types>;
+
+  protected:
+  HBUINT16              len;    /* Number of PairValueRecords */
+  PairValueRecord       firstPairValueRecord;
+                                /* Array of PairValueRecords--ordered
+                                 * by GlyphID of the second glyph */
+  public:
+  DEFINE_SIZE_MIN (2);
+
+  static size_t get_size (unsigned len1, unsigned len2)
+  {
+    return Types::HBGlyphID::static_size + Value::static_size * (len1 + len2);
+  }
+  static size_t get_size (const ValueFormat valueFormats[2])
+  {
+    unsigned len1 = valueFormats[0].get_len ();
+    unsigned len2 = valueFormats[1].get_len ();
+    return get_size (len1, len2);
+  }
+
+  struct sanitize_closure_t
+  {
+    const ValueFormat *valueFormats;
+    unsigned int len1; /* valueFormats[0].get_len() */
+    size_t stride; /* bytes */
+  };
+
+  bool sanitize (hb_sanitize_context_t *c, const sanitize_closure_t *closure) const
+  {
+    TRACE_SANITIZE (this);
+    if (!(c->check_struct (this) &&
+	  hb_barrier () &&
+          c->check_range (&firstPairValueRecord,
+                          len,
+                          closure->stride))) return_trace (false);
+    hb_barrier ();
+
+    unsigned int count = len;
+    const PairValueRecord *record = &firstPairValueRecord;
+    return_trace (c->lazy_some_gpos ||
+		  (closure->valueFormats[0].sanitize_values_stride_unsafe (c, this, &record->values[0], count, closure->stride) &&
+                   closure->valueFormats[1].sanitize_values_stride_unsafe (c, this, &record->values[closure->len1], count, closure->stride)));
+  }
+
+  bool intersects (const hb_set_t *glyphs,
+                   const ValueFormat *valueFormats) const
+  {
+    unsigned record_size = get_size (valueFormats);
+
+    const PairValueRecord *record = &firstPairValueRecord;
+    unsigned int count = len;
+    for (unsigned int i = 0; i < count; i++)
+    {
+      if (glyphs->has (record->secondGlyph))
+        return true;
+      record = &StructAtOffset<const PairValueRecord> (record, record_size);
+    }
+    return false;
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c,
+                       const ValueFormat *valueFormats) const
+  {
+    unsigned record_size = get_size (valueFormats);
+
+    const PairValueRecord *record = &firstPairValueRecord;
+    c->input->add_array (&record->secondGlyph, len, record_size);
+  }
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c,
+                                  const ValueFormat *valueFormats) const
+  {
+    unsigned record_size = get_size (valueFormats);
+
+    const PairValueRecord *record = &firstPairValueRecord;
+    unsigned count = len;
+    for (unsigned i = 0; i < count; i++)
+    {
+      if (c->glyph_set->has (record->secondGlyph))
+      { record->collect_variation_indices (c, valueFormats, this); }
+
+      record = &StructAtOffset<const PairValueRecord> (record, record_size);
+    }
+  }
+
+  bool apply (hb_ot_apply_context_t *c,
+              const ValueFormat *valueFormats,
+              unsigned int pos) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+    unsigned int len1 = valueFormats[0].get_len ();
+    unsigned int len2 = valueFormats[1].get_len ();
+    unsigned record_size = get_size (len1, len2);
+
+    const PairValueRecord *record = hb_bsearch (buffer->info[pos].codepoint,
+                                                &firstPairValueRecord,
+                                                len,
+                                                record_size);
+    if (record)
+    {
+      if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+      {
+	c->buffer->message (c->font,
+			    "try kerning glyphs at %u,%u",
+			    c->buffer->idx, pos);
+      }
+
+      bool applied_first = len1 && valueFormats[0].apply_value (c, this, &record->values[0], buffer->cur_pos());
+      bool applied_second = len2 && valueFormats[1].apply_value (c, this, &record->values[len1], buffer->pos[pos]);
+
+      if (applied_first || applied_second)
+	if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+	{
+	  c->buffer->message (c->font,
+			      "kerned glyphs at %u,%u",
+			      c->buffer->idx, pos);
+	}
+
+      if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+      {
+	c->buffer->message (c->font,
+			    "tried kerning glyphs at %u,%u",
+			    c->buffer->idx, pos);
+      }
+
+      if (applied_first || applied_second)
+        buffer->unsafe_to_break (buffer->idx, pos + 1);
+
+      if (len2)
+      {
+	pos++;
+      // https://github.com/harfbuzz/harfbuzz/issues/3824
+      // https://github.com/harfbuzz/harfbuzz/issues/3888#issuecomment-1326781116
+      buffer->unsafe_to_break (buffer->idx, pos + 1);
+      }
+
+      buffer->idx = pos;
+      return_trace (true);
+    }
+    buffer->unsafe_to_concat (buffer->idx, pos + 1);
+    return_trace (false);
+  }
+
+  bool subset (hb_subset_context_t *c,
+               const ValueFormat valueFormats[2],
+               const ValueFormat newFormats[2]) const
+  {
+    TRACE_SUBSET (this);
+    auto snap = c->serializer->snapshot ();
+
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+    out->len = 0;
+
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    unsigned len1 = valueFormats[0].get_len ();
+    unsigned len2 = valueFormats[1].get_len ();
+    unsigned record_size = get_size (len1, len2);
+
+    typename PairValueRecord::context_t context =
+    {
+      this,
+      valueFormats,
+      newFormats,
+      len1,
+      &glyph_map,
+      &c->plan->layout_variation_idx_delta_map
+    };
+
+    const PairValueRecord *record = &firstPairValueRecord;
+    unsigned count = len, num = 0;
+    for (unsigned i = 0; i < count; i++)
+    {
+      if (glyphset.has (record->secondGlyph)
+         && record->subset (c, &context)) num++;
+      record = &StructAtOffset<const PairValueRecord> (record, record_size);
+    }
+
+    out->len = num;
+    if (!num) c->serializer->revert (snap);
+    return_trace (num);
+  }
+};
+
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_PAIRSET_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/PairValueRecord.hh

