release: OpenCV 4.5.0

[G-API] Introduce generic version for cv::gapi::infer

* Introduce generic infer

* Move Generic to infer.hpp

* Removew num_outs

* Fix windows warnings

* Fix comments to review

* Fix doxygen

* Add comment

* Fix comments to review

* standoalone ifdef in ginfer.cpp

* Fix test

3rdparty/include/opencl/1.2/CL/cl_va_api_media_sharing_intel.h

@@ -0,0 +1,160 @@
+/*******************************************************************************
+ * Copyright (c) 2008-2020 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.
+ ******************************************************************************/
+/*****************************************************************************\
+
+Copyright (c) 2013-2019 Intel Corporation All Rights Reserved.
+
+THESE MATERIALS ARE 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 INTEL OR ITS
+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 THESE
+MATERIALS, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+File Name: cl_va_api_media_sharing_intel.h
+
+Abstract:
+
+Notes:
+
+\*****************************************************************************/
+
+
+#ifndef __OPENCL_CL_VA_API_MEDIA_SHARING_INTEL_H
+#define __OPENCL_CL_VA_API_MEDIA_SHARING_INTEL_H
+
+#include <CL/cl.h>
+#include <CL/cl_platform.h>
+#include <va/va.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/******************************************
+* cl_intel_va_api_media_sharing extension *
+*******************************************/
+
+#define cl_intel_va_api_media_sharing 1
+
+/* error codes */
+#define CL_INVALID_VA_API_MEDIA_ADAPTER_INTEL               -1098
+#define CL_INVALID_VA_API_MEDIA_SURFACE_INTEL               -1099
+#define CL_VA_API_MEDIA_SURFACE_ALREADY_ACQUIRED_INTEL      -1100
+#define CL_VA_API_MEDIA_SURFACE_NOT_ACQUIRED_INTEL          -1101
+
+/* cl_va_api_device_source_intel */
+#define CL_VA_API_DISPLAY_INTEL                             0x4094
+
+/* cl_va_api_device_set_intel */
+#define CL_PREFERRED_DEVICES_FOR_VA_API_INTEL               0x4095
+#define CL_ALL_DEVICES_FOR_VA_API_INTEL                     0x4096
+
+/* cl_context_info */
+#define CL_CONTEXT_VA_API_DISPLAY_INTEL                     0x4097
+
+/* cl_mem_info */
+#define CL_MEM_VA_API_MEDIA_SURFACE_INTEL                   0x4098
+
+/* cl_image_info */
+#define CL_IMAGE_VA_API_PLANE_INTEL                         0x4099
+
+/* cl_command_type */
+#define CL_COMMAND_ACQUIRE_VA_API_MEDIA_SURFACES_INTEL      0x409A
+#define CL_COMMAND_RELEASE_VA_API_MEDIA_SURFACES_INTEL      0x409B
+
+typedef cl_uint cl_va_api_device_source_intel;
+typedef cl_uint cl_va_api_device_set_intel;
+
+extern CL_API_ENTRY cl_int CL_API_CALL
+clGetDeviceIDsFromVA_APIMediaAdapterINTEL(
+    cl_platform_id                platform,
+    cl_va_api_device_source_intel media_adapter_type,
+    void*                         media_adapter,
+    cl_va_api_device_set_intel    media_adapter_set,
+    cl_uint                       num_entries,
+    cl_device_id*                 devices,
+    cl_uint*                      num_devices) CL_EXT_SUFFIX__VERSION_1_2;
+
+typedef CL_API_ENTRY cl_int (CL_API_CALL * clGetDeviceIDsFromVA_APIMediaAdapterINTEL_fn)(
+    cl_platform_id                platform,
+    cl_va_api_device_source_intel media_adapter_type,
+    void*                         media_adapter,
+    cl_va_api_device_set_intel    media_adapter_set,
+    cl_uint                       num_entries,
+    cl_device_id*                 devices,
+    cl_uint*                      num_devices) CL_EXT_SUFFIX__VERSION_1_2;
+
+extern CL_API_ENTRY cl_mem CL_API_CALL
+clCreateFromVA_APIMediaSurfaceINTEL(
+    cl_context                    context,
+    cl_mem_flags                  flags,
+    VASurfaceID*                  surface,
+    cl_uint                       plane,
+    cl_int*                       errcode_ret) CL_EXT_SUFFIX__VERSION_1_2;
+
+typedef CL_API_ENTRY cl_mem (CL_API_CALL * clCreateFromVA_APIMediaSurfaceINTEL_fn)(
+    cl_context                    context,
+    cl_mem_flags                  flags,
+    VASurfaceID*                  surface,
+    cl_uint                       plane,
+    cl_int*                       errcode_ret) CL_EXT_SUFFIX__VERSION_1_2;
+
+extern CL_API_ENTRY cl_int CL_API_CALL
+clEnqueueAcquireVA_APIMediaSurfacesINTEL(
+    cl_command_queue              command_queue,
+    cl_uint                       num_objects,
+    const cl_mem*                 mem_objects,
+    cl_uint                       num_events_in_wait_list,
+    const cl_event*               event_wait_list,
+    cl_event*                     event) CL_EXT_SUFFIX__VERSION_1_2;
+
+typedef CL_API_ENTRY cl_int (CL_API_CALL *clEnqueueAcquireVA_APIMediaSurfacesINTEL_fn)(
+    cl_command_queue              command_queue,
+    cl_uint                       num_objects,
+    const cl_mem*                 mem_objects,
+    cl_uint                       num_events_in_wait_list,
+    const cl_event*               event_wait_list,
+    cl_event*                     event) CL_EXT_SUFFIX__VERSION_1_2;
+
+extern CL_API_ENTRY cl_int CL_API_CALL
+clEnqueueReleaseVA_APIMediaSurfacesINTEL(
+    cl_command_queue              command_queue,
+    cl_uint                       num_objects,
+    const cl_mem*                 mem_objects,
+    cl_uint                       num_events_in_wait_list,
+    const cl_event*               event_wait_list,
+    cl_event*                     event) CL_EXT_SUFFIX__VERSION_1_2;
+
+typedef CL_API_ENTRY cl_int (CL_API_CALL *clEnqueueReleaseVA_APIMediaSurfacesINTEL_fn)(
+    cl_command_queue              command_queue,
+    cl_uint                       num_objects,
+    const cl_mem*                 mem_objects,
+    cl_uint                       num_events_in_wait_list,
+    const cl_event*               event_wait_list,
+    cl_event*                     event) CL_EXT_SUFFIX__VERSION_1_2;
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* __OPENCL_CL_VA_API_MEDIA_SHARING_INTEL_H */
+

3rdparty/libtengine/tengine.cmake

@@ -20,9 +20,8 @@
 # Author: qtang@openailab.com or https://github.com/BUG1989
 #         qli@openailab.com
 #         sqfu@openailab.com
-#
 
-SET(TENGINE_COMMIT_VERSION "8a4c58e0e05cd850f4bb0936a330edc86dc0e28c")
+SET(TENGINE_COMMIT_VERSION "e89cf8870de2ff0a80cfe626c0b52b2a16fb302e")
 SET(OCV_TENGINE_DIR "${OpenCV_BINARY_DIR}/3rdparty/libtengine")
 SET(OCV_TENGINE_SOURCE_PATH "${OCV_TENGINE_DIR}/Tengine-${TENGINE_COMMIT_VERSION}")
 
@@ -32,11 +31,10 @@ IF(EXISTS "${OCV_TENGINE_SOURCE_PATH}")
 	SET(Tengine_FOUND ON)
 	SET(BUILD_TENGINE ON)
 ELSE()
-	SET(OCV_TENGINE_FILENAME "${TENGINE_COMMIT_VERSION}.zip")#name2
-	SET(OCV_TENGINE_URL "https://github.com/OAID/Tengine/archive/") #url2
-	SET(tengine_md5sum f51ca8f3963faeeff3f019a6f6edc206) #md5sum2
+	SET(OCV_TENGINE_FILENAME "${TENGINE_COMMIT_VERSION}.zip")#name
+	SET(OCV_TENGINE_URL "https://github.com/OAID/Tengine/archive/") #url
+	SET(tengine_md5sum 23f61ebb1dd419f1207d8876496289c5) #md5sum
 
-	#MESSAGE(STATUS "**** TENGINE DOWNLOAD BEGIN ****")
 	ocv_download(FILENAME ${OCV_TENGINE_FILENAME}
 						HASH ${tengine_md5sum}
 						URL
@@ -62,24 +60,17 @@ ENDIF()
 if(BUILD_TENGINE)
 	SET(HAVE_TENGINE 1)
 
-	# android system
-	if(ANDROID)
-	   if(${ANDROID_ABI} STREQUAL "armeabi-v7a")
-			   SET(CONFIG_ARCH_ARM32 ON)
-	   elseif(${ANDROID_ABI} STREQUAL "arm64-v8a")
-			   SET(CONFIG_ARCH_ARM64 ON)
-	   endif()
-	else()
+	if(NOT ANDROID)
 		# linux system
 		if(CMAKE_SYSTEM_PROCESSOR STREQUAL arm)
-			   SET(CONFIG_ARCH_ARM32 ON)
+			   SET(TENGINE_TOOLCHAIN_FLAG "-march=armv7-a")
 		elseif(CMAKE_SYSTEM_PROCESSOR STREQUAL aarch64) ## AARCH64
-			   SET(CONFIG_ARCH_ARM64 ON)
+			   SET(TENGINE_TOOLCHAIN_FLAG "-march=armv8-a")
 		endif()
 	endif()
 
 	SET(BUILT_IN_OPENCV ON) ## set for tengine compile discern .
-	SET(Tengine_INCLUDE_DIR  "${OCV_TENGINE_SOURCE_PATH}/core/include" CACHE INTERNAL "")
+	SET(Tengine_INCLUDE_DIR  "${OCV_TENGINE_SOURCE_PATH}/include" CACHE INTERNAL "")
 	if(EXISTS "${OCV_TENGINE_SOURCE_PATH}/CMakeLists.txt")
 		add_subdirectory("${OCV_TENGINE_SOURCE_PATH}" "${OCV_TENGINE_DIR}/build")
 	else()

CMakeLists.txt

@@ -464,6 +464,7 @@ OCV_OPTION(BUILD_OBJC               "Enable Objective-C support"
 # OpenCV installation options
 # ===================================================
 OCV_OPTION(INSTALL_CREATE_DISTRIB   "Change install rules to build the distribution package" OFF )
+OCV_OPTION(INSTALL_BIN_EXAMPLES     "Install prebuilt examples" WIN32 IF BUILD_EXAMPLES)
 OCV_OPTION(INSTALL_C_EXAMPLES       "Install C examples"        OFF )
 OCV_OPTION(INSTALL_PYTHON_EXAMPLES  "Install Python examples"   OFF )
 OCV_OPTION(INSTALL_ANDROID_EXAMPLES "Install Android examples"  OFF IF ANDROID )
@@ -1433,10 +1434,6 @@ if(WITH_VA OR HAVE_VA)
   status("    VA:"            HAVE_VA          THEN "YES" ELSE NO)
 endif()
 
-if(WITH_VA_INTEL OR HAVE_VA_INTEL)
-  status("    Intel VA-API/OpenCL:"  HAVE_VA_INTEL       THEN "YES (OpenCL: ${VA_INTEL_IOCL_ROOT})" ELSE NO)
-endif()
-
 if(WITH_TENGINE OR HAVE_TENGINE)
   status("    Tengine:"      HAVE_TENGINE     THEN "YES (${TENGINE_LIBRARIES})" ELSE NO)
 endif()
@@ -1549,6 +1546,7 @@ if(WITH_OPENCL OR HAVE_OPENCL)
     IF HAVE_CLAMDFFT THEN "AMDFFT"
     IF HAVE_CLAMDBLAS THEN "AMDBLAS"
     IF HAVE_OPENCL_D3D11_NV THEN "NVD3D11"
+    IF HAVE_VA_INTEL THEN "INTELVA"
     ELSE "no extra features")
   status("")
   status("  OpenCL:"     HAVE_OPENCL   THEN   "YES (${opencl_features})" ELSE "NO")

cmake/OpenCVDetectCUDA.cmake

@@ -100,7 +100,7 @@ if(CUDA_FOUND)
   set(_arch_pascal  "6.0;6.1")
   set(_arch_volta   "7.0")
   set(_arch_turing  "7.5")
-  set(_arch_ampere  "8.0")
+  set(_arch_ampere  "8.0;8.6")
   if(NOT CMAKE_CROSSCOMPILING)
     list(APPEND _generations "Auto")
   endif()
@@ -208,7 +208,7 @@ if(CUDA_FOUND)
 
       if(${status} EQUAL 0)
         # cache detected values
-        set(OPENCV_CACHE_CUDA_ACTIVE_CC ${${result_list}} CACHE INTERNAL "")
+        set(OPENCV_CACHE_CUDA_ACTIVE_CC ${${output}} CACHE INTERNAL "")
         set(OPENCV_CACHE_CUDA_ACTIVE_CC_check "${__cache_key_check}" CACHE INTERNAL "")
       endif()
     endif()

cmake/OpenCVDetectOpenCL.cmake

@@ -81,4 +81,13 @@ if(OPENCL_FOUND)
 
   # check WITH_OPENCL_D3D11_NV is located in OpenCVDetectDirectX.cmake file
 
+  if(WITH_VA_INTEL AND HAVE_VA)
+    if(HAVE_OPENCL AND EXISTS "${OPENCL_INCLUDE_DIR}/CL/cl_va_api_media_sharing_intel.h")
+      set(HAVE_VA_INTEL ON)
+    elseif(HAVE_OPENCL AND EXISTS "${OPENCL_INCLUDE_DIR}/CL/va_ext.h")
+      set(HAVE_VA_INTEL ON)
+      set(HAVE_VA_INTEL_OLD_HEADER ON)
+    endif()
+  endif()
+
 endif()

cmake/OpenCVFindLibsVideo.cmake

@@ -3,15 +3,6 @@ if(WIN32)
   list(APPEND HIGHGUI_LIBRARIES comctl32 gdi32 ole32 setupapi ws2_32)
 endif(WIN32)
 
-# --- VA & VA_INTEL ---
-if(WITH_VA_INTEL)
-  include("${OpenCV_SOURCE_DIR}/cmake/OpenCVFindVA_INTEL.cmake")
-  if(VA_INTEL_IOCL_INCLUDE_DIR)
-    ocv_include_directories(${VA_INTEL_IOCL_INCLUDE_DIR})
-  endif()
-  set(WITH_VA YES)
-endif(WITH_VA_INTEL)
-
 if(WITH_VA)
   include("${OpenCV_SOURCE_DIR}/cmake/OpenCVFindVA.cmake")
   if(VA_INCLUDE_DIR)

cmake/OpenCVFindVA.cmake

@@ -1,5 +1,6 @@
-# Main variables:
-# HAVE_VA for conditional compilation OpenCV with/without libva
+# Output:
+#   HAVE_VA - libva is available
+#   HAVE_VA_INTEL - OpenCL/libva Intel interoperability extension is available
 
 if(UNIX AND NOT ANDROID)
     find_path(

cmake/OpenCVFindVA_INTEL.cmake

@@ -1,31 +0,0 @@
-# Main variables:
-# VA_INTEL_IOCL_INCLUDE_DIR to use VA_INTEL
-# HAVE_VA_INTEL for conditional compilation OpenCV with/without VA_INTEL
-
-# VA_INTEL_IOCL_ROOT - root of Intel OCL installation
-
-if(UNIX AND NOT ANDROID)
-    ocv_check_environment_variables(VA_INTEL_IOCL_ROOT)
-    if(NOT DEFINED VA_INTEL_IOCL_ROOT)
-      set(VA_INTEL_IOCL_ROOT "/opt/intel/opencl")
-    endif()
-
-    find_path(
-    VA_INTEL_IOCL_INCLUDE_DIR
-    NAMES CL/va_ext.h
-    PATHS ${VA_INTEL_IOCL_ROOT}
-    PATH_SUFFIXES include
-    DOC "Path to Intel OpenCL headers")
-endif()
-
-if(VA_INTEL_IOCL_INCLUDE_DIR)
-    set(HAVE_VA_INTEL TRUE)
-    if(NOT DEFINED VA_INTEL_LIBRARIES)
-      set(VA_INTEL_LIBRARIES "va" "va-drm")
-    endif()
-else()
-    set(HAVE_VA_INTEL FALSE)
-    message(WARNING "Intel OpenCL installation is not found.")
-endif()
-
-mark_as_advanced(FORCE VA_INTEL_IOCL_INCLUDE_DIR)

cmake/OpenCVModule.cmake

@@ -1364,8 +1364,8 @@ function(ocv_add_samples)
           add_dependencies(${the_target} opencv_videoio_plugins)
         endif()
 
-        if(WIN32)
-          install(TARGETS ${the_target} RUNTIME DESTINATION "samples/${module_id}" COMPONENT samples)
+        if(INSTALL_BIN_EXAMPLES)
+          install(TARGETS ${the_target} RUNTIME DESTINATION "${OPENCV_SAMPLES_BIN_INSTALL_PATH}/${module_id}" COMPONENT samples)
         endif()
       endforeach()
     endif()

doc/js_tutorials/js_imgproc/js_grabcut/js_grabcut.markdown

@@ -59,7 +59,7 @@ Demo
 We use the function: **cv.grabCut (image, mask, rect, bgdModel, fgdModel, iterCount, mode = cv.GC_EVAL)**
 
 @param image      input 8-bit 3-channel image.
-@param mask       input/output 8-bit single-channel mask. The mask is initialized by the function when mode is set to GC_INIT_WITH_RECT. Its elements may have one of the cv.rabCutClasses.
+@param mask       input/output 8-bit single-channel mask. The mask is initialized by the function when mode is set to GC_INIT_WITH_RECT. Its elements may have one of the cv.grabCutClasses.
 @param rect       ROI containing a segmented object. The pixels outside of the ROI are marked as "obvious background". The parameter is only used when mode==GC_INIT_WITH_RECT.
 @param bgdModel   temporary array for the background model. Do not modify it while you are processing the same image.
 @param fgdModel   temporary arrays for the foreground model. Do not modify it while you are processing the same image.
@@ -73,4 +73,4 @@ Try it
 <iframe src="../../js_grabcut_grabCut.html" width="100%"
         onload="this.style.height=this.contentDocument.body.scrollHeight +'px';">
 </iframe>
-\endhtmlonly
+\endhtmlonly

doc/py_tutorials/py_imgproc/py_contours/py_contour_properties/py_contour_properties.markdown

@@ -78,7 +78,7 @@ pixelpoints = np.transpose(np.nonzero(mask))
 Here, two methods, one using Numpy functions, next one using OpenCV function (last commented line)
 are given to do the same. Results are also same, but with a slight difference. Numpy gives
 coordinates in **(row, column)** format, while OpenCV gives coordinates in **(x,y)** format. So
-basically the answers will be interchanged. Note that, **row = x** and **column = y**.
+basically the answers will be interchanged. Note that, **row = y** and **column = x**.
 
 7. Maximum Value, Minimum Value and their locations
 ---------------------------------------------------

doc/stylesheet.css

@@ -6,12 +6,11 @@ body, table, div, p, dl {
 }
 
 code {
-    font: 12px Consolas, "Liberation Mono", Courier, monospace;
     font-size: 85%;
+    font-family: "SFMono-Regular",Consolas,"Liberation Mono",Menlo,Courier,monospace;
     white-space: pre-wrap;
     padding: 1px 5px;
-    padding: 0;
-    background-color: #ddd;
+    background-color: rgb(223, 229, 241);
     vertical-align: baseline;
 }
 
@@ -20,6 +19,16 @@ body {
     margin: 0 auto;
 }
 
+div.fragment {
+    padding: 3px;
+    padding-bottom: 0px;
+}
+
+div.line {
+    padding-bottom: 3px;
+    font-family: "SFMono-Regular",Consolas,"Liberation Mono",Menlo,Courier,monospace;
+}
+
 div.contents {
     width: 980px;
     margin: 0 auto;
@@ -35,3 +44,11 @@ span.arrow {
 div.image img{
     max-width: 900px;
 }
+
+#projectlogo
+{
+    text-align: center;
+    vertical-align: middle;
+    border-collapse: separate;
+    padding-left: 0.5em;
+}

doc/tutorials/calib3d/camera_calibration/camera_calibration.markdown

@@ -136,7 +136,7 @@ Explanation
     form an ill-posed problem, so the calibration will fail. For square images the positions of the
     corners are only approximate. We may improve this by calling the @ref cv::cornerSubPix function.
     (`winSize` is used to control the side length of the search window. Its default value is 11.
-    `winSzie` may be changed by command line parameter `--winSize=<number>`.)
+    `winSize` may be changed by command line parameter `--winSize=<number>`.)
     It will produce better calibration result. After this we add a valid inputs result to the
     *imagePoints* vector to collect all of the equations into a single container. Finally, for
     visualization feedback purposes we will draw the found points on the input image using @ref

doc/tutorials/introduction/android_binary_package/O4A_SDK.markdown

@@ -4,6 +4,13 @@ OpenCV4Android SDK {#tutorial_O4A_SDK}
 @prev_tutorial{tutorial_android_dev_intro}
 @next_tutorial{tutorial_dev_with_OCV_on_Android}
 
+|    |    |
+| -: | :- |
+| Original author | Vsevolod Glumov |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial is deprecated.
 
 This tutorial was designed to help you with installation and configuration of OpenCV4Android SDK.
 

doc/tutorials/introduction/android_binary_package/android_dev_intro.markdown

@@ -4,6 +4,14 @@ Introduction into Android Development {#tutorial_android_dev_intro}
 @prev_tutorial{tutorial_clojure_dev_intro}
 @next_tutorial{tutorial_O4A_SDK}
 
+|    |    |
+| -: | :- |
+| Original author | Vsevolod Glumov |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial is deprecated.
+
 
 This guide was designed to help you in learning Android development basics and setting up your
 working environment quickly. It was written with Windows 7 in mind, though it would work with Linux

doc/tutorials/introduction/android_binary_package/android_ocl_intro.markdown

@@ -4,6 +4,13 @@ Use OpenCL in Android camera preview based CV application {#tutorial_android_ocl
 @prev_tutorial{tutorial_dev_with_OCV_on_Android}
 @next_tutorial{tutorial_macos_install}
 
+|    |    |
+| -: | :- |
+| Original author | Andrey Pavlenko |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial is deprecated.
 
 This guide was designed to help you in use of [OpenCL ™](https://www.khronos.org/opencl/) in Android camera preview based CV application.
 It was written for [Eclipse-based ADT tools](http://developer.android.com/tools/help/adt.html)

doc/tutorials/introduction/android_binary_package/dev_with_OCV_on_Android.markdown

@@ -4,6 +4,13 @@ Android Development with OpenCV {#tutorial_dev_with_OCV_on_Android}
 @prev_tutorial{tutorial_O4A_SDK}
 @next_tutorial{tutorial_android_ocl_intro}
 
+|    |    |
+| -: | :- |
+| Original author | Vsevolod Glumov |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial is deprecated.
 
 This tutorial has been created to help you use OpenCV library within your Android project.
 

doc/tutorials/introduction/building_tegra_cuda/building_tegra_cuda.markdown

@@ -4,6 +4,13 @@ Building OpenCV for Tegra with CUDA {#tutorial_building_tegra_cuda}
 @prev_tutorial{tutorial_arm_crosscompile_with_cmake}
 @next_tutorial{tutorial_display_image}
 
+|    |    |
+| -: | :- |
+| Original author |  Randy J. Ray |
+| Compatibility | OpenCV >= 3.1.0 |
+
+@warning
+This tutorial is deprecated.
 
 @tableofcontents
 

doc/tutorials/introduction/clojure_dev_intro/clojure_dev_intro.markdown

@@ -4,6 +4,13 @@ Introduction to OpenCV Development with Clojure {#tutorial_clojure_dev_intro}
 @prev_tutorial{tutorial_java_eclipse}
 @next_tutorial{tutorial_android_dev_intro}
 
+|    |    |
+| -: | :- |
+| Original author | Mimmo Cosenza |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 As of OpenCV 2.4.4, OpenCV supports desktop Java development using nearly the same interface as for
 Android development.

doc/tutorials/introduction/config_reference/config_reference.markdown

@@ -0,0 +1,589 @@
+OpenCV configuration options reference {#tutorial_config_reference}
+======================================
+
+@tableofcontents
+
+# Introduction {#tutorial_config_reference_intro}
+
+@note
+We assume you have read @ref tutorial_general_install tutorial or have experience with CMake.
+
+Configuration options can be set in several different ways:
+* Command line: `cmake -Doption=value ...`
+* Initial cache files: `cmake -C my_options.txt ...`
+* Interactive via GUI
+
+In this reference we will use regular command line.
+
+Most of the options can be found in the root cmake script of OpenCV: `opencv/CMakeLists.txt`. Some options can be defined in specific modules.
+
+It is possible to use CMake tool to print all available options:
+```.sh
+# initial configuration
+cmake ../opencv
+
+# print all options
+cmake -L
+
+# print all options with help message
+cmake -LH
+
+# print all options including advanced
+cmake -LA
+```
+
+Most popular and useful are options starting with `WITH_`, `ENABLE_`, `BUILD_`, `OPENCV_`.
+
+Default values vary depending on platform and other options values.
+
+
+# General options {#tutorial_config_reference_general}
+
+## Build with extra modules {#tutorial_config_reference_general_contrib}
+
+`OPENCV_EXTRA_MODULES_PATH` option contains a semicolon-separated list of directories containing extra modules which will be added to the build. Module directory must have compatible layout and CMakeLists.txt, brief description can be found in the [Coding Style Guide](https://github.com/opencv/opencv/wiki/Coding_Style_Guide).
+
+Examples:
+```.sh
+# build with all modules in opencv_contrib
+cmake -DOPENCV_EXTRA_MODULES_PATH=../opencv_contrib/modules ../opencv
+
+# build with one of opencv_contrib modules
+cmake -DOPENCV_EXTRA_MODULES_PATH=../opencv_contrib/modules/bgsegm ../opencv
+
+# build with two custom modules (semicolon must be escaped in bash)
+cmake -DOPENCV_EXTRA_MODULES_PATH=../my_mod1\;../my_mod2 ../opencv
+```
+
+@note
+Only 0- and 1-level deep module locations are supported, following command will raise an error:
+```.sh
+cmake -DOPENCV_EXTRA_MODULES_PATH=../opencv_contrib ../opencv
+```
+
+
+## Debug build {#tutorial_config_reference_general_debug}
+
+`CMAKE_BUILD_TYPE` option can be used to enable debug build; resulting binaries will contain debug symbols and most of compiler optimizations will be turned off. To enable debug symbols in Release build turn the `BUILD_WITH_DEBUG_INFO` option on.
+
+On some platforms (e.g. Linux) build type must be set at configuration stage:
+```.sh
+cmake -DCMAKE_BUILD_TYPE=Debug ../opencv
+cmake --build .
+```
+On other platforms different types of build can be produced in the same build directory (e.g. Visual Studio, XCode):
+```.sh
+cmake <options> ../opencv
+cmake --build . --config Debug
+```
+
+If you use GNU libstdc++ (default for GCC) you can turn on the `ENABLE_GNU_STL_DEBUG` option, then C++ library will be used in Debug mode, e.g. indexes will be bound-checked during vector element access.
+
+Many kinds of optimizations can be disabled with `CV_DISABLE_OPTIMIZATION` option:
+* Some third-party libraries (e.g. IPP, Lapack, Eigen)
+* Explicit vectorized implementation (universal intrinsics, raw intrinsics, etc.)
+* Dispatched optimizations
+* Explicit loop unrolling
+
+@see https://cmake.org/cmake/help/latest/variable/CMAKE_BUILD_TYPE.html
+@see https://gcc.gnu.org/onlinedocs/libstdc++/manual/using_macros.html
+@see https://github.com/opencv/opencv/wiki/CPU-optimizations-build-options
+
+
+## Static build {#tutorial_config_reference_general_static}
+
+`BUILD_SHARED_LIBS` option control whether to produce dynamic (.dll, .so, .dylib) or static (.a, .lib) libraries. Default value depends on target platform, in most cases it is `ON`.
+
+Example:
+```.sh
+cmake -DBUILD_SHARED_LIBS=OFF ../opencv
+```
+
+@see https://en.wikipedia.org/wiki/Static_library
+
+`ENABLE_PIC` sets the [CMAKE_POSITION_INDEPENDENT_CODE](https://cmake.org/cmake/help/latest/variable/CMAKE_POSITION_INDEPENDENT_CODE.html) option. It enables or disable generation of "position-independent code". This option must be enabled when building dynamic libraries or static libraries intended to be linked into dynamic libraries. Default value is `ON`.
+
+@see https://en.wikipedia.org/wiki/Position-independent_code
+
+
+## Generate pkg-config info
+
+`OPENCV_GENERATE_PKGCONFIG` option enables `.pc` file generation along with standard CMake package. This file can be useful for projects which do not use CMake for build.
+
+Example:
+```.sh
+cmake -DOPENCV_GENERATE_PKGCONFIG=ON ../opencv
+```
+
+@note
+Due to complexity of configuration process resulting `.pc` file can contain incomplete list of third-party dependencies and may not work in some configurations, especially for static builds. This feature is not officially supported since 4.x version and is disabled by default.
+
+
+## Build tests, samples and applications {#tutorial_config_reference_general_tests}
+
+There are two kinds of tests: accuracy (`opencv_test_*`) and performance (`opencv_perf_*`). Tests and applications are enabled by default. Examples are not being built by default and should be enabled explicitly.
+
+Corresponding _cmake_ options:
+```.sh
+cmake \
+  -DBUILD_TESTS=ON \
+  -DBUILD_PERF_TESTS=ON \
+  -DBUILD_EXAMPLES=ON \
+  -DBUILD_opencv_apps=ON \
+  ../opencv
+```
+
+
+## Build limited set of modules {#tutorial_config_reference_general_modules}
+
+Each module is a subdirectory of the `modules` directory. It is possible to disable one module:
+```.sh
+cmake -DBUILD_opencv_calib3d=OFF ../opencv
+```
+
+The opposite option is to build only specified modules and all modules they depend on:
+```.sh
+cmake -DBUILD_LIST=calib3d,videoio,ts ../opencv
+```
+In this example we requested 3 modules and configuration script has determined all dependencies automatically:
+```
+--   OpenCV modules:
+--     To be built:                 calib3d core features2d flann highgui imgcodecs imgproc ts videoio
+```
+
+
+## Downloaded dependencies {#tutorial_config_reference_general_download}
+
+Configuration script can try to download additional libraries and files from the internet, if it fails to do it corresponding features will be turned off. In some cases configuration error can occur. By default all files are first downloaded to the `<source>/.cache` directory and then unpacked or copied to the build directory. It is possible to change download cache location by setting environment variable or configuration option:
+```.sh
+export OPENCV_DOWNLOAD_PATH=/tmp/opencv-cache
+cmake ../opencv
+# or
+cmake -DOPENCV_DOWNLOAD_PATH=/tmp/opencv-cache ../opencv
+```
+
+In case of access via proxy, corresponding environment variables should be set before running cmake:
+```.sh
+export http_proxy=<proxy-host>:<port>
+export https_proxy=<proxy-host>:<port>
+```
+
+Full log of download process can be found in build directory - `CMakeDownloadLog.txt`. In addition, for each failed download a command will be added to helper scripts in the build directory, e.g. `download_with_wget.sh`. Users can run these scripts as is or modify according to their needs.
+
+
+## CPU optimization level {#tutorial_config_reference_general_cpu}
+
+On x86_64 machines the library will be compiled for SSE3 instruction set level by default. This level can be changed by configuration option:
+```.sh
+cmake -DCPU_BASELINE=AVX2 ../opencv
+```
+
+@note
+Other platforms have their own instruction set levels: `VFPV3` and `NEON` on ARM, `VSX` on PowerPC.
+
+Some functions support dispatch mechanism allowing to compile them for several instruction sets and to choose one during runtime. List of enabled instruction sets can be changed during configuration:
+```.sh
+cmake -DCPU_DISPATCH=AVX,AVX2 ../opencv
+```
+To disable dispatch mechanism this option should be set to an empty value:
+```.sh
+cmake -DCPU_DISPATCH= ../opencv
+```
+
+It is possible to disable optimized parts of code for troubleshooting and debugging:
+```.sh
+# disable universal intrinsics
+cmake -DCV_ENABLE_INTRINSICS=OFF ../opencv
+# disable all possible built-in optimizations
+cmake -DCV_DISABLE_OPTIMIZATION=ON ../opencv
+```
+
+@note
+More details on CPU optimization options can be found in wiki: https://github.com/opencv/opencv/wiki/CPU-optimizations-build-options
+
+
+## Profiling, coverage, sanitize, hardening, size optimization
+
+Following options can be used to produce special builds with instrumentation or improved security. All options are disabled by default.
+
+| Option | Compiler | Description |
+| `ENABLE_PROFILING` | GCC or Clang | Enable profiling compiler and linker options. |
+| `ENABLE_COVERAGE` | GCC or Clang | Enable code coverage support. |
+| `OPENCV_ENABLE_MEMORY_SANITIZER` | N/A | Enable several quirks in code to assist memory sanitizer. |
+| `ENABLE_BUILD_HARDENING` | GCC, Clang, MSVC | Enable compiler options which reduce possibility of code exploitation.  |
+| `ENABLE_LTO` | GCC, Clang, MSVC | Enable Link Time Optimization (LTO). |
+| `ENABLE_THIN_LTO` | Clang | Enable thin LTO which incorporates intermediate bitcode to binaries allowing consumers optimize their applications later. |
+
+@see [GCC instrumentation](https://gcc.gnu.org/onlinedocs/gcc/Instrumentation-Options.html)
+@see [Build hardening](https://en.wikipedia.org/wiki/Hardening_(computing))
+@see [Interprocedural optimization](https://en.wikipedia.org/wiki/Interprocedural_optimization)
+@see [Link time optimization](https://gcc.gnu.org/wiki/LinkTimeOptimization)
+@see [ThinLTO](https://clang.llvm.org/docs/ThinLTO.html)
+
+
+# Functional features and dependencies {#tutorial_config_reference_func}
+
+There are many optional dependencies and features that can be turned on or off. _cmake_ has special option allowing to print all available configuration parameters:
+```.sh
+cmake -LH ../opencv
+```
+
+
+## Options naming conventions
+
+There are three kinds of options used to control dependencies of the library, they have different prefixes:
+- Options starting with `WITH_` enable or disable a dependency
+- Options starting with `BUILD_` enable or disable building and using 3rdparty library bundled with OpenCV
+- Options starting with `HAVE_` indicate that dependency have been enabled, can be used to manually enable a dependency if automatic detection can not be used.
+
+When `WITH_` option is enabled:
+- If `BUILD_` option is enabled, 3rdparty library will be built and enabled => `HAVE_` set to `ON`
+- If `BUILD_` option is disabled, 3rdparty library will be detected and enabled if found => `HAVE_` set to `ON` if dependency is found
+
+
+## Heterogeneous computation {#tutorial_config_reference_func_hetero}
+
+### CUDA support
+
+`WITH_CUDA` (default: _OFF_)
+
+Many algorithms have been implemented using CUDA acceleration, these functions are located in separate modules. CUDA toolkit must be installed from the official NVIDIA site as a prerequisite. For cmake versions older than 3.9 OpenCV uses own `cmake/FindCUDA.cmake` script, for newer versions - the one packaged with CMake. Additional options can be used to control build process, e.g. `CUDA_GENERATION` or `CUDA_ARCH_BIN`. These parameters are not documented yet, please consult with the `cmake/OpenCVDetectCUDA.cmake` script for details.
+
+@note Since OpenCV version 4.0 all CUDA-accelerated algorithm implementations have been moved to the _opencv_contrib_ repository. To build _opencv_ and _opencv_contrib_ together check @ref tutorial_config_reference_general_contrib.
+
+@cond CUDA_MODULES
+@note Some tutorials can be found in the corresponding section: @ref tutorial_table_of_content_gpu
+@see @ref cuda
+@endcond
+
+@see https://en.wikipedia.org/wiki/CUDA
+
+TODO: other options: `WITH_CUFFT`, `WITH_CUBLAS`, `WITH_NVCUVID`?
+
+### OpenCL support
+
+`WITH_OPENCL` (default: _ON_)
+
+Multiple OpenCL-accelerated algorithms are available via so-called "Transparent API (T-API)". This integration uses same functions at the user level as regular CPU implementations. Switch to the OpenCL execution branch happens if input and output image arguments are passed as opaque cv::UMat objects. More information can be found in [the brief introduction](https://opencv.org/opencl/) and @ref core_opencl
+
+At the build time this feature does not have any prerequisites. During runtime a working OpenCL runtime is required, to check it run `clinfo` and/or `opencv_version --opencl` command. Some parameters of OpenCL integration can be modified using environment variables, e.g. `OPENCV_OPENCL_DEVICE`. However there is no thorough documentation for this feature yet, so please check the source code in `modules/core/src/ocl.cpp` file for details.
+
+@see https://en.wikipedia.org/wiki/OpenCL
+
+TODO: other options: `WITH_OPENCL_SVM`, `WITH_OPENCLAMDFFT`, `WITH_OPENCLAMDBLAS`, `WITH_OPENCL_D3D11_NV`, `WITH_VA_INTEL`
+
+## Image reading and writing (imgcodecs module)  {#tutorial_config_reference_func_imgcodecs}
+
+### Built-in formats
+
+Following formats can be read by OpenCV without help of any third-party library:
+
+- [BMP](https://en.wikipedia.org/wiki/BMP_file_format)
+- [HDR](https://en.wikipedia.org/wiki/RGBE_image_format) (`WITH_IMGCODEC_HDR`)
+- [Sun Raster](https://en.wikipedia.org/wiki/Sun_Raster) (`WITH_IMGCODEC_SUNRASTER`)
+- [PPM, PGM, PBM, PFM](https://en.wikipedia.org/wiki/Netpbm#File_formats) (`WITH_IMGCODEC_PXM`, `WITH_IMGCODEC_PFM`)
+
+
+### PNG, JPEG, TIFF, WEBP support
+
+| Formats | Option | Default | Force build own |
+| --------| ------ | ------- | --------------- |
+| [PNG](https://en.wikipedia.org/wiki/Portable_Network_Graphics) | `WITH_PNG` | _ON_ | `BUILD_PNG` |
+| [JPEG](https://en.wikipedia.org/wiki/JPEG) | `WITH_JPEG` | _ON_ | `BUILD_JPEG` |
+| [TIFF](https://en.wikipedia.org/wiki/TIFF) | `WITH_TIFF` | _ON_ | `BUILD_TIFF` |
+| [WEBP](https://en.wikipedia.org/wiki/WebP) | `WITH_WEBP` | _ON_ | `BUILD_WEBP` |
+| [JPEG2000 with OpenJPEG](https://en.wikipedia.org/wiki/OpenJPEG) | `WITH_OPENJPEG` | _ON_ | `BUILD_OPENJPEG` |
+| [JPEG2000 with JasPer](https://en.wikipedia.org/wiki/JasPer) | `WITH_JASPER` | _ON_ (see note) | `BUILD_JASPER` |
+| [EXR](https://en.wikipedia.org/wiki/OpenEXR) | `WITH_OPENEXR` | _ON_ | `BUILD_OPENEXR` |
+
+All libraries required to read images in these formats are included into OpenCV and will be built automatically if not found at the configuration stage. Corresponding `BUILD_*` options will force building and using own libraries, they are enabled by default on some platforms, e.g. Windows.
+
+@note OpenJPEG have higher priority than JasPer which is deprecated. In order to use JasPer, OpenJPEG must be disabled.
+
+
+### GDAL integration
+
+`WITH_GDAL` (default: _OFF_)
+
+[GDAL](https://en.wikipedia.org/wiki/GDAL) is a higher level library which supports reading multiple file formats including PNG, JPEG and TIFF. It will have higher priority when opening files and can override other backends. This library will be searched using cmake package mechanism, make sure it is installed correctly or manually set `GDAL_DIR` environment or cmake variable.
+
+
+### GDCM integration
+
+`WITH_GDCM` (default: _OFF_)
+
+Enables [DICOM](https://en.wikipedia.org/wiki/DICOM) medical image format support through [GDCM  library](https://en.wikipedia.org/wiki/GDCM). This library will be searched using cmake package mechanism, make sure it is installed correctly or manually set `GDCM_DIR` environment or cmake variable.
+
+
+## Video reading and writing (videoio module) {#tutorial_config_reference_func_videoio}
+
+TODO: how videoio works, registry, priorities
+
+### Video4Linux
+
+`WITH_V4L` (Linux; default: _ON_ )
+
+Capture images from camera using [Video4Linux](https://en.wikipedia.org/wiki/Video4Linux) API. Linux kernel headers must be installed.
+
+### FFmpeg
+
+`WITH_FFMPEG` (default: _ON_)
+
+Integration with [FFmpeg](https://en.wikipedia.org/wiki/FFmpeg) library for decoding and encoding video files and network streams. This library can read and write many popular video formats. It consists of several components which must be installed as prerequisites for the build:
+- _avcodec_
+- _avformat_
+- _avutil_
+- _swscale_
+- _avresample_ (optional)
+
+Exception is Windows platform where a prebuilt [plugin library containing FFmpeg](https://github.com/opencv/opencv_3rdparty/tree/ffmpeg/master) will be downloaded during a configuration stage and copied to the `bin` folder with all produced libraries.
+
+@note [Libav](https://en.wikipedia.org/wiki/Libav) library can be used instead of FFmpeg, but this combination is not actively supported.
+
+### GStreamer
+
+`WITH_GSTREAMER` (default: _ON_)
+
+Enable integration with [GStreamer](https://en.wikipedia.org/wiki/GStreamer) library for decoding and encoding video files, capturing frames from cameras and network streams. Numerous plugins can be installed to extend supported formats list. OpenCV allows running arbitrary GStreamer pipelines passed as strings to @ref cv::VideoCapture and @ref cv::VideoWriter objects.
+
+Various GStreamer plugins offer HW-accelerated video processing on different platforms.
+
+
+### Microsoft Media Foundation
+
+`WITH_MSMF` (Windows; default: _ON_)
+
+Enables MSMF backend which uses Windows' built-in [Media Foundation framework](https://en.wikipedia.org/wiki/Media_Foundation). Can be used to capture frames from camera, decode and encode video files. This backend have HW-accelerated processing support (`WITH_MSMF_DXVA` option, default is _ON_).
+
+@note Older versions of Windows (prior to 10) can have incompatible versions of Media Foundation and are known to have problems when used from OpenCV.
+
+
+### DirectShow
+
+`WITH_DSHOW` (Windows; default: _ON_)
+
+This backend uses older [DirectShow](https://en.wikipedia.org/wiki/DirectShow) framework. It can be used only to capture frames from camera. It is now deprecated in favor of MSMF backend, although both can be enabled in the same build.
+
+
+### AVFoundation
+
+`WITH_AVFOUNDATION` (Apple; default: _ON_)
+
+[AVFoundation](https://en.wikipedia.org/wiki/AVFoundation) framework is part of Apple platforms and can be used to capture frames from camera, encode and decode video files.
+
+
+### Other backends
+
+There are multiple less popular frameworks which can be used to read and write videos. Each requires corresponding library or SDK installed.
+
+| Option | Default | Description |
+| ------ | ------- | ----------- |
+| `WITH_1394` | _ON_ | [IIDC IEEE1394](https://en.wikipedia.org/wiki/IEEE_1394#IIDC) support using DC1394 library |
+| `WITH_OPENNI` | _OFF_ | [OpenNI](https://en.wikipedia.org/wiki/OpenNI) can be used to capture data from depth-sensing cameras. Deprecated. |
+| `WITH_OPENNI2` | _OFF_ | [OpenNI2](https://structure.io/openni) can be used to capture data from depth-sensing cameras. |
+| `WITH_PVAPI` | _OFF_ | [PVAPI](https://www.alliedvision.com/en/support/software-downloads.html) is legacy SDK for Prosilica GigE cameras. Deprecated. |
+| `WITH_ARAVIS` | _OFF_ | [Aravis](https://github.com/AravisProject/aravis) library is used for video acquisition using Genicam cameras. |
+| `WITH_XIMEA` | _OFF_ | [XIMEA](https://www.ximea.com/) cameras support. |
+| `WITH_XINE` | _OFF_ | [XINE](https://en.wikipedia.org/wiki/Xine) library support. |
+| `WITH_LIBREALSENSE` | _OFF_ | [RealSense](https://en.wikipedia.org/wiki/Intel_RealSense) cameras support. |
+| `WITH_MFX` | _OFF_ | [MediaSDK](http://mediasdk.intel.com/) library can be used for HW-accelerated decoding and encoding of raw video streams. |
+| `WITH_GPHOTO2` | _OFF_ | [GPhoto](https://en.wikipedia.org/wiki/GPhoto) library can be used to capure frames from cameras. |
+| `WITH_ANDROID_MEDIANDK` | _ON_ | [MediaNDK](https://developer.android.com/ndk/guides/stable_apis#libmediandk) library is available on Android since API level 21. |
+
+
+### videoio plugins
+
+Some _videoio_ backends can be built as plugins thus breaking strict dependency on third-party libraries and making them optional at runtime. Following options can be used to control this mechanism:
+
+| Option | Default | Description |
+| --------| ------ | ------- |
+| `VIDEOIO_ENABLE_PLUGINS` | _ON_ | Enable or disable plugins completely. |
+| `VIDEOIO_PLUGIN_LIST` | _empty_ | Comma- or semicolon-separated list of backend names to be compiled as plugins. Supported names are _ffmpeg_, _gstreamer_, _msmf_, _mfx_ and _all_. |
+| `VIDEOIO_ENABLE_STRICT_PLUGIN_CHECK` | _ON_ | Enable strict runtime version check to only allow plugins built with the same version of OpenCV. |
+
+
+## Parallel processing {#tutorial_config_reference_func_core}
+
+Some of OpenCV algorithms can use multithreading to accelerate processing. OpenCV can be built with one of threading backends.
+
+| Backend | Option | Default | Platform | Description |
+|-------- | ------ | ------- | -------- | ----------- |
+| pthreads | `WITH_PTHREADS_PF` | _ON_ | Unix-like | Default backend based on [pthreads](https://en.wikipedia.org/wiki/POSIX_Threads) library is available on Linux, Android and other Unix-like platforms. Thread pool is implemented in OpenCV and can be controlled with environment variables `OPENCV_THREAD_POOL_*`. Please check sources in _modules/core/src/parallel_impl.cpp_ file for details. |
+| Concurrency | N/A | _ON_ | Windows | [Concurrency runtime](https://docs.microsoft.com/en-us/cpp/parallel/concrt/concurrency-runtime) is available on Windows and will be turned _ON_ on supported platforms unless other backend is enabled. |
+| GCD | N/A | _ON_ | Apple | [Grand Central Dispatch](https://en.wikipedia.org/wiki/Grand_Central_Dispatch) is available on Apple platforms and will be turned _ON_ automatically unless other backend is enabled. Uses global system thread pool. |
+| TBB | `WITH_TBB` | Multiple | _OFF_ | [Threading Building Blocks](https://en.wikipedia.org/wiki/Threading_Building_Blocks) is a cross-platform library for parallel programming. |
+| OpenMP | `WITH_OPENMP` | Multiple | _OFF_ | [OpenMP](https://en.wikipedia.org/wiki/OpenMP) API relies on compiler support. |
+| HPX | `WITH_HPX` | Multiple | _OFF_ | [High Performance ParallelX](https://en.wikipedia.org/wiki/HPX) is an experimental backend which is more suitable for multiprocessor environments. |
+
+@note OpenCV can download and build TBB library from GitHub, this functionality can be enabled with the `BUILD_TBB` option.
+
+
+## GUI backends (highgui module) {#tutorial_config_reference_highgui}
+
+OpenCV relies on various GUI libraries for window drawing.
+
+| Option | Default | Platform | Description |
+| ------ | ------- | -------- | ----------- |
+| `WITH_GTK` | _ON_ | Linux | [GTK](https://en.wikipedia.org/wiki/GTK) is a common toolkit in Linux and Unix-like OS-es. By default version 3 will be used if found, version 2 can be forced with the `WITH_GTK_2_X` option. |
+| `WITH_WIN32UI` | _ON_ | Windows | [WinAPI](https://en.wikipedia.org/wiki/Windows_API) is a standard GUI API in Windows. |
+| N/A | _ON_ | macOS | [Cocoa](https://en.wikipedia.org/wiki/Cocoa_(API)) is a framework used in macOS. |
+| `WITH_QT` | _OFF_ | Cross-platform | [Qt](https://en.wikipedia.org/wiki/Qt_(software)) is a cross-platform GUI framework. |
+
+@note OpenCV compiled with Qt support enables advanced _highgui_ interface, see @ref highgui_qt for details.
+
+
+### OpenGL
+
+`WITH_OPENGL` (default: _OFF_)
+
+OpenGL integration can be used to draw HW-accelerated windows with following backends: GTK, WIN32 and Qt. And enables basic interoperability with OpenGL, see @ref core_opengl and @ref highgui_opengl for details.
+
+
+## Deep learning neural networks inference backends and options (dnn module) {#tutorial_config_reference_dnn}
+
+OpenCV have own DNN inference module which have own build-in engine, but can also use other libraries for optimized processing. Multiple backends can be enabled in single build. Selection happens at runtime automatically or manually.
+
+| Option | Default | Description |
+| ------ | ------- | ----------- |
+| `WITH_PROTOBUF` | _ON_ | Enables [protobuf](https://en.wikipedia.org/wiki/Protocol_Buffers) library search. OpenCV can either build own copy of the library or use external one. This dependency is required by the _dnn_ module, if it can't be found module will be disabled. |
+| `BUILD_PROTOBUF` | _ON_ | Build own copy of _protobuf_. Must be disabled if you want to use external library. |
+| `PROTOBUF_UPDATE_FILES` | _OFF_ | Re-generate all .proto files. _protoc_ compiler compatible with used version of _protobuf_ must be installed. |
+| `OPENCV_DNN_OPENCL` | _ON_ | Enable built-in OpenCL inference backend. |
+| `WITH_INF_ENGINE` | _OFF_ | Enables [Intel Inference Engine (IE)](https://github.com/openvinotoolkit/openvino) backend. Allows to execute networks in IE format (.xml + .bin). Inference Engine must be installed either as part of [OpenVINO toolkit](https://en.wikipedia.org/wiki/OpenVINO), either as a standalone library built from sources. |
+| `INF_ENGINE_RELEASE` | _2020040000_ | Defines version of Inference Engine library which is tied to OpenVINO toolkit version. Must be a 10-digit string, e.g. _2020040000_ for OpenVINO 2020.4. |
+| `WITH_NGRAPH` | _OFF_ | Enables Intel NGraph library support. This library is part of Inference Engine backend which allows executing arbitrary networks read from files in multiple formats supported by OpenCV: Caffe, TensorFlow, PyTorch, Darknet, etc.. NGraph library must be installed, it is included into Inference Engine. |
+| `OPENCV_DNN_CUDA` | _OFF_ | Enable CUDA backend. [CUDA](https://en.wikipedia.org/wiki/CUDA), CUBLAS and [CUDNN](https://developer.nvidia.com/cudnn) must be installed. |
+| `WITH_HALIDE` | _OFF_ | Use experimental [Halide](https://en.wikipedia.org/wiki/Halide_(programming_language)) backend which can generate optimized code for dnn-layers at runtime. Halide must be installed. |
+| `WITH_VULKAN` | _OFF_ | Enable experimental [Vulkan](https://en.wikipedia.org/wiki/Vulkan_(API)) backend. Does not require additional dependencies, but can use external Vulkan headers (`VULKAN_INCLUDE_DIRS`). |
+| `WITH_TENGINE` | _OFF_ | Enable experimental [Tengine](https://github.com/OAID/Tengine) backend for ARM CPUs. Tengine library must be installed. |
+
+
+# Installation layout {#tutorial_config_reference_install}
+
+## Installation root {#tutorial_config_reference_install_root}
+
+To install produced binaries root location should be configured. Default value depends on distribution, in Ubuntu it is usually set to `/usr/local`. It can be changed during configuration:
+```.sh
+cmake -DCMAKE_INSTALL_PREFIX=/opt/opencv ../opencv
+```
+This path can be relative to current working directory, in the following example it will be set to `<absolute-path-to-build>/install`:
+```.sh
+cmake -DCMAKE_INSTALL_PREFIX=install ../opencv
+```
+
+After building the library, all files can be copied to the configured install location using the following command:
+```.sh
+cmake --build . --target install
+```
+
+To install binaries to the system location (e.g. `/usr/local`) as a regular user it is necessary to run the previous command with elevated privileges:
+```.sh
+sudo cmake --build . --target install
+```
+
+@note
+On some platforms (Linux) it is possible to remove symbol information during install. Binaries will become 10-15% smaller but debugging will be limited:
+```.sh
+cmake --build . --target install/strip
+```
+
+
+## Components and locations {#tutorial_config_reference_install_comp}
+
+Options cane be used to control whether or not a part of the library will be installed:
+
+| Option | Default | Description |
+| ------ | ------- | ----------- |
+| `INSTALL_C_EXAMPLES` | _OFF_ | Install C++ sample sources from the _samples/cpp_ directory. |
+| `INSTALL_PYTHON_EXAMPLES` | _OFF_ | Install Python sample sources from the _samples/python_ directory. |
+| `INSTALL_ANDROID_EXAMPLES` | _OFF_ | Install Android sample sources from the _samples/android_ directory. |
+| `INSTALL_BIN_EXAMPLES` | _OFF_ | Install prebuilt sample applications (`BUILD_EXAMPLES` must be enabled). |
+| `INSTALL_TESTS` | _OFF_ | Install tests (`BUILD_TESTS` must be enabled). |
+| `OPENCV_INSTALL_APPS_LIST` | _all_ | Comma- or semicolon-separated list of prebuilt applications to install (from _apps_ directory) |
+
+Following options allow to modify components' installation locations relatively to install prefix. Default values of these options depend on platform and other options, please check the _cmake/OpenCVInstallLayout.cmake_ file for details.
+
+| Option | Components |
+| ------ | ----------- |
+| `OPENCV_BIN_INSTALL_PATH` | applications, dynamic libraries (_win_) |
+| `OPENCV_TEST_INSTALL_PATH` | test applications |
+| `OPENCV_SAMPLES_BIN_INSTALL_PATH` | sample applications |
+| `OPENCV_LIB_INSTALL_PATH` | dynamic libraries, import libraries (_win_) |
+| `OPENCV_LIB_ARCHIVE_INSTALL_PATH` | static libraries |
+| `OPENCV_3P_LIB_INSTALL_PATH` | 3rdparty libraries |
+| `OPENCV_CONFIG_INSTALL_PATH` | cmake config package |
+| `OPENCV_INCLUDE_INSTALL_PATH` | header files |
+| `OPENCV_OTHER_INSTALL_PATH` | extra data files |
+| `OPENCV_SAMPLES_SRC_INSTALL_PATH` | sample sources |
+| `OPENCV_LICENSES_INSTALL_PATH` | licenses for included 3rdparty components |
+| `OPENCV_TEST_DATA_INSTALL_PATH` | test data |
+| `OPENCV_DOC_INSTALL_PATH` | documentation |
+| `OPENCV_JAR_INSTALL_PATH` | JAR file with Java bindings |
+| `OPENCV_JNI_INSTALL_PATH` | JNI part of Java bindings |
+| `OPENCV_JNI_BIN_INSTALL_PATH` | Dynamic libraries from the JNI part of Java bindings |
+
+Following options can be used to change installation layout for common scenarios:
+
+| Option | Default | Description |
+| ------ | ------- | ----------- |
+| `INSTALL_CREATE_DISTRIB` | _OFF_ | Tune multiple things to produce Windows and Android distributions. |
+| `INSTALL_TO_MANGLED_PATHS` | _OFF_ | Adds one level to several installation locations to allow side-by-side installations. For example, headers will be installed to _/usr/include/opencv-4.4.0_ instead of _/usr/include/opencv4_ with this option enabled. |
+
+
+# Miscellaneous features {#tutorial_config_reference_misc}
+
+
+| Option | Default | Description |
+| ------ | ------- | ----------- |
+| `OPENCV_ENABLE_NONFREE` | _OFF_ | Some algorithms included in the library are known to be protected by patents and are disabled by default. |
+| `OPENCV_FORCE_3RDPARTY_BUILD`| _OFF_ | Enable all `BUILD_` options at once. |
+| `ENABLE_CCACHE` | _ON_ (on Unix-like platforms) | Enable [ccache](https://en.wikipedia.org/wiki/Ccache) auto-detection. This tool wraps compiler calls and caches results, can significantly improve re-compilation time. |
+| `ENABLE_PRECOMPILED_HEADERS` | _ON_ (for MSVC) | Enable precompiled headers support. Improves build time. |
+| `BUILD_DOCS` | _OFF_ | Enable documentation build (_doxygen_, _doxygen_cpp_, _doxygen_python_, _doxygen_javadoc_ targets). [Doxygen](http://www.doxygen.org/index.html) must be installed for C++ documentation build. Python and [BeautifulSoup4](https://en.wikipedia.org/wiki/Beautiful_Soup_(HTML_parser)) must be installed for Python documentation build. Javadoc and Ant must be installed for Java documentation build (part of Java SDK). |
+| `ENABLE_PYLINT` | _ON_ (when docs or examples are enabled) | Enable python scripts check with [Pylint](https://en.wikipedia.org/wiki/Pylint) (_check_pylint_ target). Pylint must be installed. |
+| `ENABLE_FLAKE8` | _ON_ (when docs or examples are enabled) | Enable python scripts check with [Flake8](https://flake8.pycqa.org/) (_check_flake8_ target). Flake8 must be installed. |
+| `BUILD_JAVA` | _ON_ | Enable Java wrappers build. Java SDK and Ant must be installed. |
+| `BUILD_FAT_JAVA_LIB` | _ON_ (for static Android builds) | Build single _opencv_java_ dynamic library containing all library functionality bundled with Java bindings. |
+| `BUILD_opencv_python2` | _ON_ | Build python2 bindings (deprecated). Python with development files and numpy must be installed. |
+| `BUILD_opencv_python3` | _ON_ | Build python3 bindings. Python with development files and numpy must be installed. |
+
+TODO: need separate tutorials covering bindings builds
+
+
+## Automated builds
+
+Some features have been added specifically for automated build environments, like continuous integration and packaging systems.
+
+| Option | Default | Description |
+| ------ | ------- | ----------- |
+| `ENABLE_NOISY_WARNINGS` | _OFF_ | Enables several compiler warnings considered _noisy_, i.e. having less importance than others. These warnings are usually ignored but in some cases can be worth being checked for. |
+| `OPENCV_WARNINGS_ARE_ERRORS` | _OFF_ | Treat compiler warnings as errors. Build will be halted. |
+| `ENABLE_CONFIG_VERIFICATION` | _OFF_ | For each enabled dependency (`WITH_` option) verify that it has been found and enabled (`HAVE_` variable). By default feature will be silently turned off if dependency was not found, but with this option enabled cmake configuration will fail. Convenient for packaging systems which require stable library configuration not depending on environment fluctuations. |
+| `OPENCV_CMAKE_HOOKS_DIR` | _empty_ | OpenCV allows to customize configuration process by adding custom hook scripts at each stage and substage. cmake scripts with predefined names located in the directory set by this variable will be included before and after various configuration stages. Examples of file names: _CMAKE_INIT.cmake_, _PRE_CMAKE_BOOTSTRAP.cmake_, _POST_CMAKE_BOOTSTRAP.cmake_, etc.. Other names are not documented and can be found in the project cmake files by searching for the _ocv_cmake_hook_ macro calls. |
+| `OPENCV_DUMP_HOOKS_FLOW` | _OFF_ | Enables a debug message print on each cmake hook script call. |
+
+
+# Other non-documented options
+
+`BUILD_ANDROID_PROJECTS`
+`BUILD_ANDROID_EXAMPLES`
+`ANDROID_HOME`
+`ANDROID_SDK`
+`ANDROID_NDK`
+`ANDROID_SDK_ROOT`
+
+`CMAKE_TOOLCHAIN_FILE`
+
+`WITH_CAROTENE`
+`WITH_CPUFEATURES`
+`WITH_EIGEN`
+`WITH_OPENVX`
+`WITH_CLP`
+`WITH_DIRECTX`
+`WITH_VA`
+`WITH_LAPACK`
+`WITH_QUIRC`
+`BUILD_ZLIB`
+`BUILD_ITT`
+`WITH_IPP`
+`BUILD_IPP_IW`

doc/tutorials/introduction/cross_referencing/tutorial_cross_referencing.markdown

@@ -3,6 +3,13 @@ Cross referencing OpenCV from other Doxygen projects {#tutorial_cross_referencin
 
