Release 5.0.0-alpha.

Merge pull request #26202 from gursimarsingh:improved_tracker_samples
Improved Tracker Samples #26202 Relates to #25006 This sample has been rewritten to track a selected target in a video or camera stream. It combines VIT tracker, Nano tracker and Dasiamrpn tracker into one tracker sample ### 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
2026-07-24 12:53:04 +04:00 · 2024-12-05 11:54:05 +03:00 · 2024-12-05 11:50:03 +03:00 · 2024-12-05 11:34:49 +03:00 · 2024-12-05 09:10:41 +03:00 · 2024-12-05 09:03:51 +03:00
4737 changed files with 621636 additions and 1210146 deletions
@@ -0,0 +1,3 @@
+# These are supported funding model platforms
+
+github: opencv
@@ -34,11 +34,11 @@ This is a template helping you to create an issue which can be processed as quic
 - [ ] I report the issue, it's not a question
   <!--
   OpenCV team works with forum.opencv.org, Stack Overflow and other communities
-   to discuss problems. Tickets with question without real issue statement will be
+   to discuss problems. Tickets with questions without a real issue statement will be
   closed.
   -->
 - [ ] I checked the problem with documentation, FAQ, open issues,
-       forum.opencv.org, Stack Overflow, etc and have not found solution
+       forum.opencv.org, Stack Overflow, etc and have not found any solution
   <!--
   Places to check:
   * OpenCV documentation: https://docs.opencv.org
@@ -47,11 +47,11 @@ This is a template helping you to create an issue which can be processed as quic
   * OpenCV issue tracker: https://github.com/opencv/opencv/issues?q=is%3Aissue
   * Stack Overflow branch: https://stackoverflow.com/questions/tagged/opencv
   -->
- - [ ] I updated to latest OpenCV version and the issue is still there
+ - [ ] I updated to the latest OpenCV version and the issue is still there
   <!--
   master branch for OpenCV 4.x and 3.4 branch for OpenCV 3.x releases.
-   OpenCV team supports only latest release for each branch.
-   The ticket is closed, if the problem is not reproduced with modern version.
+   OpenCV team supports only the latest release for each branch.
+   The ticket is closed if the problem is not reproduced with the modern version.
   -->
 - [ ] There is reproducer code and related data files: videos, images, onnx, etc
   <!--
@@ -61,9 +61,9 @@ This is a template helping you to create an issue which can be processed as quic
     to reduce attachment size
   * Use PNG for images, if you report some CV related bug, but not image reader
     issue
-   * Attach the image as archive to the ticket, if you report some reader issue.
+   * Attach the image as an archive to the ticket, if you report some reader issue.
     Image hosting services compress images and it breaks the repro code.
-   * Provide ONNX file for some public model or ONNX file with with random weights,
+   * Provide ONNX file for some public model or ONNX file with random weights,
     if you report ONNX parsing or handling issue. Architecture details diagram
     from netron tool can be very useful too. See https://lutzroeder.github.io/netron/
   -->
@@ -0,0 +1,64 @@
+name: Bug Report
+description: Create a report to help us reproduce and fix the bug
+labels: ["bug"]
+
+body:
+- type: markdown
+  attributes:
+    value: >
+      #### Thank you for contributing! Before reporting a bug, please have a look at the [FAQ](https://github.com/opencv/opencv/wiki/FAQ), make sure the issue has no duplicate and hasn't been already addressed by searching through [the existing and past issues](https://github.com/opencv/opencv/issues?page=1&q=is%3Aissue+sort%3Acreated-desc).
+
+- type: textarea
+  attributes:
+    label: System Information
+    description: |
+      Please provide the following system information to help us diagnose the bug. For example:
+
+      // example for c++ user
+      OpenCV version: 4.8.0
+      Operating System / Platform: Ubuntu 20.04
+      Compiler & compiler version: GCC 9.3.0
+
+      // example for python user
+      OpenCV python version: 4.8.0.74
+      Operating System / Platform: Ubuntu 20.04
+      Python version: 3.9.6
+  validations:
+    required: true
+- type: textarea
+  attributes:
+    label: Detailed description
+    description: |
+      Please provide a clear and concise description of what the bug is and paste the error log below. It helps improving readability if the error log is wrapped in ```` ```triple quotes blocks``` ````.
+    placeholder: |
+      A clear and concise description of what the bug is.
+
+      ```
+      # error log
+      ```
+  validations:
+    required: true
+- type: textarea
+  attributes:
+    label: Steps to reproduce
+    description: |
+      Please provide a minimal example to help us reproduce the bug. Code should be wrapped with ```` ```triple quotes blocks``` ```` to improve readability. If the code is too long, please attach as a file or create and link a public gist: https://gist.github.com.
+
+      Related data files (images, onnx, etc) should be attached below as well. If the data files are too big, feel free to upload them to a online drive, share them and put the link below.
+    placeholder: |
+      ```cpp (replace cpp with python if python code)
+      # sample code to reproduce the bug
+      ```
+
+      Test data: [image](https://link/to/the/image), [model.onnx](htts://link/to/the/onnx/model)
+  validations:
+    required: true
+- type: checkboxes
+  attributes:
+    label: Issue submission checklist
+    options:
+      - label: I report the issue, it's not a question
+        required: true
+      - label: I checked the problem with documentation, FAQ, open issues, forum.opencv.org, Stack Overflow, etc and have not found any solution
+      - label: I updated to the latest OpenCV version and the issue is still there
+      - label: There is reproducer code and related data files (videos, images, onnx, etc)
@@ -0,0 +1,5 @@
+blank_issues_enabled: true
+contact_links:
+  - name: Questions
+    url: https://forum.opencv.org/
+    about: Ask questions and discuss with OpenCV community members
@@ -0,0 +1,26 @@
+name: Documentation
+description: Report an issue related to https://docs.opencv.org/
+labels: ["category: documentation"]
+
+body:
+- type: markdown
+  attributes:
+    value: >
+      #### Thank you for contributing! Before submitting a doc issue, please make sure it has no duplicate by searching through [the existing and past issues](https://github.com/opencv/opencv/issues?page=1&q=is%3Aissue+sort%3Acreated-desc)
+
+- type: textarea
+  attributes:
+    label: Describe the doc issue
+    description: >
+      Please provide a clear and concise description of what content in https://docs.opencv.org/ is an issue. Note that there are multiple active branches, such as 4.x and 5.x, so please specify the branch with the problem.
+    placeholder: |
+      A clear and concise description of what content in https://docs.opencv.org/ is an issue.
+
+      Link to the doc: https://docs.opencv.org/4.x/d3/d63/classcv_1_1Mat.html
+  validations:
+    required: true
+- type: textarea
+  attributes:
+    label: Fix suggestion
+    description: >
+      Tell us how we could improve the documentation in this regard.
@@ -0,0 +1,22 @@
+name: Feature request
+description: Submit a request for a new OpenCV feature
+labels: ["feature"]
+
+body:
+- type: markdown
+  attributes:
+    value: >
+      #### Thank you for contributing! Before submitting a feature request, please make sure the request has no duplicate by searching through [the existing and past issues](https://github.com/opencv/opencv/issues?page=1&q=is%3Aissue+sort%3Acreated-desc)
+
+- type: textarea
+  attributes:
+    label: Describe the feature and motivation
+    description: |
+      Please provide a clear and concise proposal of the feature and outline the motivation.
+  validations:
+    required: true
+- type: textarea
+  attributes:
+    label: Additional context
+    description: |
+      Add any other context, such as pseudo code, links, diagram, screenshots, to help the community better understand the feature request.
@@ -2,10 +2,10 @@

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

- [ ] I agree to contribute to the project under Apache 2 License.
- [ ] To the best of my knowledge, the proposed patch is not based on a code under GPL or other license that is incompatible with OpenCV
- [ ] The PR is proposed to proper branch
- [ ] There is reference to original bug report and related work
+- [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
+- [ ] The PR is proposed to the proper branch
+- [ ] There is a reference to the original bug report and related work
 - [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
 - [ ] The feature is well documented and sample code can be built with the project CMake
@@ -0,0 +1,67 @@
+name: PR:5.x
+
+on:
+  pull_request:
+    branches:
+      - 5.x
+
+jobs:
+  Ubuntu2004-ARM64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-ARM64.yaml@main
+
+  Ubuntu2004-ARM64-Debug:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-ARM64-Debug.yaml@main
+
+  Ubuntu2004-x64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-U20.yaml@main
+
+  Ubuntu2004-x64-OpenVINO:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-U20-OpenVINO.yaml@main
+
+  Ubuntu2204-x64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-U22.yaml@main
+
+  Ubuntu2404-x64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-U24.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
+
+  Windows10-x64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-W10.yaml@main
+
+  Windows10-x64-UWP:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-W10-UWP.yaml@main
+
+  Windows10-ARM64:
+    uses: opencv/ci-gha-workflow/.github/workflows/OCV-PR-5.x-W10-ARM64.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
@@ -2,6 +2,9 @@ name: arm64 build checks

 on: workflow_dispatch

+permissions:
+  contents: read # to fetch code (actions/checkout)
+
 jobs:
  build:

@@ -18,7 +21,6 @@ jobs:
                crossbuild-essential-arm64 \
                git \
                cmake \
-                libpython-dev:arm64 \
                libpython3-dev:arm64 \
                python-numpy \
                python3-numpy
@@ -31,10 +33,7 @@ jobs:
      run: |
        mkdir build
        cd build
-        cmake -DPYTHON2_INCLUDE_PATH=/usr/include/python2.7/ \
-              -DPYTHON2_LIBRARIES=/usr/lib/aarch64-linux-gnu/libpython2.7.so \
-              -DPYTHON2_NUMPY_INCLUDE_DIRS=/usr/lib/python2.7/dist-packages/numpy/core/include \
-              -DPYTHON3_INCLUDE_PATH=/usr/include/python3.6m/ \
+        cmake -DPYTHON3_INCLUDE_PATH=/usr/include/python3.6m/ \
              -DPYTHON3_LIBRARIES=/usr/lib/aarch64-linux-gnu/libpython3.6m.so \
              -DPYTHON3_NUMPY_INCLUDE_DIRS=/usr/lib/python3/dist-packages/numpy/core/include \
              -DCMAKE_TOOLCHAIN_FILE=../platforms/linux/aarch64-gnu.toolchain.cmake \
@@ -1,5 +1,7 @@
 name: lint_python
 on: workflow_dispatch
+permissions:
+  contents: read # to fetch code (actions/checkout)
 jobs:
  lint_python:
    runs-on: ubuntu-latest
@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 2.8.11 FATAL_ERROR)
+cmake_minimum_required(VERSION ${MIN_VER_CMAKE} FATAL_ERROR)

 project(Carotene)

@@ -27,6 +27,10 @@ if(CMAKE_COMPILER_IS_GNUCC)
    endif()
 endif()

+if(APPLE AND CV_CLANG AND WITH_NEON)
+    ocv_warnings_disable(CMAKE_CXX_FLAGS -Wno-unused-function)
+endif()
+
 add_library(carotene_objs OBJECT EXCLUDE_FROM_ALL
  ${carotene_headers}
  ${carotene_sources}
@@ -40,5 +44,9 @@ if(WITH_NEON)
    target_compile_definitions(carotene_objs PRIVATE "-DWITH_NEON")
 endif()

+ if(MINGW)
+    target_compile_definitions(carotene_objs PRIVATE "-D_USE_MATH_DEFINES=1")
+ endif()
+
 # we add dummy file to fix XCode build
 add_library(carotene STATIC ${OPENCV_3RDPARTY_EXCLUDE_FROM_ALL} "$<TARGET_OBJECTS:carotene_objs>" "${CAROTENE_SOURCE_DIR}/dummy.cpp")
@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 2.8.8 FATAL_ERROR)
+cmake_minimum_required(VERSION ${MIN_VER_CMAKE} FATAL_ERROR)

 include(CheckCCompilerFlag)
 include(CheckCXXCompilerFlag)
@@ -1286,7 +1286,6 @@ inline int TEGRA_SEPFILTERFREE(cvhalFilter2D *context)
 #undef cv_hal_sepFilterFree
 #define cv_hal_sepFilterFree TEGRA_SEPFILTERFREE

-
 struct MorphCtx
 {
    int operation;
@@ -1296,13 +1295,13 @@ struct MorphCtx
    CAROTENE_NS::BORDER_MODE border;
    uchar borderValues[4];
 };
-inline int TEGRA_MORPHINIT(cvhalFilter2D **context, int operation, int src_type, int dst_type, int, int,
+inline int TEGRA_MORPHINIT(cvhalFilter2D **context, int operation, int src_type, int dst_type, int width, int height,
                           int kernel_type, uchar *kernel_data, size_t kernel_step, int kernel_width, int kernel_height, int anchor_x, int anchor_y,
                           int borderType, const double borderValue[4], int iterations, bool allowSubmatrix, bool allowInplace)
 {
    if(!context || !kernel_data || src_type != dst_type ||
       CV_MAT_DEPTH(src_type) != CV_8U || src_type < 0 || (src_type >> CV_CN_SHIFT) > 3 ||
-
+       width < kernel_width || height < kernel_height ||
       allowSubmatrix || allowInplace || iterations != 1 ||
       !CAROTENE_NS::isSupportedConfiguration())
        return CV_HAL_ERROR_NOT_IMPLEMENTED;
@@ -1857,6 +1856,126 @@ TegraCvtColor_Invoker(bgrx2hsvf, bgrx2hsv, src_data + static_cast<size_t>(range.
 #define cv_hal_cvtTwoPlaneYUVtoBGREx TEGRA_CVT2PYUVTOBGR_EX
 #endif

+// The optimized branch was developed for old armv7 processors and leads to perf degradation on armv8
+#if defined(__ARM_ARCH) && (__ARM_ARCH == 7)
+inline CAROTENE_NS::BORDER_MODE borderCV2Carotene(int borderType)
+{
+    switch(borderType)
+    {
+    case CV_HAL_BORDER_CONSTANT:
+        return CAROTENE_NS::BORDER_MODE_CONSTANT;
+    case CV_HAL_BORDER_REPLICATE:
+        return CAROTENE_NS::BORDER_MODE_REPLICATE;
+    case CV_HAL_BORDER_REFLECT:
+        return CAROTENE_NS::BORDER_MODE_REFLECT;
+    case CV_HAL_BORDER_WRAP:
+        return CAROTENE_NS::BORDER_MODE_WRAP;
+    case CV_HAL_BORDER_REFLECT_101:
+        return CAROTENE_NS::BORDER_MODE_REFLECT101;
+    }
+
+    return CAROTENE_NS::BORDER_MODE_UNDEFINED;
+}
+
+inline int TEGRA_GaussianBlurBinomial(const uchar* src_data, size_t src_step, uchar* dst_data, size_t dst_step,
+                         int width, int height, int depth, int cn, size_t margin_left, size_t margin_top,
+                         size_t margin_right, size_t margin_bottom, size_t ksize, int border_type)
+{
+    CAROTENE_NS::Size2D sz(width, height);
+    CAROTENE_NS::BORDER_MODE border = borderCV2Carotene(border_type);
+    CAROTENE_NS::Margin mg(margin_left, margin_right, margin_top, margin_bottom);
+
+    if (ksize == 3)
+    {
+        if ((depth != CV_8U) || (cn != 1))
+            return CV_HAL_ERROR_NOT_IMPLEMENTED;
+
+        if (CAROTENE_NS::isGaussianBlur3x3MarginSupported(sz, border, mg))
+        {
+            CAROTENE_NS::gaussianBlur3x3Margin(sz, src_data, src_step, dst_data, dst_step,
+                                  border, 0, mg);
+            return CV_HAL_ERROR_OK;
+        }
+    }
+    else if (ksize == 5)
+    {
+        if (!CAROTENE_NS::isGaussianBlur5x5Supported(sz, cn, border))
+            return CV_HAL_ERROR_NOT_IMPLEMENTED;
+
+        if (depth == CV_8U)
+        {
+            CAROTENE_NS::gaussianBlur5x5(sz, cn, (uint8_t*)src_data, src_step,
+                                         (uint8_t*)dst_data, dst_step, border, 0, mg);
+            return CV_HAL_ERROR_OK;
+        }
+        else if (depth == CV_16U)
+        {
+            CAROTENE_NS::gaussianBlur5x5(sz, cn, (uint16_t*)src_data, src_step,
+                                         (uint16_t*)dst_data, dst_step, border, 0, mg);
+            return CV_HAL_ERROR_OK;
+        }
+        else if (depth == CV_16S)
+        {
+            CAROTENE_NS::gaussianBlur5x5(sz, cn, (int16_t*)src_data, src_step,
+                                         (int16_t*)dst_data, dst_step, border, 0, mg);
+           return CV_HAL_ERROR_OK;
+        }
+    }
+
+    return CV_HAL_ERROR_NOT_IMPLEMENTED;
+}
+
+#undef cv_hal_gaussianBlurBinomial
+#define cv_hal_gaussianBlurBinomial TEGRA_GaussianBlurBinomial
+
+#endif // __ARM_ARCH=7
+
 #endif // OPENCV_IMGPROC_HAL_INTERFACE_H

+// The optimized branch was developed for old armv7 processors
+#if defined(__ARM_ARCH) && (__ARM_ARCH == 7)
+inline int TEGRA_LKOpticalFlowLevel(const uchar *prev_data, size_t prev_data_step,
+                       const short* prev_deriv_data, size_t prev_deriv_step,
+                       const uchar* next_data, size_t next_step,
+                       int width, int height, int cn,
+                       const float *prev_points, float *next_points, size_t point_count,
+                       uchar *status, float *err,
+                       const int win_width, const int win_height,
+                       int termination_count, double termination_epsilon,
+                       bool get_min_eigen_vals,
+                       float min_eigen_vals_threshold)
+{
+    if (!CAROTENE_NS::isSupportedConfiguration())
+        return CV_HAL_ERROR_NOT_IMPLEMENTED;
+
+    CAROTENE_NS::pyrLKOptFlowLevel(CAROTENE_NS::Size2D(width, height), cn,
+        prev_data, prev_data_step, prev_deriv_data, prev_deriv_step,
+        next_data, next_step,
+        point_count, prev_points, next_points,
+        status, err, CAROTENE_NS::Size2D(win_width, win_height),
+        termination_count, termination_epsilon,
+        get_min_eigen_vals, min_eigen_vals_threshold);
+    return CV_HAL_ERROR_OK;
+}
+
+#undef cv_hal_LKOpticalFlowLevel
+#define cv_hal_LKOpticalFlowLevel TEGRA_LKOpticalFlowLevel
+#endif // __ARM_ARCH=7
+
+#if 0 // OpenCV provides fater parallel implementation
+inline int TEGRA_ScharrDeriv(const uchar* src_data, size_t src_step,
+                      short* dst_data, size_t dst_step,
+                      int width, int height, int cn)
+{
+    if (!CAROTENE_NS::isSupportedConfiguration())
+        return CV_HAL_ERROR_NOT_IMPLEMENTED;
+
+    CAROTENE_NS::ScharrDeriv(CAROTENE_NS::Size2D(width, height), cn, src_data, src_step, dst_data, dst_step);
+    return CV_HAL_ERROR_OK;
+}
+
+#undef cv_hal_ScharrDeriv
+#define cv_hal_ScharrDeriv TEGRA_ScharrDeriv
+#endif
+
 #endif
@@ -2485,7 +2485,7 @@ namespace CAROTENE_NS {
                           u8 *status, f32 *err,
                           const Size2D &winSize,
                           u32 terminationCount, f64 terminationEpsilon,
-                           u32 level, u32 maxLevel, bool useInitialFlow, bool getMinEigenVals,
+                           bool getMinEigenVals,
                           f32 minEigThreshold);
 }

@@ -39,6 +39,7 @@

 #include "common.hpp"
 #include "vtransform.hpp"
+#include "vround_helper.hpp"

 namespace CAROTENE_NS {

@@ -106,31 +107,31 @@ template <> struct wAdd<s32>
    {
        valpha = vdupq_n_f32(_alpha);
        vbeta = vdupq_n_f32(_beta);
-        vgamma = vdupq_n_f32(_gamma + 0.5);
+        vgamma = vdupq_n_f32(_gamma);
    }

-    void operator() (const typename VecTraits<s32>::vec128 & v_src0,
-                     const typename VecTraits<s32>::vec128 & v_src1,
-                     typename VecTraits<s32>::vec128 & v_dst) const
+    void operator() (const VecTraits<s32>::vec128 & v_src0,
+                     const VecTraits<s32>::vec128 & v_src1,
+                     VecTraits<s32>::vec128 & v_dst) const
    {
        float32x4_t vs1 = vcvtq_f32_s32(v_src0);
        float32x4_t vs2 = vcvtq_f32_s32(v_src1);

        vs1 = vmlaq_f32(vgamma, vs1, valpha);
        vs1 = vmlaq_f32(vs1, vs2, vbeta);
-        v_dst = vcvtq_s32_f32(vs1);
+        v_dst = vroundq_s32_f32(vs1);
    }

-    void operator() (const typename VecTraits<s32>::vec64 & v_src0,
-                     const typename VecTraits<s32>::vec64 & v_src1,
-                     typename VecTraits<s32>::vec64 & v_dst) const
+    void operator() (const VecTraits<s32>::vec64 & v_src0,
+                     const VecTraits<s32>::vec64 & v_src1,
+                     VecTraits<s32>::vec64 & v_dst) const
    {
        float32x2_t vs1 = vcvt_f32_s32(v_src0);
        float32x2_t vs2 = vcvt_f32_s32(v_src1);

        vs1 = vmla_f32(vget_low(vgamma), vs1, vget_low(valpha));
        vs1 = vmla_f32(vs1, vs2, vget_low(vbeta));
-        v_dst = vcvt_s32_f32(vs1);
+        v_dst = vround_s32_f32(vs1);
    }

    void operator() (const s32 * src0, const s32 * src1, s32 * dst) const
@@ -150,31 +151,31 @@ template <> struct wAdd<u32>
    {
        valpha = vdupq_n_f32(_alpha);
        vbeta = vdupq_n_f32(_beta);
-        vgamma = vdupq_n_f32(_gamma + 0.5);
+        vgamma = vdupq_n_f32(_gamma);
    }

-    void operator() (const typename VecTraits<u32>::vec128 & v_src0,
-                     const typename VecTraits<u32>::vec128 & v_src1,
-                     typename VecTraits<u32>::vec128 & v_dst) const
+    void operator() (const VecTraits<u32>::vec128 & v_src0,
+                     const VecTraits<u32>::vec128 & v_src1,
+                     VecTraits<u32>::vec128 & v_dst) const
    {
        float32x4_t vs1 = vcvtq_f32_u32(v_src0);
        float32x4_t vs2 = vcvtq_f32_u32(v_src1);

        vs1 = vmlaq_f32(vgamma, vs1, valpha);
        vs1 = vmlaq_f32(vs1, vs2, vbeta);
-        v_dst = vcvtq_u32_f32(vs1);
+        v_dst = vroundq_u32_f32(vs1);
    }

-    void operator() (const typename VecTraits<u32>::vec64 & v_src0,
-                     const typename VecTraits<u32>::vec64 & v_src1,
-                     typename VecTraits<u32>::vec64 & v_dst) const
+    void operator() (const VecTraits<u32>::vec64 & v_src0,
+                     const VecTraits<u32>::vec64 & v_src1,
+                     VecTraits<u32>::vec64 & v_dst) const
    {
        float32x2_t vs1 = vcvt_f32_u32(v_src0);
        float32x2_t vs2 = vcvt_f32_u32(v_src1);

        vs1 = vmla_f32(vget_low(vgamma), vs1, vget_low(valpha));
        vs1 = vmla_f32(vs1, vs2, vget_low(vbeta));
-        v_dst = vcvt_u32_f32(vs1);
+        v_dst = vround_u32_f32(vs1);
    }

    void operator() (const u32 * src0, const u32 * src1, u32 * dst) const
@@ -197,17 +198,17 @@ template <> struct wAdd<f32>
        vgamma = vdupq_n_f32(_gamma + 0.5);
    }

-    void operator() (const typename VecTraits<f32>::vec128 & v_src0,
-                     const typename VecTraits<f32>::vec128 & v_src1,
-                     typename VecTraits<f32>::vec128 & v_dst) const
+    void operator() (const VecTraits<f32>::vec128 & v_src0,
+                     const VecTraits<f32>::vec128 & v_src1,
+                     VecTraits<f32>::vec128 & v_dst) const
    {
        float32x4_t vs1 = vmlaq_f32(vgamma, v_src0, valpha);
        v_dst = vmlaq_f32(vs1, v_src1, vbeta);
    }

-    void operator() (const typename VecTraits<f32>::vec64 & v_src0,
-                     const typename VecTraits<f32>::vec64 & v_src1,
-                     typename VecTraits<f32>::vec64 & v_dst) const
+    void operator() (const VecTraits<f32>::vec64 & v_src0,
+                     const VecTraits<f32>::vec64 & v_src1,
+                     VecTraits<f32>::vec64 & v_dst) const
    {
        float32x2_t vs1 = vmla_f32(vget_low(vgamma), v_src0, vget_low(valpha));
        v_dst = vmla_f32(vs1, v_src1, vget_low(vbeta));
@@ -41,6 +41,7 @@

 #include "common.hpp"
 #include "saturate_cast.hpp"
+#include "vround_helper.hpp"

 namespace CAROTENE_NS {

@@ -198,7 +199,6 @@ void blur3x3(const Size2D &size, s32 cn,
 //#define FLOAT_VARIANT_1_9
 #ifdef FLOAT_VARIANT_1_9
    float32x4_t v1_9 = vdupq_n_f32 (1.0/9.0);
-    float32x4_t v0_5 = vdupq_n_f32 (.5);
 #else
    const int16x8_t vScale = vmovq_n_s16(3640);
 #endif
@@ -283,8 +283,8 @@ void blur3x3(const Size2D &size, s32 cn,
                uint32x4_t tres2 = vmovl_u16(vget_high_u16(t0));
                float32x4_t vf1 = vmulq_f32(v1_9, vcvtq_f32_u32(tres1));
                float32x4_t vf2 = vmulq_f32(v1_9, vcvtq_f32_u32(tres2));
-                tres1 = vcvtq_u32_f32(vaddq_f32(vf1, v0_5));
-                tres2 = vcvtq_u32_f32(vaddq_f32(vf2, v0_5));
+                tres1 = internal::vroundq_u32_f32(vf1);
+                tres2 = internal::vroundq_u32_f32(vf2);
                t0 = vcombine_u16(vmovn_u32(tres1),vmovn_u32(tres2));
                vst1_u8(drow + x - 8, vmovn_u16(t0));
 #else
@@ -391,9 +391,9 @@ void blur3x3(const Size2D &size, s32 cn,
                        }
                        else if (borderType == BORDER_MODE_REFLECT101)
                        {
-                            tcurr = vsetq_lane_u16(vgetq_lane_u16(tcurr, 3),tcurr, 5);
                            tcurr = vsetq_lane_u16(vgetq_lane_u16(tcurr, 4),tcurr, 6);
                            tcurr = vsetq_lane_u16(vgetq_lane_u16(tcurr, 5),tcurr, 7);
+                            tcurr = vsetq_lane_u16(vgetq_lane_u16(tcurr, 3),tcurr, 5);
                        }
                        else
                        {
@@ -445,8 +445,8 @@ void blur3x3(const Size2D &size, s32 cn,
                uint32x4_t tres2 = vmovl_u16(vget_high_u16(t0));
                float32x4_t vf1 = vmulq_f32(v1_9, vcvtq_f32_u32(tres1));
                float32x4_t vf2 = vmulq_f32(v1_9, vcvtq_f32_u32(tres2));
-                tres1 = vcvtq_u32_f32(vaddq_f32(vf1, v0_5));
-                tres2 = vcvtq_u32_f32(vaddq_f32(vf2, v0_5));
+                tres1 = internal::vroundq_u32_f32(vf1);
+                tres2 = internal::vroundq_u32_f32(vf2);
                t0 = vcombine_u16(vmovn_u32(tres1),vmovn_u32(tres2));
                vst1_u8(drow + x - 8, vmovn_u16(t0));
 #else
@@ -508,7 +508,6 @@ void blur5x5(const Size2D &size, s32 cn,
 #define FLOAT_VARIANT_1_25
 #ifdef FLOAT_VARIANT_1_25
    float32x4_t v1_25 = vdupq_n_f32 (1.0f/25.0f);
-    float32x4_t v0_5 = vdupq_n_f32 (.5f);
 #else
    const int16x8_t vScale = vmovq_n_s16(1310);
 #endif
@@ -752,8 +751,8 @@ void blur5x5(const Size2D &size, s32 cn,
            uint32x4_t tres2 = vmovl_u16(vget_high_u16(t0));
            float32x4_t vf1 = vmulq_f32(v1_25, vcvtq_f32_u32(tres1));
            float32x4_t vf2 = vmulq_f32(v1_25, vcvtq_f32_u32(tres2));
-            tres1 = vcvtq_u32_f32(vaddq_f32(vf1, v0_5));
-            tres2 = vcvtq_u32_f32(vaddq_f32(vf2, v0_5));
+            tres1 = internal::vroundq_u32_f32(vf1);
+            tres2 = internal::vroundq_u32_f32(vf2);
            t0 = vcombine_u16(vmovn_u32(tres1),vmovn_u32(tres2));
            vst1_u8(drow + x - 8, vmovn_u16(t0));
 #else
@@ -40,6 +40,7 @@
 #include "common.hpp"

 #include "saturate_cast.hpp"
+#include "vround_helper.hpp"

 namespace CAROTENE_NS {

@@ -1166,17 +1167,10 @@ inline uint8x8x3_t convertToHSV(const uint8x8_t vR, const uint8x8_t vG, const ui
    vSt3 = vmulq_f32(vHF1, vDivTab);
    vSt4 = vmulq_f32(vHF2, vDivTab);

-    float32x4_t bias = vdupq_n_f32(0.5f);
-
-    vSt1 = vaddq_f32(vSt1, bias);
-    vSt2 = vaddq_f32(vSt2, bias);
-    vSt3 = vaddq_f32(vSt3, bias);
-    vSt4 = vaddq_f32(vSt4, bias);
-
-    uint32x4_t vRes1 = vcvtq_u32_f32(vSt1);
-    uint32x4_t vRes2 = vcvtq_u32_f32(vSt2);
-    uint32x4_t vRes3 = vcvtq_u32_f32(vSt3);
-    uint32x4_t vRes4 = vcvtq_u32_f32(vSt4);
+    uint32x4_t vRes1 = internal::vroundq_u32_f32(vSt1);
+    uint32x4_t vRes2 = internal::vroundq_u32_f32(vSt2);
+    uint32x4_t vRes3 = internal::vroundq_u32_f32(vSt3);
+    uint32x4_t vRes4 = internal::vroundq_u32_f32(vSt4);

    int32x4_t vH_L = vmovl_s16(vget_low_s16(vDiff4));
    int32x4_t vH_H = vmovl_s16(vget_high_s16(vDiff4));
@@ -38,6 +38,7 @@
 */