@@ -0,0 +1,99 @@
+#ifndef OT_LAYOUT_GPOS_PAIRVALUERECORD_HH
+#define OT_LAYOUT_GPOS_PAIRVALUERECORD_HH
+
+#include "ValueFormat.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+
+template <typename Types>
+struct PairValueRecord
+{
+  template <typename Types2>
+  friend struct PairSet;
+
+  protected:
+  typename Types::HBGlyphID
+	        secondGlyph;            /* GlyphID of second glyph in the
+                                         * pair--first glyph is listed in the
+                                         * Coverage table */
+  ValueRecord   values;                 /* Positioning data for the first glyph
+                                         * followed by for second glyph */
+  public:
+  DEFINE_SIZE_ARRAY (Types::HBGlyphID::static_size, values);
+
+  int cmp (hb_codepoint_t k) const
+  { return secondGlyph.cmp (k); }
+
+  struct context_t
+  {
+    const ValueBase     *base;
+    const ValueFormat   *valueFormats;
+    const ValueFormat   *newFormats;
+    unsigned            len1; /* valueFormats[0].get_len() */
+    const hb_map_t      *glyph_map;
+    const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map;
+  };
+
+  bool subset (hb_subset_context_t *c,
+               context_t *closure) const
+  {
+    TRACE_SERIALIZE (this);
+    auto *s = c->serializer;
+    auto *out = s->start_embed (*this);
+    if (unlikely (!s->extend_min (out))) return_trace (false);
+
+    out->secondGlyph = (*closure->glyph_map)[secondGlyph];
+
+    closure->valueFormats[0].copy_values (s,
+                                          closure->newFormats[0],
+                                          closure->base, &values[0],
+                                          closure->layout_variation_idx_delta_map);
+    closure->valueFormats[1].copy_values (s,
+                                          closure->newFormats[1],
+                                          closure->base,
+                                          &values[closure->len1],
+                                          closure->layout_variation_idx_delta_map);
+
+    return_trace (true);
+  }
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c,
+                                  const ValueFormat *valueFormats,
+                                  const ValueBase *base) const
+  {
+    unsigned record1_len = valueFormats[0].get_len ();
+    unsigned record2_len = valueFormats[1].get_len ();
+    const hb_array_t<const Value> values_array = values.as_array (record1_len + record2_len);
+
+    if (valueFormats[0].has_device ())
+      valueFormats[0].collect_variation_indices (c, base, values_array.sub_array (0, record1_len));
+
+    if (valueFormats[1].has_device ())
+      valueFormats[1].collect_variation_indices (c, base, values_array.sub_array (record1_len, record2_len));
+  }
+
+  bool intersects (const hb_set_t& glyphset) const
+  {
+    return glyphset.has(secondGlyph);
+  }
+
+  const Value* get_values_1 () const
+  {
+    return &values[0];
+  }
+
+  const Value* get_values_2 (ValueFormat format1) const
+  {
+    return &values[format1.get_len ()];
+  }
+};
+
+
+}
+}
+}
+
+#endif  // OT_LAYOUT_GPOS_PAIRVALUERECORD_HH

3rdparty/harfbuzz/src/OT/Layout/GPOS/PosLookup.hh

@@ -0,0 +1,79 @@
+#ifndef OT_LAYOUT_GPOS_POSLOOKUP_HH
+#define OT_LAYOUT_GPOS_POSLOOKUP_HH
+
+#include "PosLookupSubTable.hh"
+#include "../../../hb-ot-layout-common.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct PosLookup : Lookup
+{
+  using SubTable = PosLookupSubTable;
+
+  const SubTable& get_subtable (unsigned int i) const
+  { return Lookup::get_subtable<SubTable> (i); }
+
+  bool is_reverse () const
+  {
+    return false;
+  }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    return_trace (dispatch (c));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  {
+    hb_intersects_context_t c (glyphs);
+    return dispatch (&c);
+  }
+
+  hb_collect_glyphs_context_t::return_t collect_glyphs (hb_collect_glyphs_context_t *c) const
+  { return dispatch (c); }
+
+  hb_closure_lookups_context_t::return_t closure_lookups (hb_closure_lookups_context_t *c, unsigned this_index) const
+  {
+    if (c->is_lookup_visited (this_index))
+      return hb_closure_lookups_context_t::default_return_value ();
+
+    c->set_lookup_visited (this_index);
+    if (!intersects (c->glyphs))
+    {
+      c->set_lookup_inactive (this_index);
+      return hb_closure_lookups_context_t::default_return_value ();
+    }
+
+    hb_closure_lookups_context_t::return_t ret = dispatch (c);
+    return ret;
+  }
+
+  template <typename set_t>
+  void collect_coverage (set_t *glyphs) const
+  {
+    hb_collect_coverage_context_t<set_t> c (glyphs);
+    dispatch (&c);
+  }
+
+  template <typename context_t>
+  static typename context_t::return_t dispatch_recurse_func (context_t *c, unsigned int lookup_index);
+
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  { return Lookup::dispatch<SubTable> (c, std::forward<Ts> (ds)...); }
+
+  bool subset (hb_subset_context_t *c) const
+  { return Lookup::subset<SubTable> (c); }
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  { return Lookup::sanitize<SubTable> (c); }
+};
+
+}
+}
+}
+
+#endif  /* OT_LAYOUT_GPOS_POSLOOKUP_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/PosLookupSubTable.hh

@@ -0,0 +1,79 @@
+#ifndef OT_LAYOUT_GPOS_POSLOOKUPSUBTABLE_HH
+#define OT_LAYOUT_GPOS_POSLOOKUPSUBTABLE_HH
+
+#include "SinglePos.hh"
+#include "PairPos.hh"
+#include "CursivePos.hh"
+#include "MarkBasePos.hh"
+#include "MarkLigPos.hh"
+#include "MarkMarkPos.hh"
+#include "ContextPos.hh"
+#include "ChainContextPos.hh"
+#include "ExtensionPos.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct PosLookupSubTable
+{
+  friend struct ::OT::Lookup;
+  friend struct PosLookup;
+
+  enum Type {
+    Single              = 1,
+    Pair                = 2,
+    Cursive             = 3,
+    MarkBase            = 4,
+    MarkLig             = 5,
+    MarkMark            = 6,
+    Context             = 7,
+    ChainContext        = 8,
+    Extension           = 9
+  };
+
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, unsigned int lookup_type, Ts&&... ds) const
+  {
+    TRACE_DISPATCH (this, lookup_type);
+    switch (lookup_type) {
+    case Single:                return_trace (u.single.dispatch (c, std::forward<Ts> (ds)...));
+    case Pair:                  return_trace (u.pair.dispatch (c, std::forward<Ts> (ds)...));
+    case Cursive:               return_trace (u.cursive.dispatch (c, std::forward<Ts> (ds)...));
+    case MarkBase:              return_trace (u.markBase.dispatch (c, std::forward<Ts> (ds)...));
+    case MarkLig:               return_trace (u.markLig.dispatch (c, std::forward<Ts> (ds)...));
+    case MarkMark:              return_trace (u.markMark.dispatch (c, std::forward<Ts> (ds)...));
+    case Context:               return_trace (u.context.dispatch (c, std::forward<Ts> (ds)...));
+    case ChainContext:          return_trace (u.chainContext.dispatch (c, std::forward<Ts> (ds)...));
+    case Extension:             return_trace (u.extension.dispatch (c, std::forward<Ts> (ds)...));
+    default:                    return_trace (c->default_return_value ());
+    }
+  }
+
+  bool intersects (const hb_set_t *glyphs, unsigned int lookup_type) const
+  {
+    hb_intersects_context_t c (glyphs);
+    return dispatch (&c, lookup_type);
+  }
+
+  protected:
+  union {
+  SinglePos             single;
+  PairPos               pair;
+  CursivePos            cursive;
+  MarkBasePos           markBase;
+  MarkLigPos            markLig;
+  MarkMarkPos           markMark;
+  ContextPos            context;
+  ChainContextPos       chainContext;
+  ExtensionPos          extension;
+  } u;
+  public:
+  DEFINE_SIZE_MIN (0);
+};
+
+}
+}
+}
+
+#endif  /* HB_OT_LAYOUT_GPOS_POSLOOKUPSUBTABLE_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/SinglePos.hh