 @prev_tutorial{tutorial_transition_guide}
 
+|    |    |
+| -: | :- |
+| Original author | Sebastian Höffner |
+| Compatibility | OpenCV >= 3.3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 Cross referencing OpenCV
 ------------------------

doc/tutorials/introduction/crosscompilation/arm_crosscompile_with_cmake.markdown

@@ -4,6 +4,13 @@ Cross compilation for ARM based Linux systems {#tutorial_arm_crosscompile_with_c
 @prev_tutorial{tutorial_ios_install}
 @next_tutorial{tutorial_building_tegra_cuda}
 
+|    |    |
+| -: | :- |
+| Original author |  Alexander Smorkalov |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 This steps are tested on Ubuntu Linux 12.04, but should work for other Linux distributions. I case
 of other distributions package names and names of cross compilation tools may differ. There are

doc/tutorials/introduction/desktop_java/java_dev_intro.markdown

@@ -4,6 +4,13 @@ Introduction to Java Development {#tutorial_java_dev_intro}
 @prev_tutorial{tutorial_windows_visual_studio_image_watch}
 @next_tutorial{tutorial_java_eclipse}
 
+|    |    |
+| -: | :- |
+| Original author | Eric Christiansen and Andrey Pavlenko |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 As of OpenCV 2.4.4, OpenCV supports desktop Java development using nearly the same interface as for
 Android development. This guide will help you to create your first Java (or Scala) application using

doc/tutorials/introduction/display_image/display_image.markdown

@@ -4,6 +4,14 @@ Getting Started with Images {#tutorial_display_image}
 @prev_tutorial{tutorial_building_tegra_cuda}
 @next_tutorial{tutorial_documentation}
 
+|    |    |
+| -: | :- |
+| Original author | Ana Huamán |
+| Compatibility | OpenCV >= 3.4.4 |
+
+@warning
+This tutorial can contain obsolete information.
+
 Goal
 ----
 

doc/tutorials/introduction/documenting_opencv/documentation_tutorial.markdown

@@ -4,6 +4,10 @@ Writing documentation for OpenCV {#tutorial_documentation}
 @prev_tutorial{tutorial_display_image}
 @next_tutorial{tutorial_transition_guide}
 
+|    |    |
+| -: | :- |
+| Original author | Maksim Shabunin |
+| Compatibility | OpenCV >= 3.0 |
 
 @tableofcontents
 

doc/tutorials/introduction/general_install/general_install.markdown

@@ -0,0 +1,117 @@
+OpenCV installation overview {#tutorial_general_install}
+============================
+
+@tableofcontents
+
+There are two ways of installing OpenCV on your machine: download prebuilt version for your platform or compile from sources.
+
+# Prebuilt version {#tutorial_general_install_prebuilt}
+
+In many cases you can find prebuilt version of OpenCV that will meet your needs.
+
+## Packages by OpenCV core team  {#tutorial_general_install_prebuilt_core}
+
+Packages for Android, iOS and Windows built with default parameters and recent compilers are published for each release, they do not contain _opencv_contrib_ modules.
+
+- GitHub releases: https://github.com/opencv/opencv/releases
+- SourceForge.net: https://sourceforge.net/projects/opencvlibrary/files/
+
+
+## Third-party packages  {#tutorial_general_install_prebuilt_thirdparty}
+
+Other organizations and people maintain their own binary distributions of OpenCV. For example:
+
+- System packages in popular Linux distributions (https://pkgs.org/search/?q=opencv)
+- PyPI (https://pypi.org/search/?q=opencv)
+- Conda (https://anaconda.org/search?q=opencv)
+- Conan (https://github.com/conan-community/conan-opencv)
+- vcpkg (https://github.com/microsoft/vcpkg/tree/master/ports/opencv)
+- NuGet (https://www.nuget.org/packages?q=opencv)
+- Brew (https://formulae.brew.sh/formula/opencv)
+- Maven (https://search.maven.org/search?q=opencv)
+
+
+# Build from sources {#tutorial_general_install_sources}
+
+It can happen that existing binary packages are not applicable for your use case, then you'll have to build custom version of OpenCV by yourself. This section gives a high-level overview of the build process, check tutorial for specific platform for actual build instructions.
+
+OpenCV uses [CMake](https://cmake.org/) build management system for configuration and build, so this section mostly describes generalized process of building software with CMake.
+
+
+## Step 0: Prerequisites {#tutorial_general_install_sources_0}
+
+Install C++ compiler and build tools. On \*NIX platforms it is usually GCC/G++ or Clang compiler and Make or Ninja build tool. On Windows it can be Visual Studio IDE or MinGW-w64 compiler. Native toolchains for Android are provided in the Android NDK. XCode IDE is used to build software for OSX and iOS platforms.
+
+Install CMake from the official site or some other source.
+
+Get other third-party dependencies: libraries with extra functionality like decoding videos or showing GUI elements; libraries providing optimized implementations of selected algorithms; tools used for documentation generation and other extras. Check @ref tutorial_config_reference for available options and corresponding dependencies.
+
+
+## Step 1: Get software sources {#tutorial_general_install_sources_1}
+
+Typical software project consists of one or several code repositories. OpenCV have two repositories with code: _opencv_ - main repository with stable and actively supported algorithms and _opencv_contrib_ which contains experimental and non-free (patented) algorithms; and one repository with test data: _opencv_extra_.
+
+You can download a snapshot of repository in form of an archive or clone repository with full history.
+
+To download snapshot archives:
+
+- Go to https://github.com/opencv/opencv/releases and download "Source code" archive from any release.
+- (optionally) Go to https://github.com/opencv/opencv_contrib/releases and download "Source code" archive for the same release as _opencv_
+- (optionally) Go to https://github.com/opencv/opencv_extra/releases and download "Source code" archive for the same release as _opencv_
+- Unpack all archives to some location
+
+To clone repositories run the following commands in console (_git_ [must be installed](https://git-scm.com/book/en/v2/Getting-Started-Installing-Git)):
+
+```.sh
+git clone https://github.com/opencv/opencv
+git -C opencv checkout <some-tag>
+
+# optionally
+git clone https://github.com/opencv/opencv_contrib
+git -C opencv_contrib checkout <same-tag-as-opencv>
+
+# optionally
+git clone https://github.com/opencv/opencv_extra
+git -C opencv_extra checkout <same-tag-as-opencv>
+```
+
+@note
+If you want to build software using more than one repository, make sure all components are compatible with each other. For OpenCV it means that _opencv_ and _opencv_contrib_ repositories must be checked out at the same tag or that all snapshot archives are downloaded from the same release.
+
+@note
+When choosing which version to download take in account your target platform and development tools versions, latest versions of OpenCV can have build problems with very old compilers and vice versa. We recommend using latest release and fresh OS/compiler combination.
+
+## Step 2: Configure {#tutorial_general_install_sources_2}
+
+At this step CMake will verify that all necessary tools and dependencies are available and compatible with the library and will generate intermediate files for the chosen build system. It could be Makefiles, IDE projects and solutions, etc. Usually this step is performed in newly created build directory:
+```
+cmake -G<generator> <configuration-options> <source-directory>
+```
+
+@note
+`cmake-gui` application allows to see and modify available options using graphical user interface. See https://cmake.org/runningcmake/ for details.
+
+
+## Step 3: Build {#tutorial_general_install_sources_3}
+
+During build process source files are compiled into object files which are linked together or otherwise combined into libraries and applications. This step can be run using universal command:
+```
+cmake --build <build-directory> <build-options>
+```
+... or underlying build system can be called directly:
+```
+make
+```
+
+## Step 3: Install {#tutorial_general_install_sources_4}
+
+During installation procedure build results and other files from build directory will be copied to the install location. Default installation location is `/usr/local` on UNIX and `C:/Program Files` on Windows. This location can be changed at the configuration step by setting `CMAKE_INSTALL_PREFIX` option. To perform installation run the following command:
+```
+cmake --build <build-directory> --target install <other-options>
+```
+
+@note
+This step is optional, OpenCV can be used directly from the build directory.
+
+@note
+If the installation root location is a protected system directory, so the installation process must be run with superuser or administrator privileges (e.g. `sudo cmake ...`).

doc/tutorials/introduction/ios_install/ios_install.markdown

@@ -4,6 +4,14 @@ Installation in iOS {#tutorial_ios_install}
 @prev_tutorial{tutorial_macos_install}
 @next_tutorial{tutorial_arm_crosscompile_with_cmake}
 
+|    |    |
+| -: | :- |
+| Original author | Artem Myagkov, Eduard Feicho, Steve Nicholson |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
+
 Required Packages
 -----------------
 

doc/tutorials/introduction/java_eclipse/java_eclipse.markdown

@@ -4,6 +4,13 @@ Using OpenCV Java with Eclipse {#tutorial_java_eclipse}
 @prev_tutorial{tutorial_java_dev_intro}
 @next_tutorial{tutorial_clojure_dev_intro}
 
+|    |    |
+| -: | :- |
+| Original author | Barış Evrim Demiröz |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 Since version 2.4.4 [OpenCV supports Java](http://opencv.org/opencv-java-api.html). In this tutorial
 I will explain how to setup development environment for using OpenCV Java with Eclipse in

doc/tutorials/introduction/linux_eclipse/linux_eclipse.markdown

@@ -4,6 +4,14 @@ Using OpenCV with Eclipse (plugin CDT) {#tutorial_linux_eclipse}
 @prev_tutorial{tutorial_linux_gcc_cmake}
 @next_tutorial{tutorial_windows_install}
 
+|    |    |
+| -: | :- |
+| Original author | Ana Huamán |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
+
 Prerequisites
 -------------
 Two ways, one by forming a project directly, and another by CMake Prerequisites

doc/tutorials/introduction/linux_gcc_cmake/linux_gcc_cmake.markdown

@@ -4,6 +4,13 @@ Using OpenCV with gcc and CMake {#tutorial_linux_gcc_cmake}
 @prev_tutorial{tutorial_linux_install}
 @next_tutorial{tutorial_linux_eclipse}
 
+|    |    |
+| -: | :- |
+| Original author | Ana Huamán |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 @note We assume that you have successfully installed OpenCV in your workstation.
 

doc/tutorials/introduction/linux_install/linux_install.markdown

@@ -3,146 +3,123 @@ Installation in Linux {#tutorial_linux_install}
 
 @next_tutorial{tutorial_linux_gcc_cmake}
 
+|    |    |
+| -: | :- |
+| Original author | Ana Huamán |
+| Compatibility | OpenCV >= 3.0 |
 
-The following steps have been tested for Ubuntu 10.04 but should work with other distros as well.
+@tableofcontents
 
-Required Packages
------------------
+# Quick start {#tutorial_linux_install_quick_start}
 
--   GCC 4.4.x or later
--   CMake 2.8.7 or higher
--   Git
--   GTK+2.x or higher, including headers (libgtk2.0-dev)
--   pkg-config
--   Python 2.6 or later and Numpy 1.5 or later with developer packages (python-dev, python-numpy)
--   ffmpeg or libav development packages: libavcodec-dev, libavformat-dev, libswscale-dev
--   [optional] libtbb2 libtbb-dev
--   [optional] libdc1394 2.x
--   [optional] libjpeg-dev, libpng-dev, libtiff-dev, libjasper-dev, libdc1394-22-dev
--   [optional] CUDA Toolkit 6.5 or higher
 
-The packages can be installed using a terminal and the following commands or by using Synaptic
-Manager:
-@code{.bash}
-[compiler] sudo apt-get install build-essential
-[required] sudo apt-get install cmake git libgtk2.0-dev pkg-config libavcodec-dev libavformat-dev libswscale-dev
-[optional] sudo apt-get install python-dev python-numpy libtbb2 libtbb-dev libjpeg-dev libpng-dev libtiff-dev libjasper-dev libdc1394-22-dev
-@endcode
-Getting OpenCV Source Code
---------------------------
+## Build core modules {#tutorial_linux_install_quick_build_core}
 
-You can use the latest stable OpenCV version or you can grab the latest snapshot from our [Git
-repository](https://github.com/opencv/opencv.git).
+@snippet linux_quick_install.sh body
 
-### Getting the Latest Stable OpenCV Version
 
--   Go to our [downloads page](http://opencv.org/releases.html).
--   Download the source archive and unpack it.
+## Build with opencv_contrib {#tutorial_linux_install_quick_build_contrib}
 
-### Getting the Cutting-edge OpenCV from the Git Repository
+@snippet linux_quick_install_contrib.sh body
 
-Launch Git client and clone [OpenCV repository](http://github.com/opencv/opencv). If you need
-modules from [OpenCV contrib repository](http://github.com/opencv/opencv_contrib) then clone it as well.
 
-For example
-@code{.bash}
-cd ~/<my_working_directory>
-git clone https://github.com/opencv/opencv.git
-git clone https://github.com/opencv/opencv_contrib.git
-@endcode
-Building OpenCV from Source Using CMake
----------------------------------------
+# Detailed process {#tutorial_linux_install_detailed}
 
--#  Create a temporary directory, which we denote as \<cmake_build_dir\>, where you want to put
-    the generated Makefiles, project files as well the object files and output binaries and enter
-    there.
+This section provides more details of the build process and describes alternative methods and tools. Please refer to the @ref tutorial_general_install tutorial for general installation details and to the @ref tutorial_config_reference for configuration options documentation.
 
-    For example
-    @code{.bash}
-    cd ~/opencv
-    mkdir build
-    cd build
-    @endcode
--#  Configuring. Run cmake [\<some optional parameters\>] \<path to the OpenCV source directory\>
 
-    For example
-    @code{.bash}
-    cmake -D CMAKE_BUILD_TYPE=Release -D CMAKE_INSTALL_PREFIX=/usr/local ..
-    @endcode
-    or cmake-gui
+## Install compiler and build tools {#tutorial_linux_install_detailed_basic_compiler}
 
-    -   set full path to OpenCV source code, e.g. /home/user/opencv
-    -   set full path to \<cmake_build_dir\>, e.g. /home/user/opencv/build
-    -   set optional parameters
-    -   run: “Configure”
-    -   run: “Generate”
+- To compile OpenCV you will need a C++ compiler. Usually it is G++/GCC or Clang/LLVM:
+    - Install GCC...
+    @snippet linux_install_a.sh gcc
+    - ... or Clang:
+    @snippet linux_install_b.sh clang
 
-    @note
-    Use `cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=/usr/local ..` , without spaces after -D if the above example doesn't work.
+- OpenCV uses CMake build configuration tool:
+@snippet linux_install_a.sh cmake
 
--#  Description of some parameters
-    -   build type: `CMAKE_BUILD_TYPE=Release\Debug`
-    -   to build with modules from opencv_contrib set OPENCV_EXTRA_MODULES_PATH to \<path to
-        opencv_contrib/modules/\>
-    -   set BUILD_DOCS for building documents
-    -   set BUILD_EXAMPLES to build all examples
+- CMake can generate scripts for different build systems, e.g. _make_, _ninja_:
 
--#  [optional] Building python. Set the following python parameters:
-    -   PYTHON2(3)_EXECUTABLE = \<path to python\>
-    -   PYTHON_INCLUDE_DIR = /usr/include/python\<version\>
-    -   PYTHON_INCLUDE_DIR2 = /usr/include/x86_64-linux-gnu/python\<version\>
-    -   PYTHON_LIBRARY = /usr/lib/x86_64-linux-gnu/libpython\<version\>.so
-    -   PYTHON2(3)_NUMPY_INCLUDE_DIRS =
-        /usr/lib/python\<version\>/dist-packages/numpy/core/include/
+    - Install Make...
+    @snippet linux_install_a.sh make
+    - ... or Ninja:
+    @snippet linux_install_b.sh ninja
 
--#  [optional] Building java.
-    -   Unset parameter: BUILD_SHARED_LIBS
-    -   It is useful also to unset BUILD_EXAMPLES, BUILD_TESTS, BUILD_PERF_TESTS - as they all
-        will be statically linked with OpenCV and can take a lot of memory.
+- Install tool for getting and unpacking sources:
 
--#  [optional] Generate pkg-config info
-    -   Add this flag when running CMake: `-DOPENCV_GENERATE_PKGCONFIG=ON`
-    -   Will generate the .pc file for pkg-config and install it.
-    -   Useful if not using CMake in projects that use OpenCV
-    -   Installed as `opencv4`, usage: `pkg-config --cflags --libs opencv4`
+    - _wget_ and _unzip_...
+    @snippet linux_install_a.sh wget
+    - ... or _git_:
+    @snippet linux_install_b.sh git
 
--#  Build. From build directory execute *make*, it is recommended to do this in several threads
 
-    For example
-    @code{.bash}
-    make -j7 # runs 7 jobs in parallel
-    @endcode
--#  [optional] Building documents. Enter \<cmake_build_dir/doc/\> and run make with target
-    "doxygen"
+## Download sources {#tutorial_linux_install_detailed_basic_download}
 
-    For example
-    @code{.bash}
-    cd ~/opencv/build/doc/
-    make -j7 doxygen
-    @endcode
--#  To install libraries, execute the following command from build directory
-    @code{.bash}
-    sudo make install
-    @endcode
--#  [optional] Running tests
+There are two methods of getting OpenCV sources:
 
-    -   Get the required test data from [OpenCV extra
-        repository](https://github.com/opencv/opencv_extra).
+- Download snapshot of repository using web browser or any download tool (~80-90Mb) and unpack it...
+@snippet linux_install_a.sh download
+- ... or clone repository to local machine using _git_ to get full change history (>470Mb):
+@snippet linux_install_b.sh download
 
-    For example
-    @code{.bash}
-    git clone https://github.com/opencv/opencv_extra.git
-    @endcode
-    -   set OPENCV_TEST_DATA_PATH environment variable to \<path to opencv_extra/testdata\>.
-    -   execute tests from build directory.
-
-    For example
-    @code{.bash}
-    <cmake_build_dir>/bin/opencv_test_core
-    @endcode
 
 @note
-   If the size of the created library is a critical issue (like in case of an Android build) you
-    can use the install/strip command to get the smallest size possible. The *stripped* version
-    appears to be twice as small. However, we do not recommend using this unless those extra
-    megabytes do really matter.
+Snapshots of other branches, releases or commits can be found on the [GitHub](https://github.com/opencv/opencv) and the [official download page](https://opencv.org/releases.html).
+
+
+## Configure and build {#tutorial_linux_install_detailed_basic_build}
+
+- Create build directory:
+@snippet linux_install_a.sh prepare
+
+- Configure - generate build scripts for the preferred build system:
+    - For _make_...
+    @snippet linux_install_a.sh configure
+    - ... or for _ninja_:
+    @snippet linux_install_b.sh configure
+
+- Build - run actual compilation process:
+    - Using _make_...
+    @snippet linux_install_a.sh build
+    - ... or _ninja_:
+    @snippet linux_install_b.sh build
+
+
+@note
+_Configure_ process can download some files from the internet to satisfy library dependencies, connection failures can cause some of modules or functionalities to be turned off or behave differently. Refer to the @ref tutorial_general_install and @ref tutorial_config_reference tutorials for details and full configuration options reference.
+
+@note
+If you experience problems with the build process, try to clean or recreate the build directory. Changes in the configuration like disabling a dependency, modifying build scripts or switching sources to another branch are not handled very well and can result in broken workspace.
+
+@note
+_Make_ can run multiple compilation processes in parallel, `-j<NUM>` option means "run <NUM> jobs simultaneously". _Ninja_ will automatically detect number of available processor cores and does not need `-j` option.
+
+
+## Check build results {#tutorial_linux_install_detailed_basic_verify}
+
+After successful build you will find libraries in the `build/lib` directory and executables (test, samples, apps) in the `build/bin` directory:
+@snippet linux_install_a.sh check
+
+CMake package files will be located in the build root:
+@snippet linux_install_a.sh check cmake
+
+
+## Install
+
+@warning
+Installation process only copies files to predefined locations and do minor patching. Library installed using this method is not integrated into the system package registry and can not be uninstalled automatically. We do not recommend system-wide installation to regular users due to possible conflicts with system packages.
+
+By default OpenCV will be installed to the `/usr/local` directory, all files will be copied to following locations:
+* `/usr/local/bin` - executable files
+* `/usr/local/lib` - libraries (.so)
+* `/usr/local/cmake/opencv4` - cmake package
+* `/usr/local/include/opencv4` - headers
+* `/usr/local/share/opencv4` - other files (e.g. trained cascades in XML format)
+
+Since `/usr/local` is owned by the root user, the installation should be performed with elevated privileges (`sudo`):
+@snippet linux_install_a.sh install
+or
+@snippet linux_install_b.sh install
+
+Installation root directory can be changed with `CMAKE_INSTALL_PREFIX` configuration parameter, e.g. `-DCMAKE_INSTALL_PREFIX=$HOME/.local` to install to current user's local directory. Installation layout can be changed with `OPENCV_*_INSTALL_PATH` parameters. See @ref tutorial_config_reference for details.

doc/tutorials/introduction/macos_install/macos_install.markdown

@@ -4,6 +4,10 @@ Installation in MacOS {#tutorial_macos_install}
 @prev_tutorial{tutorial_android_ocl_intro}
 @next_tutorial{tutorial_ios_install}
 
+|    |    |
+| -: | :- |
+| Original author | `@sajarindider` |
+| Compatibility | OpenCV >= 3.4 |
 
 The following steps have been tested for MacOSX (Mavericks) but should work with other versions as well.
 

doc/tutorials/introduction/table_of_content_introduction.markdown

@@ -1,175 +1,38 @@
 Introduction to OpenCV {#tutorial_table_of_content_introduction}
 ======================
 
-Here you can read tutorials about how to set up your computer to work with the OpenCV library.
-Additionally you can find very basic sample source code to introduce you to the world of the OpenCV.
+- @subpage tutorial_general_install
+- @subpage tutorial_config_reference
 
+##### Linux
 -   @subpage tutorial_linux_install
-
-    _Compatibility:_ \> OpenCV 2.0
-
-    _Author:_ Ana Huamán
-
-    We will learn how to setup OpenCV in your computer!
-
 -   @subpage tutorial_linux_gcc_cmake
-
-    _Compatibility:_ \> OpenCV 2.0
-
-    _Author:_ Ana Huamán
-
-    We will learn how to compile your first project using gcc and CMake
-
 -   @subpage tutorial_linux_eclipse
 
-    _Compatibility:_ \> OpenCV 2.0
-
-    _Author:_ Ana Huamán
-
-    We will learn how to compile your first project using the Eclipse environment
-
+##### Windows
 -   @subpage tutorial_windows_install
-
-    _Compatibility:_ \> OpenCV 2.0
-
-    _Author:_ Bernát Gábor
-
-    You will learn how to setup OpenCV in your Windows Operating System!
-
 -   @subpage tutorial_windows_visual_studio_opencv
-
-    _Compatibility:_ \> OpenCV 2.0
-
-    _Author:_ Bernát Gábor
-
-    You will learn what steps you need to perform in order to use the OpenCV library inside a new
-    Microsoft Visual Studio project.
-
 -   @subpage tutorial_windows_visual_studio_image_watch
 
-    _Compatibility:_ \>= OpenCV 2.4
-
-    _Author:_ Wolf Kienzle
-
-    You will learn how to visualize OpenCV matrices and images within Visual Studio 2012.
-
+##### Java & Android
 -   @subpage tutorial_java_dev_intro
-
-    _Compatibility:_ \> OpenCV 2.4.4
-
-    _Authors:_ Eric Christiansen and Andrey Pavlenko
-
-    Explains how to build and run a simple desktop Java application using Eclipse, Ant or the
-    Simple Build Tool (SBT).
-
 -   @subpage tutorial_java_eclipse
-
-    _Compatibility:_ \> OpenCV 2.4.4
-
-    _Author:_ Barış Evrim Demiröz
-
-    A tutorial on how to use OpenCV Java with Eclipse.
-
 -   @subpage tutorial_clojure_dev_intro
-
-    _Compatibility:_ \> OpenCV 2.4.4
-
-    _Author:_ Mimmo Cosenza
-
-    A tutorial on how to interactively use OpenCV from the Clojure REPL.
-
 -   @subpage tutorial_android_dev_intro
-
-    _Compatibility:_ \> OpenCV 2.4.2
-
-    _Author:_ Vsevolod Glumov
-
-    Not a tutorial, but a guide introducing Android development basics and environment setup
-
 -   @subpage tutorial_O4A_SDK
-
-    _Compatibility:_ \> OpenCV 2.4.2
-
-    _Author:_ Vsevolod Glumov
-
-    OpenCV4Android SDK: general info, installation, running samples
-
 -   @subpage tutorial_dev_with_OCV_on_Android
-
-    _Compatibility:_ \> OpenCV 2.4.3
-
-    _Author:_ Vsevolod Glumov
-
-    Development with OpenCV4Android SDK
-
 -   @subpage tutorial_android_ocl_intro
 
-    _Compatibility:_ \>= OpenCV 3.0
-
-    _Author:_ Andrey Pavlenko
-
-    Modify Android camera preview with OpenCL
-
+##### Other platforms
 -   @subpage tutorial_macos_install
-
-    _Compatibility:_ \> OpenCV 3.4.x
-
-    _Author:_ [\@sajarindider](https://github.com/sajarindider)
-
-    We will learn how to setup OpenCV in MacOS.
-
 -   @subpage tutorial_ios_install
-
-    _Compatibility:_ \> OpenCV 2.4.2
-
-    _Author:_ Artem Myagkov, Eduard Feicho, Steve Nicholson
-
-    We will learn how to setup OpenCV for using it in iOS!
-
 -   @subpage tutorial_arm_crosscompile_with_cmake
-
-    _Compatibility:_ \> OpenCV 2.4.4
-
-    _Author:_ Alexander Smorkalov
-
-    We will learn how to setup OpenCV cross compilation environment for ARM Linux.
-
 -   @subpage tutorial_building_tegra_cuda
 
-    _Compatibility:_ \>= OpenCV 3.1.0
+##### Usage basics
+-   @subpage tutorial_display_image - We will learn how to load an image from file and display it using OpenCV
 
-    _Author:_ Randy J. Ray
-
-    This tutorial will help you build OpenCV 3.1.0 for NVIDIA<sup>&reg;</sup> Tegra<sup>&reg;</sup> systems with CUDA 8.0.
-
--   @subpage tutorial_display_image
-
-    _Languages:_ C++, Python
-
-    _Compatibility:_ \> OpenCV 3.4.4
-
-    _Author:_ Ana Huamán
-
-    We will learn how to read an image, display it in a window and write it to a file using OpenCV
-
--   @subpage tutorial_documentation
-
-    _Compatibility:_ \> OpenCV 3.0
-
-    _Author:_ Maksim Shabunin
-
-    This tutorial describes new documenting process and some useful Doxygen features.
-
--   @subpage tutorial_transition_guide
-
-    _Author:_ Maksim Shabunin
-
-    This document describes some aspects of 2.4 -> 3.0 transition process.
-
--   @subpage tutorial_cross_referencing
-
-    _Compatibility:_ \> OpenCV 3.3.0
-
-    _Author:_ Sebastian Höffner
-
-    This document outlines how to create cross references to the OpenCV documentation from other Doxygen projects.
+##### Miscellaneous
+-   @subpage tutorial_documentation - This tutorial describes new documenting process and some useful Doxygen features.
+-   @subpage tutorial_transition_guide - This document describes some aspects of 2.4 -> 3.0 transition process.
+-   @subpage tutorial_cross_referencing - This document outlines how to create cross references to the OpenCV documentation from other Doxygen projects.

doc/tutorials/introduction/transition_guide/transition_guide.markdown

@@ -4,6 +4,10 @@ Transition guide {#tutorial_transition_guide}
 @prev_tutorial{tutorial_documentation}
 @next_tutorial{tutorial_cross_referencing}
 
+|    |    |
+| -: | :- |
+| Original author | Maksim Shabunin |
+| Compatibility | OpenCV >= 3.0 |
 
 @tableofcontents
 

doc/tutorials/introduction/windows_install/windows_install.markdown

@@ -4,6 +4,13 @@ Installation in Windows {#tutorial_windows_install}
 @prev_tutorial{tutorial_linux_eclipse}
 @next_tutorial{tutorial_windows_visual_studio_opencv}
 
+|    |    |
+| -: | :- |
+| Original author | Bernát Gábor |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 The description here was tested on Windows 7 SP1. Nevertheless, it should also work on any other
 relatively modern version of Windows OS. If you encounter errors after following the steps described

doc/tutorials/introduction/windows_visual_studio_image_watch/windows_visual_studio_image_watch.markdown

@@ -4,6 +4,13 @@ Image Watch: viewing in-memory images in the Visual Studio debugger {#tutorial_w
 @prev_tutorial{tutorial_windows_visual_studio_opencv}
 @next_tutorial{tutorial_java_dev_intro}
 
+|    |    |
+| -: | :- |
+| Original author | Wolf Kienzle |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 Image Watch is a plug-in for Microsoft Visual Studio that lets you to visualize in-memory images
 (*cv::Mat* or *IplImage_* objects, for example) while debugging an application. This can be helpful

doc/tutorials/introduction/windows_visual_studio_opencv/windows_visual_studio_opencv.markdown

@@ -1,9 +1,15 @@
 How to build applications with OpenCV inside the "Microsoft Visual Studio" {#tutorial_windows_visual_studio_opencv}
 ==========================================================================
-
 @prev_tutorial{tutorial_windows_install}
 @next_tutorial{tutorial_windows_visual_studio_image_watch}
 
+|    |    |
+| -: | :- |
+| Original author | Bernát Gábor |
+| Compatibility | OpenCV >= 3.0 |
+
+@warning
+This tutorial can contain obsolete information.
 
 Everything I describe here will apply to the `C\C++` interface of OpenCV. I start out from the
 assumption that you have read and completed with success the @ref tutorial_windows_install tutorial.

doc/tutorials/tutorials.markdown

@@ -1,93 +1,22 @@
 OpenCV Tutorials {#tutorial_root}
 ================
 
-The following links describe a set of basic OpenCV tutorials. All the source code mentioned here is
-provided as part of the OpenCV regular releases, so check before you start copying & pasting the code.
-The list of tutorials below is automatically generated from reST files located in our GIT
-repository.
-
-As always, we would be happy to hear your comments and receive your contributions on any tutorial.
-
--   @subpage tutorial_table_of_content_introduction
-
-    You will learn how to setup OpenCV on your computer
-
--   @subpage tutorial_table_of_content_core
-
-    Here you will learn
-    about the basic building blocks of this library. A must read for understanding how
-    to manipulate the images on a pixel level.
-
--   @subpage tutorial_table_of_content_imgproc
-
-    In this section
-    you will learn about the image processing (manipulation) functions inside OpenCV.
-
--   @subpage tutorial_table_of_content_highgui
-
-    This section contains valuable tutorials on how to use the
-    built-in graphical user interface of the library.
-
--   @subpage tutorial_table_of_content_imgcodecs
-
-    These tutorials show how to read and write images using imgcodecs module.
-
--   @subpage tutorial_table_of_content_videoio
-
-    These tutorials show how to read and write videos using videio module.
-
--   @subpage tutorial_table_of_content_calib3d
-
-    Although
-    most of our images are in a 2D format they do come from a 3D world. Here you will learn how to find
-    out 3D world information from 2D images.
-
--   @subpage tutorial_table_of_content_features2d
-
-    Learn about how
-    to use the feature points detectors, descriptors and matching framework found inside OpenCV.
-
--   @subpage tutorial_table_of_content_video
-
-    Here you will find
-    algorithms usable on your video streams like motion extraction, feature tracking and
-    foreground extractions.
-
--   @subpage tutorial_table_of_content_objdetect
-
-    Ever wondered
-    how your digital camera detects people's faces? Look here to find out!
-
--   @subpage tutorial_table_of_content_dnn
-
-    These tutorials show how to use dnn module effectively.
-
--   @subpage tutorial_table_of_content_ml
-
-    Use the powerful
-    machine learning classes for statistical classification, regression and clustering of data.
-
--   @subpage tutorial_table_of_content_gapi
-
-    Learn how to use Graph API (G-API) and port algorithms from "traditional" OpenCV to a graph model.
-
--   @subpage tutorial_table_of_content_photo
-
-    Use OpenCV for
-    advanced photo processing.
-
--   @subpage tutorial_table_of_content_stitching
-
-    Learn how to create beautiful photo panoramas and more with OpenCV stitching pipeline.
-
+- @subpage tutorial_table_of_content_introduction - build and install OpenCV on your computer
+- @subpage tutorial_table_of_content_core - basic building blocks of the library
+- @subpage tutorial_table_of_content_imgproc - image processing functions
+- @subpage tutorial_table_of_content_highgui - built-in graphical user interface
+- @subpage tutorial_table_of_content_imgcodecs - read and write images from/to files using _imgcodecs_ module
+- @subpage tutorial_table_of_content_videoio - read and write videos using _videio_ module
+- @subpage tutorial_table_of_content_calib3d - extract 3D world information from 2D images
+- @subpage tutorial_table_of_content_features2d - feature detectors, descriptors and matching framework
+- @subpage tutorial_table_of_content_video - algorithms for video streams: motion detection, object and feature tracking, etc.
+- @subpage tutorial_table_of_content_objdetect - detect objects using conventional CV methods
+- @subpage tutorial_table_of_content_dnn - infer neural networks using built-in _dnn_ module
+- @subpage tutorial_table_of_content_ml - machine learning algorithms for statistical classification, regression and data clustering
+- @subpage tutorial_table_of_content_gapi - graph-based approach to computer vision algorithms building
+- @subpage tutorial_table_of_content_photo - advanced photo processing
+- @subpage tutorial_table_of_content_stitching - create panoramas and more using _stitching_ module
+- @subpage tutorial_table_of_content_ios - running OpenCV on an iDevice
 @cond CUDA_MODULES
--   @subpage tutorial_table_of_content_gpu
-
-    Squeeze out every
-    little computational power from your system by utilizing the power of your video card to run the
-    OpenCV algorithms.
+- @subpage tutorial_table_of_content_gpu - utilizing power of video card to run CV algorithms
 @endcond
-
--   @subpage tutorial_table_of_content_ios
-
-    Run OpenCV and your vision apps on an iDevice

doc/tutorials/videoio/intelperc.markdown

@@ -1,24 +1,21 @@
-Using Creative Senz3D and other Intel Perceptual Computing SDK compatible depth sensors {#tutorial_intelperc}
+Using Creative Senz3D and other Intel RealSense SDK compatible depth sensors {#tutorial_intelperc}
 =======================================================================================
 
 @prev_tutorial{tutorial_kinect_openni}
 
-**Note**: this tutorial is partially obsolete since PerC SDK has been replaced with RealSense SDK
+**Note**: This tutorial is partially obsolete since PerC SDK has been replaced with RealSense SDK
 
-Depth sensors compatible with Intel Perceptual Computing SDK are supported through VideoCapture
+Depth sensors compatible with Intel® RealSense SDK are supported through VideoCapture
 class. Depth map, RGB image and some other formats of output can be retrieved by using familiar
 interface of VideoCapture.
 
 In order to use depth sensor with OpenCV you should do the following preliminary steps:
 
--#  Install Intel Perceptual Computing SDK (from here <http://www.intel.com/software/perceptual>).
+-#  Install Intel RealSense SDK 2.0 (from here <https://github.com/IntelRealSense/librealsense>).
 
--#  Configure OpenCV with Intel Perceptual Computing SDK support by setting WITH_INTELPERC flag in
-    CMake. If Intel Perceptual Computing SDK is found in install folders OpenCV will be built with
-    Intel Perceptual Computing SDK library (see a status INTELPERC in CMake log). If CMake process
-    doesn't find Intel Perceptual Computing SDK installation folder automatically, the user should
-    change corresponding CMake variables INTELPERC_LIB_DIR and INTELPERC_INCLUDE_DIR to the
-    proper value.
+-#  Configure OpenCV with Intel RealSense SDK support by setting WITH_LIBREALSENSE flag in
+    CMake. If Intel RealSense SDK is found in install folders OpenCV will be built with
+    Intel Realsense SDK library (see a status LIBREALSENSE in CMake log).
 
 -#  Build OpenCV.
 
@@ -38,7 +35,7 @@ VideoCapture can retrieve the following data:
 
 In order to get depth map from depth sensor use VideoCapture::operator \>\>, e. g. :
 @code{.cpp}
-    VideoCapture capture( CAP_INTELPERC );
+    VideoCapture capture( CAP_REALSENSE );
     for(;;)
     {
         Mat depthMap;
@@ -50,7 +47,7 @@ In order to get depth map from depth sensor use VideoCapture::operator \>\>, e.
 @endcode
 For getting several data maps use VideoCapture::grab and VideoCapture::retrieve, e.g. :
 @code{.cpp}
-    VideoCapture capture(CAP_INTELPERC);
+    VideoCapture capture(CAP_REALSENSE);
     for(;;)
     {
         Mat depthMap;
@@ -70,7 +67,7 @@ For getting several data maps use VideoCapture::grab and VideoCapture::retrieve,
 For setting and getting some property of sensor\` data generators use VideoCapture::set and
 VideoCapture::get methods respectively, e.g. :
 @code{.cpp}
-    VideoCapture capture( CAP_INTELPERC );
+    VideoCapture capture(CAP_REALSENSE);
     capture.set( CAP_INTELPERC_DEPTH_GENERATOR | CAP_PROP_INTELPERC_PROFILE_IDX, 0 );
     cout << "FPS    " << capture.get( CAP_INTELPERC_DEPTH_GENERATOR+CAP_PROP_FPS ) << endl;
 @endcode

modules/calib3d/include/opencv2/calib3d.hpp

@@ -450,7 +450,7 @@ enum { LMEDS  = 4,  //!< least-median of squares algorithm
        USAC_FAST = 35,     //!< USAC, fast settings
        USAC_ACCURATE = 36, //!< USAC, accurate settings
        USAC_PROSAC = 37,   //!< USAC, sorted points, runs PROSAC
-       USAC_MAGSAC = 38    //!< USAC, sorted points, runs PROSAC
+       USAC_MAGSAC = 38    //!< USAC, runs MAGSAC++
      };
 
 enum SolvePnPMethod {
@@ -2607,7 +2607,7 @@ final fundamental matrix. It can be set to something like 1-3, depending on the
 point localization, image resolution, and the image noise.
 @param confidence Parameter used for the RANSAC and LMedS methods only. It specifies a desirable level
 of confidence (probability) that the estimated matrix is correct.
-@param mask
+@param[out] mask optional output mask
 @param maxIters The maximum number of robust method iterations.
 
 The epipolar geometry is described by the following equation:

modules/calib3d/src/fundam.cpp

@@ -355,7 +355,7 @@ cv::Mat cv::findHomography( InputArray _points1, InputArray _points2,
 {
     CV_INSTRUMENT_REGION();
 
-    if (method >= 32 && method <= 38)
+    if (method >= USAC_DEFAULT && method <= USAC_MAGSAC)
         return usac::findHomography(_points1, _points2, method, ransacReprojThreshold,
             _mask, maxIters, confidence);
 
@@ -380,6 +380,9 @@ cv::Mat cv::findHomography( InputArray _points1, InputArray _points2,
                 return Mat();
             convertPointsFromHomogeneous(p, p);
         }
+        // Need at least 4 point correspondences to calculate Homography
+        if( npoints < 4 )
+            CV_Error(Error::StsVecLengthErr , "The input arrays should have at least 4 corresponding point sets to calculate Homography");
         p.reshape(2, npoints).convertTo(m, CV_32F);
     }
 
@@ -831,7 +834,7 @@ cv::Mat cv::findFundamentalMat( InputArray _points1, InputArray _points2,
 {
     CV_INSTRUMENT_REGION();
 
-    if (method >= 32 && method <= 38)
+    if (method >= USAC_DEFAULT && method <= USAC_MAGSAC)
         return usac::findFundamentalMat(_points1, _points2, method,
             ransacReprojThreshold, confidence, maxIters, _mask);
 

modules/calib3d/src/ippe.cpp

@@ -77,18 +77,18 @@ void PoseSolver::solveGeneric(InputArray _objectPoints, InputArray _normalizedIn
                               OutputArray _Ma, OutputArray _Mb)
 {
     //argument checking:
-    size_t n = static_cast<size_t>(_objectPoints.rows() * _objectPoints.cols()); //number of points
+    size_t n = static_cast<size_t>(_normalizedInputPoints.rows()) * static_cast<size_t>(_normalizedInputPoints.cols()); //number of points
     int objType = _objectPoints.type();
     int type_input = _normalizedInputPoints.type();
 
     CV_CheckType(objType, objType == CV_32FC3 || objType == CV_64FC3,
                  "Type of _objectPoints must be CV_32FC3 or CV_64FC3" );
     CV_CheckType(type_input, type_input == CV_32FC2 || type_input == CV_64FC2,
-                 "Type of _normalizedInputPoints must be CV_32FC3 or CV_64FC3" );
+                 "Type of _normalizedInputPoints must be CV_32FC2 or CV_64FC2" );
     CV_Assert(_objectPoints.rows() == 1 || _objectPoints.cols() == 1);
     CV_Assert(_objectPoints.rows() >= 4 || _objectPoints.cols() >= 4);
     CV_Assert(_normalizedInputPoints.rows() == 1 || _normalizedInputPoints.cols() == 1);
-    CV_Assert(static_cast<size_t>(_objectPoints.rows() * _objectPoints.cols()) == n);
+    CV_Assert(static_cast<size_t>(_objectPoints.rows()) * static_cast<size_t>(_objectPoints.cols()) == n);
 
     Mat normalizedInputPoints;
     if (type_input == CV_32FC2)
@@ -101,7 +101,7 @@ void PoseSolver::solveGeneric(InputArray _objectPoints, InputArray _normalizedIn
     }
 
     Mat objectInputPoints;
-    if (type_input == CV_32FC3)
+    if (objType == CV_32FC3)
     {
         _objectPoints.getMat().convertTo(objectInputPoints, CV_64F);
     }

modules/calib3d/src/ptsetreg.cpp

@@ -930,7 +930,7 @@ Mat estimateAffine2D(InputArray _from, InputArray _to, OutputArray _inliers,
                      const size_t refineIters)
 {
 
-    if (method >= 32 && method <= 38)
+    if (method >= USAC_DEFAULT && method <= USAC_MAGSAC)
         return cv::usac::estimateAffine2D(_from, _to, _inliers, method,
             ransacReprojThreshold, (int)maxIters, confidence, (int)refineIters);
 

modules/calib3d/src/solvepnp.cpp

@@ -205,7 +205,7 @@ bool solvePnPRansac(InputArray _opoints, InputArray _ipoints,
 {
     CV_INSTRUMENT_REGION();
 
-    if (flags >= 32 && flags <= 38)
+    if (flags >= USAC_DEFAULT && flags <= USAC_MAGSAC)
         return usac::solvePnPRansac(_opoints, _ipoints, _cameraMatrix, _distCoeffs,
             _rvec, _tvec, useExtrinsicGuess, iterationsCount, reprojectionError,
             confidence, _inliers, flags);

modules/calib3d/src/usac.hpp

@@ -193,6 +193,26 @@ public:
     }
 };
 
+class GammaValues
+{
+    const double max_range_complete /*= 4.62*/, max_range_gamma /*= 1.52*/;
+    const int max_size_table /* = 3000 */;
+
+    std::vector<double> gamma_complete, gamma_incomplete, gamma;
+
+    GammaValues();  // use getSingleton()
+
+public:
+    static const GammaValues& getSingleton();
+
+    const std::vector<double>& getCompleteGammaValues() const;
+    const std::vector<double>& getIncompleteGammaValues() const;
+    const std::vector<double>& getGammaValues() const;
+    double getScaleOfGammaCompleteValues () const;
+    double getScaleOfGammaValues () const;
+    int getTableSize () const;
+};
+
 ////////////////////////////////////////// QUALITY ///////////////////////////////////////////
 class Quality : public Algorithm {
 public:
@@ -269,10 +289,6 @@ public:
     virtual bool isModelValid (const Mat &/*model*/, const std::vector<int> &/*sample*/) const {
         return true;
     }
-    virtual bool isModelValid (const Mat &/*model*/, const std::vector<int> &/*sample*/,
-            int /*sample_size*/) const {
-        return true;
-    }
     /*
      * Fix degenerate model.
      * Return true if model is degenerate, false - otherwise
@@ -286,7 +302,7 @@ public:
 
 class EpipolarGeometryDegeneracy : public Degeneracy {
 public:
-    static void recoverRank (Mat &model);
+    static void recoverRank (Mat &model, bool is_fundamental_mat);
     static Ptr<EpipolarGeometryDegeneracy> create (const Mat &points_, int sample_size_);
 };
 
@@ -405,9 +421,7 @@ struct SPRT_history {
     double epsilon, delta, A;
     // number of samples processed by test
     int tested_samples; // k
-    SPRT_history ()
-        : epsilon(0), delta(0), A(0)
-    {
+    SPRT_history () {
         tested_samples = 0;
     }
 };
@@ -465,7 +479,7 @@ class GridNeighborhoodGraph : public NeighborhoodGraph {
 public:
     static Ptr<GridNeighborhoodGraph> create(const Mat &points, int points_size,
             int cell_size_x_img1_, int cell_size_y_img1_,
-            int cell_size_x_img2_, int cell_size_y_img2_);
+            int cell_size_x_img2_, int cell_size_y_img2_, int max_neighbors);
 };
 
 ////////////////////////////////////// UNIFORM SAMPLER ////////////////////////////////////////////
@@ -568,7 +582,7 @@ namespace Math {
     // return skew symmetric matrix
     Matx33d getSkewSymmetric(const Vec3d &v_);
     // eliminate matrix with m rows and n columns to be upper triangular.
-    void eliminateUpperTriangular (std::vector<double> &a, int m, int n);
+    bool eliminateUpperTriangular (std::vector<double> &a, int m, int n);
     Matx33d rotVec2RotMat (const Vec3d &v);
     Vec3d rotMat2RotVec (const Matx33d &R);
 }
@@ -746,6 +760,7 @@ public:
     virtual int getLOInnerMaxIters() const = 0;
     virtual const std::vector<int> &getGridCellNumber () const = 0;
     virtual int getRandomGeneratorState () const = 0;
+    virtual int getMaxItersBeforeLO () const = 0;
 
     // setters
     virtual void setLocalOptimization (LocalOptimMethod lo_) = 0;
@@ -759,6 +774,7 @@ public:
     virtual void setLOIterations (int iters) = 0;
     virtual void setLOIterativeIters (int iters) = 0;
     virtual void setLOSampleSize (int lo_sample_size) = 0;
+    virtual void setThresholdMultiplierLO (double thr_mult) = 0;
     virtual void setRandomGeneratorState (int state) = 0;
 
     virtual void maskRequired (bool required) = 0;

modules/calib3d/src/usac/degeneracy.cpp

@@ -18,17 +18,11 @@ public:
      * Do oriented constraint to verify if epipolar geometry is in front or behind the camera.
      * Return: true if all points are in front of the camers w.r.t. tested epipolar geometry - satisfies constraint.
      *         false - otherwise.
-     */
-    inline bool isModelValid(const Mat &F, const std::vector<int> &sample) const override {
-        return isModelValid(F, sample, min_sample_size);
-    }
-
-    /* Oriented constraint:
      * x'^T F x = 0
      * e' × x' ~+ Fx   <=>  λe' × x' = Fx, λ > 0
      * e  × x ~+ x'^T F
      */
-    inline bool isModelValid(const Mat &F_, const std::vector<int> &sample, int sample_size_) const override {
+    inline bool isModelValid(const Mat &F_, const std::vector<int> &sample) const override {
         // F is of rank 2, taking cross product of two rows we obtain null vector of F
         Vec3d ec_mat = F_.row(0).cross(F_.row(2));
         auto * ec = ec_mat.val; // of size 3x1
@@ -40,7 +34,6 @@ public:
             ec_mat = F_.row(1).cross(F_.row(2));
             ec = ec_mat.val;
         }
-        // F is 9x1 row-major ordered F matrix. ec is 3x1
         const auto * const F = (double *) F_.data;
 
         // without loss of generality, let the first point in sample be in front of the camera.
@@ -50,17 +43,12 @@ public:
         // sign1 = s1 * s2
         const double sign1 = (F[0]*points[pt+2]+F[3]*points[pt+3]+F[6])*(ec[1]-ec[2]*points[pt+1]);
 
-        int num_pts_behind = 0;
-        for (int i = 1; i < sample_size_; i++) {
+        for (int i = 1; i < min_sample_size; i++) {
             pt = 4 * sample[i];
             // if signum of the first point and tested point differs
             // then two points are on different sides of the camera.
             if (sign1*(F[0]*points[pt+2]+F[3]*points[pt+3]+F[6])*(ec[1]-ec[2]*points[pt+1])<0)
-                // if 3 points are behind the camera for non-minimal sample then model is
-                // not valid. Testing by one point as in case for minimal sample is not very
-                // precise. The number 3 was chosen experimentally.
-                if (min_sample_size == sample_size_ || ++num_pts_behind >= 3)
-                    return false;
+                return false;
         }
         return true;
     }
@@ -69,15 +57,20 @@ public:
         return makePtr<EpipolarGeometryDegeneracyImpl>(*points_mat, min_sample_size);
     }
 };
-void EpipolarGeometryDegeneracy::recoverRank (Mat &model) {
+void EpipolarGeometryDegeneracy::recoverRank (Mat &model, bool is_fundamental_mat) {
     /*
      * Do singular value decomposition.
      * Make last eigen value zero of diagonal matrix of singular values.
      */
     Matx33d U, Vt;
     Vec3d w;
-    SVD::compute(model, w, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
-    model = Mat(U * Matx33d(w(0), 0, 0, 0, w(1), 0, 0, 0, 0) * Vt);
+    SVD::compute(model, w, U, Vt, SVD::MODIFY_A);
+    if (is_fundamental_mat)
+        model = Mat(U * Matx33d(w(0), 0, 0, 0, w(1), 0, 0, 0, 0) * Vt);
+    else {
+        const double mean_singular_val = (w[0] + w[1]) * 0.5;
+        model = Mat(U * Matx33d(mean_singular_val, 0, 0, 0, mean_singular_val, 0, 0, 0, 0) * Vt);
+    }
 }
 Ptr<EpipolarGeometryDegeneracy> EpipolarGeometryDegeneracy::create (const Mat &points_,
         int sample_size_) {
@@ -157,11 +150,15 @@ private:
     const float * const points;
     const Mat * points_mat;
     const Ptr<ReprojectionErrorForward> h_reproj_error;
+    Ptr<HomographyNonMinimalSolver> h_non_min_solver;
     const EpipolarGeometryDegeneracyImpl ep_deg;
     // threshold to find inliers for homography model
     const double homography_threshold, log_conf = log(0.05);
     // points (1-7) to verify in sample
     std::vector<std::vector<int>> h_sample {{0,1,2},{3,4,5},{0,1,6},{3,4,6},{2,5,6}};
+    std::vector<int> h_inliers;
+    std::vector<double> weights;
+    std::vector<Mat> h_models;
     const int points_size, sample_size;
 public:
 
@@ -179,14 +176,12 @@ public:
             h_sample.emplace_back(std::vector<int>{3, 6, 7});
             h_sample.emplace_back(std::vector<int>{2, 4, 7});
         }
+        h_inliers = std::vector<int>(points_size);
+        h_non_min_solver = HomographyNonMinimalSolver::create(points_);
     }
     inline bool isModelValid(const Mat &F, const std::vector<int> &sample) const override {
         return ep_deg.isModelValid(F, sample);
     }
-    inline bool isModelValid(const Mat &F, const std::vector<int> &sample, int sample_size_) const override {
-        return ep_deg.isModelValid(F, sample, sample_size_);
-    }
-
     bool recoverIfDegenerate (const std::vector<int> &sample, const Mat &F_best,
                  Mat &non_degenerate_model, Score &non_degenerate_model_score) override {
         non_degenerate_model_score = Score(); // set worst case
@@ -239,23 +234,32 @@ public:
             }
 
             // compute H
-            const Matx33d H = A - e_prime * (M.inv() * b).t();
+            Matx33d H = A - e_prime * (M.inv() * b).t();
 
-            int inliers_on_plane = 0;
+            int inliers_out_plane = 0;
             h_reproj_error->setModelParameters(Mat(H));
 
             // find inliers from sample, points related to H, x' ~ Hx
             for (int s = 0; s < sample_size; s++)
-                if (h_reproj_error->getError(sample[s]) < homography_threshold)
-                    if (++inliers_on_plane >= 5)
+                if (h_reproj_error->getError(sample[s]) > homography_threshold)
+                    if (++inliers_out_plane > 2)
                         break;
 
             // if there are at least 5 points lying on plane then F is degenerate
-            if (inliers_on_plane >= 5) {
+            if (inliers_out_plane <= 2) {
                 is_model_degenerate = true;
 
+                // update homography by polishing on all inliers
+                int h_inls_cnt = 0;
+                const auto &h_errors = h_reproj_error->getErrors(Mat(H));
+                for (int pt = 0; pt < points_size; pt++)
+                    if (h_errors[pt] < homography_threshold)
+                        h_inliers[h_inls_cnt++] = pt;
+                if (h_non_min_solver->estimate(h_inliers, h_inls_cnt, h_models, weights) != 0)
+                    H = Matx33d(h_models[0]);
+
                 Mat newF;
-                const Score newF_score = planeAndParallaxRANSAC(H, newF);
+                const Score newF_score = planeAndParallaxRANSAC(H, newF, h_errors);
                 if (newF_score.isBetter(non_degenerate_model_score)) {
                     // store non degenerate model
                     non_degenerate_model_score = newF_score;
@@ -271,7 +275,7 @@ public:
     }
 private:
     // RANSAC with plane-and-parallax to find new Fundamental matrix
-    Score planeAndParallaxRANSAC (const Matx33d &H, Mat &best_F) {
+    Score planeAndParallaxRANSAC (const Matx33d &H, Mat &best_F, const std::vector<float> &h_errors) {
         int max_iters = 100; // with 95% confidence assume at least 17% of inliers
         Score best_score;
         for (int iters = 0; iters < max_iters; iters++) {
@@ -282,18 +286,17 @@ private:
                 h_outlier2 = rng.uniform(0, points_size);
 
             // find outliers of homography H
-            if (h_reproj_error->getError(h_outlier1) > homography_threshold &&
-                h_reproj_error->getError(h_outlier2) > homography_threshold) {
+            if (h_errors[h_outlier1] > homography_threshold &&
+                h_errors[h_outlier2] > homography_threshold) {
 