 #include "common.hpp"
+#include "vround_helper.hpp"

 namespace CAROTENE_NS {

@@ -185,7 +186,7 @@ CVTS_FUNC1(u8, 16,
 #else
 CVTS_FUNC1(u8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -209,10 +210,10 @@ CVTS_FUNC1(u8, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        int32x4_t vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        int32x4_t vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        int32x4_t vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        int32x4_t vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        uint16x8_t vRes1_u16 = vcombine_u16(vqmovun_s32(vline1_s32), vqmovun_s32(vline2_s32));
        uint16x8_t vRes2_u16 = vcombine_u16(vqmovun_s32(vline3_s32), vqmovun_s32(vline4_s32));
        vst1q_u8(_dst + i, vcombine_u8(vqmovn_u16(vRes1_u16), vqmovn_u16(vRes2_u16)));
@@ -270,7 +271,7 @@ CVTS_FUNC(u8, s8, 16,
 #else
 CVTS_FUNC(u8, s8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -294,10 +295,10 @@ CVTS_FUNC(u8, s8, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        int32x4_t vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        int32x4_t vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        int32x4_t vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        int32x4_t vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        int16x8_t vRes1_u16 = vcombine_s16(vqmovn_s32(vline1_s32), vqmovn_s32(vline2_s32));
        int16x8_t vRes2_u16 = vcombine_s16(vqmovn_s32(vline3_s32), vqmovn_s32(vline4_s32));
        vst1q_s8(_dst + i, vcombine_s8(vqmovn_s16(vRes1_u16), vqmovn_s16(vRes2_u16)));
@@ -355,7 +356,7 @@ CVTS_FUNC(u8, u16, 16,
 #else
 CVTS_FUNC(u8, u16, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -379,10 +380,10 @@ CVTS_FUNC(u8, u16, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        int32x4_t vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        int32x4_t vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        int32x4_t vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        int32x4_t vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        vst1q_u16(_dst + i + 0, vcombine_u16(vqmovun_s32(vline1_s32), vqmovun_s32(vline2_s32)));
        vst1q_u16(_dst + i + 8, vcombine_u16(vqmovun_s32(vline3_s32), vqmovun_s32(vline4_s32)));
    }
@@ -439,7 +440,7 @@ CVTS_FUNC(u8, s16, 16,
 #else
 CVTS_FUNC(u8, s16, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -463,10 +464,10 @@ CVTS_FUNC(u8, s16, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        int32x4_t vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        int32x4_t vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        int32x4_t vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        int32x4_t vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        vst1q_s16(_dst + i + 0, vcombine_s16(vqmovn_s32(vline1_s32), vqmovn_s32(vline2_s32)));
        vst1q_s16(_dst + i + 8, vcombine_s16(vqmovn_s32(vline3_s32), vqmovn_s32(vline4_s32)));
    }
@@ -526,7 +527,7 @@ CVTS_FUNC(u8, s32, 16,
 #else
 CVTS_FUNC(u8, s32, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -550,10 +551,10 @@ CVTS_FUNC(u8, s32, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        int32x4_t vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        int32x4_t vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        int32x4_t vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        int32x4_t vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        vst1q_s32(_dst + i + 0,  vline1_s32);
        vst1q_s32(_dst + i + 4,  vline2_s32);
        vst1q_s32(_dst + i + 8,  vline3_s32);
@@ -693,7 +694,7 @@ CVTS_FUNC(s8, u8, 16,
 #else
 CVTS_FUNC(s8, u8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -717,10 +718,10 @@ CVTS_FUNC(s8, u8, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        uint16x8_t vRes1_u16 = vcombine_u16(vqmovun_s32(vline1_s32), vqmovun_s32(vline2_s32));
        uint16x8_t vRes2_u16 = vcombine_u16(vqmovun_s32(vline3_s32), vqmovun_s32(vline4_s32));
        vst1q_u8(_dst + i, vcombine_u8(vqmovn_u16(vRes1_u16), vqmovn_u16(vRes2_u16)));
@@ -778,7 +779,7 @@ CVTS_FUNC1(s8, 16,
 #else
 CVTS_FUNC1(s8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -802,10 +803,10 @@ CVTS_FUNC1(s8, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        int16x8_t vRes1_s16 = vcombine_s16(vqmovn_s32(vline1_s32), vqmovn_s32(vline2_s32));
        int16x8_t vRes2_s16 = vcombine_s16(vqmovn_s32(vline3_s32), vqmovn_s32(vline4_s32));
        vst1q_s8(_dst + i, vcombine_s8(vqmovn_s16(vRes1_s16), vqmovn_s16(vRes2_s16)));
@@ -863,7 +864,7 @@ CVTS_FUNC(s8, u16, 16,
 #else
 CVTS_FUNC(s8, u16, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -887,10 +888,10 @@ CVTS_FUNC(s8, u16, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        uint16x8_t vRes1_u16 = vcombine_u16(vqmovun_s32(vline1_s32), vqmovun_s32(vline2_s32));
        uint16x8_t vRes2_u16 = vcombine_u16(vqmovun_s32(vline3_s32), vqmovun_s32(vline4_s32));
        vst1q_u16(_dst + i + 0, vRes1_u16);
@@ -949,7 +950,7 @@ CVTS_FUNC(s8, s16, 16,
 #else
 CVTS_FUNC(s8, s16, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -973,10 +974,10 @@ CVTS_FUNC(s8, s16, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        int16x8_t vRes1_s16 = vcombine_s16(vqmovn_s32(vline1_s32), vqmovn_s32(vline2_s32));
        int16x8_t vRes2_s16 = vcombine_s16(vqmovn_s32(vline3_s32), vqmovn_s32(vline4_s32));
        vst1q_s16(_dst + i + 0, vRes1_s16);
@@ -1038,7 +1039,7 @@ CVTS_FUNC(s8, s32, 16,
 #else
 CVTS_FUNC(s8, s32, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 16)
    {
@@ -1062,10 +1063,10 @@ CVTS_FUNC(s8, s32, 16,
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
        vline3_f32 = vaddq_f32(vline3_f32, vshift);
        vline4_f32 = vaddq_f32(vline4_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
-        vline3_s32 = vcvtq_s32_f32(vline3_f32);
-        vline4_s32 = vcvtq_s32_f32(vline4_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
+        vline3_s32 = internal::vroundq_s32_f32(vline3_f32);
+        vline4_s32 = internal::vroundq_s32_f32(vline4_f32);
        vst1q_s32(_dst + i + 0,  vline1_s32);
        vst1q_s32(_dst + i + 4,  vline2_s32);
        vst1q_s32(_dst + i + 8,  vline3_s32);
@@ -1190,7 +1191,7 @@ CVTS_FUNC(u16, u8, 16,
 #else
 CVTS_FUNC(u16, u8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1204,8 +1205,8 @@ CVTS_FUNC(u16, u8, 16,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        uint8x8_t vRes = vqmovun_s16(vcombine_s16(vRes1, vRes2));
@@ -1249,7 +1250,7 @@ CVTS_FUNC(u16, s8, 16,
 #else
 CVTS_FUNC(u16, s8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1263,8 +1264,8 @@ CVTS_FUNC(u16, s8, 16,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        int8x8_t vRes = vqmovn_s16(vcombine_s16(vRes1, vRes2));
@@ -1307,7 +1308,7 @@ CVTS_FUNC1(u16, 16,
 #else
 CVTS_FUNC1(u16, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1321,8 +1322,8 @@ CVTS_FUNC1(u16, 16,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        uint16x4_t vRes1 = vqmovun_s32(vline1_s32);
        uint16x4_t vRes2 = vqmovun_s32(vline2_s32);
        vst1q_u16(_dst + i, vcombine_u16(vRes1, vRes2));
@@ -1364,7 +1365,7 @@ CVTS_FUNC(u16, s16, 8,
 #else
 CVTS_FUNC(u16, s16, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1378,8 +1379,8 @@ CVTS_FUNC(u16, s16, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        vst1q_s16(_dst + i, vcombine_s16(vRes1, vRes2));
@@ -1421,7 +1422,7 @@ CVTS_FUNC(u16, s32, 8,
 #else
 CVTS_FUNC(u16, s32, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1435,8 +1436,8 @@ CVTS_FUNC(u16, s32, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        vst1q_s32(_dst + i + 0, vline1_s32);
        vst1q_s32(_dst + i + 4, vline2_s32);
    }
@@ -1530,7 +1531,7 @@ CVTS_FUNC(s16, u8, 16,
 #else
 CVTS_FUNC(s16, u8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1544,8 +1545,8 @@ CVTS_FUNC(s16, u8, 16,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        uint8x8_t vRes = vqmovun_s16(vcombine_s16(vRes1, vRes2));
@@ -1589,7 +1590,7 @@ CVTS_FUNC(s16, s8, 16,
 #else
 CVTS_FUNC(s16, s8, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1603,8 +1604,8 @@ CVTS_FUNC(s16, s8, 16,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        int8x8_t vRes = vqmovn_s16(vcombine_s16(vRes1, vRes2));
@@ -1647,7 +1648,7 @@ CVTS_FUNC(s16, u16, 8,
 #else
 CVTS_FUNC(s16, u16, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1661,8 +1662,8 @@ CVTS_FUNC(s16, u16, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        uint16x4_t vRes1 = vqmovun_s32(vline1_s32);
        uint16x4_t vRes2 = vqmovun_s32(vline2_s32);
        vst1q_u16(_dst + i, vcombine_u16(vRes1, vRes2));
@@ -1704,7 +1705,7 @@ CVTS_FUNC1(s16, 16,
 #else
 CVTS_FUNC1(s16, 16,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1718,8 +1719,8 @@ CVTS_FUNC1(s16, 16,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        vst1q_s16(_dst + i, vcombine_s16(vRes1, vRes2));
@@ -1761,7 +1762,7 @@ CVTS_FUNC(s16, s32, 8,
 #else
 CVTS_FUNC(s16, s32, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1775,8 +1776,8 @@ CVTS_FUNC(s16, s32, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        vst1q_s32(_dst + i + 0, vline1_s32);
        vst1q_s32(_dst + i + 4, vline2_s32);
    }
@@ -1870,7 +1871,7 @@ CVTS_FUNC(s32, u8, 8,
 #else
 CVTS_FUNC(s32, u8, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1883,8 +1884,8 @@ CVTS_FUNC(s32, u8, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        uint16x4_t vRes1 = vqmovun_s32(vline1_s32);
        uint16x4_t vRes2 = vqmovun_s32(vline2_s32);
        uint8x8_t vRes = vqmovn_u16(vcombine_u16(vRes1, vRes2));
@@ -1928,7 +1929,7 @@ CVTS_FUNC(s32, s8, 8,
 #else
 CVTS_FUNC(s32, s8, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1941,8 +1942,8 @@ CVTS_FUNC(s32, s8, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        int8x8_t vRes = vqmovn_s16(vcombine_s16(vRes1, vRes2));
@@ -1985,7 +1986,7 @@ CVTS_FUNC(s32, u16, 8,
 #else
 CVTS_FUNC(s32, u16, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -1998,8 +1999,8 @@ CVTS_FUNC(s32, u16, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        uint16x4_t vRes1 = vqmovun_s32(vline1_s32);
        uint16x4_t vRes2 = vqmovun_s32(vline2_s32);
        vst1q_u16(_dst + i, vcombine_u16(vRes1, vRes2));
@@ -2041,7 +2042,7 @@ CVTS_FUNC(s32, s16, 8,
 #else
 CVTS_FUNC(s32, s16, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -2054,8 +2055,8 @@ CVTS_FUNC(s32, s16, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        vst1q_s16(_dst + i, vcombine_s16(vRes1, vRes2));
@@ -2097,7 +2098,7 @@ CVTS_FUNC1(s32, 8,
 #else
 CVTS_FUNC1(s32, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -2110,8 +2111,8 @@ CVTS_FUNC1(s32, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        vst1q_s32(_dst + i + 0, vline1_s32);
        vst1q_s32(_dst + i + 4, vline2_s32);
    }
@@ -2272,7 +2273,7 @@ CVTS_FUNC(f32, s8, 8,
 #else
 CVTS_FUNC(f32, s8, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -2283,8 +2284,8 @@ CVTS_FUNC(f32, s8, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        int8x8_t vRes = vqmovn_s16(vcombine_s16(vRes1, vRes2));
@@ -2325,7 +2326,7 @@ CVTS_FUNC(f32, u16, 8,
 #else
 CVTS_FUNC(f32, u16, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -2336,8 +2337,8 @@ CVTS_FUNC(f32, u16, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        uint32x4_t vline1_u32 = vcvtq_u32_f32(vline1_f32);
-        uint32x4_t vline2_u32 = vcvtq_u32_f32(vline2_f32);
+        uint32x4_t vline1_u32 = internal::vroundq_u32_f32(vline1_f32);
+        uint32x4_t vline2_u32 = internal::vroundq_u32_f32(vline2_f32);
        uint16x4_t vRes1 = vqmovn_u32(vline1_u32);
        uint16x4_t vRes2 = vqmovn_u32(vline2_u32);
        vst1q_u16(_dst + i, vcombine_u16(vRes1, vRes2));
@@ -2377,7 +2378,7 @@ CVTS_FUNC(f32, s16, 8,
 #else
 CVTS_FUNC(f32, s16, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -2388,8 +2389,8 @@ CVTS_FUNC(f32, s16, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        int16x4_t vRes1 = vqmovn_s32(vline1_s32);
        int16x4_t vRes2 = vqmovn_s32(vline2_s32);
        vst1q_s16(_dst + i, vcombine_s16(vRes1, vRes2));
@@ -2429,7 +2430,7 @@ CVTS_FUNC(f32, s32, 8,
 #else
 CVTS_FUNC(f32, s32, 8,
    float32x4_t vscale = vdupq_n_f32((f32)alpha);
-    float32x4_t vshift = vdupq_n_f32((f32)beta + 0.5f);,
+    float32x4_t vshift = vdupq_n_f32((f32)beta);,
 {
    for (size_t i = 0; i < w; i += 8)
    {
@@ -2440,8 +2441,8 @@ CVTS_FUNC(f32, s32, 8,
        vline2_f32 = vmulq_f32(vline2_f32, vscale);
        vline1_f32 = vaddq_f32(vline1_f32, vshift);
        vline2_f32 = vaddq_f32(vline2_f32, vshift);
-        int32x4_t vline1_s32 = vcvtq_s32_f32(vline1_f32);
-        int32x4_t vline2_s32 = vcvtq_s32_f32(vline2_f32);
+        int32x4_t vline1_s32 = internal::vroundq_s32_f32(vline1_f32);
+        int32x4_t vline2_s32 = internal::vroundq_s32_f32(vline2_f32);
        vst1q_s32(_dst + i + 0, vline1_s32);
        vst1q_s32(_dst + i + 4, vline2_s32);
    }
@@ -39,6 +39,7 @@

 #include "common.hpp"
 #include "vtransform.hpp"
+#include "vround_helper.hpp"

 #include <cstring>
 #include <cfloat>
@@ -51,13 +52,6 @@ namespace {

 #ifdef CAROTENE_NEON

-inline float32x4_t vroundq(const float32x4_t& v)
-{
-    const int32x4_t signMask = vdupq_n_s32(1 << 31), half = vreinterpretq_s32_f32(vdupq_n_f32(0.5f));
-    float32x4_t v_addition = vreinterpretq_f32_s32(vorrq_s32(half, vandq_s32(signMask, vreinterpretq_s32_f32(v))));
-    return vaddq_f32(v, v_addition);
-}
-
 template <typename T>
 inline T divSaturateQ(const T &v1, const T &v2, const float scale)
 {
@@ -69,17 +63,10 @@ inline T divSaturateQ(const T &v1, const T &v2, const float scale)
 }
 template <>
 inline int32x4_t divSaturateQ<int32x4_t>(const int32x4_t &v1, const int32x4_t &v2, const float scale)
-{ return vcvtq_s32_f32(vroundq(vmulq_f32(vmulq_n_f32(vcvtq_f32_s32(v1), scale), internal::vrecpq_f32(vcvtq_f32_s32(v2))))); }
+{ return internal::vroundq_s32_f32(vmulq_f32(vmulq_n_f32(vcvtq_f32_s32(v1), scale), internal::vrecpq_f32(vcvtq_f32_s32(v2)))); }
 template <>
 inline uint32x4_t divSaturateQ<uint32x4_t>(const uint32x4_t &v1, const uint32x4_t &v2, const float scale)
-{ return vcvtq_u32_f32(vroundq(vmulq_f32(vmulq_n_f32(vcvtq_f32_u32(v1), scale), internal::vrecpq_f32(vcvtq_f32_u32(v2))))); }
-
-inline float32x2_t vround(const float32x2_t& v)
-{
-    const int32x2_t signMask = vdup_n_s32(1 << 31), half = vreinterpret_s32_f32(vdup_n_f32(0.5f));
-    float32x2_t v_addition = vreinterpret_f32_s32(vorr_s32(half, vand_s32(signMask, vreinterpret_s32_f32(v))));
-    return vadd_f32(v, v_addition);
-}
+{ return internal::vroundq_u32_f32(vmulq_f32(vmulq_n_f32(vcvtq_f32_u32(v1), scale), internal::vrecpq_f32(vcvtq_f32_u32(v2)))); }

 template <typename T>
 inline T divSaturate(const T &v1, const T &v2, const float scale)
@@ -88,10 +75,10 @@ inline T divSaturate(const T &v1, const T &v2, const float scale)
 }
 template <>
 inline int32x2_t divSaturate<int32x2_t>(const int32x2_t &v1, const int32x2_t &v2, const float scale)
-{ return vcvt_s32_f32(vround(vmul_f32(vmul_n_f32(vcvt_f32_s32(v1), scale), internal::vrecp_f32(vcvt_f32_s32(v2))))); }
+{ return internal::vround_s32_f32(vmul_f32(vmul_n_f32(vcvt_f32_s32(v1), scale), internal::vrecp_f32(vcvt_f32_s32(v2)))); }
 template <>
 inline uint32x2_t divSaturate<uint32x2_t>(const uint32x2_t &v1, const uint32x2_t &v2, const float scale)
-{ return vcvt_u32_f32(vround(vmul_f32(vmul_n_f32(vcvt_f32_u32(v1), scale), internal::vrecp_f32(vcvt_f32_u32(v2))))); }
+{ return internal::vround_u32_f32(vmul_f32(vmul_n_f32(vcvt_f32_u32(v1), scale), internal::vrecp_f32(vcvt_f32_u32(v2)))); }


 template <typename T>
@@ -157,8 +144,8 @@ void div(const Size2D &size,

    if (scale == 0.0f ||
        (std::numeric_limits<T>::is_integer &&
-         (scale * std::numeric_limits<T>::max()) <  1.0f &&
-         (scale * std::numeric_limits<T>::max()) > -1.0f))
+         (scale * static_cast<float>(std::numeric_limits<T>::max())) <  1.0f &&
+         (scale * static_cast<float>(std::numeric_limits<T>::max())) > -1.0f))
    {
        for (size_t y = 0; y < size.height; ++y)
        {
@@ -58,7 +58,7 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,
                       u8 *status, f32 *err,
                       const Size2D &winSize,
                       u32 terminationCount, f64 terminationEpsilon,
-                       u32 level, u32 maxLevel, bool useInitialFlow, bool getMinEigenVals,
+                       bool getMinEigenVals,
                       f32 minEigThreshold)
 {
    internal::assertSupportedConfiguration();
@@ -74,32 +74,11 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,

    for( u32 ptidx = 0; ptidx < ptCount; ptidx++ )
    {
-        f32 levscale = (1./(1 << level));
        u32 ptref = ptidx << 1;
-        f32 prevPtX = prevPts[ptref+0]*levscale;
-        f32 prevPtY = prevPts[ptref+1]*levscale;
-        f32 nextPtX;
-        f32 nextPtY;
-        if( level == maxLevel )
-        {
-            if( useInitialFlow )
-            {
-                nextPtX = nextPts[ptref+0]*levscale;
-                nextPtY = nextPts[ptref+1]*levscale;
-            }
-            else
-            {
-                nextPtX = prevPtX;
-                nextPtY = prevPtY;
-            }
-        }
-        else
-        {
-            nextPtX = nextPts[ptref+0]*2.f;
-            nextPtY = nextPts[ptref+1]*2.f;
-        }
-        nextPts[ptref+0] = nextPtX;
-        nextPts[ptref+1] = nextPtY;
+        f32 prevPtX = prevPts[ptref+0];
+        f32 prevPtY = prevPts[ptref+1];
+        f32 nextPtX = nextPts[ptref+0];
+        f32 nextPtY = nextPts[ptref+1];

        s32 iprevPtX, iprevPtY;
        s32 inextPtX, inextPtY;
@@ -111,13 +90,10 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,
        if( iprevPtX < -(s32)winSize.width || iprevPtX >= (s32)size.width ||
            iprevPtY < -(s32)winSize.height || iprevPtY >= (s32)size.height )
        {
-            if( level == 0 )
-            {
-                if( status )
-                    status[ptidx] = false;
-                if( err )
-                    err[ptidx] = 0;
-            }
+            if( status )
+                status[ptidx] = false;
+            if( err )
+                err[ptidx] = 0;
            continue;
        }

@@ -333,7 +309,7 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,

        if( minEig < minEigThreshold || D < FLT_EPSILON )
        {
-            if( level == 0 && status )
+            if( status )
                status[ptidx] = false;
            continue;
        }
@@ -353,7 +329,7 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,
            if( inextPtX < -(s32)winSize.width || inextPtX >= (s32)size.width ||
               inextPtY < -(s32)winSize.height || inextPtY >= (s32)size.height )
            {
-                if( level == 0 && status )
+                if( status )
                    status[ptidx] = false;
                break;
            }
@@ -469,8 +445,7 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,
            prevDeltaX = deltaX;
            prevDeltaY = deltaY;
        }
-
-        if( status && status[ptidx] && err && level == 0 && !getMinEigenVals )
+        if( status && status[ptidx] && err && !getMinEigenVals )
        {
            f32 nextPointX = nextPts[ptref+0] - halfWinX;
            f32 nextPointY = nextPts[ptref+1] - halfWinY;
@@ -526,9 +501,6 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,
    (void)winSize;
    (void)terminationCount;
    (void)terminationEpsilon;
-    (void)level;
-    (void)maxLevel;
-    (void)useInitialFlow;
    (void)getMinEigenVals;
    (void)minEigThreshold;
    (void)ptCount;
@@ -536,4 +508,3 @@ void pyrLKOptFlowLevel(const Size2D &size, s32 cn,
 }

 }//CAROTENE_NS
-
@@ -41,6 +41,7 @@
 #include <cmath>

 #include "common.hpp"
+#include "vround_helper.hpp"

 namespace CAROTENE_NS {

@@ -121,8 +122,6 @@ void phase(const Size2D &size,
    size_t roiw16 = size.width >= 15 ? size.width - 15 : 0;
    size_t roiw8 = size.width >= 7 ? size.width - 7 : 0;

-    float32x4_t v_05 = vdupq_n_f32(0.5f);
-
    for (size_t i = 0; i < size.height; ++i)
    {
        const s16 * src0 = internal::getRowPtr(src0Base, src0Stride, i);
@@ -149,8 +148,8 @@ void phase(const Size2D &size,
            float32x4_t v_dst32f1;
            FASTATAN2VECTOR(v_src1_p, v_src0_p, v_dst32f1)

-            uint16x8_t v_dst16s0 = vcombine_u16(vmovn_u32(vcvtq_u32_f32(vaddq_f32(v_dst32f0, v_05))),
-                                                vmovn_u32(vcvtq_u32_f32(vaddq_f32(v_dst32f1, v_05))));
+            uint16x8_t v_dst16s0 = vcombine_u16(vmovn_u32(internal::vroundq_u32_f32(v_dst32f0)),
+                                                vmovn_u32(internal::vroundq_u32_f32(v_dst32f1)));

            // 1
            v_src0_p = vcvtq_f32_s32(vmovl_s16(vget_low_s16(v_src01)));
@@ -161,8 +160,8 @@ void phase(const Size2D &size,
            v_src1_p = vcvtq_f32_s32(vmovl_s16(vget_high_s16(v_src11)));
            FASTATAN2VECTOR(v_src1_p, v_src0_p, v_dst32f1)

-            uint16x8_t v_dst16s1 = vcombine_u16(vmovn_u32(vcvtq_u32_f32(vaddq_f32(v_dst32f0, v_05))),
-                                                vmovn_u32(vcvtq_u32_f32(vaddq_f32(v_dst32f1, v_05))));
+            uint16x8_t v_dst16s1 = vcombine_u16(vmovn_u32(internal::vroundq_u32_f32(v_dst32f0)),
+                                                vmovn_u32(internal::vroundq_u32_f32(v_dst32f1)));

            vst1q_u8(dst + j, vcombine_u8(vmovn_u16(v_dst16s0),
                                          vmovn_u16(v_dst16s1)));
@@ -182,8 +181,8 @@ void phase(const Size2D &size,
            float32x4_t v_dst32f1;
            FASTATAN2VECTOR(v_src1_p, v_src0_p, v_dst32f1)

-            uint16x8_t v_dst = vcombine_u16(vmovn_u32(vcvtq_u32_f32(vaddq_f32(v_dst32f0, v_05))),
-                                            vmovn_u32(vcvtq_u32_f32(vaddq_f32(v_dst32f1, v_05))));
+            uint16x8_t v_dst = vcombine_u16(vmovn_u32(internal::vroundq_u32_f32(v_dst32f0)),
+                                            vmovn_u32(internal::vroundq_u32_f32(v_dst32f1)));

            vst1_u8(dst + j, vmovn_u16(v_dst));
        }
@@ -0,0 +1,102 @@
+/*
+ * By downloading, copying, installing or using the software you agree to this license.
+ * If you do not agree to this license, do not download, install,
+ * copy or use the software.
+ *
+ *
+ *                           License Agreement
+ *                For Open Source Computer Vision Library
+ *                        (3-clause BSD License)
+ *
+ * Copyright (C) 2014-2015, NVIDIA Corporation, all rights reserved.
+ * Third party copyrights are property of their respective owners.
+ *
+ * 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 in the documentation
+ *     and/or other materials provided with the distribution.
+ *
+ *   * Neither the names of the copyright holders nor the names of the contributors
+ *     may be used to endorse or promote products derived from this software
+ *     without specific prior written permission.
+ *
+ * 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 copyright holders 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.
+ */
+
+#ifndef CAROTENE_SRC_VROUND_HELPER_HPP
+#define CAROTENE_SRC_VROUND_HELPER_HPP
+
+#include "common.hpp"
+#include "vtransform.hpp"
+
+#ifdef CAROTENE_NEON
+
+/**
+ * This helper header is for rounding from float32xN to uin32xN or int32xN to nearest, ties to even.
+ * See https://en.wikipedia.org/wiki/Rounding#Rounding_half_to_even
+ */
+
+// See https://github.com/opencv/opencv/pull/24271#issuecomment-1867318007
+#define CAROTENE_ROUND_DELTA (12582912.0f)
+
+namespace CAROTENE_NS { namespace internal {
+
+inline uint32x4_t vroundq_u32_f32(const float32x4_t val)
+{
+#if defined(__ARM_ARCH) && (__ARM_ARCH >= 8)
+    return vcvtnq_u32_f32(val);
+#else
+    const float32x4_t delta = vdupq_n_f32(CAROTENE_ROUND_DELTA);
+    return vcvtq_u32_f32(vsubq_f32(vaddq_f32(val, delta), delta));
+#endif
+}
+
+inline uint32x2_t vround_u32_f32(const float32x2_t val)
+{
+#if defined(__ARM_ARCH) && (__ARM_ARCH >= 8)
+    return vcvtn_u32_f32(val);
+#else
+    const float32x2_t delta = vdup_n_f32(CAROTENE_ROUND_DELTA);
+    return vcvt_u32_f32(vsub_f32(vadd_f32(val, delta), delta));
+#endif
+}
+
+inline int32x4_t vroundq_s32_f32(const float32x4_t val)
+{
+#if defined(__ARM_ARCH) && (__ARM_ARCH >= 8)
+    return vcvtnq_s32_f32(val);
+#else
+    const float32x4_t delta = vdupq_n_f32(CAROTENE_ROUND_DELTA);
+    return vcvtq_s32_f32(vsubq_f32(vaddq_f32(val, delta), delta));
+#endif
+}
+
+inline int32x2_t vround_s32_f32(const float32x2_t val)
+{
+#if defined(__ARM_ARCH) && (__ARM_ARCH >= 8)
+    return vcvtn_s32_f32(val);
+#else
+    const float32x2_t delta = vdup_n_f32(CAROTENE_ROUND_DELTA);
+    return vcvt_s32_f32(vsub_f32(vadd_f32(val, delta), delta));
+#endif
+}
+
+} }
+
+#endif // CAROTENE_NEON
+
+#endif
@@ -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)
@@ -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__ */
@@ -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
@@ -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
@@ -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.
@@ -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()
@@ -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);
+}
@@ -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]]];
+}
@@ -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;
+}
@@ -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]);
+}
@@ -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;
+}
@@ -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;
+}
@@ -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;
+}
@@ -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);
+}
@@ -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]]];
+}
@@ -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_ */
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -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_
+
@@ -1,9 +1,9 @@
-# Binaries branch name: ffmpeg/4.x_20211220
-# Binaries were created for OpenCV: 0e274fc4bed8a64ba4f1c201a21304286e217afc
-ocv_update(FFMPEG_BINARIES_COMMIT "4d348507d156ec797a88a887cfa7f9129a35afac")
-ocv_update(FFMPEG_FILE_HASH_BIN32 "eece4ec8304188117ffc7d5dfd0fc0ae")
-ocv_update(FFMPEG_FILE_HASH_BIN64 "20deefbfe023c8b8d11a52e5a6527c6a")
-ocv_update(FFMPEG_FILE_HASH_CMAKE "8862c87496e2e8c375965e1277dee1c7")
+# Binaries branch name: ffmpeg/5.x_20241121
+# Binaries were created for OpenCV: ce7c0f0e651dbd7991f2c6a2327f2697f2102296
+ocv_update(FFMPEG_BINARIES_COMMIT "b2b3a3188ebbe73492ce4554c12b416512a5dec3")
+ocv_update(FFMPEG_FILE_HASH_BIN32 "6e9aa1b8796e9ac19fca4278523c5dff")
+ocv_update(FFMPEG_FILE_HASH_BIN64 "0fe534d69035e3801bc88418611019b4")
+ocv_update(FFMPEG_FILE_HASH_CMAKE "e09efc33312d1173be8a9446f3b088fe")