@@ -0,0 +1,98 @@
+#ifndef OT_LAYOUT_GPOS_SINGLEPOS_HH
+#define OT_LAYOUT_GPOS_SINGLEPOS_HH
+
+#include "SinglePosFormat1.hh"
+#include "SinglePosFormat2.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct SinglePos
+{
+  protected:
+  union {
+  struct { HBUINT16 v; } format;        /* Format identifier */
+  SinglePosFormat1      format1;
+  SinglePosFormat2      format2;
+  } u;
+
+  public:
+  template<typename Iterator,
+           hb_requires (hb_is_iterator (Iterator))>
+  unsigned get_format (Iterator glyph_val_iter_pairs)
+  {
+    hb_array_t<const Value> first_val_iter = hb_second (*glyph_val_iter_pairs);
+
+    for (const auto iter : glyph_val_iter_pairs)
+      for (const auto _ : hb_zip (iter.second, first_val_iter))
+        if (_.first != _.second)
+          return 2;
+
+    return 1;
+  }
+
+  template<typename Iterator,
+      typename SrcLookup,
+      hb_requires (hb_is_iterator (Iterator))>
+  void serialize (hb_serialize_context_t *c,
+                  const SrcLookup* src,
+                  Iterator glyph_val_iter_pairs,
+                  const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map,
+                  unsigned newFormat)
+  {
+    if (unlikely (!c->extend_min (u.format.v))) return;
+    unsigned format = 2;
+    ValueFormat new_format;
+    new_format = newFormat;
+
+    if (glyph_val_iter_pairs)
+      format = get_format (glyph_val_iter_pairs);
+
+    u.format.v = format;
+    switch (u.format.v) {
+    case 1: u.format1.serialize (c,
+                                 src,
+                                 glyph_val_iter_pairs,
+                                 new_format,
+                                 layout_variation_idx_delta_map);
+      return;
+    case 2: u.format2.serialize (c,
+                                 src,
+                                 glyph_val_iter_pairs,
+                                 new_format,
+                                 layout_variation_idx_delta_map);
+      return;
+    default:return;
+    }
+  }
+
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  {
+    if (unlikely (!c->may_dispatch (this, &u.format.v))) return c->no_dispatch_return_value ();
+    TRACE_DISPATCH (this, u.format.v);
+    switch (u.format.v) {
+    case 1: return_trace (c->dispatch (u.format1, std::forward<Ts> (ds)...));
+    case 2: return_trace (c->dispatch (u.format2, std::forward<Ts> (ds)...));
+    default:return_trace (c->default_return_value ());
+    }
+  }
+};
+
+
+template<typename Iterator, typename SrcLookup>
+static void
+SinglePos_serialize (hb_serialize_context_t *c,
+                     const SrcLookup *src,
+                     Iterator it,
+                     const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map,
+                     unsigned new_format)
+{ c->start_embed<SinglePos> ()->serialize (c, src, it, layout_variation_idx_delta_map, new_format); }
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_SINGLEPOS_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/SinglePosFormat1.hh

@@ -0,0 +1,190 @@
+#ifndef OT_LAYOUT_GPOS_SINGLEPOSFORMAT1_HH
+#define OT_LAYOUT_GPOS_SINGLEPOSFORMAT1_HH
+
+#include "Common.hh"
+#include "ValueFormat.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct SinglePosFormat1 : ValueBase
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  Offset16To<Coverage>
+                coverage;               /* Offset to Coverage table--from
+                                         * beginning of subtable */
+  ValueFormat   valueFormat;            /* Defines the types of data in the
+                                         * ValueRecord */
+  ValueRecord   values;                 /* Defines positioning
+                                         * value(s)--applied to all glyphs in
+                                         * the Coverage table */
+  public:
+  DEFINE_SIZE_ARRAY (6, values);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+                  coverage.sanitize (c, this) &&
+		  hb_barrier () &&
+                  /* The coverage  table may use a range to represent a set
+                   * of glyphs, which means a small number of bytes can
+                   * generate a large glyph set. Manually modify the
+                   * sanitizer max ops to take this into account.
+                   *
+                   * Note: This check *must* be right after coverage sanitize. */
+                  c->check_ops ((this + coverage).get_population () >> 1) &&
+                  valueFormat.sanitize_value (c, this, values));
+
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  { return (this+coverage).intersects (glyphs); }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    if (!valueFormat.has_device ()) return;
+
+    hb_set_t intersection;
+    (this+coverage).intersect_set (*c->glyph_set, intersection);
+    if (!intersection) return;
+
+    valueFormat.collect_variation_indices (c, this, values.as_array (valueFormat.get_len ()));
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  { if (unlikely (!(this+coverage).collect_coverage (c->input))) return; }
+
+  const Coverage &get_coverage () const { return this+coverage; }
+
+  ValueFormat get_value_format () const { return valueFormat; }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+    unsigned int index = (this+coverage).get_coverage  (buffer->cur().codepoint);
+    if (index == NOT_COVERED) return_trace (false);
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "positioning glyph at %u",
+			  c->buffer->idx);
+    }
+
+    valueFormat.apply_value (c, this, values, buffer->cur_pos());
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "positioned glyph at %u",
+			  c->buffer->idx);
+    }
+
+    buffer->idx++;
+    return_trace (true);
+  }
+
+  bool
+  position_single (hb_font_t           *font,
+		   hb_blob_t           *table_blob,
+		   hb_direction_t       direction,
+		   hb_codepoint_t       gid,
+		   hb_glyph_position_t &pos) const
+  {
+    unsigned int index = (this+coverage).get_coverage  (gid);
+    if (likely (index == NOT_COVERED)) return false;
+
+    /* This is ugly... */
+    hb_buffer_t buffer {};
+    buffer.props.direction = direction;
+    OT::hb_ot_apply_context_t c (1, font, &buffer, table_blob);
+
+    valueFormat.apply_value (&c, this, values, pos);
+    return true;
+  }
+
+  template<typename Iterator,
+      typename SrcLookup,
+      hb_requires (hb_is_iterator (Iterator))>
+  void serialize (hb_serialize_context_t *c,
+                  const SrcLookup *src,
+                  Iterator it,
+                  ValueFormat newFormat,
+                  const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map)
+  {
+    if (unlikely (!c->extend_min (this))) return;
+    if (unlikely (!c->check_assign (valueFormat,
+                                    newFormat,
+                                    HB_SERIALIZE_ERROR_INT_OVERFLOW))) return;
+
+    for (const hb_array_t<const Value>& _ : + it | hb_map (hb_second))
+    {
+      src->get_value_format ().copy_values (c, newFormat, src,  &_, layout_variation_idx_delta_map);
+      // Only serialize the first entry in the iterator, the rest are assumed to
+      // be the same.
+      break;
+    }
+
+    auto glyphs =
+    + it
+    | hb_map_retains_sorting (hb_first)
+    ;
+
+    coverage.serialize_serialize (c, glyphs);
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    hb_set_t intersection;
+    (this+coverage).intersect_set (glyphset, intersection);
+
+    unsigned new_format = valueFormat;
+
+    if (c->plan->normalized_coords)
+    {
+      new_format = valueFormat.get_effective_format (values.arrayZ, false, false, this, &c->plan->layout_variation_idx_delta_map);
+    }
+    /* do not strip hints for VF */
+    else if (c->plan->flags & HB_SUBSET_FLAGS_NO_HINTING)
+    {
+      hb_blob_t* blob = hb_face_reference_table (c->plan->source, HB_TAG ('f','v','a','r'));
+      bool has_fvar = (blob != hb_blob_get_empty ());
+      hb_blob_destroy (blob);
+
+      bool strip = !has_fvar;
+      /* special case: strip hints when a VF has no GDEF varstore after
+       * subsetting*/
+      if (has_fvar && !c->plan->has_gdef_varstore)
+        strip = true;
+      new_format = valueFormat.get_effective_format (values.arrayZ,
+                                                     strip, /* strip hints */
+                                                     true, /* strip empty */
+                                                     this, nullptr);
+    }
+
+    auto it =
+    + hb_iter (intersection)
+    | hb_map_retains_sorting (glyph_map)
+    | hb_zip (hb_repeat (values.as_array (valueFormat.get_len ())))
+    ;
+
+    bool ret = bool (it);
+    SinglePos_serialize (c->serializer, this, it, &c->plan->layout_variation_idx_delta_map, new_format);
+    return_trace (ret);
+  }
+};
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_SINGLEPOSFORMAT1_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/SinglePosFormat2.hh