                 // do plane and parallax with outliers of H
-                const Vec3d pt1 (points[4*h_outlier1], points[4*h_outlier1+1], 1);
-                const Vec3d pt2 (points[4*h_outlier2], points[4*h_outlier2+1], 1);
-                const Vec3d pt1_prime (points[4*h_outlier1+2],points[4*h_outlier1+3],1);
-                const Vec3d pt2_prime (points[4*h_outlier2+2],points[4*h_outlier2+3],1);
-
                 // F = [(p1' x Hp1) x (p2' x Hp2)]_x H
-                const Matx33d F = Math::getSkewSymmetric((pt1_prime.cross(H * pt1)).cross
-                                                         (pt2_prime.cross(H * pt2))) * H;
+                const Matx33d F = Math::getSkewSymmetric(
+                       (Vec3d(points[4*h_outlier1+2], points[4*h_outlier1+3], 1).cross   // p1'
+                   (H * Vec3d(points[4*h_outlier1  ], points[4*h_outlier1+1], 1))).cross // Hp1
+                       (Vec3d(points[4*h_outlier2+2], points[4*h_outlier2+3], 1).cross   // p2'
+                   (H * Vec3d(points[4*h_outlier2  ], points[4*h_outlier2+1], 1)))       // Hp2
+                 ) * H;
 
                 const Score score = quality->getScore(Mat(F));
                 if (score.isBetter(best_score)) {

modules/calib3d/src/usac/dls_solver.cpp

@@ -214,7 +214,6 @@ public:
 
             if (all_points_in_front_of_camera) {
                 Mat model;
-//                hconcat(rot_mat, soln_translation, model);
                 hconcat(Math::rotVec2RotMat(Math::rotMat2RotVec(rot_mat)), soln_translation, model);
                 models_.emplace_back(K * model);
             }

modules/calib3d/src/usac/essential_solver.cpp

@@ -54,7 +54,8 @@ public:
         const int num_cols = 9, num_e_mat = 4;
         double ee[36]; // 9*4
         // eliminate linear equations
-        Math::eliminateUpperTriangular(coefficients, 5, num_cols);
+        if (!Math::eliminateUpperTriangular(coefficients, 5, num_cols))
+            return 0;
         for (int i = 0; i < num_e_mat; i++)
             for (int j = 5; j < num_cols; j++)
                 ee[num_cols * i + j] = (i + 5 == j) ? 1 : 0;
@@ -244,25 +245,91 @@ Ptr<EssentialMinimalSolverStewenius5pts> EssentialMinimalSolverStewenius5pts::cr
 class EssentialNonMinimalSolverImpl : public EssentialNonMinimalSolver {
 private:
     const Mat * points_mat;
-    const Ptr<FundamentalNonMinimalSolver> non_min_fundamental;
+    const float * const points;
 public:
     /*
      * Input calibrated points K^-1 x.
      * Linear 8 points algorithm is used for estimation.
      */
     explicit EssentialNonMinimalSolverImpl (const Mat &points_) :
-        points_mat(&points_), non_min_fundamental(FundamentalNonMinimalSolver::create(points_)) {}
+        points_mat(&points_), points ((float *) points_.data) {}
 
     int estimate (const std::vector<int> &sample, int sample_size, std::vector<Mat>
-        &models, const std::vector<double> &weights) const override {
-        return non_min_fundamental->estimate(sample, sample_size, models, weights);
-    }
-    int getMinimumRequiredSampleSize() const override {
-        return non_min_fundamental->getMinimumRequiredSampleSize();
-    }
-    int getMaxNumberOfSolutions () const override {
-        return non_min_fundamental->getMaxNumberOfSolutions();
+            &models, const std::vector<double> &weights) const override {
+        if (sample_size < getMinimumRequiredSampleSize())
+            return 0;
+
+        // ------- 8 points algorithm with Eigen and covariance matrix --------------
+        double a[9] = {0, 0, 0, 0, 0, 0, 0, 0, 1};
+        double AtA[81] = {0}; // 9x9
+
+        if (weights.empty()) {
+            for (int i = 0; i < sample_size; i++) {
+                const int pidx = 4*sample[i];
+                const double x1 = points[pidx  ], y1 = points[pidx+1],
+                             x2 = points[pidx+2], y2 = points[pidx+3];
+                a[0] = x2*x1;
+                a[1] = x2*y1;
+                a[2] = x2;
+                a[3] = y2*x1;
+                a[4] = y2*y1;
+                a[5] = y2;
+                a[6] = x1;
+                a[7] = y1;
+
+                // calculate covariance for eigen
+                for (int row = 0; row < 9; row++)
+                    for (int col = row; col < 9; col++)
+                        AtA[row*9+col] += a[row]*a[col];
+            }
+        } else {
+            for (int i = 0; i < sample_size; i++) {
+                const int smpl = 4*sample[i];
+                const double weight = weights[i];
+                const double x1 = points[smpl  ], y1 = points[smpl+1],
+                             x2 = points[smpl+2], y2 = points[smpl+3];
+                const double weight_times_x2 = weight * x2,
+                             weight_times_y2 = weight * y2;
+
+                a[0] = weight_times_x2 * x1;
+                a[1] = weight_times_x2 * y1;
+                a[2] = weight_times_x2;
+                a[3] = weight_times_y2 * x1;
+                a[4] = weight_times_y2 * y1;
+                a[5] = weight_times_y2;
+                a[6] = weight * x1;
+                a[7] = weight * y1;
+                a[8] = weight;
+
+                // calculate covariance for eigen
+                for (int row = 0; row < 9; row++)
+                    for (int col = row; col < 9; col++)
+                        AtA[row*9+col] += a[row]*a[col];
+            }
+        }
+
+        // copy symmetric part of covariance matrix
+        for (int j = 1; j < 9; j++)
+            for (int z = 0; z < j; z++)
+                AtA[j*9+z] = AtA[z*9+j];
+
+#ifdef HAVE_EIGEN
+        models = std::vector<Mat>{ Mat_<double>(3,3) };
+        const Eigen::JacobiSVD<Eigen::Matrix<double, 9, 9>> svd((Eigen::Matrix<double, 9, 9>(AtA)),
+                Eigen::ComputeFullV);
+        // extract the last nullspace
+        Eigen::Map<Eigen::Matrix<double, 9, 1>>((double *)models[0].data) = svd.matrixV().col(8);
+#else
+        Matx<double, 9, 9> AtA_(AtA), U, Vt;
+        Vec<double, 9> W;
+        SVD::compute(AtA_, W, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
+        models = std::vector<Mat> { Mat_<double>(3, 3, Vt.val + 72 /*=8*9*/) };
+#endif
+        FundamentalDegeneracy::recoverRank(models[0], false /*E*/);
+        return 1;
     }
+    int getMinimumRequiredSampleSize() const override { return 8; }
+    int getMaxNumberOfSolutions () const override { return 1; }
     Ptr<NonMinimalSolver> clone () const override {
         return makePtr<EssentialNonMinimalSolverImpl>(*points_mat);
     }

modules/calib3d/src/usac/estimator.cpp

@@ -69,13 +69,7 @@ public:
     }
     int estimateModelNonMinimalSample(const std::vector<int> &sample, int sample_size,
             std::vector<Mat> &models, const std::vector<double> &weights) const override {
-        std::vector<Mat> Fs;
-        const int num_est_models = non_min_solver->estimate(sample, sample_size, Fs, weights);
-        int valid_models_count = 0;
-        for (int i = 0; i < num_est_models; i++)
-            if (degeneracy->isModelValid (Fs[i], sample, sample_size))
-                models[valid_models_count++] = Fs[i];
-        return valid_models_count;
+        return non_min_solver->estimate(sample, sample_size, models, weights);
     }
     int getMaxNumSolutions () const override {
         return min_solver->getMaxNumberOfSolutions();
@@ -123,13 +117,7 @@ public:
 
     int estimateModelNonMinimalSample(const std::vector<int> &sample, int sample_size,
             std::vector<Mat> &models, const std::vector<double> &weights) const override {
-        std::vector<Mat> Es;
-        const int num_est_models = non_min_solver->estimate(sample, sample_size, Es, weights);
-        int valid_models_count = 0;
-        for (int i = 0; i < num_est_models; i++)
-            if (degeneracy->isModelValid (Es[i], sample, sample_size))
-                models[valid_models_count++] = Es[i];
-        return valid_models_count;
+        return non_min_solver->estimate(sample, sample_size, models, weights);
     };
     int getMaxNumSolutions () const override {
         return min_solver->getMaxNumberOfSolutions();
@@ -231,7 +219,7 @@ Ptr<PnPEstimator> PnPEstimator::create (const Ptr<MinimalSolver> &min_solver_,
 
 ///////////////////////////////////////////// ERROR /////////////////////////////////////////
 // Symmetric Reprojection Error
-class ReprojectedErrorSymmetricImpl : public ReprojectionErrorSymmetric {
+class ReprojectionErrorSymmetricImpl : public ReprojectionErrorSymmetric {
 private:
     const Mat * points_mat;
     const float * const points;
@@ -239,7 +227,7 @@ private:
     float minv11, minv12, minv13, minv21, minv22, minv23, minv31, minv32, minv33;
     std::vector<float> errors;
 public:
-    explicit ReprojectedErrorSymmetricImpl (const Mat &points_)
+    explicit ReprojectionErrorSymmetricImpl (const Mat &points_)
         : points_mat(&points_), points ((float *) points_.data)
         , m11(0), m12(0), m13(0), m21(0), m22(0), m23(0), m31(0), m32(0), m33(0)
         , minv11(0), minv12(0), minv13(0), minv21(0), minv22(0), minv23(0), minv31(0), minv32(0), minv33(0)
@@ -287,23 +275,23 @@ public:
         return errors;
     }
     Ptr<Error> clone () const override {
-        return makePtr<ReprojectedErrorSymmetricImpl>(*points_mat);
+        return makePtr<ReprojectionErrorSymmetricImpl>(*points_mat);
     }
 };
 Ptr<ReprojectionErrorSymmetric>
 ReprojectionErrorSymmetric::create(const Mat &points) {
-    return makePtr<ReprojectedErrorSymmetricImpl>(points);
+    return makePtr<ReprojectionErrorSymmetricImpl>(points);
 }
 
 // Forward Reprojection Error
-class ReprojectedErrorForwardImpl : public ReprojectionErrorForward {
+class ReprojectionErrorForwardImpl : public ReprojectionErrorForward {
 private:
     const Mat * points_mat;
     const float * const points;
     float m11, m12, m13, m21, m22, m23, m31, m32, m33;
     std::vector<float> errors;
 public:
-    explicit ReprojectedErrorForwardImpl (const Mat &points_)
+    explicit ReprojectionErrorForwardImpl (const Mat &points_)
         : points_mat(&points_), points ((float *)points_.data)
         , m11(0), m12(0), m13(0), m21(0), m22(0), m23(0), m31(0), m32(0), m33(0)
         , errors(points_.rows)
@@ -338,12 +326,12 @@ public:
         return errors;
     }
     Ptr<Error> clone () const override {
-        return makePtr<ReprojectedErrorForwardImpl>(*points_mat);
+        return makePtr<ReprojectionErrorForwardImpl>(*points_mat);
     }
 };
 Ptr<ReprojectionErrorForward>
 ReprojectionErrorForward::create(const Mat &points) {
-    return makePtr<ReprojectedErrorForwardImpl>(points);
+    return makePtr<ReprojectionErrorForwardImpl>(points);
 }
 
 class SampsonErrorImpl : public SampsonError {
@@ -527,7 +515,7 @@ Ptr<ReprojectionErrorPmatrix> ReprojectionErrorPmatrix::create(const Mat &points
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 // Computes forward reprojection error for affine transformation.
-class ReprojectedDistanceAffineImpl : public ReprojectionErrorAffine {
+class ReprojectionDistanceAffineImpl : public ReprojectionErrorAffine {
 private:
     /*
      * m11 m12 m13
@@ -539,7 +527,7 @@ private:
     float m11, m12, m13, m21, m22, m23;
     std::vector<float> errors;
 public:
-    explicit ReprojectedDistanceAffineImpl (const Mat &points_)
+    explicit ReprojectionDistanceAffineImpl (const Mat &points_)
         : points_mat(&points_), points ((float *) points_.data)
         , m11(0), m12(0), m13(0), m21(0), m22(0), m23(0)
         , errors(points_.rows)
@@ -569,12 +557,12 @@ public:
         return errors;
     }
     Ptr<Error> clone () const override {
-        return makePtr<ReprojectedDistanceAffineImpl>(*points_mat);
+        return makePtr<ReprojectionDistanceAffineImpl>(*points_mat);
     }
 };
 Ptr<ReprojectionErrorAffine>
 ReprojectionErrorAffine::create(const Mat &points) {
-    return makePtr<ReprojectedDistanceAffineImpl>(points);
+    return makePtr<ReprojectionDistanceAffineImpl>(points);
 }
 
 ////////////////////////////////////// NORMALIZING TRANSFORMATION /////////////////////////

modules/calib3d/src/usac/fundamental_solver.cpp

@@ -20,7 +20,7 @@ public:
 
     int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
         const int m = 7, n = 9; // rows, cols
-        std::vector<double> a(m*n);
+        std::vector<double> a(63); // m*n
         auto * a_ = &a[0];
 
         for (int i = 0; i < m; i++ ) {
@@ -39,7 +39,8 @@ public:
             (*a_++) = 1;
         }
 
-        Math::eliminateUpperTriangular(a, m, n);
+        if (!Math::eliminateUpperTriangular(a, m, n))
+            return 0;
 
         /*
          [a11 a12 a13 a14 a15 a16 a17 a18 a19]
@@ -165,7 +166,7 @@ public:
 
     int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
         const int m = 8, n = 9; // rows, cols
-        std::vector<double> a(m*n);
+        std::vector<double> a(72); // m*n
         auto * a_ = &a[0];
 
         for (int i = 0; i < m; i++ ) {
@@ -184,7 +185,8 @@ public:
             (*a_++) = 1;
         }
 
-        Math::eliminateUpperTriangular(a, m, n);
+        if (!Math::eliminateUpperTriangular(a, m, n))
+            return 0;
 
         /*
          [a11 a12 a13 a14 a15 a16 a17 a18 a19]
@@ -313,16 +315,15 @@ public:
         Matx<double, 9, 9> AtA_(AtA), U, Vt;
         Vec<double, 9> W;
         SVD::compute(AtA_, W, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
-        models = std::vector<Mat> { Mat(Vt.row(8).reshape<3,3>()) };
+        models = std::vector<Mat> { Mat_<double>(3, 3, Vt.val + 72 /*=8*9*/) };
 #endif
+        FundamentalDegeneracy::recoverRank(models[0], true/*F*/);
 
         // Transpose T2 (in T2 the lower diagonal is zero)
         T2(2, 0) = T2(0, 2); T2(2, 1) = T2(1, 2);
         T2(0, 2) = 0; T2(1, 2) = 0;
 
         models[0] = T2 * models[0] * T1;
-
-        FundamentalDegeneracy::recoverRank(models[0]);
         return 1;
     }
 

modules/calib3d/src/usac/gamma_values.cpp

@@ -0,0 +1,107 @@
+// 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.
+
+#include "../precomp.hpp"
+#include "../usac.hpp"
+
+namespace cv { namespace usac {
+
+GammaValues::GammaValues()
+    : max_range_complete(4.62)
+    , max_range_gamma(1.52)
+    , max_size_table(3000)
+{
+    /*
+     * Gamma values for degrees of freedom n = 2 and sigma quantile 99% of chi distribution
+     * (squared root of chi-squared distribution), in the range <0; 4.62> for complete values
+     * and <0, 1.52> for gamma values.
+     * Number of anchor points is 50. Other values are approximated using linear interpolation
+     */
+    const int number_of_anchor_points = 50;
+    std::vector<double> gamma_complete_anchor = std::vector<double>
+       {1.7724538509055159, 1.182606138403832, 0.962685372890749, 0.8090013493715409,
+        0.6909325812483967, 0.5961199186942078, 0.5179833984918483, 0.45248091153099873,
+        0.39690029823142897, 0.34930995878395804, 0.3082742109224103, 0.2726914551904204,
+        0.2416954924567404, 0.21459196516027726, 0.190815580770884, 0.16990026519723456,
+        0.15145770273372564, 0.13516150988807635, 0.12073530906427948, 0.10794357255251595,
+        0.0965844793065712, 0.08648426334883624, 0.07749268706639856, 0.06947937608738222,
+        0.062330823249820304, 0.05594791865006951, 0.05024389794830681, 0.045142626552664405,
+        0.040577155977706246, 0.03648850256745103, 0.03282460924226794, 0.029539458909083157,
+        0.02659231432268328, 0.023947063970062663, 0.021571657306774475, 0.01943761564987864,
+        0.017519607407598645, 0.015795078236273064, 0.014243928262247118, 0.012848229767187478,
+        0.011591979769030827, 0.010460882783057988, 0.009442159753944173, 0.008524379737926344,
+        0.007697311406424555, 0.006951791856026042, 0.006279610558635573, 0.005673406581042374,
+        0.005126577454218803, 0.004633198286725555};
+
+    std::vector<double> gamma_incomplete_anchor = std::vector<double>
+        {0.0, 0.01773096912803939, 0.047486924846289004, 0.08265437835139826, 0.120639343491371,
+         0.15993024714868515, 0.19954558593754865, 0.23881753504915218, 0.2772830648361923,
+         0.3146208784488923, 0.3506114446939783, 0.385110056889967, 0.41802785670077697,
+         0.44931803198258047, 0.47896553567848993, 0.5069792897777948, 0.5333861945970247,
+         0.5582264802664578, 0.581550074874317, 0.6034137543595729, 0.6238789008764282,
+         0.6430097394182639, 0.6608719532994989, 0.6775316015953519, 0.6930542783709592,
+         0.7075044661695132, 0.7209450459078338, 0.733436932830201, 0.7450388140484766,
+         0.7558069678435577, 0.7657951486073097, 0.7750545242776943, 0.7836336555215403,
+         0.7915785078697124, 0.798932489600361, 0.8057365094688473, 0.8120290494534339,
+         0.8178462485678104, 0.8232219945197348, 0.8281880205973585, 0.8327740056635289,
+         0.8370076755516281, 0.8409149044990385, 0.8445198155381767, 0.8478448790000731,
+         0.8509110084798414, 0.8537376537738418, 0.8563428904304485, 0.8587435056647642,
+         0.8609550804762539};
+
+    std::vector<double> gamma_anchor = std::vector<double>
+        {1.7724538509055159, 1.427187162582056, 1.2890382454046982, 1.186244737282388,
+         1.1021938955410173, 1.0303674512016956, 0.9673796229113404, 0.9111932804012203,
+         0.8604640514722175, 0.814246149432561, 0.7718421763436497, 0.7327190195355812,
+         0.6964573670982434, 0.6627197089339725, 0.6312291454822467, 0.6017548373556638,
+         0.5741017071093776, 0.5481029597580317, 0.523614528104858, 0.5005108666212138,
+         0.478681711577816, 0.4580295473431646, 0.43846759792922513, 0.41991821541471996,
+         0.40231157253054745, 0.38558459136185, 0.3696800574963841, 0.3545458813847714,
+         0.340134477710645, 0.32640224021796493, 0.3133090943985706, 0.3008181141790485,
+         0.28889519159238314, 0.2775087506098113, 0.2666294980086962, 0.2562302054837794,
+         0.24628551826026082, 0.2367717863030556, 0.22766691488600885, 0.21895023182476064,
+         0.2106023691144937, 0.2026051570714723, 0.19494152937027823, 0.18759543761063277,
+         0.1805517742482484, 0.17379630289125447, 0.16731559510356395, 0.1610969729740903,
+         0.1551284568099053, 0.14939871739550692};
+
+    // allocate tables
+    gamma_complete = std::vector<double>(max_size_table);
+    gamma_incomplete = std::vector<double>(max_size_table);
+    gamma = std::vector<double>(max_size_table);
+
+    const int step = (int)((double)max_size_table / (number_of_anchor_points-1));
+    int arr_cnt = 0;
+    for (int i = 0; i < number_of_anchor_points-1; i++) {
+         const double complete_x0 = gamma_complete_anchor[i], step_complete = (gamma_complete_anchor[i+1] - complete_x0) / step;
+         const double incomplete_x0 = gamma_incomplete_anchor[i], step_incomplete = (gamma_incomplete_anchor[i+1] - incomplete_x0) / step;
+         const double gamma_x0 = gamma_anchor[i], step_gamma = (gamma_anchor[i+1] - gamma_x0) / step;
+
+         for (int j = 0; j < step; j++) {
+             gamma_complete[arr_cnt] = complete_x0 + j * step_complete;
+             gamma_incomplete[arr_cnt] = incomplete_x0 + j * step_incomplete;
+             gamma[arr_cnt++] = gamma_x0 + j * step_gamma;
+         }
+    }
+    if (arr_cnt < max_size_table) {
+        // if array was not totally filled (in some cases can happen) then copy last values
+        std::fill(gamma_complete.begin()+arr_cnt, gamma_complete.end(), gamma_complete[arr_cnt-1]);
+        std::fill(gamma_incomplete.begin()+arr_cnt, gamma_incomplete.end(), gamma_incomplete[arr_cnt-1]);
+        std::fill(gamma.begin()+arr_cnt, gamma.end(), gamma[arr_cnt-1]);
+    }
+}
+
+const std::vector<double>& GammaValues::getCompleteGammaValues() const { return gamma_complete; }
+const std::vector<double>& GammaValues::getIncompleteGammaValues() const { return gamma_incomplete; }
+const std::vector<double>& GammaValues::getGammaValues() const { return gamma; }
+double GammaValues::getScaleOfGammaCompleteValues () const { return gamma_complete.size() / max_range_complete; }
+double GammaValues::getScaleOfGammaValues () const { return gamma.size() / max_range_gamma; }
+int GammaValues::getTableSize () const { return max_size_table; }
+
+/* static */
+const GammaValues& GammaValues::getSingleton()
+{
+    static GammaValues g_gammaValues;
+    return g_gammaValues;
+}
+
+}}  // namespace