 function(download_win_ffmpeg script_var)
  set(${script_var} "" PARENT_SCOPE)
@@ -0,0 +1,202 @@
+
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+   limitations under the License.
@@ -0,0 +1 @@
+Origin: https://github.com/google/flatbuffers/tree/v23.5.9
@@ -0,0 +1,68 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_ALLOCATOR_H_
+#define FLATBUFFERS_ALLOCATOR_H_
+
+#include "flatbuffers/base.h"
+
+namespace flatbuffers {
+
+// Allocator interface. This is flatbuffers-specific and meant only for
+// `vector_downward` usage.
+class Allocator {
+ public:
+  virtual ~Allocator() {}
+
+  // Allocate `size` bytes of memory.
+  virtual uint8_t *allocate(size_t size) = 0;
+
+  // Deallocate `size` bytes of memory at `p` allocated by this allocator.
+  virtual void deallocate(uint8_t *p, size_t size) = 0;
+
+  // Reallocate `new_size` bytes of memory, replacing the old region of size
+  // `old_size` at `p`. In contrast to a normal realloc, this grows downwards,
+  // and is intended specifcally for `vector_downward` use.
+  // `in_use_back` and `in_use_front` indicate how much of `old_size` is
+  // actually in use at each end, and needs to be copied.
+  virtual uint8_t *reallocate_downward(uint8_t *old_p, size_t old_size,
+                                       size_t new_size, size_t in_use_back,
+                                       size_t in_use_front) {
+    FLATBUFFERS_ASSERT(new_size > old_size);  // vector_downward only grows
+    uint8_t *new_p = allocate(new_size);
+    memcpy_downward(old_p, old_size, new_p, new_size, in_use_back,
+                    in_use_front);
+    deallocate(old_p, old_size);
+    return new_p;
+  }
+
+ protected:
+  // Called by `reallocate_downward` to copy memory from `old_p` of `old_size`
+  // to `new_p` of `new_size`. Only memory of size `in_use_front` and
+  // `in_use_back` will be copied from the front and back of the old memory
+  // allocation.
+  void memcpy_downward(uint8_t *old_p, size_t old_size, uint8_t *new_p,
+                       size_t new_size, size_t in_use_back,
+                       size_t in_use_front) {
+    memcpy(new_p + new_size - in_use_back, old_p + old_size - in_use_back,
+           in_use_back);
+    memcpy(new_p, old_p, in_use_front);
+  }
+};
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_ALLOCATOR_H_
@@ -0,0 +1,256 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_ARRAY_H_
+#define FLATBUFFERS_ARRAY_H_
+
+#include <cstdint>
+#include <memory>
+
+#include "flatbuffers/base.h"
+#include "flatbuffers/stl_emulation.h"
+#include "flatbuffers/vector.h"
+
+namespace flatbuffers {
+
+// This is used as a helper type for accessing arrays.
+template<typename T, uint16_t length> class Array {
+  // Array<T> can carry only POD data types (scalars or structs).
+  typedef typename flatbuffers::bool_constant<flatbuffers::is_scalar<T>::value>
+      scalar_tag;
+  typedef
+      typename flatbuffers::conditional<scalar_tag::value, T, const T *>::type
+          IndirectHelperType;
+
+ public:
+  typedef uint16_t size_type;
+  typedef typename IndirectHelper<IndirectHelperType>::return_type return_type;
+  typedef VectorConstIterator<T, return_type, uoffset_t> const_iterator;
+  typedef VectorReverseIterator<const_iterator> const_reverse_iterator;
+
+  // If T is a LE-scalar or a struct (!scalar_tag::value).
+  static FLATBUFFERS_CONSTEXPR bool is_span_observable =
+      (scalar_tag::value && (FLATBUFFERS_LITTLEENDIAN || sizeof(T) == 1)) ||
+      !scalar_tag::value;
+
+  FLATBUFFERS_CONSTEXPR uint16_t size() const { return length; }
+
+  return_type Get(uoffset_t i) const {
+    FLATBUFFERS_ASSERT(i < size());
+    return IndirectHelper<IndirectHelperType>::Read(Data(), i);
+  }
+
+  return_type operator[](uoffset_t i) const { return Get(i); }
+
+  // If this is a Vector of enums, T will be its storage type, not the enum
+  // type. This function makes it convenient to retrieve value with enum
+  // type E.
+  template<typename E> E GetEnum(uoffset_t i) const {
+    return static_cast<E>(Get(i));
+  }
+
+  const_iterator begin() const { return const_iterator(Data(), 0); }
+  const_iterator end() const { return const_iterator(Data(), size()); }
+
+  const_reverse_iterator rbegin() const {
+    return const_reverse_iterator(end());
+  }
+  const_reverse_iterator rend() const {
+    return const_reverse_iterator(begin());
+  }
+
+  const_iterator cbegin() const { return begin(); }
+  const_iterator cend() const { return end(); }
+
+  const_reverse_iterator crbegin() const { return rbegin(); }
+  const_reverse_iterator crend() const { return rend(); }
+
+  // Get a mutable pointer to elements inside this array.
+  // This method used to mutate arrays of structs followed by a @p Mutate
+  // operation. For primitive types use @p Mutate directly.
+  // @warning Assignments and reads to/from the dereferenced pointer are not
+  //  automatically converted to the correct endianness.
+  typename flatbuffers::conditional<scalar_tag::value, void, T *>::type
+  GetMutablePointer(uoffset_t i) const {
+    FLATBUFFERS_ASSERT(i < size());
+    return const_cast<T *>(&data()[i]);
+  }
+
+  // Change elements if you have a non-const pointer to this object.
+  void Mutate(uoffset_t i, const T &val) { MutateImpl(scalar_tag(), i, val); }
+
+  // The raw data in little endian format. Use with care.
+  const uint8_t *Data() const { return data_; }
+
+  uint8_t *Data() { return data_; }
+
+  // Similarly, but typed, much like std::vector::data
+  const T *data() const { return reinterpret_cast<const T *>(Data()); }
+  T *data() { return reinterpret_cast<T *>(Data()); }
+
+  // Copy data from a span with endian conversion.
+  // If this Array and the span overlap, the behavior is undefined.
+  void CopyFromSpan(flatbuffers::span<const T, length> src) {
+    const auto p1 = reinterpret_cast<const uint8_t *>(src.data());
+    const auto p2 = Data();
+    FLATBUFFERS_ASSERT(!(p1 >= p2 && p1 < (p2 + length)) &&
+                       !(p2 >= p1 && p2 < (p1 + length)));
+    (void)p1;
+    (void)p2;
+    CopyFromSpanImpl(flatbuffers::bool_constant<is_span_observable>(), src);
+  }
+
+ protected:
+  void MutateImpl(flatbuffers::true_type, uoffset_t i, const T &val) {
+    FLATBUFFERS_ASSERT(i < size());
+    WriteScalar(data() + i, val);
+  }
+
+  void MutateImpl(flatbuffers::false_type, uoffset_t i, const T &val) {
+    *(GetMutablePointer(i)) = val;
+  }
+
+  void CopyFromSpanImpl(flatbuffers::true_type,
+                        flatbuffers::span<const T, length> src) {
+    // Use std::memcpy() instead of std::copy() to avoid performance degradation
+    // due to aliasing if T is char or unsigned char.
+    // The size is known at compile time, so memcpy would be inlined.
+    std::memcpy(data(), src.data(), length * sizeof(T));
+  }
+
+  // Copy data from flatbuffers::span with endian conversion.
+  void CopyFromSpanImpl(flatbuffers::false_type,
+                        flatbuffers::span<const T, length> src) {
+    for (size_type k = 0; k < length; k++) { Mutate(k, src[k]); }
+  }
+
+  // This class is only used to access pre-existing data. Don't ever
+  // try to construct these manually.
+  // 'constexpr' allows us to use 'size()' at compile time.
+  // @note Must not use 'FLATBUFFERS_CONSTEXPR' here, as const is not allowed on
+  //  a constructor.
+#if defined(__cpp_constexpr)
+  constexpr Array();
+#else
+  Array();
+#endif
+
+  uint8_t data_[length * sizeof(T)];
+
+ private:
+  // This class is a pointer. Copying will therefore create an invalid object.
+  // Private and unimplemented copy constructor.
+  Array(const Array &);
+  Array &operator=(const Array &);
+};
+
+// Specialization for Array[struct] with access using Offset<void> pointer.
+// This specialization used by idl_gen_text.cpp.
+template<typename T, uint16_t length, template<typename> class OffsetT>
+class Array<OffsetT<T>, length> {
+  static_assert(flatbuffers::is_same<T, void>::value, "unexpected type T");
+
+ public:
+  typedef const void *return_type;
+  typedef uint16_t size_type;
+
+  const uint8_t *Data() const { return data_; }
+
+  // Make idl_gen_text.cpp::PrintContainer happy.
+  return_type operator[](uoffset_t) const {
+    FLATBUFFERS_ASSERT(false);
+    return nullptr;
+  }
+
+ private:
+  // This class is only used to access pre-existing data.
+  Array();
+  Array(const Array &);
+  Array &operator=(const Array &);
+
+  uint8_t data_[1];
+};
+
+template<class U, uint16_t N>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<U, N> make_span(Array<U, N> &arr)
+    FLATBUFFERS_NOEXCEPT {
+  static_assert(
+      Array<U, N>::is_span_observable,
+      "wrong type U, only plain struct, LE-scalar, or byte types are allowed");
+  return span<U, N>(arr.data(), N);
+}
+
+template<class U, uint16_t N>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<const U, N> make_span(
+    const Array<U, N> &arr) FLATBUFFERS_NOEXCEPT {
+  static_assert(
+      Array<U, N>::is_span_observable,
+      "wrong type U, only plain struct, LE-scalar, or byte types are allowed");
+  return span<const U, N>(arr.data(), N);
+}
+
+template<class U, uint16_t N>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<uint8_t, sizeof(U) * N>
+make_bytes_span(Array<U, N> &arr) FLATBUFFERS_NOEXCEPT {
+  static_assert(Array<U, N>::is_span_observable,
+                "internal error, Array<T> might hold only scalars or structs");
+  return span<uint8_t, sizeof(U) * N>(arr.Data(), sizeof(U) * N);
+}
+
+template<class U, uint16_t N>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<const uint8_t, sizeof(U) * N>
+make_bytes_span(const Array<U, N> &arr) FLATBUFFERS_NOEXCEPT {
+  static_assert(Array<U, N>::is_span_observable,
+                "internal error, Array<T> might hold only scalars or structs");
+  return span<const uint8_t, sizeof(U) * N>(arr.Data(), sizeof(U) * N);
+}
+
+// Cast a raw T[length] to a raw flatbuffers::Array<T, length>
+// without endian conversion. Use with care.
+// TODO: move these Cast-methods to `internal` namespace.
+template<typename T, uint16_t length>
+Array<T, length> &CastToArray(T (&arr)[length]) {
+  return *reinterpret_cast<Array<T, length> *>(arr);
+}
+
+template<typename T, uint16_t length>
+const Array<T, length> &CastToArray(const T (&arr)[length]) {
+  return *reinterpret_cast<const Array<T, length> *>(arr);
+}
+
+template<typename E, typename T, uint16_t length>
+Array<E, length> &CastToArrayOfEnum(T (&arr)[length]) {
+  static_assert(sizeof(E) == sizeof(T), "invalid enum type E");
+  return *reinterpret_cast<Array<E, length> *>(arr);
+}
+
+template<typename E, typename T, uint16_t length>
+const Array<E, length> &CastToArrayOfEnum(const T (&arr)[length]) {
+  static_assert(sizeof(E) == sizeof(T), "invalid enum type E");
+  return *reinterpret_cast<const Array<E, length> *>(arr);
+}
+
+template<typename T, uint16_t length>
+bool operator==(const Array<T, length> &lhs,
+                const Array<T, length> &rhs) noexcept {
+  return std::addressof(lhs) == std::addressof(rhs) ||
+         (lhs.size() == rhs.size() &&
+          std::memcmp(lhs.Data(), rhs.Data(), rhs.size() * sizeof(T)) == 0);
+}
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_ARRAY_H_
@@ -0,0 +1,495 @@
+#ifndef FLATBUFFERS_BASE_H_
+#define FLATBUFFERS_BASE_H_
+
+// clang-format off
+
+// If activate should be declared and included first.
+#if defined(FLATBUFFERS_MEMORY_LEAK_TRACKING) && \
+    defined(_MSC_VER) && defined(_DEBUG)
+  // The _CRTDBG_MAP_ALLOC inside <crtdbg.h> will replace
+  // calloc/free (etc) to its debug version using #define directives.
+  #define _CRTDBG_MAP_ALLOC
+  #include <stdlib.h>
+  #include <crtdbg.h>
+  // Replace operator new by trace-enabled version.
+  #define DEBUG_NEW new(_NORMAL_BLOCK, __FILE__, __LINE__)
+  #define new DEBUG_NEW
+#endif
+
+#if !defined(FLATBUFFERS_ASSERT)
+#include <assert.h>
+#define FLATBUFFERS_ASSERT assert
+#elif defined(FLATBUFFERS_ASSERT_INCLUDE)
+// Include file with forward declaration
+#include FLATBUFFERS_ASSERT_INCLUDE
+#endif
+
+#ifndef ARDUINO
+#include <cstdint>
+#endif
+
+#include <cstddef>
+#include <cstdlib>
+#include <cstring>
+
+#if defined(ARDUINO) && !defined(ARDUINOSTL_M_H) && defined(__AVR__)
+  #include <utility.h>
+#else
+  #include <utility>
+#endif
+
+#include <string>
+#include <type_traits>
+#include <vector>
+#include <set>
+#include <algorithm>
+#include <limits>
+#include <iterator>
+#include <memory>
+
+#if defined(__unix__) && !defined(FLATBUFFERS_LOCALE_INDEPENDENT)
+  #include <unistd.h>
+#endif
+
+#ifdef __ANDROID__
+  #include <android/api-level.h>
+#endif
+
+#if defined(__ICCARM__)
+#include <intrinsics.h>
+#endif
+
+// Note the __clang__ check is needed, because clang presents itself
+// as an older GNUC compiler (4.2).
+// Clang 3.3 and later implement all of the ISO C++ 2011 standard.
+// Clang 3.4 and later implement all of the ISO C++ 2014 standard.
+// http://clang.llvm.org/cxx_status.html
+
+// Note the MSVC value '__cplusplus' may be incorrect:
+// The '__cplusplus' predefined macro in the MSVC stuck at the value 199711L,
+// indicating (erroneously!) that the compiler conformed to the C++98 Standard.
+// This value should be correct starting from MSVC2017-15.7-Preview-3.
+// The '__cplusplus' will be valid only if MSVC2017-15.7-P3 and the `/Zc:__cplusplus` switch is set.
+// Workaround (for details see MSDN):
+// Use the _MSC_VER and _MSVC_LANG definition instead of the __cplusplus  for compatibility.
+// The _MSVC_LANG macro reports the Standard version regardless of the '/Zc:__cplusplus' switch.
+
+#if defined(__GNUC__) && !defined(__clang__)
+  #define FLATBUFFERS_GCC (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__)
+#else
+  #define FLATBUFFERS_GCC 0
+#endif
+
+#if defined(__clang__)
+  #define FLATBUFFERS_CLANG (__clang_major__ * 10000 + __clang_minor__ * 100 + __clang_patchlevel__)
+#else
+  #define FLATBUFFERS_CLANG 0
+#endif
+
+/// @cond FLATBUFFERS_INTERNAL
+#if __cplusplus <= 199711L && \
+    (!defined(_MSC_VER) || _MSC_VER < 1600) && \
+    (!defined(__GNUC__) || \
+      (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__ < 40400))
+  #error A C++11 compatible compiler with support for the auto typing is \
+         required for FlatBuffers.
+  #error __cplusplus _MSC_VER __GNUC__  __GNUC_MINOR__  __GNUC_PATCHLEVEL__
+#endif
+
+#if !defined(__clang__) && \
+    defined(__GNUC__) && \
+    (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__ < 40600)
+  // Backwards compatibility for g++ 4.4, and 4.5 which don't have the nullptr
+  // and constexpr keywords. Note the __clang__ check is needed, because clang
+  // presents itself as an older GNUC compiler.
+  #ifndef nullptr_t
+    const class nullptr_t {
+    public:
+      template<class T> inline operator T*() const { return 0; }
+    private:
+      void operator&() const;
+    } nullptr = {};
+  #endif
+  #ifndef constexpr
+    #define constexpr const
+  #endif
+#endif
+
+// The wire format uses a little endian encoding (since that's efficient for
+// the common platforms).
+#if defined(__s390x__)
+  #define FLATBUFFERS_LITTLEENDIAN 0
+#endif // __s390x__
+#if !defined(FLATBUFFERS_LITTLEENDIAN)
+  #if defined(__GNUC__) || defined(__clang__) || defined(__ICCARM__)
+    #if (defined(__BIG_ENDIAN__) || \
+         (defined(__BYTE_ORDER__) && __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__))
+      #define FLATBUFFERS_LITTLEENDIAN 0
+    #else
+      #define FLATBUFFERS_LITTLEENDIAN 1
+    #endif // __BIG_ENDIAN__
+  #elif defined(_MSC_VER)
+    #if defined(_M_PPC)
+      #define FLATBUFFERS_LITTLEENDIAN 0
+    #else
+      #define FLATBUFFERS_LITTLEENDIAN 1
+    #endif
+  #else
+    #error Unable to determine endianness, define FLATBUFFERS_LITTLEENDIAN.
+  #endif
+#endif // !defined(FLATBUFFERS_LITTLEENDIAN)
+
+#define FLATBUFFERS_VERSION_MAJOR 23
+#define FLATBUFFERS_VERSION_MINOR 5
+#define FLATBUFFERS_VERSION_REVISION 9
+#define FLATBUFFERS_STRING_EXPAND(X) #X
+#define FLATBUFFERS_STRING(X) FLATBUFFERS_STRING_EXPAND(X)
+namespace flatbuffers {
+  // Returns version as string  "MAJOR.MINOR.REVISION".
+  const char* FLATBUFFERS_VERSION();
+}
+
+#if (!defined(_MSC_VER) || _MSC_VER > 1600) && \
+    (!defined(__GNUC__) || (__GNUC__ * 100 + __GNUC_MINOR__ >= 407)) || \
+    defined(__clang__)
+  #define FLATBUFFERS_FINAL_CLASS final
+  #define FLATBUFFERS_OVERRIDE override
+  #define FLATBUFFERS_EXPLICIT_CPP11 explicit
+  #define FLATBUFFERS_VTABLE_UNDERLYING_TYPE : flatbuffers::voffset_t
+#else
+  #define FLATBUFFERS_FINAL_CLASS
+  #define FLATBUFFERS_OVERRIDE
+  #define FLATBUFFERS_EXPLICIT_CPP11
+  #define FLATBUFFERS_VTABLE_UNDERLYING_TYPE
+#endif
+
+#if (!defined(_MSC_VER) || _MSC_VER >= 1900) && \
+    (!defined(__GNUC__) || (__GNUC__ * 100 + __GNUC_MINOR__ >= 406)) || \
+    (defined(__cpp_constexpr) && __cpp_constexpr >= 200704)
+  #define FLATBUFFERS_CONSTEXPR constexpr
+  #define FLATBUFFERS_CONSTEXPR_CPP11 constexpr
+  #define FLATBUFFERS_CONSTEXPR_DEFINED
+#else
+  #define FLATBUFFERS_CONSTEXPR const
+  #define FLATBUFFERS_CONSTEXPR_CPP11
+#endif
+
+#if (defined(__cplusplus) && __cplusplus >= 201402L) || \
+    (defined(__cpp_constexpr) && __cpp_constexpr >= 201304)
+  #define FLATBUFFERS_CONSTEXPR_CPP14 FLATBUFFERS_CONSTEXPR_CPP11
+#else
+  #define FLATBUFFERS_CONSTEXPR_CPP14
+#endif
+
+#if (defined(__GXX_EXPERIMENTAL_CXX0X__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 406)) || \
+    (defined(_MSC_FULL_VER) && (_MSC_FULL_VER >= 190023026)) || \
+    defined(__clang__)
+  #define FLATBUFFERS_NOEXCEPT noexcept
+#else
+  #define FLATBUFFERS_NOEXCEPT
+#endif
+
+// NOTE: the FLATBUFFERS_DELETE_FUNC macro may change the access mode to
+// private, so be sure to put it at the end or reset access mode explicitly.
+#if (!defined(_MSC_VER) || _MSC_FULL_VER >= 180020827) && \
+    (!defined(__GNUC__) || (__GNUC__ * 100 + __GNUC_MINOR__ >= 404)) || \
+    defined(__clang__)
+  #define FLATBUFFERS_DELETE_FUNC(func) func = delete
+#else
+  #define FLATBUFFERS_DELETE_FUNC(func) private: func
+#endif
+
+#if (!defined(_MSC_VER) || _MSC_VER >= 1900) && \
+    (!defined(__GNUC__) || (__GNUC__ * 100 + __GNUC_MINOR__ >= 409)) || \
+    defined(__clang__)
+  #define FLATBUFFERS_DEFAULT_DECLARATION
+#endif
+
+// Check if we can use template aliases
+// Not possible if Microsoft Compiler before 2012
+// Possible is the language feature __cpp_alias_templates is defined well
+// Or possible if the C++ std is C+11 or newer
+#if (defined(_MSC_VER) && _MSC_VER > 1700 /* MSVC2012 */) \
+    || (defined(__cpp_alias_templates) && __cpp_alias_templates >= 200704) \
+    || (defined(__cplusplus) && __cplusplus >= 201103L)
+  #define FLATBUFFERS_TEMPLATES_ALIASES
+#endif
+
+#ifndef FLATBUFFERS_HAS_STRING_VIEW
+  // Only provide flatbuffers::string_view if __has_include can be used
+  // to detect a header that provides an implementation
+  #if defined(__has_include)
+    // Check for std::string_view (in c++17)
+    #if __has_include(<string_view>) && (__cplusplus >= 201606 || (defined(_HAS_CXX17) && _HAS_CXX17))
+      #include <string_view>
+      namespace flatbuffers {
+        typedef std::string_view string_view;
+      }
+      #define FLATBUFFERS_HAS_STRING_VIEW 1
+    // Check for std::experimental::string_view (in c++14, compiler-dependent)
+    #elif __has_include(<experimental/string_view>) && (__cplusplus >= 201411)
+      #include <experimental/string_view>
+      namespace flatbuffers {
+        typedef std::experimental::string_view string_view;
+      }
+      #define FLATBUFFERS_HAS_STRING_VIEW 1
+    // Check for absl::string_view
+    #elif __has_include("absl/strings/string_view.h") && \
+          __has_include("absl/base/config.h") && \
+          (__cplusplus >= 201411)
+      #include "absl/base/config.h"
+      #if !defined(ABSL_USES_STD_STRING_VIEW)
+        #include "absl/strings/string_view.h"
+        namespace flatbuffers {
+          typedef absl::string_view string_view;
+        }
+        #define FLATBUFFERS_HAS_STRING_VIEW 1
+      #endif
+    #endif
+  #endif // __has_include
+#endif // !FLATBUFFERS_HAS_STRING_VIEW
+
+#ifndef FLATBUFFERS_GENERAL_HEAP_ALLOC_OK
+  // Allow heap allocations to be used
+  #define FLATBUFFERS_GENERAL_HEAP_ALLOC_OK 1
+#endif // !FLATBUFFERS_GENERAL_HEAP_ALLOC_OK
+
+#ifndef FLATBUFFERS_HAS_NEW_STRTOD
+  // Modern (C++11) strtod and strtof functions are available for use.
+  // 1) nan/inf strings as argument of strtod;
+  // 2) hex-float  as argument of  strtod/strtof.
+  #if (defined(_MSC_VER) && _MSC_VER >= 1900) || \
+      (defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 409)) || \
+      (defined(__clang__))
+    #define FLATBUFFERS_HAS_NEW_STRTOD 1
+  #endif
+#endif // !FLATBUFFERS_HAS_NEW_STRTOD
+
+#ifndef FLATBUFFERS_LOCALE_INDEPENDENT
+  // Enable locale independent functions {strtof_l, strtod_l,strtoll_l,
+  // strtoull_l}.
+  #if (defined(_MSC_VER) && _MSC_VER >= 1800) || \
+      (defined(__ANDROID_API__) && __ANDROID_API__>= 21) || \
+      (defined(_XOPEN_VERSION) && (_XOPEN_VERSION >= 700)) && \
+        (!defined(__Fuchsia__) && !defined(__ANDROID_API__))
+    #define FLATBUFFERS_LOCALE_INDEPENDENT 1
+  #else
+    #define FLATBUFFERS_LOCALE_INDEPENDENT 0
+  #endif
+#endif  // !FLATBUFFERS_LOCALE_INDEPENDENT
+
+// Suppress Undefined Behavior Sanitizer (recoverable only). Usage:
+// - __suppress_ubsan__("undefined")
+// - __suppress_ubsan__("signed-integer-overflow")
+#if defined(__clang__) && (__clang_major__ > 3 || (__clang_major__ == 3 && __clang_minor__ >=7))
+  #define __suppress_ubsan__(type) __attribute__((no_sanitize(type)))
+#elif defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 409)
+  #define __suppress_ubsan__(type) __attribute__((no_sanitize_undefined))
+#else
+  #define __suppress_ubsan__(type)
+#endif
+
+// This is constexpr function used for checking compile-time constants.
+// Avoid `#pragma warning(disable: 4127) // C4127: expression is constant`.
+template<typename T> FLATBUFFERS_CONSTEXPR inline bool IsConstTrue(T t) {
+  return !!t;
+}
+
+// Enable C++ attribute [[]] if std:c++17 or higher.
+#if ((__cplusplus >= 201703L) \
+    || (defined(_MSVC_LANG) &&  (_MSVC_LANG >= 201703L)))
+  // All attributes unknown to an implementation are ignored without causing an error.
+  #define FLATBUFFERS_ATTRIBUTE(attr) attr
+
+  #define FLATBUFFERS_FALLTHROUGH() [[fallthrough]]
+#else
+  #define FLATBUFFERS_ATTRIBUTE(attr)
+
+  #if FLATBUFFERS_CLANG >= 30800
+    #define FLATBUFFERS_FALLTHROUGH() [[clang::fallthrough]]
+  #elif FLATBUFFERS_GCC >= 70300
+    #define FLATBUFFERS_FALLTHROUGH() [[gnu::fallthrough]]
+  #else
+    #define FLATBUFFERS_FALLTHROUGH()
+  #endif
+#endif
+
+/// @endcond
+
+/// @file
+namespace flatbuffers {
+
+/// @cond FLATBUFFERS_INTERNAL
+// Our default offset / size type, 32bit on purpose on 64bit systems.
+// Also, using a consistent offset type maintains compatibility of serialized
+// offset values between 32bit and 64bit systems.
+typedef uint32_t uoffset_t;
+typedef uint64_t uoffset64_t;
+
+// Signed offsets for references that can go in both directions.
+typedef int32_t soffset_t;
+typedef int64_t soffset64_t;
+
+// Offset/index used in v-tables, can be changed to uint8_t in
+// format forks to save a bit of space if desired.
+typedef uint16_t voffset_t;
+
+typedef uintmax_t largest_scalar_t;
+
+// In 32bits, this evaluates to 2GB - 1
+#define FLATBUFFERS_MAX_BUFFER_SIZE std::numeric_limits<::flatbuffers::soffset_t>::max()
+#define FLATBUFFERS_MAX_64_BUFFER_SIZE std::numeric_limits<::flatbuffers::soffset64_t>::max()
+
+// The minimum size buffer that can be a valid flatbuffer.
+// Includes the offset to the root table (uoffset_t), the offset to the vtable
+// of the root table (soffset_t), the size of the vtable (uint16_t), and the
+// size of the referring table (uint16_t).
+#define FLATBUFFERS_MIN_BUFFER_SIZE sizeof(uoffset_t) + sizeof(soffset_t) + \
+   sizeof(uint16_t) + sizeof(uint16_t)
+
+// We support aligning the contents of buffers up to this size.
+#ifndef FLATBUFFERS_MAX_ALIGNMENT
+  #define FLATBUFFERS_MAX_ALIGNMENT 32
+#endif
+
+/// @brief The length of a FlatBuffer file header.
+static const size_t kFileIdentifierLength = 4;
+
+inline bool VerifyAlignmentRequirements(size_t align, size_t min_align = 1) {
+  return (min_align <= align) && (align <= (FLATBUFFERS_MAX_ALIGNMENT)) &&
+         (align & (align - 1)) == 0;  // must be power of 2
+}
+
+#if defined(_MSC_VER)
+  #pragma warning(disable: 4351) // C4351: new behavior: elements of array ... will be default initialized
+  #pragma warning(push)
+  #pragma warning(disable: 4127) // C4127: conditional expression is constant
+#endif
+
+template<typename T> T EndianSwap(T t) {
+  #if defined(_MSC_VER)
+    #define FLATBUFFERS_BYTESWAP16 _byteswap_ushort
+    #define FLATBUFFERS_BYTESWAP32 _byteswap_ulong
+    #define FLATBUFFERS_BYTESWAP64 _byteswap_uint64
+  #elif defined(__ICCARM__)
+    #define FLATBUFFERS_BYTESWAP16 __REV16
+    #define FLATBUFFERS_BYTESWAP32 __REV
+    #define FLATBUFFERS_BYTESWAP64(x) \
+       ((__REV(static_cast<uint32_t>(x >> 32U))) | (static_cast<uint64_t>(__REV(static_cast<uint32_t>(x)))) << 32U)
+  #else
+    #if defined(__GNUC__) && __GNUC__ * 100 + __GNUC_MINOR__ < 408 && !defined(__clang__)
+      // __builtin_bswap16 was missing prior to GCC 4.8.
+      #define FLATBUFFERS_BYTESWAP16(x) \
+        static_cast<uint16_t>(__builtin_bswap32(static_cast<uint32_t>(x) << 16))
+    #else
+      #define FLATBUFFERS_BYTESWAP16 __builtin_bswap16
+    #endif
+    #define FLATBUFFERS_BYTESWAP32 __builtin_bswap32
+    #define FLATBUFFERS_BYTESWAP64 __builtin_bswap64
+  #endif
+  if (sizeof(T) == 1) {   // Compile-time if-then's.
+    return t;
+  } else if (sizeof(T) == 2) {
+    union { T t; uint16_t i; } u = { t };
+    u.i = FLATBUFFERS_BYTESWAP16(u.i);
+    return u.t;
+  } else if (sizeof(T) == 4) {
+    union { T t; uint32_t i; } u = { t };
+    u.i = FLATBUFFERS_BYTESWAP32(u.i);
+    return u.t;
+  } else if (sizeof(T) == 8) {
+    union { T t; uint64_t i; } u = { t };
+    u.i = FLATBUFFERS_BYTESWAP64(u.i);
+    return u.t;
+  } else {
+    FLATBUFFERS_ASSERT(0);
+    return t;
+  }
+}
+
+#if defined(_MSC_VER)
+  #pragma warning(pop)
+#endif
+
+
+template<typename T> T EndianScalar(T t) {
+  #if FLATBUFFERS_LITTLEENDIAN
+    return t;
+  #else
+    return EndianSwap(t);
+  #endif
+}
+
+template<typename T>
+// UBSAN: C++ aliasing type rules, see std::bit_cast<> for details.
+__suppress_ubsan__("alignment")
+T ReadScalar(const void *p) {
+  return EndianScalar(*reinterpret_cast<const T *>(p));
+}
+
+// See https://github.com/google/flatbuffers/issues/5950
+
+#if (FLATBUFFERS_GCC >= 100000) && (FLATBUFFERS_GCC < 110000)
+  #pragma GCC diagnostic push
+  #pragma GCC diagnostic ignored "-Wstringop-overflow"
+#endif
+
+template<typename T>
+// UBSAN: C++ aliasing type rules, see std::bit_cast<> for details.
+__suppress_ubsan__("alignment")
+void WriteScalar(void *p, T t) {
+  *reinterpret_cast<T *>(p) = EndianScalar(t);
+}
+
+template<typename T> struct Offset;
+template<typename T> __suppress_ubsan__("alignment") void WriteScalar(void *p, Offset<T> t) {
+  *reinterpret_cast<uoffset_t *>(p) = EndianScalar(t.o);
+}
+
+#if (FLATBUFFERS_GCC >= 100000) && (FLATBUFFERS_GCC < 110000)
+  #pragma GCC diagnostic pop
+#endif
+
+// Computes how many bytes you'd have to pad to be able to write an
+// "scalar_size" scalar if the buffer had grown to "buf_size" (downwards in
+// memory).
+__suppress_ubsan__("unsigned-integer-overflow")
+inline size_t PaddingBytes(size_t buf_size, size_t scalar_size) {
+  return ((~buf_size) + 1) & (scalar_size - 1);
+}
+
+// Generic 'operator==' with conditional specialisations.
+// T e - new value of a scalar field.
+// T def - default of scalar (is known at compile-time).
+template<typename T> inline bool IsTheSameAs(T e, T def) { return e == def; }
+
+#if defined(FLATBUFFERS_NAN_DEFAULTS) && \
+    defined(FLATBUFFERS_HAS_NEW_STRTOD) && (FLATBUFFERS_HAS_NEW_STRTOD > 0)
+// Like `operator==(e, def)` with weak NaN if T=(float|double).
+template<typename T> inline bool IsFloatTheSameAs(T e, T def) {
+  return (e == def) || ((def != def) && (e != e));
+}
+template<> inline bool IsTheSameAs<float>(float e, float def) {
+  return IsFloatTheSameAs(e, def);
+}
+template<> inline bool IsTheSameAs<double>(double e, double def) {
+  return IsFloatTheSameAs(e, def);
+}
+#endif
+
+// Check 'v' is out of closed range [low; high].
+// Workaround for GCC warning [-Werror=type-limits]:
+// comparison is always true due to limited range of data type.
+template<typename T>
+inline bool IsOutRange(const T &v, const T &low, const T &high) {
+  return (v < low) || (high < v);
+}
+
+// Check 'v' is in closed range [low; high].
+template<typename T>
+inline bool IsInRange(const T &v, const T &low, const T &high) {
+  return !IsOutRange(v, low, high);
+}
+
+}  // namespace flatbuffers
+#endif  // FLATBUFFERS_BASE_H_
@@ -0,0 +1,199 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_BUFFER_H_
+#define FLATBUFFERS_BUFFER_H_
+
+#include <algorithm>
+
+#include "flatbuffers/base.h"
+
+namespace flatbuffers {
+
+// Wrapper for uoffset_t to allow safe template specialization.
+// Value is allowed to be 0 to indicate a null object (see e.g. AddOffset).
+template<typename T = void> struct Offset {
+  // The type of offset to use.
+  typedef uoffset_t offset_type;
+
+  offset_type o;
+  Offset() : o(0) {}
+  Offset(const offset_type _o) : o(_o) {}
+  Offset<> Union() const { return o; }
+  bool IsNull() const { return !o; }
+};
+
+// Wrapper for uoffset64_t Offsets.
+template<typename T = void> struct Offset64 {
+  // The type of offset to use.
+  typedef uoffset64_t offset_type;
+
+  offset_type o;
+  Offset64() : o(0) {}
+  Offset64(const offset_type offset) : o(offset) {}
+  Offset64<> Union() const { return o; }
+  bool IsNull() const { return !o; }
+};
+
+// Litmus check for ensuring the Offsets are the expected size.
+static_assert(sizeof(Offset<>) == 4, "Offset has wrong size");
+static_assert(sizeof(Offset64<>) == 8, "Offset64 has wrong size");
+
+inline void EndianCheck() {
+  int endiantest = 1;
+  // If this fails, see FLATBUFFERS_LITTLEENDIAN above.
+  FLATBUFFERS_ASSERT(*reinterpret_cast<char *>(&endiantest) ==
+                     FLATBUFFERS_LITTLEENDIAN);
+  (void)endiantest;
+}
+
+template<typename T> FLATBUFFERS_CONSTEXPR size_t AlignOf() {
+  // clang-format off
+  #ifdef _MSC_VER
+    return __alignof(T);
+  #else
+    #ifndef alignof
+      return __alignof__(T);
+    #else
+      return alignof(T);
+    #endif
+  #endif
+  // clang-format on
+}
+
+// Lexicographically compare two strings (possibly containing nulls), and
+// return true if the first is less than the second.
+static inline bool StringLessThan(const char *a_data, uoffset_t a_size,
+                                  const char *b_data, uoffset_t b_size) {
+  const auto cmp = memcmp(a_data, b_data, (std::min)(a_size, b_size));
+  return cmp == 0 ? a_size < b_size : cmp < 0;
+}
+
+// When we read serialized data from memory, in the case of most scalars,
+// we want to just read T, but in the case of Offset, we want to actually
+// perform the indirection and return a pointer.
+// The template specialization below does just that.
+// It is wrapped in a struct since function templates can't overload on the
+// return type like this.
+// The typedef is for the convenience of callers of this function
+// (avoiding the need for a trailing return decltype)
+template<typename T> struct IndirectHelper {
+  typedef T return_type;
+  typedef T mutable_return_type;
+  static const size_t element_stride = sizeof(T);
+
+  static return_type Read(const uint8_t *p, const size_t i) {
+    return EndianScalar((reinterpret_cast<const T *>(p))[i]);
+  }
+  static mutable_return_type Read(uint8_t *p, const size_t i) {
+    return reinterpret_cast<mutable_return_type>(
+        Read(const_cast<const uint8_t *>(p), i));