@@ -0,0 +1,213 @@
+#ifndef OT_LAYOUT_GPOS_SINGLEPOSFORMAT2_HH
+#define OT_LAYOUT_GPOS_SINGLEPOSFORMAT2_HH
+
+#include "Common.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+struct SinglePosFormat2 : ValueBase
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 2 */
+  Offset16To<Coverage>
+                coverage;               /* Offset to Coverage table--from
+                                         * beginning of subtable */
+  ValueFormat   valueFormat;            /* Defines the types of data in the
+                                         * ValueRecord */
+  HBUINT16      valueCount;             /* Number of ValueRecords */
+  ValueRecord   values;                 /* Array of ValueRecords--positioning
+                                         * values applied to glyphs */
+  public:
+  DEFINE_SIZE_ARRAY (8, values);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (c->check_struct (this) &&
+                  coverage.sanitize (c, this) &&
+                  valueFormat.sanitize_values (c, this, values, valueCount));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  { return (this+coverage).intersects (glyphs); }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c) const
+  {
+    if (!valueFormat.has_device ()) return;
+
+    auto it =
+    + hb_zip (this+coverage, hb_range ((unsigned) valueCount))
+    | hb_filter (c->glyph_set, hb_first)
+    ;
+
+    if (!it) return;
+
+    unsigned sub_length = valueFormat.get_len ();
+    const hb_array_t<const Value> values_array = values.as_array (valueCount * sub_length);
+
+    for (unsigned i : + it
+                      | hb_map (hb_second))
+      valueFormat.collect_variation_indices (c, this, values_array.sub_array (i * sub_length, sub_length));
+
+  }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  { if (unlikely (!(this+coverage).collect_coverage (c->input))) return; }
+
+  const Coverage &get_coverage () const { return this+coverage; }
+
+  ValueFormat get_value_format () const { return valueFormat; }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    hb_buffer_t *buffer = c->buffer;
+    unsigned int index = (this+coverage).get_coverage  (buffer->cur().codepoint);
+    if (index == NOT_COVERED) return_trace (false);
+
+    if (unlikely (index >= valueCount)) return_trace (false);
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "positioning glyph at %u",
+			  c->buffer->idx);
+    }
+
+    valueFormat.apply_value (c, this,
+                             &values[index * valueFormat.get_len ()],
+                             buffer->cur_pos());
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "positioned glyph at %u",
+			  c->buffer->idx);
+    }
+
+    buffer->idx++;
+    return_trace (true);
+  }
+
+  bool
+  position_single (hb_font_t           *font,
+		   hb_blob_t           *table_blob,
+		   hb_direction_t       direction,
+		   hb_codepoint_t       gid,
+		   hb_glyph_position_t &pos) const
+  {
+    unsigned int index = (this+coverage).get_coverage  (gid);
+    if (likely (index == NOT_COVERED)) return false;
+    if (unlikely (index >= valueCount)) return false;
+
+    /* This is ugly... */
+    hb_buffer_t buffer {};
+    buffer.props.direction = direction;
+    OT::hb_ot_apply_context_t c (1, font, &buffer, table_blob);
+
+    valueFormat.apply_value (&c, this,
+                             &values[index * valueFormat.get_len ()],
+                             pos);
+    return true;
+  }
+
+
+  template<typename Iterator,
+      typename SrcLookup,
+      hb_requires (hb_is_iterator (Iterator))>
+  void serialize (hb_serialize_context_t *c,
+                  const SrcLookup *src,
+                  Iterator it,
+                  ValueFormat newFormat,
+                  const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map)
+  {
+    auto out = c->extend_min (this);
+    if (unlikely (!out)) return;
+    if (unlikely (!c->check_assign (valueFormat, newFormat, HB_SERIALIZE_ERROR_INT_OVERFLOW))) return;
+    if (unlikely (!c->check_assign (valueCount, it.len (), HB_SERIALIZE_ERROR_ARRAY_OVERFLOW))) return;
+
+    + it
+    | hb_map (hb_second)
+    | hb_apply ([&] (hb_array_t<const Value> _)
+    { src->get_value_format ().copy_values (c, newFormat, src, &_, layout_variation_idx_delta_map); })
+    ;
+
+    auto glyphs =
+    + it
+    | hb_map_retains_sorting (hb_first)
+    ;
+
+    coverage.serialize_serialize (c, glyphs);
+  }
+
+  template<typename Iterator,
+      hb_requires (hb_is_iterator (Iterator))>
+  unsigned compute_effective_format (const hb_face_t *face,
+                                     Iterator it,
+                                     bool is_instancing, bool strip_hints,
+                                     bool has_gdef_varstore,
+                                     const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *varidx_delta_map) const
+  {
+    hb_blob_t* blob = hb_face_reference_table (face, HB_TAG ('f','v','a','r'));
+    bool has_fvar = (blob != hb_blob_get_empty ());
+    hb_blob_destroy (blob);
+
+    unsigned new_format = 0;
+    if (is_instancing)
+    {
+      new_format = new_format | valueFormat.get_effective_format (+ it | hb_map (hb_second), false, false, this, varidx_delta_map);
+    }
+    /* do not strip hints for VF */
+    else if (strip_hints)
+    {
+      bool strip = !has_fvar;
+      if (has_fvar && !has_gdef_varstore)
+        strip = true;
+      new_format = new_format | valueFormat.get_effective_format (+ it | hb_map (hb_second), strip, true, this, nullptr);
+    }
+    else
+      new_format = valueFormat;
+
+    return new_format;
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    unsigned sub_length = valueFormat.get_len ();
+    auto values_array = values.as_array (valueCount * sub_length);
+
+    auto it =
+    + hb_zip (this+coverage, hb_range ((unsigned) valueCount))
+    | hb_filter (glyphset, hb_first)
+    | hb_map_retains_sorting ([&] (const hb_pair_t<hb_codepoint_t, unsigned>& _)
+                              {
+                                return hb_pair (glyph_map[_.first],
+                                                values_array.sub_array (_.second * sub_length,
+                                                                        sub_length));
+                              })
+    ;
+
+    unsigned new_format = compute_effective_format (c->plan->source, it,
+                                                    bool (c->plan->normalized_coords),
+                                                    bool (c->plan->flags & HB_SUBSET_FLAGS_NO_HINTING),
+                                                    c->plan->has_gdef_varstore,
+                                                    &c->plan->layout_variation_idx_delta_map);
+    bool ret = bool (it);
+    SinglePos_serialize (c->serializer, this, it, &c->plan->layout_variation_idx_delta_map, new_format);
+    return_trace (ret);
+  }
+};
+
+
+}
+}
+}
+
+#endif /* OT_LAYOUT_GPOS_SINGLEPOSFORMAT2_HH */