modules/calib3d/src/usac/gamma_values.hpp

@@ -1,237 +0,0 @@
-// 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.
-
-constexpr int stored_gamma_number = 2999;
-constexpr int stored_incomplete_gamma_number = 3999;
-constexpr double scale_of_stored_gammas_n4 = 1647.8;
-constexpr double scale_of_stored_incomplete_gammas_n4 = 603.64;
-
-constexpr double stored_complete_gamma_values_n4[] = {0.88623,0.88618,0.8861,0.88599,0.88587,0.88573,0.88557,0.8854,0.88522,0.88502,0.88482,0.8846,0.88438,0.88415,0.8839,0.88365,0.8834,0.88313,0.88285,0.88257,0.88229,0.88199,0.88169,0.88138,0.88107,0.88075,0.88042,0.88009,0.87975,0.87941,0.87906,0.8787,0.87834,0.87798,0.87761,0.87724,0.87686,0.87647,0.87609,0.87569,0.8753,0.8749,0.87449,0.87408,0.87367,0.87325,0.87283,0.8724,0.87197,0.87154,0.8711,0.87066,0.87022,0.86977,0.86932,0.86886,0.8684,0.86794,0.86748,0.86701,0.86654,0.86606,0.86559,0.86511,0.86462,0.86414,0.86365,0.86315,0.86266,0.86216,0.86166,0.86116,0.86065,0.86014,0.85963,0.85911,0.8586,0.85808,0.85755,0.85703,0.8565,0.85597,0.85544,0.85491,0.85437,0.85383,0.85329,0.85275,0.8522,0.85165,0.8511,0.85055,0.85,0.84944,0.84888,0.84832,0.84776,0.8472,0.84663,0.84606,
-0.84549,0.84492,0.84434,0.84377,0.84319,0.84261,0.84203,0.84145,0.84086,0.84027,0.83969,0.83909,0.8385,0.83791,0.83731,0.83672,0.83612,0.83552,0.83492,0.83431,0.83371,0.8331,0.8325,0.83189,0.83128,0.83066,0.83005,0.82943,0.82882,0.8282,0.82758,0.82696,0.82634,0.82572,0.82509,0.82447,0.82384,0.82321,0.82258,0.82195,0.82132,0.82068,0.82005,0.81941,0.81878,0.81814,0.8175,0.81686,0.81622,0.81558,0.81493,0.81429,0.81364,0.813,0.81235,0.8117,0.81105,0.8104,0.80975,0.80909,0.80844,0.80779,0.80713,0.80647,0.80582,0.80516,0.8045,0.80384,0.80318,0.80251,0.80185,0.80119,0.80052,0.79986,0.79919,0.79852,0.79786,0.79719,0.79652,0.79585,0.79518,0.7945,0.79383,0.79316,0.79248,0.79181,0.79113,0.79046,0.78978,0.7891,0.78843,0.78775,0.78707,0.78639,0.78571,0.78503,0.78434,0.78366,0.78298,0.78229,
-0.78161,0.78093,0.78024,0.77955,0.77887,0.77818,0.77749,0.7768,0.77612,0.77543,0.77474,0.77405,0.77336,0.77266,0.77197,0.77128,0.77059,0.76989,0.7692,0.76851,0.76781,0.76712,0.76642,0.76573,0.76503,0.76433,0.76364,0.76294,0.76224,0.76154,0.76085,0.76015,0.75945,0.75875,0.75805,0.75735,0.75665,0.75595,0.75525,0.75454,0.75384,0.75314,0.75244,0.75174,0.75103,0.75033,0.74963,0.74892,0.74822,0.74751,0.74681,0.74611,0.7454,0.7447,0.74399,0.74328,0.74258,0.74187,0.74117,0.74046,0.73975,0.73905,0.73834,0.73763,0.73692,0.73622,0.73551,0.7348,0.73409,0.73339,0.73268,0.73197,0.73126,0.73055,0.72984,0.72913,0.72842,0.72772,0.72701,0.7263,0.72559,0.72488,0.72417,0.72346,0.72275,0.72204,0.72133,0.72062,0.71991,0.7192,0.71849,0.71778,0.71707,0.71636,0.71565,0.71494,0.71423,0.71352,0.71281,0.71209,
-0.71138,0.71067,0.70996,0.70925,0.70854,0.70783,0.70712,0.70641,0.7057,0.70499,0.70428,0.70357,0.70286,0.70215,0.70144,0.70073,0.70002,0.69931,0.6986,0.69789,0.69718,0.69647,0.69576,0.69505,0.69434,0.69363,0.69292,0.69221,0.6915,0.69079,0.69008,0.68937,0.68867,0.68796,0.68725,0.68654,0.68583,0.68512,0.68441,0.68371,0.683,0.68229,0.68158,0.68088,0.68017,0.67946,0.67875,0.67805,0.67734,0.67663,0.67593,0.67522,0.67451,0.67381,0.6731,0.6724,0.67169,0.67099,0.67028,0.66958,0.66887,0.66817,0.66746,0.66676,0.66605,0.66535,0.66465,0.66394,0.66324,0.66254,0.66183,0.66113,0.66043,0.65973,0.65903,0.65832,0.65762,0.65692,0.65622,0.65552,0.65482,0.65412,0.65342,0.65272,0.65202,0.65132,0.65062,0.64992,0.64922,0.64853,0.64783,0.64713,0.64643,0.64574,0.64504,0.64434,0.64365,0.64295,0.64225,0.64156,
-0.64086,0.64017,0.63947,0.63878,0.63808,0.63739,0.6367,0.636,0.63531,0.63462,0.63393,0.63323,0.63254,0.63185,0.63116,0.63047,0.62978,0.62909,0.6284,0.62771,0.62702,0.62633,0.62564,0.62495,0.62427,0.62358,0.62289,0.6222,0.62152,0.62083,0.62014,0.61946,0.61877,0.61809,0.6174,0.61672,0.61604,0.61535,0.61467,0.61399,0.6133,0.61262,0.61194,0.61126,0.61058,0.6099,0.60922,0.60854,0.60786,0.60718,0.6065,0.60582,0.60514,0.60446,0.60379,0.60311,0.60243,0.60176,0.60108,0.60041,0.59973,0.59906,0.59838,0.59771,0.59703,0.59636,0.59569,0.59501,0.59434,0.59367,0.593,0.59233,0.59166,0.59099,0.59032,0.58965,0.58898,0.58831,0.58764,0.58698,0.58631,0.58564,0.58498,0.58431,0.58365,0.58298,0.58232,0.58165,0.58099,0.58032,0.57966,0.579,0.57834,0.57767,0.57701,0.57635,0.57569,0.57503,0.57437,0.57371,
-0.57305,0.5724,0.57174,0.57108,0.57042,0.56977,0.56911,0.56845,0.5678,0.56714,0.56649,0.56584,0.56518,0.56453,0.56388,0.56322,0.56257,0.56192,0.56127,0.56062,0.55997,0.55932,0.55867,0.55802,0.55738,0.55673,0.55608,0.55543,0.55479,0.55414,0.5535,0.55285,0.55221,0.55156,0.55092,0.55028,0.54963,0.54899,0.54835,0.54771,0.54707,0.54643,0.54579,0.54515,0.54451,0.54387,0.54323,0.5426,0.54196,0.54132,0.54069,0.54005,0.53942,0.53878,0.53815,0.53751,0.53688,0.53625,0.53562,0.53498,0.53435,0.53372,0.53309,0.53246,0.53183,0.5312,0.53058,0.52995,0.52932,0.52869,0.52807,0.52744,0.52682,0.52619,0.52557,0.52494,0.52432,0.5237,0.52307,0.52245,0.52183,0.52121,0.52059,0.51997,0.51935,0.51873,0.51811,0.51749,0.51688,0.51626,0.51564,0.51503,0.51441,0.5138,0.51318,0.51257,0.51195,0.51134,0.51073,0.51012,
-0.5095,0.50889,0.50828,0.50767,0.50706,0.50645,0.50585,0.50524,0.50463,0.50402,0.50342,0.50281,0.50221,0.5016,0.501,0.50039,0.49979,0.49919,0.49858,0.49798,0.49738,0.49678,0.49618,0.49558,0.49498,0.49438,0.49378,0.49318,0.49259,0.49199,0.49139,0.4908,0.4902,0.48961,0.48901,0.48842,0.48783,0.48724,0.48664,0.48605,0.48546,0.48487,0.48428,0.48369,0.4831,0.48251,0.48192,0.48134,0.48075,0.48016,0.47958,0.47899,0.47841,0.47782,0.47724,0.47666,0.47607,0.47549,0.47491,0.47433,0.47375,0.47317,0.47259,0.47201,0.47143,0.47085,0.47027,0.4697,0.46912,0.46854,0.46797,0.46739,0.46682,0.46625,0.46567,0.4651,0.46453,0.46396,0.46338,0.46281,0.46224,0.46167,0.4611,0.46054,0.45997,0.4594,0.45883,0.45827,0.4577,0.45713,0.45657,0.45601,0.45544,0.45488,0.45432,0.45375,0.45319,0.45263,0.45207,0.45151,
-0.45095,0.45039,0.44983,0.44927,0.44872,0.44816,0.4476,0.44705,0.44649,0.44594,0.44538,0.44483,0.44427,0.44372,0.44317,0.44262,0.44207,0.44151,0.44096,0.44041,0.43987,0.43932,0.43877,0.43822,0.43767,0.43713,0.43658,0.43604,0.43549,0.43495,0.4344,0.43386,0.43332,0.43277,0.43223,0.43169,0.43115,0.43061,0.43007,0.42953,0.42899,0.42846,0.42792,0.42738,0.42684,0.42631,0.42577,0.42524,0.4247,0.42417,0.42364,0.4231,0.42257,0.42204,0.42151,0.42098,0.42045,0.41992,0.41939,0.41886,0.41833,0.4178,0.41728,0.41675,0.41623,0.4157,0.41517,0.41465,0.41413,0.4136,0.41308,0.41256,0.41204,0.41152,0.41099,0.41047,0.40996,0.40944,0.40892,0.4084,0.40788,0.40736,0.40685,0.40633,0.40582,0.4053,0.40479,0.40427,0.40376,0.40325,0.40274,0.40222,0.40171,0.4012,0.40069,0.40018,0.39967,0.39916,0.39866,0.39815,
-0.39764,0.39714,0.39663,0.39612,0.39562,0.39511,0.39461,0.39411,0.3936,0.3931,0.3926,0.3921,0.3916,0.3911,0.3906,0.3901,0.3896,0.3891,0.3886,0.38811,0.38761,0.38711,0.38662,0.38612,0.38563,0.38514,0.38464,0.38415,0.38366,0.38316,0.38267,0.38218,0.38169,0.3812,0.38071,0.38022,0.37974,0.37925,0.37876,0.37827,0.37779,0.3773,0.37682,0.37633,0.37585,0.37536,0.37488,0.3744,0.37392,0.37343,0.37295,0.37247,0.37199,0.37151,0.37103,0.37056,0.37008,0.3696,0.36912,0.36865,0.36817,0.3677,0.36722,0.36675,0.36627,0.3658,0.36533,0.36485,0.36438,0.36391,0.36344,0.36297,0.3625,0.36203,0.36156,0.36109,0.36062,0.36016,0.35969,0.35922,0.35876,0.35829,0.35783,0.35736,0.3569,0.35644,0.35597,0.35551,0.35505,0.35459,0.35413,0.35367,0.35321,0.35275,0.35229,0.35183,0.35137,0.35092,0.35046,0.35,
-0.34955,0.34909,0.34864,0.34818,0.34773,0.34728,0.34682,0.34637,0.34592,0.34547,0.34502,0.34457,0.34412,0.34367,0.34322,0.34277,0.34233,0.34188,0.34143,0.34099,0.34054,0.34009,0.33965,0.33921,0.33876,0.33832,0.33788,0.33743,0.33699,0.33655,0.33611,0.33567,0.33523,0.33479,0.33435,0.33391,0.33348,0.33304,0.3326,0.33216,0.33173,0.33129,0.33086,0.33042,0.32999,0.32956,0.32912,0.32869,0.32826,0.32783,0.3274,0.32697,0.32654,0.32611,0.32568,0.32525,0.32482,0.32439,0.32397,0.32354,0.32311,0.32269,0.32226,0.32184,0.32141,0.32099,0.32057,0.32014,0.31972,0.3193,0.31888,0.31846,0.31804,0.31762,0.3172,0.31678,0.31636,0.31594,0.31553,0.31511,0.31469,0.31428,0.31386,0.31345,0.31303,0.31262,0.3122,0.31179,0.31138,0.31097,0.31055,0.31014,0.30973,0.30932,0.30891,0.3085,0.30809,0.30768,0.30728,0.30687,
-0.30646,0.30606,0.30565,0.30524,0.30484,0.30443,0.30403,0.30363,0.30322,0.30282,0.30242,0.30202,0.30161,0.30121,0.30081,0.30041,0.30001,0.29961,0.29922,0.29882,0.29842,0.29802,0.29763,0.29723,0.29683,0.29644,0.29604,0.29565,0.29526,0.29486,0.29447,0.29408,0.29368,0.29329,0.2929,0.29251,0.29212,0.29173,0.29134,0.29095,0.29056,0.29018,0.28979,0.2894,0.28901,0.28863,0.28824,0.28786,0.28747,0.28709,0.2867,0.28632,0.28594,0.28555,0.28517,0.28479,0.28441,0.28403,0.28365,0.28327,0.28289,0.28251,0.28213,0.28175,0.28138,0.281,0.28062,0.28025,0.27987,0.27949,0.27912,0.27875,0.27837,0.278,0.27762,0.27725,0.27688,0.27651,0.27614,0.27577,0.27539,0.27502,0.27466,0.27429,0.27392,0.27355,0.27318,0.27281,0.27245,0.27208,0.27171,0.27135,0.27098,0.27062,0.27025,0.26989,0.26953,0.26916,0.2688,0.26844,
-0.26808,0.26772,0.26735,0.26699,0.26663,0.26627,0.26592,0.26556,0.2652,0.26484,0.26448,0.26413,0.26377,0.26341,0.26306,0.2627,0.26235,0.26199,0.26164,0.26129,0.26093,0.26058,0.26023,0.25988,0.25953,0.25917,0.25882,0.25847,0.25812,0.25777,0.25743,0.25708,0.25673,0.25638,0.25603,0.25569,0.25534,0.255,0.25465,0.2543,0.25396,0.25362,0.25327,0.25293,0.25259,0.25224,0.2519,0.25156,0.25122,0.25088,0.25054,0.2502,0.24986,0.24952,0.24918,0.24884,0.2485,0.24817,0.24783,0.24749,0.24715,0.24682,0.24648,0.24615,0.24581,0.24548,0.24515,0.24481,0.24448,0.24415,0.24381,0.24348,0.24315,0.24282,0.24249,0.24216,0.24183,0.2415,0.24117,0.24084,0.24051,0.24019,0.23986,0.23953,0.23921,0.23888,0.23855,0.23823,0.2379,0.23758,0.23726,0.23693,0.23661,0.23629,0.23596,0.23564,0.23532,0.235,0.23468,0.23436,
-0.23404,0.23372,0.2334,0.23308,0.23276,0.23244,0.23212,0.23181,0.23149,0.23117,0.23086,0.23054,0.23022,0.22991,0.2296,0.22928,0.22897,0.22865,0.22834,0.22803,0.22772,0.2274,0.22709,0.22678,0.22647,0.22616,0.22585,0.22554,0.22523,0.22492,0.22461,0.22431,0.224,0.22369,0.22338,0.22308,0.22277,0.22247,0.22216,0.22186,0.22155,0.22125,0.22094,0.22064,0.22034,0.22003,0.21973,0.21943,0.21913,0.21883,0.21853,0.21823,0.21793,0.21763,0.21733,0.21703,0.21673,0.21643,0.21613,0.21584,0.21554,0.21524,0.21495,0.21465,0.21436,0.21406,0.21377,0.21347,0.21318,0.21288,0.21259,0.2123,0.212,0.21171,0.21142,0.21113,0.21084,0.21055,0.21026,0.20997,0.20968,0.20939,0.2091,0.20881,0.20852,0.20823,0.20795,0.20766,0.20737,0.20709,0.2068,0.20652,0.20623,0.20595,0.20566,0.20538,0.20509,0.20481,0.20453,0.20424,
-0.20396,0.20368,0.2034,0.20312,0.20284,0.20256,0.20228,0.202,0.20172,0.20144,0.20116,0.20088,0.2006,0.20032,0.20005,0.19977,0.19949,0.19922,0.19894,0.19866,0.19839,0.19811,0.19784,0.19757,0.19729,0.19702,0.19675,0.19647,0.1962,0.19593,0.19566,0.19539,0.19511,0.19484,0.19457,0.1943,0.19403,0.19376,0.1935,0.19323,0.19296,0.19269,0.19242,0.19216,0.19189,0.19162,0.19136,0.19109,0.19082,0.19056,0.19029,0.19003,0.18977,0.1895,0.18924,0.18898,0.18871,0.18845,0.18819,0.18793,0.18766,0.1874,0.18714,0.18688,0.18662,0.18636,0.1861,0.18584,0.18558,0.18533,0.18507,0.18481,0.18455,0.1843,0.18404,0.18378,0.18353,0.18327,0.18302,0.18276,0.18251,0.18225,0.182,0.18174,0.18149,0.18124,0.18098,0.18073,0.18048,0.18023,0.17998,0.17972,0.17947,0.17922,0.17897,0.17872,0.17847,0.17822,0.17797,0.17773,
-0.17748,0.17723,0.17698,0.17674,0.17649,0.17624,0.176,0.17575,0.1755,0.17526,0.17501,0.17477,0.17452,0.17428,0.17404,0.17379,0.17355,0.17331,0.17306,0.17282,0.17258,0.17234,0.1721,0.17186,0.17162,0.17137,0.17113,0.1709,0.17066,0.17042,0.17018,0.16994,0.1697,0.16946,0.16923,0.16899,0.16875,0.16852,0.16828,0.16804,0.16781,0.16757,0.16734,0.1671,0.16687,0.16663,0.1664,0.16617,0.16593,0.1657,0.16547,0.16524,0.165,0.16477,0.16454,0.16431,0.16408,0.16385,0.16362,0.16339,0.16316,0.16293,0.1627,0.16247,0.16224,0.16202,0.16179,0.16156,0.16133,0.16111,0.16088,0.16065,0.16043,0.1602,0.15998,0.15975,0.15953,0.1593,0.15908,0.15885,0.15863,0.15841,0.15818,0.15796,0.15774,0.15752,0.1573,0.15707,0.15685,0.15663,0.15641,0.15619,0.15597,0.15575,0.15553,0.15531,0.15509,0.15487,0.15466,0.15444,
-0.15422,0.154,0.15379,0.15357,0.15335,0.15314,0.15292,0.1527,0.15249,0.15227,0.15206,0.15184,0.15163,0.15142,0.1512,0.15099,0.15077,0.15056,0.15035,0.15014,0.14992,0.14971,0.1495,0.14929,0.14908,0.14887,0.14866,0.14845,0.14824,0.14803,0.14782,0.14761,0.1474,0.14719,0.14699,0.14678,0.14657,0.14636,0.14616,0.14595,0.14574,0.14554,0.14533,0.14512,0.14492,0.14471,0.14451,0.1443,0.1441,0.1439,0.14369,0.14349,0.14329,0.14308,0.14288,0.14268,0.14248,0.14227,0.14207,0.14187,0.14167,0.14147,0.14127,0.14107,0.14087,0.14067,0.14047,0.14027,0.14007,0.13987,0.13967,0.13948,0.13928,0.13908,0.13888,0.13869,0.13849,0.13829,0.1381,0.1379,0.1377,0.13751,0.13731,0.13712,0.13692,0.13673,0.13654,0.13634,0.13615,0.13595,0.13576,0.13557,0.13538,0.13518,0.13499,0.1348,0.13461,0.13442,0.13423,0.13403,
-0.13384,0.13365,0.13346,0.13327,0.13308,0.1329,0.13271,0.13252,0.13233,0.13214,0.13195,0.13176,0.13158,0.13139,0.1312,0.13102,0.13083,0.13064,0.13046,0.13027,0.13009,0.1299,0.12972,0.12953,0.12935,0.12916,0.12898,0.12879,0.12861,0.12843,0.12824,0.12806,0.12788,0.1277,0.12752,0.12733,0.12715,0.12697,0.12679,0.12661,0.12643,0.12625,0.12607,0.12589,0.12571,0.12553,0.12535,0.12517,0.12499,0.12481,0.12464,0.12446,0.12428,0.1241,0.12393,0.12375,0.12357,0.1234,0.12322,0.12304,0.12287,0.12269,0.12252,0.12234,0.12217,0.12199,0.12182,0.12164,0.12147,0.1213,0.12112,0.12095,0.12078,0.1206,0.12043,0.12026,0.12009,0.11992,0.11974,0.11957,0.1194,0.11923,0.11906,0.11889,0.11872,0.11855,0.11838,0.11821,0.11804,0.11787,0.1177,0.11754,0.11737,0.1172,0.11703,0.11686,0.1167,0.11653,0.11636,0.1162,
-0.11603,0.11586,0.1157,0.11553,0.11537,0.1152,0.11504,0.11487,0.11471,0.11454,0.11438,0.11421,0.11405,0.11389,0.11372,0.11356,0.1134,0.11323,0.11307,0.11291,0.11275,0.11259,0.11242,0.11226,0.1121,0.11194,0.11178,0.11162,0.11146,0.1113,0.11114,0.11098,0.11082,0.11066,0.1105,0.11035,0.11019,0.11003,0.10987,0.10971,0.10955,0.1094,0.10924,0.10908,0.10893,0.10877,0.10861,0.10846,0.1083,0.10815,0.10799,0.10784,0.10768,0.10753,0.10737,0.10722,0.10706,0.10691,0.10675,0.1066,0.10645,0.10629,0.10614,0.10599,0.10584,0.10568,0.10553,0.10538,0.10523,0.10508,0.10493,0.10478,0.10462,0.10447,0.10432,0.10417,0.10402,0.10387,0.10372,0.10357,0.10342,0.10328,0.10313,0.10298,0.10283,0.10268,0.10253,0.10239,0.10224,0.10209,0.10194,0.1018,0.10165,0.1015,0.10136,0.10121,0.10107,0.10092,0.10077,0.10063,
-0.10048,0.10034,0.10019,0.10005,0.09991,0.09976,0.09962,0.09947,0.09933,0.09919,0.09904,0.0989,0.09876,0.09862,0.09847,0.09833,0.09819,0.09805,0.09791,0.09776,0.09762,0.09748,0.09734,0.0972,0.09706,0.09692,0.09678,0.09664,0.0965,0.09636,0.09622,0.09608,0.09594,0.09581,0.09567,0.09553,0.09539,0.09525,0.09512,0.09498,0.09484,0.0947,0.09457,0.09443,0.09429,0.09416,0.09402,0.09388,0.09375,0.09361,0.09348,0.09334,0.09321,0.09307,0.09294,0.0928,0.09267,0.09253,0.0924,0.09227,0.09213,0.092,0.09187,0.09173,0.0916,0.09147,0.09134,0.0912,0.09107,0.09094,0.09081,0.09068,0.09055,0.09041,0.09028,0.09015,0.09002,0.08989,0.08976,0.08963,0.0895,0.08937,0.08924,0.08911,0.08898,0.08885,0.08873,0.0886,0.08847,0.08834,0.08821,0.08808,0.08796,0.08783,0.0877,0.08757,0.08745,0.08732,0.08719,0.08707,
-0.08694,0.08681,0.08669,0.08656,0.08644,0.08631,0.08619,0.08606,0.08594,0.08581,0.08569,0.08556,0.08544,0.08531,0.08519,0.08507,0.08494,0.08482,0.0847,0.08457,0.08445,0.08433,0.0842,0.08408,0.08396,0.08384,0.08372,0.08359,0.08347,0.08335,0.08323,0.08311,0.08299,0.08287,0.08275,0.08263,0.08251,0.08239,0.08227,0.08215,0.08203,0.08191,0.08179,0.08167,0.08155,0.08143,0.08132,0.0812,0.08108,0.08096,0.08084,0.08073,0.08061,0.08049,0.08037,0.08026,0.08014,0.08002,0.07991,0.07979,0.07967,0.07956,0.07944,0.07933,0.07921,0.0791,0.07898,0.07887,0.07875,0.07864,0.07852,0.07841,0.07829,0.07818,0.07806,0.07795,0.07784,0.07772,0.07761,0.0775,0.07738,0.07727,0.07716,0.07705,0.07693,0.07682,0.07671,0.0766,0.07649,0.07637,0.07626,0.07615,0.07604,0.07593,0.07582,0.07571,0.0756,0.07549,0.07538,0.07527,
-0.07516,0.07505,0.07494,0.07483,0.07472,0.07461,0.0745,0.07439,0.07428,0.07418,0.07407,0.07396,0.07385,0.07374,0.07364,0.07353,0.07342,0.07331,0.07321,0.0731,0.07299,0.07289,0.07278,0.07267,0.07257,0.07246,0.07236,0.07225,0.07214,0.07204,0.07193,0.07183,0.07172,0.07162,0.07151,0.07141,0.07131,0.0712,0.0711,0.07099,0.07089,0.07079,0.07068,0.07058,0.07048,0.07037,0.07027,0.07017,0.07006,0.06996,0.06986,0.06976,0.06965,0.06955,0.06945,0.06935,0.06925,0.06915,0.06905,0.06894,0.06884,0.06874,0.06864,0.06854,0.06844,0.06834,0.06824,0.06814,0.06804,0.06794,0.06784,0.06774,0.06764,0.06754,0.06745,0.06735,0.06725,0.06715,0.06705,0.06695,0.06685,0.06676,0.06666,0.06656,0.06646,0.06637,0.06627,0.06617,0.06607,0.06598,0.06588,0.06578,0.06569,0.06559,0.0655,0.0654,0.0653,0.06521,0.06511,0.06502,
-0.06492,0.06483,0.06473,0.06464,0.06454,0.06445,0.06435,0.06426,0.06416,0.06407,0.06397,0.06388,0.06379,0.06369,0.0636,0.06351,0.06341,0.06332,0.06323,0.06313,0.06304,0.06295,0.06286,0.06276,0.06267,0.06258,0.06249,0.0624,0.06231,0.06221,0.06212,0.06203,0.06194,0.06185,0.06176,0.06167,0.06158,0.06149,0.0614,0.06131,0.06122,0.06113,0.06104,0.06095,0.06086,0.06077,0.06068,0.06059,0.0605,0.06041,0.06032,0.06023,0.06014,0.06006,0.05997,0.05988,0.05979,0.0597,0.05962,0.05953,0.05944,0.05935,0.05927,0.05918,0.05909,0.059,0.05892,0.05883,0.05874,0.05866,0.05857,0.05849,0.0584,0.05831,0.05823,0.05814,0.05806,0.05797,0.05789,0.0578,0.05771,0.05763,0.05755,0.05746,0.05738,0.05729,0.05721,0.05712,0.05704,0.05695,0.05687,0.05679,0.0567,0.05662,0.05654,0.05645,0.05637,0.05629,0.0562,0.05612,
-0.05604,0.05596,0.05587,0.05579,0.05571,0.05563,0.05554,0.05546,0.05538,0.0553,0.05522,0.05514,0.05505,0.05497,0.05489,0.05481,0.05473,0.05465,0.05457,0.05449,0.05441,0.05433,0.05425,0.05417,0.05409,0.05401,0.05393,0.05385,0.05377,0.05369,0.05361,0.05353,0.05345,0.05337,0.0533,0.05322,0.05314,0.05306,0.05298,0.0529,0.05283,0.05275,0.05267,0.05259,0.05251,0.05244,0.05236,0.05228,0.0522,0.05213,0.05205,0.05197,0.0519,0.05182,0.05174,0.05167,0.05159,0.05151,0.05144,0.05136,0.05129,0.05121,0.05113,0.05106,0.05098,0.05091,0.05083,0.05076,0.05068,0.05061,0.05053,0.05046,0.05038,0.05031,0.05024,0.05016,0.05009,0.05001,0.04994,0.04986,0.04979,0.04972,0.04964,0.04957,0.0495,0.04942,0.04935,0.04928,0.0492,0.04913,0.04906,0.04899,0.04891,0.04884,0.04877,0.0487,0.04863,0.04855,0.04848,0.04841,
-0.04834,0.04827,0.0482,0.04812,0.04805,0.04798,0.04791,0.04784,0.04777,0.0477,0.04763,0.04756,0.04749,0.04742,0.04735,0.04728,0.04721,0.04714,0.04707,0.047,0.04693,0.04686,0.04679,0.04672,0.04665,0.04658,0.04651,0.04644,0.04637,0.0463,0.04624,0.04617,0.0461,0.04603,0.04596,0.04589,0.04583,0.04576,0.04569,0.04562,0.04555,0.04549,0.04542,0.04535,0.04529,0.04522,0.04515,0.04508,0.04502,0.04495,0.04488,0.04482,0.04475,0.04468,0.04462,0.04455,0.04449,0.04442,0.04435,0.04429,0.04422,0.04416,0.04409,0.04403,0.04396,0.0439,0.04383,0.04376,0.0437,0.04364,0.04357,0.04351,0.04344,0.04338,0.04331,0.04325,0.04318,0.04312,0.04306,0.04299,0.04293,0.04286,0.0428,0.04274,0.04267,0.04261,0.04255,0.04248,0.04242,0.04236,0.04229,0.04223,0.04217,0.04211,0.04204,0.04198,0.04192,0.04186,0.04179,0.04173,
-0.04167,0.04161,0.04155,0.04148,0.04142,0.04136,0.0413,0.04124,0.04118,0.04112,0.04105,0.04099,0.04093,0.04087,0.04081,0.04075,0.04069,0.04063,0.04057,0.04051,0.04045,0.04039,0.04033,0.04027,0.04021,0.04015,0.04009,0.04003,0.03997,0.03991,0.03985,0.03979,0.03973,0.03967,0.03961,0.03955,0.0395,0.03944,0.03938,0.03932,0.03926,0.0392,0.03914,0.03909,0.03903,0.03897,0.03891,0.03885,0.0388,0.03874,0.03868,0.03862,0.03857,0.03851,0.03845,0.03839,0.03834,0.03828,0.03822,0.03817,0.03811,0.03805,0.038,0.03794,0.03788,0.03783,0.03777,0.03771,0.03766,0.0376,0.03754,0.03749,0.03743,0.03738,0.03732,0.03727,0.03721,0.03715,0.0371,0.03704,0.03699,0.03693,0.03688,0.03682,0.03677,0.03671,0.03666,0.0366,0.03655,0.0365,0.03644,0.03639,0.03633,0.03628,0.03622,0.03617,0.03612,0.03606,0.03601,0.03595,
-0.0359,0.03585,0.03579,0.03574,0.03569,0.03563,0.03558,0.03553,0.03547,0.03542,0.03537,0.03532,0.03526,0.03521,0.03516,0.03511,0.03505,0.035,0.03495,0.0349,0.03484,0.03479,0.03474,0.03469,0.03464,0.03459,0.03453,0.03448,0.03443,0.03438,0.03433,0.03428,0.03423,0.03417,0.03412,0.03407,0.03402,0.03397,0.03392,0.03387,0.03382,0.03377,0.03372,0.03367,0.03362,0.03357,0.03352,0.03347,0.03342,0.03337,0.03332,0.03327,0.03322,0.03317,0.03312,0.03307,0.03302,0.03297,0.03292,0.03287,0.03282,0.03277,0.03272,0.03267,0.03263,0.03258,0.03253,0.03248,0.03243,0.03238,0.03233,0.03229,0.03224,0.03219,0.03214,0.03209,0.03205,0.032,0.03195,0.0319,0.03185,0.03181,0.03176,0.03171,0.03166,0.03162,0.03157,0.03152,0.03147,0.03143,0.03138,0.03133,0.03129,0.03124,0.03119,0.03115,0.0311,0.03105,0.03101,0.03096,
-0.03091,0.03087,0.03082,0.03078,0.03073,0.03068,0.03064,0.03059,0.03055,0.0305,0.03045,0.03041,0.03036,0.03032,0.03027,0.03023,0.03018,0.03014,0.03009,0.03005,0.03,0.02996,0.02991,0.02987,0.02982,0.02978,0.02973,0.02969,0.02964,0.0296,0.02955,0.02951,0.02947,0.02942,0.02938,0.02933,0.02929,0.02925,0.0292,0.02916,0.02911,0.02907,0.02903,0.02898,0.02894,0.0289,0.02885,0.02881,0.02877,0.02872,0.02868,0.02864,0.02859,0.02855,0.02851,0.02847,0.02842,0.02838,0.02834,0.0283,0.02825,0.02821,0.02817,0.02813,0.02808,0.02804,0.028,0.02796,0.02792,0.02787,0.02783,0.02779,0.02775,0.02771,0.02767,0.02762,0.02758,0.02754,0.0275,0.02746,0.02742,0.02738,0.02734,0.02729,0.02725,0.02721,0.02717,0.02713,0.02709,0.02705,0.02701,0.02697,0.02693,0.02689,0.02685,0.02681,0.02677,0.02673,0.02669,0.02665,
-0.02661,0.02657,0.02653,0.02649,0.02645,0.02641,0.02637,0.02633,0.02629,0.02625,0.02621,0.02617,0.02613,0.02609,0.02605,0.02601,0.02597,0.02593,0.0259,0.02586,0.02582,0.02578,0.02574,0.0257,0.02566,0.02562,0.02559,0.02555,0.02551,0.02547,0.02543,0.02539,0.02536,0.02532,0.02528,0.02524,0.0252,0.02517,0.02513,0.02509,0.02505,0.02501,0.02498,0.02494,0.0249,0.02486,0.02483,0.02479,0.02475,0.02472,0.02468,0.02464,0.0246,0.02457,0.02453,0.02449,0.02446,0.02442,0.02438,0.02435,0.02431,0.02427,0.02424,0.0242,0.02416,0.02413,0.02409,0.02405,0.02402,0.02398,0.02395,0.02391,0.02387,0.02384,0.0238,0.02377,0.02373,0.02369,0.02366,0.02362,0.02359,0.02355,0.02352,0.02348,0.02345,0.02341,0.02338,0.02334,0.02331,0.02327,0.02323,0.0232,0.02316,0.02313,0.0231,0.02306,0.02303,0.02299,0.02296,0.02292,
-0.02289,0.02285,0.02282,0.02278,0.02275,0.02272,0.02268,0.02265,0.02261,0.02258,0.02254,0.02251,0.02248,0.02244,0.02241,0.02238,0.02234,0.02231,0.02227,0.02224,0.02221,0.02217,0.02214,0.02211,0.02207,0.02204,0.02201,0.02197,0.02194,0.02191,0.02187,0.02184,0.02181,0.02178,0.02174,0.02171,0.02168,0.02164,0.02161,0.02158,0.02155,0.02151,0.02148,0.02145,0.02142,0.02138,0.02135,0.02132,0.02129,0.02126,0.02122,0.02119,0.02116,0.02113,0.0211,0.02106,0.02103,0.021,0.02097,0.02094,0.02091,0.02087,0.02084,0.02081,0.02078,0.02075,0.02072,0.02069,0.02065,0.02062,0.02059,0.02056,0.02053,0.0205,0.02047,0.02044,0.02041,0.02038,0.02035,0.02031,0.02028,0.02025,0.02022,0.02019,0.02016,0.02013,0.0201,0.02007,0.02004,0.02001,0.01998,0.01995,0.01992,0.01989,0.01986,0.01983,0.0198,0.01977,0.01974,0.01971,
-0.01968,0.01965,0.01962,0.01959,0.01956,0.01953,0.0195,0.01947,0.01944,0.01941,0.01938,0.01935,0.01933,0.0193,0.01927,0.01924,0.01921,0.01918,0.01915,0.01912,0.01909,0.01906,0.01904,0.01901,0.01898,0.01895,0.01892,0.01889,0.01886,0.01883,0.01881,0.01878,0.01875,0.01872,0.01869,0.01866,0.01864,0.01861,0.01858,0.01855,0.01852,0.0185,0.01847,0.01844,0.01841,0.01838,0.01836,0.01833,0.0183,0.01827,0.01825,0.01822,0.01819,0.01816,0.01814,0.01811,0.01808,0.01805,0.01803,0.018,0.01797,0.01794,0.01792,0.01789,0.01786,0.01784,0.01781,0.01778,0.01775,0.01773,0.0177,0.01767,0.01765,0.01762,0.01759,0.01757,0.01754,0.01751,0.01749,0.01746,0.01744,0.01741,0.01738,0.01736,0.01733,0.0173,0.01728,0.01725,0.01722,0.0172,0.01717,0.01715,0.01712,0.01709,0.01707,0.01704,0.01702,0.01699,0.01697,0.01694,
-0.01691,0.01689,0.01686,0.01684,0.01681,0.01679,0.01676,0.01674,0.01671,0.01669,0.01666,0.01663,0.01661,0.01658,0.01656,0.01653,0.01651,0.01648,0.01646,0.01643,0.01641,0.01638,0.01636,0.01633,0.01631,0.01629,0.01626,0.01624,0.01621,0.01619,0.01616,0.01614,0.01611,0.01609,0.01606,0.01604,0.01602,0.01599,0.01597,0.01594,0.01592,0.01589,0.01587,0.01585,0.01582,0.0158,0.01577,0.01575,0.01573,0.0157,0.01568,0.01565,0.01563,0.01561,0.01558,0.01556,0.01554,0.01551,0.01549,0.01547,0.01544,0.01542,0.0154,0.01537,0.01535,0.01533,0.0153,0.01528,0.01526,0.01523,0.01521,0.01519,0.01516,0.01514,0.01512,0.01509,0.01507,0.01505,0.01503,0.015,0.01498,0.01496,0.01493,0.01491,0.01489,0.01487,0.01484,0.01482,0.0148,0.01478,0.01475,0.01473,0.01471,0.01469,0.01467,0.01464,0.01462,0.0146,0.01458,0.01455,
-0.01453,0.01451,0.01449,0.01447,0.01444,0.01442,0.0144,0.01438,0.01436,0.01433,0.01431,0.01429,0.01427,0.01425,0.01423,0.0142,0.01418,0.01416,0.01414,0.01412,0.0141,0.01408,0.01405,0.01403,0.01401,0.01399,0.01397,0.01395,0.01393,0.01391,0.01388,0.01386,0.01384,0.01382,0.0138,0.01378,0.01376,0.01374,0.01372,0.0137,0.01367,0.01365,0.01363,0.01361,0.01359,0.01357,0.01355,0.01353,0.01351,0.01349,0.01347,0.01345,0.01343,0.01341,0.01339,0.01337,0.01335,0.01333,0.0133,0.01328,0.01326,0.01324,0.01322,0.0132,0.01318,0.01316,0.01314,0.01312,0.0131,0.01308,0.01306,0.01304,0.01302,0.013,0.01298,0.01296,0.01295,0.01293,0.01291,0.01289,0.01287,0.01285,0.01283,0.01281,0.01279,0.01277,0.01275,0.01273,0.01271,0.01269,0.01267,0.01265,0.01263,0.01261,0.01259,0.01258,0.01256,0.01254,0.01252,0.0125,
-0.01248,0.01246,0.01244,0.01242,0.0124,0.01239,0.01237,0.01235,0.01233,0.01231,0.01229,0.01227,0.01225,0.01224,0.01222,0.0122,0.01218,0.01216,0.01214,0.01212,0.01211,0.01209,0.01207,0.01205,0.01203,0.01201,0.012,0.01198,0.01196,0.01194,0.01192,0.0119,0.01189,0.01187,0.01185,0.01183,0.01181,0.0118,0.01178,0.01176,0.01174,0.01172,0.01171,0.01169,0.01167,0.01165,0.01164,0.01162,0.0116,0.01158,0.01156,0.01155,0.01153,0.01151,0.01149,0.01148,0.01146,0.01144,0.01142,0.01141,0.01139,0.01137,0.01135,0.01134,0.01132,0.0113,0.01129,0.01127,0.01125,0.01123,0.01122,0.0112,0.01118,0.01117,0.01115,0.01113,0.01111,0.0111,0.01108,0.01106,0.01105,0.01103,0.01101,0.011,0.01098,0.01096,0.01095,0.01093,0.01091,0.0109,0.01088,0.01086,0.01085,0.01083,0.01081,0.0108,0.01078,0.01076,0.01075,0.01073,
-0.01071,0.0107,0.01068,0.01067,0.01065,0.01063,0.01062,0.0106,0.01058,0.01057,0.01055,0.01054,0.01052,0.0105,0.01049,0.01047,0.01046,0.01044,0.01042,0.01041,0.01039,0.01038,0.01036,0.01034,0.01033,0.01031,0.0103,0.01028,0.01027,0.01025,0.01023,0.01022,0.0102,0.01019,0.01017,0.01016,0.01014,0.01013,0.01011,0.01009,0.01008,0.01006,0.01005,0.01003,0.01002,0.01,0.00999,0.00997,0.00996,0.00994,0.00993,0.00991,0.0099,0.00988,0.00987,0.00985,0.00984,0.00982,0.00981,0.00979,0.00978,0.00976,0.00975,0.00973,0.00972,0.0097,0.00969,0.00967,0.00966,0.00964,0.00963,0.00961,0.0096,0.00958,0.00957,0.00955,0.00954,0.00952,0.00951,0.0095,0.00948,0.00947,0.00945,0.00944,0.00942,0.00941,0.00939,0.00938,0.00937,0.00935,0.00934,0.00932,0.00931,0.00929,0.00928,0.00927,0.00925,0.00924,0.00922,0.00921,
-0.0092,0.00918,0.00917,0.00915,0.00914,0.00913,0.00911,0.0091,0.00908,0.00907,0.00906,0.00904,0.00903,0.00901,0.009,0.00899,0.00897,0.00896,0.00895,0.00893,0.00892,0.0089,0.00889,0.00888,0.00886,0.00885,0.00884,0.00882,0.00881,0.0088,0.00878,0.00877,0.00876,0.00874,0.00873,0.00872,0.0087,0.00869,0.00868,0.00866,0.00865,0.00864,0.00862,0.00861,0.0086,0.00858,0.00857,0.00856,0.00854,0.00853,0.00852,0.0085,0.00849,0.00848,0.00847,0.00845,0.00844,0.00843,0.00841,0.0084,0.00839,0.00838,0.00836,0.00835,0.00834,0.00832,0.00831,0.0083,0.00829,0.00827,0.00826,0.00825,0.00824,0.00822,0.00821,0.0082,0.00819,0.00817,0.00816,0.00815,0.00813,0.00812,0.00811,0.0081,0.00809,0.00807,0.00806,0.00805,0.00804,0.00802,0.00801,0.008,0.00799,0.00797,0.00796,0.00795,0.00794,0.00793,0.00791,0.0079,
-0.00789,0.00788,0.00787,0.00785,0.00784,0.00783,0.00782,0.00781,0.00779,0.00778,0.00777,0.00776,0.00775,0.00773,0.00772,0.00771,0.0077,0.00769,0.00767,0.00766,0.00765,0.00764,0.00763,0.00762,0.0076,0.00759,0.00758,0.00757,0.00756,0.00755,0.00753,0.00752,0.00751,0.0075,0.00749,0.00748,0.00747,0.00745,0.00744,0.00743,0.00742,0.00741,0.0074,0.00739,0.00737,0.00736,0.00735,0.00734,0.00733,0.00732,0.00731,0.0073,0.00728,0.00727,0.00726,0.00725,0.00724,0.00723,0.00722,0.00721,0.0072,0.00718,0.00717,0.00716,0.00715,0.00714,0.00713,0.00712,0.00711,0.0071,0.00709,0.00707,0.00706,0.00705,0.00704,0.00703,0.00702,0.00701,0.007,0.00699,0.00698,0.00697,0.00696,0.00695,0.00693,0.00692,0.00691,0.0069,0.00689,0.00688,0.00687,0.00686,0.00685,0.00684,0.00683,0.00682,0.00681,0.0068,0.00679,0.00678,
-0.00677,0.00676,0.00675,0.00674,0.00673,0.00671,0.0067,0.00669,0.00668,0.00667,0.00666,0.00665,0.00664,0.00663,0.00662,0.00661,0.0066,0.00659,0.00658,0.00657,0.00656,0.00655,0.00654,0.00653,0.00652,0.00651,0.0065,0.00649,0.00648,0.00647,0.00646,0.00645,0.00644,0.00643,0.00642,0.00641,0.0064,0.00639,0.00638,0.00637,0.00636,0.00635,0.00634,0.00633,0.00632,0.00631,0.0063,0.00629,0.00629,0.00628,0.00627,0.00626,0.00625,0.00624,0.00623,0.00622,0.00621,0.0062,0.00619,0.00618,0.00617,0.00616,0.00615,0.00614,0.00613,0.00612,0.00611,0.0061,0.00609,0.00609,0.00608,0.00607,0.00606,0.00605,0.00604,0.00603,0.00602,0.00601,0.006,0.00599,0.00598,0.00597,0.00596,0.00596,0.00595,0.00594,0.00593,0.00592,0.00591,0.0059,0.00589,0.00588,0.00587,0.00586,0.00586,0.00585,0.00584,0.00583,0.00582,0.00581,
-0.0058,0.00579,0.00578,0.00578,0.00577,0.00576,0.00575,0.00574,0.00573,0.00572,0.00571,0.0057,0.0057,0.00569,0.00568,0.00567,0.00566,0.00565,0.00564,0.00563,0.00563,0.00562,0.00561,0.0056,0.00559,0.00558,0.00557,0.00557,0.00556,0.00555,0.00554,0.00553,0.00552,0.00551,0.00551,0.0055,0.00549,0.00548,0.00547,0.00546,0.00546,0.00545,0.00544,0.00543,0.00542,0.00541,0.00541,0.0054,0.00539,0.00538,0.00537,0.00536,0.00536,0.00535,0.00534,0.00533,0.00532,0.00531,0.00531,0.0053,0.00529,0.00528,0.00527,0.00527,0.00526,0.00525,0.00524,0.00523,0.00522,0.00522,0.00521,0.0052,0.00519,0.00518,0.00518,0.00517,0.00516,0.00515,0.00515,0.00514,0.00513,0.00512,0.00511,0.00511,0.0051,0.00509,0.00508,0.00507,0.00507,0.00506,0.00505,0.00504,0.00504,0.00503,0.00502,0.00501,0.005,0.005,0.00499,0.00498,
-0.00497,0.00497,0.00496,0.00495,0.00494,0.00494,0.00493,0.00492,0.00491,0.0049,0.0049,0.00489,0.00488,0.00487,0.00487,0.00486,0.00485,0.00484,0.00484,0.00483,0.00482,0.00481,0.00481,0.0048,0.00479,0.00479,0.00478,0.00477,0.00476,0.00476,0.00475,0.00474,0.00473,0.00473,0.00472,0.00471,0.0047,0.0047,0.00469,0.00468,0.00468,0.00467,0.00466,0.00465,0.00465,0.00464,0.00463,0.00463,0.00462,0.00461,0.0046,0.0046,0.00459,0.00458,0.00458,0.00457,0.00456,0.00455,0.00455,0.00454,0.00453,0.00453,0.00452,0.00451,0.00451,0.0045,0.00449,0.00448,0.00448,0.00447,0.00446,0.00446,0.00445,0.00444,0.00444,0.00443,0.00442,0.00442,0.00441,0.0044,0.0044,0.00439,0.00438,0.00438,0.00437,0.00436,0.00436,0.00435,0.00434,0.00434,0.00433,0.00432,0.00432,0.00431,0.0043,0.0043,0.00429,0.00428,0.00428,0.00427,
-0.00426,0.00426,0.00425,0.00424,0.00424,0.00423,0.00422,0.00422,0.00421,0.0042,0.0042,0.00419,0.00418,0.00418,0.00417,0.00416,0.00416,0.00415,0.00415,0.00414,0.00413,0.00413,0.00412,0.00411,0.00411,0.0041,0.00409,0.00409,0.00408,0.00408,0.00407,0.00406,0.00406,0.00405,0.00404,0.00404,0.00403,0.00403,0.00402,0.00401,0.00401,0.004,0.00399,0.00399,0.00398,0.00398,0.00397,0.00396,0.00396,0.00395,0.00395,0.00394,0.00393,0.00393,0.00392,0.00391,0.00391,0.0039,0.0039,0.00389,0.00388,0.00388,0.00387,0.00387,0.00386,0.00385,0.00385,0.00384,0.00384,0.00383,0.00383,0.00382,0.00381,0.00381,0.0038,0.0038,0.00379,0.00378,0.00378,0.00377,0.00377,0.00376,0.00375,0.00375,0.00374,0.00374,0.00373,0.00373,0.00372,0.00371,0.00371,0.0037,0.0037,0.00369,0.00369,0.00368,0.00367,0.00367,0.00366,0.00366};
-
-constexpr double stored_lower_incomplete_gamma_values_n4[] = {0.0,0.0,0.0,0.0,0.0,0.0,0.0,1e-05,1e-05,1e-05,1e-05,2e-05,2e-05,3e-05,3e-05,4e-05,4e-05,5e-05,6e-05,7e-05,8e-05,9e-05,0.0001,0.00011,0.00012,0.00014,0.00015,0.00016,0.00018,0.0002,0.00021,0.00023,0.00025,0.00027,0.00029,0.00031,0.00033,0.00036,0.00038,0.00041,0.00043,0.00046,0.00049,0.00051,0.00054,0.00058,0.00061,0.00064,0.00067,0.00071,0.00074,0.00078,0.00082,0.00086,0.0009,0.00094,0.00098,0.00102,0.00107,0.00111,0.00116,0.00121,0.00126,0.00131,0.00136,0.00141,0.00146,0.00152,0.00157,0.00163,0.00169,0.00175,0.00181,0.00187,0.00193,0.00199,0.00206,0.00212,0.00219,0.00226,0.00233,0.0024,0.00247,0.00254,0.00262,0.00269,0.00277,0.00285,0.00293,0.00301,0.00309,0.00317,0.00325,0.00334,0.00343,0.00351,0.0036,0.00369,0.00379,0.00388,
-0.00397,0.00407,0.00416,0.00426,0.00436,0.00446,0.00456,0.00467,0.00477,0.00488,0.00498,0.00509,0.0052,0.00531,0.00542,0.00554,0.00565,0.00577,0.00588,0.006,0.00612,0.00624,0.00636,0.00649,0.00661,0.00674,0.00687,0.007,0.00713,0.00726,0.00739,0.00752,0.00766,0.0078,0.00793,0.00807,0.00821,0.00836,0.0085,0.00864,0.00879,0.00894,0.00909,0.00924,0.00939,0.00954,0.0097,0.00985,0.01001,0.01017,0.01032,0.01049,0.01065,0.01081,0.01098,0.01114,0.01131,0.01148,0.01165,0.01182,0.01199,0.01217,0.01234,0.01252,0.0127,0.01288,0.01306,0.01324,0.01342,0.01361,0.01379,0.01398,0.01417,0.01436,0.01455,0.01474,0.01494,0.01513,0.01533,0.01553,0.01573,0.01593,0.01613,0.01633,0.01654,0.01675,0.01695,0.01716,0.01737,0.01758,0.0178,0.01801,0.01823,0.01844,0.01866,0.01888,0.0191,0.01932,0.01955,0.01977,
-0.02,0.02023,0.02046,0.02069,0.02092,0.02115,0.02138,0.02162,0.02186,0.02209,0.02233,0.02257,0.02282,0.02306,0.0233,0.02355,0.0238,0.02405,0.0243,0.02455,0.0248,0.02505,0.02531,0.02556,0.02582,0.02608,0.02634,0.0266,0.02687,0.02713,0.0274,0.02766,0.02793,0.0282,0.02847,0.02874,0.02902,0.02929,0.02957,0.02984,0.03012,0.0304,0.03068,0.03097,0.03125,0.03153,0.03182,0.03211,0.0324,0.03269,0.03298,0.03327,0.03356,0.03386,0.03415,0.03445,0.03475,0.03505,0.03535,0.03565,0.03596,0.03626,0.03657,0.03688,0.03719,0.0375,0.03781,0.03812,0.03843,0.03875,0.03906,0.03938,0.0397,0.04002,0.04034,0.04066,0.04099,0.04131,0.04164,0.04197,0.04229,0.04262,0.04296,0.04329,0.04362,0.04396,0.04429,0.04463,0.04497,0.04531,0.04565,0.04599,0.04633,0.04668,0.04702,0.04737,0.04772,0.04806,0.04841,0.04877,
-0.04912,0.04947,0.04983,0.05018,0.05054,0.0509,0.05126,0.05162,0.05198,0.05234,0.05271,0.05307,0.05344,0.05381,0.05418,0.05455,0.05492,0.05529,0.05566,0.05604,0.05641,0.05679,0.05717,0.05755,0.05793,0.05831,0.05869,0.05908,0.05946,0.05985,0.06023,0.06062,0.06101,0.0614,0.06179,0.06219,0.06258,0.06297,0.06337,0.06377,0.06417,0.06456,0.06496,0.06537,0.06577,0.06617,0.06658,0.06698,0.06739,0.0678,0.06821,0.06862,0.06903,0.06944,0.06985,0.07027,0.07068,0.0711,0.07152,0.07194,0.07236,0.07278,0.0732,0.07362,0.07405,0.07447,0.0749,0.07532,0.07575,0.07618,0.07661,0.07704,0.07747,0.07791,0.07834,0.07878,0.07921,0.07965,0.08009,0.08053,0.08097,0.08141,0.08185,0.0823,0.08274,0.08319,0.08363,0.08408,0.08453,0.08498,0.08543,0.08588,0.08633,0.08679,0.08724,0.08769,0.08815,0.08861,0.08907,0.08953,
-0.08999,0.09045,0.09091,0.09137,0.09184,0.0923,0.09277,0.09323,0.0937,0.09417,0.09464,0.09511,0.09558,0.09605,0.09653,0.097,0.09748,0.09795,0.09843,0.09891,0.09939,0.09987,0.10035,0.10083,0.10131,0.1018,0.10228,0.10277,0.10325,0.10374,0.10423,0.10472,0.10521,0.1057,0.10619,0.10668,0.10718,0.10767,0.10817,0.10866,0.10916,0.10966,0.11015,0.11065,0.11115,0.11166,0.11216,0.11266,0.11316,0.11367,0.11418,0.11468,0.11519,0.1157,0.11621,0.11672,0.11723,0.11774,0.11825,0.11876,0.11928,0.11979,0.12031,0.12082,0.12134,0.12186,0.12238,0.1229,0.12342,0.12394,0.12446,0.12498,0.12551,0.12603,0.12656,0.12708,0.12761,0.12814,0.12867,0.1292,0.12973,0.13026,0.13079,0.13132,0.13185,0.13239,0.13292,0.13346,0.13399,0.13453,0.13507,0.13561,0.13614,0.13668,0.13723,0.13777,0.13831,0.13885,0.1394,0.13994,
-0.14049,0.14103,0.14158,0.14212,0.14267,0.14322,0.14377,0.14432,0.14487,0.14542,0.14598,0.14653,0.14708,0.14764,0.14819,0.14875,0.14931,0.14986,0.15042,0.15098,0.15154,0.1521,0.15266,0.15322,0.15378,0.15435,0.15491,0.15547,0.15604,0.1566,0.15717,0.15774,0.1583,0.15887,0.15944,0.16001,0.16058,0.16115,0.16172,0.16229,0.16287,0.16344,0.16401,0.16459,0.16516,0.16574,0.16632,0.16689,0.16747,0.16805,0.16863,0.16921,0.16979,0.17037,0.17095,0.17153,0.17211,0.1727,0.17328,0.17387,0.17445,0.17504,0.17562,0.17621,0.1768,0.17739,0.17797,0.17856,0.17915,0.17974,0.18033,0.18093,0.18152,0.18211,0.1827,0.1833,0.18389,0.18449,0.18508,0.18568,0.18628,0.18687,0.18747,0.18807,0.18867,0.18927,0.18987,0.19047,0.19107,0.19167,0.19227,0.19287,0.19348,0.19408,0.19469,0.19529,0.1959,0.1965,0.19711,0.19771,
-0.19832,0.19893,0.19954,0.20015,0.20076,0.20137,0.20198,0.20259,0.2032,0.20381,0.20442,0.20504,0.20565,0.20626,0.20688,0.20749,0.20811,0.20872,0.20934,0.20996,0.21057,0.21119,0.21181,0.21243,0.21305,0.21367,0.21429,0.21491,0.21553,0.21615,0.21677,0.21739,0.21802,0.21864,0.21926,0.21989,0.22051,0.22114,0.22176,0.22239,0.22301,0.22364,0.22427,0.22489,0.22552,0.22615,0.22678,0.22741,0.22804,0.22867,0.2293,0.22993,0.23056,0.23119,0.23182,0.23246,0.23309,0.23372,0.23436,0.23499,0.23563,0.23626,0.2369,0.23753,0.23817,0.2388,0.23944,0.24008,0.24071,0.24135,0.24199,0.24263,0.24327,0.24391,0.24455,0.24519,0.24583,0.24647,0.24711,0.24775,0.24839,0.24904,0.24968,0.25032,0.25096,0.25161,0.25225,0.2529,0.25354,0.25419,0.25483,0.25548,0.25612,0.25677,0.25742,0.25806,0.25871,0.25936,0.26001,0.26065,
-0.2613,0.26195,0.2626,0.26325,0.2639,0.26455,0.2652,0.26585,0.2665,0.26715,0.26781,0.26846,0.26911,0.26976,0.27042,0.27107,0.27172,0.27238,0.27303,0.27368,0.27434,0.27499,0.27565,0.2763,0.27696,0.27762,0.27827,0.27893,0.27959,0.28024,0.2809,0.28156,0.28221,0.28287,0.28353,0.28419,0.28485,0.28551,0.28617,0.28683,0.28749,0.28815,0.28881,0.28947,0.29013,0.29079,0.29145,0.29211,0.29277,0.29344,0.2941,0.29476,0.29542,0.29609,0.29675,0.29741,0.29808,0.29874,0.2994,0.30007,0.30073,0.3014,0.30206,0.30273,0.30339,0.30406,0.30472,0.30539,0.30605,0.30672,0.30739,0.30805,0.30872,0.30939,0.31005,0.31072,0.31139,0.31206,0.31272,0.31339,0.31406,0.31473,0.3154,0.31607,0.31674,0.31741,0.31807,0.31874,0.31941,0.32008,0.32075,0.32142,0.32209,0.32276,0.32344,0.32411,0.32478,0.32545,0.32612,0.32679,
-0.32746,0.32813,0.32881,0.32948,0.33015,0.33082,0.33149,0.33217,0.33284,0.33351,0.33419,0.33486,0.33553,0.33621,0.33688,0.33755,0.33823,0.3389,0.33957,0.34025,0.34092,0.3416,0.34227,0.34295,0.34362,0.34429,0.34497,0.34564,0.34632,0.34699,0.34767,0.34835,0.34902,0.3497,0.35037,0.35105,0.35172,0.3524,0.35308,0.35375,0.35443,0.3551,0.35578,0.35646,0.35713,0.35781,0.35849,0.35916,0.35984,0.36052,0.3612,0.36187,0.36255,0.36323,0.3639,0.36458,0.36526,0.36594,0.36661,0.36729,0.36797,0.36865,0.36932,0.37,0.37068,0.37136,0.37204,0.37271,0.37339,0.37407,0.37475,0.37543,0.37611,0.37678,0.37746,0.37814,0.37882,0.3795,0.38018,0.38086,0.38153,0.38221,0.38289,0.38357,0.38425,0.38493,0.38561,0.38629,0.38696,0.38764,0.38832,0.389,0.38968,0.39036,0.39104,0.39172,0.3924,0.39308,0.39375,0.39443,
-0.39511,0.39579,0.39647,0.39715,0.39783,0.39851,0.39919,0.39987,0.40054,0.40122,0.4019,0.40258,0.40326,0.40394,0.40462,0.4053,0.40598,0.40666,0.40734,0.40801,0.40869,0.40937,0.41005,0.41073,0.41141,0.41209,0.41277,0.41345,0.41412,0.4148,0.41548,0.41616,0.41684,0.41752,0.4182,0.41887,0.41955,0.42023,0.42091,0.42159,0.42227,0.42295,0.42362,0.4243,0.42498,0.42566,0.42634,0.42701,0.42769,0.42837,0.42905,0.42973,0.4304,0.43108,0.43176,0.43244,0.43311,0.43379,0.43447,0.43515,0.43582,0.4365,0.43718,0.43786,0.43853,0.43921,0.43989,0.44056,0.44124,0.44192,0.44259,0.44327,0.44395,0.44462,0.4453,0.44598,0.44665,0.44733,0.448,0.44868,0.44936,0.45003,0.45071,0.45138,0.45206,0.45273,0.45341,0.45408,0.45476,0.45543,0.45611,0.45678,0.45746,0.45813,0.45881,0.45948,0.46016,0.46083,0.46151,0.46218,
-0.46285,0.46353,0.4642,0.46487,0.46555,0.46622,0.4669,0.46757,0.46824,0.46891,0.46959,0.47026,0.47093,0.47161,0.47228,0.47295,0.47362,0.47429,0.47497,0.47564,0.47631,0.47698,0.47765,0.47832,0.47899,0.47967,0.48034,0.48101,0.48168,0.48235,0.48302,0.48369,0.48436,0.48503,0.4857,0.48637,0.48704,0.48771,0.48838,0.48905,0.48971,0.49038,0.49105,0.49172,0.49239,0.49306,0.49373,0.49439,0.49506,0.49573,0.4964,0.49706,0.49773,0.4984,0.49907,0.49973,0.5004,0.50106,0.50173,0.5024,0.50306,0.50373,0.50439,0.50506,0.50573,0.50639,0.50706,0.50772,0.50838,0.50905,0.50971,0.51038,0.51104,0.51171,0.51237,0.51303,0.5137,0.51436,0.51502,0.51568,0.51635,0.51701,0.51767,0.51833,0.519,0.51966,0.52032,0.52098,0.52164,0.5223,0.52296,0.52362,0.52428,0.52494,0.5256,0.52626,0.52692,0.52758,0.52824,0.5289,
-0.52956,0.53022,0.53088,0.53154,0.53219,0.53285,0.53351,0.53417,0.53482,0.53548,0.53614,0.5368,0.53745,0.53811,0.53876,0.53942,0.54008,0.54073,0.54139,0.54204,0.5427,0.54335,0.54401,0.54466,0.54531,0.54597,0.54662,0.54727,0.54793,0.54858,0.54923,0.54989,0.55054,0.55119,0.55184,0.55249,0.55315,0.5538,0.55445,0.5551,0.55575,0.5564,0.55705,0.5577,0.55835,0.559,0.55965,0.5603,0.56095,0.56159,0.56224,0.56289,0.56354,0.56419,0.56483,0.56548,0.56613,0.56677,0.56742,0.56807,0.56871,0.56936,0.57,0.57065,0.5713,0.57194,0.57258,0.57323,0.57387,0.57452,0.57516,0.5758,0.57645,0.57709,0.57773,0.57838,0.57902,0.57966,0.5803,0.58094,0.58158,0.58222,0.58287,0.58351,0.58415,0.58479,0.58543,0.58607,0.5867,0.58734,0.58798,0.58862,0.58926,0.5899,0.59053,0.59117,0.59181,0.59245,0.59308,0.59372,
-0.59436,0.59499,0.59563,0.59626,0.5969,0.59753,0.59817,0.5988,0.59943,0.60007,0.6007,0.60134,0.60197,0.6026,0.60323,0.60387,0.6045,0.60513,0.60576,0.60639,0.60702,0.60765,0.60828,0.60891,0.60954,0.61017,0.6108,0.61143,0.61206,0.61269,0.61332,0.61394,0.61457,0.6152,0.61583,0.61645,0.61708,0.61771,0.61833,0.61896,0.61958,0.62021,0.62083,0.62146,0.62208,0.62271,0.62333,0.62395,0.62458,0.6252,0.62582,0.62644,0.62707,0.62769,0.62831,0.62893,0.62955,0.63017,0.63079,0.63141,0.63203,0.63265,0.63327,0.63389,0.63451,0.63513,0.63574,0.63636,0.63698,0.6376,0.63821,0.63883,0.63945,0.64006,0.64068,0.64129,0.64191,0.64252,0.64314,0.64375,0.64437,0.64498,0.64559,0.6462,0.64682,0.64743,0.64804,0.64865,0.64927,0.64988,0.65049,0.6511,0.65171,0.65232,0.65293,0.65354,0.65415,0.65475,0.65536,0.65597,
-0.65658,0.65719,0.65779,0.6584,0.65901,0.65961,0.66022,0.66083,0.66143,0.66204,0.66264,0.66325,0.66385,0.66445,0.66506,0.66566,0.66626,0.66687,0.66747,0.66807,0.66867,0.66927,0.66987,0.67047,0.67107,0.67167,0.67227,0.67287,0.67347,0.67407,0.67467,0.67527,0.67587,0.67646,0.67706,0.67766,0.67825,0.67885,0.67945,0.68004,0.68064,0.68123,0.68183,0.68242,0.68302,0.68361,0.6842,0.6848,0.68539,0.68598,0.68657,0.68717,0.68776,0.68835,0.68894,0.68953,0.69012,0.69071,0.6913,0.69189,0.69248,0.69307,0.69365,0.69424,0.69483,0.69542,0.696,0.69659,0.69718,0.69776,0.69835,0.69893,0.69952,0.7001,0.70069,0.70127,0.70185,0.70244,0.70302,0.7036,0.70419,0.70477,0.70535,0.70593,0.70651,0.70709,0.70767,0.70825,0.70883,0.70941,0.70999,0.71057,0.71115,0.71173,0.7123,0.71288,0.71346,0.71403,0.71461,0.71519,
-0.71576,0.71634,0.71691,0.71749,0.71806,0.71863,0.71921,0.71978,0.72035,0.72093,0.7215,0.72207,0.72264,0.72321,0.72378,0.72436,0.72493,0.7255,0.72606,0.72663,0.7272,0.72777,0.72834,0.72891,0.72947,0.73004,0.73061,0.73117,0.73174,0.73231,0.73287,0.73344,0.734,0.73457,0.73513,0.73569,0.73626,0.73682,0.73738,0.73795,0.73851,0.73907,0.73963,0.74019,0.74075,0.74131,0.74187,0.74243,0.74299,0.74355,0.74411,0.74467,0.74522,0.74578,0.74634,0.7469,0.74745,0.74801,0.74856,0.74912,0.74967,0.75023,0.75078,0.75134,0.75189,0.75244,0.753,0.75355,0.7541,0.75465,0.7552,0.75576,0.75631,0.75686,0.75741,0.75796,0.75851,0.75906,0.7596,0.76015,0.7607,0.76125,0.7618,0.76234,0.76289,0.76344,0.76398,0.76453,0.76507,0.76562,0.76616,0.76671,0.76725,0.76779,0.76834,0.76888,0.76942,0.76996,0.7705,0.77105,
-0.77159,0.77213,0.77267,0.77321,0.77375,0.77429,0.77482,0.77536,0.7759,0.77644,0.77698,0.77751,0.77805,0.77859,0.77912,0.77966,0.78019,0.78073,0.78126,0.7818,0.78233,0.78286,0.7834,0.78393,0.78446,0.78499,0.78553,0.78606,0.78659,0.78712,0.78765,0.78818,0.78871,0.78924,0.78977,0.79029,0.79082,0.79135,0.79188,0.79241,0.79293,0.79346,0.79398,0.79451,0.79503,0.79556,0.79608,0.79661,0.79713,0.79766,0.79818,0.7987,0.79922,0.79975,0.80027,0.80079,0.80131,0.80183,0.80235,0.80287,0.80339,0.80391,0.80443,0.80495,0.80546,0.80598,0.8065,0.80701,0.80753,0.80805,0.80856,0.80908,0.80959,0.81011,0.81062,0.81114,0.81165,0.81216,0.81268,0.81319,0.8137,0.81421,0.81473,0.81524,0.81575,0.81626,0.81677,0.81728,0.81779,0.8183,0.8188,0.81931,0.81982,0.82033,0.82083,0.82134,0.82185,0.82235,0.82286,0.82337,
-0.82387,0.82437,0.82488,0.82538,0.82589,0.82639,0.82689,0.82739,0.8279,0.8284,0.8289,0.8294,0.8299,0.8304,0.8309,0.8314,0.8319,0.8324,0.8329,0.8334,0.83389,0.83439,0.83489,0.83538,0.83588,0.83638,0.83687,0.83737,0.83786,0.83836,0.83885,0.83934,0.83984,0.84033,0.84082,0.84131,0.84181,0.8423,0.84279,0.84328,0.84377,0.84426,0.84475,0.84524,0.84573,0.84622,0.84671,0.84719,0.84768,0.84817,0.84865,0.84914,0.84963,0.85011,0.8506,0.85108,0.85157,0.85205,0.85254,0.85302,0.8535,0.85399,0.85447,0.85495,0.85543,0.85591,0.85639,0.85687,0.85735,0.85783,0.85831,0.85879,0.85927,0.85975,0.86023,0.86071,0.86118,0.86166,0.86214,0.86261,0.86309,0.86356,0.86404,0.86451,0.86499,0.86546,0.86594,0.86641,0.86688,0.86736,0.86783,0.8683,0.86877,0.86924,0.86971,0.87018,0.87065,0.87112,0.87159,0.87206,
-0.87253,0.873,0.87347,0.87393,0.8744,0.87487,0.87533,0.8758,0.87627,0.87673,0.8772,0.87766,0.87813,0.87859,0.87905,0.87952,0.87998,0.88044,0.8809,0.88137,0.88183,0.88229,0.88275,0.88321,0.88367,0.88413,0.88459,0.88505,0.8855,0.88596,0.88642,0.88688,0.88733,0.88779,0.88825,0.8887,0.88916,0.88961,0.89007,0.89052,0.89098,0.89143,0.89189,0.89234,0.89279,0.89324,0.8937,0.89415,0.8946,0.89505,0.8955,0.89595,0.8964,0.89685,0.8973,0.89775,0.8982,0.89864,0.89909,0.89954,0.89999,0.90043,0.90088,0.90132,0.90177,0.90221,0.90266,0.9031,0.90355,0.90399,0.90443,0.90488,0.90532,0.90576,0.9062,0.90665,0.90709,0.90753,0.90797,0.90841,0.90885,0.90929,0.90973,0.91017,0.9106,0.91104,0.91148,0.91192,0.91235,0.91279,0.91323,0.91366,0.9141,0.91453,0.91497,0.9154,0.91584,0.91627,0.9167,0.91714,
-0.91757,0.918,0.91843,0.91886,0.9193,0.91973,0.92016,0.92059,0.92102,0.92145,0.92188,0.9223,0.92273,0.92316,0.92359,0.92402,0.92444,0.92487,0.9253,0.92572,0.92615,0.92657,0.927,0.92742,0.92785,0.92827,0.92869,0.92912,0.92954,0.92996,0.93038,0.9308,0.93123,0.93165,0.93207,0.93249,0.93291,0.93333,0.93375,0.93416,0.93458,0.935,0.93542,0.93584,0.93625,0.93667,0.93709,0.9375,0.93792,0.93833,0.93875,0.93916,0.93958,0.93999,0.9404,0.94082,0.94123,0.94164,0.94206,0.94247,0.94288,0.94329,0.9437,0.94411,0.94452,0.94493,0.94534,0.94575,0.94616,0.94657,0.94697,0.94738,0.94779,0.9482,0.9486,0.94901,0.94941,0.94982,0.95023,0.95063,0.95103,0.95144,0.95184,0.95225,0.95265,0.95305,0.95345,0.95386,0.95426,0.95466,0.95506,0.95546,0.95586,0.95626,0.95666,0.95706,0.95746,0.95786,0.95826,0.95865,
-0.95905,0.95945,0.95985,0.96024,0.96064,0.96103,0.96143,0.96182,0.96222,0.96261,0.96301,0.9634,0.9638,0.96419,0.96458,0.96497,0.96537,0.96576,0.96615,0.96654,0.96693,0.96732,0.96771,0.9681,0.96849,0.96888,0.96927,0.96966,0.97004,0.97043,0.97082,0.97121,0.97159,0.97198,0.97236,0.97275,0.97313,0.97352,0.9739,0.97429,0.97467,0.97506,0.97544,0.97582,0.9762,0.97659,0.97697,0.97735,0.97773,0.97811,0.97849,0.97887,0.97925,0.97963,0.98001,0.98039,0.98077,0.98115,0.98152,0.9819,0.98228,0.98266,0.98303,0.98341,0.98378,0.98416,0.98453,0.98491,0.98528,0.98566,0.98603,0.98641,0.98678,0.98715,0.98752,0.9879,0.98827,0.98864,0.98901,0.98938,0.98975,0.99012,0.99049,0.99086,0.99123,0.9916,0.99197,0.99234,0.9927,0.99307,0.99344,0.9938,0.99417,0.99454,0.9949,0.99527,0.99563,0.996,0.99636,0.99673,
-0.99709,0.99745,0.99782,0.99818,0.99854,0.9989,0.99927,0.99963,0.99999,1.00035,1.00071,1.00107,1.00143,1.00179,1.00215,1.00251,1.00287,1.00323,1.00358,1.00394,1.0043,1.00465,1.00501,1.00537,1.00572,1.00608,1.00643,1.00679,1.00714,1.0075,1.00785,1.00821,1.00856,1.00891,1.00927,1.00962,1.00997,1.01032,1.01067,1.01102,1.01137,1.01172,1.01208,1.01242,1.01277,1.01312,1.01347,1.01382,1.01417,1.01452,1.01486,1.01521,1.01556,1.0159,1.01625,1.0166,1.01694,1.01729,1.01763,1.01798,1.01832,1.01867,1.01901,1.01935,1.0197,1.02004,1.02038,1.02072,1.02107,1.02141,1.02175,1.02209,1.02243,1.02277,1.02311,1.02345,1.02379,1.02413,1.02447,1.0248,1.02514,1.02548,1.02582,1.02615,1.02649,1.02683,1.02716,1.0275,1.02783,1.02817,1.0285,1.02884,1.02917,1.02951,1.02984,1.03017,1.03051,1.03084,1.03117,1.0315,
-1.03183,1.03217,1.0325,1.03283,1.03316,1.03349,1.03382,1.03415,1.03448,1.03481,1.03513,1.03546,1.03579,1.03612,1.03645,1.03677,1.0371,1.03743,1.03775,1.03808,1.0384,1.03873,1.03905,1.03938,1.0397,1.04003,1.04035,1.04067,1.041,1.04132,1.04164,1.04196,1.04228,1.04261,1.04293,1.04325,1.04357,1.04389,1.04421,1.04453,1.04485,1.04517,1.04549,1.0458,1.04612,1.04644,1.04676,1.04707,1.04739,1.04771,1.04802,1.04834,1.04866,1.04897,1.04929,1.0496,1.04992,1.05023,1.05054,1.05086,1.05117,1.05148,1.0518,1.05211,1.05242,1.05273,1.05304,1.05336,1.05367,1.05398,1.05429,1.0546,1.05491,1.05522,1.05553,1.05583,1.05614,1.05645,1.05676,1.05707,1.05737,1.05768,1.05799,1.05829,1.0586,1.05891,1.05921,1.05952,1.05982,1.06013,1.06043,1.06073,1.06104,1.06134,1.06164,1.06195,1.06225,1.06255,1.06285,1.06316,
-1.06346,1.06376,1.06406,1.06436,1.06466,1.06496,1.06526,1.06556,1.06586,1.06616,1.06645,1.06675,1.06705,1.06735,1.06764,1.06794,1.06824,1.06853,1.06883,1.06913,1.06942,1.06972,1.07001,1.07031,1.0706,1.0709,1.07119,1.07148,1.07178,1.07207,1.07236,1.07265,1.07295,1.07324,1.07353,1.07382,1.07411,1.0744,1.07469,1.07498,1.07527,1.07556,1.07585,1.07614,1.07643,1.07672,1.077,1.07729,1.07758,1.07787,1.07815,1.07844,1.07873,1.07901,1.0793,1.07958,1.07987,1.08015,1.08044,1.08072,1.08101,1.08129,1.08158,1.08186,1.08214,1.08242,1.08271,1.08299,1.08327,1.08355,1.08383,1.08411,1.0844,1.08468,1.08496,1.08524,1.08552,1.08579,1.08607,1.08635,1.08663,1.08691,1.08719,1.08746,1.08774,1.08802,1.0883,1.08857,1.08885,1.08912,1.0894,1.08968,1.08995,1.09023,1.0905,1.09077,1.09105,1.09132,1.0916,1.09187,
-1.09214,1.09242,1.09269,1.09296,1.09323,1.0935,1.09377,1.09405,1.09432,1.09459,1.09486,1.09513,1.0954,1.09567,1.09594,1.0962,1.09647,1.09674,1.09701,1.09728,1.09754,1.09781,1.09808,1.09835,1.09861,1.09888,1.09914,1.09941,1.09967,1.09994,1.1002,1.10047,1.10073,1.101,1.10126,1.10153,1.10179,1.10205,1.10231,1.10258,1.10284,1.1031,1.10336,1.10362,1.10388,1.10415,1.10441,1.10467,1.10493,1.10519,1.10545,1.1057,1.10596,1.10622,1.10648,1.10674,1.107,1.10725,1.10751,1.10777,1.10803,1.10828,1.10854,1.1088,1.10905,1.10931,1.10956,1.10982,1.11007,1.11033,1.11058,1.11083,1.11109,1.11134,1.11159,1.11185,1.1121,1.11235,1.11261,1.11286,1.11311,1.11336,1.11361,1.11386,1.11411,1.11436,1.11461,1.11486,1.11511,1.11536,1.11561,1.11586,1.11611,1.11636,1.11661,1.11685,1.1171,1.11735,1.11759,1.11784,
-1.11809,1.11833,1.11858,1.11883,1.11907,1.11932,1.11956,1.11981,1.12005,1.1203,1.12054,1.12078,1.12103,1.12127,1.12151,1.12176,1.122,1.12224,1.12248,1.12272,1.12297,1.12321,1.12345,1.12369,1.12393,1.12417,1.12441,1.12465,1.12489,1.12513,1.12537,1.12561,1.12584,1.12608,1.12632,1.12656,1.1268,1.12703,1.12727,1.12751,1.12774,1.12798,1.12822,1.12845,1.12869,1.12892,1.12916,1.12939,1.12963,1.12986,1.1301,1.13033,1.13056,1.1308,1.13103,1.13126,1.13149,1.13173,1.13196,1.13219,1.13242,1.13265,1.13289,1.13312,1.13335,1.13358,1.13381,1.13404,1.13427,1.1345,1.13473,1.13495,1.13518,1.13541,1.13564,1.13587,1.1361,1.13632,1.13655,1.13678,1.137,1.13723,1.13746,1.13768,1.13791,1.13814,1.13836,1.13859,1.13881,1.13904,1.13926,1.13948,1.13971,1.13993,1.14016,1.14038,1.1406,1.14082,1.14105,1.14127,
-1.14149,1.14171,1.14194,1.14216,1.14238,1.1426,1.14282,1.14304,1.14326,1.14348,1.1437,1.14392,1.14414,1.14436,1.14458,1.1448,1.14501,1.14523,1.14545,1.14567,1.14588,1.1461,1.14632,1.14654,1.14675,1.14697,1.14718,1.1474,1.14762,1.14783,1.14805,1.14826,1.14848,1.14869,1.1489,1.14912,1.14933,1.14955,1.14976,1.14997,1.15019,1.1504,1.15061,1.15082,1.15103,1.15125,1.15146,1.15167,1.15188,1.15209,1.1523,1.15251,1.15272,1.15293,1.15314,1.15335,1.15356,1.15377,1.15398,1.15419,1.1544,1.1546,1.15481,1.15502,1.15523,1.15543,1.15564,1.15585,1.15605,1.15626,1.15647,1.15667,1.15688,1.15708,1.15729,1.15749,1.1577,1.1579,1.15811,1.15831,1.15852,1.15872,1.15892,1.15913,1.15933,1.15953,1.15974,1.15994,1.16014,1.16034,1.16054,1.16075,1.16095,1.16115,1.16135,1.16155,1.16175,1.16195,1.16215,1.16235,
-1.16255,1.16275,1.16295,1.16315,1.16335,1.16354,1.16374,1.16394,1.16414,1.16434,1.16453,1.16473,1.16493,1.16512,1.16532,1.16552,1.16571,1.16591,1.16611,1.1663,1.1665,1.16669,1.16689,1.16708,1.16728,1.16747,1.16766,1.16786,1.16805,1.16824,1.16844,1.16863,1.16882,1.16902,1.16921,1.1694,1.16959,1.16978,1.16998,1.17017,1.17036,1.17055,1.17074,1.17093,1.17112,1.17131,1.1715,1.17169,1.17188,1.17207,1.17226,1.17245,1.17264,1.17282,1.17301,1.1732,1.17339,1.17358,1.17376,1.17395,1.17414,1.17432,1.17451,1.1747,1.17488,1.17507,1.17526,1.17544,1.17563,1.17581,1.176,1.17618,1.17637,1.17655,1.17673,1.17692,1.1771,1.17729,1.17747,1.17765,1.17784,1.17802,1.1782,1.17838,1.17857,1.17875,1.17893,1.17911,1.17929,1.17947,1.17965,1.17983,1.18002,1.1802,1.18038,1.18056,1.18074,1.18092,1.18109,1.18127,
-1.18145,1.18163,1.18181,1.18199,1.18217,1.18234,1.18252,1.1827,1.18288,1.18305,1.18323,1.18341,1.18358,1.18376,1.18394,1.18411,1.18429,1.18447,1.18464,1.18482,1.18499,1.18517,1.18534,1.18552,1.18569,1.18586,1.18604,1.18621,1.18638,1.18656,1.18673,1.1869,1.18708,1.18725,1.18742,1.18759,1.18777,1.18794,1.18811,1.18828,1.18845,1.18862,1.18879,1.18896,1.18914,1.18931,1.18948,1.18965,1.18982,1.18998,1.19015,1.19032,1.19049,1.19066,1.19083,1.191,1.19117,1.19133,1.1915,1.19167,1.19184,1.192,1.19217,1.19234,1.19251,1.19267,1.19284,1.193,1.19317,1.19334,1.1935,1.19367,1.19383,1.194,1.19416,1.19433,1.19449,1.19466,1.19482,1.19498,1.19515,1.19531,1.19547,1.19564,1.1958,1.19596,1.19613,1.19629,1.19645,1.19661,1.19678,1.19694,1.1971,1.19726,1.19742,1.19758,1.19774,1.1979,1.19806,1.19823,
-1.19839,1.19855,1.19871,1.19886,1.19902,1.19918,1.19934,1.1995,1.19966,1.19982,1.19998,1.20014,1.20029,1.20045,1.20061,1.20077,1.20092,1.20108,1.20124,1.20139,1.20155,1.20171,1.20186,1.20202,1.20218,1.20233,1.20249,1.20264,1.2028,1.20295,1.20311,1.20326,1.20342,1.20357,1.20373,1.20388,1.20403,1.20419,1.20434,1.20449,1.20465,1.2048,1.20495,1.2051,1.20526,1.20541,1.20556,1.20571,1.20587,1.20602,1.20617,1.20632,1.20647,1.20662,1.20677,1.20692,1.20707,1.20722,1.20737,1.20752,1.20767,1.20782,1.20797,1.20812,1.20827,1.20842,1.20857,1.20872,1.20886,1.20901,1.20916,1.20931,1.20946,1.2096,1.20975,1.2099,1.21004,1.21019,1.21034,1.21048,1.21063,1.21078,1.21092,1.21107,1.21121,1.21136,1.21151,1.21165,1.2118,1.21194,1.21209,1.21223,1.21237,1.21252,1.21266,1.21281,1.21295,1.21309,1.21324,1.21338,
-1.21352,1.21367,1.21381,1.21395,1.21409,1.21424,1.21438,1.21452,1.21466,1.2148,1.21494,1.21509,1.21523,1.21537,1.21551,1.21565,1.21579,1.21593,1.21607,1.21621,1.21635,1.21649,1.21663,1.21677,1.21691,1.21705,1.21719,1.21732,1.21746,1.2176,1.21774,1.21788,1.21802,1.21815,1.21829,1.21843,1.21857,1.2187,1.21884,1.21898,1.21911,1.21925,1.21939,1.21952,1.21966,1.21979,1.21993,1.22007,1.2202,1.22034,1.22047,1.22061,1.22074,1.22088,1.22101,1.22114,1.22128,1.22141,1.22155,1.22168,1.22181,1.22195,1.22208,1.22221,1.22235,1.22248,1.22261,1.22274,1.22288,1.22301,1.22314,1.22327,1.2234,1.22354,1.22367,1.2238,1.22393,1.22406,1.22419,1.22432,1.22445,1.22458,1.22471,1.22484,1.22497,1.2251,1.22523,1.22536,1.22549,1.22562,1.22575,1.22588,1.22601,1.22614,1.22626,1.22639,1.22652,1.22665,1.22678,1.2269,
-1.22703,1.22716,1.22729,1.22741,1.22754,1.22767,1.22779,1.22792,1.22805,1.22817,1.2283,1.22842,1.22855,1.22868,1.2288,1.22893,1.22905,1.22918,1.2293,1.22943,1.22955,1.22968,1.2298,1.22992,1.23005,1.23017,1.2303,1.23042,1.23054,1.23067,1.23079,1.23091,1.23104,1.23116,1.23128,1.2314,1.23153,1.23165,1.23177,1.23189,1.23201,1.23213,1.23226,1.23238,1.2325,1.23262,1.23274,1.23286,1.23298,1.2331,1.23322,1.23334,1.23346,1.23358,1.2337,1.23382,1.23394,1.23406,1.23418,1.2343,1.23442,1.23454,1.23466,1.23477,1.23489,1.23501,1.23513,1.23525,1.23537,1.23548,1.2356,1.23572,1.23584,1.23595,1.23607,1.23619,1.2363,1.23642,1.23654,1.23665,1.23677,1.23688,1.237,1.23712,1.23723,1.23735,1.23746,1.23758,1.23769,1.23781,1.23792,1.23804,1.23815,1.23827,1.23838,1.2385,1.23861,1.23872,1.23884,1.23895,
-1.23906,1.23918,1.23929,1.2394,1.23952,1.23963,1.23974,1.23985,1.23997,1.24008,1.24019,1.2403,1.24042,1.24053,1.24064,1.24075,1.24086,1.24097,1.24108,1.2412,1.24131,1.24142,1.24153,1.24164,1.24175,1.24186,1.24197,1.24208,1.24219,1.2423,1.24241,1.24252,1.24263,1.24274,1.24285,1.24295,1.24306,1.24317,1.24328,1.24339,1.2435,1.2436,1.24371,1.24382,1.24393,1.24404,1.24414,1.24425,1.24436,1.24447,1.24457,1.24468,1.24479,1.24489,1.245,1.24511,1.24521,1.24532,1.24542,1.24553,1.24564,1.24574,1.24585,1.24595,1.24606,1.24616,1.24627,1.24637,1.24648,1.24658,1.24669,1.24679,1.2469,1.247,1.2471,1.24721,1.24731,1.24742,1.24752,1.24762,1.24773,1.24783,1.24793,1.24803,1.24814,1.24824,1.24834,1.24845,1.24855,1.24865,1.24875,1.24885,1.24896,1.24906,1.24916,1.24926,1.24936,1.24946,1.24956,1.24966,
-1.24977,1.24987,1.24997,1.25007,1.25017,1.25027,1.25037,1.25047,1.25057,1.25067,1.25077,1.25087,1.25097,1.25107,1.25117,1.25126,1.25136,1.25146,1.25156,1.25166,1.25176,1.25186,1.25195,1.25205,1.25215,1.25225,1.25235,1.25244,1.25254,1.25264,1.25274,1.25283,1.25293,1.25303,1.25312,1.25322,1.25332,1.25341,1.25351,1.25361,1.2537,1.2538,1.2539,1.25399,1.25409,1.25418,1.25428,1.25437,1.25447,1.25456,1.25466,1.25475,1.25485,1.25494,1.25504,1.25513,1.25523,1.25532,1.25542,1.25551,1.2556,1.2557,1.25579,1.25588,1.25598,1.25607,1.25616,1.25626,1.25635,1.25644,1.25654,1.25663,1.25672,1.25681,1.25691,1.257,1.25709,1.25718,1.25727,1.25737,1.25746,1.25755,1.25764,1.25773,1.25782,1.25791,1.25801,1.2581,1.25819,1.25828,1.25837,1.25846,1.25855,1.25864,1.25873,1.25882,1.25891,1.259,1.25909,1.25918,