+  }
+};
+
+// For vector of Offsets.
+template<typename T, template<typename> class OffsetT>
+struct IndirectHelper<OffsetT<T>> {
+  typedef const T *return_type;
+  typedef T *mutable_return_type;
+  typedef typename OffsetT<T>::offset_type offset_type;
+  static const offset_type element_stride = sizeof(offset_type);
+
+  static return_type Read(const uint8_t *const p, const offset_type i) {
+    // Offsets are relative to themselves, so first update the pointer to
+    // point to the offset location.
+    const uint8_t *const offset_location = p + i * element_stride;
+
+    // Then read the scalar value of the offset (which may be 32 or 64-bits) and
+    // then determine the relative location from the offset location.
+    return reinterpret_cast<return_type>(
+        offset_location + ReadScalar<offset_type>(offset_location));
+  }
+  static mutable_return_type Read(uint8_t *const p, const offset_type i) {
+    // Offsets are relative to themselves, so first update the pointer to
+    // point to the offset location.
+    uint8_t *const offset_location = p + i * element_stride;
+
+    // Then read the scalar value of the offset (which may be 32 or 64-bits) and
+    // then determine the relative location from the offset location.
+    return reinterpret_cast<mutable_return_type>(
+        offset_location + ReadScalar<offset_type>(offset_location));
+  }
+};
+
+// For vector of structs.
+template<typename T> struct IndirectHelper<const T *> {
+  typedef const T *return_type;
+  typedef T *mutable_return_type;
+  static const size_t element_stride = sizeof(T);
+
+  static return_type Read(const uint8_t *const p, const size_t i) {
+    // Structs are stored inline, relative to the first struct pointer.
+    return reinterpret_cast<return_type>(p + i * element_stride);
+  }
+  static mutable_return_type Read(uint8_t *const p, const size_t i) {
+    // Structs are stored inline, relative to the first struct pointer.
+    return reinterpret_cast<mutable_return_type>(p + i * element_stride);
+  }
+};
+
+/// @brief Get a pointer to the file_identifier section of the buffer.
+/// @return Returns a const char pointer to the start of the file_identifier
+/// characters in the buffer.  The returned char * has length
+/// 'flatbuffers::FlatBufferBuilder::kFileIdentifierLength'.
+/// This function is UNDEFINED for FlatBuffers whose schema does not include
+/// a file_identifier (likely points at padding or the start of a the root
+/// vtable).
+inline const char *GetBufferIdentifier(const void *buf,
+                                       bool size_prefixed = false) {
+  return reinterpret_cast<const char *>(buf) +
+         ((size_prefixed) ? 2 * sizeof(uoffset_t) : sizeof(uoffset_t));
+}
+
+// Helper to see if the identifier in a buffer has the expected value.
+inline bool BufferHasIdentifier(const void *buf, const char *identifier,
+                                bool size_prefixed = false) {
+  return strncmp(GetBufferIdentifier(buf, size_prefixed), identifier,
+                 flatbuffers::kFileIdentifierLength) == 0;
+}
+
+/// @cond FLATBUFFERS_INTERNAL
+// Helpers to get a typed pointer to the root object contained in the buffer.
+template<typename T> T *GetMutableRoot(void *buf) {
+  if (!buf) return nullptr;
+  EndianCheck();
+  return reinterpret_cast<T *>(
+      reinterpret_cast<uint8_t *>(buf) +
+      EndianScalar(*reinterpret_cast<uoffset_t *>(buf)));
+}
+
+template<typename T, typename SizeT = uoffset_t>
+T *GetMutableSizePrefixedRoot(void *buf) {
+  return GetMutableRoot<T>(reinterpret_cast<uint8_t *>(buf) + sizeof(SizeT));
+}
+
+template<typename T> const T *GetRoot(const void *buf) {
+  return GetMutableRoot<T>(const_cast<void *>(buf));
+}
+
+template<typename T, typename SizeT = uoffset_t>
+const T *GetSizePrefixedRoot(const void *buf) {
+  return GetRoot<T>(reinterpret_cast<const uint8_t *>(buf) + sizeof(SizeT));
+}
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_BUFFER_H_
@@ -0,0 +1,53 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_BUFFER_REF_H_
+#define FLATBUFFERS_BUFFER_REF_H_
+
+#include "flatbuffers/base.h"
+#include "flatbuffers/verifier.h"
+
+namespace flatbuffers {
+
+// Convenient way to bundle a buffer and its length, to pass it around
+// typed by its root.
+// A BufferRef does not own its buffer.
+struct BufferRefBase {};  // for std::is_base_of
+
+template<typename T> struct BufferRef : BufferRefBase {
+  BufferRef() : buf(nullptr), len(0), must_free(false) {}
+  BufferRef(uint8_t *_buf, uoffset_t _len)
+      : buf(_buf), len(_len), must_free(false) {}
+
+  ~BufferRef() {
+    if (must_free) free(buf);
+  }
+
+  const T *GetRoot() const { return flatbuffers::GetRoot<T>(buf); }
+
+  bool Verify() {
+    Verifier verifier(buf, len);
+    return verifier.VerifyBuffer<T>(nullptr);
+  }
+
+  uint8_t *buf;
+  uoffset_t len;
+  bool must_free;
+};
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_BUFFER_REF_H_
@@ -0,0 +1,64 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_DEFAULT_ALLOCATOR_H_
+#define FLATBUFFERS_DEFAULT_ALLOCATOR_H_
+
+#include "flatbuffers/allocator.h"
+#include "flatbuffers/base.h"
+
+namespace flatbuffers {
+
+// DefaultAllocator uses new/delete to allocate memory regions
+class DefaultAllocator : public Allocator {
+ public:
+  uint8_t *allocate(size_t size) FLATBUFFERS_OVERRIDE {
+    return new uint8_t[size];
+  }
+
+  void deallocate(uint8_t *p, size_t) FLATBUFFERS_OVERRIDE { delete[] p; }
+
+  static void dealloc(void *p, size_t) { delete[] static_cast<uint8_t *>(p); }
+};
+
+// These functions allow for a null allocator to mean use the default allocator,
+// as used by DetachedBuffer and vector_downward below.
+// This is to avoid having a statically or dynamically allocated default
+// allocator, or having to move it between the classes that may own it.
+inline uint8_t *Allocate(Allocator *allocator, size_t size) {
+  return allocator ? allocator->allocate(size)
+                   : DefaultAllocator().allocate(size);
+}
+
+inline void Deallocate(Allocator *allocator, uint8_t *p, size_t size) {
+  if (allocator)
+    allocator->deallocate(p, size);
+  else
+    DefaultAllocator().deallocate(p, size);
+}
+
+inline uint8_t *ReallocateDownward(Allocator *allocator, uint8_t *old_p,
+                                   size_t old_size, size_t new_size,
+                                   size_t in_use_back, size_t in_use_front) {
+  return allocator ? allocator->reallocate_downward(old_p, old_size, new_size,
+                                                    in_use_back, in_use_front)
+                   : DefaultAllocator().reallocate_downward(
+                         old_p, old_size, new_size, in_use_back, in_use_front);
+}
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_DEFAULT_ALLOCATOR_H_
@@ -0,0 +1,114 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_DETACHED_BUFFER_H_
+#define FLATBUFFERS_DETACHED_BUFFER_H_
+
+#include "flatbuffers/allocator.h"
+#include "flatbuffers/base.h"
+#include "flatbuffers/default_allocator.h"
+
+namespace flatbuffers {
+
+// DetachedBuffer is a finished flatbuffer memory region, detached from its
+// builder. The original memory region and allocator are also stored so that
+// the DetachedBuffer can manage the memory lifetime.
+class DetachedBuffer {
+ public:
+  DetachedBuffer()
+      : allocator_(nullptr),
+        own_allocator_(false),
+        buf_(nullptr),
+        reserved_(0),
+        cur_(nullptr),
+        size_(0) {}
+
+  DetachedBuffer(Allocator *allocator, bool own_allocator, uint8_t *buf,
+                 size_t reserved, uint8_t *cur, size_t sz)
+      : allocator_(allocator),
+        own_allocator_(own_allocator),
+        buf_(buf),
+        reserved_(reserved),
+        cur_(cur),
+        size_(sz) {}
+
+  DetachedBuffer(DetachedBuffer &&other) noexcept
+      : allocator_(other.allocator_),
+        own_allocator_(other.own_allocator_),
+        buf_(other.buf_),
+        reserved_(other.reserved_),
+        cur_(other.cur_),
+        size_(other.size_) {
+    other.reset();
+  }
+
+  DetachedBuffer &operator=(DetachedBuffer &&other) noexcept {
+    if (this == &other) return *this;
+
+    destroy();
+
+    allocator_ = other.allocator_;
+    own_allocator_ = other.own_allocator_;
+    buf_ = other.buf_;
+    reserved_ = other.reserved_;
+    cur_ = other.cur_;
+    size_ = other.size_;
+
+    other.reset();
+
+    return *this;
+  }
+
+  ~DetachedBuffer() { destroy(); }
+
+  const uint8_t *data() const { return cur_; }
+
+  uint8_t *data() { return cur_; }
+
+  size_t size() const { return size_; }
+
+  // These may change access mode, leave these at end of public section
+  FLATBUFFERS_DELETE_FUNC(DetachedBuffer(const DetachedBuffer &other));
+  FLATBUFFERS_DELETE_FUNC(
+      DetachedBuffer &operator=(const DetachedBuffer &other));
+
+ protected:
+  Allocator *allocator_;
+  bool own_allocator_;
+  uint8_t *buf_;
+  size_t reserved_;
+  uint8_t *cur_;
+  size_t size_;
+
+  inline void destroy() {
+    if (buf_) Deallocate(allocator_, buf_, reserved_);
+    if (own_allocator_ && allocator_) { delete allocator_; }
+    reset();
+  }
+
+  inline void reset() {
+    allocator_ = nullptr;
+    own_allocator_ = false;
+    buf_ = nullptr;
+    reserved_ = 0;
+    cur_ = nullptr;
+    size_ = 0;
+  }
+};
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_DETACHED_BUFFER_H_
@@ -0,0 +1,273 @@
+/*
+ * Copyright 2014 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_H_
+#define FLATBUFFERS_H_
+
+#include <algorithm>
+
+// TODO: These includes are for mitigating the pains of users editing their
+// source because they relied on flatbuffers.h to include everything for them.
+#include "flatbuffers/array.h"
+#include "flatbuffers/base.h"
+#include "flatbuffers/buffer.h"
+#include "flatbuffers/buffer_ref.h"
+#include "flatbuffers/detached_buffer.h"
+#include "flatbuffers/flatbuffer_builder.h"
+#include "flatbuffers/stl_emulation.h"
+#include "flatbuffers/string.h"
+#include "flatbuffers/struct.h"
+#include "flatbuffers/table.h"
+#include "flatbuffers/vector.h"
+#include "flatbuffers/vector_downward.h"
+#include "flatbuffers/verifier.h"
+
+namespace flatbuffers {
+
+/// @brief This can compute the start of a FlatBuffer from a root pointer, i.e.
+/// it is the opposite transformation of GetRoot().
+/// This may be useful if you want to pass on a root and have the recipient
+/// delete the buffer afterwards.
+inline const uint8_t *GetBufferStartFromRootPointer(const void *root) {
+  auto table = reinterpret_cast<const Table *>(root);
+  auto vtable = table->GetVTable();
+  // Either the vtable is before the root or after the root.
+  auto start = (std::min)(vtable, reinterpret_cast<const uint8_t *>(root));
+  // Align to at least sizeof(uoffset_t).
+  start = reinterpret_cast<const uint8_t *>(reinterpret_cast<uintptr_t>(start) &
+                                            ~(sizeof(uoffset_t) - 1));
+  // Additionally, there may be a file_identifier in the buffer, and the root
+  // offset. The buffer may have been aligned to any size between
+  // sizeof(uoffset_t) and FLATBUFFERS_MAX_ALIGNMENT (see "force_align").
+  // Sadly, the exact alignment is only known when constructing the buffer,
+  // since it depends on the presence of values with said alignment properties.
+  // So instead, we simply look at the next uoffset_t values (root,
+  // file_identifier, and alignment padding) to see which points to the root.
+  // None of the other values can "impersonate" the root since they will either
+  // be 0 or four ASCII characters.
+  static_assert(flatbuffers::kFileIdentifierLength == sizeof(uoffset_t),
+                "file_identifier is assumed to be the same size as uoffset_t");
+  for (auto possible_roots = FLATBUFFERS_MAX_ALIGNMENT / sizeof(uoffset_t) + 1;
+       possible_roots; possible_roots--) {
+    start -= sizeof(uoffset_t);
+    if (ReadScalar<uoffset_t>(start) + start ==
+        reinterpret_cast<const uint8_t *>(root))
+      return start;
+  }
+  // We didn't find the root, either the "root" passed isn't really a root,
+  // or the buffer is corrupt.
+  // Assert, because calling this function with bad data may cause reads
+  // outside of buffer boundaries.
+  FLATBUFFERS_ASSERT(false);
+  return nullptr;
+}
+
+/// @brief This return the prefixed size of a FlatBuffer.
+template<typename SizeT = uoffset_t>
+inline SizeT GetPrefixedSize(const uint8_t *buf) {
+  return ReadScalar<SizeT>(buf);
+}
+
+// Base class for native objects (FlatBuffer data de-serialized into native
+// C++ data structures).
+// Contains no functionality, purely documentative.
+struct NativeTable {};
+
+/// @brief Function types to be used with resolving hashes into objects and
+/// back again. The resolver gets a pointer to a field inside an object API
+/// object that is of the type specified in the schema using the attribute
+/// `cpp_type` (it is thus important whatever you write to this address
+/// matches that type). The value of this field is initially null, so you
+/// may choose to implement a delayed binding lookup using this function
+/// if you wish. The resolver does the opposite lookup, for when the object
+/// is being serialized again.
+typedef uint64_t hash_value_t;
+typedef std::function<void(void **pointer_adr, hash_value_t hash)>
+    resolver_function_t;
+typedef std::function<hash_value_t(void *pointer)> rehasher_function_t;
+
+// Helper function to test if a field is present, using any of the field
+// enums in the generated code.
+// `table` must be a generated table type. Since this is a template parameter,
+// this is not typechecked to be a subclass of Table, so beware!
+// Note: this function will return false for fields equal to the default
+// value, since they're not stored in the buffer (unless force_defaults was
+// used).
+template<typename T>
+bool IsFieldPresent(const T *table, typename T::FlatBuffersVTableOffset field) {
+  // Cast, since Table is a private baseclass of any table types.
+  return reinterpret_cast<const Table *>(table)->CheckField(
+      static_cast<voffset_t>(field));
+}
+
+// Utility function for reverse lookups on the EnumNames*() functions
+// (in the generated C++ code)
+// names must be NULL terminated.
+inline int LookupEnum(const char **names, const char *name) {
+  for (const char **p = names; *p; p++)
+    if (!strcmp(*p, name)) return static_cast<int>(p - names);
+  return -1;
+}
+
+// These macros allow us to layout a struct with a guarantee that they'll end
+// up looking the same on different compilers and platforms.
+// It does this by disallowing the compiler to do any padding, and then
+// does padding itself by inserting extra padding fields that make every
+// element aligned to its own size.
+// Additionally, it manually sets the alignment of the struct as a whole,
+// which is typically its largest element, or a custom size set in the schema
+// by the force_align attribute.
+// These are used in the generated code only.
+
+// clang-format off
+#if defined(_MSC_VER)
+  #define FLATBUFFERS_MANUALLY_ALIGNED_STRUCT(alignment) \
+    __pragma(pack(1)) \
+    struct __declspec(align(alignment))
+  #define FLATBUFFERS_STRUCT_END(name, size) \
+    __pragma(pack()) \
+    static_assert(sizeof(name) == size, "compiler breaks packing rules")
+#elif defined(__GNUC__) || defined(__clang__) || defined(__ICCARM__)
+  #define FLATBUFFERS_MANUALLY_ALIGNED_STRUCT(alignment) \
+    _Pragma("pack(1)") \
+    struct __attribute__((aligned(alignment)))
+  #define FLATBUFFERS_STRUCT_END(name, size) \
+    _Pragma("pack()") \
+    static_assert(sizeof(name) == size, "compiler breaks packing rules")
+#else
+  #error Unknown compiler, please define structure alignment macros
+#endif
+// clang-format on
+
+// Minimal reflection via code generation.
+// Besides full-fat reflection (see reflection.h) and parsing/printing by
+// loading schemas (see idl.h), we can also have code generation for minimal
+// reflection data which allows pretty-printing and other uses without needing
+// a schema or a parser.
+// Generate code with --reflect-types (types only) or --reflect-names (names
+// also) to enable.
+// See minireflect.h for utilities using this functionality.
+
+// These types are organized slightly differently as the ones in idl.h.
+enum SequenceType { ST_TABLE, ST_STRUCT, ST_UNION, ST_ENUM };
+
+// Scalars have the same order as in idl.h
+// clang-format off
+#define FLATBUFFERS_GEN_ELEMENTARY_TYPES(ET) \
+  ET(ET_UTYPE) \
+  ET(ET_BOOL) \
+  ET(ET_CHAR) \
+  ET(ET_UCHAR) \
+  ET(ET_SHORT) \
+  ET(ET_USHORT) \
+  ET(ET_INT) \
+  ET(ET_UINT) \
+  ET(ET_LONG) \
+  ET(ET_ULONG) \
+  ET(ET_FLOAT) \
+  ET(ET_DOUBLE) \
+  ET(ET_STRING) \
+  ET(ET_SEQUENCE)  // See SequenceType.
+
+enum ElementaryType {
+  #define FLATBUFFERS_ET(E) E,
+    FLATBUFFERS_GEN_ELEMENTARY_TYPES(FLATBUFFERS_ET)
+  #undef FLATBUFFERS_ET
+};
+
+inline const char * const *ElementaryTypeNames() {
+  static const char * const names[] = {
+    #define FLATBUFFERS_ET(E) #E,
+      FLATBUFFERS_GEN_ELEMENTARY_TYPES(FLATBUFFERS_ET)
+    #undef FLATBUFFERS_ET
+  };
+  return names;
+}
+// clang-format on
+
+// Basic type info cost just 16bits per field!
+// We're explicitly defining the signedness since the signedness of integer
+// bitfields is otherwise implementation-defined and causes warnings on older
+// GCC compilers.
+struct TypeCode {
+  // ElementaryType
+  unsigned short base_type : 4;
+  // Either vector (in table) or array (in struct)
+  unsigned short is_repeating : 1;
+  // Index into type_refs below, or -1 for none.
+  signed short sequence_ref : 11;
+};
+
+static_assert(sizeof(TypeCode) == 2, "TypeCode");
+
+struct TypeTable;
+
+// Signature of the static method present in each type.
+typedef const TypeTable *(*TypeFunction)();
+
+struct TypeTable {
+  SequenceType st;
+  size_t num_elems;  // of type_codes, values, names (but not type_refs).
+  const TypeCode *type_codes;     // num_elems count
+  const TypeFunction *type_refs;  // less than num_elems entries (see TypeCode).
+  const int16_t *array_sizes;     // less than num_elems entries (see TypeCode).
+  const int64_t *values;  // Only set for non-consecutive enum/union or structs.
+  const char *const *names;  // Only set if compiled with --reflect-names.
+};
+
+// String which identifies the current version of FlatBuffers.
+inline const char *flatbuffers_version_string() {
+  return "FlatBuffers " FLATBUFFERS_STRING(FLATBUFFERS_VERSION_MAJOR) "."
+      FLATBUFFERS_STRING(FLATBUFFERS_VERSION_MINOR) "."
+      FLATBUFFERS_STRING(FLATBUFFERS_VERSION_REVISION);
+}
+
+// clang-format off
+#define FLATBUFFERS_DEFINE_BITMASK_OPERATORS(E, T)\
+    inline E operator | (E lhs, E rhs){\
+        return E(T(lhs) | T(rhs));\
+    }\
+    inline E operator & (E lhs, E rhs){\
+        return E(T(lhs) & T(rhs));\
+    }\
+    inline E operator ^ (E lhs, E rhs){\
+        return E(T(lhs) ^ T(rhs));\
+    }\
+    inline E operator ~ (E lhs){\
+        return E(~T(lhs));\
+    }\
+    inline E operator |= (E &lhs, E rhs){\
+        lhs = lhs | rhs;\
+        return lhs;\
+    }\
+    inline E operator &= (E &lhs, E rhs){\
+        lhs = lhs & rhs;\
+        return lhs;\
+    }\
+    inline E operator ^= (E &lhs, E rhs){\
+        lhs = lhs ^ rhs;\
+        return lhs;\
+    }\
+    inline bool operator !(E rhs) \
+    {\
+        return !bool(T(rhs)); \
+    }
+/// @endcond
+}  // namespace flatbuffers
+
+// clang-format on
+
+#endif  // FLATBUFFERS_H_
@@ -0,0 +1,513 @@
+/*
+ * Copyright 2017 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_STL_EMULATION_H_
+#define FLATBUFFERS_STL_EMULATION_H_
+
+// clang-format off
+#include "flatbuffers/base.h"
+
+#include <string>
+#include <type_traits>
+#include <vector>
+#include <memory>
+#include <limits>
+
+#ifndef FLATBUFFERS_USE_STD_OPTIONAL
+  // Detect C++17 compatible compiler.
+  // __cplusplus >= 201703L - a compiler has support of 'static inline' variables.
+  #if (defined(__cplusplus) && __cplusplus >= 201703L) \
+      || (defined(_MSVC_LANG) && _MSVC_LANG >= 201703L)
+    #define FLATBUFFERS_USE_STD_OPTIONAL 1
+  #else
+    #define FLATBUFFERS_USE_STD_OPTIONAL 0
+  #endif // (defined(__cplusplus) && __cplusplus >= 201703L) ...
+#endif // FLATBUFFERS_USE_STD_OPTIONAL
+
+#if FLATBUFFERS_USE_STD_OPTIONAL
+  #include <optional>
+#endif
+
+#ifndef FLATBUFFERS_USE_STD_SPAN
+  // Testing __cpp_lib_span requires including either <version> or <span>,
+  // both of which were added in C++20.
+  // See: https://en.cppreference.com/w/cpp/utility/feature_test
+  #if defined(__cplusplus) && __cplusplus >= 202002L
+    #define FLATBUFFERS_USE_STD_SPAN 1
+  #endif
+#endif // FLATBUFFERS_USE_STD_SPAN
+
+#if defined(FLATBUFFERS_USE_STD_SPAN)
+  #include <array>
+  #include <span>
+#else
+  // Disable non-trivial ctors if FLATBUFFERS_SPAN_MINIMAL defined.
+  #if !defined(FLATBUFFERS_TEMPLATES_ALIASES)
+    #define FLATBUFFERS_SPAN_MINIMAL
+  #else
+    // Enable implicit construction of a span<T,N> from a std::array<T,N>.
+    #include <array>
+  #endif
+#endif // defined(FLATBUFFERS_USE_STD_SPAN)
+
+// This header provides backwards compatibility for older versions of the STL.
+namespace flatbuffers {
+
+#if defined(FLATBUFFERS_TEMPLATES_ALIASES)
+  template <typename T>
+  using numeric_limits = std::numeric_limits<T>;
+#else
+  template <typename T> class numeric_limits :
+    public std::numeric_limits<T> {};
+#endif  // defined(FLATBUFFERS_TEMPLATES_ALIASES)
+
+#if defined(FLATBUFFERS_TEMPLATES_ALIASES)
+  template <typename T> using is_scalar = std::is_scalar<T>;
+  template <typename T, typename U> using is_same = std::is_same<T,U>;
+  template <typename T> using is_floating_point = std::is_floating_point<T>;
+  template <typename T> using is_unsigned = std::is_unsigned<T>;
+  template <typename T> using is_enum = std::is_enum<T>;
+  template <typename T> using make_unsigned = std::make_unsigned<T>;
+  template<bool B, class T, class F>
+  using conditional = std::conditional<B, T, F>;
+  template<class T, T v>
+  using integral_constant = std::integral_constant<T, v>;
+  template <bool B>
+  using bool_constant = integral_constant<bool, B>;
+  using true_type  = std::true_type;
+  using false_type = std::false_type;
+#else
+  // MSVC 2010 doesn't support C++11 aliases.
+  template <typename T> struct is_scalar : public std::is_scalar<T> {};
+  template <typename T, typename U> struct is_same : public std::is_same<T,U> {};
+  template <typename T> struct is_floating_point :
+        public std::is_floating_point<T> {};
+  template <typename T> struct is_unsigned : public std::is_unsigned<T> {};
+  template <typename T> struct is_enum : public std::is_enum<T> {};
+  template <typename T> struct make_unsigned : public std::make_unsigned<T> {};
+  template<bool B, class T, class F>
+  struct conditional : public std::conditional<B, T, F> {};
+  template<class T, T v>
+  struct integral_constant : public std::integral_constant<T, v> {};
+  template <bool B>
+  struct bool_constant : public integral_constant<bool, B> {};
+  typedef bool_constant<true>  true_type;
+  typedef bool_constant<false> false_type;
+#endif  // defined(FLATBUFFERS_TEMPLATES_ALIASES)
+
+#if defined(FLATBUFFERS_TEMPLATES_ALIASES)
+  template <class T> using unique_ptr = std::unique_ptr<T>;
+#else
+  // MSVC 2010 doesn't support C++11 aliases.
+  // We're manually "aliasing" the class here as we want to bring unique_ptr
+  // into the flatbuffers namespace.  We have unique_ptr in the flatbuffers
+  // namespace we have a completely independent implementation (see below)
+  // for C++98 STL implementations.
+  template <class T> class unique_ptr : public std::unique_ptr<T> {
+    public:
+    unique_ptr() {}
+    explicit unique_ptr(T* p) : std::unique_ptr<T>(p) {}
+    unique_ptr(std::unique_ptr<T>&& u) { *this = std::move(u); }
+    unique_ptr(unique_ptr&& u) { *this = std::move(u); }
+    unique_ptr& operator=(std::unique_ptr<T>&& u) {
+      std::unique_ptr<T>::reset(u.release());
+      return *this;
+    }
+    unique_ptr& operator=(unique_ptr&& u) {
+      std::unique_ptr<T>::reset(u.release());
+      return *this;
+    }
+    unique_ptr& operator=(T* p) {
+      return std::unique_ptr<T>::operator=(p);
+    }
+  };
+#endif  // defined(FLATBUFFERS_TEMPLATES_ALIASES)
+
+#if FLATBUFFERS_USE_STD_OPTIONAL
+template<class T>
+using Optional = std::optional<T>;
+using nullopt_t = std::nullopt_t;
+inline constexpr nullopt_t nullopt = std::nullopt;
+
+#else
+// Limited implementation of Optional<T> type for a scalar T.
+// This implementation limited by trivial types compatible with
+// std::is_arithmetic<T> or std::is_enum<T> type traits.
+
+// A tag to indicate an empty flatbuffers::optional<T>.
+struct nullopt_t {
+  explicit FLATBUFFERS_CONSTEXPR_CPP11 nullopt_t(int) {}
+};
+
+#if defined(FLATBUFFERS_CONSTEXPR_DEFINED)
+  namespace internal {
+    template <class> struct nullopt_holder {
+      static constexpr nullopt_t instance_ = nullopt_t(0);
+    };
+    template<class Dummy>
+    constexpr nullopt_t nullopt_holder<Dummy>::instance_;
+  }
+  static constexpr const nullopt_t &nullopt = internal::nullopt_holder<void>::instance_;
+
+#else
+  namespace internal {
+    template <class> struct nullopt_holder {
+      static const nullopt_t instance_;
+    };
+    template<class Dummy>
+    const nullopt_t nullopt_holder<Dummy>::instance_  = nullopt_t(0);
+  }
+  static const nullopt_t &nullopt = internal::nullopt_holder<void>::instance_;
+
+#endif
+
+template<class T>
+class Optional FLATBUFFERS_FINAL_CLASS {
+  // Non-scalar 'T' would extremely complicated Optional<T>.
+  // Use is_scalar<T> checking because flatbuffers flatbuffers::is_arithmetic<T>
+  // isn't implemented.
+  static_assert(flatbuffers::is_scalar<T>::value, "unexpected type T");
+
+ public:
+  ~Optional() {}
+
+  FLATBUFFERS_CONSTEXPR_CPP11 Optional() FLATBUFFERS_NOEXCEPT
+    : value_(), has_value_(false) {}
+
+  FLATBUFFERS_CONSTEXPR_CPP11 Optional(nullopt_t) FLATBUFFERS_NOEXCEPT
+    : value_(), has_value_(false) {}
+
+  FLATBUFFERS_CONSTEXPR_CPP11 Optional(T val) FLATBUFFERS_NOEXCEPT
+    : value_(val), has_value_(true) {}
+
+  FLATBUFFERS_CONSTEXPR_CPP11 Optional(const Optional &other) FLATBUFFERS_NOEXCEPT
+    : value_(other.value_), has_value_(other.has_value_) {}
+
+  FLATBUFFERS_CONSTEXPR_CPP14 Optional &operator=(const Optional &other) FLATBUFFERS_NOEXCEPT {
+    value_ = other.value_;
+    has_value_ = other.has_value_;
+    return *this;
+  }
+
+  FLATBUFFERS_CONSTEXPR_CPP14 Optional &operator=(nullopt_t) FLATBUFFERS_NOEXCEPT {
+    value_ = T();
+    has_value_ = false;
+    return *this;
+  }
+
+  FLATBUFFERS_CONSTEXPR_CPP14 Optional &operator=(T val) FLATBUFFERS_NOEXCEPT {
+    value_ = val;
+    has_value_ = true;
+    return *this;
+  }
+
+  void reset() FLATBUFFERS_NOEXCEPT {
+    *this = nullopt;
+  }
+
+  void swap(Optional &other) FLATBUFFERS_NOEXCEPT {
+    std::swap(value_, other.value_);
+    std::swap(has_value_, other.has_value_);
+  }
+
+  FLATBUFFERS_CONSTEXPR_CPP11 FLATBUFFERS_EXPLICIT_CPP11 operator bool() const FLATBUFFERS_NOEXCEPT {
+    return has_value_;
+  }
+
+  FLATBUFFERS_CONSTEXPR_CPP11 bool has_value() const FLATBUFFERS_NOEXCEPT {
+    return has_value_;
+  }
+
+  FLATBUFFERS_CONSTEXPR_CPP11 const T& operator*() const FLATBUFFERS_NOEXCEPT {
+    return value_;
+  }
+
+  const T& value() const {
+    FLATBUFFERS_ASSERT(has_value());
+    return value_;
+  }
+
+  T value_or(T default_value) const FLATBUFFERS_NOEXCEPT {
+    return has_value() ? value_ : default_value;
+  }
+
+ private:
+  T value_;
+  bool has_value_;
+};
+
+template<class T>
+FLATBUFFERS_CONSTEXPR_CPP11 bool operator==(const Optional<T>& opt, nullopt_t) FLATBUFFERS_NOEXCEPT {
+  return !opt;
+}
+template<class T>
+FLATBUFFERS_CONSTEXPR_CPP11 bool operator==(nullopt_t, const Optional<T>& opt) FLATBUFFERS_NOEXCEPT {
+  return !opt;
+}
+
+template<class T, class U>
+FLATBUFFERS_CONSTEXPR_CPP11 bool operator==(const Optional<T>& lhs, const U& rhs) FLATBUFFERS_NOEXCEPT {
+  return static_cast<bool>(lhs) && (*lhs == rhs);
+}
+
+template<class T, class U>
+FLATBUFFERS_CONSTEXPR_CPP11 bool operator==(const T& lhs, const Optional<U>& rhs) FLATBUFFERS_NOEXCEPT {
+  return static_cast<bool>(rhs) && (lhs == *rhs);
+}
+
+template<class T, class U>
+FLATBUFFERS_CONSTEXPR_CPP11 bool operator==(const Optional<T>& lhs, const Optional<U>& rhs) FLATBUFFERS_NOEXCEPT {
+  return static_cast<bool>(lhs) != static_cast<bool>(rhs)
+              ? false
+              : !static_cast<bool>(lhs) ? false : (*lhs == *rhs);
+}
+#endif // FLATBUFFERS_USE_STD_OPTIONAL
+
+
+// Very limited and naive partial implementation of C++20 std::span<T,Extent>.
+#if defined(FLATBUFFERS_USE_STD_SPAN)
+  inline constexpr std::size_t dynamic_extent = std::dynamic_extent;
+  template<class T, std::size_t Extent = std::dynamic_extent>
+  using span = std::span<T, Extent>;
+
+#else // !defined(FLATBUFFERS_USE_STD_SPAN)
+FLATBUFFERS_CONSTEXPR std::size_t dynamic_extent = static_cast<std::size_t>(-1);
+
+// Exclude this code if MSVC2010 or non-STL Android is active.
+// The non-STL Android doesn't have `std::is_convertible` required for SFINAE.
+#if !defined(FLATBUFFERS_SPAN_MINIMAL)
+namespace internal {
+  // This is SFINAE helper class for checking of a common condition:
+  // > This overload only participates in overload resolution
+  // > Check whether a pointer to an array of From can be converted
+  // > to a pointer to an array of To.
+  // This helper is used for checking of 'From -> const From'.
+  template<class To, std::size_t Extent, class From, std::size_t N>
+  struct is_span_convertible {
+    using type =
+      typename std::conditional<std::is_convertible<From (*)[], To (*)[]>::value
+                                && (Extent == dynamic_extent || N == Extent),
+                                int, void>::type;
+  };
+
+  template<typename T>
+  struct SpanIterator {
+    // TODO: upgrade to std::random_access_iterator_tag.
+    using iterator_category = std::forward_iterator_tag;
+    using difference_type  = std::ptrdiff_t;
+    using value_type = typename std::remove_cv<T>::type;
+    using reference = T&;
+    using pointer   = T*;
+
+    // Convince MSVC compiler that this iterator is trusted (it is verified).
+    #ifdef _MSC_VER
+      using _Unchecked_type = pointer;
+    #endif // _MSC_VER
+
+    SpanIterator(pointer ptr) : ptr_(ptr) {}
+    reference operator*() const { return *ptr_; }
+    pointer operator->() { return ptr_; }
+    SpanIterator& operator++() { ptr_++; return *this; }  
+    SpanIterator  operator++(int) { auto tmp = *this; ++(*this); return tmp; }
+
+    friend bool operator== (const SpanIterator& lhs, const SpanIterator& rhs) { return lhs.ptr_ == rhs.ptr_; }
+    friend bool operator!= (const SpanIterator& lhs, const SpanIterator& rhs) { return lhs.ptr_ != rhs.ptr_; }
+
+   private:
+    pointer ptr_;
+  };
+}  // namespace internal
+#endif  // !defined(FLATBUFFERS_SPAN_MINIMAL)
+
+// T - element type; must be a complete type that is not an abstract
+// class type.
+// Extent - the number of elements in the sequence, or dynamic.
+template<class T, std::size_t Extent = dynamic_extent>
+class span FLATBUFFERS_FINAL_CLASS {
+ public:
+  typedef T element_type;
+  typedef T& reference;
+  typedef const T& const_reference;
+  typedef T* pointer;
+  typedef const T* const_pointer;
+  typedef std::size_t size_type;
+
+  static FLATBUFFERS_CONSTEXPR size_type extent = Extent;
+
+  // Returns the number of elements in the span.
+  FLATBUFFERS_CONSTEXPR_CPP11 size_type size() const FLATBUFFERS_NOEXCEPT {
+    return count_;
+  }
+
+  // Returns the size of the sequence in bytes.
+  FLATBUFFERS_CONSTEXPR_CPP11
+  size_type size_bytes() const FLATBUFFERS_NOEXCEPT {
+    return size() * sizeof(element_type);
+  }
+
+  // Checks if the span is empty.
+  FLATBUFFERS_CONSTEXPR_CPP11 bool empty() const FLATBUFFERS_NOEXCEPT {