3rdparty/harfbuzz/src/OT/Layout/GPOS/ValueFormat.hh

@@ -0,0 +1,446 @@
+#ifndef OT_LAYOUT_GPOS_VALUEFORMAT_HH
+#define OT_LAYOUT_GPOS_VALUEFORMAT_HH
+
+#include "../../../hb-ot-layout-gsubgpos.hh"
+
+namespace OT {
+namespace Layout {
+namespace GPOS_impl {
+
+typedef HBUINT16 Value;
+
+struct ValueBase {}; // Dummy base class tag for OffsetTo<Value> bases.
+
+typedef UnsizedArrayOf<Value> ValueRecord;
+
+struct ValueFormat : HBUINT16
+{
+  enum Flags {
+    xPlacement  = 0x0001u,      /* Includes horizontal adjustment for placement */
+    yPlacement  = 0x0002u,      /* Includes vertical adjustment for placement */
+    xAdvance    = 0x0004u,      /* Includes horizontal adjustment for advance */
+    yAdvance    = 0x0008u,      /* Includes vertical adjustment for advance */
+    xPlaDevice  = 0x0010u,      /* Includes horizontal Device table for placement */
+    yPlaDevice  = 0x0020u,      /* Includes vertical Device table for placement */
+    xAdvDevice  = 0x0040u,      /* Includes horizontal Device table for advance */
+    yAdvDevice  = 0x0080u,      /* Includes vertical Device table for advance */
+    ignored     = 0x0F00u,      /* Was used in TrueType Open for MM fonts */
+    reserved    = 0xF000u,      /* For future use */
+
+    devices     = 0x00F0u       /* Mask for having any Device table */
+  };
+
+/* All fields are options.  Only those available advance the value pointer. */
+#if 0
+  HBINT16               xPlacement;     /* Horizontal adjustment for
+                                         * placement--in design units */
+  HBINT16               yPlacement;     /* Vertical adjustment for
+                                         * placement--in design units */
+  HBINT16               xAdvance;       /* Horizontal adjustment for
+                                         * advance--in design units (only used
+                                         * for horizontal writing) */
+  HBINT16               yAdvance;       /* Vertical adjustment for advance--in
+                                         * design units (only used for vertical
+                                         * writing) */
+  Offset16To<Device>    xPlaDevice;     /* Offset to Device table for
+                                         * horizontal placement--measured from
+                                         * beginning of PosTable (may be NULL) */
+  Offset16To<Device>    yPlaDevice;     /* Offset to Device table for vertical
+                                         * placement--measured from beginning
+                                         * of PosTable (may be NULL) */
+  Offset16To<Device>    xAdvDevice;     /* Offset to Device table for
+                                         * horizontal advance--measured from
+                                         * beginning of PosTable (may be NULL) */
+  Offset16To<Device>    yAdvDevice;     /* Offset to Device table for vertical
+                                         * advance--measured from beginning of
+                                         * PosTable (may be NULL) */
+#endif
+
+  NumType& operator = (uint16_t i) { v = i; return *this; }
+
+  // Note: spec says skip 2 bytes per bit in the valueformat. But reports
+  // from Microsoft developers indicate that only the fields that are
+  // currently defined are counted. We don't expect any new fields to
+  // be added to ValueFormat. As such, we use the faster hb_popcount8
+  // that only processes the lowest 8 bits.
+  unsigned int get_len () const  { return hb_popcount8 ((uint8_t) *this); }
+  size_t get_size () const { return get_len () * Value::static_size; }
+
+  hb_vector_t<unsigned> get_device_table_indices () const {
+    unsigned i = 0;
+    hb_vector_t<unsigned> result;
+    unsigned format = *this;
+
+    if (format & xPlacement) i++;
+    if (format & yPlacement) i++;
+    if (format & xAdvance)   i++;
+    if (format & yAdvance)   i++;
+
+    if (format & xPlaDevice) result.push (i++);
+    if (format & yPlaDevice) result.push (i++);
+    if (format & xAdvDevice) result.push (i++);
+    if (format & yAdvDevice) result.push (i++);
+
+    return result;
+  }
+
+  bool apply_value (hb_ot_apply_context_t *c,
+                    const ValueBase       *base,
+                    const Value           *values,
+                    hb_glyph_position_t   &glyph_pos) const
+  {
+    bool ret = false;
+    unsigned int format = *this;
+    if (!format) return ret;
+
+    hb_font_t *font = c->font;
+    bool horizontal =
+#ifndef HB_NO_VERTICAL
+      HB_DIRECTION_IS_HORIZONTAL (c->direction)
+#else
+      true
+#endif
+      ;
+
+    if (format & xPlacement) glyph_pos.x_offset  += font->em_scale_x (get_short (values++, &ret));
+    if (format & yPlacement) glyph_pos.y_offset  += font->em_scale_y (get_short (values++, &ret));
+    if (format & xAdvance) {
+      if (likely (horizontal)) glyph_pos.x_advance += font->em_scale_x (get_short (values, &ret));
+      values++;
+    }
+    /* y_advance values grow downward but font-space grows upward, hence negation */
+    if (format & yAdvance) {
+      if (unlikely (!horizontal)) glyph_pos.y_advance -= font->em_scale_y (get_short (values, &ret));
+      values++;
+    }
+
+    if (!has_device ()) return ret;
+
+    bool use_x_device = font->x_ppem || font->has_nonzero_coords;
+    bool use_y_device = font->y_ppem || font->has_nonzero_coords;
+
+    if (!use_x_device && !use_y_device) return ret;
+
+    const ItemVariationStore &store = c->var_store;
+    auto *cache = c->var_store_cache;
+
+    /* pixel -> fractional pixel */
+    if (format & xPlaDevice)
+    {
+      if (use_x_device) glyph_pos.x_offset  += get_device (values, &ret, base, c->sanitizer).get_x_delta (font, store, cache);
+      values++;
+    }
+    if (format & yPlaDevice)
+    {
+      if (use_y_device) glyph_pos.y_offset  += get_device (values, &ret, base, c->sanitizer).get_y_delta (font, store, cache);
+      values++;
+    }
+    if (format & xAdvDevice)
+    {
+      if (horizontal && use_x_device) glyph_pos.x_advance += get_device (values, &ret, base, c->sanitizer).get_x_delta (font, store, cache);
+      values++;
+    }
+    if (format & yAdvDevice)
+    {
+      /* y_advance values grow downward but font-space grows upward, hence negation */
+      if (!horizontal && use_y_device) glyph_pos.y_advance -= get_device (values, &ret, base, c->sanitizer).get_y_delta (font, store, cache);
+      values++;
+    }
+    return ret;
+  }
+
+  unsigned int get_effective_format (const Value *values, bool strip_hints, bool strip_empty, const ValueBase *base,
+                                     const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *varidx_delta_map) const
+  {
+    unsigned int format = *this;
+    for (unsigned flag = xPlacement; flag <= yAdvDevice; flag = flag << 1) {
+      if (format & flag)
+      {
+        if (strip_hints && flag >= xPlaDevice)
+        {
+          format = format & ~flag;
+          values++;
+          continue;
+        }
+        if (varidx_delta_map && flag >= xPlaDevice)
+        {
+          update_var_flag (values++, (Flags) flag, &format, base, varidx_delta_map);
+          continue;
+        }
+        /* do not strip empty when instancing, cause we don't know whether the new
+         * default value is 0 or not */
+        if (strip_empty) should_drop (*values, (Flags) flag, &format);
+        values++;
+      }
+    }
+
+    return format;
+  }
+
+  template<typename Iterator,
+      hb_requires (hb_is_iterator (Iterator))>
+  unsigned int get_effective_format (Iterator it, bool strip_hints, bool strip_empty, const ValueBase *base,
+                                     const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *varidx_delta_map) const {
+    unsigned int new_format = 0;
+
+    for (const hb_array_t<const Value>& values : it)
+      new_format = new_format | get_effective_format (&values, strip_hints, strip_empty, base, varidx_delta_map);
+
+    return new_format;
+  }
+
+  void copy_values (hb_serialize_context_t *c,
+                    unsigned int new_format,
+                    const ValueBase *base,