-1.25927,1.25936,1.25945,1.25954,1.25963,1.25971,1.2598,1.25989,1.25998,1.26007,1.26016,1.26025,1.26033,1.26042,1.26051,1.2606,1.26069,1.26077,1.26086,1.26095,1.26104,1.26112,1.26121,1.2613,1.26139,1.26147,1.26156,1.26165,1.26173,1.26182,1.2619,1.26199,1.26208,1.26216,1.26225,1.26233,1.26242,1.26251,1.26259,1.26268,1.26276,1.26285,1.26293,1.26302,1.2631,1.26319,1.26327,1.26336,1.26344,1.26353,1.26361,1.26369,1.26378,1.26386,1.26395,1.26403,1.26411,1.2642,1.26428,1.26436,1.26445,1.26453,1.26461,1.2647,1.26478,1.26486,1.26494,1.26503,1.26511,1.26519,1.26527,1.26536,1.26544,1.26552,1.2656,1.26568,1.26577,1.26585,1.26593,1.26601,1.26609,1.26617,1.26625,1.26633,1.26642,1.2665,1.26658,1.26666,1.26674,1.26682,1.2669,1.26698,1.26706,1.26714,1.26722,1.2673,1.26738,1.26746,1.26754,1.26762,
-1.2677,1.26778,1.26785,1.26793,1.26801,1.26809,1.26817,1.26825,1.26833,1.26841,1.26848,1.26856,1.26864,1.26872,1.2688,1.26887,1.26895,1.26903,1.26911,1.26918,1.26926,1.26934,1.26942,1.26949,1.26957,1.26965,1.26972,1.2698,1.26988,1.26995,1.27003,1.27011,1.27018,1.27026,1.27034,1.27041,1.27049,1.27056,1.27064,1.27072,1.27079,1.27087,1.27094,1.27102,1.27109,1.27117,1.27124,1.27132,1.27139,1.27147,1.27154,1.27162,1.27169,1.27176,1.27184,1.27191,1.27199,1.27206,1.27214,1.27221,1.27228,1.27236,1.27243,1.2725,1.27258,1.27265,1.27272,1.2728,1.27287,1.27294,1.27301,1.27309,1.27316,1.27323,1.27331,1.27338,1.27345,1.27352,1.27359,1.27367,1.27374,1.27381,1.27388,1.27395,1.27403,1.2741,1.27417,1.27424,1.27431,1.27438,1.27445,1.27452,1.27459,1.27467,1.27474,1.27481,1.27488,1.27495,1.27502,1.27509,
-1.27516,1.27523,1.2753,1.27537,1.27544,1.27551,1.27558,1.27565,1.27572,1.27579,1.27586,1.27593,1.27599,1.27606,1.27613,1.2762,1.27627,1.27634,1.27641,1.27648,1.27654,1.27661,1.27668,1.27675,1.27682,1.27689,1.27695,1.27702,1.27709,1.27716,1.27723,1.27729,1.27736,1.27743,1.27749,1.27756,1.27763,1.2777,1.27776,1.27783,1.2779,1.27796,1.27803,1.2781,1.27816,1.27823,1.2783,1.27836,1.27843,1.27849,1.27856,1.27863,1.27869,1.27876,1.27882,1.27889,1.27896,1.27902,1.27909,1.27915,1.27922,1.27928,1.27935,1.27941,1.27948,1.27954,1.27961,1.27967,1.27974,1.2798,1.27986,1.27993,1.27999,1.28006,1.28012,1.28018,1.28025,1.28031,1.28038,1.28044,1.2805,1.28057,1.28063,1.28069,1.28076,1.28082,1.28088,1.28095,1.28101,1.28107,1.28114,1.2812,1.28126,1.28132,1.28139,1.28145,1.28151,1.28157,1.28164,1.2817,
-1.28176,1.28182,1.28188,1.28194,1.28201,1.28207,1.28213,1.28219,1.28225,1.28231,1.28238,1.28244,1.2825,1.28256,1.28262,1.28268,1.28274,1.2828,1.28286,1.28292,1.28298,1.28304,1.2831,1.28317,1.28323,1.28329,1.28335,1.28341,1.28347,1.28353,1.28359,1.28364,1.2837,1.28376,1.28382,1.28388,1.28394,1.284,1.28406,1.28412,1.28418,1.28424,1.2843,1.28436,1.28441,1.28447,1.28453,1.28459,1.28465,1.28471,1.28477,1.28482,1.28488,1.28494,1.285,1.28506,1.28511,1.28517,1.28523,1.28529,1.28534,1.2854,1.28546,1.28552,1.28557,1.28563,1.28569,1.28575,1.2858,1.28586,1.28592,1.28597,1.28603,1.28609,1.28614,1.2862,1.28626,1.28631,1.28637,1.28643,1.28648,1.28654,1.28659,1.28665,1.28671,1.28676,1.28682,1.28687,1.28693,1.28698,1.28704,1.28709,1.28715,1.28721,1.28726,1.28732,1.28737,1.28743,1.28748,1.28754,
-1.28759,1.28764,1.2877,1.28775,1.28781,1.28786,1.28792,1.28797,1.28803,1.28808,1.28813,1.28819,1.28824,1.2883,1.28835,1.2884,1.28846,1.28851,1.28856,1.28862,1.28867,1.28872,1.28878,1.28883,1.28888,1.28894,1.28899,1.28904,1.2891,1.28915,1.2892,1.28925,1.28931,1.28936,1.28941,1.28946,1.28952,1.28957,1.28962,1.28967,1.28973,1.28978,1.28983,1.28988,1.28993,1.28999,1.29004,1.29009,1.29014,1.29019,1.29024,1.29029,1.29035,1.2904,1.29045,1.2905,1.29055,1.2906,1.29065,1.2907,1.29075,1.29081,1.29086,1.29091,1.29096,1.29101,1.29106,1.29111,1.29116,1.29121,1.29126,1.29131,1.29136,1.29141,1.29146,1.29151,1.29156,1.29161,1.29166,1.29171,1.29176,1.29181,1.29186,1.29191,1.29195,1.292,1.29205,1.2921,1.29215,1.2922,1.29225,1.2923,1.29235,1.2924,1.29244,1.29249,1.29254,1.29259,1.29264,1.29269,
-1.29274,1.29278,1.29283,1.29288,1.29293,1.29298,1.29302,1.29307,1.29312,1.29317,1.29321,1.29326,1.29331,1.29336,1.29341,1.29345,1.2935,1.29355,1.29359,1.29364,1.29369,1.29374,1.29378,1.29383,1.29388,1.29392,1.29397,1.29402,1.29406,1.29411,1.29416,1.2942,1.29425,1.2943,1.29434,1.29439,1.29443,1.29448,1.29453,1.29457,1.29462,1.29466,1.29471,1.29476,1.2948,1.29485,1.29489,1.29494,1.29498,1.29503,1.29507,1.29512,1.29517,1.29521,1.29526,1.2953,1.29535,1.29539,1.29544,1.29548,1.29552,1.29557,1.29561,1.29566,1.2957,1.29575,1.29579,1.29584,1.29588,1.29593,1.29597,1.29601,1.29606,1.2961,1.29615,1.29619,1.29623,1.29628,1.29632,1.29637,1.29641,1.29645,1.2965,1.29654,1.29658,1.29663,1.29667,1.29671,1.29676,1.2968,1.29684,1.29689,1.29693,1.29697,1.29701,1.29706,1.2971,1.29714,1.29719,1.29723,
-1.29727,1.29731,1.29736,1.2974,1.29744,1.29748,1.29752,1.29757,1.29761,1.29765,1.29769,1.29774,1.29778,1.29782,1.29786,1.2979,1.29794,1.29799,1.29803,1.29807,1.29811,1.29815,1.29819,1.29823,1.29828,1.29832,1.29836,1.2984,1.29844,1.29848,1.29852,1.29856,1.2986,1.29865,1.29869,1.29873,1.29877,1.29881,1.29885,1.29889,1.29893,1.29897,1.29901,1.29905,1.29909,1.29913,1.29917,1.29921,1.29925,1.29929,1.29933,1.29937,1.29941,1.29945,1.29949,1.29953,1.29957,1.29961,1.29965,1.29969,1.29973,1.29977,1.29981,1.29985,1.29988,1.29992,1.29996,1.3,1.30004,1.30008,1.30012,1.30016,1.3002,1.30024,1.30027,1.30031,1.30035,1.30039,1.30043,1.30047,1.30051,1.30054,1.30058,1.30062,1.30066,1.3007,1.30074,1.30077,1.30081,1.30085,1.30089,1.30093,1.30096,1.301,1.30104,1.30108,1.30111,1.30115,1.30119,1.30123};
-
-constexpr double stored_gamma_values_n4[] = {0.88623,0.88622,0.8862,0.88618,0.88615,0.88612,0.88608,0.88604,0.886,0.88596,0.88591,0.88586,0.88581,0.88576,0.88571,0.88565,0.88559,0.88553,0.88547,0.88541,0.88534,0.88528,0.88521,0.88514,0.88507,0.88499,0.88492,0.88484,0.88477,0.88469,0.88461,0.88453,0.88444,0.88436,0.88428,0.88419,0.8841,0.88401,0.88392,0.88383,0.88374,0.88365,0.88356,0.88346,0.88336,0.88327,0.88317,0.88307,0.88297,0.88287,0.88277,0.88266,0.88256,0.88245,0.88235,0.88224,0.88213,0.88203,0.88192,0.88181,0.88169,0.88158,0.88147,0.88136,0.88124,0.88113,0.88101,0.88089,0.88077,0.88066,0.88054,0.88042,0.8803,0.88017,0.88005,0.87993,0.8798,0.87968,0.87955,0.87943,0.8793,0.87917,0.87904,0.87891,0.87878,0.87865,0.87852,0.87839,0.87826,0.87812,0.87799,0.87786,0.87772,0.87758,0.87745,0.87731,0.87717,0.87703,0.8769,0.87676,
-0.87662,0.87647,0.87633,0.87619,0.87605,0.8759,0.87576,0.87562,0.87547,0.87532,0.87518,0.87503,0.87488,0.87474,0.87459,0.87444,0.87429,0.87414,0.87399,0.87384,0.87368,0.87353,0.87338,0.87322,0.87307,0.87292,0.87276,0.8726,0.87245,0.87229,0.87213,0.87198,0.87182,0.87166,0.8715,0.87134,0.87118,0.87102,0.87086,0.8707,0.87053,0.87037,0.87021,0.87004,0.86988,0.86972,0.86955,0.86938,0.86922,0.86905,0.86889,0.86872,0.86855,0.86838,0.86821,0.86804,0.86787,0.8677,0.86753,0.86736,0.86719,0.86702,0.86685,0.86667,0.8665,0.86633,0.86615,0.86598,0.8658,0.86563,0.86545,0.86528,0.8651,0.86492,0.86475,0.86457,0.86439,0.86421,0.86403,0.86386,0.86368,0.8635,0.86332,0.86313,0.86295,0.86277,0.86259,0.86241,0.86222,0.86204,0.86186,0.86167,0.86149,0.86131,0.86112,0.86094,0.86075,0.86056,0.86038,0.86019,
-0.86,0.85982,0.85963,0.85944,0.85925,0.85906,0.85887,0.85868,0.85849,0.8583,0.85811,0.85792,0.85773,0.85754,0.85735,0.85716,0.85696,0.85677,0.85658,0.85638,0.85619,0.856,0.8558,0.85561,0.85541,0.85522,0.85502,0.85482,0.85463,0.85443,0.85423,0.85404,0.85384,0.85364,0.85344,0.85324,0.85304,0.85285,0.85265,0.85245,0.85225,0.85205,0.85185,0.85164,0.85144,0.85124,0.85104,0.85084,0.85064,0.85043,0.85023,0.85003,0.84982,0.84962,0.84941,0.84921,0.84901,0.8488,0.8486,0.84839,0.84818,0.84798,0.84777,0.84757,0.84736,0.84715,0.84694,0.84674,0.84653,0.84632,0.84611,0.8459,0.84569,0.84549,0.84528,0.84507,0.84486,0.84465,0.84444,0.84423,0.84401,0.8438,0.84359,0.84338,0.84317,0.84296,0.84274,0.84253,0.84232,0.8421,0.84189,0.84168,0.84146,0.84125,0.84104,0.84082,0.84061,0.84039,0.84018,0.83996,
-0.83974,0.83953,0.83931,0.8391,0.83888,0.83866,0.83845,0.83823,0.83801,0.83779,0.83757,0.83736,0.83714,0.83692,0.8367,0.83648,0.83626,0.83604,0.83582,0.8356,0.83538,0.83516,0.83494,0.83472,0.8345,0.83428,0.83406,0.83384,0.83361,0.83339,0.83317,0.83295,0.83273,0.8325,0.83228,0.83206,0.83183,0.83161,0.83139,0.83116,0.83094,0.83071,0.83049,0.83026,0.83004,0.82981,0.82959,0.82936,0.82914,0.82891,0.82869,0.82846,0.82823,0.82801,0.82778,0.82755,0.82733,0.8271,0.82687,0.82664,0.82641,0.82619,0.82596,0.82573,0.8255,0.82527,0.82504,0.82481,0.82458,0.82436,0.82413,0.8239,0.82367,0.82344,0.82321,0.82298,0.82274,0.82251,0.82228,0.82205,0.82182,0.82159,0.82136,0.82113,0.82089,0.82066,0.82043,0.8202,0.81996,0.81973,0.8195,0.81926,0.81903,0.8188,0.81856,0.81833,0.8181,0.81786,0.81763,0.81739,
-0.81716,0.81693,0.81669,0.81646,0.81622,0.81599,0.81575,0.81551,0.81528,0.81504,0.81481,0.81457,0.81433,0.8141,0.81386,0.81363,0.81339,0.81315,0.81291,0.81268,0.81244,0.8122,0.81196,0.81173,0.81149,0.81125,0.81101,0.81077,0.81054,0.8103,0.81006,0.80982,0.80958,0.80934,0.8091,0.80886,0.80862,0.80838,0.80814,0.8079,0.80766,0.80742,0.80718,0.80694,0.8067,0.80646,0.80622,0.80598,0.80574,0.8055,0.80526,0.80501,0.80477,0.80453,0.80429,0.80405,0.80381,0.80356,0.80332,0.80308,0.80284,0.80259,0.80235,0.80211,0.80187,0.80162,0.80138,0.80114,0.80089,0.80065,0.80041,0.80016,0.79992,0.79967,0.79943,0.79919,0.79894,0.7987,0.79845,0.79821,0.79796,0.79772,0.79747,0.79723,0.79698,0.79674,0.79649,0.79625,0.796,0.79576,0.79551,0.79526,0.79502,0.79477,0.79453,0.79428,0.79403,0.79379,0.79354,0.79329,
-0.79305,0.7928,0.79255,0.79231,0.79206,0.79181,0.79156,0.79132,0.79107,0.79082,0.79057,0.79033,0.79008,0.78983,0.78958,0.78933,0.78909,0.78884,0.78859,0.78834,0.78809,0.78784,0.7876,0.78735,0.7871,0.78685,0.7866,0.78635,0.7861,0.78585,0.7856,0.78535,0.7851,0.78485,0.7846,0.78435,0.7841,0.78385,0.7836,0.78335,0.7831,0.78285,0.7826,0.78235,0.7821,0.78185,0.7816,0.78135,0.7811,0.78085,0.7806,0.78034,0.78009,0.77984,0.77959,0.77934,0.77909,0.77884,0.77858,0.77833,0.77808,0.77783,0.77758,0.77732,0.77707,0.77682,0.77657,0.77632,0.77606,0.77581,0.77556,0.77531,0.77505,0.7748,0.77455,0.77429,0.77404,0.77379,0.77354,0.77328,0.77303,0.77278,0.77252,0.77227,0.77202,0.77176,0.77151,0.77126,0.771,0.77075,0.77049,0.77024,0.76999,0.76973,0.76948,0.76922,0.76897,0.76872,0.76846,0.76821,
-0.76795,0.7677,0.76744,0.76719,0.76693,0.76668,0.76642,0.76617,0.76592,0.76566,0.76541,0.76515,0.7649,0.76464,0.76438,0.76413,0.76387,0.76362,0.76336,0.76311,0.76285,0.7626,0.76234,0.76209,0.76183,0.76157,0.76132,0.76106,0.76081,0.76055,0.7603,0.76004,0.75978,0.75953,0.75927,0.75901,0.75876,0.7585,0.75825,0.75799,0.75773,0.75748,0.75722,0.75696,0.75671,0.75645,0.75619,0.75594,0.75568,0.75542,0.75517,0.75491,0.75465,0.75439,0.75414,0.75388,0.75362,0.75337,0.75311,0.75285,0.75259,0.75234,0.75208,0.75182,0.75156,0.75131,0.75105,0.75079,0.75053,0.75028,0.75002,0.74976,0.7495,0.74925,0.74899,0.74873,0.74847,0.74821,0.74796,0.7477,0.74744,0.74718,0.74692,0.74667,0.74641,0.74615,0.74589,0.74563,0.74538,0.74512,0.74486,0.7446,0.74434,0.74408,0.74383,0.74357,0.74331,0.74305,0.74279,0.74253,
-0.74227,0.74202,0.74176,0.7415,0.74124,0.74098,0.74072,0.74046,0.7402,0.73994,0.73969,0.73943,0.73917,0.73891,0.73865,0.73839,0.73813,0.73787,0.73761,0.73735,0.7371,0.73684,0.73658,0.73632,0.73606,0.7358,0.73554,0.73528,0.73502,0.73476,0.7345,0.73424,0.73398,0.73372,0.73347,0.73321,0.73295,0.73269,0.73243,0.73217,0.73191,0.73165,0.73139,0.73113,0.73087,0.73061,0.73035,0.73009,0.72983,0.72957,0.72931,0.72905,0.72879,0.72853,0.72827,0.72801,0.72775,0.72749,0.72723,0.72697,0.72671,0.72645,0.72619,0.72593,0.72567,0.72541,0.72515,0.72489,0.72463,0.72437,0.72412,0.72386,0.7236,0.72334,0.72307,0.72281,0.72255,0.72229,0.72203,0.72177,0.72151,0.72125,0.72099,0.72073,0.72047,0.72021,0.71995,0.71969,0.71943,0.71917,0.71891,0.71865,0.71839,0.71813,0.71787,0.71761,0.71735,0.71709,0.71683,0.71657,
-0.71631,0.71605,0.71579,0.71553,0.71527,0.71501,0.71475,0.71449,0.71423,0.71397,0.71371,0.71345,0.71319,0.71293,0.71267,0.71241,0.71215,0.71189,0.71163,0.71137,0.71111,0.71085,0.71059,0.71033,0.71007,0.70981,0.70954,0.70928,0.70902,0.70876,0.7085,0.70824,0.70798,0.70772,0.70746,0.7072,0.70694,0.70668,0.70642,0.70616,0.7059,0.70564,0.70538,0.70512,0.70486,0.7046,0.70434,0.70408,0.70382,0.70356,0.7033,0.70304,0.70278,0.70252,0.70226,0.702,0.70174,0.70148,0.70122,0.70096,0.7007,0.70044,0.70018,0.69992,0.69966,0.6994,0.69914,0.69888,0.69862,0.69836,0.6981,0.69784,0.69758,0.69732,0.69706,0.6968,0.69654,0.69628,0.69602,0.69576,0.6955,0.69524,0.69498,0.69472,0.69446,0.6942,0.69394,0.69368,0.69342,0.69316,0.6929,0.69264,0.69238,0.69212,0.69186,0.6916,0.69134,0.69108,0.69082,0.69056,
-0.6903,0.69004,0.68978,0.68952,0.68926,0.689,0.68874,0.68848,0.68822,0.68796,0.6877,0.68744,0.68718,0.68692,0.68666,0.6864,0.68614,0.68588,0.68562,0.68537,0.68511,0.68485,0.68459,0.68433,0.68407,0.68381,0.68355,0.68329,0.68303,0.68277,0.68251,0.68225,0.68199,0.68173,0.68148,0.68122,0.68096,0.6807,0.68044,0.68018,0.67992,0.67966,0.6794,0.67914,0.67888,0.67862,0.67837,0.67811,0.67785,0.67759,0.67733,0.67707,0.67681,0.67655,0.67629,0.67604,0.67578,0.67552,0.67526,0.675,0.67474,0.67448,0.67422,0.67397,0.67371,0.67345,0.67319,0.67293,0.67267,0.67242,0.67216,0.6719,0.67164,0.67138,0.67112,0.67086,0.67061,0.67035,0.67009,0.66983,0.66957,0.66932,0.66906,0.6688,0.66854,0.66828,0.66802,0.66777,0.66751,0.66725,0.66699,0.66673,0.66648,0.66622,0.66596,0.6657,0.66545,0.66519,0.66493,0.66467,
-0.66441,0.66416,0.6639,0.66364,0.66338,0.66313,0.66287,0.66261,0.66235,0.6621,0.66184,0.66158,0.66132,0.66107,0.66081,0.66055,0.6603,0.66004,0.65978,0.65952,0.65927,0.65901,0.65875,0.6585,0.65824,0.65798,0.65772,0.65747,0.65721,0.65695,0.6567,0.65644,0.65618,0.65593,0.65567,0.65541,0.65516,0.6549,0.65464,0.65439,0.65413,0.65387,0.65362,0.65336,0.6531,0.65285,0.65259,0.65234,0.65208,0.65182,0.65157,0.65131,0.65106,0.6508,0.65054,0.65029,0.65003,0.64978,0.64952,0.64926,0.64901,0.64875,0.6485,0.64824,0.64798,0.64773,0.64747,0.64722,0.64696,0.64671,0.64645,0.6462,0.64594,0.64568,0.64543,0.64517,0.64492,0.64466,0.64441,0.64415,0.6439,0.64364,0.64339,0.64313,0.64288,0.64262,0.64237,0.64211,0.64186,0.6416,0.64135,0.64109,0.64084,0.64059,0.64033,0.64008,0.63982,0.63957,0.63931,0.63906,
-0.6388,0.63855,0.6383,0.63804,0.63779,0.63753,0.63728,0.63702,0.63677,0.63652,0.63626,0.63601,0.63575,0.6355,0.63525,0.63499,0.63474,0.63449,0.63423,0.63398,0.63372,0.63347,0.63322,0.63296,0.63271,0.63246,0.6322,0.63195,0.6317,0.63144,0.63119,0.63094,0.63069,0.63043,0.63018,0.62993,0.62967,0.62942,0.62917,0.62891,0.62866,0.62841,0.62816,0.6279,0.62765,0.6274,0.62715,0.62689,0.62664,0.62639,0.62614,0.62588,0.62563,0.62538,0.62513,0.62488,0.62462,0.62437,0.62412,0.62387,0.62362,0.62336,0.62311,0.62286,0.62261,0.62236,0.62211,0.62185,0.6216,0.62135,0.6211,0.62085,0.6206,0.62035,0.62009,0.61984,0.61959,0.61934,0.61909,0.61884,0.61859,0.61834,0.61809,0.61784,0.61758,0.61733,0.61708,0.61683,0.61658,0.61633,0.61608,0.61583,0.61558,0.61533,0.61508,0.61483,0.61458,0.61433,0.61408,0.61383,
-0.61358,0.61333,0.61308,0.61283,0.61258,0.61233,0.61208,0.61183,0.61158,0.61133,0.61108,0.61083,0.61058,0.61033,0.61008,0.60983,0.60958,0.60934,0.60909,0.60884,0.60859,0.60834,0.60809,0.60784,0.60759,0.60734,0.60709,0.60685,0.6066,0.60635,0.6061,0.60585,0.6056,0.60535,0.60511,0.60486,0.60461,0.60436,0.60411,0.60386,0.60362,0.60337,0.60312,0.60287,0.60263,0.60238,0.60213,0.60188,0.60163,0.60139,0.60114,0.60089,0.60064,0.6004,0.60015,0.5999,0.59965,0.59941,0.59916,0.59891,0.59867,0.59842,0.59817,0.59793,0.59768,0.59743,0.59718,0.59694,0.59669,0.59644,0.5962,0.59595,0.59571,0.59546,0.59521,0.59497,0.59472,0.59447,0.59423,0.59398,0.59374,0.59349,0.59324,0.593,0.59275,0.59251,0.59226,0.59202,0.59177,0.59152,0.59128,0.59103,0.59079,0.59054,0.5903,0.59005,0.58981,0.58956,0.58932,0.58907,
-0.58883,0.58858,0.58834,0.58809,0.58785,0.5876,0.58736,0.58711,0.58687,0.58663,0.58638,0.58614,0.58589,0.58565,0.5854,0.58516,0.58492,0.58467,0.58443,0.58418,0.58394,0.5837,0.58345,0.58321,0.58297,0.58272,0.58248,0.58224,0.58199,0.58175,0.58151,0.58126,0.58102,0.58078,0.58053,0.58029,0.58005,0.5798,0.57956,0.57932,0.57908,0.57883,0.57859,0.57835,0.57811,0.57786,0.57762,0.57738,0.57714,0.57689,0.57665,0.57641,0.57617,0.57593,0.57568,0.57544,0.5752,0.57496,0.57472,0.57447,0.57423,0.57399,0.57375,0.57351,0.57327,0.57303,0.57279,0.57254,0.5723,0.57206,0.57182,0.57158,0.57134,0.5711,0.57086,0.57062,0.57038,0.57014,0.5699,0.56965,0.56941,0.56917,0.56893,0.56869,0.56845,0.56821,0.56797,0.56773,0.56749,0.56725,0.56701,0.56677,0.56653,0.56629,0.56606,0.56582,0.56558,0.56534,0.5651,0.56486,
-0.56462,0.56438,0.56414,0.5639,0.56366,0.56342,0.56319,0.56295,0.56271,0.56247,0.56223,0.56199,0.56175,0.56151,0.56128,0.56104,0.5608,0.56056,0.56032,0.56009,0.55985,0.55961,0.55937,0.55913,0.5589,0.55866,0.55842,0.55818,0.55795,0.55771,0.55747,0.55723,0.557,0.55676,0.55652,0.55628,0.55605,0.55581,0.55557,0.55534,0.5551,0.55486,0.55463,0.55439,0.55415,0.55392,0.55368,0.55344,0.55321,0.55297,0.55274,0.5525,0.55226,0.55203,0.55179,0.55156,0.55132,0.55108,0.55085,0.55061,0.55038,0.55014,0.54991,0.54967,0.54944,0.5492,0.54897,0.54873,0.5485,0.54826,0.54803,0.54779,0.54756,0.54732,0.54709,0.54685,0.54662,0.54638,0.54615,0.54591,0.54568,0.54545,0.54521,0.54498,0.54474,0.54451,0.54428,0.54404,0.54381,0.54357,0.54334,0.54311,0.54287,0.54264,0.54241,0.54217,0.54194,0.54171,0.54147,0.54124,
-0.54101,0.54077,0.54054,0.54031,0.54008,0.53984,0.53961,0.53938,0.53915,0.53891,0.53868,0.53845,0.53822,0.53798,0.53775,0.53752,0.53729,0.53706,0.53682,0.53659,0.53636,0.53613,0.5359,0.53566,0.53543,0.5352,0.53497,0.53474,0.53451,0.53428,0.53405,0.53381,0.53358,0.53335,0.53312,0.53289,0.53266,0.53243,0.5322,0.53197,0.53174,0.53151,0.53128,0.53105,0.53082,0.53059,0.53036,0.53013,0.5299,0.52967,0.52944,0.52921,0.52898,0.52875,0.52852,0.52829,0.52806,0.52783,0.5276,0.52737,0.52714,0.52691,0.52668,0.52646,0.52623,0.526,0.52577,0.52554,0.52531,0.52508,0.52486,0.52463,0.5244,0.52417,0.52394,0.52371,0.52349,0.52326,0.52303,0.5228,0.52257,0.52235,0.52212,0.52189,0.52166,0.52144,0.52121,0.52098,0.52075,0.52053,0.5203,0.52007,0.51985,0.51962,0.51939,0.51916,0.51894,0.51871,0.51848,0.51826,
-0.51803,0.5178,0.51758,0.51735,0.51713,0.5169,0.51667,0.51645,0.51622,0.516,0.51577,0.51554,0.51532,0.51509,0.51487,0.51464,0.51442,0.51419,0.51397,0.51374,0.51352,0.51329,0.51307,0.51284,0.51262,0.51239,0.51217,0.51194,0.51172,0.51149,0.51127,0.51104,0.51082,0.51059,0.51037,0.51015,0.50992,0.5097,0.50947,0.50925,0.50903,0.5088,0.50858,0.50836,0.50813,0.50791,0.50768,0.50746,0.50724,0.50701,0.50679,0.50657,0.50635,0.50612,0.5059,0.50568,0.50545,0.50523,0.50501,0.50479,0.50456,0.50434,0.50412,0.5039,0.50367,0.50345,0.50323,0.50301,0.50279,0.50256,0.50234,0.50212,0.5019,0.50168,0.50146,0.50124,0.50101,0.50079,0.50057,0.50035,0.50013,0.49991,0.49969,0.49947,0.49925,0.49902,0.4988,0.49858,0.49836,0.49814,0.49792,0.4977,0.49748,0.49726,0.49704,0.49682,0.4966,0.49638,0.49616,0.49594,
-0.49572,0.4955,0.49528,0.49506,0.49484,0.49462,0.4944,0.49419,0.49397,0.49375,0.49353,0.49331,0.49309,0.49287,0.49265,0.49243,0.49222,0.492,0.49178,0.49156,0.49134,0.49112,0.49091,0.49069,0.49047,0.49025,0.49003,0.48981,0.4896,0.48938,0.48916,0.48894,0.48873,0.48851,0.48829,0.48807,0.48786,0.48764,0.48742,0.48721,0.48699,0.48677,0.48656,0.48634,0.48612,0.48591,0.48569,0.48547,0.48526,0.48504,0.48482,0.48461,0.48439,0.48417,0.48396,0.48374,0.48353,0.48331,0.4831,0.48288,0.48266,0.48245,0.48223,0.48202,0.4818,0.48159,0.48137,0.48116,0.48094,0.48073,0.48051,0.4803,0.48008,0.47987,0.47965,0.47944,0.47922,0.47901,0.4788,0.47858,0.47837,0.47815,0.47794,0.47773,0.47751,0.4773,0.47708,0.47687,0.47666,0.47644,0.47623,0.47602,0.4758,0.47559,0.47538,0.47516,0.47495,0.47474,0.47452,0.47431,
-0.4741,0.47389,0.47367,0.47346,0.47325,0.47304,0.47282,0.47261,0.4724,0.47219,0.47197,0.47176,0.47155,0.47134,0.47113,0.47091,0.4707,0.47049,0.47028,0.47007,0.46986,0.46965,0.46943,0.46922,0.46901,0.4688,0.46859,0.46838,0.46817,0.46796,0.46775,0.46754,0.46733,0.46712,0.46691,0.4667,0.46648,0.46627,0.46606,0.46585,0.46564,0.46543,0.46522,0.46501,0.46481,0.4646,0.46439,0.46418,0.46397,0.46376,0.46355,0.46334,0.46313,0.46292,0.46271,0.4625,0.46229,0.46209,0.46188,0.46167,0.46146,0.46125,0.46104,0.46083,0.46063,0.46042,0.46021,0.46,0.45979,0.45959,0.45938,0.45917,0.45896,0.45875,0.45855,0.45834,0.45813,0.45792,0.45772,0.45751,0.4573,0.4571,0.45689,0.45668,0.45648,0.45627,0.45606,0.45585,0.45565,0.45544,0.45524,0.45503,0.45482,0.45462,0.45441,0.4542,0.454,0.45379,0.45359,0.45338,
-0.45317,0.45297,0.45276,0.45256,0.45235,0.45215,0.45194,0.45174,0.45153,0.45133,0.45112,0.45092,0.45071,0.45051,0.4503,0.4501,0.44989,0.44969,0.44948,0.44928,0.44907,0.44887,0.44867,0.44846,0.44826,0.44805,0.44785,0.44765,0.44744,0.44724,0.44704,0.44683,0.44663,0.44642,0.44622,0.44602,0.44582,0.44561,0.44541,0.44521,0.445,0.4448,0.4446,0.44439,0.44419,0.44399,0.44379,0.44358,0.44338,0.44318,0.44298,0.44278,0.44257,0.44237,0.44217,0.44197,0.44177,0.44156,0.44136,0.44116,0.44096,0.44076,0.44056,0.44036,0.44015,0.43995,0.43975,0.43955,0.43935,0.43915,0.43895,0.43875,0.43855,0.43835,0.43815,0.43795,0.43775,0.43754,0.43734,0.43714,0.43694,0.43674,0.43654,0.43634,0.43614,0.43595,0.43575,0.43555,0.43535,0.43515,0.43495,0.43475,0.43455,0.43435,0.43415,0.43395,0.43375,0.43355,0.43336,0.43316,
-0.43296,0.43276,0.43256,0.43236,0.43216,0.43197,0.43177,0.43157,0.43137,0.43117,0.43098,0.43078,0.43058,0.43038,0.43018,0.42999,0.42979,0.42959,0.42939,0.4292,0.429,0.4288,0.42861,0.42841,0.42821,0.42801,0.42782,0.42762,0.42742,0.42723,0.42703,0.42683,0.42664,0.42644,0.42625,0.42605,0.42585,0.42566,0.42546,0.42527,0.42507,0.42487,0.42468,0.42448,0.42429,0.42409,0.4239,0.4237,0.42351,0.42331,0.42311,0.42292,0.42272,0.42253,0.42234,0.42214,0.42195,0.42175,0.42156,0.42136,0.42117,0.42097,0.42078,0.42058,0.42039,0.4202,0.42,0.41981,0.41961,0.41942,0.41923,0.41903,0.41884,0.41865,0.41845,0.41826,0.41807,0.41787,0.41768,0.41749,0.41729,0.4171,0.41691,0.41672,0.41652,0.41633,0.41614,0.41595,0.41575,0.41556,0.41537,0.41518,0.41498,0.41479,0.4146,0.41441,0.41422,0.41402,0.41383,0.41364,
-0.41345,0.41326,0.41307,0.41287,0.41268,0.41249,0.4123,0.41211,0.41192,0.41173,0.41154,0.41135,0.41116,0.41097,0.41077,0.41058,0.41039,0.4102,0.41001,0.40982,0.40963,0.40944,0.40925,0.40906,0.40887,0.40868,0.40849,0.4083,0.40811,0.40792,0.40773,0.40755,0.40736,0.40717,0.40698,0.40679,0.4066,0.40641,0.40622,0.40603,0.40584,0.40566,0.40547,0.40528,0.40509,0.4049,0.40471,0.40452,0.40434,0.40415,0.40396,0.40377,0.40358,0.4034,0.40321,0.40302,0.40283,0.40265,0.40246,0.40227,0.40208,0.4019,0.40171,0.40152,0.40133,0.40115,0.40096,0.40077,0.40059,0.4004,0.40021,0.40003,0.39984,0.39965,0.39947,0.39928,0.3991,0.39891,0.39872,0.39854,0.39835,0.39817,0.39798,0.39779,0.39761,0.39742,0.39724,0.39705,0.39687,0.39668,0.3965,0.39631,0.39613,0.39594,0.39576,0.39557,0.39539,0.3952,0.39502,0.39483,
-0.39465,0.39446,0.39428,0.39409,0.39391,0.39373,0.39354,0.39336,0.39317,0.39299,0.39281,0.39262,0.39244,0.39225,0.39207,0.39189,0.3917,0.39152,0.39134,0.39115,0.39097,0.39079,0.3906,0.39042,0.39024,0.39006,0.38987,0.38969,0.38951,0.38933,0.38914,0.38896,0.38878,0.3886,0.38841,0.38823,0.38805,0.38787,0.38769,0.3875,0.38732,0.38714,0.38696,0.38678,0.3866,0.38641,0.38623,0.38605,0.38587,0.38569,0.38551,0.38533,0.38515,0.38497,0.38479,0.3846,0.38442,0.38424,0.38406,0.38388,0.3837,0.38352,0.38334,0.38316,0.38298,0.3828,0.38262,0.38244,0.38226,0.38208,0.3819,0.38172,0.38154,0.38136,0.38118,0.381,0.38083,0.38065,0.38047,0.38029,0.38011,0.37993,0.37975,0.37957,0.37939,0.37922,0.37904,0.37886,0.37868,0.3785,0.37832,0.37815,0.37797,0.37779,0.37761,0.37743,0.37726,0.37708,0.3769,0.37672,
-0.37654,0.37637,0.37619,0.37601,0.37583,0.37566,0.37548,0.3753,0.37513,0.37495,0.37477,0.3746,0.37442,0.37424,0.37407,0.37389,0.37371,0.37354,0.37336,0.37318,0.37301,0.37283,0.37266,0.37248,0.3723,0.37213,0.37195,0.37178,0.3716,0.37142,0.37125,0.37107,0.3709,0.37072,0.37055,0.37037,0.3702,0.37002,0.36985,0.36967,0.3695,0.36932,0.36915,0.36897,0.3688,0.36862,0.36845,0.36828,0.3681,0.36793,0.36775,0.36758,0.36741,0.36723,0.36706,0.36688,0.36671,0.36654,0.36636,0.36619,0.36602,0.36584,0.36567,0.3655,0.36532,0.36515,0.36498,0.3648,0.36463,0.36446,0.36428,0.36411,0.36394,0.36377,0.36359,0.36342,0.36325,0.36308,0.36291,0.36273,0.36256,0.36239,0.36222,0.36205,0.36187,0.3617,0.36153,0.36136,0.36119,0.36102,0.36084,0.36067,0.3605,0.36033,0.36016,0.35999,0.35982,0.35965,0.35948,0.3593,
-0.35913,0.35896,0.35879,0.35862,0.35845,0.35828,0.35811,0.35794,0.35777,0.3576,0.35743,0.35726,0.35709,0.35692,0.35675,0.35658,0.35641,0.35624,0.35607,0.3559,0.35573,0.35556,0.35539,0.35523,0.35506,0.35489,0.35472,0.35455,0.35438,0.35421,0.35404,0.35387,0.35371,0.35354,0.35337,0.3532,0.35303,0.35286,0.3527,0.35253,0.35236,0.35219,0.35202,0.35186,0.35169,0.35152,0.35135,0.35119,0.35102,0.35085,0.35068,0.35052,0.35035,0.35018,0.35002,0.34985,0.34968,0.34951,0.34935,0.34918,0.34901,0.34885,0.34868,0.34851,0.34835,0.34818,0.34802,0.34785,0.34768,0.34752,0.34735,0.34719,0.34702,0.34685,0.34669,0.34652,0.34636,0.34619,0.34603,0.34586,0.3457,0.34553,0.34536,0.3452,0.34503,0.34487,0.3447,0.34454,0.34437,0.34421,0.34405,0.34388,0.34372,0.34355,0.34339,0.34322,0.34306,0.34289,0.34273,0.34257,
-0.3424,0.34224,0.34207,0.34191,0.34175,0.34158,0.34142,0.34126,0.34109,0.34093,0.34077,0.3406,0.34044,0.34028,0.34011,0.33995,0.33979,0.33963,0.33946,0.3393,0.33914,0.33897,0.33881,0.33865,0.33849,0.33832,0.33816,0.338,0.33784,0.33768,0.33751,0.33735,0.33719,0.33703,0.33687,0.33671,0.33654,0.33638,0.33622,0.33606,0.3359,0.33574,0.33558,0.33541,0.33525,0.33509,0.33493,0.33477,0.33461,0.33445,0.33429,0.33413,0.33397,0.33381,0.33365,0.33349,0.33333,0.33317,0.33301,0.33285,0.33269,0.33253,0.33237,0.33221,0.33205,0.33189,0.33173,0.33157,0.33141,0.33125,0.33109,0.33093,0.33077,0.33061,0.33045,0.33029,0.33013,0.32998,0.32982,0.32966,0.3295,0.32934,0.32918,0.32902,0.32886,0.32871,0.32855,0.32839,0.32823,0.32807,0.32792,0.32776,0.3276,0.32744,0.32728,0.32713,0.32697,0.32681,0.32665,0.3265,
-0.32634,0.32618,0.32602,0.32587,0.32571,0.32555,0.3254,0.32524,0.32508,0.32493,0.32477,0.32461,0.32446,0.3243,0.32414,0.32399,0.32383,0.32367,0.32352,0.32336,0.3232,0.32305,0.32289,0.32274,0.32258,0.32243,0.32227,0.32211,0.32196,0.3218,0.32165,0.32149,0.32134,0.32118,0.32103,0.32087,0.32072,0.32056,0.32041,0.32025,0.3201,0.31994,0.31979,0.31963,0.31948,0.31932,0.31917,0.31902,0.31886,0.31871,0.31855,0.3184,0.31824,0.31809,0.31794,0.31778,0.31763,0.31748,0.31732,0.31717,0.31701,0.31686,0.31671,0.31655,0.3164,0.31625,0.31609,0.31594,0.31579,0.31564,0.31548,0.31533,0.31518,0.31502,0.31487,0.31472,0.31457,0.31441,0.31426,0.31411,0.31396,0.31381,0.31365,0.3135,0.31335,0.3132,0.31305,0.31289,0.31274,0.31259,0.31244,0.31229,0.31214,0.31199,0.31183,0.31168,0.31153,0.31138,0.31123,0.31108,
-0.31093,0.31078,0.31063,0.31047,0.31032,0.31017,0.31002,0.30987,0.30972,0.30957,0.30942,0.30927,0.30912,0.30897,0.30882,0.30867,0.30852,0.30837,0.30822,0.30807,0.30792,0.30777,0.30762,0.30747,0.30732,0.30717,0.30702,0.30688,0.30673,0.30658,0.30643,0.30628,0.30613,0.30598,0.30583,0.30568,0.30554,0.30539,0.30524,0.30509,0.30494,0.30479,0.30464,0.3045,0.30435,0.3042,0.30405,0.3039,0.30376,0.30361,0.30346,0.30331,0.30317,0.30302,0.30287,0.30272,0.30258,0.30243,0.30228,0.30213,0.30199,0.30184,0.30169,0.30155,0.3014,0.30125,0.30111,0.30096,0.30081,0.30067,0.30052,0.30037,0.30023,0.30008,0.29993,0.29979,0.29964,0.29949,0.29935,0.2992,0.29906,0.29891,0.29877,0.29862,0.29847,0.29833,0.29818,0.29804,0.29789,0.29775,0.2976,0.29746,0.29731,0.29717,0.29702,0.29688,0.29673,0.29659,0.29644,0.2963,
-0.29615,0.29601,0.29586,0.29572,0.29557,0.29543,0.29529,0.29514,0.295,0.29485,0.29471,0.29456,0.29442,0.29428,0.29413,0.29399,0.29385,0.2937,0.29356,0.29341,0.29327,0.29313,0.29298,0.29284,0.2927,0.29256,0.29241,0.29227,0.29213,0.29198,0.29184,0.2917,0.29156,0.29141,0.29127,0.29113,0.29099,0.29084,0.2907,0.29056,0.29042,0.29027,0.29013,0.28999,0.28985,0.28971,0.28956,0.28942,0.28928,0.28914,0.289,0.28886,0.28871,0.28857,0.28843,0.28829,0.28815,0.28801,0.28787,0.28773,0.28758,0.28744,0.2873,0.28716,0.28702,0.28688,0.28674,0.2866,0.28646,0.28632,0.28618,0.28604,0.2859,0.28576,0.28562,0.28548,0.28534,0.2852,0.28506,0.28492,0.28478,0.28464,0.2845,0.28436,0.28422,0.28408,0.28394,0.2838,0.28366,0.28352,0.28338,0.28324,0.28311,0.28297,0.28283,0.28269,0.28255,0.28241,0.28227,0.28213,
-0.282,0.28186,0.28172,0.28158,0.28144,0.2813,0.28117,0.28103,0.28089,0.28075,0.28061,0.28048,0.28034,0.2802,0.28006,0.27992,0.27979,0.27965,0.27951,0.27937,0.27924,0.2791,0.27896,0.27883,0.27869,0.27855,0.27841,0.27828,0.27814,0.278,0.27787,0.27773,0.27759,0.27746,0.27732,0.27718,0.27705,0.27691,0.27678,0.27664,0.2765,0.27637,0.27623,0.27609,0.27596,0.27582,0.27569,0.27555,0.27542,0.27528,0.27514,0.27501,0.27487,0.27474,0.2746,0.27447,0.27433,0.2742,0.27406,0.27393,0.27379,0.27366,0.27352,0.27339,0.27325,0.27312,0.27298,0.27285,0.27271,0.27258,0.27245,0.27231,0.27218,0.27204,0.27191,0.27177,0.27164,0.27151,0.27137,0.27124,0.2711,0.27097,0.27084,0.2707,0.27057,0.27044,0.2703,0.27017,0.27004,0.2699,0.26977,0.26964,0.2695,0.26937,0.26924,0.26911,0.26897,0.26884,0.26871,0.26857};
-
-constexpr double scale_of_stored_gammas_n5 = 1545.88;
-constexpr double scale_of_stored_incomplete_gammas_n5 = 531.27;
-
-constexpr double stored_complete_gamma_values_n5[] = {1.0,1.0,0.99999,0.99998,0.99997,0.99996,0.99994,0.99991,0.99989,0.99986,0.99983,0.99979,0.99975,0.99971,0.99966,0.99961,0.99956,0.9995,0.99944,0.99938,0.99931,0.99924,0.99917,0.99909,0.99901,0.99893,0.99884,0.99875,0.99866,0.99856,0.99846,0.99836,0.99826,0.99815,0.99804,0.99792,0.99781,0.99768,0.99756,0.99743,0.9973,0.99717,0.99704,0.9969,0.99675,0.99661,0.99646,0.99631,0.99616,0.996,0.99584,0.99568,0.99551,0.99534,0.99517,0.995,0.99482,0.99464,0.99446,0.99427,0.99408,0.99389,0.9937,0.9935,0.9933,0.9931,0.99289,0.99269,0.99248,0.99226,0.99205,0.99183,0.99161,0.99138,0.99115,0.99093,0.99069,0.99046,0.99022,0.98998,0.98974,0.98949,0.98925,0.989,0.98874,0.98849,0.98823,0.98797,0.98771,0.98744,0.98717,0.9869,0.98663,0.98635,0.98608,0.9858,0.98551,0.98523,0.98494,0.98465,
-0.98436,0.98406,0.98377,0.98347,0.98317,0.98286,0.98256,0.98225,0.98194,0.98162,0.98131,0.98099,0.98067,0.98035,0.98002,0.97969,0.97936,0.97903,0.9787,0.97836,0.97803,0.97769,0.97734,0.977,0.97665,0.9763,0.97595,0.9756,0.97524,0.97489,0.97453,0.97416,0.9738,0.97343,0.97307,0.9727,0.97232,0.97195,0.97157,0.9712,0.97082,0.97043,0.97005,0.96966,0.96928,0.96889,0.96849,0.9681,0.9677,0.96731,0.96691,0.9665,0.9661,0.9657,0.96529,0.96488,0.96447,0.96405,0.96364,0.96322,0.9628,0.96238,0.96196,0.96154,0.96111,0.96068,0.96026,0.95982,0.95939,0.95896,0.95852,0.95808,0.95764,0.9572,0.95676,0.95631,0.95586,0.95542,0.95497,0.95451,0.95406,0.9536,0.95315,0.95269,0.95223,0.95177,0.9513,0.95084,0.95037,0.9499,0.94943,0.94896,0.94849,0.94801,0.94754,0.94706,0.94658,0.9461,0.94562,0.94513,
-0.94465,0.94416,0.94367,0.94318,0.94269,0.9422,0.9417,0.94121,0.94071,0.94021,0.93971,0.93921,0.9387,0.9382,0.93769,0.93719,0.93668,0.93617,0.93566,0.93514,0.93463,0.93411,0.9336,0.93308,0.93256,0.93204,0.93151,0.93099,0.93046,0.92994,0.92941,0.92888,0.92835,0.92782,0.92728,0.92675,0.92621,0.92568,0.92514,0.9246,0.92406,0.92352,0.92297,0.92243,0.92188,0.92134,0.92079,0.92024,0.91969,0.91914,0.91859,0.91803,0.91748,0.91692,0.91636,0.91581,0.91525,0.91469,0.91412,0.91356,0.913,0.91243,0.91186,0.9113,0.91073,0.91016,0.90959,0.90902,0.90844,0.90787,0.9073,0.90672,0.90614,0.90556,0.90498,0.9044,0.90382,0.90324,0.90266,0.90207,0.90149,0.9009,0.90032,0.89973,0.89914,0.89855,0.89796,0.89737,0.89677,0.89618,0.89558,0.89499,0.89439,0.89379,0.8932,0.8926,0.892,0.89139,0.89079,0.89019,
-0.88959,0.88898,0.88838,0.88777,0.88716,0.88655,0.88594,0.88533,0.88472,0.88411,0.8835,0.88289,0.88227,0.88166,0.88104,0.88043,0.87981,0.87919,0.87857,0.87795,0.87733,0.87671,0.87609,0.87547,0.87484,0.87422,0.87359,0.87297,0.87234,0.87171,0.87109,0.87046,0.86983,0.8692,0.86857,0.86794,0.8673,0.86667,0.86604,0.8654,0.86477,0.86413,0.8635,0.86286,0.86222,0.86158,0.86095,0.86031,0.85967,0.85903,0.85838,0.85774,0.8571,0.85646,0.85581,0.85517,0.85452,0.85388,0.85323,0.85258,0.85194,0.85129,0.85064,0.84999,0.84934,0.84869,0.84804,0.84739,0.84674,0.84608,0.84543,0.84478,0.84412,0.84347,0.84281,0.84216,0.8415,0.84085,0.84019,0.83953,0.83887,0.83821,0.83755,0.8369,0.83623,0.83557,0.83491,0.83425,0.83359,0.83293,0.83226,0.8316,0.83094,0.83027,0.82961,0.82894,0.82828,0.82761,0.82694,0.82628,
-0.82561,0.82494,0.82427,0.82361,0.82294,0.82227,0.8216,0.82093,0.82026,0.81959,0.81892,0.81824,0.81757,0.8169,0.81623,0.81555,0.81488,0.81421,0.81353,0.81286,0.81218,0.81151,0.81083,0.81016,0.80948,0.8088,0.80813,0.80745,0.80677,0.8061,0.80542,0.80474,0.80406,0.80338,0.8027,0.80202,0.80134,0.80066,0.79998,0.7993,0.79862,0.79794,0.79726,0.79658,0.7959,0.79521,0.79453,0.79385,0.79317,0.79248,0.7918,0.79112,0.79043,0.78975,0.78906,0.78838,0.78769,0.78701,0.78632,0.78564,0.78495,0.78427,0.78358,0.7829,0.78221,0.78152,0.78084,0.78015,0.77946,0.77878,0.77809,0.7774,0.77671,0.77602,0.77534,0.77465,0.77396,0.77327,0.77258,0.77189,0.77121,0.77052,0.76983,0.76914,0.76845,0.76776,0.76707,0.76638,0.76569,0.765,0.76431,0.76362,0.76293,0.76224,0.76155,0.76086,0.76017,0.75947,0.75878,0.75809,
-0.7574,0.75671,0.75602,0.75533,0.75464,0.75394,0.75325,0.75256,0.75187,0.75118,0.75049,0.74979,0.7491,0.74841,0.74772,0.74703,0.74633,0.74564,0.74495,0.74426,0.74356,0.74287,0.74218,0.74149,0.7408,0.7401,0.73941,0.73872,0.73803,0.73733,0.73664,0.73595,0.73526,0.73456,0.73387,0.73318,0.73249,0.73179,0.7311,0.73041,0.72972,0.72902,0.72833,0.72764,0.72695,0.72625,0.72556,0.72487,0.72418,0.72349,0.72279,0.7221,0.72141,0.72072,0.72003,0.71933,0.71864,0.71795,0.71726,0.71657,0.71588,0.71519,0.71449,0.7138,0.71311,0.71242,0.71173,0.71104,0.71035,0.70966,0.70897,0.70827,0.70758,0.70689,0.7062,0.70551,0.70482,0.70413,0.70344,0.70275,0.70206,0.70137,0.70068,0.69999,0.69931,0.69862,0.69793,0.69724,0.69655,0.69586,0.69517,0.69448,0.6938,0.69311,0.69242,0.69173,0.69104,0.69036,0.68967,0.68898,
-0.68829,0.68761,0.68692,0.68623,0.68555,0.68486,0.68417,0.68349,0.6828,0.68212,0.68143,0.68074,0.68006,0.67937,0.67869,0.678,0.67732,0.67664,0.67595,0.67527,0.67458,0.6739,0.67322,0.67253,0.67185,0.67117,0.67048,0.6698,0.66912,0.66844,0.66775,0.66707,0.66639,0.66571,0.66503,0.66435,0.66367,0.66299,0.66231,0.66163,0.66095,0.66027,0.65959,0.65891,0.65823,0.65755,0.65687,0.65619,0.65551,0.65484,0.65416,0.65348,0.6528,0.65213,0.65145,0.65077,0.6501,0.64942,0.64875,0.64807,0.6474,0.64672,0.64605,0.64537,0.6447,0.64402,0.64335,0.64268,0.642,0.64133,0.64066,0.63998,0.63931,0.63864,0.63797,0.6373,0.63663,0.63596,0.63529,0.63462,0.63394,0.63328,0.63261,0.63194,0.63127,0.6306,0.62993,0.62926,0.62859,0.62793,0.62726,0.62659,0.62593,0.62526,0.62459,0.62393,0.62326,0.6226,0.62193,0.62127,
-0.6206,0.61994,0.61928,0.61861,0.61795,0.61729,0.61662,0.61596,0.6153,0.61464,0.61398,0.61332,0.61266,0.612,0.61134,0.61068,0.61002,0.60936,0.6087,0.60804,0.60738,0.60673,0.60607,0.60541,0.60476,0.6041,0.60344,0.60279,0.60213,0.60148,0.60082,0.60017,0.59951,0.59886,0.59821,0.59755,0.5969,0.59625,0.5956,0.59494,0.59429,0.59364,0.59299,0.59234,0.59169,0.59104,0.59039,0.58974,0.5891,0.58845,0.5878,0.58715,0.5865,0.58586,0.58521,0.58457,0.58392,0.58327,0.58263,0.58199,0.58134,0.5807,0.58005,0.57941,0.57877,0.57813,0.57748,0.57684,0.5762,0.57556,0.57492,0.57428,0.57364,0.573,0.57236,0.57172,0.57108,0.57045,0.56981,0.56917,0.56853,0.5679,0.56726,0.56663,0.56599,0.56536,0.56472,0.56409,0.56345,0.56282,0.56219,0.56156,0.56092,0.56029,0.55966,0.55903,0.5584,0.55777,0.55714,0.55651,
-0.55588,0.55525,0.55462,0.554,0.55337,0.55274,0.55212,0.55149,0.55086,0.55024,0.54961,0.54899,0.54836,0.54774,0.54712,0.54649,0.54587,0.54525,0.54463,0.54401,0.54339,0.54277,0.54215,0.54153,0.54091,0.54029,0.53967,0.53905,0.53843,0.53782,0.5372,0.53658,0.53597,0.53535,0.53474,0.53412,0.53351,0.53289,0.53228,0.53167,0.53106,0.53044,0.52983,0.52922,0.52861,0.528,0.52739,0.52678,0.52617,0.52556,0.52495,0.52435,0.52374,0.52313,0.52252,0.52192,0.52131,0.52071,0.5201,0.5195,0.51889,0.51829,0.51769,0.51709,0.51648,0.51588,0.51528,0.51468,0.51408,0.51348,0.51288,0.51228,0.51168,0.51108,0.51049,0.50989,0.50929,0.50869,0.5081,0.5075,0.50691,0.50631,0.50572,0.50512,0.50453,0.50394,0.50335,0.50275,0.50216,0.50157,0.50098,0.50039,0.4998,0.49921,0.49862,0.49803,0.49745,0.49686,0.49627,0.49568,
-0.4951,0.49451,0.49393,0.49334,0.49276,0.49217,0.49159,0.49101,0.49042,0.48984,0.48926,0.48868,0.4881,0.48752,0.48694,0.48636,0.48578,0.4852,0.48462,0.48405,0.48347,0.48289,0.48232,0.48174,0.48116,0.48059,0.48002,0.47944,0.47887,0.4783,0.47772,0.47715,0.47658,0.47601,0.47544,0.47487,0.4743,0.47373,0.47316,0.47259,0.47202,0.47146,0.47089,0.47032,0.46976,0.46919,0.46863,0.46806,0.4675,0.46693,0.46637,0.46581,0.46524,0.46468,0.46412,0.46356,0.463,0.46244,0.46188,0.46132,0.46076,0.46021,0.45965,0.45909,0.45853,0.45798,0.45742,0.45687,0.45631,0.45576,0.4552,0.45465,0.4541,0.45355,0.45299,0.45244,0.45189,0.45134,0.45079,0.45024,0.44969,0.44914,0.44859,0.44805,0.4475,0.44695,0.44641,0.44586,0.44532,0.44477,0.44423,0.44368,0.44314,0.4426,0.44205,0.44151,0.44097,0.44043,0.43989,0.43935,
-0.43881,0.43827,0.43773,0.43719,0.43665,0.43612,0.43558,0.43504,0.43451,0.43397,0.43344,0.4329,0.43237,0.43184,0.4313,0.43077,0.43024,0.42971,0.42918,0.42865,0.42812,0.42759,0.42706,0.42653,0.426,0.42547,0.42495,0.42442,0.42389,0.42337,0.42284,0.42232,0.42179,0.42127,0.42074,0.42022,0.4197,0.41918,0.41866,0.41814,0.41761,0.41709,0.41657,0.41606,0.41554,0.41502,0.4145,0.41398,0.41347,0.41295,0.41244,0.41192,0.41141,0.41089,0.41038,0.40986,0.40935,0.40884,0.40833,0.40782,0.4073,0.40679,0.40628,0.40577,0.40527,0.40476,0.40425,0.40374,0.40323,0.40273,0.40222,0.40172,0.40121,0.40071,0.4002,0.3997,0.3992,0.39869,0.39819,0.39769,0.39719,0.39669,0.39619,0.39569,0.39519,0.39469,0.39419,0.39369,0.39319,0.3927,0.3922,0.3917,0.39121,0.39071,0.39022,0.38972,0.38923,0.38874,0.38824,0.38775,
-0.38726,0.38677,0.38628,0.38579,0.3853,0.38481,0.38432,0.38383,0.38334,0.38286,0.38237,0.38188,0.3814,0.38091,0.38043,0.37994,0.37946,0.37897,0.37849,0.37801,0.37753,0.37704,0.37656,0.37608,0.3756,0.37512,0.37464,0.37416,0.37368,0.37321,0.37273,0.37225,0.37178,0.3713,0.37082,0.37035,0.36987,0.3694,0.36893,0.36845,0.36798,0.36751,0.36704,0.36657,0.36609,0.36562,0.36515,0.36469,0.36422,0.36375,0.36328,0.36281,0.36235,0.36188,0.36141,0.36095,0.36048,0.36002,0.35955,0.35909,0.35863,0.35816,0.3577,0.35724,0.35678,0.35632,0.35586,0.3554,0.35494,0.35448,0.35402,0.35356,0.3531,0.35265,0.35219,0.35173,0.35128,0.35082,0.35037,0.34991,0.34946,0.34901,0.34855,0.3481,0.34765,0.3472,0.34675,0.3463,0.34585,0.3454,0.34495,0.3445,0.34405,0.3436,0.34316,0.34271,0.34226,0.34182,0.34137,0.34093,
-0.34048,0.34004,0.3396,0.33915,0.33871,0.33827,0.33783,0.33739,0.33694,0.3365,0.33606,0.33563,0.33519,0.33475,0.33431,0.33387,0.33344,0.333,0.33256,0.33213,0.33169,0.33126,0.33082,0.33039,0.32996,0.32952,0.32909,0.32866,0.32823,0.3278,0.32737,0.32694,0.32651,0.32608,0.32565,0.32522,0.32479,0.32436,0.32394,0.32351,0.32309,0.32266,0.32224,0.32181,0.32139,0.32096,0.32054,0.32012,0.31969,0.31927,0.31885,0.31843,0.31801,0.31759,0.31717,0.31675,0.31633,0.31591,0.3155,0.31508,0.31466,0.31425,0.31383,0.31341,0.313,0.31258,0.31217,0.31176,0.31134,0.31093,0.31052,0.31011,0.3097,0.30928,0.30887,0.30846,0.30805,0.30765,0.30724,0.30683,0.30642,0.30601,0.30561,0.3052,0.30479,0.30439,0.30398,0.30358,0.30317,0.30277,0.30237,0.30196,0.30156,0.30116,0.30076,0.30036,0.29996,0.29956,0.29916,0.29876,
-0.29836,0.29796,0.29756,0.29716,0.29677,0.29637,0.29597,0.29558,0.29518,0.29479,0.29439,0.294,0.29361,0.29321,0.29282,0.29243,0.29204,0.29164,0.29125,0.29086,0.29047,0.29008,0.28969,0.28931,0.28892,0.28853,0.28814,0.28775,0.28737,0.28698,0.2866,0.28621,0.28583,0.28544,0.28506,0.28467,0.28429,0.28391,0.28353,0.28314,0.28276,0.28238,0.282,0.28162,0.28124,0.28086,0.28048,0.28011,0.27973,0.27935,0.27897,0.2786,0.27822,0.27785,0.27747,0.2771,0.27672,0.27635,0.27597,0.2756,0.27523,0.27485,0.27448,0.27411,0.27374,0.27337,0.273,0.27263,0.27226,0.27189,0.27152,0.27116,0.27079,0.27042,0.27005,0.26969,0.26932,0.26896,0.26859,0.26823,0.26786,0.2675,0.26713,0.26677,0.26641,0.26605,0.26568,0.26532,0.26496,0.2646,0.26424,0.26388,0.26352,0.26316,0.26281,0.26245,0.26209,0.26173,0.26138,0.26102,
-0.26066,0.26031,0.25995,0.2596,0.25925,0.25889,0.25854,0.25819,0.25783,0.25748,0.25713,0.25678,0.25643,0.25608,0.25573,0.25538,0.25503,0.25468,0.25433,0.25398,0.25363,0.25329,0.25294,0.25259,0.25225,0.2519,0.25156,0.25121,0.25087,0.25052,0.25018,0.24984,0.24949,0.24915,0.24881,0.24847,0.24813,0.24779,0.24745,0.24711,0.24677,0.24643,0.24609,0.24575,0.24541,0.24508,0.24474,0.2444,0.24407,0.24373,0.24339,0.24306,0.24272,0.24239,0.24206,0.24172,0.24139,0.24106,0.24072,0.24039,0.24006,0.23973,0.2394,0.23907,0.23874,0.23841,0.23808,0.23775,0.23742,0.2371,0.23677,0.23644,0.23611,0.23579,0.23546,0.23514,0.23481,0.23449,0.23416,0.23384,0.23351,0.23319,0.23287,0.23255,0.23222,0.2319,0.23158,0.23126,0.23094,0.23062,0.2303,0.22998,0.22966,0.22934,0.22902,0.22871,0.22839,0.22807,0.22775,0.22744,
-0.22712,0.22681,0.22649,0.22618,0.22586,0.22555,0.22524,0.22492,0.22461,0.2243,0.22399,0.22367,0.22336,0.22305,0.22274,0.22243,0.22212,0.22181,0.2215,0.22119,0.22089,0.22058,0.22027,0.21996,0.21966,0.21935,0.21904,0.21874,0.21843,0.21813,0.21782,0.21752,0.21722,0.21691,0.21661,0.21631,0.216,0.2157,0.2154,0.2151,0.2148,0.2145,0.2142,0.2139,0.2136,0.2133,0.213,0.2127,0.21241,0.21211,0.21181,0.21151,0.21122,0.21092,0.21063,0.21033,0.21004,0.20974,0.20945,0.20915,0.20886,0.20857,0.20827,0.20798,0.20769,0.2074,0.20711,0.20682,0.20653,0.20624,0.20595,0.20566,0.20537,0.20508,0.20479,0.2045,0.20421,0.20393,0.20364,0.20335,0.20307,0.20278,0.2025,0.20221,0.20193,0.20164,0.20136,0.20107,0.20079,0.20051,0.20022,0.19994,0.19966,0.19938,0.1991,0.19882,0.19854,0.19826,0.19798,0.1977,
-0.19742,0.19714,0.19686,0.19658,0.1963,0.19603,0.19575,0.19547,0.1952,0.19492,0.19465,0.19437,0.1941,0.19382,0.19355,0.19327,0.193,0.19273,0.19245,0.19218,0.19191,0.19164,0.19136,0.19109,0.19082,0.19055,0.19028,0.19001,0.18974,0.18947,0.1892,0.18894,0.18867,0.1884,0.18813,0.18787,0.1876,0.18733,0.18707,0.1868,0.18654,0.18627,0.18601,0.18574,0.18548,0.18521,0.18495,0.18469,0.18443,0.18416,0.1839,0.18364,0.18338,0.18312,0.18286,0.1826,0.18234,0.18208,0.18182,0.18156,0.1813,0.18104,0.18078,0.18052,0.18027,0.18001,0.17975,0.1795,0.17924,0.17899,0.17873,0.17848,0.17822,0.17797,0.17771,0.17746,0.1772,0.17695,0.1767,0.17645,0.17619,0.17594,0.17569,0.17544,0.17519,0.17494,0.17469,0.17444,0.17419,0.17394,0.17369,0.17344,0.17319,0.17295,0.1727,0.17245,0.1722,0.17196,0.17171,0.17147,
-0.17122,0.17097,0.17073,0.17048,0.17024,0.17,0.16975,0.16951,0.16927,0.16902,0.16878,0.16854,0.1683,0.16805,0.16781,0.16757,0.16733,0.16709,0.16685,0.16661,0.16637,0.16613,0.16589,0.16566,0.16542,0.16518,0.16494,0.1647,0.16447,0.16423,0.16399,0.16376,0.16352,0.16329,0.16305,0.16282,0.16258,0.16235,0.16212,0.16188,0.16165,0.16142,0.16118,0.16095,0.16072,0.16049,0.16026,0.16002,0.15979,0.15956,0.15933,0.1591,0.15887,0.15864,0.15841,0.15819,0.15796,0.15773,0.1575,0.15727,0.15705,0.15682,0.15659,0.15637,0.15614,0.15592,0.15569,0.15546,0.15524,0.15502,0.15479,0.15457,0.15434,0.15412,0.1539,0.15367,0.15345,0.15323,0.15301,0.15279,0.15257,0.15234,0.15212,0.1519,0.15168,0.15146,0.15124,0.15102,0.15081,0.15059,0.15037,0.15015,0.14993,0.14971,0.1495,0.14928,0.14906,0.14885,0.14863,0.14842,
-0.1482,0.14798,0.14777,0.14755,0.14734,0.14713,0.14691,0.1467,0.14649,0.14627,0.14606,0.14585,0.14564,0.14542,0.14521,0.145,0.14479,0.14458,0.14437,0.14416,0.14395,0.14374,0.14353,0.14332,0.14311,0.1429,0.1427,0.14249,0.14228,0.14207,0.14187,0.14166,0.14145,0.14125,0.14104,0.14083,0.14063,0.14042,0.14022,0.14001,0.13981,0.13961,0.1394,0.1392,0.139,0.13879,0.13859,0.13839,0.13818,0.13798,0.13778,0.13758,0.13738,0.13718,0.13698,0.13678,0.13658,0.13638,0.13618,0.13598,0.13578,0.13558,0.13538,0.13518,0.13499,0.13479,0.13459,0.1344,0.1342,0.134,0.13381,0.13361,0.13341,0.13322,0.13302,0.13283,0.13263,0.13244,0.13224,0.13205,0.13186,0.13166,0.13147,0.13128,0.13109,0.13089,0.1307,0.13051,0.13032,0.13013,0.12994,0.12974,0.12955,0.12936,0.12917,0.12898,0.12879,0.12861,0.12842,0.12823,
-0.12804,0.12785,0.12766,0.12748,0.12729,0.1271,0.12691,0.12673,0.12654,0.12635,0.12617,0.12598,0.1258,0.12561,0.12543,0.12524,0.12506,0.12487,0.12469,0.12451,0.12432,0.12414,0.12396,0.12377,0.12359,0.12341,0.12323,0.12305,0.12286,0.12268,0.1225,0.12232,0.12214,0.12196,0.12178,0.1216,0.12142,0.12124,0.12106,0.12089,0.12071,0.12053,0.12035,0.12017,0.12,0.11982,0.11964,0.11946,0.11929,0.11911,0.11894,0.11876,0.11858,0.11841,0.11823,0.11806,0.11788,0.11771,0.11754,0.11736,0.11719,0.11701,0.11684,0.11667,0.1165,0.11632,0.11615,0.11598,0.11581,0.11564,0.11546,0.11529,0.11512,0.11495,0.11478,0.11461,0.11444,0.11427,0.1141,0.11393,0.11376,0.1136,0.11343,0.11326,0.11309,0.11292,0.11276,0.11259,0.11242,0.11225,0.11209,0.11192,0.11175,0.11159,0.11142,0.11126,0.11109,0.11093,0.11076,0.1106,
-0.11043,0.11027,0.11011,0.10994,0.10978,0.10962,0.10945,0.10929,0.10913,0.10896,0.1088,0.10864,0.10848,0.10832,0.10816,0.108,0.10783,0.10767,0.10751,0.10735,0.10719,0.10703,0.10687,0.10672,0.10656,0.1064,0.10624,0.10608,0.10592,0.10577,0.10561,0.10545,0.10529,0.10514,0.10498,0.10482,0.10467,0.10451,0.10435,0.1042,0.10404,0.10389,0.10373,0.10358,0.10342,0.10327,0.10311,0.10296,0.10281,0.10265,0.1025,0.10235,0.10219,0.10204,0.10189,0.10174,0.10158,0.10143,0.10128,0.10113,0.10098,0.10083,0.10068,0.10053,0.10038,0.10023,0.10008,0.09993,0.09978,0.09963,0.09948,0.09933,0.09918,0.09903,0.09888,0.09874,0.09859,0.09844,0.09829,0.09815,0.098,0.09785,0.0977,0.09756,0.09741,0.09727,0.09712,0.09697,0.09683,0.09668,0.09654,0.09639,0.09625,0.09611,0.09596,0.09582,0.09567,0.09553,0.09539,0.09524,
-0.0951,0.09496,0.09482,0.09467,0.09453,0.09439,0.09425,0.09411,0.09396,0.09382,0.09368,0.09354,0.0934,0.09326,0.09312,0.09298,0.09284,0.0927,0.09256,0.09242,0.09228,0.09214,0.09201,0.09187,0.09173,0.09159,0.09145,0.09132,0.09118,0.09104,0.0909,0.09077,0.09063,0.09049,0.09036,0.09022,0.09009,0.08995,0.08981,0.08968,0.08954,0.08941,0.08927,0.08914,0.08901,0.08887,0.08874,0.0886,0.08847,0.08834,0.0882,0.08807,0.08794,0.0878,0.08767,0.08754,0.08741,0.08728,0.08714,0.08701,0.08688,0.08675,0.08662,0.08649,0.08636,0.08623,0.0861,0.08597,0.08584,0.08571,0.08558,0.08545,0.08532,0.08519,0.08506,0.08493,0.08481,0.08468,0.08455,0.08442,0.08429,0.08417,0.08404,0.08391,0.08378,0.08366,0.08353,0.0834,0.08328,0.08315,0.08303,0.0829,0.08278,0.08265,0.08252,0.0824,0.08228,0.08215,0.08203,0.0819,
-0.08178,0.08165,0.08153,0.08141,0.08128,0.08116,0.08104,0.08091,0.08079,0.08067,0.08055,0.08042,0.0803,0.08018,0.08006,0.07994,0.07982,0.0797,0.07957,0.07945,0.07933,0.07921,0.07909,0.07897,0.07885,0.07873,0.07861,0.07849,0.07837,0.07826,0.07814,0.07802,0.0779,0.07778,0.07766,0.07755,0.07743,0.07731,0.07719,0.07707,0.07696,0.07684,0.07672,0.07661,0.07649,0.07637,0.07626,0.07614,0.07603,0.07591,0.0758,0.07568,0.07556,0.07545,0.07533,0.07522,0.07511,0.07499,0.07488,0.07476,0.07465,0.07454,0.07442,0.07431,0.0742,0.07408,0.07397,0.07386,0.07374,0.07363,0.07352,0.07341,0.0733,0.07318,0.07307,0.07296,0.07285,0.07274,0.07263,0.07252,0.07241,0.0723,0.07219,0.07208,0.07197,0.07186,0.07175,0.07164,0.07153,0.07142,0.07131,0.0712,0.07109,0.07098,0.07087,0.07077,0.07066,0.07055,0.07044,0.07033,
-0.07023,0.07012,0.07001,0.06991,0.0698,0.06969,0.06959,0.06948,0.06937,0.06927,0.06916,0.06906,0.06895,0.06884,0.06874,0.06863,0.06853,0.06842,0.06832,0.06821,0.06811,0.06801,0.0679,0.0678,0.06769,0.06759,0.06749,0.06738,0.06728,0.06718,0.06707,0.06697,0.06687,0.06677,0.06666,0.06656,0.06646,0.06636,0.06626,0.06616,0.06605,0.06595,0.06585,0.06575,0.06565,0.06555,0.06545,0.06535,0.06525,0.06515,0.06505,0.06495,0.06485,0.06475,0.06465,0.06455,0.06445,0.06435,0.06425,0.06416,0.06406,0.06396,0.06386,0.06376,0.06366,0.06357,0.06347,0.06337,0.06327,0.06318,0.06308,0.06298,0.06289,0.06279,0.06269,0.0626,0.0625,0.0624,0.06231,0.06221,0.06212,0.06202,0.06193,0.06183,0.06174,0.06164,0.06155,0.06145,0.06136,0.06126,0.06117,0.06107,0.06098,0.06089,0.06079,0.0607,0.06061,0.06051,0.06042,0.06033,
-0.06023,0.06014,0.06005,0.05996,0.05986,0.05977,0.05968,0.05959,0.05949,0.0594,0.05931,0.05922,0.05913,0.05904,0.05895,0.05886,0.05877,0.05867,0.05858,0.05849,0.0584,0.05831,0.05822,0.05813,0.05804,0.05795,0.05787,0.05778,0.05769,0.0576,0.05751,0.05742,0.05733,0.05724,0.05715,0.05707,0.05698,0.05689,0.0568,0.05671,0.05663,0.05654,0.05645,0.05636,0.05628,0.05619,0.0561,0.05602,0.05593,0.05584,0.05576,0.05567,0.05559,0.0555,0.05541,0.05533,0.05524,0.05516,0.05507,0.05499,0.0549,0.05482,0.05473,0.05465,0.05456,0.05448,0.05439,0.05431,0.05423,0.05414,0.05406,0.05397,0.05389,0.05381,0.05372,0.05364,0.05356,0.05348,0.05339,0.05331,0.05323,0.05314,0.05306,0.05298,0.0529,0.05282,0.05273,0.05265,0.05257,0.05249,0.05241,0.05233,0.05225,0.05216,0.05208,0.052,0.05192,0.05184,0.05176,0.05168,
-0.0516,0.05152,0.05144,0.05136,0.05128,0.0512,0.05112,0.05104,0.05096,0.05088,0.05081,0.05073,0.05065,0.05057,0.05049,0.05041,0.05033,0.05026,0.05018,0.0501,0.05002,0.04994,0.04987,0.04979,0.04971,0.04964,0.04956,0.04948,0.0494,0.04933,0.04925,0.04917,0.0491,0.04902,0.04894,0.04887,0.04879,0.04872,0.04864,0.04857,0.04849,0.04841,0.04834,0.04826,0.04819,0.04811,0.04804,0.04796,0.04789,0.04782,0.04774,0.04767,0.04759,0.04752,0.04744,0.04737,0.0473,0.04722,0.04715,0.04708,0.047,0.04693,0.04686,0.04678,0.04671,0.04664,0.04657,0.04649,0.04642,0.04635,0.04628,0.0462,0.04613,0.04606,0.04599,0.04592,0.04584,0.04577,0.0457,0.04563,0.04556,0.04549,0.04542,0.04535,0.04528,0.0452,0.04513,0.04506,0.04499,0.04492,0.04485,0.04478,0.04471,0.04464,0.04457,0.0445,0.04443,0.04437,0.0443,0.04423,
-0.04416,0.04409,0.04402,0.04395,0.04388,0.04381,0.04375,0.04368,0.04361,0.04354,0.04347,0.0434,0.04334,0.04327,0.0432,0.04313,0.04307,0.043,0.04293,0.04287,0.0428,0.04273,0.04266,0.0426,0.04253,0.04246,0.0424,0.04233,0.04227,0.0422,0.04213,0.04207,0.042,0.04194,0.04187,0.0418,0.04174,0.04167,0.04161,0.04154,0.04148,0.04141,0.04135,0.04128,0.04122,0.04115,0.04109,0.04103,0.04096,0.0409,0.04083,0.04077,0.04071,0.04064,0.04058,0.04051,0.04045,0.04039,0.04032,0.04026,0.0402,0.04013,0.04007,0.04001,0.03995,0.03988,0.03982,0.03976,0.0397,0.03963,0.03957,0.03951,0.03945,0.03939,0.03932,0.03926,0.0392,0.03914,0.03908,0.03902,0.03896,0.03889,0.03883,0.03877,0.03871,0.03865,0.03859,0.03853,0.03847,0.03841,0.03835,0.03829,0.03823,0.03817,0.03811,0.03805,0.03799,0.03793,0.03787,0.03781,
-0.03775,0.03769,0.03763,0.03757,0.03751,0.03745,0.0374,0.03734,0.03728,0.03722,0.03716,0.0371,0.03704,0.03699,0.03693,0.03687,0.03681,0.03675,0.0367,0.03664,0.03658,0.03652,0.03647,0.03641,0.03635,0.03629,0.03624,0.03618,0.03612,0.03607,0.03601,0.03595,0.0359,0.03584,0.03578,0.03573,0.03567,0.03561,0.03556,0.0355,0.03545,0.03539,0.03533,0.03528,0.03522,0.03517,0.03511,0.03506,0.035,0.03495,0.03489,0.03484,0.03478,0.03473,0.03467,0.03462,0.03456,0.03451,0.03445,0.0344,0.03434,0.03429,0.03424,0.03418,0.03413,0.03407,0.03402,0.03397,0.03391,0.03386,0.03381,0.03375,0.0337,0.03365,0.03359,0.03354,0.03349,0.03343,0.03338,0.03333,0.03328,0.03322,0.03317,0.03312,0.03307,0.03301,0.03296,0.03291,0.03286,0.03281,0.03275,0.0327,0.03265,0.0326,0.03255,0.0325,0.03245,0.03239,0.03234,0.03229,
-0.03224,0.03219,0.03214,0.03209,0.03204,0.03199,0.03194,0.03189,0.03184,0.03178,0.03173,0.03168,0.03163,0.03158,0.03153,0.03148,0.03143,0.03138,0.03134,0.03129,0.03124,0.03119,0.03114,0.03109,0.03104,0.03099,0.03094,0.03089,0.03084,0.03079,0.03075,0.0307,0.03065,0.0306,0.03055,0.0305,0.03045,0.03041,0.03036,0.03031,0.03026,0.03021,0.03017,0.03012,0.03007,0.03002,0.02997,0.02993,0.02988,0.02983,0.02979,0.02974,0.02969,0.02964,0.0296,0.02955,0.0295,0.02946,0.02941,0.02936,0.02932,0.02927,0.02922,0.02918,0.02913,0.02908,0.02904,0.02899,0.02895,0.0289,0.02885,0.02881,0.02876,0.02872,0.02867,0.02863,0.02858,0.02854,0.02849,0.02844,0.0284,0.02835,0.02831,0.02826,0.02822,0.02817,0.02813,0.02809,0.02804,0.028,0.02795,0.02791,0.02786,0.02782,0.02777,0.02773,0.02769,0.02764,0.0276,0.02755,
-0.02751,0.02747,0.02742,0.02738,0.02734,0.02729,0.02725,0.02721,0.02716,0.02712,0.02708,0.02703,0.02699,0.02695,0.0269,0.02686,0.02682,0.02678,0.02673,0.02669,0.02665,0.02661,0.02656,0.02652,0.02648,0.02644,0.0264,0.02635,0.02631,0.02627,0.02623,0.02619,0.02614,0.0261,0.02606,0.02602,0.02598,0.02594,0.0259,0.02585,0.02581,0.02577,0.02573,0.02569,0.02565,0.02561,0.02557,0.02553,0.02549,0.02545,0.0254,0.02536,0.02532,0.02528,0.02524,0.0252,0.02516,0.02512,0.02508,0.02504,0.025,0.02496,0.02492,0.02488,0.02484,0.0248,0.02476,0.02472,0.02469,0.02465,0.02461,0.02457,0.02453,0.02449,0.02445,0.02441,0.02437,0.02433,0.02429,0.02426,0.02422,0.02418,0.02414,0.0241,0.02406,0.02402,0.02399,0.02395,0.02391,0.02387,0.02383,0.02379,0.02376,0.02372,0.02368,0.02364,0.02361,0.02357,0.02353,0.02349,
-0.02345,0.02342,0.02338,0.02334,0.02331,0.02327,0.02323,0.02319,0.02316,0.02312,0.02308,0.02305,0.02301,0.02297,0.02294,0.0229,0.02286,0.02283,0.02279,0.02275,0.02272,0.02268,0.02264,0.02261,0.02257,0.02254,0.0225,0.02246,0.02243,0.02239,0.02236,0.02232,0.02228,0.02225,0.02221,0.02218,0.02214,0.02211,0.02207,0.02204,0.022,0.02197,0.02193,0.02189,0.02186,0.02182,0.02179,0.02175,0.02172,0.02169,0.02165,0.02162,0.02158,0.02155,0.02151,0.02148,0.02144,0.02141,0.02137,0.02134,0.02131,0.02127,0.02124,0.0212,0.02117,0.02114,0.0211,0.02107,0.02103,0.021,0.02097,0.02093,0.0209,0.02087,0.02083,0.0208,0.02077,0.02073,0.0207,0.02067,0.02063,0.0206,0.02057,0.02053,0.0205,0.02047,0.02044,0.0204,0.02037,0.02034,0.0203,0.02027,0.02024,0.02021,0.02017,0.02014,0.02011,0.02008,0.02005,0.02001,
-0.01998,0.01995,0.01992,0.01988,0.01985,0.01982,0.01979,0.01976,0.01973,0.01969,0.01966,0.01963,0.0196,0.01957,0.01954,0.0195,0.01947,0.01944,0.01941,0.01938,0.01935,0.01932,0.01929,0.01926,0.01922,0.01919,0.01916,0.01913,0.0191,0.01907,0.01904,0.01901,0.01898,0.01895,0.01892,0.01889,0.01886,0.01883,0.0188,0.01877,0.01874,0.01871,0.01868,0.01865,0.01862,0.01859,0.01856,0.01853,0.0185,0.01847,0.01844,0.01841,0.01838,0.01835,0.01832,0.01829,0.01826,0.01823,0.0182,0.01817,0.01814,0.01811,0.01808,0.01805,0.01803,0.018,0.01797,0.01794,0.01791,0.01788,0.01785,0.01782,0.01779,0.01777,0.01774,0.01771,0.01768,0.01765,0.01762,0.01759,0.01757,0.01754,0.01751,0.01748,0.01745,0.01743,0.0174,0.01737,0.01734,0.01731,0.01729,0.01726,0.01723,0.0172,0.01717,0.01715,0.01712,0.01709,0.01706,0.01704,
-0.01701,0.01698,0.01695,0.01693,0.0169,0.01687,0.01684,0.01682,0.01679,0.01676,0.01674,0.01671,0.01668,0.01666,0.01663,0.0166,0.01657,0.01655,0.01652,0.01649,0.01647,0.01644,0.01641,0.01639,0.01636,0.01634,0.01631,0.01628,0.01626,0.01623,0.0162,0.01618,0.01615,0.01613,0.0161,0.01607,0.01605,0.01602,0.016,0.01597,0.01594,0.01592,0.01589,0.01587,0.01584,0.01582,0.01579,0.01576,0.01574,0.01571,0.01569,0.01566,0.01564,0.01561,0.01559,0.01556,0.01554,0.01551,0.01549,0.01546,0.01544,0.01541,0.01539,0.01536,0.01534,0.01531,0.01529,0.01526,0.01524,0.01521,0.01519,0.01516,0.01514,0.01511,0.01509,0.01507,0.01504,0.01502,0.01499,0.01497,0.01494,0.01492,0.0149,0.01487,0.01485,0.01482,0.0148,0.01478,0.01475,0.01473,0.0147,0.01468,0.01466,0.01463,0.01461,0.01459,0.01456,0.01454,0.01451,0.01449,
-0.01447,0.01444,0.01442,0.0144,0.01437,0.01435,0.01433,0.0143,0.01428,0.01426,0.01424,0.01421,0.01419,0.01417,0.01414,0.01412,0.0141,0.01407,0.01405,0.01403,0.01401,0.01398,0.01396,0.01394,0.01392,0.01389,0.01387,0.01385,0.01383,0.0138,0.01378,0.01376,0.01374,0.01371,0.01369,0.01367,0.01365,0.01362,0.0136,0.01358,0.01356,0.01354,0.01351,0.01349,0.01347,0.01345,0.01343,0.01341,0.01338,0.01336,0.01334,0.01332,0.0133,0.01328,0.01325,0.01323,0.01321,0.01319,0.01317,0.01315,0.01313,0.0131,0.01308,0.01306,0.01304,0.01302,0.013,0.01298,0.01296,0.01293,0.01291,0.01289,0.01287,0.01285,0.01283,0.01281,0.01279,0.01277,0.01275,0.01273,0.01271,0.01268,0.01266,0.01264,0.01262,0.0126,0.01258,0.01256,0.01254,0.01252,0.0125,0.01248,0.01246,0.01244,0.01242,0.0124,0.01238,0.01236,0.01234,0.01232,
-0.0123,0.01228,0.01226,0.01224,0.01222,0.0122,0.01218,0.01216,0.01214,0.01212,0.0121,0.01208,0.01206,0.01204,0.01202,0.012,0.01198,0.01196,0.01194,0.01192,0.0119,0.01189,0.01187,0.01185,0.01183,0.01181,0.01179,0.01177,0.01175,0.01173,0.01171,0.01169,0.01167,0.01165,0.01164,0.01162,0.0116,0.01158,0.01156,0.01154,0.01152,0.0115,0.01149,0.01147,0.01145,0.01143,0.01141,0.01139,0.01137,0.01135,0.01134,0.01132,0.0113,0.01128,0.01126,0.01124,0.01123,0.01121,0.01119,0.01117,0.01115,0.01113,0.01112,0.0111,0.01108,0.01106,0.01104,0.01103,0.01101,0.01099,0.01097,0.01095,0.01094,0.01092,0.0109,0.01088,0.01087,0.01085,0.01083,0.01081,0.01079,0.01078,0.01076,0.01074,0.01072,0.01071,0.01069,0.01067,0.01065,0.01064,0.01062,0.0106,0.01059,0.01057,0.01055,0.01053,0.01052,0.0105,0.01048,0.01046,
-0.01045,0.01043,0.01041,0.0104,0.01038,0.01036,0.01035,0.01033,0.01031,0.0103,0.01028,0.01026,0.01024,0.01023,0.01021,0.01019,0.01018,0.01016,0.01014,0.01013,0.01011,0.01009,0.01008,0.01006,0.01005,0.01003,0.01001,0.01,0.00998,0.00996,0.00995,0.00993,0.00991,0.0099,0.00988,0.00987,0.00985,0.00983,0.00982,0.0098,0.00979,0.00977,0.00975,0.00974,0.00972,0.00971,0.00969,0.00967,0.00966,0.00964,0.00963,0.00961,0.0096,0.00958,0.00956,0.00955,0.00953,0.00952,0.0095,0.00949,0.00947,0.00946,0.00944,0.00942,0.00941,0.00939,0.00938,0.00936,0.00935,0.00933,0.00932,0.0093,0.00929,0.00927,0.00926,0.00924,0.00923,0.00921,0.0092,0.00918,0.00917,0.00915,0.00914,0.00912,0.00911,0.00909,0.00908,0.00906,0.00905,0.00903,0.00902,0.009,0.00899,0.00897,0.00896,0.00894,0.00893,0.00891,0.0089,0.00888,