+    return size() == 0;
+  }
+
+  // Returns a pointer to the beginning of the sequence.
+  FLATBUFFERS_CONSTEXPR_CPP11 pointer data() const FLATBUFFERS_NOEXCEPT {
+    return data_;
+  }
+
+  #if !defined(FLATBUFFERS_SPAN_MINIMAL)
+    using Iterator = internal::SpanIterator<T>;
+
+    Iterator begin() const { return Iterator(data()); }
+    Iterator end() const   { return Iterator(data() + size()); }
+  #endif
+
+  // Returns a reference to the idx-th element of the sequence.
+  // The behavior is undefined if the idx is greater than or equal to size().
+  FLATBUFFERS_CONSTEXPR_CPP11 reference operator[](size_type idx) const {
+    return data()[idx];
+  }
+
+  FLATBUFFERS_CONSTEXPR_CPP11 span(const span &other) FLATBUFFERS_NOEXCEPT
+      : data_(other.data_), count_(other.count_) {}
+
+  FLATBUFFERS_CONSTEXPR_CPP14 span &operator=(const span &other)
+      FLATBUFFERS_NOEXCEPT {
+    data_ = other.data_;
+    count_ = other.count_;
+  }
+
+  // Limited implementation of
+  // `template <class It> constexpr std::span(It first, size_type count);`.
+  //
+  // Constructs a span that is a view over the range [first, first + count);
+  // the resulting span has: data() == first and size() == count.
+  // The behavior is undefined if [first, first + count) is not a valid range,
+  // or if (extent != flatbuffers::dynamic_extent && count != extent).
+  FLATBUFFERS_CONSTEXPR_CPP11
+  explicit span(pointer first, size_type count) FLATBUFFERS_NOEXCEPT
+    : data_ (Extent == dynamic_extent ? first : (Extent == count ? first : nullptr)),
+      count_(Extent == dynamic_extent ? count : (Extent == count ? Extent : 0)) {
+      // Make span empty if the count argument is incompatible with span<T,N>.
+  }
+
+  // Exclude this code if MSVC2010 is active. The MSVC2010 isn't C++11
+  // compliant, it doesn't support default template arguments for functions.
+  #if defined(FLATBUFFERS_SPAN_MINIMAL)
+  FLATBUFFERS_CONSTEXPR_CPP11 span() FLATBUFFERS_NOEXCEPT : data_(nullptr),
+                                                            count_(0) {
+    static_assert(extent == 0 || extent == dynamic_extent, "invalid span");
+  }
+
+  #else
+  // Constructs an empty span whose data() == nullptr and size() == 0.
+  // This overload only participates in overload resolution if
+  // extent == 0 || extent == flatbuffers::dynamic_extent.
+  // A dummy template argument N is need dependency for SFINAE.
+  template<std::size_t N = 0,
+    typename internal::is_span_convertible<element_type, Extent, element_type, (N - N)>::type = 0>
+  FLATBUFFERS_CONSTEXPR_CPP11 span() FLATBUFFERS_NOEXCEPT : data_(nullptr),
+                                                            count_(0) {
+    static_assert(extent == 0 || extent == dynamic_extent, "invalid span");
+  }
+
+  // Constructs a span that is a view over the array arr; the resulting span
+  // has size() == N and data() == std::data(arr). These overloads only
+  // participate in overload resolution if
+  // extent == std::dynamic_extent || N == extent is true and
+  // std::remove_pointer_t<decltype(std::data(arr))>(*)[]
+  // is convertible to element_type (*)[].
+  template<std::size_t N,
+    typename internal::is_span_convertible<element_type, Extent, element_type, N>::type = 0>
+  FLATBUFFERS_CONSTEXPR_CPP11 span(element_type (&arr)[N]) FLATBUFFERS_NOEXCEPT
+      : data_(arr), count_(N) {}
+
+  template<class U, std::size_t N,
+    typename internal::is_span_convertible<element_type, Extent, U, N>::type = 0>
+  FLATBUFFERS_CONSTEXPR_CPP11 span(std::array<U, N> &arr) FLATBUFFERS_NOEXCEPT
+     : data_(arr.data()), count_(N) {}
+
+  //template<class U, std::size_t N,
+  //  int = 0>
+  //FLATBUFFERS_CONSTEXPR_CPP11 span(std::array<U, N> &arr) FLATBUFFERS_NOEXCEPT
+  //   : data_(arr.data()), count_(N) {}
+
+  template<class U, std::size_t N,
+    typename internal::is_span_convertible<element_type, Extent, U, N>::type = 0>
+  FLATBUFFERS_CONSTEXPR_CPP11 span(const std::array<U, N> &arr) FLATBUFFERS_NOEXCEPT
+    : data_(arr.data()), count_(N) {}
+
+  // Converting constructor from another span s;
+  // the resulting span has size() == s.size() and data() == s.data().
+  // This overload only participates in overload resolution
+  // if extent == std::dynamic_extent || N == extent is true and U (*)[]
+  // is convertible to element_type (*)[].
+  template<class U, std::size_t N,
+    typename internal::is_span_convertible<element_type, Extent, U, N>::type = 0>
+  FLATBUFFERS_CONSTEXPR_CPP11 span(const flatbuffers::span<U, N> &s) FLATBUFFERS_NOEXCEPT
+      : span(s.data(), s.size()) {
+  }
+
+  #endif  // !defined(FLATBUFFERS_SPAN_MINIMAL)
+
+ private:
+  // This is a naive implementation with 'count_' member even if (Extent != dynamic_extent).
+  pointer const data_;
+  size_type count_;
+};
+#endif  // defined(FLATBUFFERS_USE_STD_SPAN)
+
+#if !defined(FLATBUFFERS_SPAN_MINIMAL)
+template<class ElementType, std::size_t Extent>
+FLATBUFFERS_CONSTEXPR_CPP11
+flatbuffers::span<ElementType, Extent> make_span(ElementType(&arr)[Extent]) FLATBUFFERS_NOEXCEPT {
+  return span<ElementType, Extent>(arr);
+}
+
+template<class ElementType, std::size_t Extent>
+FLATBUFFERS_CONSTEXPR_CPP11
+flatbuffers::span<const ElementType, Extent> make_span(const ElementType(&arr)[Extent]) FLATBUFFERS_NOEXCEPT {
+  return span<const ElementType, Extent>(arr);
+}
+
+template<class ElementType, std::size_t Extent>
+FLATBUFFERS_CONSTEXPR_CPP11
+flatbuffers::span<ElementType, Extent> make_span(std::array<ElementType, Extent> &arr) FLATBUFFERS_NOEXCEPT {
+  return span<ElementType, Extent>(arr);
+}
+
+template<class ElementType, std::size_t Extent>
+FLATBUFFERS_CONSTEXPR_CPP11
+flatbuffers::span<const ElementType, Extent> make_span(const std::array<ElementType, Extent> &arr) FLATBUFFERS_NOEXCEPT {
+  return span<const ElementType, Extent>(arr);
+}
+
+template<class ElementType, std::size_t Extent>
+FLATBUFFERS_CONSTEXPR_CPP11
+flatbuffers::span<ElementType, dynamic_extent> make_span(ElementType *first, std::size_t count) FLATBUFFERS_NOEXCEPT {
+  return span<ElementType, dynamic_extent>(first, count);
+}
+
+template<class ElementType, std::size_t Extent>
+FLATBUFFERS_CONSTEXPR_CPP11
+flatbuffers::span<const ElementType, dynamic_extent> make_span(const ElementType *first, std::size_t count) FLATBUFFERS_NOEXCEPT {
+  return span<const ElementType, dynamic_extent>(first, count);
+}
+#endif // !defined(FLATBUFFERS_SPAN_MINIMAL)
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_STL_EMULATION_H_
@@ -0,0 +1,64 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_STRING_H_
+#define FLATBUFFERS_STRING_H_
+
+#include "flatbuffers/base.h"
+#include "flatbuffers/vector.h"
+
+namespace flatbuffers {
+
+struct String : public Vector<char> {
+  const char *c_str() const { return reinterpret_cast<const char *>(Data()); }
+  std::string str() const { return std::string(c_str(), size()); }
+
+  // clang-format off
+  #ifdef FLATBUFFERS_HAS_STRING_VIEW
+  flatbuffers::string_view string_view() const {
+    return flatbuffers::string_view(c_str(), size());
+  }
+  #endif // FLATBUFFERS_HAS_STRING_VIEW
+  // clang-format on
+
+  bool operator<(const String &o) const {
+    return StringLessThan(this->data(), this->size(), o.data(), o.size());
+  }
+};
+
+// Convenience function to get std::string from a String returning an empty
+// string on null pointer.
+static inline std::string GetString(const String *str) {
+  return str ? str->str() : "";
+}
+
+// Convenience function to get char* from a String returning an empty string on
+// null pointer.
+static inline const char *GetCstring(const String *str) {
+  return str ? str->c_str() : "";
+}
+
+#ifdef FLATBUFFERS_HAS_STRING_VIEW
+// Convenience function to get string_view from a String returning an empty
+// string_view on null pointer.
+static inline flatbuffers::string_view GetStringView(const String *str) {
+  return str ? str->string_view() : flatbuffers::string_view();
+}
+#endif  // FLATBUFFERS_HAS_STRING_VIEW
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_STRING_H_
@@ -0,0 +1,53 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_STRUCT_H_
+#define FLATBUFFERS_STRUCT_H_
+
+#include "flatbuffers/base.h"
+
+namespace flatbuffers {
+
+// "structs" are flat structures that do not have an offset table, thus
+// always have all members present and do not support forwards/backwards
+// compatible extensions.
+
+class Struct FLATBUFFERS_FINAL_CLASS {
+ public:
+  template<typename T> T GetField(uoffset_t o) const {
+    return ReadScalar<T>(&data_[o]);
+  }
+
+  template<typename T> T GetStruct(uoffset_t o) const {
+    return reinterpret_cast<T>(&data_[o]);
+  }
+
+  const uint8_t *GetAddressOf(uoffset_t o) const { return &data_[o]; }
+  uint8_t *GetAddressOf(uoffset_t o) { return &data_[o]; }
+
+ private:
+  // private constructor & copy constructor: you obtain instances of this
+  // class by pointing to existing data only
+  Struct();
+  Struct(const Struct &);
+  Struct &operator=(const Struct &);
+
+  uint8_t data_[1];
+};
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_STRUCT_H_
@@ -0,0 +1,188 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_TABLE_H_
+#define FLATBUFFERS_TABLE_H_
+
+#include "flatbuffers/base.h"
+#include "flatbuffers/verifier.h"
+
+namespace flatbuffers {
+
+// "tables" use an offset table (possibly shared) that allows fields to be
+// omitted and added at will, but uses an extra indirection to read.
+class Table {
+ public:
+  const uint8_t *GetVTable() const {
+    return data_ - ReadScalar<soffset_t>(data_);
+  }
+
+  // This gets the field offset for any of the functions below it, or 0
+  // if the field was not present.
+  voffset_t GetOptionalFieldOffset(voffset_t field) const {
+    // The vtable offset is always at the start.
+    auto vtable = GetVTable();
+    // The first element is the size of the vtable (fields + type id + itself).
+    auto vtsize = ReadScalar<voffset_t>(vtable);
+    // If the field we're accessing is outside the vtable, we're reading older
+    // data, so it's the same as if the offset was 0 (not present).
+    return field < vtsize ? ReadScalar<voffset_t>(vtable + field) : 0;
+  }
+
+  template<typename T> T GetField(voffset_t field, T defaultval) const {
+    auto field_offset = GetOptionalFieldOffset(field);
+    return field_offset ? ReadScalar<T>(data_ + field_offset) : defaultval;
+  }
+
+  template<typename P, typename OffsetSize = uoffset_t>
+  P GetPointer(voffset_t field) {
+    auto field_offset = GetOptionalFieldOffset(field);
+    auto p = data_ + field_offset;
+    return field_offset ? reinterpret_cast<P>(p + ReadScalar<OffsetSize>(p))
+                        : nullptr;
+  }
+  template<typename P, typename OffsetSize = uoffset_t>
+  P GetPointer(voffset_t field) const {
+    return const_cast<Table *>(this)->GetPointer<P, OffsetSize>(field);
+  }
+
+  template<typename P> P GetPointer64(voffset_t field) {
+    return GetPointer<P, uoffset64_t>(field);
+  }
+
+  template<typename P> P GetPointer64(voffset_t field) const {
+    return GetPointer<P, uoffset64_t>(field);
+  }
+
+  template<typename P> P GetStruct(voffset_t field) const {
+    auto field_offset = GetOptionalFieldOffset(field);
+    auto p = const_cast<uint8_t *>(data_ + field_offset);
+    return field_offset ? reinterpret_cast<P>(p) : nullptr;
+  }
+
+  template<typename Raw, typename Face>
+  flatbuffers::Optional<Face> GetOptional(voffset_t field) const {
+    auto field_offset = GetOptionalFieldOffset(field);
+    auto p = data_ + field_offset;
+    return field_offset ? Optional<Face>(static_cast<Face>(ReadScalar<Raw>(p)))
+                        : Optional<Face>();
+  }
+
+  template<typename T> bool SetField(voffset_t field, T val, T def) {
+    auto field_offset = GetOptionalFieldOffset(field);
+    if (!field_offset) return IsTheSameAs(val, def);
+    WriteScalar(data_ + field_offset, val);
+    return true;
+  }
+  template<typename T> bool SetField(voffset_t field, T val) {
+    auto field_offset = GetOptionalFieldOffset(field);
+    if (!field_offset) return false;
+    WriteScalar(data_ + field_offset, val);
+    return true;
+  }
+
+  bool SetPointer(voffset_t field, const uint8_t *val) {
+    auto field_offset = GetOptionalFieldOffset(field);
+    if (!field_offset) return false;
+    WriteScalar(data_ + field_offset,
+                static_cast<uoffset_t>(val - (data_ + field_offset)));
+    return true;
+  }
+
+  uint8_t *GetAddressOf(voffset_t field) {
+    auto field_offset = GetOptionalFieldOffset(field);
+    return field_offset ? data_ + field_offset : nullptr;
+  }
+  const uint8_t *GetAddressOf(voffset_t field) const {
+    return const_cast<Table *>(this)->GetAddressOf(field);
+  }
+
+  bool CheckField(voffset_t field) const {
+    return GetOptionalFieldOffset(field) != 0;
+  }
+
+  // Verify the vtable of this table.
+  // Call this once per table, followed by VerifyField once per field.
+  bool VerifyTableStart(Verifier &verifier) const {
+    return verifier.VerifyTableStart(data_);
+  }
+
+  // Verify a particular field.
+  template<typename T>
+  bool VerifyField(const Verifier &verifier, voffset_t field,
+                   size_t align) const {
+    // Calling GetOptionalFieldOffset should be safe now thanks to
+    // VerifyTable().
+    auto field_offset = GetOptionalFieldOffset(field);
+    // Check the actual field.
+    return !field_offset || verifier.VerifyField<T>(data_, field_offset, align);
+  }
+
+  // VerifyField for required fields.
+  template<typename T>
+  bool VerifyFieldRequired(const Verifier &verifier, voffset_t field,
+                           size_t align) const {
+    auto field_offset = GetOptionalFieldOffset(field);
+    return verifier.Check(field_offset != 0) &&
+           verifier.VerifyField<T>(data_, field_offset, align);
+  }
+
+  // Versions for offsets.
+  template<typename OffsetT = uoffset_t>
+  bool VerifyOffset(const Verifier &verifier, voffset_t field) const {
+    auto field_offset = GetOptionalFieldOffset(field);
+    return !field_offset || verifier.VerifyOffset<OffsetT>(data_, field_offset);
+  }
+
+  template<typename OffsetT = uoffset_t>
+  bool VerifyOffsetRequired(const Verifier &verifier, voffset_t field) const {
+    auto field_offset = GetOptionalFieldOffset(field);
+    return verifier.Check(field_offset != 0) &&
+           verifier.VerifyOffset<OffsetT>(data_, field_offset);
+  }
+ 
+  bool VerifyOffset64(const Verifier &verifier, voffset_t field) const {
+    return VerifyOffset<uoffset64_t>(verifier, field);
+  }
+
+  bool VerifyOffset64Required(const Verifier &verifier, voffset_t field) const {
+    return VerifyOffsetRequired<uoffset64_t>(verifier, field);
+  }
+
+ private:
+  // private constructor & copy constructor: you obtain instances of this
+  // class by pointing to existing data only
+  Table();
+  Table(const Table &other);
+  Table &operator=(const Table &);
+
+  uint8_t data_[1];
+};
+
+// This specialization allows avoiding warnings like:
+// MSVC C4800: type: forcing value to bool 'true' or 'false'.
+template<>
+inline flatbuffers::Optional<bool> Table::GetOptional<uint8_t, bool>(
+    voffset_t field) const {
+  auto field_offset = GetOptionalFieldOffset(field);
+  auto p = data_ + field_offset;
+  return field_offset ? Optional<bool>(ReadScalar<uint8_t>(p) != 0)
+                      : Optional<bool>();
+}
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_TABLE_H_
@@ -0,0 +1,400 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_VECTOR_H_
+#define FLATBUFFERS_VECTOR_H_
+
+#include "flatbuffers/base.h"
+#include "flatbuffers/buffer.h"
+#include "flatbuffers/stl_emulation.h"
+
+namespace flatbuffers {
+
+struct String;
+
+// An STL compatible iterator implementation for Vector below, effectively
+// calling Get() for every element.
+template<typename T, typename IT, typename Data = uint8_t *,
+         typename SizeT = uoffset_t>
+struct VectorIterator {
+  typedef std::random_access_iterator_tag iterator_category;
+  typedef IT value_type;
+  typedef ptrdiff_t difference_type;
+  typedef IT *pointer;
+  typedef IT &reference;
+
+  static const SizeT element_stride = IndirectHelper<T>::element_stride;
+
+  VectorIterator(Data data, SizeT i) : data_(data + element_stride * i) {}
+  VectorIterator(const VectorIterator &other) : data_(other.data_) {}
+  VectorIterator() : data_(nullptr) {}
+
+  VectorIterator &operator=(const VectorIterator &other) {
+    data_ = other.data_;
+    return *this;
+  }
+
+  VectorIterator &operator=(VectorIterator &&other) {
+    data_ = other.data_;
+    return *this;
+  }
+
+  bool operator==(const VectorIterator &other) const {
+    return data_ == other.data_;
+  }
+
+  bool operator<(const VectorIterator &other) const {
+    return data_ < other.data_;
+  }
+
+  bool operator!=(const VectorIterator &other) const {
+    return data_ != other.data_;
+  }
+
+  difference_type operator-(const VectorIterator &other) const {
+    return (data_ - other.data_) / element_stride;
+  }
+
+  // Note: return type is incompatible with the standard
+  // `reference operator*()`.
+  IT operator*() const { return IndirectHelper<T>::Read(data_, 0); }
+
+  // Note: return type is incompatible with the standard
+  // `pointer operator->()`.
+  IT operator->() const { return IndirectHelper<T>::Read(data_, 0); }
+
+  VectorIterator &operator++() {
+    data_ += element_stride;
+    return *this;
+  }
+
+  VectorIterator operator++(int) {
+    VectorIterator temp(data_, 0);
+    data_ += element_stride;
+    return temp;
+  }
+
+  VectorIterator operator+(const SizeT &offset) const {
+    return VectorIterator(data_ + offset * element_stride, 0);
+  }
+
+  VectorIterator &operator+=(const SizeT &offset) {
+    data_ += offset * element_stride;
+    return *this;
+  }
+
+  VectorIterator &operator--() {
+    data_ -= element_stride;
+    return *this;
+  }
+
+  VectorIterator operator--(int) {
+    VectorIterator temp(data_, 0);
+    data_ -= element_stride;
+    return temp;
+  }
+
+  VectorIterator operator-(const SizeT &offset) const {
+    return VectorIterator(data_ - offset * element_stride, 0);
+  }
+
+  VectorIterator &operator-=(const SizeT &offset) {
+    data_ -= offset * element_stride;
+    return *this;
+  }
+
+ private:
+  Data data_;
+};
+
+template<typename T, typename IT, typename SizeT = uoffset_t>
+using VectorConstIterator = VectorIterator<T, IT, const uint8_t *, SizeT>;
+
+template<typename Iterator>
+struct VectorReverseIterator : public std::reverse_iterator<Iterator> {
+  explicit VectorReverseIterator(Iterator iter)
+      : std::reverse_iterator<Iterator>(iter) {}
+
+  // Note: return type is incompatible with the standard
+  // `reference operator*()`.
+  typename Iterator::value_type operator*() const {
+    auto tmp = std::reverse_iterator<Iterator>::current;
+    return *--tmp;
+  }
+
+  // Note: return type is incompatible with the standard
+  // `pointer operator->()`.
+  typename Iterator::value_type operator->() const {
+    auto tmp = std::reverse_iterator<Iterator>::current;
+    return *--tmp;
+  }
+};
+
+// This is used as a helper type for accessing vectors.
+// Vector::data() assumes the vector elements start after the length field.
+template<typename T, typename SizeT = uoffset_t> class Vector {
+ public:
+  typedef VectorIterator<T,
+                         typename IndirectHelper<T>::mutable_return_type,
+                         uint8_t *, SizeT>
+      iterator;
+  typedef VectorConstIterator<T, typename IndirectHelper<T>::return_type,
+                              SizeT>
+      const_iterator;
+  typedef VectorReverseIterator<iterator> reverse_iterator;
+  typedef VectorReverseIterator<const_iterator> const_reverse_iterator;
+
+  typedef typename flatbuffers::bool_constant<flatbuffers::is_scalar<T>::value>
+      scalar_tag;
+
+  static FLATBUFFERS_CONSTEXPR bool is_span_observable =
+      scalar_tag::value && (FLATBUFFERS_LITTLEENDIAN || sizeof(T) == 1);
+
+  SizeT size() const { return EndianScalar(length_); }
+
+  // Deprecated: use size(). Here for backwards compatibility.
+  FLATBUFFERS_ATTRIBUTE([[deprecated("use size() instead")]])
+  SizeT Length() const { return size(); }
+
+  typedef SizeT size_type;
+  typedef typename IndirectHelper<T>::return_type return_type;
+  typedef typename IndirectHelper<T>::mutable_return_type
+      mutable_return_type;
+  typedef return_type value_type;
+
+  return_type Get(SizeT i) const {
+    FLATBUFFERS_ASSERT(i < size());
+    return IndirectHelper<T>::Read(Data(), i);
+  }
+
+  return_type operator[](SizeT i) const { return Get(i); }
+
+  // If this is a Vector of enums, T will be its storage type, not the enum
+  // type. This function makes it convenient to retrieve value with enum
+  // type E.
+  template<typename E> E GetEnum(SizeT i) const {
+    return static_cast<E>(Get(i));
+  }
+
+  // If this a vector of unions, this does the cast for you. There's no check
+  // to make sure this is the right type!
+  template<typename U> const U *GetAs(SizeT i) const {
+    return reinterpret_cast<const U *>(Get(i));
+  }
+
+  // If this a vector of unions, this does the cast for you. There's no check
+  // to make sure this is actually a string!
+  const String *GetAsString(SizeT i) const {
+    return reinterpret_cast<const String *>(Get(i));
+  }
+
+  const void *GetStructFromOffset(size_t o) const {
+    return reinterpret_cast<const void *>(Data() + o);
+  }
+
+  iterator begin() { return iterator(Data(), 0); }
+  const_iterator begin() const { return const_iterator(Data(), 0); }
+
+  iterator end() { return iterator(Data(), size()); }
+  const_iterator end() const { return const_iterator(Data(), size()); }
+
+  reverse_iterator rbegin() { return reverse_iterator(end()); }
+  const_reverse_iterator rbegin() const {
+    return const_reverse_iterator(end());
+  }
+
+  reverse_iterator rend() { return reverse_iterator(begin()); }
+  const_reverse_iterator rend() const {
+    return const_reverse_iterator(begin());
+  }
+
+  const_iterator cbegin() const { return begin(); }
+
+  const_iterator cend() const { return end(); }
+
+  const_reverse_iterator crbegin() const { return rbegin(); }
+
+  const_reverse_iterator crend() const { return rend(); }
+
+  // Change elements if you have a non-const pointer to this object.
+  // Scalars only. See reflection.h, and the documentation.
+  void Mutate(SizeT i, const T &val) {
+    FLATBUFFERS_ASSERT(i < size());
+    WriteScalar(data() + i, val);
+  }
+
+  // Change an element of a vector of tables (or strings).
+  // "val" points to the new table/string, as you can obtain from
+  // e.g. reflection::AddFlatBuffer().
+  void MutateOffset(SizeT i, const uint8_t *val) {
+    FLATBUFFERS_ASSERT(i < size());
+    static_assert(sizeof(T) == sizeof(SizeT), "Unrelated types");
+    WriteScalar(data() + i,
+                static_cast<SizeT>(val - (Data() + i * sizeof(SizeT))));
+  }
+
+  // Get a mutable pointer to tables/strings inside this vector.
+  mutable_return_type GetMutableObject(SizeT i) const {
+    FLATBUFFERS_ASSERT(i < size());
+    return const_cast<mutable_return_type>(IndirectHelper<T>::Read(Data(), i));
+  }
+
+  // The raw data in little endian format. Use with care.
+  const uint8_t *Data() const {
+    return reinterpret_cast<const uint8_t *>(&length_ + 1);
+  }
+
+  uint8_t *Data() { return reinterpret_cast<uint8_t *>(&length_ + 1); }
+
+  // Similarly, but typed, much like std::vector::data
+  const T *data() const { return reinterpret_cast<const T *>(Data()); }
+  T *data() { return reinterpret_cast<T *>(Data()); }
+
+  template<typename K> return_type LookupByKey(K key) const {
+    void *search_result = std::bsearch(
+        &key, Data(), size(), IndirectHelper<T>::element_stride, KeyCompare<K>);
+
+    if (!search_result) {
+      return nullptr;  // Key not found.
+    }
+
+    const uint8_t *element = reinterpret_cast<const uint8_t *>(search_result);
+
+    return IndirectHelper<T>::Read(element, 0);
+  }
+
+  template<typename K> mutable_return_type MutableLookupByKey(K key) {
+    return const_cast<mutable_return_type>(LookupByKey(key));
+  }
+
+ protected:
+  // This class is only used to access pre-existing data. Don't ever
+  // try to construct these manually.
+  Vector();
+
+  SizeT length_;
+
+ private:
+  // This class is a pointer. Copying will therefore create an invalid object.
+  // Private and unimplemented copy constructor.
+  Vector(const Vector &);
+  Vector &operator=(const Vector &);
+
+  template<typename K> static int KeyCompare(const void *ap, const void *bp) {
+    const K *key = reinterpret_cast<const K *>(ap);
+    const uint8_t *data = reinterpret_cast<const uint8_t *>(bp);
+    auto table = IndirectHelper<T>::Read(data, 0);
+
+    // std::bsearch compares with the operands transposed, so we negate the
+    // result here.
+    return -table->KeyCompareWithValue(*key);
+  }
+};
+
+template<typename T> using Vector64 = Vector<T, uoffset64_t>;
+
+template<class U>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<U> make_span(Vector<U> &vec)
+    FLATBUFFERS_NOEXCEPT {
+  static_assert(Vector<U>::is_span_observable,
+                "wrong type U, only LE-scalar, or byte types are allowed");
+  return span<U>(vec.data(), vec.size());
+}
+
+template<class U>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<const U> make_span(
+    const Vector<U> &vec) FLATBUFFERS_NOEXCEPT {
+  static_assert(Vector<U>::is_span_observable,
+                "wrong type U, only LE-scalar, or byte types are allowed");
+  return span<const U>(vec.data(), vec.size());
+}
+
+template<class U>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<uint8_t> make_bytes_span(
+    Vector<U> &vec) FLATBUFFERS_NOEXCEPT {
+  static_assert(Vector<U>::scalar_tag::value,
+                "wrong type U, only LE-scalar, or byte types are allowed");
+  return span<uint8_t>(vec.Data(), vec.size() * sizeof(U));
+}
+
+template<class U>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<const uint8_t> make_bytes_span(
+    const Vector<U> &vec) FLATBUFFERS_NOEXCEPT {
+  static_assert(Vector<U>::scalar_tag::value,
+                "wrong type U, only LE-scalar, or byte types are allowed");
+  return span<const uint8_t>(vec.Data(), vec.size() * sizeof(U));
+}
+
+// Convenient helper functions to get a span of any vector, regardless
+// of whether it is null or not (the field is not set).
+template<class U>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<U> make_span(Vector<U> *ptr)
+    FLATBUFFERS_NOEXCEPT {
+  static_assert(Vector<U>::is_span_observable,
+                "wrong type U, only LE-scalar, or byte types are allowed");
+  return ptr ? make_span(*ptr) : span<U>();
+}
+
+template<class U>
+FLATBUFFERS_CONSTEXPR_CPP11 flatbuffers::span<const U> make_span(
+    const Vector<U> *ptr) FLATBUFFERS_NOEXCEPT {
+  static_assert(Vector<U>::is_span_observable,
+                "wrong type U, only LE-scalar, or byte types are allowed");
+  return ptr ? make_span(*ptr) : span<const U>();
+}
+
+// Represent a vector much like the template above, but in this case we
+// don't know what the element types are (used with reflection.h).
+class VectorOfAny {
+ public:
+  uoffset_t size() const { return EndianScalar(length_); }
+
+  const uint8_t *Data() const {
+    return reinterpret_cast<const uint8_t *>(&length_ + 1);
+  }
+  uint8_t *Data() { return reinterpret_cast<uint8_t *>(&length_ + 1); }
+
+ protected:
+  VectorOfAny();
+
+  uoffset_t length_;
+
+ private:
+  VectorOfAny(const VectorOfAny &);
+  VectorOfAny &operator=(const VectorOfAny &);
+};
+
+template<typename T, typename U>
+Vector<Offset<T>> *VectorCast(Vector<Offset<U>> *ptr) {
+  static_assert(std::is_base_of<T, U>::value, "Unrelated types");
+  return reinterpret_cast<Vector<Offset<T>> *>(ptr);
+}
+
+template<typename T, typename U>
+const Vector<Offset<T>> *VectorCast(const Vector<Offset<U>> *ptr) {
+  static_assert(std::is_base_of<T, U>::value, "Unrelated types");
+  return reinterpret_cast<const Vector<Offset<T>> *>(ptr);
+}
+
+// Convenient helper function to get the length of any vector, regardless
+// of whether it is null or not (the field is not set).
+template<typename T> static inline size_t VectorLength(const Vector<T> *v) {
+  return v ? v->size() : 0;
+}
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_VERIFIER_H_
@@ -0,0 +1,288 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_VECTOR_DOWNWARD_H_
+#define FLATBUFFERS_VECTOR_DOWNWARD_H_
+
+#include <cstdint>
+
+#include <algorithm>
+
+#include "flatbuffers/base.h"
+#include "flatbuffers/default_allocator.h"
+#include "flatbuffers/detached_buffer.h"
+
+namespace flatbuffers {
+
+// This is a minimal replication of std::vector<uint8_t> functionality,
+// except growing from higher to lower addresses. i.e. push_back() inserts data
+// in the lowest address in the vector.
+// Since this vector leaves the lower part unused, we support a "scratch-pad"
+// that can be stored there for temporary data, to share the allocated space.
+// Essentially, this supports 2 std::vectors in a single buffer.
+template<typename SizeT = uoffset_t> class vector_downward {
+ public:
+  explicit vector_downward(size_t initial_size, Allocator *allocator,
+                           bool own_allocator, size_t buffer_minalign,
+                           const SizeT max_size = FLATBUFFERS_MAX_BUFFER_SIZE)
+      : allocator_(allocator),
+        own_allocator_(own_allocator),
+        initial_size_(initial_size),
+        max_size_(max_size),
+        buffer_minalign_(buffer_minalign),
+        reserved_(0),
+        size_(0),
+        buf_(nullptr),
+        cur_(nullptr),
+        scratch_(nullptr) {}
+
+  vector_downward(vector_downward &&other) noexcept
+      // clang-format on
+      : allocator_(other.allocator_),
+        own_allocator_(other.own_allocator_),
+        initial_size_(other.initial_size_),
+        max_size_(other.max_size_),
+        buffer_minalign_(other.buffer_minalign_),
+        reserved_(other.reserved_),
+        size_(other.size_),
+        buf_(other.buf_),
+        cur_(other.cur_),
+        scratch_(other.scratch_) {
+    // No change in other.allocator_
+    // No change in other.initial_size_
+    // No change in other.buffer_minalign_
+    other.own_allocator_ = false;
+    other.reserved_ = 0;
+    other.buf_ = nullptr;
+    other.cur_ = nullptr;
+    other.scratch_ = nullptr;
+  }
+
+  vector_downward &operator=(vector_downward &&other) noexcept {
+    // Move construct a temporary and swap idiom
+    vector_downward temp(std::move(other));
+    swap(temp);
+    return *this;
+  }
+
+  ~vector_downward() {
+    clear_buffer();
+    clear_allocator();
+  }
+
+  void reset() {
+    clear_buffer();
+    clear();
+  }
+
+  void clear() {
+    if (buf_) {
+      cur_ = buf_ + reserved_;
+    } else {
+      reserved_ = 0;
+      cur_ = nullptr;
+    }
+    size_ = 0;
+    clear_scratch();
+  }
+
+  void clear_scratch() { scratch_ = buf_; }
+
+  void clear_allocator() {
+    if (own_allocator_ && allocator_) { delete allocator_; }
+    allocator_ = nullptr;
+    own_allocator_ = false;
+  }
+
+  void clear_buffer() {
+    if (buf_) Deallocate(allocator_, buf_, reserved_);
+    buf_ = nullptr;
+  }
+
+  // Relinquish the pointer to the caller.
+  uint8_t *release_raw(size_t &allocated_bytes, size_t &offset) {
+    auto *buf = buf_;
+    allocated_bytes = reserved_;
+    offset = vector_downward::offset();
+
+    // release_raw only relinquishes the buffer ownership.
+    // Does not deallocate or reset the allocator. Destructor will do that.
+    buf_ = nullptr;
+    clear();
+    return buf;
+  }
+
+  // Relinquish the pointer to the caller.
+  DetachedBuffer release() {
+    // allocator ownership (if any) is transferred to DetachedBuffer.
+    DetachedBuffer fb(allocator_, own_allocator_, buf_, reserved_, cur_,
+                      size());
+    if (own_allocator_) {
+      allocator_ = nullptr;