+                    const Value *values,
+                    const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map) const
+  {
+    unsigned int format = *this;
+    if (!format) return;
+
+    HBINT16 *x_placement = nullptr, *y_placement = nullptr, *x_adv = nullptr, *y_adv = nullptr;
+    if (format & xPlacement) x_placement = copy_value (c, new_format, xPlacement, *values++);
+    if (format & yPlacement) y_placement = copy_value (c, new_format, yPlacement, *values++);
+    if (format & xAdvance)   x_adv = copy_value (c, new_format, xAdvance, *values++);
+    if (format & yAdvance)   y_adv = copy_value (c, new_format, yAdvance, *values++);
+
+    if (!has_device ())
+      return;
+
+    if (format & xPlaDevice)
+    {
+      add_delta_to_value (x_placement, base, values, layout_variation_idx_delta_map);
+      copy_device (c, base, values++, layout_variation_idx_delta_map, new_format, xPlaDevice);
+    }
+
+    if (format & yPlaDevice)
+    {
+      add_delta_to_value (y_placement, base, values, layout_variation_idx_delta_map);
+      copy_device (c, base, values++, layout_variation_idx_delta_map, new_format, yPlaDevice);
+    }
+
+    if (format & xAdvDevice)
+    {
+      add_delta_to_value (x_adv, base, values, layout_variation_idx_delta_map);
+      copy_device (c, base, values++, layout_variation_idx_delta_map, new_format, xAdvDevice);
+    }
+
+    if (format & yAdvDevice)
+    {
+      add_delta_to_value (y_adv, base, values, layout_variation_idx_delta_map);
+      copy_device (c, base, values++, layout_variation_idx_delta_map, new_format, yAdvDevice);
+    }
+  }
+
+  HBINT16* copy_value (hb_serialize_context_t *c,
+                       unsigned int new_format,
+                       Flags flag,
+                       Value value) const
+  {
+    // Filter by new format.
+    if (!(new_format & flag)) return nullptr;
+    return reinterpret_cast<HBINT16 *> (c->copy (value));
+  }
+
+  void collect_variation_indices (hb_collect_variation_indices_context_t *c,
+                                  const ValueBase *base,
+                                  const hb_array_t<const Value>& values) const
+  {
+    unsigned format = *this;
+    unsigned i = 0;
+    if (format & xPlacement) i++;
+    if (format & yPlacement) i++;
+    if (format & xAdvance) i++;
+    if (format & yAdvance) i++;
+    if (format & xPlaDevice)
+    {
+      (base + get_device (&(values[i]))).collect_variation_indices (c);
+      i++;
+    }
+
+    if (format & ValueFormat::yPlaDevice)
+    {
+      (base + get_device (&(values[i]))).collect_variation_indices (c);
+      i++;
+    }
+
+    if (format & ValueFormat::xAdvDevice)
+    {
+      (base + get_device (&(values[i]))).collect_variation_indices (c);
+      i++;
+    }
+
+    if (format & ValueFormat::yAdvDevice)
+    {
+      (base + get_device (&(values[i]))).collect_variation_indices (c);
+      i++;
+    }
+  }
+
+  private:
+  bool sanitize_value_devices (hb_sanitize_context_t *c, const ValueBase *base, const Value *values) const
+  {
+    unsigned int format = *this;
+
+    if (format & xPlacement) values++;
+    if (format & yPlacement) values++;
+    if (format & xAdvance)   values++;
+    if (format & yAdvance)   values++;
+
+    if ((format & xPlaDevice) && !get_device (values++).sanitize (c, base)) return false;
+    if ((format & yPlaDevice) && !get_device (values++).sanitize (c, base)) return false;
+    if ((format & xAdvDevice) && !get_device (values++).sanitize (c, base)) return false;
+    if ((format & yAdvDevice) && !get_device (values++).sanitize (c, base)) return false;
+
+    return true;
+  }
+
+  static inline Offset16To<Device, ValueBase>& get_device (Value* value)
+  {
+    return *static_cast<Offset16To<Device, ValueBase> *> (value);
+  }
+  static inline const Offset16To<Device, ValueBase>& get_device (const Value* value)
+  {
+    return *static_cast<const Offset16To<Device, ValueBase> *> (value);
+  }
+  static inline const Device& get_device (const Value* value,
+					  bool *worked,
+					  const ValueBase *base,
+					  hb_sanitize_context_t &c)
+  {
+    if (worked) *worked |= bool (*value);
+    auto &offset = *static_cast<const Offset16To<Device> *> (value);
+
+    if (unlikely (!offset.sanitize (&c, base)))
+      return Null(Device);
+    hb_barrier ();
+
+    return base + offset;
+  }
+
+  void add_delta_to_value (HBINT16 *value,
+                           const ValueBase *base,
+                           const Value *src_value,
+                           const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map) const
+  {
+    if (!value) return;
+    unsigned varidx = (base + get_device (src_value)).get_variation_index ();
+    hb_pair_t<unsigned, int> *varidx_delta;
+    if (!layout_variation_idx_delta_map->has (varidx, &varidx_delta)) return;
+
+    *value += hb_second (*varidx_delta);
+  }
+
+  bool copy_device (hb_serialize_context_t *c,
+                    const ValueBase *base,
+                    const Value *src_value,
+                    const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *layout_variation_idx_delta_map,
+                    unsigned int new_format, Flags flag) const
+  {
+    // Filter by new format.
+    if (!(new_format & flag)) return true;
+
+    Value       *dst_value = c->copy (*src_value);
+
+    if (!dst_value) return false;
+    if (*dst_value == 0) return true;
+
+    *dst_value = 0;
+    c->push ();
+    if ((base + get_device (src_value)).copy (c, layout_variation_idx_delta_map))
+    {
+      c->add_link (*dst_value, c->pop_pack ());
+      return true;
+    }
+    else
+    {
+      c->pop_discard ();
+      return false;
+    }
+  }
+
+  static inline const HBINT16& get_short (const Value* value, bool *worked=nullptr)
+  {
+    if (worked) *worked |= bool (*value);
+    return *reinterpret_cast<const HBINT16 *> (value);
+  }
+
+  public:
+
+  bool has_device () const
+  {
+    unsigned int format = *this;
+    return (format & devices) != 0;
+  }
+
+  bool sanitize_value (hb_sanitize_context_t *c, const ValueBase *base, const Value *values) const
+  {
+    TRACE_SANITIZE (this);
+
+    if (unlikely (!c->check_range (values, get_size ()))) return_trace (false);
+
+    if (c->lazy_some_gpos)
+      return_trace (true);
+
+    return_trace (!has_device () || sanitize_value_devices (c, base, values));
+  }
+
+  bool sanitize_values (hb_sanitize_context_t *c, const ValueBase *base, const Value *values, unsigned int count) const
+  {
+    TRACE_SANITIZE (this);
+    unsigned size = get_size ();
+
+    if (!c->check_range (values, count, size)) return_trace (false);
+
+    if (c->lazy_some_gpos)
+      return_trace (true);
+
+    hb_barrier ();
+    return_trace (sanitize_values_stride_unsafe (c, base, values, count, size));
+  }
+
+  /* Just sanitize referenced Device tables.  Doesn't check the values themselves. */
+  bool sanitize_values_stride_unsafe (hb_sanitize_context_t *c, const ValueBase *base, const Value *values, unsigned int count, unsigned int stride) const
+  {
+    TRACE_SANITIZE (this);
+
+    if (!has_device ()) return_trace (true);
+
+    for (unsigned int i = 0; i < count; i++) {
+      if (!sanitize_value_devices (c, base, values))
+        return_trace (false);
+      values = &StructAtOffset<const Value> (values, stride);
+    }
+
+    return_trace (true);
+  }
+
+ private:
+
+  void should_drop (Value value, Flags flag, unsigned int* format) const
+  {
+    if (value) return;
+    *format = *format & ~flag;
+  }
+
+  void update_var_flag (const Value* value, Flags flag,
+                        unsigned int* format, const ValueBase *base,
+                        const hb_hashmap_t<unsigned, hb_pair_t<unsigned, int>> *varidx_delta_map) const
+  {
+    if (*value)
+    {
+      unsigned varidx = (base + get_device (value)).get_variation_index ();
+      hb_pair_t<unsigned, int> *varidx_delta;
+      if (varidx_delta_map->has (varidx, &varidx_delta) &&
+          varidx_delta->first != HB_OT_LAYOUT_NO_VARIATIONS_INDEX)
+        return;
+    }
+    *format = *format & ~flag;
+  }
+};
+
+}
+}
+}
+
+#endif  // #ifndef OT_LAYOUT_GPOS_VALUEFORMAT_HH