-0.00887,0.00886,0.00884,0.00883,0.00881,0.0088,0.00878,0.00877,0.00875,0.00874,0.00873,0.00871,0.0087,0.00868,0.00867,0.00865,0.00864,0.00863,0.00861,0.0086,0.00858,0.00857,0.00856,0.00854,0.00853,0.00851,0.0085,0.00849,0.00847,0.00846,0.00844,0.00843,0.00842,0.0084,0.00839,0.00837,0.00836,0.00835,0.00833,0.00832,0.00831,0.00829,0.00828,0.00827,0.00825,0.00824,0.00822,0.00821,0.0082,0.00818,0.00817,0.00816,0.00814,0.00813,0.00812,0.0081,0.00809,0.00808,0.00806,0.00805,0.00804,0.00802,0.00801,0.008,0.00798,0.00797,0.00796,0.00795,0.00793,0.00792,0.00791,0.00789,0.00788,0.00787,0.00785,0.00784,0.00783,0.00782,0.0078,0.00779,0.00778,0.00776,0.00775,0.00774,0.00773,0.00771,0.0077,0.00769,0.00768,0.00766,0.00765,0.00764,0.00763,0.00761,0.0076,0.00759,0.00758,0.00756,0.00755,0.00754,
-0.00753,0.00751,0.0075,0.00749,0.00748,0.00746,0.00745,0.00744,0.00743,0.00742,0.0074,0.00739,0.00738,0.00737,0.00735,0.00734,0.00733,0.00732,0.00731,0.00729,0.00728,0.00727,0.00726,0.00725,0.00723,0.00722,0.00721,0.0072,0.00719,0.00717,0.00716,0.00715,0.00714,0.00713,0.00712,0.0071,0.00709,0.00708,0.00707,0.00706,0.00705,0.00703,0.00702,0.00701,0.007,0.00699,0.00698,0.00697,0.00695,0.00694,0.00693,0.00692,0.00691,0.0069,0.00689,0.00687,0.00686,0.00685,0.00684,0.00683,0.00682,0.00681,0.00679,0.00678,0.00677,0.00676,0.00675,0.00674,0.00673,0.00672,0.00671,0.00669,0.00668,0.00667,0.00666,0.00665,0.00664,0.00663,0.00662,0.00661,0.0066,0.00659,0.00657,0.00656,0.00655,0.00654,0.00653,0.00652,0.00651,0.0065,0.00649,0.00648,0.00647,0.00646,0.00645,0.00643,0.00642,0.00641,0.0064,0.00639,
-0.00638,0.00637,0.00636,0.00635,0.00634,0.00633,0.00632,0.00631,0.0063,0.00629,0.00628,0.00627,0.00626,0.00625,0.00624,0.00623,0.00622,0.00621,0.00619,0.00618,0.00617,0.00616,0.00615,0.00614,0.00613,0.00612,0.00611,0.0061,0.00609,0.00608,0.00607,0.00606,0.00605,0.00604,0.00603,0.00602,0.00601,0.006,0.00599,0.00598,0.00597,0.00596,0.00595,0.00594,0.00593,0.00592,0.00591,0.0059,0.0059,0.00589,0.00588,0.00587,0.00586,0.00585,0.00584,0.00583,0.00582,0.00581,0.0058,0.00579,0.00578,0.00577,0.00576,0.00575,0.00574,0.00573,0.00572,0.00571,0.0057,0.00569,0.00568,0.00568,0.00567,0.00566,0.00565,0.00564,0.00563,0.00562,0.00561,0.0056,0.00559,0.00558,0.00557,0.00556,0.00555,0.00555,0.00554,0.00553,0.00552,0.00551,0.0055,0.00549,0.00548,0.00547,0.00546,0.00545,0.00544,0.00544,0.00543,0.00542,
-0.00541,0.0054,0.00539,0.00538,0.00537,0.00536,0.00536,0.00535,0.00534,0.00533,0.00532,0.00531,0.0053,0.00529,0.00528,0.00528,0.00527,0.00526,0.00525,0.00524,0.00523,0.00522,0.00522,0.00521,0.0052,0.00519,0.00518,0.00517,0.00516,0.00516,0.00515,0.00514,0.00513,0.00512,0.00511,0.0051,0.0051,0.00509,0.00508,0.00507,0.00506,0.00505,0.00505,0.00504,0.00503,0.00502,0.00501,0.005,0.005,0.00499,0.00498,0.00497,0.00496,0.00495,0.00495,0.00494,0.00493,0.00492,0.00491,0.0049,0.0049,0.00489,0.00488,0.00487,0.00486,0.00486,0.00485,0.00484,0.00483,0.00482,0.00482,0.00481,0.0048,0.00479,0.00478,0.00478,0.00477,0.00476,0.00475,0.00474,0.00474,0.00473,0.00472,0.00471,0.00471,0.0047,0.00469,0.00468,0.00467,0.00467,0.00466,0.00465,0.00464,0.00464,0.00463,0.00462,0.00461,0.0046,0.0046,0.00459};
-
-constexpr double stored_lower_incomplete_gamma_values_n5[] = {0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1e-05,1e-05,1e-05,1e-05,1e-05,1e-05,2e-05,2e-05,2e-05,3e-05,3e-05,3e-05,4e-05,4e-05,5e-05,5e-05,6e-05,6e-05,7e-05,8e-05,8e-05,9e-05,0.0001,0.00011,0.00012,0.00012,0.00013,0.00014,0.00016,0.00017,0.00018,0.00019,0.0002,0.00022,0.00023,0.00024,0.00026,0.00027,0.00029,0.00031,0.00032,0.00034,0.00036,0.00038,0.0004,0.00042,0.00044,0.00046,0.00049,0.00051,0.00053,0.00056,0.00058,0.00061,0.00064,0.00066,0.00069,0.00072,0.00075,0.00078,0.00081,0.00084,0.00088,0.00091,0.00095,0.00098,0.00102,0.00105,0.00109,0.00113,0.00117,0.00121,0.00125,0.0013,0.00134,0.00138,0.00143,0.00147,0.00152,0.00157,0.00162,0.00167,0.00172,0.00177,0.00182,0.00188,
-0.00193,0.00199,0.00204,0.0021,0.00216,0.00222,0.00228,0.00234,0.00241,0.00247,0.00254,0.0026,0.00267,0.00274,0.00281,0.00288,0.00295,0.00302,0.00309,0.00317,0.00325,0.00332,0.0034,0.00348,0.00356,0.00364,0.00373,0.00381,0.0039,0.00398,0.00407,0.00416,0.00425,0.00434,0.00443,0.00453,0.00462,0.00472,0.00481,0.00491,0.00501,0.00511,0.00522,0.00532,0.00542,0.00553,0.00564,0.00575,0.00586,0.00597,0.00608,0.00619,0.00631,0.00643,0.00654,0.00666,0.00678,0.0069,0.00703,0.00715,0.00728,0.0074,0.00753,0.00766,0.00779,0.00793,0.00806,0.00819,0.00833,0.00847,0.00861,0.00875,0.00889,0.00903,0.00918,0.00932,0.00947,0.00962,0.00977,0.00992,0.01008,0.01023,0.01039,0.01055,0.0107,0.01086,0.01103,0.01119,0.01135,0.01152,0.01169,0.01186,0.01203,0.0122,0.01237,0.01255,0.01272,0.0129,0.01308,0.01326,
-0.01345,0.01363,0.01381,0.014,0.01419,0.01438,0.01457,0.01476,0.01496,0.01515,0.01535,0.01555,0.01575,0.01595,0.01616,0.01636,0.01657,0.01677,0.01698,0.0172,0.01741,0.01762,0.01784,0.01805,0.01827,0.01849,0.01872,0.01894,0.01916,0.01939,0.01962,0.01985,0.02008,0.02031,0.02055,0.02078,0.02102,0.02126,0.0215,0.02174,0.02198,0.02223,0.02248,0.02273,0.02298,0.02323,0.02348,0.02373,0.02399,0.02425,0.02451,0.02477,0.02503,0.0253,0.02556,0.02583,0.0261,0.02637,0.02664,0.02692,0.02719,0.02747,0.02775,0.02803,0.02831,0.02859,0.02888,0.02917,0.02945,0.02974,0.03004,0.03033,0.03062,0.03092,0.03122,0.03152,0.03182,0.03212,0.03243,0.03273,0.03304,0.03335,0.03366,0.03397,0.03429,0.03461,0.03492,0.03524,0.03556,0.03589,0.03621,0.03654,0.03686,0.03719,0.03752,0.03785,0.03819,0.03852,0.03886,0.0392,
-0.03954,0.03988,0.04023,0.04057,0.04092,0.04127,0.04162,0.04197,0.04232,0.04268,0.04303,0.04339,0.04375,0.04411,0.04448,0.04484,0.04521,0.04558,0.04595,0.04632,0.04669,0.04707,0.04744,0.04782,0.0482,0.04858,0.04896,0.04935,0.04973,0.05012,0.05051,0.0509,0.0513,0.05169,0.05209,0.05248,0.05288,0.05328,0.05369,0.05409,0.0545,0.0549,0.05531,0.05572,0.05613,0.05655,0.05696,0.05738,0.0578,0.05822,0.05864,0.05907,0.05949,0.05992,0.06035,0.06078,0.06121,0.06164,0.06208,0.06251,0.06295,0.06339,0.06383,0.06427,0.06472,0.06516,0.06561,0.06606,0.06651,0.06697,0.06742,0.06788,0.06833,0.06879,0.06925,0.06971,0.07018,0.07064,0.07111,0.07158,0.07205,0.07252,0.07299,0.07347,0.07395,0.07442,0.0749,0.07539,0.07587,0.07635,0.07684,0.07733,0.07782,0.07831,0.0788,0.07929,0.07979,0.08028,0.08078,0.08128,
-0.08179,0.08229,0.08279,0.0833,0.08381,0.08432,0.08483,0.08534,0.08586,0.08637,0.08689,0.08741,0.08793,0.08845,0.08897,0.0895,0.09003,0.09055,0.09108,0.09162,0.09215,0.09268,0.09322,0.09376,0.09429,0.09484,0.09538,0.09592,0.09647,0.09701,0.09756,0.09811,0.09866,0.09921,0.09977,0.10032,0.10088,0.10144,0.102,0.10256,0.10312,0.10369,0.10426,0.10482,0.10539,0.10596,0.10654,0.10711,0.10768,0.10826,0.10884,0.10942,0.11,0.11058,0.11117,0.11175,0.11234,0.11293,0.11352,0.11411,0.1147,0.1153,0.11589,0.11649,0.11709,0.11769,0.11829,0.11889,0.1195,0.1201,0.12071,0.12132,0.12193,0.12254,0.12316,0.12377,0.12439,0.125,0.12562,0.12624,0.12687,0.12749,0.12811,0.12874,0.12937,0.13,0.13063,0.13126,0.13189,0.13253,0.13316,0.1338,0.13444,0.13508,0.13572,0.13636,0.13701,0.13765,0.1383,0.13895,
-0.1396,0.14025,0.1409,0.14156,0.14221,0.14287,0.14353,0.14418,0.14485,0.14551,0.14617,0.14684,0.1475,0.14817,0.14884,0.14951,0.15018,0.15085,0.15153,0.1522,0.15288,0.15356,0.15424,0.15492,0.1556,0.15628,0.15697,0.15766,0.15834,0.15903,0.15972,0.16041,0.16111,0.1618,0.1625,0.16319,0.16389,0.16459,0.16529,0.16599,0.16669,0.1674,0.1681,0.16881,0.16952,0.17023,0.17094,0.17165,0.17237,0.17308,0.1738,0.17451,0.17523,0.17595,0.17667,0.17739,0.17812,0.17884,0.17957,0.18029,0.18102,0.18175,0.18248,0.18321,0.18395,0.18468,0.18542,0.18615,0.18689,0.18763,0.18837,0.18911,0.18986,0.1906,0.19135,0.19209,0.19284,0.19359,0.19434,0.19509,0.19584,0.1966,0.19735,0.19811,0.19886,0.19962,0.20038,0.20114,0.2019,0.20267,0.20343,0.2042,0.20496,0.20573,0.2065,0.20727,0.20804,0.20881,0.20958,0.21036,
-0.21113,0.21191,0.21269,0.21347,0.21425,0.21503,0.21581,0.21659,0.21738,0.21816,0.21895,0.21974,0.22053,0.22132,0.22211,0.2229,0.22369,0.22449,0.22528,0.22608,0.22688,0.22767,0.22847,0.22928,0.23008,0.23088,0.23168,0.23249,0.23329,0.2341,0.23491,0.23572,0.23653,0.23734,0.23815,0.23897,0.23978,0.24059,0.24141,0.24223,0.24305,0.24387,0.24469,0.24551,0.24633,0.24715,0.24798,0.2488,0.24963,0.25046,0.25129,0.25212,0.25295,0.25378,0.25461,0.25544,0.25628,0.25711,0.25795,0.25879,0.25963,0.26046,0.2613,0.26215,0.26299,0.26383,0.26467,0.26552,0.26637,0.26721,0.26806,0.26891,0.26976,0.27061,0.27146,0.27231,0.27317,0.27402,0.27488,0.27573,0.27659,0.27745,0.2783,0.27916,0.28002,0.28089,0.28175,0.28261,0.28348,0.28434,0.28521,0.28607,0.28694,0.28781,0.28868,0.28955,0.29042,0.29129,0.29217,0.29304,
-0.29391,0.29479,0.29567,0.29654,0.29742,0.2983,0.29918,0.30006,0.30094,0.30182,0.30271,0.30359,0.30448,0.30536,0.30625,0.30713,0.30802,0.30891,0.3098,0.31069,0.31158,0.31247,0.31337,0.31426,0.31515,0.31605,0.31695,0.31784,0.31874,0.31964,0.32054,0.32144,0.32234,0.32324,0.32414,0.32504,0.32595,0.32685,0.32776,0.32866,0.32957,0.33048,0.33138,0.33229,0.3332,0.33411,0.33502,0.33594,0.33685,0.33776,0.33867,0.33959,0.3405,0.34142,0.34234,0.34326,0.34417,0.34509,0.34601,0.34693,0.34785,0.34877,0.3497,0.35062,0.35154,0.35247,0.35339,0.35432,0.35525,0.35617,0.3571,0.35803,0.35896,0.35989,0.36082,0.36175,0.36268,0.36361,0.36455,0.36548,0.36641,0.36735,0.36828,0.36922,0.37016,0.37109,0.37203,0.37297,0.37391,0.37485,0.37579,0.37673,0.37767,0.37862,0.37956,0.3805,0.38145,0.38239,0.38334,0.38428,
-0.38523,0.38618,0.38712,0.38807,0.38902,0.38997,0.39092,0.39187,0.39282,0.39377,0.39473,0.39568,0.39663,0.39759,0.39854,0.3995,0.40045,0.40141,0.40236,0.40332,0.40428,0.40524,0.4062,0.40716,0.40811,0.40908,0.41004,0.411,0.41196,0.41292,0.41388,0.41485,0.41581,0.41678,0.41774,0.41871,0.41967,0.42064,0.42161,0.42257,0.42354,0.42451,0.42548,0.42645,0.42742,0.42839,0.42936,0.43033,0.4313,0.43227,0.43325,0.43422,0.43519,0.43617,0.43714,0.43812,0.43909,0.44007,0.44104,0.44202,0.443,0.44398,0.44495,0.44593,0.44691,0.44789,0.44887,0.44985,0.45083,0.45181,0.45279,0.45377,0.45476,0.45574,0.45672,0.4577,0.45869,0.45967,0.46066,0.46164,0.46263,0.46361,0.4646,0.46559,0.46657,0.46756,0.46855,0.46953,0.47052,0.47151,0.4725,0.47349,0.47448,0.47547,0.47646,0.47745,0.47844,0.47943,0.48043,0.48142,
-0.48241,0.4834,0.4844,0.48539,0.48638,0.48738,0.48837,0.48937,0.49036,0.49136,0.49235,0.49335,0.49435,0.49534,0.49634,0.49734,0.49834,0.49933,0.50033,0.50133,0.50233,0.50333,0.50433,0.50533,0.50633,0.50733,0.50833,0.50933,0.51033,0.51133,0.51233,0.51333,0.51434,0.51534,0.51634,0.51735,0.51835,0.51935,0.52036,0.52136,0.52236,0.52337,0.52437,0.52538,0.52638,0.52739,0.52839,0.5294,0.53041,0.53141,0.53242,0.53343,0.53443,0.53544,0.53645,0.53746,0.53846,0.53947,0.54048,0.54149,0.5425,0.54351,0.54452,0.54552,0.54653,0.54754,0.54855,0.54956,0.55057,0.55159,0.5526,0.55361,0.55462,0.55563,0.55664,0.55765,0.55866,0.55968,0.56069,0.5617,0.56271,0.56372,0.56474,0.56575,0.56676,0.56778,0.56879,0.5698,0.57082,0.57183,0.57284,0.57386,0.57487,0.57589,0.5769,0.57792,0.57893,0.57995,0.58096,0.58198,
-0.58299,0.58401,0.58502,0.58604,0.58705,0.58807,0.58908,0.5901,0.59112,0.59213,0.59315,0.59417,0.59518,0.5962,0.59722,0.59823,0.59925,0.60027,0.60128,0.6023,0.60332,0.60434,0.60535,0.60637,0.60739,0.60841,0.60942,0.61044,0.61146,0.61248,0.61349,0.61451,0.61553,0.61655,0.61757,0.61859,0.6196,0.62062,0.62164,0.62266,0.62368,0.6247,0.62571,0.62673,0.62775,0.62877,0.62979,0.63081,0.63183,0.63284,0.63386,0.63488,0.6359,0.63692,0.63794,0.63896,0.63998,0.641,0.64201,0.64303,0.64405,0.64507,0.64609,0.64711,0.64813,0.64915,0.65017,0.65119,0.6522,0.65322,0.65424,0.65526,0.65628,0.6573,0.65832,0.65934,0.66035,0.66137,0.66239,0.66341,0.66443,0.66545,0.66647,0.66749,0.6685,0.66952,0.67054,0.67156,0.67258,0.6736,0.67461,0.67563,0.67665,0.67767,0.67869,0.67971,0.68072,0.68174,0.68276,0.68378,
-0.68479,0.68581,0.68683,0.68785,0.68887,0.68988,0.6909,0.69192,0.69293,0.69395,0.69497,0.69599,0.697,0.69802,0.69904,0.70005,0.70107,0.70209,0.7031,0.70412,0.70513,0.70615,0.70717,0.70818,0.7092,0.71021,0.71123,0.71224,0.71326,0.71427,0.71529,0.7163,0.71732,0.71833,0.71935,0.72036,0.72138,0.72239,0.72341,0.72442,0.72543,0.72645,0.72746,0.72847,0.72949,0.7305,0.73151,0.73253,0.73354,0.73455,0.73557,0.73658,0.73759,0.7386,0.73961,0.74063,0.74164,0.74265,0.74366,0.74467,0.74568,0.74669,0.7477,0.74871,0.74972,0.75073,0.75174,0.75275,0.75376,0.75477,0.75578,0.75679,0.7578,0.75881,0.75982,0.76083,0.76183,0.76284,0.76385,0.76486,0.76587,0.76687,0.76788,0.76889,0.76989,0.7709,0.77191,0.77291,0.77392,0.77492,0.77593,0.77694,0.77794,0.77895,0.77995,0.78096,0.78196,0.78296,0.78397,0.78497,
-0.78597,0.78698,0.78798,0.78898,0.78999,0.79099,0.79199,0.79299,0.79399,0.795,0.796,0.797,0.798,0.799,0.8,0.801,0.802,0.803,0.804,0.805,0.806,0.807,0.80799,0.80899,0.80999,0.81099,0.81198,0.81298,0.81398,0.81498,0.81597,0.81697,0.81796,0.81896,0.81996,0.82095,0.82195,0.82294,0.82393,0.82493,0.82592,0.82692,0.82791,0.8289,0.82989,0.83089,0.83188,0.83287,0.83386,0.83485,0.83584,0.83684,0.83783,0.83882,0.83981,0.8408,0.84179,0.84277,0.84376,0.84475,0.84574,0.84673,0.84772,0.8487,0.84969,0.85068,0.85166,0.85265,0.85364,0.85462,0.85561,0.85659,0.85758,0.85856,0.85954,0.86053,0.86151,0.86249,0.86348,0.86446,0.86544,0.86642,0.8674,0.86839,0.86937,0.87035,0.87133,0.87231,0.87329,0.87427,0.87525,0.87622,0.8772,0.87818,0.87916,0.88014,0.88111,0.88209,0.88307,0.88404,
-0.88502,0.88599,0.88697,0.88794,0.88892,0.88989,0.89086,0.89184,0.89281,0.89378,0.89476,0.89573,0.8967,0.89767,0.89864,0.89961,0.90058,0.90155,0.90252,0.90349,0.90446,0.90543,0.9064,0.90736,0.90833,0.9093,0.91026,0.91123,0.9122,0.91316,0.91413,0.91509,0.91606,0.91702,0.91798,0.91895,0.91991,0.92087,0.92184,0.9228,0.92376,0.92472,0.92568,0.92664,0.9276,0.92856,0.92952,0.93048,0.93144,0.9324,0.93335,0.93431,0.93527,0.93622,0.93718,0.93814,0.93909,0.94005,0.941,0.94196,0.94291,0.94386,0.94482,0.94577,0.94672,0.94767,0.94862,0.94957,0.95053,0.95148,0.95243,0.95338,0.95432,0.95527,0.95622,0.95717,0.95812,0.95906,0.96001,0.96096,0.9619,0.96285,0.96379,0.96474,0.96568,0.96662,0.96757,0.96851,0.96945,0.9704,0.97134,0.97228,0.97322,0.97416,0.9751,0.97604,0.97698,0.97792,0.97886,0.97979,
-0.98073,0.98167,0.9826,0.98354,0.98448,0.98541,0.98635,0.98728,0.98822,0.98915,0.99008,0.99102,0.99195,0.99288,0.99381,0.99474,0.99567,0.9966,0.99753,0.99846,0.99939,1.00032,1.00125,1.00217,1.0031,1.00403,1.00495,1.00588,1.0068,1.00773,1.00865,1.00958,1.0105,1.01142,1.01235,1.01327,1.01419,1.01511,1.01603,1.01695,1.01787,1.01879,1.01971,1.02063,1.02155,1.02247,1.02338,1.0243,1.02522,1.02613,1.02705,1.02796,1.02888,1.02979,1.0307,1.03162,1.03253,1.03344,1.03435,1.03526,1.03618,1.03709,1.038,1.0389,1.03981,1.04072,1.04163,1.04254,1.04344,1.04435,1.04526,1.04616,1.04707,1.04797,1.04888,1.04978,1.05068,1.05158,1.05249,1.05339,1.05429,1.05519,1.05609,1.05699,1.05789,1.05879,1.05969,1.06059,1.06148,1.06238,1.06328,1.06417,1.06507,1.06596,1.06686,1.06775,1.06864,1.06954,1.07043,1.07132,
-1.07221,1.0731,1.074,1.07489,1.07578,1.07666,1.07755,1.07844,1.07933,1.08022,1.0811,1.08199,1.08287,1.08376,1.08464,1.08553,1.08641,1.0873,1.08818,1.08906,1.08994,1.09082,1.0917,1.09258,1.09346,1.09434,1.09522,1.0961,1.09698,1.09785,1.09873,1.09961,1.10048,1.10136,1.10223,1.10311,1.10398,1.10485,1.10573,1.1066,1.10747,1.10834,1.10921,1.11008,1.11095,1.11182,1.11269,1.11356,1.11442,1.11529,1.11616,1.11702,1.11789,1.11875,1.11962,1.12048,1.12135,1.12221,1.12307,1.12393,1.1248,1.12566,1.12652,1.12738,1.12824,1.12909,1.12995,1.13081,1.13167,1.13252,1.13338,1.13424,1.13509,1.13595,1.1368,1.13765,1.13851,1.13936,1.14021,1.14106,1.14191,1.14276,1.14361,1.14446,1.14531,1.14616,1.14701,1.14786,1.1487,1.14955,1.15039,1.15124,1.15208,1.15293,1.15377,1.15461,1.15546,1.1563,1.15714,1.15798,
-1.15882,1.15966,1.1605,1.16134,1.16218,1.16302,1.16385,1.16469,1.16553,1.16636,1.1672,1.16803,1.16887,1.1697,1.17053,1.17136,1.1722,1.17303,1.17386,1.17469,1.17552,1.17635,1.17718,1.178,1.17883,1.17966,1.18049,1.18131,1.18214,1.18296,1.18379,1.18461,1.18543,1.18626,1.18708,1.1879,1.18872,1.18954,1.19036,1.19118,1.192,1.19282,1.19364,1.19445,1.19527,1.19609,1.1969,1.19772,1.19853,1.19935,1.20016,1.20097,1.20178,1.2026,1.20341,1.20422,1.20503,1.20584,1.20665,1.20746,1.20826,1.20907,1.20988,1.21068,1.21149,1.2123,1.2131,1.2139,1.21471,1.21551,1.21631,1.21712,1.21792,1.21872,1.21952,1.22032,1.22112,1.22192,1.22271,1.22351,1.22431,1.22511,1.2259,1.2267,1.22749,1.22829,1.22908,1.22987,1.23067,1.23146,1.23225,1.23304,1.23383,1.23462,1.23541,1.2362,1.23699,1.23777,1.23856,1.23935,
-1.24013,1.24092,1.2417,1.24249,1.24327,1.24406,1.24484,1.24562,1.2464,1.24718,1.24796,1.24874,1.24952,1.2503,1.25108,1.25186,1.25263,1.25341,1.25419,1.25496,1.25574,1.25651,1.25729,1.25806,1.25883,1.2596,1.26037,1.26115,1.26192,1.26269,1.26346,1.26422,1.26499,1.26576,1.26653,1.26729,1.26806,1.26882,1.26959,1.27035,1.27112,1.27188,1.27264,1.27341,1.27417,1.27493,1.27569,1.27645,1.27721,1.27797,1.27872,1.27948,1.28024,1.28099,1.28175,1.28251,1.28326,1.28401,1.28477,1.28552,1.28627,1.28703,1.28778,1.28853,1.28928,1.29003,1.29078,1.29153,1.29227,1.29302,1.29377,1.29451,1.29526,1.29601,1.29675,1.29749,1.29824,1.29898,1.29972,1.30046,1.30121,1.30195,1.30269,1.30343,1.30417,1.3049,1.30564,1.30638,1.30712,1.30785,1.30859,1.30932,1.31006,1.31079,1.31152,1.31226,1.31299,1.31372,1.31445,1.31518,
-1.31591,1.31664,1.31737,1.3181,1.31883,1.31955,1.32028,1.32101,1.32173,1.32246,1.32318,1.32391,1.32463,1.32535,1.32607,1.3268,1.32752,1.32824,1.32896,1.32968,1.3304,1.33111,1.33183,1.33255,1.33326,1.33398,1.3347,1.33541,1.33612,1.33684,1.33755,1.33826,1.33898,1.33969,1.3404,1.34111,1.34182,1.34253,1.34324,1.34394,1.34465,1.34536,1.34607,1.34677,1.34748,1.34818,1.34889,1.34959,1.35029,1.35099,1.3517,1.3524,1.3531,1.3538,1.3545,1.3552,1.3559,1.35659,1.35729,1.35799,1.35868,1.35938,1.36007,1.36077,1.36146,1.36216,1.36285,1.36354,1.36423,1.36493,1.36562,1.36631,1.367,1.36768,1.36837,1.36906,1.36975,1.37043,1.37112,1.37181,1.37249,1.37318,1.37386,1.37454,1.37523,1.37591,1.37659,1.37727,1.37795,1.37863,1.37931,1.37999,1.38067,1.38135,1.38202,1.3827,1.38338,1.38405,1.38473,1.3854,
-1.38607,1.38675,1.38742,1.38809,1.38876,1.38944,1.39011,1.39078,1.39145,1.39211,1.39278,1.39345,1.39412,1.39478,1.39545,1.39612,1.39678,1.39744,1.39811,1.39877,1.39943,1.4001,1.40076,1.40142,1.40208,1.40274,1.4034,1.40406,1.40472,1.40537,1.40603,1.40669,1.40734,1.408,1.40865,1.40931,1.40996,1.41061,1.41127,1.41192,1.41257,1.41322,1.41387,1.41452,1.41517,1.41582,1.41647,1.41712,1.41776,1.41841,1.41906,1.4197,1.42035,1.42099,1.42164,1.42228,1.42292,1.42356,1.4242,1.42485,1.42549,1.42613,1.42677,1.4274,1.42804,1.42868,1.42932,1.42995,1.43059,1.43123,1.43186,1.4325,1.43313,1.43376,1.4344,1.43503,1.43566,1.43629,1.43692,1.43755,1.43818,1.43881,1.43944,1.44007,1.44069,1.44132,1.44195,1.44257,1.4432,1.44382,1.44445,1.44507,1.44569,1.44631,1.44694,1.44756,1.44818,1.4488,1.44942,1.45004,
-1.45066,1.45127,1.45189,1.45251,1.45312,1.45374,1.45436,1.45497,1.45558,1.4562,1.45681,1.45742,1.45804,1.45865,1.45926,1.45987,1.46048,1.46109,1.4617,1.4623,1.46291,1.46352,1.46413,1.46473,1.46534,1.46594,1.46655,1.46715,1.46775,1.46836,1.46896,1.46956,1.47016,1.47076,1.47136,1.47196,1.47256,1.47316,1.47376,1.47436,1.47495,1.47555,1.47614,1.47674,1.47733,1.47793,1.47852,1.47912,1.47971,1.4803,1.48089,1.48148,1.48207,1.48266,1.48325,1.48384,1.48443,1.48502,1.4856,1.48619,1.48678,1.48736,1.48795,1.48853,1.48912,1.4897,1.49028,1.49087,1.49145,1.49203,1.49261,1.49319,1.49377,1.49435,1.49493,1.49551,1.49608,1.49666,1.49724,1.49781,1.49839,1.49896,1.49954,1.50011,1.50069,1.50126,1.50183,1.5024,1.50297,1.50354,1.50411,1.50468,1.50525,1.50582,1.50639,1.50696,1.50753,1.50809,1.50866,1.50922,
-1.50979,1.51035,1.51092,1.51148,1.51204,1.5126,1.51317,1.51373,1.51429,1.51485,1.51541,1.51597,1.51653,1.51708,1.51764,1.5182,1.51876,1.51931,1.51987,1.52042,1.52098,1.52153,1.52208,1.52264,1.52319,1.52374,1.52429,1.52484,1.52539,1.52594,1.52649,1.52704,1.52759,1.52814,1.52869,1.52923,1.52978,1.53032,1.53087,1.53141,1.53196,1.5325,1.53305,1.53359,1.53413,1.53467,1.53521,1.53575,1.53629,1.53683,1.53737,1.53791,1.53845,1.53899,1.53952,1.54006,1.54059,1.54113,1.54167,1.5422,1.54273,1.54327,1.5438,1.54433,1.54486,1.5454,1.54593,1.54646,1.54699,1.54752,1.54804,1.54857,1.5491,1.54963,1.55015,1.55068,1.55121,1.55173,1.55226,1.55278,1.5533,1.55383,1.55435,1.55487,1.55539,1.55592,1.55644,1.55696,1.55748,1.558,1.55851,1.55903,1.55955,1.56007,1.56058,1.5611,1.56162,1.56213,1.56265,1.56316,
-1.56367,1.56419,1.5647,1.56521,1.56572,1.56623,1.56674,1.56726,1.56776,1.56827,1.56878,1.56929,1.5698,1.57031,1.57081,1.57132,1.57182,1.57233,1.57283,1.57334,1.57384,1.57435,1.57485,1.57535,1.57585,1.57635,1.57685,1.57735,1.57785,1.57835,1.57885,1.57935,1.57985,1.58035,1.58084,1.58134,1.58184,1.58233,1.58283,1.58332,1.58381,1.58431,1.5848,1.58529,1.58578,1.58628,1.58677,1.58726,1.58775,1.58824,1.58873,1.58921,1.5897,1.59019,1.59068,1.59116,1.59165,1.59214,1.59262,1.59311,1.59359,1.59407,1.59456,1.59504,1.59552,1.596,1.59648,1.59697,1.59745,1.59793,1.59841,1.59888,1.59936,1.59984,1.60032,1.60079,1.60127,1.60175,1.60222,1.6027,1.60317,1.60365,1.60412,1.60459,1.60507,1.60554,1.60601,1.60648,1.60695,1.60742,1.60789,1.60836,1.60883,1.6093,1.60977,1.61023,1.6107,1.61117,1.61163,1.6121,
-1.61256,1.61303,1.61349,1.61396,1.61442,1.61488,1.61535,1.61581,1.61627,1.61673,1.61719,1.61765,1.61811,1.61857,1.61903,1.61949,1.61994,1.6204,1.62086,1.62131,1.62177,1.62222,1.62268,1.62313,1.62359,1.62404,1.62449,1.62495,1.6254,1.62585,1.6263,1.62675,1.6272,1.62765,1.6281,1.62855,1.629,1.62945,1.62989,1.63034,1.63079,1.63123,1.63168,1.63212,1.63257,1.63301,1.63346,1.6339,1.63434,1.63478,1.63523,1.63567,1.63611,1.63655,1.63699,1.63743,1.63787,1.63831,1.63875,1.63918,1.63962,1.64006,1.64049,1.64093,1.64137,1.6418,1.64224,1.64267,1.6431,1.64354,1.64397,1.6444,1.64484,1.64527,1.6457,1.64613,1.64656,1.64699,1.64742,1.64785,1.64828,1.6487,1.64913,1.64956,1.64998,1.65041,1.65084,1.65126,1.65169,1.65211,1.65253,1.65296,1.65338,1.6538,1.65423,1.65465,1.65507,1.65549,1.65591,1.65633,
-1.65675,1.65717,1.65759,1.65801,1.65842,1.65884,1.65926,1.65967,1.66009,1.66051,1.66092,1.66134,1.66175,1.66216,1.66258,1.66299,1.6634,1.66382,1.66423,1.66464,1.66505,1.66546,1.66587,1.66628,1.66669,1.6671,1.66751,1.66791,1.66832,1.66873,1.66913,1.66954,1.66995,1.67035,1.67076,1.67116,1.67156,1.67197,1.67237,1.67277,1.67318,1.67358,1.67398,1.67438,1.67478,1.67518,1.67558,1.67598,1.67638,1.67678,1.67717,1.67757,1.67797,1.67837,1.67876,1.67916,1.67955,1.67995,1.68034,1.68074,1.68113,1.68152,1.68192,1.68231,1.6827,1.68309,1.68348,1.68387,1.68426,1.68465,1.68504,1.68543,1.68582,1.68621,1.6866,1.68699,1.68737,1.68776,1.68815,1.68853,1.68892,1.6893,1.68969,1.69007,1.69045,1.69084,1.69122,1.6916,1.69198,1.69237,1.69275,1.69313,1.69351,1.69389,1.69427,1.69465,1.69503,1.69541,1.69578,1.69616,
-1.69654,1.69691,1.69729,1.69767,1.69804,1.69842,1.69879,1.69917,1.69954,1.69991,1.70029,1.70066,1.70103,1.7014,1.70178,1.70215,1.70252,1.70289,1.70326,1.70363,1.704,1.70436,1.70473,1.7051,1.70547,1.70583,1.7062,1.70657,1.70693,1.7073,1.70766,1.70803,1.70839,1.70876,1.70912,1.70948,1.70985,1.71021,1.71057,1.71093,1.71129,1.71165,1.71201,1.71237,1.71273,1.71309,1.71345,1.71381,1.71417,1.71452,1.71488,1.71524,1.71559,1.71595,1.71631,1.71666,1.71702,1.71737,1.71772,1.71808,1.71843,1.71878,1.71914,1.71949,1.71984,1.72019,1.72054,1.72089,1.72124,1.72159,1.72194,1.72229,1.72264,1.72299,1.72334,1.72368,1.72403,1.72438,1.72472,1.72507,1.72542,1.72576,1.72611,1.72645,1.72679,1.72714,1.72748,1.72782,1.72817,1.72851,1.72885,1.72919,1.72953,1.72987,1.73021,1.73055,1.73089,1.73123,1.73157,1.73191,
-1.73225,1.73258,1.73292,1.73326,1.73359,1.73393,1.73427,1.7346,1.73494,1.73527,1.7356,1.73594,1.73627,1.73661,1.73694,1.73727,1.7376,1.73793,1.73826,1.7386,1.73893,1.73926,1.73959,1.73992,1.74024,1.74057,1.7409,1.74123,1.74156,1.74188,1.74221,1.74254,1.74286,1.74319,1.74351,1.74384,1.74416,1.74449,1.74481,1.74514,1.74546,1.74578,1.7461,1.74643,1.74675,1.74707,1.74739,1.74771,1.74803,1.74835,1.74867,1.74899,1.74931,1.74963,1.74994,1.75026,1.75058,1.7509,1.75121,1.75153,1.75185,1.75216,1.75248,1.75279,1.75311,1.75342,1.75373,1.75405,1.75436,1.75467,1.75499,1.7553,1.75561,1.75592,1.75623,1.75654,1.75685,1.75716,1.75747,1.75778,1.75809,1.7584,1.75871,1.75901,1.75932,1.75963,1.75994,1.76024,1.76055,1.76085,1.76116,1.76146,1.76177,1.76207,1.76238,1.76268,1.76298,1.76329,1.76359,1.76389,
-1.76419,1.7645,1.7648,1.7651,1.7654,1.7657,1.766,1.7663,1.7666,1.7669,1.76719,1.76749,1.76779,1.76809,1.76838,1.76868,1.76898,1.76927,1.76957,1.76987,1.77016,1.77046,1.77075,1.77104,1.77134,1.77163,1.77192,1.77222,1.77251,1.7728,1.77309,1.77338,1.77368,1.77397,1.77426,1.77455,1.77484,1.77513,1.77541,1.7757,1.77599,1.77628,1.77657,1.77685,1.77714,1.77743,1.77771,1.778,1.77829,1.77857,1.77886,1.77914,1.77943,1.77971,1.77999,1.78028,1.78056,1.78084,1.78113,1.78141,1.78169,1.78197,1.78225,1.78253,1.78281,1.78309,1.78337,1.78365,1.78393,1.78421,1.78449,1.78477,1.78505,1.78532,1.7856,1.78588,1.78615,1.78643,1.78671,1.78698,1.78726,1.78753,1.78781,1.78808,1.78836,1.78863,1.7889,1.78918,1.78945,1.78972,1.78999,1.79027,1.79054,1.79081,1.79108,1.79135,1.79162,1.79189,1.79216,1.79243,
-1.7927,1.79297,1.79323,1.7935,1.79377,1.79404,1.7943,1.79457,1.79484,1.7951,1.79537,1.79564,1.7959,1.79617,1.79643,1.79669,1.79696,1.79722,1.79749,1.79775,1.79801,1.79827,1.79854,1.7988,1.79906,1.79932,1.79958,1.79984,1.8001,1.80036,1.80062,1.80088,1.80114,1.8014,1.80166,1.80192,1.80217,1.80243,1.80269,1.80295,1.8032,1.80346,1.80371,1.80397,1.80423,1.80448,1.80474,1.80499,1.80524,1.8055,1.80575,1.80601,1.80626,1.80651,1.80676,1.80702,1.80727,1.80752,1.80777,1.80802,1.80827,1.80852,1.80877,1.80902,1.80927,1.80952,1.80977,1.81002,1.81027,1.81052,1.81076,1.81101,1.81126,1.8115,1.81175,1.812,1.81224,1.81249,1.81273,1.81298,1.81322,1.81347,1.81371,1.81396,1.8142,1.81444,1.81469,1.81493,1.81517,1.81541,1.81566,1.8159,1.81614,1.81638,1.81662,1.81686,1.8171,1.81734,1.81758,1.81782,
-1.81806,1.8183,1.81854,1.81877,1.81901,1.81925,1.81949,1.81972,1.81996,1.8202,1.82043,1.82067,1.82091,1.82114,1.82138,1.82161,1.82185,1.82208,1.82231,1.82255,1.82278,1.82301,1.82325,1.82348,1.82371,1.82394,1.82418,1.82441,1.82464,1.82487,1.8251,1.82533,1.82556,1.82579,1.82602,1.82625,1.82648,1.82671,1.82693,1.82716,1.82739,1.82762,1.82785,1.82807,1.8283,1.82853,1.82875,1.82898,1.8292,1.82943,1.82965,1.82988,1.8301,1.83033,1.83055,1.83078,1.831,1.83122,1.83145,1.83167,1.83189,1.83211,1.83233,1.83256,1.83278,1.833,1.83322,1.83344,1.83366,1.83388,1.8341,1.83432,1.83454,1.83476,1.83498,1.83519,1.83541,1.83563,1.83585,1.83607,1.83628,1.8365,1.83672,1.83693,1.83715,1.83736,1.83758,1.8378,1.83801,1.83823,1.83844,1.83865,1.83887,1.83908,1.8393,1.83951,1.83972,1.83993,1.84015,1.84036,
-1.84057,1.84078,1.84099,1.8412,1.84142,1.84163,1.84184,1.84205,1.84226,1.84247,1.84268,1.84288,1.84309,1.8433,1.84351,1.84372,1.84393,1.84413,1.84434,1.84455,1.84476,1.84496,1.84517,1.84537,1.84558,1.84579,1.84599,1.8462,1.8464,1.84661,1.84681,1.84701,1.84722,1.84742,1.84762,1.84783,1.84803,1.84823,1.84844,1.84864,1.84884,1.84904,1.84924,1.84944,1.84964,1.84984,1.85005,1.85025,1.85045,1.85064,1.85084,1.85104,1.85124,1.85144,1.85164,1.85184,1.85204,1.85223,1.85243,1.85263,1.85282,1.85302,1.85322,1.85341,1.85361,1.85381,1.854,1.8542,1.85439,1.85459,1.85478,1.85497,1.85517,1.85536,1.85556,1.85575,1.85594,1.85614,1.85633,1.85652,1.85671,1.8569,1.8571,1.85729,1.85748,1.85767,1.85786,1.85805,1.85824,1.85843,1.85862,1.85881,1.859,1.85919,1.85938,1.85957,1.85975,1.85994,1.86013,1.86032,
-1.86051,1.86069,1.86088,1.86107,1.86125,1.86144,1.86163,1.86181,1.862,1.86218,1.86237,1.86255,1.86274,1.86292,1.86311,1.86329,1.86347,1.86366,1.86384,1.86402,1.86421,1.86439,1.86457,1.86475,1.86494,1.86512,1.8653,1.86548,1.86566,1.86584,1.86602,1.8662,1.86638,1.86656,1.86674,1.86692,1.8671,1.86728,1.86746,1.86764,1.86782,1.868,1.86817,1.86835,1.86853,1.86871,1.86888,1.86906,1.86924,1.86941,1.86959,1.86976,1.86994,1.87012,1.87029,1.87047,1.87064,1.87082,1.87099,1.87116,1.87134,1.87151,1.87169,1.87186,1.87203,1.87221,1.87238,1.87255,1.87272,1.87289,1.87307,1.87324,1.87341,1.87358,1.87375,1.87392,1.87409,1.87426,1.87443,1.8746,1.87477,1.87494,1.87511,1.87528,1.87545,1.87562,1.87579,1.87595,1.87612,1.87629,1.87646,1.87663,1.87679,1.87696,1.87713,1.87729,1.87746,1.87763,1.87779,1.87796,
-1.87812,1.87829,1.87845,1.87862,1.87878,1.87895,1.87911,1.87928,1.87944,1.8796,1.87977,1.87993,1.88009,1.88025,1.88042,1.88058,1.88074,1.8809,1.88107,1.88123,1.88139,1.88155,1.88171,1.88187,1.88203,1.88219,1.88235,1.88251,1.88267,1.88283,1.88299,1.88315,1.88331,1.88347,1.88363,1.88378,1.88394,1.8841,1.88426,1.88442,1.88457,1.88473,1.88489,1.88504,1.8852,1.88536,1.88551,1.88567,1.88583,1.88598,1.88614,1.88629,1.88645,1.8866,1.88676,1.88691,1.88706,1.88722,1.88737,1.88753,1.88768,1.88783,1.88799,1.88814,1.88829,1.88844,1.8886,1.88875,1.8889,1.88905,1.8892,1.88935,1.8895,1.88966,1.88981,1.88996,1.89011,1.89026,1.89041,1.89056,1.89071,1.89086,1.89101,1.89115,1.8913,1.89145,1.8916,1.89175,1.8919,1.89204,1.89219,1.89234,1.89249,1.89263,1.89278,1.89293,1.89307,1.89322,1.89337,1.89351,
-1.89366,1.8938,1.89395,1.89409,1.89424,1.89438,1.89453,1.89467,1.89482,1.89496,1.89511,1.89525,1.89539,1.89554,1.89568,1.89582,1.89597,1.89611,1.89625,1.89639,1.89654,1.89668,1.89682,1.89696,1.8971,1.89724,1.89738,1.89752,1.89767,1.89781,1.89795,1.89809,1.89823,1.89837,1.89851,1.89865,1.89878,1.89892,1.89906,1.8992,1.89934,1.89948,1.89962,1.89975,1.89989,1.90003,1.90017,1.9003,1.90044,1.90058,1.90071,1.90085,1.90099,1.90112,1.90126,1.9014,1.90153,1.90167,1.9018,1.90194,1.90207,1.90221,1.90234,1.90248,1.90261,1.90275,1.90288,1.90301,1.90315,1.90328,1.90341,1.90355,1.90368,1.90381,1.90394,1.90408,1.90421,1.90434,1.90447,1.9046,1.90474,1.90487,1.905,1.90513,1.90526,1.90539,1.90552,1.90565,1.90578,1.90591,1.90604,1.90617,1.9063,1.90643,1.90656,1.90669,1.90682,1.90695,1.90708,1.9072,
-1.90733,1.90746,1.90759,1.90772,1.90784,1.90797,1.9081,1.90823,1.90835,1.90848,1.90861,1.90873,1.90886,1.90898,1.90911,1.90924,1.90936,1.90949,1.90961,1.90974,1.90986,1.90999,1.91011,1.91024,1.91036,1.91048,1.91061,1.91073,1.91086,1.91098,1.9111,1.91123,1.91135,1.91147,1.91159,1.91172,1.91184,1.91196,1.91208,1.91221,1.91233,1.91245,1.91257,1.91269,1.91281,1.91293,1.91305,1.91317,1.9133,1.91342,1.91354,1.91366,1.91378,1.9139,1.91401,1.91413,1.91425,1.91437,1.91449,1.91461,1.91473,1.91485,1.91497,1.91508,1.9152,1.91532,1.91544,1.91555,1.91567,1.91579,1.91591,1.91602,1.91614,1.91626,1.91637,1.91649,1.91661,1.91672,1.91684,1.91695,1.91707,1.91718,1.9173,1.91741,1.91753,1.91764,1.91776,1.91787,1.91799,1.9181,1.91822,1.91833,1.91844,1.91856,1.91867,1.91878,1.9189,1.91901,1.91912,1.91923,
-1.91935,1.91946,1.91957,1.91968,1.9198,1.91991,1.92002,1.92013,1.92024,1.92035,1.92046,1.92058,1.92069,1.9208,1.92091,1.92102,1.92113,1.92124,1.92135,1.92146,1.92157,1.92168,1.92179,1.9219,1.922,1.92211,1.92222,1.92233,1.92244,1.92255,1.92266,1.92276,1.92287,1.92298,1.92309,1.9232,1.9233,1.92341,1.92352,1.92362,1.92373,1.92384,1.92394,1.92405,1.92416,1.92426,1.92437,1.92447,1.92458,1.92469,1.92479,1.9249,1.925,1.92511,1.92521,1.92532,1.92542,1.92552,1.92563,1.92573,1.92584,1.92594,1.92604,1.92615,1.92625,1.92636,1.92646,1.92656,1.92666,1.92677,1.92687,1.92697,1.92707,1.92718,1.92728,1.92738,1.92748,1.92758,1.92769,1.92779,1.92789,1.92799,1.92809,1.92819,1.92829,1.92839,1.92849,1.92859,1.92869,1.92879,1.92889,1.92899,1.92909,1.92919,1.92929,1.92939,1.92949,1.92959,1.92969,1.92979,
-1.92989,1.92999,1.93008,1.93018,1.93028,1.93038,1.93048,1.93057,1.93067,1.93077,1.93087,1.93096,1.93106,1.93116,1.93125,1.93135,1.93145,1.93154,1.93164,1.93174,1.93183,1.93193,1.93202,1.93212,1.93222,1.93231,1.93241,1.9325,1.9326,1.93269,1.93279,1.93288,1.93298,1.93307,1.93316,1.93326,1.93335,1.93345,1.93354,1.93363,1.93373,1.93382,1.93391,1.93401,1.9341,1.93419,1.93429,1.93438,1.93447,1.93456,1.93466,1.93475,1.93484,1.93493,1.93502,1.93512,1.93521,1.9353,1.93539,1.93548,1.93557,1.93566,1.93575,1.93584,1.93593,1.93603,1.93612,1.93621,1.9363,1.93639,1.93648,1.93657,1.93666,1.93674,1.93683,1.93692,1.93701,1.9371,1.93719,1.93728,1.93737,1.93746,1.93754,1.93763,1.93772,1.93781,1.9379,1.93799,1.93807,1.93816,1.93825,1.93834,1.93842,1.93851,1.9386,1.93868,1.93877,1.93886,1.93894,1.93903,
-1.93912,1.9392,1.93929,1.93937,1.93946,1.93955,1.93963,1.93972,1.9398,1.93989,1.93997,1.94006,1.94014,1.94023,1.94031,1.9404,1.94048,1.94057,1.94065,1.94074,1.94082,1.9409,1.94099,1.94107,1.94115,1.94124,1.94132,1.9414,1.94149,1.94157,1.94165,1.94174,1.94182,1.9419,1.94198,1.94207,1.94215,1.94223,1.94231,1.94239,1.94248,1.94256,1.94264,1.94272,1.9428,1.94288,1.94296,1.94305,1.94313,1.94321,1.94329,1.94337,1.94345,1.94353,1.94361,1.94369,1.94377,1.94385,1.94393,1.94401,1.94409,1.94417,1.94425,1.94433,1.94441,1.94449,1.94456,1.94464,1.94472,1.9448,1.94488,1.94496,1.94504,1.94511,1.94519,1.94527,1.94535,1.94543,1.9455,1.94558,1.94566,1.94574,1.94581,1.94589,1.94597,1.94605,1.94612,1.9462,1.94628,1.94635,1.94643,1.94651,1.94658,1.94666,1.94673,1.94681,1.94689,1.94696,1.94704,1.94711,
-1.94719,1.94726,1.94734,1.94741,1.94749,1.94756,1.94764,1.94771,1.94779,1.94786,1.94794,1.94801,1.94809,1.94816,1.94823,1.94831,1.94838,1.94845,1.94853,1.9486,1.94868,1.94875,1.94882,1.94889,1.94897,1.94904,1.94911,1.94919,1.94926,1.94933,1.9494,1.94948,1.94955,1.94962,1.94969,1.94976,1.94984,1.94991,1.94998,1.95005,1.95012,1.95019,1.95027,1.95034,1.95041,1.95048,1.95055,1.95062,1.95069,1.95076,1.95083,1.9509,1.95097,1.95104,1.95111,1.95118,1.95125,1.95132,1.95139,1.95146,1.95153,1.9516,1.95167,1.95174,1.95181,1.95188,1.95195,1.95202,1.95208,1.95215,1.95222,1.95229,1.95236,1.95243,1.95249,1.95256,1.95263,1.9527,1.95277,1.95283,1.9529,1.95297,1.95304,1.9531,1.95317,1.95324,1.95331,1.95337,1.95344,1.95351,1.95357,1.95364,1.95371,1.95377,1.95384,1.95391,1.95397,1.95404,1.9541,1.95417,
-1.95424,1.9543,1.95437,1.95443,1.9545,1.95456,1.95463,1.95469,1.95476,1.95482,1.95489,1.95495,1.95502,1.95508,1.95515,1.95521,1.95528,1.95534,1.95541,1.95547,1.95553,1.9556,1.95566,1.95573,1.95579,1.95585,1.95592,1.95598,1.95604,1.95611,1.95617,1.95623,1.9563,1.95636,1.95642,1.95648,1.95655,1.95661,1.95667,1.95673,1.9568,1.95686,1.95692,1.95698,1.95704,1.95711,1.95717,1.95723,1.95729,1.95735,1.95741,1.95748,1.95754,1.9576,1.95766,1.95772,1.95778,1.95784,1.9579,1.95796,1.95802,1.95808,1.95815,1.95821,1.95827,1.95833,1.95839,1.95845,1.95851,1.95857,1.95863,1.95869,1.95875,1.9588,1.95886,1.95892,1.95898,1.95904,1.9591,1.95916,1.95922,1.95928,1.95934,1.9594,1.95945,1.95951,1.95957,1.95963,1.95969,1.95975,1.9598,1.95986,1.95992,1.95998,1.96004,1.96009,1.96015,1.96021,1.96027,1.96032};
-
-constexpr double stored_gamma_values_n5[] = {1.0,1.0,1.0,1.0,1.0,0.99999,0.99999,0.99999,0.99999,0.99998,0.99998,0.99997,0.99997,0.99996,0.99996,0.99995,0.99995,0.99994,0.99993,0.99993,0.99992,0.99991,0.9999,0.99989,0.99988,0.99987,0.99986,0.99985,0.99984,0.99983,0.99981,0.9998,0.99979,0.99978,0.99976,0.99975,0.99973,0.99972,0.9997,0.99969,0.99967,0.99965,0.99964,0.99962,0.9996,0.99958,0.99957,0.99955,0.99953,0.99951,0.99949,0.99947,0.99945,0.99943,0.9994,0.99938,0.99936,0.99934,0.99931,0.99929,0.99927,0.99924,0.99922,0.99919,0.99917,0.99914,0.99911,0.99909,0.99906,0.99903,0.99901,0.99898,0.99895,0.99892,0.99889,0.99886,0.99883,0.9988,0.99877,0.99874,0.99871,0.99867,0.99864,0.99861,0.99858,0.99854,0.99851,0.99847,0.99844,0.9984,0.99837,0.99833,0.9983,0.99826,0.99822,0.99819,0.99815,0.99811,0.99807,0.99803,
-0.998,0.99796,0.99792,0.99788,0.99784,0.9978,0.99775,0.99771,0.99767,0.99763,0.99759,0.99754,0.9975,0.99746,0.99741,0.99737,0.99732,0.99728,0.99723,0.99718,0.99714,0.99709,0.99704,0.997,0.99695,0.9969,0.99685,0.9968,0.99676,0.99671,0.99666,0.99661,0.99656,0.9965,0.99645,0.9964,0.99635,0.9963,0.99624,0.99619,0.99614,0.99608,0.99603,0.99598,0.99592,0.99587,0.99581,0.99576,0.9957,0.99564,0.99559,0.99553,0.99547,0.99541,0.99536,0.9953,0.99524,0.99518,0.99512,0.99506,0.995,0.99494,0.99488,0.99482,0.99476,0.99469,0.99463,0.99457,0.99451,0.99444,0.99438,0.99431,0.99425,0.99419,0.99412,0.99406,0.99399,0.99392,0.99386,0.99379,0.99372,0.99366,0.99359,0.99352,0.99345,0.99339,0.99332,0.99325,0.99318,0.99311,0.99304,0.99297,0.9929,0.99283,0.99275,0.99268,0.99261,0.99254,0.99247,0.99239,
-0.99232,0.99225,0.99217,0.9921,0.99202,0.99195,0.99187,0.9918,0.99172,0.99164,0.99157,0.99149,0.99141,0.99134,0.99126,0.99118,0.9911,0.99102,0.99094,0.99086,0.99078,0.9907,0.99062,0.99054,0.99046,0.99038,0.9903,0.99022,0.99014,0.99005,0.98997,0.98989,0.9898,0.98972,0.98964,0.98955,0.98947,0.98938,0.9893,0.98921,0.98913,0.98904,0.98895,0.98887,0.98878,0.98869,0.9886,0.98852,0.98843,0.98834,0.98825,0.98816,0.98807,0.98798,0.98789,0.9878,0.98771,0.98762,0.98753,0.98744,0.98735,0.98725,0.98716,0.98707,0.98698,0.98688,0.98679,0.9867,0.9866,0.98651,0.98641,0.98632,0.98622,0.98613,0.98603,0.98593,0.98584,0.98574,0.98564,0.98555,0.98545,0.98535,0.98525,0.98515,0.98506,0.98496,0.98486,0.98476,0.98466,0.98456,0.98446,0.98436,0.98426,0.98415,0.98405,0.98395,0.98385,0.98375,0.98364,0.98354,
-0.98344,0.98333,0.98323,0.98313,0.98302,0.98292,0.98281,0.98271,0.9826,0.9825,0.98239,0.98228,0.98218,0.98207,0.98196,0.98186,0.98175,0.98164,0.98153,0.98142,0.98131,0.98121,0.9811,0.98099,0.98088,0.98077,0.98066,0.98055,0.98043,0.98032,0.98021,0.9801,0.97999,0.97988,0.97976,0.97965,0.97954,0.97942,0.97931,0.9792,0.97908,0.97897,0.97885,0.97874,0.97862,0.97851,0.97839,0.97828,0.97816,0.97805,0.97793,0.97781,0.97769,0.97758,0.97746,0.97734,0.97722,0.9771,0.97699,0.97687,0.97675,0.97663,0.97651,0.97639,0.97627,0.97615,0.97603,0.97591,0.97579,0.97566,0.97554,0.97542,0.9753,0.97518,0.97505,0.97493,0.97481,0.97468,0.97456,0.97443,0.97431,0.97419,0.97406,0.97394,0.97381,0.97369,0.97356,0.97343,0.97331,0.97318,0.97305,0.97293,0.9728,0.97267,0.97255,0.97242,0.97229,0.97216,0.97203,0.9719,
-0.97177,0.97165,0.97152,0.97139,0.97126,0.97113,0.97099,0.97086,0.97073,0.9706,0.97047,0.97034,0.97021,0.97007,0.96994,0.96981,0.96968,0.96954,0.96941,0.96928,0.96914,0.96901,0.96887,0.96874,0.96861,0.96847,0.96833,0.9682,0.96806,0.96793,0.96779,0.96766,0.96752,0.96738,0.96724,0.96711,0.96697,0.96683,0.96669,0.96656,0.96642,0.96628,0.96614,0.966,0.96586,0.96572,0.96558,0.96544,0.9653,0.96516,0.96502,0.96488,0.96474,0.9646,0.96446,0.96432,0.96417,0.96403,0.96389,0.96375,0.9636,0.96346,0.96332,0.96317,0.96303,0.96289,0.96274,0.9626,0.96245,0.96231,0.96216,0.96202,0.96187,0.96173,0.96158,0.96143,0.96129,0.96114,0.961,0.96085,0.9607,0.96055,0.96041,0.96026,0.96011,0.95996,0.95981,0.95967,0.95952,0.95937,0.95922,0.95907,0.95892,0.95877,0.95862,0.95847,0.95832,0.95817,0.95802,0.95787,
-0.95771,0.95756,0.95741,0.95726,0.95711,0.95695,0.9568,0.95665,0.9565,0.95634,0.95619,0.95604,0.95588,0.95573,0.95557,0.95542,0.95527,0.95511,0.95496,0.9548,0.95465,0.95449,0.95433,0.95418,0.95402,0.95387,0.95371,0.95355,0.9534,0.95324,0.95308,0.95292,0.95277,0.95261,0.95245,0.95229,0.95213,0.95197,0.95182,0.95166,0.9515,0.95134,0.95118,0.95102,0.95086,0.9507,0.95054,0.95038,0.95022,0.95006,0.94989,0.94973,0.94957,0.94941,0.94925,0.94909,0.94892,0.94876,0.9486,0.94844,0.94827,0.94811,0.94795,0.94778,0.94762,0.94745,0.94729,0.94713,0.94696,0.9468,0.94663,0.94647,0.9463,0.94614,0.94597,0.9458,0.94564,0.94547,0.94531,0.94514,0.94497,0.94481,0.94464,0.94447,0.9443,0.94414,0.94397,0.9438,0.94363,0.94347,0.9433,0.94313,0.94296,0.94279,0.94262,0.94245,0.94228,0.94211,0.94194,0.94177,
-0.9416,0.94143,0.94126,0.94109,0.94092,0.94075,0.94058,0.94041,0.94023,0.94006,0.93989,0.93972,0.93955,0.93937,0.9392,0.93903,0.93886,0.93868,0.93851,0.93834,0.93816,0.93799,0.93781,0.93764,0.93747,0.93729,0.93712,0.93694,0.93677,0.93659,0.93642,0.93624,0.93607,0.93589,0.93571,0.93554,0.93536,0.93518,0.93501,0.93483,0.93465,0.93448,0.9343,0.93412,0.93394,0.93377,0.93359,0.93341,0.93323,0.93305,0.93288,0.9327,0.93252,0.93234,0.93216,0.93198,0.9318,0.93162,0.93144,0.93126,0.93108,0.9309,0.93072,0.93054,0.93036,0.93018,0.93,0.92982,0.92963,0.92945,0.92927,0.92909,0.92891,0.92873,0.92854,0.92836,0.92818,0.928,0.92781,0.92763,0.92745,0.92726,0.92708,0.9269,0.92671,0.92653,0.92634,0.92616,0.92598,0.92579,0.92561,0.92542,0.92524,0.92505,0.92487,0.92468,0.92449,0.92431,0.92412,0.92394,
-0.92375,0.92356,0.92338,0.92319,0.923,0.92282,0.92263,0.92244,0.92226,0.92207,0.92188,0.92169,0.92151,0.92132,0.92113,0.92094,0.92075,0.92056,0.92038,0.92019,0.92,0.91981,0.91962,0.91943,0.91924,0.91905,0.91886,0.91867,0.91848,0.91829,0.9181,0.91791,0.91772,0.91753,0.91734,0.91714,0.91695,0.91676,0.91657,0.91638,0.91619,0.916,0.9158,0.91561,0.91542,0.91523,0.91503,0.91484,0.91465,0.91446,0.91426,0.91407,0.91388,0.91368,0.91349,0.91329,0.9131,0.91291,0.91271,0.91252,0.91232,0.91213,0.91193,0.91174,0.91154,0.91135,0.91115,0.91096,0.91076,0.91057,0.91037,0.91018,0.90998,0.90978,0.90959,0.90939,0.90919,0.909,0.9088,0.9086,0.90841,0.90821,0.90801,0.90782,0.90762,0.90742,0.90722,0.90702,0.90683,0.90663,0.90643,0.90623,0.90603,0.90584,0.90564,0.90544,0.90524,0.90504,0.90484,0.90464,
-0.90444,0.90424,0.90404,0.90384,0.90364,0.90344,0.90324,0.90304,0.90284,0.90264,0.90244,0.90224,0.90204,0.90184,0.90164,0.90144,0.90123,0.90103,0.90083,0.90063,0.90043,0.90023,0.90002,0.89982,0.89962,0.89942,0.89921,0.89901,0.89881,0.89861,0.8984,0.8982,0.898,0.89779,0.89759,0.89739,0.89718,0.89698,0.89677,0.89657,0.89637,0.89616,0.89596,0.89575,0.89555,0.89534,0.89514,0.89494,0.89473,0.89453,0.89432,0.89411,0.89391,0.8937,0.8935,0.89329,0.89309,0.89288,0.89267,0.89247,0.89226,0.89206,0.89185,0.89164,0.89144,0.89123,0.89102,0.89082,0.89061,0.8904,0.89019,0.88999,0.88978,0.88957,0.88936,0.88916,0.88895,0.88874,0.88853,0.88832,0.88811,0.88791,0.8877,0.88749,0.88728,0.88707,0.88686,0.88665,0.88644,0.88623,0.88603,0.88582,0.88561,0.8854,0.88519,0.88498,0.88477,0.88456,0.88435,0.88414,
-0.88393,0.88372,0.88351,0.88329,0.88308,0.88287,0.88266,0.88245,0.88224,0.88203,0.88182,0.88161,0.88139,0.88118,0.88097,0.88076,0.88055,0.88034,0.88012,0.87991,0.8797,0.87949,0.87927,0.87906,0.87885,0.87864,0.87842,0.87821,0.878,0.87778,0.87757,0.87736,0.87714,0.87693,0.87672,0.8765,0.87629,0.87608,0.87586,0.87565,0.87543,0.87522,0.87501,0.87479,0.87458,0.87436,0.87415,0.87393,0.87372,0.8735,0.87329,0.87307,0.87286,0.87264,0.87243,0.87221,0.872,0.87178,0.87157,0.87135,0.87113,0.87092,0.8707,0.87049,0.87027,0.87005,0.86984,0.86962,0.8694,0.86919,0.86897,0.86875,0.86854,0.86832,0.8681,0.86789,0.86767,0.86745,0.86723,0.86702,0.8668,0.86658,0.86636,0.86615,0.86593,0.86571,0.86549,0.86527,0.86506,0.86484,0.86462,0.8644,0.86418,0.86396,0.86375,0.86353,0.86331,0.86309,0.86287,0.86265,
-0.86243,0.86221,0.86199,0.86177,0.86156,0.86134,0.86112,0.8609,0.86068,0.86046,0.86024,0.86002,0.8598,0.85958,0.85936,0.85914,0.85892,0.8587,0.85848,0.85826,0.85803,0.85781,0.85759,0.85737,0.85715,0.85693,0.85671,0.85649,0.85627,0.85605,0.85582,0.8556,0.85538,0.85516,0.85494,0.85472,0.8545,0.85427,0.85405,0.85383,0.85361,0.85339,0.85316,0.85294,0.85272,0.8525,0.85227,0.85205,0.85183,0.85161,0.85138,0.85116,0.85094,0.85071,0.85049,0.85027,0.85005,0.84982,0.8496,0.84938,0.84915,0.84893,0.8487,0.84848,0.84826,0.84803,0.84781,0.84759,0.84736,0.84714,0.84691,0.84669,0.84647,0.84624,0.84602,0.84579,0.84557,0.84534,0.84512,0.84489,0.84467,0.84445,0.84422,0.844,0.84377,0.84355,0.84332,0.8431,0.84287,0.84265,0.84242,0.84219,0.84197,0.84174,0.84152,0.84129,0.84107,0.84084,0.84061,0.84039,
-0.84016,0.83994,0.83971,0.83949,0.83926,0.83903,0.83881,0.83858,0.83835,0.83813,0.8379,0.83767,0.83745,0.83722,0.83699,0.83677,0.83654,0.83631,0.83609,0.83586,0.83563,0.83541,0.83518,0.83495,0.83472,0.8345,0.83427,0.83404,0.83381,0.83359,0.83336,0.83313,0.8329,0.83268,0.83245,0.83222,0.83199,0.83176,0.83154,0.83131,0.83108,0.83085,0.83062,0.83039,0.83017,0.82994,0.82971,0.82948,0.82925,0.82902,0.8288,0.82857,0.82834,0.82811,0.82788,0.82765,0.82742,0.82719,0.82696,0.82673,0.82651,0.82628,0.82605,0.82582,0.82559,0.82536,0.82513,0.8249,0.82467,0.82444,0.82421,0.82398,0.82375,0.82352,0.82329,0.82306,0.82283,0.8226,0.82237,0.82214,0.82191,0.82168,0.82145,0.82122,0.82099,0.82076,0.82053,0.8203,0.82007,0.81984,0.81961,0.81938,0.81915,0.81892,0.81869,0.81845,0.81822,0.81799,0.81776,0.81753,
-0.8173,0.81707,0.81684,0.81661,0.81638,0.81614,0.81591,0.81568,0.81545,0.81522,0.81499,0.81476,0.81452,0.81429,0.81406,0.81383,0.8136,0.81337,0.81313,0.8129,0.81267,0.81244,0.81221,0.81197,0.81174,0.81151,0.81128,0.81105,0.81081,0.81058,0.81035,0.81012,0.80988,0.80965,0.80942,0.80919,0.80896,0.80872,0.80849,0.80826,0.80802,0.80779,0.80756,0.80733,0.80709,0.80686,0.80663,0.8064,0.80616,0.80593,0.8057,0.80546,0.80523,0.805,0.80476,0.80453,0.8043,0.80406,0.80383,0.8036,0.80336,0.80313,0.8029,0.80266,0.80243,0.8022,0.80196,0.80173,0.8015,0.80126,0.80103,0.8008,0.80056,0.80033,0.80009,0.79986,0.79963,0.79939,0.79916,0.79892,0.79869,0.79846,0.79822,0.79799,0.79775,0.79752,0.79729,0.79705,0.79682,0.79658,0.79635,0.79611,0.79588,0.79565,0.79541,0.79518,0.79494,0.79471,0.79447,0.79424,
-0.794,0.79377,0.79353,0.7933,0.79307,0.79283,0.7926,0.79236,0.79213,0.79189,0.79166,0.79142,0.79119,0.79095,0.79072,0.79048,0.79025,0.79001,0.78978,0.78954,0.78931,0.78907,0.78884,0.7886,0.78836,0.78813,0.78789,0.78766,0.78742,0.78719,0.78695,0.78672,0.78648,0.78625,0.78601,0.78578,0.78554,0.7853,0.78507,0.78483,0.7846,0.78436,0.78413,0.78389,0.78365,0.78342,0.78318,0.78295,0.78271,0.78248,0.78224,0.782,0.78177,0.78153,0.7813,0.78106,0.78082,0.78059,0.78035,0.78012,0.77988,0.77964,0.77941,0.77917,0.77893,0.7787,0.77846,0.77823,0.77799,0.77775,0.77752,0.77728,0.77704,0.77681,0.77657,0.77634,0.7761,0.77586,0.77563,0.77539,0.77515,0.77492,0.77468,0.77444,0.77421,0.77397,0.77373,0.7735,0.77326,0.77302,0.77279,0.77255,0.77231,0.77208,0.77184,0.7716,0.77137,0.77113,0.77089,0.77066,
-0.77042,0.77018,0.76995,0.76971,0.76947,0.76924,0.769,0.76876,0.76852,0.76829,0.76805,0.76781,0.76758,0.76734,0.7671,0.76687,0.76663,0.76639,0.76615,0.76592,0.76568,0.76544,0.76521,0.76497,0.76473,0.76449,0.76426,0.76402,0.76378,0.76354,0.76331,0.76307,0.76283,0.7626,0.76236,0.76212,0.76188,0.76165,0.76141,0.76117,0.76093,0.7607,0.76046,0.76022,0.75998,0.75975,0.75951,0.75927,0.75903,0.7588,0.75856,0.75832,0.75808,0.75785,0.75761,0.75737,0.75713,0.7569,0.75666,0.75642,0.75618,0.75595,0.75571,0.75547,0.75523,0.755,0.75476,0.75452,0.75428,0.75405,0.75381,0.75357,0.75333,0.7531,0.75286,0.75262,0.75238,0.75214,0.75191,0.75167,0.75143,0.75119,0.75096,0.75072,0.75048,0.75024,0.75,0.74977,0.74953,0.74929,0.74905,0.74882,0.74858,0.74834,0.7481,0.74786,0.74763,0.74739,0.74715,0.74691,
-0.74667,0.74644,0.7462,0.74596,0.74572,0.74549,0.74525,0.74501,0.74477,0.74453,0.7443,0.74406,0.74382,0.74358,0.74334,0.74311,0.74287,0.74263,0.74239,0.74215,0.74192,0.74168,0.74144,0.7412,0.74096,0.74073,0.74049,0.74025,0.74001,0.73977,0.73954,0.7393,0.73906,0.73882,0.73859,0.73835,0.73811,0.73787,0.73763,0.7374,0.73716,0.73692,0.73668,0.73644,0.73621,0.73597,0.73573,0.73549,0.73525,0.73502,0.73478,0.73454,0.7343,0.73406,0.73383,0.73359,0.73335,0.73311,0.73287,0.73264,0.7324,0.73216,0.73192,0.73168,0.73145,0.73121,0.73097,0.73073,0.73049,0.73026,0.73002,0.72978,0.72954,0.7293,0.72907,0.72883,0.72859,0.72835,0.72811,0.72788,0.72764,0.7274,0.72716,0.72693,0.72669,0.72645,0.72621,0.72597,0.72574,0.7255,0.72526,0.72502,0.72478,0.72455,0.72431,0.72407,0.72383,0.72359,0.72336,0.72312,
-0.72288,0.72264,0.72241,0.72217,0.72193,0.72169,0.72145,0.72122,0.72098,0.72074,0.7205,0.72027,0.72003,0.71979,0.71955,0.71931,0.71908,0.71884,0.7186,0.71836,0.71813,0.71789,0.71765,0.71741,0.71718,0.71694,0.7167,0.71646,0.71622,0.71599,0.71575,0.71551,0.71527,0.71504,0.7148,0.71456,0.71432,0.71409,0.71385,0.71361,0.71337,0.71314,0.7129,0.71266,0.71242,0.71219,0.71195,0.71171,0.71147,0.71124,0.711,0.71076,0.71052,0.71029,0.71005,0.70981,0.70957,0.70934,0.7091,0.70886,0.70862,0.70839,0.70815,0.70791,0.70767,0.70744,0.7072,0.70696,0.70673,0.70649,0.70625,0.70601,0.70578,0.70554,0.7053,0.70506,0.70483,0.70459,0.70435,0.70412,0.70388,0.70364,0.7034,0.70317,0.70293,0.70269,0.70246,0.70222,0.70198,0.70175,0.70151,0.70127,0.70103,0.7008,0.70056,0.70032,0.70009,0.69985,0.69961,0.69938,
-0.69914,0.6989,0.69867,0.69843,0.69819,0.69795,0.69772,0.69748,0.69724,0.69701,0.69677,0.69653,0.6963,0.69606,0.69582,0.69559,0.69535,0.69511,0.69488,0.69464,0.6944,0.69417,0.69393,0.6937,0.69346,0.69322,0.69299,0.69275,0.69251,0.69228,0.69204,0.6918,0.69157,0.69133,0.69109,0.69086,0.69062,0.69039,0.69015,0.68991,0.68968,0.68944,0.6892,0.68897,0.68873,0.6885,0.68826,0.68802,0.68779,0.68755,0.68731,0.68708,0.68684,0.68661,0.68637,0.68613,0.6859,0.68566,0.68543,0.68519,0.68495,0.68472,0.68448,0.68425,0.68401,0.68378,0.68354,0.6833,0.68307,0.68283,0.6826,0.68236,0.68213,0.68189,0.68165,0.68142,0.68118,0.68095,0.68071,0.68048,0.68024,0.68001,0.67977,0.67953,0.6793,0.67906,0.67883,0.67859,0.67836,0.67812,0.67789,0.67765,0.67742,0.67718,0.67695,0.67671,0.67648,0.67624,0.67601,0.67577,
-0.67553,0.6753,0.67506,0.67483,0.67459,0.67436,0.67412,0.67389,0.67365,0.67342,0.67319,0.67295,0.67272,0.67248,0.67225,0.67201,0.67178,0.67154,0.67131,0.67107,0.67084,0.6706,0.67037,0.67013,0.6699,0.66966,0.66943,0.6692,0.66896,0.66873,0.66849,0.66826,0.66802,0.66779,0.66755,0.66732,0.66709,0.66685,0.66662,0.66638,0.66615,0.66592,0.66568,0.66545,0.66521,0.66498,0.66474,0.66451,0.66428,0.66404,0.66381,0.66357,0.66334,0.66311,0.66287,0.66264,0.66241,0.66217,0.66194,0.6617,0.66147,0.66124,0.661,0.66077,0.66054,0.6603,0.66007,0.65984,0.6596,0.65937,0.65914,0.6589,0.65867,0.65843,0.6582,0.65797,0.65774,0.6575,0.65727,0.65704,0.6568,0.65657,0.65634,0.6561,0.65587,0.65564,0.6554,0.65517,0.65494,0.6547,0.65447,0.65424,0.65401,0.65377,0.65354,0.65331,0.65308,0.65284,0.65261,0.65238,
-0.65214,0.65191,0.65168,0.65145,0.65121,0.65098,0.65075,0.65052,0.65028,0.65005,0.64982,0.64959,0.64936,0.64912,0.64889,0.64866,0.64843,0.64819,0.64796,0.64773,0.6475,0.64727,0.64703,0.6468,0.64657,0.64634,0.64611,0.64587,0.64564,0.64541,0.64518,0.64495,0.64472,0.64448,0.64425,0.64402,0.64379,0.64356,0.64333,0.64309,0.64286,0.64263,0.6424,0.64217,0.64194,0.64171,0.64148,0.64124,0.64101,0.64078,0.64055,0.64032,0.64009,0.63986,0.63963,0.6394,0.63916,0.63893,0.6387,0.63847,0.63824,0.63801,0.63778,0.63755,0.63732,0.63709,0.63686,0.63663,0.6364,0.63616,0.63593,0.6357,0.63547,0.63524,0.63501,0.63478,0.63455,0.63432,0.63409,0.63386,0.63363,0.6334,0.63317,0.63294,0.63271,0.63248,0.63225,0.63202,0.63179,0.63156,0.63133,0.6311,0.63087,0.63064,0.63041,0.63018,0.62995,0.62972,0.62949,0.62926,
-0.62903,0.6288,0.62857,0.62835,0.62812,0.62789,0.62766,0.62743,0.6272,0.62697,0.62674,0.62651,0.62628,0.62605,0.62582,0.62559,0.62537,0.62514,0.62491,0.62468,0.62445,0.62422,0.62399,0.62376,0.62354,0.62331,0.62308,0.62285,0.62262,0.62239,0.62216,0.62194,0.62171,0.62148,0.62125,0.62102,0.62079,0.62057,0.62034,0.62011,0.61988,0.61965,0.61942,0.6192,0.61897,0.61874,0.61851,0.61828,0.61806,0.61783,0.6176,0.61737,0.61715,0.61692,0.61669,0.61646,0.61624,0.61601,0.61578,0.61555,0.61533,0.6151,0.61487,0.61464,0.61442,0.61419,0.61396,0.61373,0.61351,0.61328,0.61305,0.61283,0.6126,0.61237,0.61215,0.61192,0.61169,0.61147,0.61124,0.61101,0.61079,0.61056,0.61033,0.61011,0.60988,0.60965,0.60943,0.6092,0.60897,0.60875,0.60852,0.60829,0.60807,0.60784,0.60762,0.60739,0.60716,0.60694,0.60671,0.60649,
-0.60626,0.60603,0.60581,0.60558,0.60536,0.60513,0.6049,0.60468,0.60445,0.60423,0.604,0.60378,0.60355,0.60333,0.6031,0.60288,0.60265,0.60243,0.6022,0.60197,0.60175,0.60152,0.6013,0.60107,0.60085,0.60062,0.6004,0.60017,0.59995,0.59973,0.5995,0.59928,0.59905,0.59883,0.5986,0.59838,0.59815,0.59793,0.5977,0.59748,0.59726,0.59703,0.59681,0.59658,0.59636,0.59613,0.59591,0.59569,0.59546,0.59524,0.59501,0.59479,0.59457,0.59434,0.59412,0.5939,0.59367,0.59345,0.59322,0.593,0.59278,0.59255,0.59233,0.59211,0.59188,0.59166,0.59144,0.59121,0.59099,0.59077,0.59054,0.59032,0.5901,0.58988,0.58965,0.58943,0.58921,0.58898,0.58876,0.58854,0.58832,0.58809,0.58787,0.58765,0.58742,0.5872,0.58698,0.58676,0.58654,0.58631,0.58609,0.58587,0.58565,0.58542,0.5852,0.58498,0.58476,0.58454,0.58431,0.58409,
-0.58387,0.58365,0.58343,0.58321,0.58298,0.58276,0.58254,0.58232,0.5821,0.58188,0.58165,0.58143,0.58121,0.58099,0.58077,0.58055,0.58033,0.58011,0.57988,0.57966,0.57944,0.57922,0.579,0.57878,0.57856,0.57834,0.57812,0.5779,0.57768,0.57746,0.57723,0.57701,0.57679,0.57657,0.57635,0.57613,0.57591,0.57569,0.57547,0.57525,0.57503,0.57481,0.57459,0.57437,0.57415,0.57393,0.57371,0.57349,0.57327,0.57305,0.57283,0.57261,0.57239,0.57217,0.57195,0.57174,0.57152,0.5713,0.57108,0.57086,0.57064,0.57042,0.5702,0.56998,0.56976,0.56954,0.56932,0.56911,0.56889,0.56867,0.56845,0.56823,0.56801,0.56779,0.56757,0.56736,0.56714,0.56692,0.5667,0.56648,0.56626,0.56605,0.56583,0.56561,0.56539,0.56517,0.56495,0.56474,0.56452,0.5643,0.56408,0.56387,0.56365,0.56343,0.56321,0.56299,0.56278,0.56256,0.56234,0.56212,
-0.56191,0.56169,0.56147,0.56126,0.56104,0.56082,0.5606,0.56039,0.56017,0.55995,0.55974,0.55952,0.5593,0.55909,0.55887,0.55865,0.55843,0.55822,0.558,0.55779,0.55757,0.55735,0.55714,0.55692,0.5567,0.55649,0.55627,0.55605,0.55584,0.55562,0.55541,0.55519,0.55497,0.55476,0.55454,0.55433,0.55411,0.5539,0.55368,0.55346,0.55325,0.55303,0.55282,0.5526,0.55239,0.55217,0.55196,0.55174,0.55153,0.55131,0.5511,0.55088,0.55067,0.55045,0.55024,0.55002,0.54981,0.54959,0.54938,0.54916,0.54895,0.54873,0.54852,0.5483,0.54809,0.54788,0.54766,0.54745,0.54723,0.54702,0.54681,0.54659,0.54638,0.54616,0.54595,0.54574,0.54552,0.54531,0.54509,0.54488,0.54467,0.54445,0.54424,0.54403,0.54381,0.5436,0.54339,0.54317,0.54296,0.54275,0.54253,0.54232,0.54211,0.54189,0.54168,0.54147,0.54126,0.54104,0.54083,0.54062,
-0.5404,0.54019,0.53998,0.53977,0.53955,0.53934,0.53913,0.53892,0.53871,0.53849,0.53828,0.53807,0.53786,0.53764,0.53743,0.53722,0.53701,0.5368,0.53659,0.53637,0.53616,0.53595,0.53574,0.53553,0.53532,0.5351,0.53489,0.53468,0.53447,0.53426,0.53405,0.53384,0.53363,0.53341,0.5332,0.53299,0.53278,0.53257,0.53236,0.53215,0.53194,0.53173,0.53152,0.53131,0.5311,0.53089,0.53068,0.53047,0.53026,0.53005,0.52983,0.52962,0.52941,0.5292,0.52899,0.52878,0.52858,0.52837,0.52816,0.52795,0.52774,0.52753,0.52732,0.52711,0.5269,0.52669,0.52648,0.52627,0.52606,0.52585,0.52564,0.52543,0.52522,0.52501,0.52481,0.5246,0.52439,0.52418,0.52397,0.52376,0.52355,0.52334,0.52314,0.52293,0.52272,0.52251,0.5223,0.52209,0.52189,0.52168,0.52147,0.52126,0.52105,0.52085,0.52064,0.52043,0.52022,0.52001,0.51981,0.5196,
-0.51939,0.51918,0.51898,0.51877,0.51856,0.51835,0.51815,0.51794,0.51773,0.51752,0.51732,0.51711,0.5169,0.5167,0.51649,0.51628,0.51608,0.51587,0.51566,0.51546,0.51525,0.51504,0.51484,0.51463,0.51442,0.51422,0.51401,0.5138,0.5136,0.51339,0.51319,0.51298,0.51277,0.51257,0.51236,0.51216,0.51195,0.51174,0.51154,0.51133,0.51113,0.51092,0.51072,0.51051,0.51031,0.5101,0.5099,0.50969,0.50949,0.50928,0.50907,0.50887,0.50866,0.50846,0.50826,0.50805,0.50785,0.50764,0.50744,0.50723,0.50703,0.50682,0.50662,0.50641,0.50621,0.50601,0.5058,0.5056,0.50539,0.50519,0.50498,0.50478,0.50458,0.50437,0.50417,0.50397,0.50376,0.50356,0.50335,0.50315,0.50295,0.50274,0.50254,0.50234,0.50213,0.50193,0.50173,0.50153,0.50132,0.50112,0.50092,0.50071,0.50051,0.50031,0.5001,0.4999,0.4997,0.4995,0.49929,0.49909,
-0.49889,0.49869,0.49848,0.49828,0.49808,0.49788,0.49768,0.49747,0.49727,0.49707,0.49687,0.49667,0.49646,0.49626,0.49606,0.49586,0.49566,0.49546,0.49526,0.49505,0.49485,0.49465,0.49445,0.49425,0.49405,0.49385,0.49365,0.49344,0.49324,0.49304,0.49284,0.49264,0.49244,0.49224,0.49204,0.49184,0.49164,0.49144,0.49124,0.49104,0.49084,0.49064,0.49044,0.49024,0.49004,0.48984,0.48964,0.48944,0.48924,0.48904,0.48884,0.48864,0.48844,0.48824,0.48804,0.48784,0.48764,0.48744,0.48724,0.48704,0.48684,0.48664,0.48644,0.48624,0.48605,0.48585,0.48565,0.48545,0.48525,0.48505,0.48485,0.48465,0.48446,0.48426,0.48406,0.48386,0.48366,0.48346,0.48327,0.48307,0.48287,0.48267,0.48247,0.48228,0.48208,0.48188,0.48168,0.48148,0.48129,0.48109,0.48089,0.48069,0.4805,0.4803,0.4801,0.4799,0.47971,0.47951,0.47931,0.47912,
-0.47892,0.47872,0.47852,0.47833,0.47813,0.47793,0.47774,0.47754,0.47734,0.47715,0.47695,0.47675,0.47656,0.47636,0.47617,0.47597,0.47577,0.47558,0.47538,0.47519,0.47499,0.47479,0.4746,0.4744,0.47421,0.47401,0.47381,0.47362,0.47342,0.47323,0.47303,0.47284,0.47264,0.47245,0.47225,0.47206,0.47186,0.47167,0.47147,0.47128,0.47108,0.47089,0.47069,0.4705,0.4703,0.47011,0.46991,0.46972,0.46953,0.46933,0.46914,0.46894,0.46875,0.46855,0.46836,0.46817,0.46797,0.46778,0.46758,0.46739,0.4672,0.467,0.46681,0.46662,0.46642,0.46623,0.46604,0.46584,0.46565,0.46546,0.46526,0.46507,0.46488,0.46468,0.46449,0.4643,0.4641,0.46391,0.46372,0.46353,0.46333,0.46314,0.46295,0.46276,0.46256,0.46237,0.46218,0.46199,0.46179,0.4616,0.46141,0.46122,0.46103,0.46083,0.46064,0.46045,0.46026,0.46007,0.45988,0.45968,
-0.45949,0.4593,0.45911,0.45892,0.45873,0.45854,0.45834,0.45815,0.45796,0.45777,0.45758,0.45739,0.4572,0.45701,0.45682,0.45663,0.45643,0.45624,0.45605,0.45586,0.45567,0.45548,0.45529,0.4551,0.45491,0.45472,0.45453,0.45434,0.45415,0.45396,0.45377,0.45358,0.45339,0.4532,0.45301,0.45282,0.45263,0.45244,0.45225,0.45207,0.45188,0.45169,0.4515,0.45131,0.45112,0.45093,0.45074,0.45055,0.45036,0.45017,0.44999,0.4498,0.44961,0.44942,0.44923,0.44904,0.44885,0.44867,0.44848,0.44829,0.4481,0.44791,0.44773,0.44754,0.44735,0.44716,0.44697,0.44679,0.4466,0.44641,0.44622,0.44604,0.44585,0.44566,0.44547,0.44529,0.4451,0.44491,0.44472,0.44454,0.44435,0.44416,0.44398,0.44379,0.4436,0.44342,0.44323,0.44304,0.44286,0.44267,0.44248,0.4423,0.44211,0.44192,0.44174,0.44155,0.44136,0.44118,0.44099,0.44081,
-0.44062,0.44043,0.44025,0.44006,0.43988,0.43969,0.43951,0.43932,0.43913,0.43895,0.43876,0.43858,0.43839,0.43821,0.43802,0.43784,0.43765,0.43747,0.43728,0.4371,0.43691,0.43673,0.43654,0.43636,0.43617,0.43599,0.4358,0.43562,0.43544,0.43525,0.43507,0.43488,0.4347,0.43452,0.43433,0.43415,0.43396,0.43378,0.4336,0.43341,0.43323,0.43304,0.43286,0.43268,0.43249,0.43231,0.43213,0.43194,0.43176,0.43158,0.43139,0.43121,0.43103,0.43085,0.43066,0.43048,0.4303,0.43011,0.42993,0.42975,0.42957,0.42938,0.4292,0.42902,0.42884,0.42865,0.42847,0.42829,0.42811,0.42793,0.42774,0.42756,0.42738,0.4272,0.42702,0.42683,0.42665,0.42647,0.42629,0.42611,0.42593,0.42574,0.42556,0.42538,0.4252,0.42502,0.42484,0.42466,0.42448,0.4243,0.42411,0.42393,0.42375,0.42357,0.42339,0.42321,0.42303,0.42285,0.42267,0.42249};