+      own_allocator_ = false;
+    }
+    buf_ = nullptr;
+    clear();
+    return fb;
+  }
+
+  size_t ensure_space(size_t len) {
+    FLATBUFFERS_ASSERT(cur_ >= scratch_ && scratch_ >= buf_);
+    // If the length is larger than the unused part of the buffer, we need to
+    // grow.
+    if (len > unused_buffer_size()) { reallocate(len); }
+    FLATBUFFERS_ASSERT(size() < max_size_);
+    return len;
+  }
+
+  inline uint8_t *make_space(size_t len) {
+    if (len) {
+      ensure_space(len);
+      cur_ -= len;
+      size_ += static_cast<SizeT>(len);
+    }
+    return cur_;
+  }
+
+  // Returns nullptr if using the DefaultAllocator.
+  Allocator *get_custom_allocator() { return allocator_; }
+
+  // The current offset into the buffer.
+  size_t offset() const { return cur_ - buf_; }
+
+  // The total size of the vector (both the buffer and scratch parts).
+  inline SizeT size() const { return size_; }
+
+  // The size of the buffer part of the vector that is currently unused.
+  SizeT unused_buffer_size() const { return static_cast<SizeT>(cur_ - scratch_); }
+
+  // The size of the scratch part of the vector.
+  SizeT scratch_size() const { return static_cast<SizeT>(scratch_ - buf_); }
+
+  size_t capacity() const { return reserved_; }
+
+  uint8_t *data() const {
+    FLATBUFFERS_ASSERT(cur_);
+    return cur_;
+  }
+
+  uint8_t *scratch_data() const {
+    FLATBUFFERS_ASSERT(buf_);
+    return buf_;
+  }
+
+  uint8_t *scratch_end() const {
+    FLATBUFFERS_ASSERT(scratch_);
+    return scratch_;
+  }
+
+  uint8_t *data_at(size_t offset) const { return buf_ + reserved_ - offset; }
+
+  void push(const uint8_t *bytes, size_t num) {
+    if (num > 0) { memcpy(make_space(num), bytes, num); }
+  }
+
+  // Specialized version of push() that avoids memcpy call for small data.
+  template<typename T> void push_small(const T &little_endian_t) {
+    make_space(sizeof(T));
+    *reinterpret_cast<T *>(cur_) = little_endian_t;
+  }
+
+  template<typename T> void scratch_push_small(const T &t) {
+    ensure_space(sizeof(T));
+    *reinterpret_cast<T *>(scratch_) = t;
+    scratch_ += sizeof(T);
+  }
+
+  // fill() is most frequently called with small byte counts (<= 4),
+  // which is why we're using loops rather than calling memset.
+  void fill(size_t zero_pad_bytes) {
+    make_space(zero_pad_bytes);
+    for (size_t i = 0; i < zero_pad_bytes; i++) cur_[i] = 0;
+  }
+
+  // Version for when we know the size is larger.
+  // Precondition: zero_pad_bytes > 0
+  void fill_big(size_t zero_pad_bytes) {
+    memset(make_space(zero_pad_bytes), 0, zero_pad_bytes);
+  }
+
+  void pop(size_t bytes_to_remove) {
+    cur_ += bytes_to_remove;
+    size_ -= static_cast<SizeT>(bytes_to_remove);
+  }
+
+  void scratch_pop(size_t bytes_to_remove) { scratch_ -= bytes_to_remove; }
+
+  void swap(vector_downward &other) {
+    using std::swap;
+    swap(allocator_, other.allocator_);
+    swap(own_allocator_, other.own_allocator_);
+    swap(initial_size_, other.initial_size_);
+    swap(buffer_minalign_, other.buffer_minalign_);
+    swap(reserved_, other.reserved_);
+    swap(size_, other.size_);
+    swap(max_size_, other.max_size_);
+    swap(buf_, other.buf_);
+    swap(cur_, other.cur_);
+    swap(scratch_, other.scratch_);
+  }
+
+  void swap_allocator(vector_downward &other) {
+    using std::swap;
+    swap(allocator_, other.allocator_);
+    swap(own_allocator_, other.own_allocator_);
+  }
+
+ private:
+  // You shouldn't really be copying instances of this class.
+  FLATBUFFERS_DELETE_FUNC(vector_downward(const vector_downward &));
+  FLATBUFFERS_DELETE_FUNC(vector_downward &operator=(const vector_downward &));
+
+  Allocator *allocator_;
+  bool own_allocator_;
+  size_t initial_size_;
+
+  // The maximum size the vector can be.
+  SizeT max_size_;
+  size_t buffer_minalign_;
+  size_t reserved_;
+  SizeT size_;
+  uint8_t *buf_;
+  uint8_t *cur_;  // Points at location between empty (below) and used (above).
+  uint8_t *scratch_;  // Points to the end of the scratchpad in use.
+
+  void reallocate(size_t len) {
+    auto old_reserved = reserved_;
+    auto old_size = size();
+    auto old_scratch_size = scratch_size();
+    reserved_ +=
+        (std::max)(len, old_reserved ? old_reserved / 2 : initial_size_);
+    reserved_ = (reserved_ + buffer_minalign_ - 1) & ~(buffer_minalign_ - 1);
+    if (buf_) {
+      buf_ = ReallocateDownward(allocator_, buf_, old_reserved, reserved_,
+                                old_size, old_scratch_size);
+    } else {
+      buf_ = Allocate(allocator_, reserved_);
+    }
+    cur_ = buf_ + reserved_ - old_size;
+    scratch_ = buf_ + old_scratch_size;
+  }
+};
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_VECTOR_DOWNWARD_H_
@@ -0,0 +1,330 @@
+/*
+ * Copyright 2021 Google Inc. All rights reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef FLATBUFFERS_VERIFIER_H_
+#define FLATBUFFERS_VERIFIER_H_
+
+#include "flatbuffers/base.h"
+#include "flatbuffers/vector.h"
+
+namespace flatbuffers {
+
+// Helper class to verify the integrity of a FlatBuffer
+class Verifier FLATBUFFERS_FINAL_CLASS {
+ public:
+  struct Options {
+    // The maximum nesting of tables and vectors before we call it invalid.
+    uoffset_t max_depth = 64;
+    // The maximum number of tables we will verify before we call it invalid.
+    uoffset_t max_tables = 1000000;
+    // If true, verify all data is aligned.
+    bool check_alignment = true;
+    // If true, run verifier on nested flatbuffers
+    bool check_nested_flatbuffers = true;
+    // The maximum size of a buffer.
+    size_t max_size = FLATBUFFERS_MAX_BUFFER_SIZE;
+    // Use assertions to check for errors.
+    bool assert = false;
+  };
+
+  explicit Verifier(const uint8_t *const buf, const size_t buf_len,
+                    const Options &opts)
+      : buf_(buf), size_(buf_len), opts_(opts) {
+    FLATBUFFERS_ASSERT(size_ < opts.max_size);
+  }
+
+  // Deprecated API, please construct with Verifier::Options.
+  Verifier(const uint8_t *const buf, const size_t buf_len,
+           const uoffset_t max_depth = 64, const uoffset_t max_tables = 1000000,
+           const bool check_alignment = true)
+      : Verifier(buf, buf_len, [&] {
+          Options opts;
+          opts.max_depth = max_depth;
+          opts.max_tables = max_tables;
+          opts.check_alignment = check_alignment;
+          return opts;
+        }()) {}
+
+  // Central location where any verification failures register.
+  bool Check(const bool ok) const {
+    // clang-format off
+    #ifdef FLATBUFFERS_DEBUG_VERIFICATION_FAILURE
+       if (opts_.assert) { FLATBUFFERS_ASSERT(ok); }
+    #endif
+    #ifdef FLATBUFFERS_TRACK_VERIFIER_BUFFER_SIZE
+      if (!ok)
+        upper_bound_ = 0;
+    #endif
+    // clang-format on
+    return ok;
+  }
+
+  // Verify any range within the buffer.
+  bool Verify(const size_t elem, const size_t elem_len) const {
+    // clang-format off
+    #ifdef FLATBUFFERS_TRACK_VERIFIER_BUFFER_SIZE
+      auto upper_bound = elem + elem_len;
+      if (upper_bound_ < upper_bound)
+        upper_bound_ =  upper_bound;
+    #endif
+    // clang-format on
+    return Check(elem_len < size_ && elem <= size_ - elem_len);
+  }
+
+  bool VerifyAlignment(const size_t elem, const size_t align) const {
+    return Check((elem & (align - 1)) == 0 || !opts_.check_alignment);
+  }
+
+  // Verify a range indicated by sizeof(T).
+  template<typename T> bool Verify(const size_t elem) const {
+    return VerifyAlignment(elem, sizeof(T)) && Verify(elem, sizeof(T));
+  }
+
+  bool VerifyFromPointer(const uint8_t *const p, const size_t len) {
+    return Verify(static_cast<size_t>(p - buf_), len);
+  }
+
+  // Verify relative to a known-good base pointer.
+  bool VerifyFieldStruct(const uint8_t *const base, const voffset_t elem_off,
+                         const size_t elem_len, const size_t align) const {
+    const auto f = static_cast<size_t>(base - buf_) + elem_off;
+    return VerifyAlignment(f, align) && Verify(f, elem_len);
+  }
+
+  template<typename T>
+  bool VerifyField(const uint8_t *const base, const voffset_t elem_off,
+                   const size_t align) const {
+    const auto f = static_cast<size_t>(base - buf_) + elem_off;
+    return VerifyAlignment(f, align) && Verify(f, sizeof(T));
+  }
+
+  // Verify a pointer (may be NULL) of a table type.
+  template<typename T> bool VerifyTable(const T *const table) {
+    return !table || table->Verify(*this);
+  }
+
+  // Verify a pointer (may be NULL) of any vector type.
+  template<int &..., typename T, typename LenT>
+  bool VerifyVector(const Vector<T, LenT> *const vec) const {
+    return !vec || VerifyVectorOrString<LenT>(
+                       reinterpret_cast<const uint8_t *>(vec), sizeof(T));
+  }
+
+  // Verify a pointer (may be NULL) of a vector to struct.
+  template<int &..., typename T, typename LenT>
+  bool VerifyVector(const Vector<const T *, LenT> *const vec) const {
+    return VerifyVector(reinterpret_cast<const Vector<T, LenT> *>(vec));
+  }
+
+  // Verify a pointer (may be NULL) to string.
+  bool VerifyString(const String *const str) const {
+    size_t end;
+    return !str || (VerifyVectorOrString<uoffset_t>(
+                        reinterpret_cast<const uint8_t *>(str), 1, &end) &&
+                    Verify(end, 1) &&           // Must have terminator
+                    Check(buf_[end] == '\0'));  // Terminating byte must be 0.
+  }
+
+  // Common code between vectors and strings.
+  template<typename LenT = uoffset_t>
+  bool VerifyVectorOrString(const uint8_t *const vec, const size_t elem_size,
+                            size_t *const end = nullptr) const {
+    const auto vec_offset = static_cast<size_t>(vec - buf_);
+    // Check we can read the size field.
+    if (!Verify<LenT>(vec_offset)) return false;
+    // Check the whole array. If this is a string, the byte past the array must
+    // be 0.
+    const LenT size = ReadScalar<LenT>(vec);
+    const auto max_elems = opts_.max_size / elem_size;
+    if (!Check(size < max_elems))
+      return false;  // Protect against byte_size overflowing.
+    const auto byte_size = sizeof(LenT) + elem_size * size;
+    if (end) *end = vec_offset + byte_size;
+    return Verify(vec_offset, byte_size);
+  }
+
+  // Special case for string contents, after the above has been called.
+  bool VerifyVectorOfStrings(const Vector<Offset<String>> *const vec) const {
+    if (vec) {
+      for (uoffset_t i = 0; i < vec->size(); i++) {
+        if (!VerifyString(vec->Get(i))) return false;
+      }
+    }
+    return true;
+  }
+
+  // Special case for table contents, after the above has been called.
+  template<typename T>
+  bool VerifyVectorOfTables(const Vector<Offset<T>> *const vec) {
+    if (vec) {
+      for (uoffset_t i = 0; i < vec->size(); i++) {
+        if (!vec->Get(i)->Verify(*this)) return false;
+      }
+    }
+    return true;
+  }
+
+  __suppress_ubsan__("unsigned-integer-overflow") bool VerifyTableStart(
+      const uint8_t *const table) {
+    // Check the vtable offset.
+    const auto tableo = static_cast<size_t>(table - buf_);
+    if (!Verify<soffset_t>(tableo)) return false;
+    // This offset may be signed, but doing the subtraction unsigned always
+    // gives the result we want.
+    const auto vtableo =
+        tableo - static_cast<size_t>(ReadScalar<soffset_t>(table));
+    // Check the vtable size field, then check vtable fits in its entirety.
+    if (!(VerifyComplexity() && Verify<voffset_t>(vtableo) &&
+          VerifyAlignment(ReadScalar<voffset_t>(buf_ + vtableo),
+                          sizeof(voffset_t))))
+      return false;
+    const auto vsize = ReadScalar<voffset_t>(buf_ + vtableo);
+    return Check((vsize & 1) == 0) && Verify(vtableo, vsize);
+  }
+
+  template<typename T>
+  bool VerifyBufferFromStart(const char *const identifier, const size_t start) {
+    // Buffers have to be of some size to be valid. The reason it is a runtime
+    // check instead of static_assert, is that nested flatbuffers go through
+    // this call and their size is determined at runtime.
+    if (!Check(size_ >= FLATBUFFERS_MIN_BUFFER_SIZE)) return false;
+
+    // If an identifier is provided, check that we have a buffer
+    if (identifier && !Check((size_ >= 2 * sizeof(flatbuffers::uoffset_t) &&
+                              BufferHasIdentifier(buf_ + start, identifier)))) {
+      return false;
+    }
+
+    // Call T::Verify, which must be in the generated code for this type.
+    const auto o = VerifyOffset<uoffset_t>(start);
+    return Check(o != 0) &&
+           reinterpret_cast<const T *>(buf_ + start + o)->Verify(*this)
+    // clang-format off
+    #ifdef FLATBUFFERS_TRACK_VERIFIER_BUFFER_SIZE
+           && GetComputedSize()
+    #endif
+        ;
+    // clang-format on
+  }
+
+  template<typename T, int &..., typename SizeT>
+  bool VerifyNestedFlatBuffer(const Vector<uint8_t, SizeT> *const buf,
+                              const char *const identifier) {
+    // Caller opted out of this.
+    if (!opts_.check_nested_flatbuffers) return true;
+
+    // An empty buffer is OK as it indicates not present.
+    if (!buf) return true;
+
+    // If there is a nested buffer, it must be greater than the min size.
+    if (!Check(buf->size() >= FLATBUFFERS_MIN_BUFFER_SIZE)) return false;
+
+    Verifier nested_verifier(buf->data(), buf->size(), opts_);
+    return nested_verifier.VerifyBuffer<T>(identifier);
+  }
+
+  // Verify this whole buffer, starting with root type T.
+  template<typename T> bool VerifyBuffer() { return VerifyBuffer<T>(nullptr); }
+
+  template<typename T> bool VerifyBuffer(const char *const identifier) {
+    return VerifyBufferFromStart<T>(identifier, 0);
+  }
+
+  template<typename T, typename SizeT = uoffset_t>
+  bool VerifySizePrefixedBuffer(const char *const identifier) {
+    return Verify<SizeT>(0U) &&
+           Check(ReadScalar<SizeT>(buf_) == size_ - sizeof(SizeT)) &&
+           VerifyBufferFromStart<T>(identifier, sizeof(SizeT));
+  }
+
+  template<typename OffsetT = uoffset_t, typename SOffsetT = soffset_t>
+  size_t VerifyOffset(const size_t start) const {
+    if (!Verify<OffsetT>(start)) return 0;
+    const auto o = ReadScalar<OffsetT>(buf_ + start);
+    // May not point to itself.
+    if (!Check(o != 0)) return 0;
+    // Can't wrap around larger than the max size.
+    if (!Check(static_cast<SOffsetT>(o) >= 0)) return 0;
+    // Must be inside the buffer to create a pointer from it (pointer outside
+    // buffer is UB).
+    if (!Verify(start + o, 1)) return 0;
+    return o;
+  }
+
+  template<typename OffsetT = uoffset_t>
+  size_t VerifyOffset(const uint8_t *const base, const voffset_t start) const {
+    return VerifyOffset<OffsetT>(static_cast<size_t>(base - buf_) + start);
+  }
+
+  // Called at the start of a table to increase counters measuring data
+  // structure depth and amount, and possibly bails out with false if limits set
+  // by the constructor have been hit. Needs to be balanced with EndTable().
+  bool VerifyComplexity() {
+    depth_++;
+    num_tables_++;
+    return Check(depth_ <= opts_.max_depth && num_tables_ <= opts_.max_tables);
+  }
+
+  // Called at the end of a table to pop the depth count.
+  bool EndTable() {
+    depth_--;
+    return true;
+  }
+
+  // Returns the message size in bytes
+  size_t GetComputedSize() const {
+    // clang-format off
+    #ifdef FLATBUFFERS_TRACK_VERIFIER_BUFFER_SIZE
+      uintptr_t size = upper_bound_;
+      // Align the size to uoffset_t
+      size = (size - 1 + sizeof(uoffset_t)) & ~(sizeof(uoffset_t) - 1);
+      return (size > size_) ?  0 : size;
+    #else
+      // Must turn on FLATBUFFERS_TRACK_VERIFIER_BUFFER_SIZE for this to work.
+      (void)upper_bound_;
+      FLATBUFFERS_ASSERT(false);
+      return 0;
+    #endif
+    // clang-format on
+  }
+
+  std::vector<uint8_t> *GetFlexReuseTracker() { return flex_reuse_tracker_; }
+
+  void SetFlexReuseTracker(std::vector<uint8_t> *const rt) {
+    flex_reuse_tracker_ = rt;
+  }
+
+ private:
+  const uint8_t *buf_;
+  const size_t size_;
+  const Options opts_;
+
+  mutable size_t upper_bound_ = 0;
+
+  uoffset_t depth_ = 0;
+  uoffset_t num_tables_ = 0;
+  std::vector<uint8_t> *flex_reuse_tracker_ = nullptr;
+};
+
+// Specialization for 64-bit offsets.
+template<>
+inline size_t Verifier::VerifyOffset<uoffset64_t>(const size_t start) const {
+  return VerifyOffset<uoffset64_t, soffset64_t>(start);
+}
+
+}  // namespace flatbuffers
+
+#endif  // FLATBUFFERS_VERIFIER_H_
@@ -0,0 +1,9 @@
+cmake_minimum_required(VERSION ${MIN_VER_CMAKE} FATAL_ERROR)
+
+set(HAL_LIB_NAME "")
+
+set(RVV_HAL_FOUND TRUE CACHE INTERNAL "")
+set(RVV_HAL_VERSION "0.0.1" CACHE INTERNAL "")
+set(RVV_HAL_LIBRARIES ${HAL_LIB_NAME} CACHE INTERNAL "")
+set(RVV_HAL_HEADERS "hal_rvv.hpp" CACHE INTERNAL "")
+set(RVV_HAL_INCLUDE_DIRS "${CMAKE_CURRENT_SOURCE_DIR}" CACHE INTERNAL "")
@@ -0,0 +1,26 @@
+// This file is part of OpenCV project.
+// It is subject to the license terms in the LICENSE file found in the top-level directory
+// of this distribution and at http://opencv.org/license.html.
+
+#ifndef OPENCV_HAL_RVV_HPP_INCLUDED
+#define OPENCV_HAL_RVV_HPP_INCLUDED
+
+#include "opencv2/core/hal/interface.h"
+
+#ifndef CV_HAL_RVV_071_ENABLED
+#  if defined(__GNUC__) && __GNUC__ == 10 && __GNUC_MINOR__ == 4 && defined(__THEAD_VERSION__) && defined(__riscv_v) && __riscv_v == 7000
+#    define CV_HAL_RVV_071_ENABLED 1
+#  else
+#    define CV_HAL_RVV_071_ENABLED 0
+#  endif
+#endif
+
+#if CV_HAL_RVV_071_ENABLED
+#include "version/hal_rvv_071.hpp"
+#endif
+
+#if defined(__riscv_v) && __riscv_v == 1000000
+#include "hal_rvv_1p0/merge.hpp" // core
+#endif
+
+#endif
@@ -0,0 +1,366 @@
+// This file is part of OpenCV project.
+// It is subject to the license terms in the LICENSE file found in the top-level directory
+// of this distribution and at http://opencv.org/license.html.
+#ifndef OPENCV_HAL_RVV_MERGE_HPP_INCLUDED
+#define OPENCV_HAL_RVV_MERGE_HPP_INCLUDED
+
+#include <riscv_vector.h>
+
+namespace cv { namespace cv_hal_rvv {
+
+#undef cv_hal_merge8u
+#define cv_hal_merge8u cv::cv_hal_rvv::merge8u
+#undef cv_hal_merge16u
+#define cv_hal_merge16u cv::cv_hal_rvv::merge16u
+#undef cv_hal_merge32s
+#define cv_hal_merge32s cv::cv_hal_rvv::merge32s
+#undef cv_hal_merge64s
+#define cv_hal_merge64s cv::cv_hal_rvv::merge64s
+
+#if defined __GNUC__
+__attribute__((optimize("no-tree-vectorize")))
+#endif
+static int merge8u(const uchar** src, uchar* dst, int len, int cn ) {
+    int k = cn % 4 ? cn % 4 : 4;
+    int i = 0, j;
+    int vl = __riscv_vsetvlmax_e8m1();
+    if( k == 1 )
+    {
+        const uchar* src0 = src[0];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle8_v_u8m1(src0 + i, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn, sizeof(uchar)*2, a, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++)
+            dst[i*cn] = src0[i];
+    }
+    else if( k == 2 )
+    {
+        const uchar *src0 = src[0], *src1 = src[1];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle8_v_u8m1(src0 + i, vl);
+            auto b = __riscv_vle8_v_u8m1(src1 + i, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn, sizeof(uchar)*2, a, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn + 1, sizeof(uchar)*2, b, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++ )
+        {
+            dst[i*cn] = src0[i];
+            dst[i*cn+1] = src1[i];
+        }
+    }
+    else if( k == 3 )
+    {
+        const uchar *src0 = src[0], *src1 = src[1], *src2 = src[2];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle8_v_u8m1(src0 + i, vl);
+            auto b = __riscv_vle8_v_u8m1(src1 + i, vl);
+            auto c = __riscv_vle8_v_u8m1(src2 + i, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn, sizeof(uchar)*3, a, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn + 1, sizeof(uchar)*3, b, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn + 2, sizeof(uchar)*3, c, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++ )
+        {
+            dst[i*cn] = src0[i];
+            dst[i*cn+1] = src1[i];
+            dst[i*cn+2] = src2[i];
+        }
+    }
+    else
+    {
+        const uchar *src0 = src[0], *src1 = src[1], *src2 = src[2], *src3 = src[3];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle8_v_u8m1(src0 + i, vl);
+            auto b = __riscv_vle8_v_u8m1(src1 + i, vl);
+            auto c = __riscv_vle8_v_u8m1(src2 + i, vl);
+            auto d = __riscv_vle8_v_u8m1(src3 + i, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn, sizeof(uchar)*4, a, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn + 1, sizeof(uchar)*4, b, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn + 2, sizeof(uchar)*4, c, vl);
+            __riscv_vsse8_v_u8m1(dst + i*cn + 3, sizeof(uchar)*4, d, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++ )
+        {
+            dst[i*cn] = src0[i];
+            dst[i*cn+1] = src1[i];
+            dst[i*cn+2] = src2[i];
+            dst[i*cn+3] = src3[i];
+        }
+    }
+    #if defined(__clang__)
+    #pragma clang loop vectorize(disable)
+    #endif
+    for( ; k < cn; k += 4 )
+    {
+        const uchar *src0 = src[k], *src1 = src[k+1], *src2 = src[k+2], *src3 = src[k+3];
+        for( i = 0, j = k; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i]; dst[j+1] = src1[i];
+            dst[j+2] = src2[i]; dst[j+3] = src3[i];
+        }
+    }
+    return CV_HAL_ERROR_OK;
+}
+
+#if defined __GNUC__
+__attribute__((optimize("no-tree-vectorize")))
+#endif
+static int merge16u(const ushort** src, ushort* dst, int len, int cn ) {
+    int k = cn % 4 ? cn % 4 : 4;
+    int i = 0, j;
+    int vl = __riscv_vsetvlmax_e16m1();
+    if( k == 1 )
+    {
+        const ushort* src0 = src[0];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle16_v_u16m1(src0 + i, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn, sizeof(ushort)*2, a, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++)
+            dst[i*cn] = src0[i];
+    }
+    else if( k == 2 )
+    {
+        const ushort *src0 = src[0], *src1 = src[1];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle16_v_u16m1(src0 + i, vl);
+            auto b = __riscv_vle16_v_u16m1(src1 + i, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn, sizeof(ushort)*2, a, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn + 1, sizeof(ushort)*2, b, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++ )
+        {
+            dst[i*cn] = src0[i];
+            dst[i*cn+1] = src1[i];
+        }
+    }
+    else if( k == 3 )
+    {
+        const ushort *src0 = src[0], *src1 = src[1], *src2 = src[2];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle16_v_u16m1(src0 + i, vl);
+            auto b = __riscv_vle16_v_u16m1(src1 + i, vl);
+            auto c = __riscv_vle16_v_u16m1(src2 + i, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn, sizeof(ushort)*3, a, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn + 1, sizeof(ushort)*3, b, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn + 2, sizeof(ushort)*3, c, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++ )
+        {
+            dst[i*cn] = src0[i];
+            dst[i*cn+1] = src1[i];
+            dst[i*cn+2] = src2[i];
+        }
+    }
+    else
+    {
+        const ushort *src0 = src[0], *src1 = src[1], *src2 = src[2], *src3 = src[3];
+        for( ; i <= len - vl; i += vl)
+        {
+            auto a = __riscv_vle16_v_u16m1(src0 + i, vl);
+            auto b = __riscv_vle16_v_u16m1(src1 + i, vl);
+            auto c = __riscv_vle16_v_u16m1(src2 + i, vl);
+            auto d = __riscv_vle16_v_u16m1(src3 + i, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn, sizeof(ushort)*4, a, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn + 1, sizeof(ushort)*4, b, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn + 2, sizeof(ushort)*4, c, vl);
+            __riscv_vsse16_v_u16m1(dst + i*cn + 3, sizeof(ushort)*4, d, vl);
+        }
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++ )
+        {
+            dst[i*cn] = src0[i];
+            dst[i*cn+1] = src1[i];
+            dst[i*cn+2] = src2[i];
+            dst[i*cn+3] = src3[i];
+        }
+    }
+    #if defined(__clang__)
+    #pragma clang loop vectorize(disable)
+    #endif
+    for( ; k < cn; k += 4 )
+    {
+        const uint16_t *src0 = src[k], *src1 = src[k+1], *src2 = src[k+2], *src3 = src[k+3];
+        for( i = 0, j = k; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i]; dst[j+1] = src1[i];
+            dst[j+2] = src2[i]; dst[j+3] = src3[i];
+        }
+    }
+    return CV_HAL_ERROR_OK;
+}
+
+#if defined __GNUC__
+__attribute__((optimize("no-tree-vectorize")))
+#endif
+static int merge32s(const int** src, int* dst, int len, int cn ) {
+    int k = cn % 4 ? cn % 4 : 4;
+    int i, j;
+    if( k == 1 )
+    {
+        const int* src0 = src[0];
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( i = j = 0; i < len; i++, j += cn )
+            dst[j] = src0[i];
+    }
+    else if( k == 2 )
+    {
+        const int *src0 = src[0], *src1 = src[1];
+        i = j = 0;
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i];
+            dst[j+1] = src1[i];
+        }
+    }
+    else if( k == 3 )
+    {
+        const int *src0 = src[0], *src1 = src[1], *src2 = src[2];
+        i = j = 0;
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i];
+            dst[j+1] = src1[i];
+            dst[j+2] = src2[i];
+        }
+    }
+    else
+    {
+        const int *src0 = src[0], *src1 = src[1], *src2 = src[2], *src3 = src[3];
+        i = j = 0;
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i]; dst[j+1] = src1[i];
+            dst[j+2] = src2[i]; dst[j+3] = src3[i];
+        }
+    }
+    #if defined(__clang__)
+    #pragma clang loop vectorize(disable)
+    #endif
+    for( ; k < cn; k += 4 )
+    {
+        const int *src0 = src[k], *src1 = src[k+1], *src2 = src[k+2], *src3 = src[k+3];
+        for( i = 0, j = k; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i]; dst[j+1] = src1[i];
+            dst[j+2] = src2[i]; dst[j+3] = src3[i];
+        }
+    }
+    return CV_HAL_ERROR_OK;
+}
+
+#if defined __GNUC__
+__attribute__((optimize("no-tree-vectorize")))
+#endif
+static int merge64s(const int64** src, int64* dst, int len, int cn ) {
+    int k = cn % 4 ? cn % 4 : 4;
+    int i, j;
+    if( k == 1 )
+    {
+        const int64* src0 = src[0];
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( i = j = 0; i < len; i++, j += cn )
+            dst[j] = src0[i];
+    }
+    else if( k == 2 )
+    {
+        const int64 *src0 = src[0], *src1 = src[1];
+        i = j = 0;
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i];
+            dst[j+1] = src1[i];
+        }
+    }
+    else if( k == 3 )
+    {
+        const int64 *src0 = src[0], *src1 = src[1], *src2 = src[2];
+        i = j = 0;
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i];
+            dst[j+1] = src1[i];
+            dst[j+2] = src2[i];
+        }
+    }
+    else
+    {
+        const int64 *src0 = src[0], *src1 = src[1], *src2 = src[2], *src3 = src[3];
+        i = j = 0;
+        #if defined(__clang__)
+        #pragma clang loop vectorize(disable)
+        #endif
+        for( ; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i]; dst[j+1] = src1[i];
+            dst[j+2] = src2[i]; dst[j+3] = src3[i];
+        }
+    }
+    #if defined(__clang__)
+    #pragma clang loop vectorize(disable)
+    #endif
+    for( ; k < cn; k += 4 )
+    {
+        const int64 *src0 = src[k], *src1 = src[k+1], *src2 = src[k+2], *src3 = src[k+3];
+        for( i = 0, j = k; i < len; i++, j += cn )
+        {
+            dst[j] = src0[i]; dst[j+1] = src1[i];
+            dst[j+2] = src2[i]; dst[j+3] = src3[i];
+        }
+    }
+    return CV_HAL_ERROR_OK;
+}
+
+}}
+
+#endif
@@ -0,0 +1,109 @@
+// This file is part of OpenCV project.
+// It is subject to the license terms in the LICENSE file found in the top-level directory
+// of this distribution and at http://opencv.org/license.html.
+
+#ifndef OPENCV_HAL_RVV_071_HPP_INCLUDED
+#define OPENCV_HAL_RVV_071_HPP_INCLUDED
+
+#include <riscv_vector.h>
+
+#include <limits>
+
+namespace cv { namespace cv_hal_rvv {
+
+#undef cv_hal_cvtBGRtoBGR
+#define cv_hal_cvtBGRtoBGR cv::cv_hal_rvv::cvtBGRtoBGR
+
+static const unsigned char index_array_32 [32]
+                        { 2, 1, 0, 3, 6, 5, 4, 7, 10, 9, 8, 11, 14, 13, 12, 15, 18, 17, 16, 19, 22, 21, 20, 23, 26, 25, 24, 27, 30, 29, 28, 31  };
+
+static const unsigned char index_array_24 [24]
+                        { 2, 1, 0, 5, 4, 3, 8, 7, 6, 11, 10, 9, 14, 13, 12, 17, 16, 15, 20, 19, 18, 23, 22, 21  };
+
+static void vBGRtoBGR(const unsigned char* src, unsigned char * dst, const unsigned char * index, int n, int scn, int dcn, int vsize_pixels, const int vsize)
+{
+    vuint8m2_t vec_index = vle8_v_u8m2(index, vsize);
+
+    int i = 0;
+
+    for ( ; i <= n-vsize; i += vsize_pixels, src += vsize, dst += vsize)
+    {
+        vuint8m2_t vec_src = vle8_v_u8m2(src, vsize);
+        vuint8m2_t vec_dst = vrgather_vv_u8m2(vec_src, vec_index, vsize);
+        vse8_v_u8m2(dst, vec_dst, vsize);
+    }
+
+    for ( ; i < n; i++, src += scn, dst += dcn )
+    {
+        unsigned char t0 = src[0], t1 = src[1], t2 = src[2];
+        dst[2] = t0;
+        dst[1] = t1;
+        dst[0] = t2;
+        if(dcn == 4)
+        {
+            unsigned char d = src[3];
+            dst[3] = d;
+        }
+    }
+}
+
+static void sBGRtoBGR(const unsigned char* src, unsigned char * dst, int n, int scn, int dcn, int bi)
+{
+    for (int i = 0; i < n; i++, src += scn, dst += dcn)
+    {
+        unsigned char t0 = src[0], t1 = src[1], t2 = src[2];
+        dst[bi  ] = t0;
+        dst[1]    = t1;
+        dst[bi^2] = t2;
+        if(dcn == 4)
+        {
+            unsigned char d = scn == 4 ? src[3] : std::numeric_limits<unsigned char>::max();
+            dst[3] = d;
+        }
+    }
+}
+
+static int cvtBGRtoBGR(const unsigned char * src_data, size_t src_step, unsigned char * dst_data, size_t dst_step, int width, int height, int depth, int scn, int dcn, bool swapBlue)
+{
+    if (depth != CV_8U)
+    {
+        return CV_HAL_ERROR_NOT_IMPLEMENTED;
+    }
+
+    const int blueIdx = swapBlue ? 2 : 0;
+    if (scn == dcn)
+    {
+        if (!swapBlue)
+        {
+            return CV_HAL_ERROR_NOT_IMPLEMENTED;
+        }
+
+        const int vsize_pixels = 8;
+
+        if (scn == 4)
+        {
+            for (int i = 0; i < height; i++, src_data += src_step, dst_data += dst_step)
+            {
+                vBGRtoBGR(src_data, dst_data, index_array_32, width, scn, dcn, vsize_pixels, 32);
+            }
+        }
+        else
+        {
+            for (int i = 0; i < height; i++, src_data += src_step, dst_data += dst_step)
+            {
+                vBGRtoBGR(src_data, dst_data, index_array_24, width, scn, dcn, vsize_pixels, 24);
+            }
+        }
+    }
+    else
+    {
+        for (int i = 0; i < height; i++, src_data += src_step, dst_data += dst_step)
+            sBGRtoBGR(src_data, dst_data, width, scn, dcn, blueIdx);
+    }
+
+    return CV_HAL_ERROR_OK;
+}
+
+}}
+
+#endif
@@ -2,19 +2,9 @@
 // File: vk_platform.h
 //
 /*
-** Copyright (c) 2014-2017 The Khronos Group Inc.
+** Copyright 2014-2023 The Khronos Group Inc.
 **
-** Licensed under the Apache License, Version 2.0 (the "License");
-** you may not use this file except in compliance with the License.
-** You may obtain a copy of the License at
-**
-**     http://www.apache.org/licenses/LICENSE-2.0
-**
-** Unless required by applicable law or agreed to in writing, software
-** distributed under the License is distributed on an "AS IS" BASIS,
-** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-** See the License for the specific language governing permissions and
-** limitations under the License.
+** SPDX-License-Identifier: Apache-2.0
 */