3rdparty/harfbuzz/src/OT/Layout/GSUB/AlternateSet.hh

@@ -0,0 +1,139 @@
+#ifndef OT_LAYOUT_GSUB_ALTERNATESET_HH
+#define OT_LAYOUT_GSUB_ALTERNATESET_HH
+
+#include "Common.hh"
+
+namespace OT {
+namespace Layout {
+namespace GSUB_impl {
+
+template <typename Types>
+struct AlternateSet
+{
+  protected:
+  Array16Of<typename Types::HBGlyphID>
+                alternates;             /* Array of alternate GlyphIDs--in
+                                         * arbitrary order */
+  public:
+  DEFINE_SIZE_ARRAY (2, alternates);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (alternates.sanitize (c));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  { return hb_any (alternates, glyphs); }
+
+  void closure (hb_closure_context_t *c) const
+  { c->output->add_array (alternates.arrayZ, alternates.len); }
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  { c->output->add_array (alternates.arrayZ, alternates.len); }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+    unsigned int count = alternates.len;
+
+    if (unlikely (!count)) return_trace (false);
+
+    hb_mask_t glyph_mask = c->buffer->cur().mask;
+    hb_mask_t lookup_mask = c->lookup_mask;
+
+    /* Note: This breaks badly if two features enabled this lookup together. */
+    unsigned int shift = hb_ctz (lookup_mask);
+    unsigned int alt_index = ((lookup_mask & glyph_mask) >> shift);
+
+    /* If alt_index is MAX_VALUE, randomize feature if it is the rand feature. */
+    if (alt_index == HB_OT_MAP_MAX_VALUE && c->random)
+    {
+      /* Maybe we can do better than unsafe-to-break all; but since we are
+       * changing random state, it would be hard to track that.  Good 'nough. */
+      c->buffer->unsafe_to_break (0, c->buffer->len);
+      alt_index = c->random_number () % count + 1;
+    }
+
+    if (unlikely (alt_index > count || alt_index == 0)) return_trace (false);
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->sync_so_far ();
+      c->buffer->message (c->font,
+			  "replacing glyph at %u (alternate substitution)",
+			  c->buffer->idx);
+    }
+
+    c->replace_glyph (alternates[alt_index - 1]);
+
+    if (HB_BUFFER_MESSAGE_MORE && c->buffer->messaging ())
+    {
+      c->buffer->message (c->font,
+			  "replaced glyph at %u (alternate substitution)",
+			  c->buffer->idx - 1u);
+    }
+
+    return_trace (true);
+  }
+
+  unsigned
+  get_alternates (unsigned        start_offset,
+                  unsigned       *alternate_count  /* IN/OUT.  May be NULL. */,
+                  hb_codepoint_t *alternate_glyphs /* OUT.     May be NULL. */) const
+  {
+    if (alternates.len && alternate_count)
+    {
+      + alternates.as_array ().sub_array (start_offset, alternate_count)
+      | hb_sink (hb_array (alternate_glyphs, *alternate_count))
+      ;
+    }
+    return alternates.len;
+  }
+
+  void
+  collect_alternates (hb_codepoint_t gid,
+		      hb_map_t  *alternate_count /* IN/OUT */,
+		      hb_map_t  *alternate_glyphs /* IN/OUT */) const
+  {
+    + hb_enumerate (alternates)
+    | hb_map ([gid] (hb_pair_t<unsigned, hb_codepoint_t> _) { return hb_pair (gid + (_.first << 24), _.second); })
+    | hb_apply ([&] (const hb_pair_t<hb_codepoint_t, hb_codepoint_t> &p) -> void
+		{ _hb_collect_glyph_alternates_add (p.first, p.second,
+						    alternate_count, alternate_glyphs); })
+    ;
+  }
+
+  template <typename Iterator,
+            hb_requires (hb_is_source_of (Iterator, hb_codepoint_t))>
+  bool serialize (hb_serialize_context_t *c,
+                  Iterator alts)
+  {
+    TRACE_SERIALIZE (this);
+    return_trace (alternates.serialize (c, alts));
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    auto it =
+      + hb_iter (alternates)
+      | hb_filter (glyphset)
+      | hb_map (glyph_map)
+      ;
+
+    auto *out = c->serializer->start_embed (*this);
+    return_trace (out->serialize (c->serializer, it) &&
+                  out->alternates);
+  }
+};
+
+}
+}
+}
+
+
+#endif /* OT_LAYOUT_GSUB_ALTERNATESET_HH */