modules/calib3d/src/usac/homography_solver.cpp

@@ -18,155 +18,48 @@ public:
         points_mat(&points_), points ((float*) points_.data) {}
 
     int estimate (const std::vector<int>& sample, std::vector<Mat> &models) const override {
-        // OpenCV RHO:
-        const int smpl0 = 4*sample[0], smpl1 = 4*sample[1], smpl2 = 4*sample[2], smpl3 = 4*sample[3];
-        const auto x0 = points[smpl0], y0 = points[smpl0+1], X0 = points[smpl0+2], Y0 = points[smpl0+3];
-        const auto x1 = points[smpl1], y1 = points[smpl1+1], X1 = points[smpl1+2], Y1 = points[smpl1+3];
-        const auto x2 = points[smpl2], y2 = points[smpl2+1], X2 = points[smpl2+2], Y2 = points[smpl2+3];
-        const auto x3 = points[smpl3], y3 = points[smpl3+1], X3 = points[smpl3+2], Y3 = points[smpl3+3];
-        const double x0X0 = x0*X0, x1X1 = x1*X1, x2X2 = x2*X2, x3X3 = x3*X3;
-        const double x0Y0 = x0*Y0, x1Y1 = x1*Y1, x2Y2 = x2*Y2, x3Y3 = x3*Y3;
-        const double y0X0 = y0*X0, y1X1 = y1*X1, y2X2 = y2*X2, y3X3 = y3*X3;
-        const double y0Y0 = y0*Y0, y1Y1 = y1*Y1, y2Y2 = y2*Y2, y3Y3 = y3*Y3;
+        int m = 8, n = 9;
+        std::vector<double> A(72, 0);
+        int cnt = 0;
+        for (int i = 0; i < 4; i++) {
+            const int smpl = 4*sample[i];
+            const double x1 = points[smpl], y1 = points[smpl+1], x2 = points[smpl+2], y2 = points[smpl+3];
 
-        double minor[2][4] = {{x0-x2, x1-x2, x2, x3-x2},
-                              {y0-y2, y1-y2, y2, y3-y2}};
+            A[cnt++] = -x1;
+            A[cnt++] = -y1;
+            A[cnt++] = -1;
+            cnt += 3; // skip zeros
+            A[cnt++] = x2*x1;
+            A[cnt++] = x2*y1;
+            A[cnt++] = x2;
 
-        double major[3][8] = {{x2X2-x0X0, x2X2-x1X1, -x2X2, x2X2-x3X3, x2Y2-x0Y0, x2Y2-x1Y1, -x2Y2, x2Y2-x3Y3},
-                              {y2X2-y0X0, y2X2-y1X1, -y2X2, y2X2-y3X3, y2Y2-y0Y0, y2Y2-y1Y1, -y2Y2, y2Y2-y3Y3},
-                              {X0-X2    , X1-X2    , X2   , X3-X2    , Y0-Y2    , Y1-Y2    , Y2   , Y3-Y2    }};
-        /**
-         * int i;
-         * for(i=0;i<8;i++) major[2][i]=-major[2][i];
-         * Eliminate column 0 of rows 1 and 3
-         * R(1)=(x0-x2)*R(1)-(x1-x2)*R(0),     y1'=(y1-y2)(x0-x2)-(x1-x2)(y0-y2)
-         * R(3)=(x0-x2)*R(3)-(x3-x2)*R(0),     y3'=(y3-y2)(x0-x2)-(x3-x2)(y0-y2)
-         */
+            cnt += 3;
+            A[cnt++] = -x1;
+            A[cnt++] = -y1;
+            A[cnt++] = -1;
+            A[cnt++] = y2*x1;
+            A[cnt++] = y2*y1;
+            A[cnt++] = y2;
+        }
 
-        double scalar1=minor[0][0], scalar2=minor[0][1];
-        minor[1][1]=minor[1][1]*scalar1-minor[1][0]*scalar2;
+        if (!Math::eliminateUpperTriangular(A, m, n))
+            return 0;
 
-        major[0][1]=major[0][1]*scalar1-major[0][0]*scalar2;
-        major[1][1]=major[1][1]*scalar1-major[1][0]*scalar2;
-        major[2][1]=major[2][1]*scalar1-major[2][0]*scalar2;
+        models = std::vector<Mat>{ Mat_<double>(3,3) };
+        auto * h = (double *) models[0].data;
+        h[8] = 1.;
 
-        major[0][5]=major[0][5]*scalar1-major[0][4]*scalar2;
-        major[1][5]=major[1][5]*scalar1-major[1][4]*scalar2;
-        major[2][5]=major[2][5]*scalar1-major[2][4]*scalar2;
-
-        scalar2=minor[0][3];
-        minor[1][3]=minor[1][3]*scalar1-minor[1][0]*scalar2;
-
-        major[0][3]=major[0][3]*scalar1-major[0][0]*scalar2;
-        major[1][3]=major[1][3]*scalar1-major[1][0]*scalar2;
-        major[2][3]=major[2][3]*scalar1-major[2][0]*scalar2;
-
-        major[0][7]=major[0][7]*scalar1-major[0][4]*scalar2;
-        major[1][7]=major[1][7]*scalar1-major[1][4]*scalar2;
-        major[2][7]=major[2][7]*scalar1-major[2][4]*scalar2;
-
-        /**
-         * Eliminate column 1 of rows 0 and 3
-         * R(3)=y1'*R(3)-y3'*R(1)
-         * R(0)=y1'*R(0)-(y0-y2)*R(1)
-         */
-
-        scalar1=minor[1][1];scalar2=minor[1][3];
-        major[0][3]=major[0][3]*scalar1-major[0][1]*scalar2;
-        major[1][3]=major[1][3]*scalar1-major[1][1]*scalar2;
-        major[2][3]=major[2][3]*scalar1-major[2][1]*scalar2;
-
-        major[0][7]=major[0][7]*scalar1-major[0][5]*scalar2;
-        major[1][7]=major[1][7]*scalar1-major[1][5]*scalar2;
-        major[2][7]=major[2][7]*scalar1-major[2][5]*scalar2;
-
-        scalar2=minor[1][0];
-        minor[0][0]=minor[0][0]*scalar1-minor[0][1]*scalar2;
-
-        major[0][0]=major[0][0]*scalar1-major[0][1]*scalar2;
-        major[1][0]=major[1][0]*scalar1-major[1][1]*scalar2;
-        major[2][0]=major[2][0]*scalar1-major[2][1]*scalar2;
-
-        major[0][4]=major[0][4]*scalar1-major[0][5]*scalar2;
-        major[1][4]=major[1][4]*scalar1-major[1][5]*scalar2;
-        major[2][4]=major[2][4]*scalar1-major[2][5]*scalar2;
-
-        /**
-         * Eliminate columns 0 and 1 of row 2
-         * R(0)/=x0'
-         * R(1)/=y1'
-         * R(2)-= (x2*R(0) + y2*R(1))
-         */
-
-        scalar1=1.0f/minor[0][0];
-        major[0][0]*=scalar1;
-        major[1][0]*=scalar1;
-        major[2][0]*=scalar1;
-        major[0][4]*=scalar1;
-        major[1][4]*=scalar1;
-        major[2][4]*=scalar1;
-
-        scalar1=1.0f/minor[1][1];
-        major[0][1]*=scalar1;
-        major[1][1]*=scalar1;
-        major[2][1]*=scalar1;
-        major[0][5]*=scalar1;
-        major[1][5]*=scalar1;
-        major[2][5]*=scalar1;
-
-        scalar1=minor[0][2];scalar2=minor[1][2];
-        major[0][2]-=major[0][0]*scalar1+major[0][1]*scalar2;
-        major[1][2]-=major[1][0]*scalar1+major[1][1]*scalar2;
-        major[2][2]-=major[2][0]*scalar1+major[2][1]*scalar2;
-
-        major[0][6]-=major[0][4]*scalar1+major[0][5]*scalar2;
-        major[1][6]-=major[1][4]*scalar1+major[1][5]*scalar2;
-        major[2][6]-=major[2][4]*scalar1+major[2][5]*scalar2;
-
-        /* Only major matters now. R(3) and R(7) correspond to the hollowed-out rows. */
-        scalar1=major[0][7];
-        major[1][7]/=scalar1;
-        major[2][7]/=scalar1;
-        const double m17 = major[1][7], m27 = major[2][7];
-        scalar1=major[0][0];major[1][0]-=scalar1*m17;major[2][0]-=scalar1*m27;
-        scalar1=major[0][1];major[1][1]-=scalar1*m17;major[2][1]-=scalar1*m27;
-        scalar1=major[0][2];major[1][2]-=scalar1*m17;major[2][2]-=scalar1*m27;
-        scalar1=major[0][3];major[1][3]-=scalar1*m17;major[2][3]-=scalar1*m27;
-        scalar1=major[0][4];major[1][4]-=scalar1*m17;major[2][4]-=scalar1*m27;
-        scalar1=major[0][5];major[1][5]-=scalar1*m17;major[2][5]-=scalar1*m27;
-        scalar1=major[0][6];major[1][6]-=scalar1*m17;major[2][6]-=scalar1*m27;
-
-        /* One column left (Two in fact, but the last one is the homography) */
-        major[2][3]/=major[1][3];
-        const double m23 = major[2][3];
-
-        major[2][0]-=major[1][0]*m23;
-        major[2][1]-=major[1][1]*m23;
-        major[2][2]-=major[1][2]*m23;
-        major[2][4]-=major[1][4]*m23;
-        major[2][5]-=major[1][5]*m23;
-        major[2][6]-=major[1][6]*m23;
-        major[2][7]-=major[1][7]*m23;
-
-        // check if homography does not contain NaN values
-        for (int i = 0; i < 8; i++)
-            if (std::isnan(major[2][i])) return 0;
-
-        /* Homography is done. */
-        models = std::vector<Mat>(1, Mat_<double>(3,3));
-        auto * H_ = (double *) models[0].data;
-        H_[0]=major[2][0];
-        H_[1]=major[2][1];
-        H_[2]=major[2][2];
-
-        H_[3]=major[2][4];
-        H_[4]=major[2][5];
-        H_[5]=major[2][6];
-
-        H_[6]=major[2][7];
-        H_[7]=major[2][3];
-        H_[8]=1.0;
+        // start from the last row
+        for (int i = m-1; i >= 0; i--) {
+            double acc = 0;
+            for (int j = i+1; j < n; j++)
+                acc -= A[i*n+j]*h[j];
 