@@ -52,7 +42,7 @@ extern "C"
    #define VKAPI_CALL __stdcall
    #define VKAPI_PTR  VKAPI_CALL
 #elif defined(__ANDROID__) && defined(__ARM_ARCH) && __ARM_ARCH < 7
-    #error "Vulkan isn't supported for the 'armeabi' NDK ABI"
+    #error "Vulkan is not supported for the 'armeabi' NDK ABI"
 #elif defined(__ANDROID__) && defined(__ARM_ARCH) && __ARM_ARCH >= 7 && defined(__ARM_32BIT_STATE)
    // On Android 32-bit ARM targets, Vulkan functions use the "hardfloat"
    // calling convention, i.e. float parameters are passed in registers. This
@@ -68,7 +58,9 @@ extern "C"
    #define VKAPI_PTR
 #endif

-#include <stddef.h>
+#if !defined(VK_NO_STDDEF_H)
+    #include <stddef.h>
+#endif // !defined(VK_NO_STDDEF_H)

 #if !defined(VK_NO_STDINT_H)
    #if defined(_MSC_VER) && (_MSC_VER < 1600)
@@ -2,19 +2,9 @@
 #define VULKAN_H_ 1

 /*
-** Copyright (c) 2015-2018 The Khronos Group Inc.
+** Copyright 2015-2023 The Khronos Group Inc.
 **
-** Licensed under the Apache License, Version 2.0 (the "License");
-** you may not use this file except in compliance with the License.
-** You may obtain a copy of the License at
-**
-**     http://www.apache.org/licenses/LICENSE-2.0
-**
-** Unless required by applicable law or agreed to in writing, software
-** distributed under the License is distributed on an "AS IS" BASIS,
-** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-** See the License for the specific language governing permissions and
-** limitations under the License.
+** SPDX-License-Identifier: Apache-2.0
 */

 #include "vk_platform.h"
@@ -38,20 +28,16 @@
 #include "vulkan_macos.h"
 #endif

-
-#ifdef VK_USE_PLATFORM_MIR_KHR
-#include <mir_toolkit/client_types.h>
-#include "vulkan_mir.h"
+#ifdef VK_USE_PLATFORM_METAL_EXT
+#include "vulkan_metal.h"
 #endif

-
 #ifdef VK_USE_PLATFORM_VI_NN
 #include "vulkan_vi.h"
 #endif


 #ifdef VK_USE_PLATFORM_WAYLAND_KHR
-#include <wayland-client.h>
 #include "vulkan_wayland.h"
 #endif

@@ -74,10 +60,40 @@
 #endif


+#ifdef VK_USE_PLATFORM_DIRECTFB_EXT
+#include <directfb.h>
+#include "vulkan_directfb.h"
+#endif
+
+
 #ifdef VK_USE_PLATFORM_XLIB_XRANDR_EXT
 #include <X11/Xlib.h>
 #include <X11/extensions/Xrandr.h>
 #include "vulkan_xlib_xrandr.h"
 #endif

+
+#ifdef VK_USE_PLATFORM_GGP
+#include <ggp_c/vulkan_types.h>
+#include "vulkan_ggp.h"
+#endif
+
+
+#ifdef VK_USE_PLATFORM_SCREEN_QNX
+#include <screen/screen.h>
+#include "vulkan_screen.h"
+#endif
+
+
+#ifdef VK_USE_PLATFORM_SCI
+#include <nvscisync.h>
+#include <nvscibuf.h>
+#include "vulkan_sci.h"
+#endif
+
+
+#ifdef VK_ENABLE_BETA_EXTENSIONS
+#include "vulkan_beta.h"
+#endif
+
 #endif // VULKAN_H_
@@ -1,24 +1,10 @@
 #ifndef VULKAN_ANDROID_H_
 #define VULKAN_ANDROID_H_ 1

-#ifdef __cplusplus
-extern "C" {
-#endif
-
 /*
-** Copyright (c) 2015-2018 The Khronos Group Inc.
+** Copyright 2015-2023 The Khronos Group Inc.
 **
-** Licensed under the Apache License, Version 2.0 (the "License");
-** you may not use this file except in compliance with the License.
-** You may obtain a copy of the License at
-**
-**     http://www.apache.org/licenses/LICENSE-2.0
-**
-** Unless required by applicable law or agreed to in writing, software
-** distributed under the License is distributed on an "AS IS" BASIS,
-** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-** See the License for the specific language governing permissions and
-** limitations under the License.
+** SPDX-License-Identifier: Apache-2.0
 */

 /*
@@ -27,14 +13,17 @@ extern "C" {
 */


+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+
 #define VK_KHR_android_surface 1
 struct ANativeWindow;
-
 #define VK_KHR_ANDROID_SURFACE_SPEC_VERSION 6
 #define VK_KHR_ANDROID_SURFACE_EXTENSION_NAME "VK_KHR_android_surface"
-
 typedef VkFlags VkAndroidSurfaceCreateFlagsKHR;
-
 typedef struct VkAndroidSurfaceCreateInfoKHR {
    VkStructureType                   sType;
    const void*                       pNext;
@@ -42,7 +31,6 @@ typedef struct VkAndroidSurfaceCreateInfoKHR {
    struct ANativeWindow*             window;
 } VkAndroidSurfaceCreateInfoKHR;

-
 typedef VkResult (VKAPI_PTR *PFN_vkCreateAndroidSurfaceKHR)(VkInstance instance, const VkAndroidSurfaceCreateInfoKHR* pCreateInfo, const VkAllocationCallbacks* pAllocator, VkSurfaceKHR* pSurface);

 #ifndef VK_NO_PROTOTYPES
@@ -53,12 +41,11 @@ VKAPI_ATTR VkResult VKAPI_CALL vkCreateAndroidSurfaceKHR(
    VkSurfaceKHR*                               pSurface);
 #endif

+
 #define VK_ANDROID_external_memory_android_hardware_buffer 1
 struct AHardwareBuffer;
-
-#define VK_ANDROID_EXTERNAL_MEMORY_ANDROID_HARDWARE_BUFFER_SPEC_VERSION 3
+#define VK_ANDROID_EXTERNAL_MEMORY_ANDROID_HARDWARE_BUFFER_SPEC_VERSION 5
 #define VK_ANDROID_EXTERNAL_MEMORY_ANDROID_HARDWARE_BUFFER_EXTENSION_NAME "VK_ANDROID_external_memory_android_hardware_buffer"
-
 typedef struct VkAndroidHardwareBufferUsageANDROID {
    VkStructureType    sType;
    void*              pNext;
@@ -103,6 +90,18 @@ typedef struct VkExternalFormatANDROID {
    uint64_t           externalFormat;
 } VkExternalFormatANDROID;

+typedef struct VkAndroidHardwareBufferFormatProperties2ANDROID {
+    VkStructureType                  sType;
+    void*                            pNext;
+    VkFormat                         format;
+    uint64_t                         externalFormat;
+    VkFormatFeatureFlags2            formatFeatures;
+    VkComponentMapping               samplerYcbcrConversionComponents;
+    VkSamplerYcbcrModelConversion    suggestedYcbcrModel;
+    VkSamplerYcbcrRange              suggestedYcbcrRange;
+    VkChromaLocation                 suggestedXChromaOffset;
+    VkChromaLocation                 suggestedYChromaOffset;
+} VkAndroidHardwareBufferFormatProperties2ANDROID;

 typedef VkResult (VKAPI_PTR *PFN_vkGetAndroidHardwareBufferPropertiesANDROID)(VkDevice device, const struct AHardwareBuffer* buffer, VkAndroidHardwareBufferPropertiesANDROID* pProperties);
 typedef VkResult (VKAPI_PTR *PFN_vkGetMemoryAndroidHardwareBufferANDROID)(VkDevice device, const VkMemoryGetAndroidHardwareBufferInfoANDROID* pInfo, struct AHardwareBuffer** pBuffer);
@@ -0,0 +1,492 @@
+#ifndef VULKAN_BETA_H_
+#define VULKAN_BETA_H_ 1
+
+/*
+** Copyright 2015-2023 The Khronos Group Inc.
+**
+** SPDX-License-Identifier: Apache-2.0
+*/
+
+/*
+** This header is generated from the Khronos Vulkan XML API Registry.
+**
+*/
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+
+#define VK_KHR_portability_subset 1
+#define VK_KHR_PORTABILITY_SUBSET_SPEC_VERSION 1
+#define VK_KHR_PORTABILITY_SUBSET_EXTENSION_NAME "VK_KHR_portability_subset"
+typedef struct VkPhysicalDevicePortabilitySubsetFeaturesKHR {
+    VkStructureType    sType;
+    void*              pNext;
+    VkBool32           constantAlphaColorBlendFactors;
+    VkBool32           events;
+    VkBool32           imageViewFormatReinterpretation;
+    VkBool32           imageViewFormatSwizzle;
+    VkBool32           imageView2DOn3DImage;
+    VkBool32           multisampleArrayImage;
+    VkBool32           mutableComparisonSamplers;
+    VkBool32           pointPolygons;
+    VkBool32           samplerMipLodBias;
+    VkBool32           separateStencilMaskRef;
+    VkBool32           shaderSampleRateInterpolationFunctions;
+    VkBool32           tessellationIsolines;
+    VkBool32           tessellationPointMode;
+    VkBool32           triangleFans;
+    VkBool32           vertexAttributeAccessBeyondStride;
+} VkPhysicalDevicePortabilitySubsetFeaturesKHR;
+
+typedef struct VkPhysicalDevicePortabilitySubsetPropertiesKHR {
+    VkStructureType    sType;
+    void*              pNext;
+    uint32_t           minVertexInputBindingStrideAlignment;
+} VkPhysicalDevicePortabilitySubsetPropertiesKHR;
+
+
+
+#define VK_KHR_video_encode_queue 1
+#define VK_KHR_VIDEO_ENCODE_QUEUE_SPEC_VERSION 8
+#define VK_KHR_VIDEO_ENCODE_QUEUE_EXTENSION_NAME "VK_KHR_video_encode_queue"
+
+typedef enum VkVideoEncodeTuningModeKHR {
+    VK_VIDEO_ENCODE_TUNING_MODE_DEFAULT_KHR = 0,
+    VK_VIDEO_ENCODE_TUNING_MODE_HIGH_QUALITY_KHR = 1,
+    VK_VIDEO_ENCODE_TUNING_MODE_LOW_LATENCY_KHR = 2,
+    VK_VIDEO_ENCODE_TUNING_MODE_ULTRA_LOW_LATENCY_KHR = 3,
+    VK_VIDEO_ENCODE_TUNING_MODE_LOSSLESS_KHR = 4,
+    VK_VIDEO_ENCODE_TUNING_MODE_MAX_ENUM_KHR = 0x7FFFFFFF
+} VkVideoEncodeTuningModeKHR;
+typedef VkFlags VkVideoEncodeFlagsKHR;
+
+typedef enum VkVideoEncodeCapabilityFlagBitsKHR {
+    VK_VIDEO_ENCODE_CAPABILITY_PRECEDING_EXTERNALLY_ENCODED_BYTES_BIT_KHR = 0x00000001,
+    VK_VIDEO_ENCODE_CAPABILITY_FLAG_BITS_MAX_ENUM_KHR = 0x7FFFFFFF
+} VkVideoEncodeCapabilityFlagBitsKHR;
+typedef VkFlags VkVideoEncodeCapabilityFlagsKHR;
+
+typedef enum VkVideoEncodeRateControlModeFlagBitsKHR {
+    VK_VIDEO_ENCODE_RATE_CONTROL_MODE_DEFAULT_KHR = 0,
+    VK_VIDEO_ENCODE_RATE_CONTROL_MODE_DISABLED_BIT_KHR = 0x00000001,
+    VK_VIDEO_ENCODE_RATE_CONTROL_MODE_CBR_BIT_KHR = 0x00000002,
+    VK_VIDEO_ENCODE_RATE_CONTROL_MODE_VBR_BIT_KHR = 0x00000004,
+    VK_VIDEO_ENCODE_RATE_CONTROL_MODE_FLAG_BITS_MAX_ENUM_KHR = 0x7FFFFFFF
+} VkVideoEncodeRateControlModeFlagBitsKHR;
+typedef VkFlags VkVideoEncodeRateControlModeFlagsKHR;
+
+typedef enum VkVideoEncodeFeedbackFlagBitsKHR {
+    VK_VIDEO_ENCODE_FEEDBACK_BITSTREAM_BUFFER_OFFSET_BIT_KHR = 0x00000001,
+    VK_VIDEO_ENCODE_FEEDBACK_BITSTREAM_BYTES_WRITTEN_BIT_KHR = 0x00000002,
+    VK_VIDEO_ENCODE_FEEDBACK_FLAG_BITS_MAX_ENUM_KHR = 0x7FFFFFFF
+} VkVideoEncodeFeedbackFlagBitsKHR;
+typedef VkFlags VkVideoEncodeFeedbackFlagsKHR;
+
+typedef enum VkVideoEncodeUsageFlagBitsKHR {
+    VK_VIDEO_ENCODE_USAGE_DEFAULT_KHR = 0,
+    VK_VIDEO_ENCODE_USAGE_TRANSCODING_BIT_KHR = 0x00000001,
+    VK_VIDEO_ENCODE_USAGE_STREAMING_BIT_KHR = 0x00000002,
+    VK_VIDEO_ENCODE_USAGE_RECORDING_BIT_KHR = 0x00000004,
+    VK_VIDEO_ENCODE_USAGE_CONFERENCING_BIT_KHR = 0x00000008,
+    VK_VIDEO_ENCODE_USAGE_FLAG_BITS_MAX_ENUM_KHR = 0x7FFFFFFF
+} VkVideoEncodeUsageFlagBitsKHR;
+typedef VkFlags VkVideoEncodeUsageFlagsKHR;
+
+typedef enum VkVideoEncodeContentFlagBitsKHR {
+    VK_VIDEO_ENCODE_CONTENT_DEFAULT_KHR = 0,
+    VK_VIDEO_ENCODE_CONTENT_CAMERA_BIT_KHR = 0x00000001,
+    VK_VIDEO_ENCODE_CONTENT_DESKTOP_BIT_KHR = 0x00000002,
+    VK_VIDEO_ENCODE_CONTENT_RENDERED_BIT_KHR = 0x00000004,
+    VK_VIDEO_ENCODE_CONTENT_FLAG_BITS_MAX_ENUM_KHR = 0x7FFFFFFF
+} VkVideoEncodeContentFlagBitsKHR;
+typedef VkFlags VkVideoEncodeContentFlagsKHR;
+typedef VkFlags VkVideoEncodeRateControlFlagsKHR;
+typedef struct VkVideoEncodeInfoKHR {
+    VkStructureType                       sType;
+    const void*                           pNext;
+    VkVideoEncodeFlagsKHR                 flags;
+    uint32_t                              qualityLevel;
+    VkBuffer                              dstBuffer;
+    VkDeviceSize                          dstBufferOffset;
+    VkDeviceSize                          dstBufferRange;
+    VkVideoPictureResourceInfoKHR         srcPictureResource;
+    const VkVideoReferenceSlotInfoKHR*    pSetupReferenceSlot;
+    uint32_t                              referenceSlotCount;
+    const VkVideoReferenceSlotInfoKHR*    pReferenceSlots;
+    uint32_t                              precedingExternallyEncodedBytes;
+} VkVideoEncodeInfoKHR;
+
+typedef struct VkVideoEncodeCapabilitiesKHR {
+    VkStructureType                         sType;
+    void*                                   pNext;
+    VkVideoEncodeCapabilityFlagsKHR         flags;
+    VkVideoEncodeRateControlModeFlagsKHR    rateControlModes;
+    uint32_t                                maxRateControlLayers;
+    uint32_t                                maxQualityLevels;
+    VkExtent2D                              inputImageDataFillAlignment;
+    VkVideoEncodeFeedbackFlagsKHR           supportedEncodeFeedbackFlags;
+} VkVideoEncodeCapabilitiesKHR;
+
+typedef struct VkQueryPoolVideoEncodeFeedbackCreateInfoKHR {
+    VkStructureType                  sType;
+    const void*                      pNext;
+    VkVideoEncodeFeedbackFlagsKHR    encodeFeedbackFlags;
+} VkQueryPoolVideoEncodeFeedbackCreateInfoKHR;
+
+typedef struct VkVideoEncodeUsageInfoKHR {
+    VkStructureType                 sType;
+    const void*                     pNext;
+    VkVideoEncodeUsageFlagsKHR      videoUsageHints;
+    VkVideoEncodeContentFlagsKHR    videoContentHints;
+    VkVideoEncodeTuningModeKHR      tuningMode;
+} VkVideoEncodeUsageInfoKHR;
+
+typedef struct VkVideoEncodeRateControlLayerInfoKHR {
+    VkStructureType    sType;
+    const void*        pNext;
+    uint64_t           averageBitrate;
+    uint64_t           maxBitrate;
+    uint32_t           frameRateNumerator;
+    uint32_t           frameRateDenominator;
+    uint32_t           virtualBufferSizeInMs;
+    uint32_t           initialVirtualBufferSizeInMs;
+} VkVideoEncodeRateControlLayerInfoKHR;
+
+typedef struct VkVideoEncodeRateControlInfoKHR {
+    VkStructureType                                sType;
+    const void*                                    pNext;
+    VkVideoEncodeRateControlFlagsKHR               flags;
+    VkVideoEncodeRateControlModeFlagBitsKHR        rateControlMode;
+    uint32_t                                       layerCount;
+    const VkVideoEncodeRateControlLayerInfoKHR*    pLayers;
+} VkVideoEncodeRateControlInfoKHR;
+
+typedef void (VKAPI_PTR *PFN_vkCmdEncodeVideoKHR)(VkCommandBuffer commandBuffer, const VkVideoEncodeInfoKHR* pEncodeInfo);
+
+#ifndef VK_NO_PROTOTYPES
+VKAPI_ATTR void VKAPI_CALL vkCmdEncodeVideoKHR(
+    VkCommandBuffer                             commandBuffer,
+    const VkVideoEncodeInfoKHR*                 pEncodeInfo);
+#endif
+
+
+#define VK_EXT_video_encode_h264 1
+#include "vk_video/vulkan_video_codec_h264std.h"
+#include "vk_video/vulkan_video_codec_h264std_encode.h"
+#define VK_EXT_VIDEO_ENCODE_H264_SPEC_VERSION 10
+#define VK_EXT_VIDEO_ENCODE_H264_EXTENSION_NAME "VK_EXT_video_encode_h264"
+
+typedef enum VkVideoEncodeH264RateControlStructureEXT {
+    VK_VIDEO_ENCODE_H264_RATE_CONTROL_STRUCTURE_UNKNOWN_EXT = 0,
+    VK_VIDEO_ENCODE_H264_RATE_CONTROL_STRUCTURE_FLAT_EXT = 1,
+    VK_VIDEO_ENCODE_H264_RATE_CONTROL_STRUCTURE_DYADIC_EXT = 2,
+    VK_VIDEO_ENCODE_H264_RATE_CONTROL_STRUCTURE_MAX_ENUM_EXT = 0x7FFFFFFF
+} VkVideoEncodeH264RateControlStructureEXT;
+
+typedef enum VkVideoEncodeH264CapabilityFlagBitsEXT {
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DIRECT_8X8_INFERENCE_ENABLED_BIT_EXT = 0x00000001,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DIRECT_8X8_INFERENCE_DISABLED_BIT_EXT = 0x00000002,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_SEPARATE_COLOUR_PLANE_BIT_EXT = 0x00000004,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_QPPRIME_Y_ZERO_TRANSFORM_BYPASS_BIT_EXT = 0x00000008,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_SCALING_LISTS_BIT_EXT = 0x00000010,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_HRD_COMPLIANCE_BIT_EXT = 0x00000020,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_CHROMA_QP_OFFSET_BIT_EXT = 0x00000040,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_SECOND_CHROMA_QP_OFFSET_BIT_EXT = 0x00000080,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_PIC_INIT_QP_MINUS26_BIT_EXT = 0x00000100,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_WEIGHTED_PRED_BIT_EXT = 0x00000200,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_WEIGHTED_BIPRED_EXPLICIT_BIT_EXT = 0x00000400,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_WEIGHTED_BIPRED_IMPLICIT_BIT_EXT = 0x00000800,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_WEIGHTED_PRED_NO_TABLE_BIT_EXT = 0x00001000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_TRANSFORM_8X8_BIT_EXT = 0x00002000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_CABAC_BIT_EXT = 0x00004000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_CAVLC_BIT_EXT = 0x00008000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DEBLOCKING_FILTER_DISABLED_BIT_EXT = 0x00010000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DEBLOCKING_FILTER_ENABLED_BIT_EXT = 0x00020000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DEBLOCKING_FILTER_PARTIAL_BIT_EXT = 0x00040000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DISABLE_DIRECT_SPATIAL_MV_PRED_BIT_EXT = 0x00080000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_MULTIPLE_SLICE_PER_FRAME_BIT_EXT = 0x00100000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_SLICE_MB_COUNT_BIT_EXT = 0x00200000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_ROW_UNALIGNED_SLICE_BIT_EXT = 0x00400000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DIFFERENT_SLICE_TYPE_BIT_EXT = 0x00800000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_B_FRAME_IN_L1_LIST_BIT_EXT = 0x01000000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_DIFFERENT_REFERENCE_FINAL_LISTS_BIT_EXT = 0x02000000,
+    VK_VIDEO_ENCODE_H264_CAPABILITY_FLAG_BITS_MAX_ENUM_EXT = 0x7FFFFFFF
+} VkVideoEncodeH264CapabilityFlagBitsEXT;
+typedef VkFlags VkVideoEncodeH264CapabilityFlagsEXT;
+typedef struct VkVideoEncodeH264CapabilitiesEXT {
+    VkStructureType                        sType;
+    void*                                  pNext;
+    VkVideoEncodeH264CapabilityFlagsEXT    flags;
+    uint32_t                               maxPPictureL0ReferenceCount;
+    uint32_t                               maxBPictureL0ReferenceCount;
+    uint32_t                               maxL1ReferenceCount;
+    VkBool32                               motionVectorsOverPicBoundariesFlag;
+    uint32_t                               maxBytesPerPicDenom;
+    uint32_t                               maxBitsPerMbDenom;
+    uint32_t                               log2MaxMvLengthHorizontal;
+    uint32_t                               log2MaxMvLengthVertical;
+} VkVideoEncodeH264CapabilitiesEXT;
+
+typedef struct VkVideoEncodeH264SessionParametersAddInfoEXT {
+    VkStructureType                            sType;
+    const void*                                pNext;
+    uint32_t                                   stdSPSCount;
+    const StdVideoH264SequenceParameterSet*    pStdSPSs;
+    uint32_t                                   stdPPSCount;
+    const StdVideoH264PictureParameterSet*     pStdPPSs;
+} VkVideoEncodeH264SessionParametersAddInfoEXT;
+
+typedef struct VkVideoEncodeH264SessionParametersCreateInfoEXT {
+    VkStructureType                                        sType;
+    const void*                                            pNext;
+    uint32_t                                               maxStdSPSCount;
+    uint32_t                                               maxStdPPSCount;
+    const VkVideoEncodeH264SessionParametersAddInfoEXT*    pParametersAddInfo;
+} VkVideoEncodeH264SessionParametersCreateInfoEXT;
+
+typedef struct VkVideoEncodeH264NaluSliceInfoEXT {
+    VkStructureType                                sType;
+    const void*                                    pNext;
+    uint32_t                                       mbCount;
+    const StdVideoEncodeH264ReferenceListsInfo*    pStdReferenceFinalLists;
+    const StdVideoEncodeH264SliceHeader*           pStdSliceHeader;
+} VkVideoEncodeH264NaluSliceInfoEXT;
+
+typedef struct VkVideoEncodeH264VclFrameInfoEXT {
+    VkStructureType                                sType;
+    const void*                                    pNext;
+    const StdVideoEncodeH264ReferenceListsInfo*    pStdReferenceFinalLists;
+    uint32_t                                       naluSliceEntryCount;
+    const VkVideoEncodeH264NaluSliceInfoEXT*       pNaluSliceEntries;
+    const StdVideoEncodeH264PictureInfo*           pStdPictureInfo;
+} VkVideoEncodeH264VclFrameInfoEXT;
+
+typedef struct VkVideoEncodeH264DpbSlotInfoEXT {
+    VkStructureType                           sType;
+    const void*                               pNext;
+    const StdVideoEncodeH264ReferenceInfo*    pStdReferenceInfo;
+} VkVideoEncodeH264DpbSlotInfoEXT;
+
+typedef struct VkVideoEncodeH264ProfileInfoEXT {
+    VkStructureType           sType;
+    const void*               pNext;
+    StdVideoH264ProfileIdc    stdProfileIdc;
+} VkVideoEncodeH264ProfileInfoEXT;
+
+typedef struct VkVideoEncodeH264RateControlInfoEXT {
+    VkStructureType                             sType;
+    const void*                                 pNext;
+    uint32_t                                    gopFrameCount;
+    uint32_t                                    idrPeriod;
+    uint32_t                                    consecutiveBFrameCount;
+    VkVideoEncodeH264RateControlStructureEXT    rateControlStructure;
+    uint32_t                                    temporalLayerCount;
+} VkVideoEncodeH264RateControlInfoEXT;
+
+typedef struct VkVideoEncodeH264QpEXT {
+    int32_t    qpI;
+    int32_t    qpP;
+    int32_t    qpB;
+} VkVideoEncodeH264QpEXT;
+
+typedef struct VkVideoEncodeH264FrameSizeEXT {
+    uint32_t    frameISize;
+    uint32_t    framePSize;
+    uint32_t    frameBSize;
+} VkVideoEncodeH264FrameSizeEXT;
+
+typedef struct VkVideoEncodeH264RateControlLayerInfoEXT {
+    VkStructureType                  sType;
+    const void*                      pNext;
+    uint32_t                         temporalLayerId;
+    VkBool32                         useInitialRcQp;
+    VkVideoEncodeH264QpEXT           initialRcQp;
+    VkBool32                         useMinQp;
+    VkVideoEncodeH264QpEXT           minQp;
+    VkBool32                         useMaxQp;
+    VkVideoEncodeH264QpEXT           maxQp;
+    VkBool32                         useMaxFrameSize;
+    VkVideoEncodeH264FrameSizeEXT    maxFrameSize;
+} VkVideoEncodeH264RateControlLayerInfoEXT;
+
+
+
+#define VK_EXT_video_encode_h265 1
+#include "vk_video/vulkan_video_codec_h265std.h"
+#include "vk_video/vulkan_video_codec_h265std_encode.h"
+#define VK_EXT_VIDEO_ENCODE_H265_SPEC_VERSION 10
+#define VK_EXT_VIDEO_ENCODE_H265_EXTENSION_NAME "VK_EXT_video_encode_h265"
+
+typedef enum VkVideoEncodeH265RateControlStructureEXT {
+    VK_VIDEO_ENCODE_H265_RATE_CONTROL_STRUCTURE_UNKNOWN_EXT = 0,
+    VK_VIDEO_ENCODE_H265_RATE_CONTROL_STRUCTURE_FLAT_EXT = 1,
+    VK_VIDEO_ENCODE_H265_RATE_CONTROL_STRUCTURE_DYADIC_EXT = 2,
+    VK_VIDEO_ENCODE_H265_RATE_CONTROL_STRUCTURE_MAX_ENUM_EXT = 0x7FFFFFFF
+} VkVideoEncodeH265RateControlStructureEXT;
+
+typedef enum VkVideoEncodeH265CapabilityFlagBitsEXT {
+    VK_VIDEO_ENCODE_H265_CAPABILITY_SEPARATE_COLOUR_PLANE_BIT_EXT = 0x00000001,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_SCALING_LISTS_BIT_EXT = 0x00000002,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_SAMPLE_ADAPTIVE_OFFSET_ENABLED_BIT_EXT = 0x00000004,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_PCM_ENABLE_BIT_EXT = 0x00000008,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_SPS_TEMPORAL_MVP_ENABLED_BIT_EXT = 0x00000010,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_HRD_COMPLIANCE_BIT_EXT = 0x00000020,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_INIT_QP_MINUS26_BIT_EXT = 0x00000040,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_LOG2_PARALLEL_MERGE_LEVEL_MINUS2_BIT_EXT = 0x00000080,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_SIGN_DATA_HIDING_ENABLED_BIT_EXT = 0x00000100,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_TRANSFORM_SKIP_ENABLED_BIT_EXT = 0x00000200,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_TRANSFORM_SKIP_DISABLED_BIT_EXT = 0x00000400,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_PPS_SLICE_CHROMA_QP_OFFSETS_PRESENT_BIT_EXT = 0x00000800,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_WEIGHTED_PRED_BIT_EXT = 0x00001000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_WEIGHTED_BIPRED_BIT_EXT = 0x00002000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_WEIGHTED_PRED_NO_TABLE_BIT_EXT = 0x00004000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_TRANSQUANT_BYPASS_ENABLED_BIT_EXT = 0x00008000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_ENTROPY_CODING_SYNC_ENABLED_BIT_EXT = 0x00010000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_DEBLOCKING_FILTER_OVERRIDE_ENABLED_BIT_EXT = 0x00020000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_MULTIPLE_TILE_PER_FRAME_BIT_EXT = 0x00040000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_MULTIPLE_SLICE_PER_TILE_BIT_EXT = 0x00080000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_MULTIPLE_TILE_PER_SLICE_BIT_EXT = 0x00100000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_SLICE_SEGMENT_CTB_COUNT_BIT_EXT = 0x00200000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_ROW_UNALIGNED_SLICE_SEGMENT_BIT_EXT = 0x00400000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_DEPENDENT_SLICE_SEGMENT_BIT_EXT = 0x00800000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_DIFFERENT_SLICE_TYPE_BIT_EXT = 0x01000000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_B_FRAME_IN_L1_LIST_BIT_EXT = 0x02000000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_DIFFERENT_REFERENCE_FINAL_LISTS_BIT_EXT = 0x04000000,
+    VK_VIDEO_ENCODE_H265_CAPABILITY_FLAG_BITS_MAX_ENUM_EXT = 0x7FFFFFFF
+} VkVideoEncodeH265CapabilityFlagBitsEXT;
+typedef VkFlags VkVideoEncodeH265CapabilityFlagsEXT;
+
+typedef enum VkVideoEncodeH265CtbSizeFlagBitsEXT {
+    VK_VIDEO_ENCODE_H265_CTB_SIZE_16_BIT_EXT = 0x00000001,
+    VK_VIDEO_ENCODE_H265_CTB_SIZE_32_BIT_EXT = 0x00000002,
+    VK_VIDEO_ENCODE_H265_CTB_SIZE_64_BIT_EXT = 0x00000004,
+    VK_VIDEO_ENCODE_H265_CTB_SIZE_FLAG_BITS_MAX_ENUM_EXT = 0x7FFFFFFF
+} VkVideoEncodeH265CtbSizeFlagBitsEXT;
+typedef VkFlags VkVideoEncodeH265CtbSizeFlagsEXT;
+
+typedef enum VkVideoEncodeH265TransformBlockSizeFlagBitsEXT {
+    VK_VIDEO_ENCODE_H265_TRANSFORM_BLOCK_SIZE_4_BIT_EXT = 0x00000001,
+    VK_VIDEO_ENCODE_H265_TRANSFORM_BLOCK_SIZE_8_BIT_EXT = 0x00000002,
+    VK_VIDEO_ENCODE_H265_TRANSFORM_BLOCK_SIZE_16_BIT_EXT = 0x00000004,
+    VK_VIDEO_ENCODE_H265_TRANSFORM_BLOCK_SIZE_32_BIT_EXT = 0x00000008,
+    VK_VIDEO_ENCODE_H265_TRANSFORM_BLOCK_SIZE_FLAG_BITS_MAX_ENUM_EXT = 0x7FFFFFFF
+} VkVideoEncodeH265TransformBlockSizeFlagBitsEXT;
+typedef VkFlags VkVideoEncodeH265TransformBlockSizeFlagsEXT;
+typedef struct VkVideoEncodeH265CapabilitiesEXT {
+    VkStructureType                                sType;
+    void*                                          pNext;
+    VkVideoEncodeH265CapabilityFlagsEXT            flags;
+    VkVideoEncodeH265CtbSizeFlagsEXT               ctbSizes;
+    VkVideoEncodeH265TransformBlockSizeFlagsEXT    transformBlockSizes;
+    uint32_t                                       maxPPictureL0ReferenceCount;
+    uint32_t                                       maxBPictureL0ReferenceCount;
+    uint32_t                                       maxL1ReferenceCount;
+    uint32_t                                       maxSubLayersCount;
+    uint32_t                                       minLog2MinLumaCodingBlockSizeMinus3;
+    uint32_t                                       maxLog2MinLumaCodingBlockSizeMinus3;
+    uint32_t                                       minLog2MinLumaTransformBlockSizeMinus2;
+    uint32_t                                       maxLog2MinLumaTransformBlockSizeMinus2;
+    uint32_t                                       minMaxTransformHierarchyDepthInter;
+    uint32_t                                       maxMaxTransformHierarchyDepthInter;
+    uint32_t                                       minMaxTransformHierarchyDepthIntra;
+    uint32_t                                       maxMaxTransformHierarchyDepthIntra;
+    uint32_t                                       maxDiffCuQpDeltaDepth;
+    uint32_t                                       minMaxNumMergeCand;
+    uint32_t                                       maxMaxNumMergeCand;
+} VkVideoEncodeH265CapabilitiesEXT;
+
+typedef struct VkVideoEncodeH265SessionParametersAddInfoEXT {
+    VkStructureType                            sType;
+    const void*                                pNext;
+    uint32_t                                   stdVPSCount;
+    const StdVideoH265VideoParameterSet*       pStdVPSs;
+    uint32_t                                   stdSPSCount;
+    const StdVideoH265SequenceParameterSet*    pStdSPSs;
+    uint32_t                                   stdPPSCount;
+    const StdVideoH265PictureParameterSet*     pStdPPSs;
+} VkVideoEncodeH265SessionParametersAddInfoEXT;
+
+typedef struct VkVideoEncodeH265SessionParametersCreateInfoEXT {
+    VkStructureType                                        sType;
+    const void*                                            pNext;
+    uint32_t                                               maxStdVPSCount;
+    uint32_t                                               maxStdSPSCount;
+    uint32_t                                               maxStdPPSCount;
+    const VkVideoEncodeH265SessionParametersAddInfoEXT*    pParametersAddInfo;
+} VkVideoEncodeH265SessionParametersCreateInfoEXT;
+
+typedef struct VkVideoEncodeH265NaluSliceSegmentInfoEXT {
+    VkStructureType                                sType;
+    const void*                                    pNext;
+    uint32_t                                       ctbCount;
+    const StdVideoEncodeH265ReferenceListsInfo*    pStdReferenceFinalLists;
+    const StdVideoEncodeH265SliceSegmentHeader*    pStdSliceSegmentHeader;
+} VkVideoEncodeH265NaluSliceSegmentInfoEXT;
+
+typedef struct VkVideoEncodeH265VclFrameInfoEXT {
+    VkStructureType                                    sType;
+    const void*                                        pNext;
+    const StdVideoEncodeH265ReferenceListsInfo*        pStdReferenceFinalLists;
+    uint32_t                                           naluSliceSegmentEntryCount;
+    const VkVideoEncodeH265NaluSliceSegmentInfoEXT*    pNaluSliceSegmentEntries;
+    const StdVideoEncodeH265PictureInfo*               pStdPictureInfo;
+} VkVideoEncodeH265VclFrameInfoEXT;
+
+typedef struct VkVideoEncodeH265DpbSlotInfoEXT {
+    VkStructureType                           sType;
+    const void*                               pNext;
+    const StdVideoEncodeH265ReferenceInfo*    pStdReferenceInfo;
+} VkVideoEncodeH265DpbSlotInfoEXT;
+
+typedef struct VkVideoEncodeH265ProfileInfoEXT {
+    VkStructureType           sType;
+    const void*               pNext;
+    StdVideoH265ProfileIdc    stdProfileIdc;
+} VkVideoEncodeH265ProfileInfoEXT;
+
+typedef struct VkVideoEncodeH265RateControlInfoEXT {
+    VkStructureType                             sType;
+    const void*                                 pNext;
+    uint32_t                                    gopFrameCount;
+    uint32_t                                    idrPeriod;
+    uint32_t                                    consecutiveBFrameCount;
+    VkVideoEncodeH265RateControlStructureEXT    rateControlStructure;
+    uint32_t                                    subLayerCount;
+} VkVideoEncodeH265RateControlInfoEXT;
+
+typedef struct VkVideoEncodeH265QpEXT {
+    int32_t    qpI;
+    int32_t    qpP;
+    int32_t    qpB;
+} VkVideoEncodeH265QpEXT;
+
+typedef struct VkVideoEncodeH265FrameSizeEXT {
+    uint32_t    frameISize;
+    uint32_t    framePSize;
+    uint32_t    frameBSize;
+} VkVideoEncodeH265FrameSizeEXT;
+
+typedef struct VkVideoEncodeH265RateControlLayerInfoEXT {
+    VkStructureType                  sType;
+    const void*                      pNext;
+    uint32_t                         temporalId;
+    VkBool32                         useInitialRcQp;
+    VkVideoEncodeH265QpEXT           initialRcQp;
+    VkBool32                         useMinQp;
+    VkVideoEncodeH265QpEXT           minQp;
+    VkBool32                         useMaxQp;
+    VkVideoEncodeH265QpEXT           maxQp;
+    VkBool32                         useMaxFrameSize;
+    VkVideoEncodeH265FrameSizeEXT    maxFrameSize;
+} VkVideoEncodeH265RateControlLayerInfoEXT;
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
@@ -0,0 +1,54 @@
+#ifndef VULKAN_DIRECTFB_H_
+#define VULKAN_DIRECTFB_H_ 1
+
+/*
+** Copyright 2015-2023 The Khronos Group Inc.
+**
+** SPDX-License-Identifier: Apache-2.0
+*/
+
+/*
+** This header is generated from the Khronos Vulkan XML API Registry.
+**
+*/
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+
+#define VK_EXT_directfb_surface 1
+#define VK_EXT_DIRECTFB_SURFACE_SPEC_VERSION 1
+#define VK_EXT_DIRECTFB_SURFACE_EXTENSION_NAME "VK_EXT_directfb_surface"
+typedef VkFlags VkDirectFBSurfaceCreateFlagsEXT;
+typedef struct VkDirectFBSurfaceCreateInfoEXT {
+    VkStructureType                    sType;
+    const void*                        pNext;
+    VkDirectFBSurfaceCreateFlagsEXT    flags;
+    IDirectFB*                         dfb;
+    IDirectFBSurface*                  surface;
+} VkDirectFBSurfaceCreateInfoEXT;
+
+typedef VkResult (VKAPI_PTR *PFN_vkCreateDirectFBSurfaceEXT)(VkInstance instance, const VkDirectFBSurfaceCreateInfoEXT* pCreateInfo, const VkAllocationCallbacks* pAllocator, VkSurfaceKHR* pSurface);
+typedef VkBool32 (VKAPI_PTR *PFN_vkGetPhysicalDeviceDirectFBPresentationSupportEXT)(VkPhysicalDevice physicalDevice, uint32_t queueFamilyIndex, IDirectFB* dfb);
+
+#ifndef VK_NO_PROTOTYPES
+VKAPI_ATTR VkResult VKAPI_CALL vkCreateDirectFBSurfaceEXT(
+    VkInstance                                  instance,
+    const VkDirectFBSurfaceCreateInfoEXT*       pCreateInfo,
+    const VkAllocationCallbacks*                pAllocator,
+    VkSurfaceKHR*                               pSurface);
+
+VKAPI_ATTR VkBool32 VKAPI_CALL vkGetPhysicalDeviceDirectFBPresentationSupportEXT(
+    VkPhysicalDevice                            physicalDevice,
+    uint32_t                                    queueFamilyIndex,
+    IDirectFB*                                  dfb);
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
@@ -1,24 +1,10 @@
 #ifndef VULKAN_FUCHSIA_H_
 #define VULKAN_FUCHSIA_H_ 1