3rdparty/harfbuzz/src/OT/Layout/GSUB/AlternateSubst.hh

@@ -0,0 +1,62 @@
+#ifndef OT_LAYOUT_GSUB_ALTERNATESUBST_HH
+#define OT_LAYOUT_GSUB_ALTERNATESUBST_HH
+
+#include "AlternateSubstFormat1.hh"
+#include "Common.hh"
+
+namespace OT {
+namespace Layout {
+namespace GSUB_impl {
+
+struct AlternateSubst
+{
+  protected:
+  union {
+  struct { HBUINT16 v; }		format;         /* Format identifier */
+  AlternateSubstFormat1_2<SmallTypes>	format1;
+#ifndef HB_NO_BEYOND_64K
+  AlternateSubstFormat1_2<MediumTypes>	format2;
+#endif
+  } u;
+  public:
+
+  template <typename context_t, typename ...Ts>
+  typename context_t::return_t dispatch (context_t *c, Ts&&... ds) const
+  {
+    if (unlikely (!c->may_dispatch (this, &u.format.v))) return c->no_dispatch_return_value ();
+    TRACE_DISPATCH (this, u.format.v);
+    switch (u.format.v) {
+    case 1: return_trace (c->dispatch (u.format1, std::forward<Ts> (ds)...));
+#ifndef HB_NO_BEYOND_64K
+    case 2: return_trace (c->dispatch (u.format2, std::forward<Ts> (ds)...));
+#endif
+    default:return_trace (c->default_return_value ());
+    }
+  }
+
+  /* TODO This function is unused and not updated to 24bit GIDs. Should be done by using
+   * iterators. While at it perhaps using iterator of arrays of hb_codepoint_t instead. */
+  bool serialize (hb_serialize_context_t *c,
+                  hb_sorted_array_t<const HBGlyphID16> glyphs,
+                  hb_array_t<const unsigned int> alternate_len_list,
+                  hb_array_t<const HBGlyphID16> alternate_glyphs_list)
+  {
+    TRACE_SERIALIZE (this);
+    if (unlikely (!c->extend_min (u.format.v))) return_trace (false);
+    unsigned int format = 1;
+    u.format.v = format;
+    switch (u.format.v) {
+    case 1: return_trace (u.format1.serialize (c, glyphs, alternate_len_list, alternate_glyphs_list));
+    default:return_trace (false);
+    }
+  }
+
+  /* TODO subset() should choose format. */
+
+};
+
+}
+}
+}
+
+#endif  /* OT_LAYOUT_GSUB_ALTERNATESUBST_HH */

3rdparty/harfbuzz/src/OT/Layout/GSUB/AlternateSubstFormat1.hh

@@ -0,0 +1,141 @@
+#ifndef OT_LAYOUT_GSUB_ALTERNATESUBSTFORMAT1_HH
+#define OT_LAYOUT_GSUB_ALTERNATESUBSTFORMAT1_HH
+
+#include "AlternateSet.hh"
+#include "Common.hh"
+
+namespace OT {
+namespace Layout {
+namespace GSUB_impl {
+
+template <typename Types>
+struct AlternateSubstFormat1_2
+{
+  protected:
+  HBUINT16      format;                 /* Format identifier--format = 1 */
+  typename Types::template OffsetTo<Coverage>
+                coverage;               /* Offset to Coverage table--from
+                                         * beginning of Substitution table */
+  Array16Of<typename Types::template OffsetTo<AlternateSet<Types>>>
+                alternateSet;           /* Array of AlternateSet tables
+                                         * ordered by Coverage Index */
+  public:
+  DEFINE_SIZE_ARRAY (2 + 2 * Types::size, alternateSet);
+
+  bool sanitize (hb_sanitize_context_t *c) const
+  {
+    TRACE_SANITIZE (this);
+    return_trace (coverage.sanitize (c, this) && alternateSet.sanitize (c, this));
+  }
+
+  bool intersects (const hb_set_t *glyphs) const
+  { return (this+coverage).intersects (glyphs); }
+
+  bool may_have_non_1to1 () const
+  { return false; }
+
+  void closure (hb_closure_context_t *c) const
+  {
+    + hb_zip (this+coverage, alternateSet)
+    | hb_filter (c->parent_active_glyphs (), hb_first)
+    | hb_map (hb_second)
+    | hb_map (hb_add (this))
+    | hb_apply ([c] (const AlternateSet<Types> &_) { _.closure (c); })
+    ;
+  }
+
+  void closure_lookups (hb_closure_lookups_context_t *c) const {}
+
+  void collect_glyphs (hb_collect_glyphs_context_t *c) const
+  {
+    if (unlikely (!(this+coverage).collect_coverage (c->input))) return;
+    + hb_zip (this+coverage, alternateSet)
+    | hb_map (hb_second)
+    | hb_map (hb_add (this))
+    | hb_apply ([c] (const AlternateSet<Types> &_) { _.collect_glyphs (c); })
+    ;
+  }
+
+  const Coverage &get_coverage () const { return this+coverage; }
+
+  bool would_apply (hb_would_apply_context_t *c) const
+  { return c->len == 1 && (this+coverage).get_coverage (c->glyphs[0]) != NOT_COVERED; }
+
+  unsigned
+  get_glyph_alternates (hb_codepoint_t  gid,
+                        unsigned        start_offset,
+                        unsigned       *alternate_count  /* IN/OUT.  May be NULL. */,
+                        hb_codepoint_t *alternate_glyphs /* OUT.     May be NULL. */) const
+  { return (this+alternateSet[(this+coverage).get_coverage (gid)])
+           .get_alternates (start_offset, alternate_count, alternate_glyphs); }
+
+  void
+  collect_glyph_alternates (hb_map_t  *alternate_count /* IN/OUT */,
+			    hb_map_t  *alternate_glyphs /* IN/OUT */) const
+  {
+    + hb_iter (alternateSet)
+    | hb_map (hb_add (this))
+    | hb_zip (this+coverage)
+    | hb_apply ([&] (const hb_pair_t<const AlternateSet<Types> &, hb_codepoint_t> _) {
+		  _.first.collect_alternates (_.second, alternate_count, alternate_glyphs);
+		})
+    ;
+  }
+
+  bool apply (hb_ot_apply_context_t *c) const
+  {
+    TRACE_APPLY (this);
+
+    unsigned int index = (this+coverage).get_coverage (c->buffer->cur().codepoint);
+    if (index == NOT_COVERED) return_trace (false);
+
+    return_trace ((this+alternateSet[index]).apply (c));
+  }
+
+  bool serialize (hb_serialize_context_t *c,
+                  hb_sorted_array_t<const HBGlyphID16> glyphs,
+                  hb_array_t<const unsigned int> alternate_len_list,
+                  hb_array_t<const HBGlyphID16> alternate_glyphs_list)
+  {
+    TRACE_SERIALIZE (this);
+    if (unlikely (!c->extend_min (this))) return_trace (false);
+    if (unlikely (!alternateSet.serialize (c, glyphs.length))) return_trace (false);
+    for (unsigned int i = 0; i < glyphs.length; i++)
+    {
+      unsigned int alternate_len = alternate_len_list[i];
+      if (unlikely (!alternateSet[i]
+                        .serialize_serialize (c, alternate_glyphs_list.sub_array (0, alternate_len))))
+        return_trace (false);
+      alternate_glyphs_list += alternate_len;
+    }
+    return_trace (coverage.serialize_serialize (c, glyphs));
+  }
+
+  bool subset (hb_subset_context_t *c) const
+  {
+    TRACE_SUBSET (this);
+    const hb_set_t &glyphset = *c->plan->glyphset_gsub ();
+    const hb_map_t &glyph_map = *c->plan->glyph_map;
+
+    auto *out = c->serializer->start_embed (*this);
+    if (unlikely (!c->serializer->extend_min (out))) return_trace (false);
+    out->format = format;
+
+    hb_sorted_vector_t<hb_codepoint_t> new_coverage;
+    + hb_zip (this+coverage, alternateSet)
+    | hb_filter (glyphset, hb_first)
+    | hb_filter (subset_offset_array (c, out->alternateSet, this), hb_second)
+    | hb_map (hb_first)
+    | hb_map (glyph_map)
+    | hb_sink (new_coverage)
+    ;
+    out->coverage.serialize_serialize (c->serializer, new_coverage.iter ());
+    return_trace (bool (new_coverage));
+  }
+};
+
+}
+}
+}
+
+#endif  /* OT_LAYOUT_GSUB_ALTERNATESUBSTFORMAT1_HH */