-#ifdef __cplusplus
-extern "C" {
-#endif
-
 /*
-** Copyright (c) 2015-2018 The Khronos Group Inc.
+** Copyright 2015-2023 The Khronos Group Inc.
 **
-** Licensed under the Apache License, Version 2.0 (the "License");
-** you may not use this file except in compliance with the License.
-** You may obtain a copy of the License at
-**
-**     http://www.apache.org/licenses/LICENSE-2.0
-**
-** Unless required by applicable law or agreed to in writing, software
-** distributed under the License is distributed on an "AS IS" BASIS,
-** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-** See the License for the specific language governing permissions and
-** limitations under the License.
+** SPDX-License-Identifier: Apache-2.0
 */

 /*
@@ -27,12 +13,16 @@ extern "C" {
 */


+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+
 #define VK_FUCHSIA_imagepipe_surface 1
 #define VK_FUCHSIA_IMAGEPIPE_SURFACE_SPEC_VERSION 1
 #define VK_FUCHSIA_IMAGEPIPE_SURFACE_EXTENSION_NAME "VK_FUCHSIA_imagepipe_surface"
-
 typedef VkFlags VkImagePipeSurfaceCreateFlagsFUCHSIA;
-
 typedef struct VkImagePipeSurfaceCreateInfoFUCHSIA {
    VkStructureType                         sType;
    const void*                             pNext;
@@ -40,7 +30,6 @@ typedef struct VkImagePipeSurfaceCreateInfoFUCHSIA {
    zx_handle_t                             imagePipeHandle;
 } VkImagePipeSurfaceCreateInfoFUCHSIA;

-
 typedef VkResult (VKAPI_PTR *PFN_vkCreateImagePipeSurfaceFUCHSIA)(VkInstance instance, const VkImagePipeSurfaceCreateInfoFUCHSIA* pCreateInfo, const VkAllocationCallbacks* pAllocator, VkSurfaceKHR* pSurface);

 #ifndef VK_NO_PROTOTYPES
@@ -51,6 +40,217 @@ VKAPI_ATTR VkResult VKAPI_CALL vkCreateImagePipeSurfaceFUCHSIA(
    VkSurfaceKHR*                               pSurface);
 #endif

+
+#define VK_FUCHSIA_external_memory 1
+#define VK_FUCHSIA_EXTERNAL_MEMORY_SPEC_VERSION 1
+#define VK_FUCHSIA_EXTERNAL_MEMORY_EXTENSION_NAME "VK_FUCHSIA_external_memory"
+typedef struct VkImportMemoryZirconHandleInfoFUCHSIA {
+    VkStructureType                       sType;
+    const void*                           pNext;
+    VkExternalMemoryHandleTypeFlagBits    handleType;
+    zx_handle_t                           handle;
+} VkImportMemoryZirconHandleInfoFUCHSIA;
+
+typedef struct VkMemoryZirconHandlePropertiesFUCHSIA {
+    VkStructureType    sType;
+    void*              pNext;
+    uint32_t           memoryTypeBits;
+} VkMemoryZirconHandlePropertiesFUCHSIA;
+
+typedef struct VkMemoryGetZirconHandleInfoFUCHSIA {
+    VkStructureType                       sType;
+    const void*                           pNext;
+    VkDeviceMemory                        memory;
+    VkExternalMemoryHandleTypeFlagBits    handleType;
+} VkMemoryGetZirconHandleInfoFUCHSIA;
+
+typedef VkResult (VKAPI_PTR *PFN_vkGetMemoryZirconHandleFUCHSIA)(VkDevice device, const VkMemoryGetZirconHandleInfoFUCHSIA* pGetZirconHandleInfo, zx_handle_t* pZirconHandle);
+typedef VkResult (VKAPI_PTR *PFN_vkGetMemoryZirconHandlePropertiesFUCHSIA)(VkDevice device, VkExternalMemoryHandleTypeFlagBits handleType, zx_handle_t zirconHandle, VkMemoryZirconHandlePropertiesFUCHSIA* pMemoryZirconHandleProperties);
+
+#ifndef VK_NO_PROTOTYPES
+VKAPI_ATTR VkResult VKAPI_CALL vkGetMemoryZirconHandleFUCHSIA(
+    VkDevice                                    device,
+    const VkMemoryGetZirconHandleInfoFUCHSIA*   pGetZirconHandleInfo,
+    zx_handle_t*                                pZirconHandle);
+
+VKAPI_ATTR VkResult VKAPI_CALL vkGetMemoryZirconHandlePropertiesFUCHSIA(
+    VkDevice                                    device,
+    VkExternalMemoryHandleTypeFlagBits          handleType,
+    zx_handle_t                                 zirconHandle,
+    VkMemoryZirconHandlePropertiesFUCHSIA*      pMemoryZirconHandleProperties);
+#endif
+
+
+#define VK_FUCHSIA_external_semaphore 1
+#define VK_FUCHSIA_EXTERNAL_SEMAPHORE_SPEC_VERSION 1
+#define VK_FUCHSIA_EXTERNAL_SEMAPHORE_EXTENSION_NAME "VK_FUCHSIA_external_semaphore"
+typedef struct VkImportSemaphoreZirconHandleInfoFUCHSIA {
+    VkStructureType                          sType;
+    const void*                              pNext;
+    VkSemaphore                              semaphore;
+    VkSemaphoreImportFlags                   flags;
+    VkExternalSemaphoreHandleTypeFlagBits    handleType;
+    zx_handle_t                              zirconHandle;
+} VkImportSemaphoreZirconHandleInfoFUCHSIA;
+
+typedef struct VkSemaphoreGetZirconHandleInfoFUCHSIA {
+    VkStructureType                          sType;
+    const void*                              pNext;
+    VkSemaphore                              semaphore;
+    VkExternalSemaphoreHandleTypeFlagBits    handleType;
+} VkSemaphoreGetZirconHandleInfoFUCHSIA;
+
+typedef VkResult (VKAPI_PTR *PFN_vkImportSemaphoreZirconHandleFUCHSIA)(VkDevice device, const VkImportSemaphoreZirconHandleInfoFUCHSIA* pImportSemaphoreZirconHandleInfo);
+typedef VkResult (VKAPI_PTR *PFN_vkGetSemaphoreZirconHandleFUCHSIA)(VkDevice device, const VkSemaphoreGetZirconHandleInfoFUCHSIA* pGetZirconHandleInfo, zx_handle_t* pZirconHandle);
+
+#ifndef VK_NO_PROTOTYPES
+VKAPI_ATTR VkResult VKAPI_CALL vkImportSemaphoreZirconHandleFUCHSIA(
+    VkDevice                                    device,
+    const VkImportSemaphoreZirconHandleInfoFUCHSIA* pImportSemaphoreZirconHandleInfo);
+
+VKAPI_ATTR VkResult VKAPI_CALL vkGetSemaphoreZirconHandleFUCHSIA(
+    VkDevice                                    device,
+    const VkSemaphoreGetZirconHandleInfoFUCHSIA* pGetZirconHandleInfo,
+    zx_handle_t*                                pZirconHandle);
+#endif
+
+
+#define VK_FUCHSIA_buffer_collection 1
+VK_DEFINE_NON_DISPATCHABLE_HANDLE(VkBufferCollectionFUCHSIA)
+#define VK_FUCHSIA_BUFFER_COLLECTION_SPEC_VERSION 2
+#define VK_FUCHSIA_BUFFER_COLLECTION_EXTENSION_NAME "VK_FUCHSIA_buffer_collection"
+typedef VkFlags VkImageFormatConstraintsFlagsFUCHSIA;
+
+typedef enum VkImageConstraintsInfoFlagBitsFUCHSIA {
+    VK_IMAGE_CONSTRAINTS_INFO_CPU_READ_RARELY_FUCHSIA = 0x00000001,
+    VK_IMAGE_CONSTRAINTS_INFO_CPU_READ_OFTEN_FUCHSIA = 0x00000002,
+    VK_IMAGE_CONSTRAINTS_INFO_CPU_WRITE_RARELY_FUCHSIA = 0x00000004,
+    VK_IMAGE_CONSTRAINTS_INFO_CPU_WRITE_OFTEN_FUCHSIA = 0x00000008,
+    VK_IMAGE_CONSTRAINTS_INFO_PROTECTED_OPTIONAL_FUCHSIA = 0x00000010,
+    VK_IMAGE_CONSTRAINTS_INFO_FLAG_BITS_MAX_ENUM_FUCHSIA = 0x7FFFFFFF
+} VkImageConstraintsInfoFlagBitsFUCHSIA;
+typedef VkFlags VkImageConstraintsInfoFlagsFUCHSIA;
+typedef struct VkBufferCollectionCreateInfoFUCHSIA {
+    VkStructureType    sType;
+    const void*        pNext;
+    zx_handle_t        collectionToken;
+} VkBufferCollectionCreateInfoFUCHSIA;
+
+typedef struct VkImportMemoryBufferCollectionFUCHSIA {
+    VkStructureType              sType;
+    const void*                  pNext;
+    VkBufferCollectionFUCHSIA    collection;
+    uint32_t                     index;
+} VkImportMemoryBufferCollectionFUCHSIA;
+
+typedef struct VkBufferCollectionImageCreateInfoFUCHSIA {
+    VkStructureType              sType;
+    const void*                  pNext;
+    VkBufferCollectionFUCHSIA    collection;
+    uint32_t                     index;
+} VkBufferCollectionImageCreateInfoFUCHSIA;
+
+typedef struct VkBufferCollectionConstraintsInfoFUCHSIA {
+    VkStructureType    sType;
+    const void*        pNext;
+    uint32_t           minBufferCount;
+    uint32_t           maxBufferCount;
+    uint32_t           minBufferCountForCamping;
+    uint32_t           minBufferCountForDedicatedSlack;
+    uint32_t           minBufferCountForSharedSlack;
+} VkBufferCollectionConstraintsInfoFUCHSIA;
+
+typedef struct VkBufferConstraintsInfoFUCHSIA {
+    VkStructureType                             sType;
+    const void*                                 pNext;
+    VkBufferCreateInfo                          createInfo;
+    VkFormatFeatureFlags                        requiredFormatFeatures;
+    VkBufferCollectionConstraintsInfoFUCHSIA    bufferCollectionConstraints;
+} VkBufferConstraintsInfoFUCHSIA;
+
+typedef struct VkBufferCollectionBufferCreateInfoFUCHSIA {
+    VkStructureType              sType;
+    const void*                  pNext;
+    VkBufferCollectionFUCHSIA    collection;
+    uint32_t                     index;
+} VkBufferCollectionBufferCreateInfoFUCHSIA;
+
+typedef struct VkSysmemColorSpaceFUCHSIA {
+    VkStructureType    sType;
+    const void*        pNext;
+    uint32_t           colorSpace;
+} VkSysmemColorSpaceFUCHSIA;
+
+typedef struct VkBufferCollectionPropertiesFUCHSIA {
+    VkStructureType                  sType;
+    void*                            pNext;
+    uint32_t                         memoryTypeBits;
+    uint32_t                         bufferCount;
+    uint32_t                         createInfoIndex;
+    uint64_t                         sysmemPixelFormat;
+    VkFormatFeatureFlags             formatFeatures;
+    VkSysmemColorSpaceFUCHSIA        sysmemColorSpaceIndex;
+    VkComponentMapping               samplerYcbcrConversionComponents;
+    VkSamplerYcbcrModelConversion    suggestedYcbcrModel;
+    VkSamplerYcbcrRange              suggestedYcbcrRange;
+    VkChromaLocation                 suggestedXChromaOffset;
+    VkChromaLocation                 suggestedYChromaOffset;
+} VkBufferCollectionPropertiesFUCHSIA;
+
+typedef struct VkImageFormatConstraintsInfoFUCHSIA {
+    VkStructureType                         sType;
+    const void*                             pNext;
+    VkImageCreateInfo                       imageCreateInfo;
+    VkFormatFeatureFlags                    requiredFormatFeatures;
+    VkImageFormatConstraintsFlagsFUCHSIA    flags;
+    uint64_t                                sysmemPixelFormat;
+    uint32_t                                colorSpaceCount;
+    const VkSysmemColorSpaceFUCHSIA*        pColorSpaces;
+} VkImageFormatConstraintsInfoFUCHSIA;
+
+typedef struct VkImageConstraintsInfoFUCHSIA {
+    VkStructureType                               sType;
+    const void*                                   pNext;
+    uint32_t                                      formatConstraintsCount;
+    const VkImageFormatConstraintsInfoFUCHSIA*    pFormatConstraints;
+    VkBufferCollectionConstraintsInfoFUCHSIA      bufferCollectionConstraints;
+    VkImageConstraintsInfoFlagsFUCHSIA            flags;
+} VkImageConstraintsInfoFUCHSIA;
+
+typedef VkResult (VKAPI_PTR *PFN_vkCreateBufferCollectionFUCHSIA)(VkDevice device, const VkBufferCollectionCreateInfoFUCHSIA* pCreateInfo, const VkAllocationCallbacks* pAllocator, VkBufferCollectionFUCHSIA* pCollection);
+typedef VkResult (VKAPI_PTR *PFN_vkSetBufferCollectionImageConstraintsFUCHSIA)(VkDevice device, VkBufferCollectionFUCHSIA collection, const VkImageConstraintsInfoFUCHSIA* pImageConstraintsInfo);
+typedef VkResult (VKAPI_PTR *PFN_vkSetBufferCollectionBufferConstraintsFUCHSIA)(VkDevice device, VkBufferCollectionFUCHSIA collection, const VkBufferConstraintsInfoFUCHSIA* pBufferConstraintsInfo);
+typedef void (VKAPI_PTR *PFN_vkDestroyBufferCollectionFUCHSIA)(VkDevice device, VkBufferCollectionFUCHSIA collection, const VkAllocationCallbacks* pAllocator);
+typedef VkResult (VKAPI_PTR *PFN_vkGetBufferCollectionPropertiesFUCHSIA)(VkDevice device, VkBufferCollectionFUCHSIA collection, VkBufferCollectionPropertiesFUCHSIA* pProperties);
+
+#ifndef VK_NO_PROTOTYPES
+VKAPI_ATTR VkResult VKAPI_CALL vkCreateBufferCollectionFUCHSIA(
+    VkDevice                                    device,
+    const VkBufferCollectionCreateInfoFUCHSIA*  pCreateInfo,
+    const VkAllocationCallbacks*                pAllocator,
+    VkBufferCollectionFUCHSIA*                  pCollection);
+
+VKAPI_ATTR VkResult VKAPI_CALL vkSetBufferCollectionImageConstraintsFUCHSIA(
+    VkDevice                                    device,
+    VkBufferCollectionFUCHSIA                   collection,
+    const VkImageConstraintsInfoFUCHSIA*        pImageConstraintsInfo);
+
+VKAPI_ATTR VkResult VKAPI_CALL vkSetBufferCollectionBufferConstraintsFUCHSIA(
+    VkDevice                                    device,
+    VkBufferCollectionFUCHSIA                   collection,
+    const VkBufferConstraintsInfoFUCHSIA*       pBufferConstraintsInfo);
+
+VKAPI_ATTR void VKAPI_CALL vkDestroyBufferCollectionFUCHSIA(
+    VkDevice                                    device,
+    VkBufferCollectionFUCHSIA                   collection,
+    const VkAllocationCallbacks*                pAllocator);
+
+VKAPI_ATTR VkResult VKAPI_CALL vkGetBufferCollectionPropertiesFUCHSIA(
+    VkDevice                                    device,
+    VkBufferCollectionFUCHSIA                   collection,
+    VkBufferCollectionPropertiesFUCHSIA*        pProperties);
+#endif
+
 #ifdef __cplusplus
 }
 #endif
@@ -0,0 +1,58 @@
+#ifndef VULKAN_GGP_H_
+#define VULKAN_GGP_H_ 1
+
+/*
+** Copyright 2015-2023 The Khronos Group Inc.
+**
+** SPDX-License-Identifier: Apache-2.0
+*/
+
+/*
+** This header is generated from the Khronos Vulkan XML API Registry.
+**
+*/
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+
+#define VK_GGP_stream_descriptor_surface 1
+#define VK_GGP_STREAM_DESCRIPTOR_SURFACE_SPEC_VERSION 1
+#define VK_GGP_STREAM_DESCRIPTOR_SURFACE_EXTENSION_NAME "VK_GGP_stream_descriptor_surface"
+typedef VkFlags VkStreamDescriptorSurfaceCreateFlagsGGP;
+typedef struct VkStreamDescriptorSurfaceCreateInfoGGP {
+    VkStructureType                            sType;
+    const void*                                pNext;
+    VkStreamDescriptorSurfaceCreateFlagsGGP    flags;
+    GgpStreamDescriptor                        streamDescriptor;
+} VkStreamDescriptorSurfaceCreateInfoGGP;
+
+typedef VkResult (VKAPI_PTR *PFN_vkCreateStreamDescriptorSurfaceGGP)(VkInstance instance, const VkStreamDescriptorSurfaceCreateInfoGGP* pCreateInfo, const VkAllocationCallbacks* pAllocator, VkSurfaceKHR* pSurface);
+
+#ifndef VK_NO_PROTOTYPES
+VKAPI_ATTR VkResult VKAPI_CALL vkCreateStreamDescriptorSurfaceGGP(
+    VkInstance                                  instance,
+    const VkStreamDescriptorSurfaceCreateInfoGGP* pCreateInfo,
+    const VkAllocationCallbacks*                pAllocator,
+    VkSurfaceKHR*                               pSurface);
+#endif
+
+
+#define VK_GGP_frame_token 1
+#define VK_GGP_FRAME_TOKEN_SPEC_VERSION   1
+#define VK_GGP_FRAME_TOKEN_EXTENSION_NAME "VK_GGP_frame_token"
+typedef struct VkPresentFrameTokenGGP {
+    VkStructureType    sType;
+    const void*        pNext;
+    GgpFrameToken      frameToken;
+} VkPresentFrameTokenGGP;
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
@@ -1,24 +1,10 @@
 #ifndef VULKAN_IOS_H_
 #define VULKAN_IOS_H_ 1

-#ifdef __cplusplus
-extern "C" {
-#endif
-
 /*
-** Copyright (c) 2015-2018 The Khronos Group Inc.
+** Copyright 2015-2023 The Khronos Group Inc.
 **
-** Licensed under the Apache License, Version 2.0 (the "License");
-** you may not use this file except in compliance with the License.
-** You may obtain a copy of the License at
-**
-**     http://www.apache.org/licenses/LICENSE-2.0
-**
-** Unless required by applicable law or agreed to in writing, software
-** distributed under the License is distributed on an "AS IS" BASIS,
-** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-** See the License for the specific language governing permissions and
-** limitations under the License.
+** SPDX-License-Identifier: Apache-2.0
 */

 /*
@@ -27,12 +13,16 @@ extern "C" {
 */


+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+
 #define VK_MVK_ios_surface 1
-#define VK_MVK_IOS_SURFACE_SPEC_VERSION   2
+#define VK_MVK_IOS_SURFACE_SPEC_VERSION   3
 #define VK_MVK_IOS_SURFACE_EXTENSION_NAME "VK_MVK_ios_surface"
-
 typedef VkFlags VkIOSSurfaceCreateFlagsMVK;
-
 typedef struct VkIOSSurfaceCreateInfoMVK {
    VkStructureType               sType;
    const void*                   pNext;
@@ -40,7 +30,6 @@ typedef struct VkIOSSurfaceCreateInfoMVK {
    const void*                   pView;
 } VkIOSSurfaceCreateInfoMVK;

-
 typedef VkResult (VKAPI_PTR *PFN_vkCreateIOSSurfaceMVK)(VkInstance instance, const VkIOSSurfaceCreateInfoMVK* pCreateInfo, const VkAllocationCallbacks* pAllocator, VkSurfaceKHR* pSurface);

 #ifndef VK_NO_PROTOTYPES
--- a/Show More
+++ b/Show More
				`@@ -0,0 +1 @@`
				`Origin: https://github.com/google/flatbuffers/tree/v23.5.9`