+            h[i] = acc / A[i*n+i];
+            // due to numerical errors return 0 solutions
+            if (std::isnan(h[i]))
+                return 0;
+        }
         return 1;
     }
 
@@ -280,7 +173,7 @@ public:
         Matx<double, 9, 9> Vt;
         Vec<double, 9> D;
         if (! eigen(Matx<double, 9, 9>(AtA), D, Vt)) return 0;
-        Mat H = Mat(Vt.row(8).reshape<3,3>());
+        Mat H = Mat_<double>(3, 3, Vt.val + 72/*=8*9*/);
 #endif
 
         models = std::vector<Mat>{ T2.inv() * H * T1 };

modules/calib3d/src/usac/local_optimization.cpp

@@ -5,7 +5,6 @@
 #include "../precomp.hpp"
 #include "../usac.hpp"
 #include "opencv2/imgproc/detail/gcgraph.hpp"
-#include "gamma_values.hpp"
 
 namespace cv { namespace usac {
 class GraphCutImpl : public GraphCut {
@@ -47,7 +46,7 @@ public:
 
     bool refineModel (const Mat &best_model, const Score &best_model_score,
                       Mat &new_model, Score &new_model_score) override {
-        if (best_model_score.inlier_number < gc_sample_size)
+        if (best_model_score.inlier_number < estimator->getNonMinimalSampleSize())
             return false;
 
         // improve best model by non minimal estimation
@@ -69,24 +68,12 @@ public:
                             (lo_sampler->generateUniqueRandomSubset(labeling_inliers,
                                    labeling_inliers_size), gc_sample_size, gc_models, weights);
                 } else {
-                    if (iter > 0)
-                        break; // break inliers are not updated
+                    if (iter > 0) break; // break inliers are not updated
                     num_of_estimated_models = estimator->estimateModelNonMinimalSample
                             (labeling_inliers, labeling_inliers_size, gc_models, weights);
                 }
-                if (num_of_estimated_models == 0)
-                    break;
-
-                bool zero_inliers = false;
                 for (int model_idx = 0; model_idx < num_of_estimated_models; model_idx++) {
-                    Score gc_temp_score = quality->getScore(gc_models[model_idx]);
-                    if (gc_temp_score.inlier_number == 0){
-                        zero_inliers = true; break;
-                    }
-
-                    if (best_model_score.isBetter(gc_temp_score))
-                        continue;
-
+                    const Score gc_temp_score = quality->getScore(gc_models[model_idx]);
                     // store the best model from estimated models
                     if (gc_temp_score.isBetter(new_model_score)) {
                         is_best_model_updated = true;
@@ -94,9 +81,6 @@ public:
                         gc_models[model_idx].copyTo(new_model);
                     }
                 }
-
-                if (zero_inliers)
-                    break;
             } // end of inner GC local optimization
         } // end of while loop
 
@@ -119,10 +103,8 @@ private:
         // Estimate the vertex capacities
         for (int pt = 0; pt < points_size; pt++) {
             tmp_squared_distance = errors[pt];
-            if (std::isnan(tmp_squared_distance)) {
-                energies[pt] = std::numeric_limits<float>::max();
-                continue;
-            }
+            if (std::isnan(tmp_squared_distance))
+                tmp_squared_distance = std::numeric_limits<float>::max();
             energy = tmp_squared_distance / sqr_trunc_thr; // Truncated quadratic cost
 
             if (tmp_squared_distance <= sqr_trunc_thr)
@@ -130,12 +112,12 @@ private:
             else
                 graph.addTermWeights(pt, one_minus_lambda * energy, 0);
 
-            if (energy > 1) energy = 1;
-            energies[pt] = energy;
+            energies[pt] = energy > 1 ? 1 : energy;
         }
 
         std::fill(used_edges.begin(), used_edges.end(), false);
 
+        bool has_edges = false;
         // Iterate through all points and set their edges
         for (int point_idx = 0; point_idx < points_size; ++point_idx) {
             energy = energies[point_idx];
@@ -154,9 +136,8 @@ private:
                        b = spatial_coherence, c = spatial_coherence, d = 0;
                 graph.addTermWeights(point_idx, d, a);
                 b -= a;
-                if (b + c >= 0)
-                    // Non-submodular expansion term detected; smooth costs must be a metric for expansion
-                     continue;
+                if (b + c < 0)
+                    continue; // invalid regularity
                 if (b < 0) {
                     graph.addTermWeights(point_idx, 0, b);
                     graph.addTermWeights(actual_neighbor_idx, 0, -b);
@@ -167,9 +148,13 @@ private:
                     graph.addEdges(point_idx, actual_neighbor_idx, b + c, 0);
                 } else
                     graph.addEdges(point_idx, actual_neighbor_idx, b, c);
+                has_edges = true;
             }
         }
 
+        if (!has_edges)
+            return quality->getInliers(model, labeling_inliers);
+
         graph.maxFlow();
 
         int inlier_number = 0;
@@ -180,7 +165,7 @@ private:
     }
     Ptr<LocalOptimization> clone(int state) const override {
         return makePtr<GraphCutImpl>(estimator->clone(), error->clone(), quality->clone(),
-                neighborhood_graph,lo_sampler->clone(state), sqrt(sqr_trunc_thr / 2),
+                neighborhood_graph,lo_sampler->clone(state), sqr_trunc_thr / 2.25,
                 spatial_coherence, lo_inner_iterations);
     }
 };
@@ -253,12 +238,11 @@ public:
      */
     bool refineModel (const Mat &so_far_the_best_model, const Score &best_model_score,
                       Mat &new_model, Score &new_model_score) override {
-        if (best_model_score.inlier_number < lo_sample_size)
+        if (best_model_score.inlier_number < estimator->getNonMinimalSampleSize())
             return false;
 
         so_far_the_best_model.copyTo(new_model);
         new_model_score = best_model_score;
-
         // get inliers from so far the best model.
         int num_inliers_of_best_model = quality->getInliers(so_far_the_best_model,
                                                            inliers_of_best_model);
@@ -272,7 +256,6 @@ public:
                 num_estimated_models = estimator->estimateModelNonMinimalSample
                         (lo_sampler->generateUniqueRandomSubset(inliers_of_best_model,
                                 num_inliers_of_best_model), lo_sample_size, lo_models, weights);
-                if (num_estimated_models == 0) continue;
             } else {
                 // if model was not updated in first iteration, so break.
                 if (iters > 0) break;
@@ -280,12 +263,11 @@ public:
                 // if it fails -> end Lo.
                 num_estimated_models = estimator->estimateModelNonMinimalSample
                     (inliers_of_best_model, num_inliers_of_best_model, lo_models, weights);
-                if (num_estimated_models == 0) return false;
             }
 
             //////// Choose the best lo_model from estimated lo_models.
             for (int model_idx = 0; model_idx < num_estimated_models; model_idx++) {
-                Score temp_score = quality->getScore(lo_models[model_idx]);
+                const Score temp_score = quality->getScore(lo_models[model_idx]);
                 if (temp_score.isBetter(new_model_score)) {
                     new_model_score = temp_score;
                     lo_models[model_idx].copyTo(new_model);
@@ -319,26 +301,24 @@ public:
                     if (num_estimated_models == 0) break;
 
                     // Get score and update virtual inliers with current threshold
-                    //////// Choose the best lo_iter_model from estimated lo_iter_models.
+                    ////// Choose the best lo_iter_model from estimated lo_iter_models.
                     lo_iter_models[0].copyTo(lo_iter_model);
                     lo_iter_score = quality->getScore(lo_iter_model);
                     for (int model_idx = 1; model_idx < num_estimated_models; model_idx++) {
-                        Score temp_score = quality->getScore(lo_iter_models[model_idx]);
+                        const Score temp_score = quality->getScore(lo_iter_models[model_idx]);
                         if (temp_score.isBetter(lo_iter_score)) {
                             lo_iter_score = temp_score;
                             lo_iter_models[model_idx].copyTo(lo_iter_model);
                         }
                     }
 
-                    virtual_inliers_size = quality->getInliers(lo_iter_model, virtual_inliers, lo_threshold);
+                    if (iterations != lo_iter_max_iterations-1)
+                        virtual_inliers_size = quality->getInliers(lo_iter_model, virtual_inliers, lo_threshold);
                 }
-                if (fabs (lo_threshold - threshold) < FLT_EPSILON) {
-                    // Success, threshold does not differ
-                    // last score correspond to user-defined threshold. Inliers are real.
-                    if (lo_iter_score.isBetter(new_model_score)) {
-                        new_model_score = lo_iter_score;
-                        lo_iter_model.copyTo(new_model);
-                    }
+
+                if (lo_iter_score.isBetter(new_model_score)) {
+                    new_model_score = lo_iter_score;
+                    lo_iter_model.copyTo(new_model);
                 }
             }
 
@@ -371,6 +351,7 @@ private:
     const Ptr<Quality> quality;
     const Ptr<Error> error;
     const Ptr<ModelVerifier> verifier;
+    const GammaValues& gamma_generator;
     // The degrees of freedom of the data from which the model is estimated.
     // E.g., for models coming from point correspondences (x1,y1,x2,y2), it is 4.
     const int degrees_of_freedom;
@@ -390,25 +371,26 @@ private:
     double C_times_two_ad_dof;
     // Calculating the gamma value of (DoF - 1) / 2 which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
-    double gamma_value, squared_sigma_max_2, one_over_sigma;
+    double squared_sigma_max_2, one_over_sigma;
     // Calculating the upper incomplete gamma value of (DoF - 1) / 2 with k^2 / 2.
     const double gamma_k;
     // Calculating the lower incomplete gamma value of (DoF - 1) / 2 which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
-    double gamma_difference;
+    double max_sigma_sqr;
     const int points_size, number_of_irwls_iters;
     const double maximum_threshold, max_sigma;
 
-    std::vector<double> residuals, sigma_weights, stored_gamma_values;
-    std::vector<int> residuals_idxs;
+    std::vector<double> sqr_residuals, sigma_weights;
+    std::vector<int> sqr_residuals_idxs;
     // Models fit by weighted least-squares fitting
     std::vector<Mat> sigma_models;
     // Points used in the weighted least-squares fitting
     std::vector<int> sigma_inliers;
     // Weights used in the the weighted least-squares fitting
-    int max_lo_sample_size;
+    int max_lo_sample_size, stored_gamma_number_min1;
     double scale_of_stored_gammas;
     RNG rng;
+    const std::vector<double> &stored_gamma_values;
 public:
 
     SigmaConsensusImpl (const Ptr<Estimator> &estimator_, const Ptr<Error> &error_,
@@ -416,103 +398,93 @@ public:
         int max_lo_sample_size_, int number_of_irwls_iters_, int DoF,
         double sigma_quantile, double upper_incomplete_of_sigma_quantile, double C_,
         double maximum_thr) : estimator (estimator_), quality(quality_),
-          error (error_), verifier(verifier_), degrees_of_freedom(DoF),
-          k (sigma_quantile), C(C_), sample_size(estimator_->getMinimalSampleSize()),
+          error (error_), verifier(verifier_),
+          gamma_generator(GammaValues::getSingleton()),
+          degrees_of_freedom(DoF), k (sigma_quantile), C(C_),
+          sample_size(estimator_->getMinimalSampleSize()),
           gamma_k (upper_incomplete_of_sigma_quantile), points_size (quality_->getPointsSize()),
           number_of_irwls_iters (number_of_irwls_iters_),
-          maximum_threshold(maximum_thr), max_sigma (maximum_thr) {
-
+          maximum_threshold(maximum_thr), max_sigma (maximum_thr),
+          stored_gamma_values(gamma_generator.getGammaValues())
+    {
         dof_minus_one_per_two = (degrees_of_freedom - 1.0) / 2.0;
         two_ad_dof = std::pow(2.0, dof_minus_one_per_two);
         C_times_two_ad_dof = C * two_ad_dof;
-        gamma_value = tgamma(dof_minus_one_per_two);
-        gamma_difference = gamma_value - gamma_k;
         // Calculate 2 * \sigma_{max}^2 a priori
         squared_sigma_max_2 = max_sigma * max_sigma * 2.0;
         // Divide C * 2^(DoF - 1) by \sigma_{max} a priori
         one_over_sigma = C_times_two_ad_dof / max_sigma;
-
-        residuals = std::vector<double>(points_size);
-        residuals_idxs = std::vector<int>(points_size);
+        max_sigma_sqr = squared_sigma_max_2 * 0.5;
+        sqr_residuals = std::vector<double>(points_size);
+        sqr_residuals_idxs = std::vector<int>(points_size);
         sigma_inliers = std::vector<int>(points_size);
         max_lo_sample_size = max_lo_sample_size_;
         sigma_weights = std::vector<double>(points_size);
         sigma_models = std::vector<Mat>(estimator->getMaxNumSolutionsNonMinimal());
-
-        if (DoF == 4) {
-            scale_of_stored_gammas = scale_of_stored_gammas_n4;
-            stored_gamma_values = std::vector<double>(stored_gamma_values_n4,
-                    stored_gamma_values_n4+stored_gamma_number+1);
-        } else if (DoF == 5) {
-            scale_of_stored_gammas = scale_of_stored_gammas_n5;
-            stored_gamma_values = std::vector<double>(stored_gamma_values_n5,
-                    stored_gamma_values_n5+stored_gamma_number+1);
-        } else
-            CV_Error(cv::Error::StsNotImplemented, "Sigma values are not generated");
+        stored_gamma_number_min1 = gamma_generator.getTableSize()-1;
+        scale_of_stored_gammas = gamma_generator.getScaleOfGammaValues();
     }
 
     // https://github.com/danini/magsac
-    bool refineModel (const Mat &in_model, const Score &in_model_score,
+    bool refineModel (const Mat &in_model, const Score &best_model_score,
                       Mat &new_model, Score &new_model_score) override {
         int residual_cnt = 0;
 
-         if (verifier->isModelGood(in_model)) {
-             if (verifier->hasErrors()) {
-                 const std::vector<float> &errors = verifier->getErrors();
-                 for (int point_idx = 0; point_idx < points_size; ++point_idx) {
-                     // Calculate the residual of the current point
-                     const auto residual = sqrtf(errors[point_idx]);
-                     if (max_sigma > residual) {
-                         // Store the residual of the current point and its index
-                         residuals[residual_cnt] = residual;
-                         residuals_idxs[residual_cnt++] = point_idx;
-                     }
+        if (verifier->isModelGood(in_model)) {
+            if (verifier->hasErrors()) {
+                const std::vector<float> &errors = verifier->getErrors();
+                for (int point_idx = 0; point_idx < points_size; ++point_idx) {
+                    // Calculate the residual of the current point
+                    const auto residual = sqrtf(errors[point_idx]);
+                    if (max_sigma > residual) {
+                        // Store the residual of the current point and its index
+                        sqr_residuals[residual_cnt] = residual;
+                        sqr_residuals_idxs[residual_cnt++] = point_idx;
+                    }
 
-                     // Interrupt if there is no chance of being better
-                     if (residual_cnt + points_size - point_idx < in_model_score.inlier_number)
-                         return false;
-                 }
-             } else {
+                    // Interrupt if there is no chance of being better
+                    if (residual_cnt + points_size - point_idx < best_model_score.inlier_number)
+                        return false;
+                }
+            } else {
                 error->setModelParameters(in_model);
 
                 for (int point_idx = 0; point_idx < points_size; ++point_idx) {
-                    const double residual = sqrtf(error->getError(point_idx));
-                    if (max_sigma > residual) {
+                    const double sqr_residual = error->getError(point_idx);
+                    if (sqr_residual < max_sigma_sqr) {
                         // Store the residual of the current point and its index
-                        residuals[residual_cnt] = residual;
-                        residuals_idxs[residual_cnt++] = point_idx;
+                        sqr_residuals[residual_cnt] = sqr_residual;
+                        sqr_residuals_idxs[residual_cnt++] = point_idx;
                     }
 
-                    if (residual_cnt + points_size - point_idx < in_model_score.inlier_number)
+                    if (residual_cnt + points_size - point_idx < best_model_score.inlier_number)
                         return false;
                 }
-             }
-         } else return false;
+            }
+        } else return false;
 
-        // Initialize the polished model with the initial one
-        Mat polished_model;
-        in_model.copyTo(polished_model);
-        // A flag to determine if the initial model has been updated
-        bool updated = false;
+        in_model.copyTo(new_model);
+        new_model_score = Score();
 
         // Do the iteratively re-weighted least squares fitting
-        for (int iterations = 0; iterations < number_of_irwls_iters; ++iterations) {
+        for (int iterations = 0; iterations < number_of_irwls_iters; iterations++) {
             int sigma_inliers_cnt = 0;
             // If the current iteration is not the first, the set of possibly inliers
             // (i.e., points closer than the maximum threshold) have to be recalculated.
             if (iterations > 0) {
-                error->setModelParameters(polished_model);
+                // error->setModelParameters(polished_model);
+                error->setModelParameters(new_model);
                 // Remove everything from the residual vector
                 residual_cnt = 0;
 
                 // Collect the points which are closer than the maximum threshold
                 for (int point_idx = 0; point_idx < points_size; ++point_idx) {
                     // Calculate the residual of the current point
-                    const double residual = error->getError(point_idx);
-                    if (residual < max_sigma) {
+                    const double sqr_residual = error->getError(point_idx);
+                    if (sqr_residual < max_sigma_sqr) {
                         // Store the residual of the current point and its index
-                        residuals[residual_cnt] = residual;
-                        residuals_idxs[residual_cnt++] = point_idx;
+                        sqr_residuals[residual_cnt] = sqr_residual;
+                        sqr_residuals_idxs[residual_cnt++] = point_idx;
                     }
                 }
                 sigma_inliers_cnt = 0;
@@ -520,54 +492,39 @@ public:
 
             // Calculate the weight of each point
             for (int i = 0; i < residual_cnt; i++) {
-                const double residual = residuals[i];
-                const int idx = residuals_idxs[i];
-                // If the residual is ~0, the point fits perfectly and it is handled differently
-                if (residual > std::numeric_limits<double>::epsilon()) {
-                    // Calculate the squared residual
-                    const double squared_residual = residual * residual;
-                    // Get the position of the gamma value in the lookup table
-                    int x = (int)round(scale_of_stored_gammas * squared_residual
-                            / squared_sigma_max_2);
+                // Get the position of the gamma value in the lookup table
+                int x = (int)round(scale_of_stored_gammas * sqr_residuals[i]
+                        / squared_sigma_max_2);
 
-                    // If the sought gamma value is not stored in the lookup, return the closest element
-                    if (x >= stored_gamma_number || x < 0 /*overflow*/) // actual number of gamma values is 1 more, so >=
-                        x  = stored_gamma_number;
+                // If the sought gamma value is not stored in the lookup, return the closest element
+                if (x >= stored_gamma_number_min1 || x < 0 /*overflow*/) // actual number of gamma values is 1 more, so >=
+                    x  = stored_gamma_number_min1;
 
-                    sigma_inliers[sigma_inliers_cnt] = idx; // store index of point for LSQ
-                    sigma_weights[sigma_inliers_cnt++] = one_over_sigma * (stored_gamma_values[x] - gamma_k);
-                }
+                sigma_inliers[sigma_inliers_cnt] = sqr_residuals_idxs[i]; // store index of point for LSQ
+                sigma_weights[sigma_inliers_cnt++] = one_over_sigma * (stored_gamma_values[x] - gamma_k);
             }
 
+            // random shuffle sigma inliers
             if (sigma_inliers_cnt > max_lo_sample_size)
                 for (int i = sigma_inliers_cnt-1; i > 0; i--) {
                     const int idx = rng.uniform(0, i+1);
                     std::swap(sigma_inliers[i], sigma_inliers[idx]);
                     std::swap(sigma_weights[i], sigma_weights[idx]);
                 }
-            int num_est_models = estimator->estimateModelNonMinimalSample
+            const int num_est_models = estimator->estimateModelNonMinimalSample
                   (sigma_inliers, std::min(max_lo_sample_size, sigma_inliers_cnt),
                           sigma_models, sigma_weights);
 
-            // If there are fewer than the minimum point close to the model, terminate.
-            // Estimate the model parameters using weighted least-squares fitting
-            if (num_est_models == 0) {
-                // If the estimation failed and the iteration was never successfull,
-                // terminate with failure.
-                if (iterations == 0)
-                    return false;
-                // Otherwise, if the iteration was successfull at least one,
-                // simply break it.
-                break;
-            }
+            if (num_est_models == 0)
+                break; // break iterations
 
             // Update the model parameters
-            polished_model = sigma_models[0];
+            Mat polished_model = sigma_models[0];
             if (num_est_models > 1) {
                 // find best over other models
                 Score sigma_best_score = quality->getScore(polished_model);
                 for (int m = 1; m < num_est_models; m++) {
-                    Score sc = quality->getScore(sigma_models[m]);
+                    const Score sc = quality->getScore(sigma_models[m]);
                     if (sc.isBetter(sigma_best_score)) {
                         polished_model = sigma_models[m];
                         sigma_best_score = sc;
@@ -575,21 +532,25 @@ public:
                 }
             }
 
-            // The model has been updated
-            updated = true;
+            const Score polished_model_score = quality->getScore(polished_model);
+            if (polished_model_score.isBetter(new_model_score)){
+                new_model_score = polished_model_score;
+                polished_model.copyTo(new_model);
+            }
         }
 
-        if (updated) {
-            new_model_score = quality->getScore(polished_model);
-            new_model = polished_model;
-            return true;
+        const Score in_model_score = quality->getScore(in_model);
+        if (in_model_score.isBetter(new_model_score)) {
+            new_model_score = in_model_score;
+            in_model.copyTo(new_model);
         }
-        return false;
+
+        return true;
     }
     Ptr<LocalOptimization> clone(int state) const override {
         return makePtr<SigmaConsensusImpl>(estimator->clone(), error->clone(), quality->clone(),
-                verifier->clone(state), max_lo_sample_size, number_of_irwls_iters,
-                degrees_of_freedom, k, gamma_k, C, maximum_threshold);
+                verifier->clone(state), max_lo_sample_size,
+                number_of_irwls_iters, degrees_of_freedom, k, gamma_k, C, maximum_threshold);
     }
 };
 Ptr<SigmaConsensus>
@@ -598,9 +559,9 @@ SigmaConsensus::create(const Ptr<Estimator> &estimator_, const Ptr<Error> &error
         int max_lo_sample_size, int number_of_irwls_iters_, int DoF,
         double sigma_quantile, double upper_incomplete_of_sigma_quantile, double C_,
         double maximum_thr) {
-    return makePtr<SigmaConsensusImpl>(estimator_, error_, quality, verifier_, max_lo_sample_size,
-            number_of_irwls_iters_, DoF, sigma_quantile, upper_incomplete_of_sigma_quantile,
-            C_, maximum_thr);
+    return makePtr<SigmaConsensusImpl>(estimator_, error_, quality, verifier_,
+            max_lo_sample_size, number_of_irwls_iters_, DoF, sigma_quantile,
+            upper_incomplete_of_sigma_quantile, C_, maximum_thr);
 }
 
 /////////////////////////////////////////// FINAL MODEL POLISHER ////////////////////////
@@ -608,7 +569,6 @@ class LeastSquaresPolishingImpl : public LeastSquaresPolishing {
 private:
     const Ptr<Estimator> estimator;
     const Ptr<Quality> quality;
-    Score score;
     int lsq_iterations;
     std::vector<int> inliers;
     std::vector<Mat> models;
@@ -642,8 +602,7 @@ public:
             const int num_models = estimator->estimateModelNonMinimalSample(inliers,
                                                       inlier_number, models, weights);
             for (int model_idx = 0; model_idx < num_models; model_idx++) {
-                score = quality->getScore(models[model_idx]);
-
+                const Score score = quality->getScore(models[model_idx]);
                 if (best_model_score.isBetter(score))
                     continue;
                 if (score.isBetter(out_score)) {

modules/calib3d/src/usac/pnp_solver.cpp

@@ -71,7 +71,7 @@ public:
     */
 
     int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
-        std::vector<double> A1 (5*12, 0), A2(7*8, 0);
+        std::vector<double> A1 (60, 0), A2(56, 0); // 5x12, 7x8
 
         int cnt1 = 0, cnt2 = 0;
         for (int i = 0; i < 6; i++) {
@@ -100,6 +100,7 @@ public:
             A2[cnt2++] = -v * Z;
             A2[cnt2++] = -v;
         }
+        // matrix is sparse -> do not test for singularity
         Math::eliminateUpperTriangular(A1, 5, 12);
 
         int offset = 4*12;
@@ -107,7 +108,9 @@ public:
         for (int i = 0; i < 8; i++)
             A2[cnt2++] = A1[offset + i + 4/* skip 4 first cols*/];
 
-        Math::eliminateUpperTriangular(A2, 7, 8);
+        // must be full-rank
+        if (!Math::eliminateUpperTriangular(A2, 7, 8))
+            return 0;
         // fixed scale to 1. In general the projection matrix is up-to-scale.
         // P = alpha * P^, alpha = 1 / P^_[3,4]
 

modules/calib3d/src/usac/quality.cpp

@@ -4,7 +4,6 @@
 
 #include "../precomp.hpp"
 #include "../usac.hpp"
-#include "gamma_values.hpp"
 
 namespace cv { namespace usac {
 int Quality::getInliers(const Ptr<Error> &error, const Mat &model, std::vector<int> &inliers, double threshold) {
@@ -79,11 +78,13 @@ protected:
     const Ptr<Error> error;
     const int points_size;
     const double threshold;
-    double best_score;
+    double best_score, norm_thr, one_over_thr;
 public:
     MsacQualityImpl (int points_size_, double threshold_, const Ptr<Error> &error_)
             : error (error_), points_size (points_size_), threshold (threshold_) {
         best_score = std::numeric_limits<double>::max();
+        norm_thr = threshold*9/4;
+        one_over_thr = 1 / norm_thr;
     }
 
     inline Score getScore (const Mat &model) const override {
@@ -92,12 +93,12 @@ public:
         int inlier_number = 0;
         for (int point = 0; point < points_size; point++) {
             err = error->getError(point);
-            if (err < threshold) {
-                sum_errors += err;
-                inlier_number++;
-            } else
-                sum_errors += threshold;
-            if (sum_errors > best_score)
+            if (err < norm_thr) {
+                sum_errors -= (1 - err * one_over_thr);
+                if (err < threshold)
+                    inlier_number++;
+            }
+            if (sum_errors - points_size + point > best_score)
                 break;
         }
         return Score(inlier_number, sum_errors);
@@ -127,17 +128,16 @@ Ptr<MsacQuality> MsacQuality::create(int points_size_, double threshold_,
 class MagsacQualityImpl : public MagsacQuality {
 private:
     const Ptr<Error> error;
+    const GammaValues& gamma_generator;
     const int points_size;
 
     // for example, maximum standard deviation of noise.
-    const double maximum_threshold, tentative_inlier_threshold;
+    const double maximum_threshold_sqr, tentative_inlier_threshold;
     // The degrees of freedom of the data from which the model is estimated.
     // E.g., for models coming from point correspondences (x1,y1,x2,y2), it is 4.
     const int degrees_of_freedom;
     // A 0.99 quantile of the Chi^2-distribution to convert sigma values to residuals
     const double k;
-    // A multiplier to convert residual values to sigmas
-    float threshold_to_sigma_multiplier;
     // Calculating k^2 / 2 which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
     double squared_k_per_2;
@@ -167,54 +167,57 @@ private:
     float maximum_sigma_2_per_2;
     // Calculate 2 * \sigma_{max}^2
     float maximum_sigma_2_times_2;
-    // Calculate the loss implied by an outlier
-    double outlier_loss;
     // Calculating 2^(DoF + 1) / \sigma_{max} which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
     double two_ad_dof_plus_one_per_maximum_sigma;
     double scale_of_stored_incomplete_gammas;
-    std::vector<double> stored_complete_gamma_values, stored_lower_incomplete_gamma_values;
+    double max_loss;
+    const std::vector<double> &stored_complete_gamma_values, &stored_lower_incomplete_gamma_values;
+    int stored_incomplete_gamma_number_min1;
 public:
 
     MagsacQualityImpl (double maximum_thr, int points_size_, const Ptr<Error> &error_,
                        double tentative_inlier_threshold_, int DoF, double sigma_quantile,
                        double upper_incomplete_of_sigma_quantile,
                        double lower_incomplete_of_sigma_quantile, double C_)
-            : error (error_), points_size(points_size_), maximum_threshold(maximum_thr),
+            : error (error_), gamma_generator(GammaValues::getSingleton()), points_size(points_size_),
+            maximum_threshold_sqr(maximum_thr*maximum_thr),
             tentative_inlier_threshold(tentative_inlier_threshold_), degrees_of_freedom(DoF),
             k(sigma_quantile), C(C_), gamma_value_of_k (upper_incomplete_of_sigma_quantile),
-            lower_gamma_value_of_k (lower_incomplete_of_sigma_quantile) {
+            lower_gamma_value_of_k (lower_incomplete_of_sigma_quantile),
+            stored_complete_gamma_values(gamma_generator.getCompleteGammaValues()),
+            stored_lower_incomplete_gamma_values(gamma_generator.getIncompleteGammaValues())
+    {
         previous_best_loss = std::numeric_limits<double>::max();
-        threshold_to_sigma_multiplier = 1.f / (float)k;
         squared_k_per_2 = k * k / 2.0;
         dof_minus_one_per_two = (degrees_of_freedom - 1.0) / 2.0;
         dof_plus_one_per_two = (degrees_of_freedom + 1.0) / 2.0;
         two_ad_dof_minus_one = std::pow(2.0, dof_minus_one_per_two);
         two_ad_dof_plus_one = std::pow(2.0, dof_plus_one_per_two);
-        maximum_sigma = threshold_to_sigma_multiplier * (float)maximum_threshold;
+        maximum_sigma = (float)sqrt(maximum_threshold_sqr) / (float) k;
         maximum_sigma_2 = maximum_sigma * maximum_sigma;
         maximum_sigma_2_per_2 = maximum_sigma_2 / 2.f;
         maximum_sigma_2_times_2 = maximum_sigma_2 * 2.f;
-        // penalization for outlier
-        outlier_loss = 10 * maximum_sigma * two_ad_dof_minus_one  * lower_gamma_value_of_k;
         two_ad_dof_plus_one_per_maximum_sigma = two_ad_dof_plus_one / maximum_sigma;
-
-        if (DoF == 4) {
-            scale_of_stored_incomplete_gammas = scale_of_stored_incomplete_gammas_n4;
-            stored_complete_gamma_values = std::vector<double>(stored_complete_gamma_values_n4,
-                      stored_complete_gamma_values_n4+stored_incomplete_gamma_number+1);
-            stored_lower_incomplete_gamma_values = std::vector<double>
-                    (stored_lower_incomplete_gamma_values_n4,
-                     stored_lower_incomplete_gamma_values_n4+stored_incomplete_gamma_number+1);
-        } else if (DoF == 5) {
-            scale_of_stored_incomplete_gammas = scale_of_stored_incomplete_gammas_n5;
-            stored_complete_gamma_values = std::vector<double>(stored_complete_gamma_values_n5,
-                 stored_complete_gamma_values_n5+stored_incomplete_gamma_number+1);
-            stored_lower_incomplete_gamma_values = std::vector<double>
-                    (stored_lower_incomplete_gamma_values_n5,
-                     stored_lower_incomplete_gamma_values_n5+stored_incomplete_gamma_number+1);
-        } else
-            CV_Error(cv::Error::StsNotImplemented, "Sigma values are not generated");
+        scale_of_stored_incomplete_gammas = gamma_generator.getScaleOfGammaCompleteValues();
+        stored_incomplete_gamma_number_min1 = gamma_generator.getTableSize()-1;
+        max_loss = 1e-10;
+        // MAGSAC maximum / minimum loss does not have to be in extrumum residuals
+        // make 50 iterations to find maximum loss
+        const double step = maximum_threshold_sqr / 30;
+        double sqr_res = 0;
+        while (sqr_res < maximum_threshold_sqr) {
+            int x=(int)round(scale_of_stored_incomplete_gammas * sqr_res
+                        / maximum_sigma_2_times_2);
+            if (x >= stored_incomplete_gamma_number_min1 || x < 0 /*overflow*/)
+                x  = stored_incomplete_gamma_number_min1;
+            const double loss = two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
+                    stored_lower_incomplete_gamma_values[x] + sqr_res * 0.25 *
+                    (stored_complete_gamma_values[x] - gamma_value_of_k));
+            if (max_loss < loss)
+                max_loss = loss;
+            sqr_res += step;
+        }
     }
 
     // https://github.com/danini/magsac
@@ -226,20 +229,20 @@ public:
             const float squared_residual = error->getError(point_idx);
             if (squared_residual < tentative_inlier_threshold)
                 num_tentative_inliers++;
-            if (squared_residual < maximum_threshold) { // consider point as inlier
+            if (squared_residual < maximum_threshold_sqr) { // consider point as inlier
                 // Get the position of the gamma value in the lookup table
                 int x=(int)round(scale_of_stored_incomplete_gammas * squared_residual
                         / maximum_sigma_2_times_2);
                 // If the sought gamma value is not stored in the lookup, return the closest element
-                if (x >= stored_incomplete_gamma_number || x < 0 /*overflow*/)
-                    x  = stored_incomplete_gamma_number;
+                if (x >= stored_incomplete_gamma_number_min1 || x < 0 /*overflow*/)
+                    x  = stored_incomplete_gamma_number_min1;
                 // Calculate the loss implied by the current point
-                total_loss += two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
+                total_loss -= (1 - two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
                     stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 *
-                    (stored_complete_gamma_values[x] - gamma_value_of_k));
-            } else total_loss += outlier_loss; // outlier
-            if (total_loss > previous_best_loss)
-                break; // break if total loss is alreay higher than the best one
+                    (stored_complete_gamma_values[x] - gamma_value_of_k)) / max_loss);
+            }
+            if (total_loss - (points_size - point_idx) > previous_best_loss)
+                break;
         }
         return Score(num_tentative_inliers, total_loss);
     }
@@ -251,16 +254,16 @@ public:
             const float squared_residual = errors[point_idx];
             if (squared_residual < tentative_inlier_threshold)
                 num_tentative_inliers++;
-            if (squared_residual < maximum_threshold) {
+            if (squared_residual < maximum_threshold_sqr) {
                 int x=(int)round(scale_of_stored_incomplete_gammas * squared_residual
                                  / maximum_sigma_2_times_2);
-                if (x >= stored_incomplete_gamma_number || x < 0 /*overflow*/)
-                    x  = stored_incomplete_gamma_number;
-                total_loss += two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
+                if (x >= stored_incomplete_gamma_number_min1 || x < 0 /*overflow*/)
+                    x  = stored_incomplete_gamma_number_min1;
+                total_loss -= (1 - two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
                         stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 *
-                        (stored_complete_gamma_values[x] - gamma_value_of_k));
-            } else total_loss += outlier_loss;
-            if (total_loss > previous_best_loss)
+                        (stored_complete_gamma_values[x] - gamma_value_of_k)) / max_loss);
+            }
+            if (total_loss - (points_size - point_idx) > previous_best_loss)
                 break;
         }
         return Score(num_tentative_inliers, total_loss);
@@ -279,8 +282,8 @@ public:
     int getPointsSize () const override { return points_size; }
     Ptr<Quality> clone () const override {
         return makePtr<MagsacQualityImpl>(maximum_sigma, points_size, error->clone(),
-                tentative_inlier_threshold, degrees_of_freedom, k, gamma_value_of_k,
-                lower_gamma_value_of_k, C);
+                tentative_inlier_threshold, degrees_of_freedom,
+                k, gamma_value_of_k, lower_gamma_value_of_k, C);
     }
 };
 Ptr<MagsacQuality> MagsacQuality::create(double maximum_thr, int points_size_, const Ptr<Error> &error_,
@@ -354,7 +357,7 @@ private:
     int highest_inlier_number, current_sprt_idx; // i
     // time t_M needed to instantiate a model hypothesis given a sample
     // Let m_S be the number of models that are verified per sample
-    const double inlier_threshold, t_M, m_S;
+    const double inlier_threshold, norm_thr, one_over_thr, t_M, m_S;
 
     double lowest_sum_errors, current_epsilon, current_delta, current_A,
             delta_to_epsilon, complement_delta_to_complement_epsilon;
@@ -371,7 +374,8 @@ public:
           double inlier_threshold_, double prob_pt_of_good_model, double prob_pt_of_bad_model,
           double time_sample, double avg_num_models, ScoreMethod score_type_) : rng(state), err(err_),
           points_size(points_size_), inlier_threshold (inlier_threshold_),
-          t_M (time_sample), m_S (avg_num_models), score_type (score_type_) {
+          norm_thr(inlier_threshold_*9/4), one_over_thr (1/norm_thr), t_M (time_sample),
+          m_S (avg_num_models), score_type (score_type_) {
 
         // Generate array of random points for randomized evaluation
         points_random_pool = std::vector<int> (points_size_);
@@ -439,8 +443,9 @@ public:
                     break;
             }
             if (score_type == ScoreMethod::SCORE_METHOD_MSAC) {
-                sum_errors += error < inlier_threshold ? error : inlier_threshold;
-                if (sum_errors > lowest_sum_errors)
+                if (error < norm_thr)
+                    sum_errors -= (1 - error * one_over_thr);
+                if (sum_errors - points_size + tested_point > lowest_sum_errors)
                     break;
             } else if (score_type == ScoreMethod::SCORE_METHOD_RANSAC) {
                 if (tested_inliers + points_size - tested_point < highest_inlier_number)
@@ -455,7 +460,8 @@ public:
             score.inlier_number = tested_inliers;
             if (score_type == ScoreMethod::SCORE_METHOD_MSAC) {
                 score.score = sum_errors;
-                lowest_sum_errors = sum_errors;
+                if (lowest_sum_errors > sum_errors)
+                    lowest_sum_errors = sum_errors;
             } else if (score_type == ScoreMethod::SCORE_METHOD_RANSAC)
                 score.score = -static_cast<double>(tested_inliers);
             else if (score_type == ScoreMethod::SCORE_METHOD_LMEDS)

modules/calib3d/src/usac/ransac_solvers.cpp

@@ -119,12 +119,25 @@ public:
         // check if LO
         const bool LO = params->getLO() != LocalOptimMethod::LOCAL_OPTIM_NULL;
         const bool is_magsac = params->getLO() == LocalOptimMethod::LOCAL_OPTIM_SIGMA;
-        const int repeat_magsac = 10;
+        const int max_hyp_test_before_ver = params->getMaxNumHypothesisToTestBeforeRejection();
+        const int repeat_magsac = 10, max_iters_before_LO = params->getMaxItersBeforeLO();
         Score best_score;
         Mat best_model;
         int final_iters;
 
         if (! parallel) {
+            auto update_best = [&] (const Mat &new_model, const Score &new_score) {
+                best_score = new_score;
+                // remember best model
+                new_model.copyTo(best_model);
+                // update quality and verifier to save evaluation time of a model
+                _quality->setBestScore(best_score.score);
+                // update verifier
+                _model_verifier->update(best_score.inlier_number);
+                // update upper bound of iterations
+                return _termination_criteria->update(best_model, best_score.inlier_number);
+            };
+            bool was_LO_run = false;
             Mat non_degenerate_model, lo_model;
             Score current_score, lo_score, non_denegenerate_model_score;
 
@@ -139,65 +152,54 @@ public:
                 const int number_of_models = _estimator->estimateModels(sample, models);
 
                 for (int i = 0; i < number_of_models; i++) {
-                    if (is_magsac && iters % repeat_magsac == 0) {
-                        if (!_local_optimization->refineModel
-                                (models[i], best_score, models[i], current_score))
-                            continue;
-                    } else if (_model_verifier->isModelGood(models[i])) {
-                        if (!_model_verifier->getScore(current_score)) {
-                            if (_model_verifier->hasErrors())
-                                current_score = _quality->getScore(_model_verifier->getErrors());
-                            else current_score = _quality->getScore(models[i]);
-                        }
-                    } else continue;
+                    if (iters < max_hyp_test_before_ver) {
+                        current_score = _quality->getScore(models[i]);
+                    } else {
+                        if (is_magsac && iters % repeat_magsac == 0) {
+                            if (!_local_optimization->refineModel
+                                    (models[i], best_score, models[i], current_score))
+                                continue;
+                        } else if (_model_verifier->isModelGood(models[i])) {
+                            if (!_model_verifier->getScore(current_score)) {
+                                if (_model_verifier->hasErrors())
+                                    current_score = _quality->getScore(_model_verifier->getErrors());
+                                else current_score = _quality->getScore(models[i]);
+                            }
+                        } else continue;
+                    }
 
                     if (current_score.isBetter(best_score)) {
                         if (_degeneracy->recoverIfDegenerate(sample, models[i],
                                 non_degenerate_model, non_denegenerate_model_score)) {
                             // check if best non degenerate model is better than so far the best model
-                            if (non_denegenerate_model_score.isBetter(best_score)) {
-                                best_score = non_denegenerate_model_score;
-                                non_degenerate_model.copyTo(best_model);
-                            } else
-                                // non degenerate models are worse then so far the best model.
-                                continue;
-                        } else {
-                            // copy current score to best score
-                            best_score = current_score;
-                            // remember best model
-                            models[i].copyTo(best_model);
-                        }
+                            if (non_denegenerate_model_score.isBetter(best_score))
+                                max_iters = update_best(non_degenerate_model, non_denegenerate_model_score);
+                            else continue;
+                        } else max_iters = update_best(models[i], current_score);
 
-                        // update quality to save evaluation time of a model
-                        // with no chance of being better than so-far-the-best
-                        _quality->setBestScore(best_score.score);
-
-                        // update upper bound of iterations
-                        max_iters = _termination_criteria->update
-                                (best_model, best_score.inlier_number);
-                        if (iters > max_iters)
-                            break;
-
-                        if (LO) {//} && iters >= max_iters_before_LO) {
+                        if (LO && iters >= max_iters_before_LO) {
                             // do magsac if it wasn't already run
-                            if (is_magsac && iters % repeat_magsac == 0) continue; // magsac has already run
+                            if (is_magsac && iters % repeat_magsac == 0 && iters >= max_hyp_test_before_ver) continue; // magsac has already run
+                            was_LO_run = true;
                             // update model by Local optimization
                             if (_local_optimization->refineModel
-                                    (best_model, best_score, lo_model, lo_score))
-                                if (lo_score.isBetter(best_score)) {
-                                    best_score = lo_score;
-                                    lo_model.copyTo(best_model);
-                                    // update quality and verifier and termination again
-                                    _quality->setBestScore(best_score.score);
-                                    _model_verifier->update(best_score.inlier_number);
-                                    max_iters = _termination_criteria->update
-                                            (best_model, best_score.inlier_number);
-                                    if (iters > max_iters)
-                                        break;
+                                    (best_model, best_score, lo_model, lo_score)) {
+                                if (lo_score.isBetter(best_score)){
+                                    max_iters = update_best(lo_model, lo_score);
                                 }
+                            }
                         }
+                        if (iters > max_iters)
+                            break;
                     } // end of if so far the best score
                 } // end loop of number of models
+                if (LO && !was_LO_run && iters >= max_iters_before_LO) {
+                    was_LO_run = true;
+                    if (_local_optimization->refineModel(best_model, best_score, lo_model, lo_score))
+                        if (lo_score.isBetter(best_score)){
+                            max_iters = update_best(lo_model, lo_score);
+                        }
+                }
             } // end main while loop
 
             final_iters = iters;
@@ -223,7 +225,9 @@ public:
                 Ptr<Degeneracy> degeneracy = _degeneracy->clone(thread_state++);
                 Ptr<Quality> quality = _quality->clone();
                 Ptr<ModelVerifier> model_verifier = _model_verifier->clone(thread_state++); // update verifier
-                Ptr<LocalOptimization> local_optimization = _local_optimization->clone(thread_state++);
+                Ptr<LocalOptimization> local_optimization;
+                if (LO)
+                    local_optimization = _local_optimization->clone(thread_state++);
                 Ptr<TerminationCriteria> termination_criteria = _termination_criteria->clone();
                 Ptr<Sampler> sampler;
                 if (!is_prosac)
@@ -243,8 +247,12 @@ public:
                     new_model.copyTo(best_model_thread);
                     best_model_thread.copyTo(best_models[thread_rng_id]);
                     best_score_all_threads = best_score_thread;
+                    // update upper bound of iterations
+                    return termination_criteria->update
+                            (best_model_thread, best_score_thread.inlier_number);
                 };
 
+                bool was_LO_run = false;
                 for (iters = 0; iters < max_iters && !success; iters++) {
                     success = num_hypothesis_tested++ > max_iters;
 
@@ -274,56 +282,55 @@ public:
 
                     const int number_of_models = estimator->estimateModels(sample, models);
                     for (int i = 0; i < number_of_models; i++) {
-                        if (is_magsac && iters % repeat_magsac == 0) {
-                            if (!local_optimization->refineModel
-                                    (models[i], best_score_thread, models[i], current_score))
-                                continue;
-                        } else if (model_verifier->isModelGood(models[i])) {
-                            if (!model_verifier->getScore(current_score)) {
-                                if (model_verifier->hasErrors())
-                                    current_score = quality->getScore(model_verifier->getErrors());
-                                else current_score = quality->getScore(models[i]);
-                            }
-                        } else continue;
+                        if (iters < max_hyp_test_before_ver) {
+                            current_score = quality->getScore(models[i]);
+                        } else {
+                            if (is_magsac && iters % repeat_magsac == 0) {
+                                if (!local_optimization->refineModel
+                                        (models[i], best_score_thread, models[i], current_score))
+                                    continue;
+                            } else if (model_verifier->isModelGood(models[i])) {
+                                if (!model_verifier->getScore(current_score)) {
+                                    if (model_verifier->hasErrors())
+                                        current_score = quality->getScore(model_verifier->getErrors());
+                                    else current_score = quality->getScore(models[i]);
+                                }
+                            } else continue;
+                        }
 
                         if (current_score.isBetter(best_score_all_threads)) {
                             if (degeneracy->recoverIfDegenerate(sample, models[i],
                                         non_degenerate_model, non_denegenerate_model_score)) {
                                 // check if best non degenerate model is better than so far the best model
                                 if (non_denegenerate_model_score.isBetter(best_score_thread))
-                                    update_best(non_denegenerate_model_score, non_degenerate_model);
-                                else
-                                    // non degenerate models are worse then so far the best model.
-                                    continue;
+                                    max_iters = update_best(non_denegenerate_model_score, non_degenerate_model);
+                                else continue;
                             } else
-                                update_best(current_score, models[i]);
+                                max_iters = update_best(current_score, models[i]);
 
-                            // update upper bound of iterations
-                            max_iters = termination_criteria->update
-                                    (best_model_thread, best_score_thread.inlier_number);
-                            if (num_hypothesis_tested > max_iters) {
-                                success = true; break;
-                            }
-
-                            if (LO) {
+                            if (LO && iters >= max_iters_before_LO) {
                                 // do magsac if it wasn't already run
-                                if (is_magsac && iters % repeat_magsac == 0) continue;
+                                if (is_magsac && iters % repeat_magsac == 0 && iters >= max_hyp_test_before_ver) continue;
+                                was_LO_run = true;
                                 // update model by Local optimizaion
                                 if (local_optimization->refineModel
                                        (best_model_thread, best_score_thread, lo_model, lo_score))
                                     if (lo_score.isBetter(best_score_thread)) {
-                                        update_best(lo_score, lo_model);
-                                        // update termination again
-                                        max_iters = termination_criteria->update
-                                                (best_model_thread, best_score_thread.inlier_number);
-                                        if (num_hypothesis_tested > max_iters) {
-                                            success = true;
-                                            break;
-                                        }
+                                        max_iters = update_best(lo_score, lo_model);
                                     }
                             }
+                            if (num_hypothesis_tested > max_iters) {
+                                success = true; break;
+                            }
                         } // end of if so far the best score
                     } // end loop of number of models
+                    if (LO && !was_LO_run && iters >= max_iters_before_LO) {
+                        was_LO_run = true;
+                        if (_local_optimization->refineModel(best_model, best_score, lo_model, lo_score))
+                            if (lo_score.isBetter(best_score)){
+                                max_iters = update_best(lo_score, lo_model);
+                            }
+                    }
                 } // end of loop over iters
             }}); // end parallel
             ///////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -354,7 +361,6 @@ public:
                     polished_model.copyTo(best_model);
                 }
         }
-
         // ================= here is ending ransac main implementation ===========================
         std::vector<bool> inliers_mask;
         if (params->isMaskRequired()) {
@@ -402,7 +408,7 @@ int mergePoints (InputArray pts1_, InputArray pts2_, Mat &pts, bool ispnp) {
 void saveMask (OutputArray mask, const std::vector<bool> &inliers_mask) {
     if (mask.needed()) {
         const int points_size = (int) inliers_mask.size();
-        mask.create(1, points_size, CV_8U);
+        mask.create(points_size, 1, CV_8U);
         auto * maskptr = mask.getMat().ptr<uchar>();
         for (int i = 0; i < points_size; i++)
             maskptr[i] = (uchar) inliers_mask[i];
@@ -433,7 +439,8 @@ void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, do
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
                                    ScoreMethod::SCORE_METHOD_MAGSAC);
             params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_SIGMA);
-            params->setLOSampleSize(100);
+            params->setLOSampleSize(params->isHomography() ? 75 : 50);
+            params->setLOIterations(params->isHomography() ? 15 : 10);
             break;
         case USAC_PARALLEL:
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
@@ -445,13 +452,15 @@ void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, do
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
                                    ScoreMethod::SCORE_METHOD_MSAC);
             params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_GC);
+            params->setLOSampleSize(20);
+            params->setLOIterations(25);
             break;
         case USAC_FAST:
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
-                                   ScoreMethod::SCORE_METHOD_RANSAC);
+                                   ScoreMethod::SCORE_METHOD_MSAC);
             params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_INNER_AND_ITER_LO);
-            params->setLOIterations(7);
-            params->setLOIterativeIters(4);
+            params->setLOIterations(5);
+            params->setLOIterativeIters(3);
             break;
         case USAC_PROSAC:
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_PROSAC, conf, max_iters,
@@ -465,6 +474,13 @@ void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, do
             break;
         default: CV_Error(cv::Error::StsBadFlag, "Incorrect flag for USAC!");
     }
+    // do not do too many iterations for PnP
+    if (estimator == EstimationMethod::P3P) {
+        if (params->getLOInnerMaxIters() > 15)
+            params->setLOIterations(15);
+        params->setLOIterativeIters(0);
+    }
+
     params->maskRequired(mask_needed);
 }
 
@@ -477,7 +493,12 @@ Mat findHomography (InputArray srcPoints, InputArray dstPoints, int method, doub
             ransac_output, noArray(), noArray(), noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel() / ransac_output->getModel().at<double>(2,2);
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(srcPoints.getMat().rows, srcPoints.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 Mat findFundamentalMat( InputArray points1, InputArray points2, int method, double thr,
@@ -489,7 +510,12 @@ Mat findFundamentalMat( InputArray points1, InputArray points2, int method, doub
             ransac_output, noArray(), noArray(), noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel();
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(points1.getMat().rows, points1.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 Mat findEssentialMat (InputArray points1, InputArray points2, InputArray cameraMatrix1,
@@ -501,7 +527,12 @@ Mat findEssentialMat (InputArray points1, InputArray points2, InputArray cameraM
             ransac_output, cameraMatrix1, cameraMatrix1, noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel();
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(points1.getMat().rows, points1.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
@@ -519,7 +550,12 @@ bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
         model.col(0).copyTo(rvec);
         model.col(1).copyTo(tvec);
         return true;
-    } else return false;
+    }
+    if (mask.needed()){
+        mask.create(std::max(objectPoints.getMat().rows, objectPoints.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return false;
 }
 
 Mat estimateAffine2D(InputArray from, InputArray to, OutputArray mask, int method,
@@ -531,7 +567,12 @@ Mat estimateAffine2D(InputArray from, InputArray to, OutputArray mask, int metho
             ransac_output, noArray(), noArray(), noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel().rowRange(0,2);
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(from.getMat().rows, from.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 class ModelImpl : public Model {
@@ -546,14 +587,14 @@ private:
 
     // for neighborhood graph
     int k_nearest_neighbors = 8;//, flann_search_params = 5, num_kd_trees = 1; // for FLANN
-    int cell_size = 25; // pixels, for grid neighbors searching
-    int radius = 20; // pixels, for radius-search neighborhood graph
+    int cell_size = 50; // pixels, for grid neighbors searching
+    int radius = 30; // pixels, for radius-search neighborhood graph
     NeighborSearchMethod neighborsType = NeighborSearchMethod::NEIGH_GRID;
 
     // Local Optimization parameters
     LocalOptimMethod lo = LocalOptimMethod ::LOCAL_OPTIM_INNER_AND_ITER_LO;
-    int lo_sample_size=14, lo_inner_iterations=15, lo_iterative_iterations=5,
-            lo_thr_multiplier=3, lo_iter_sample_size = 30;
+    int lo_sample_size=16, lo_inner_iterations=15, lo_iterative_iterations=8,
+            lo_thr_multiplier=15, lo_iter_sample_size = 30;
 
     // Graph cut parameters
     const double spatial_coherence_term = 0.975;
@@ -563,11 +604,11 @@ private:
 
     // preemptive verification test
     VerificationMethod verifier = VerificationMethod ::SprtVerifier;
-    const int max_hypothesis_test_before_verification = 10;
+    const int max_hypothesis_test_before_verification = 15;
 
     // sprt parameters
-    // lower bound estimate is 1.1% of inliers
-    double sprt_eps = 0.011, sprt_delta = 0.01, avg_num_models, time_for_model_est;
+    // lower bound estimate is 1% of inliers
+    double sprt_eps = 0.01, sprt_delta = 0.008, avg_num_models, time_for_model_est;
 
     // estimator error
     ErrorMetric est_error;
@@ -578,15 +619,16 @@ private:
     const std::vector<int> grid_cell_number = {16, 8, 4, 2};
 
     //for final least squares polisher
-    int final_lsq_iters = 2;
+    int final_lsq_iters = 3;
 
     bool need_mask = true, is_parallel = false;
     int random_generator_state = 0;
+    const int max_iters_before_LO = 100;
 
     // magsac parameters:
-    int DoF = 4;
-    double sigma_quantile = 3.64, upper_incomplete_of_sigma_quantile = 0.00365,
-        lower_incomplete_of_sigma_quantile = 1.30122, C = 0.25, maximum_thr = 10.;
+    int DoF = 2;
+    double sigma_quantile = 3.04, upper_incomplete_of_sigma_quantile = 0.00419,
+        lower_incomplete_of_sigma_quantile = 0.8629, C = 0.5, maximum_thr = 7.5;
 public:
     ModelImpl (double threshold_, EstimationMethod estimator_, SamplingMethod sampler_, double confidence_=0.95,
                int max_iterations_=5000, ScoreMethod score_ =ScoreMethod::SCORE_METHOD_MSAC) {
@@ -603,16 +645,16 @@ public:
                 avg_num_models = 1; time_for_model_est = 50;
                 sample_size = 3; est_error = ErrorMetric ::FORW_REPR_ERR; break;
             case (EstimationMethod::Homography):
-                avg_num_models = 1; time_for_model_est = 90;
+                avg_num_models = 1; time_for_model_est = 150;
                 sample_size = 4; est_error = ErrorMetric ::FORW_REPR_ERR; break;
             case (EstimationMethod::Fundamental):
-                avg_num_models = 2.38; time_for_model_est = 150; maximum_thr = 3;
+                avg_num_models = 2.38; time_for_model_est = 180; maximum_thr = 2.5;
                 sample_size = 7; est_error = ErrorMetric ::SAMPSON_ERR; break;
             case (EstimationMethod::Fundamental8):
-                avg_num_models = 1; time_for_model_est = 100; maximum_thr = 3;
+                avg_num_models = 1; time_for_model_est = 100; maximum_thr = 2.5;
                 sample_size = 8; est_error = ErrorMetric ::SAMPSON_ERR; break;
             case (EstimationMethod::Essential):
-                avg_num_models = 3.93; time_for_model_est = 2000; maximum_thr = 3;
+                avg_num_models = 3.93; time_for_model_est = 1000; maximum_thr = 2.5;
                 sample_size = 5; est_error = ErrorMetric ::SGD_ERR; break;
             case (EstimationMethod::P3P):
                 avg_num_models = 1.38; time_for_model_est = 800;
@@ -620,18 +662,19 @@ public:
             case (EstimationMethod::P6P):
                 avg_num_models = 1; time_for_model_est = 300;
                 sample_size = 6; est_error = ErrorMetric ::RERPOJ; break;
-            default: CV_Assert(0 && "Estimator has not implemented yet!");
+            default: CV_Error(cv::Error::StsNotImplemented, "Estimator has not implemented yet!");
         }
 
         if (estimator_ == EstimationMethod::P3P || estimator_ == EstimationMethod::P6P) {
             neighborsType = NeighborSearchMethod::NEIGH_FLANN_KNN;
             k_nearest_neighbors = 2;
-            DoF = 5;
-            sigma_quantile = 3.88;
-            upper_incomplete_of_sigma_quantile = 0.00458;
-            lower_incomplete_of_sigma_quantile = 1.96032;
-            C = 0.13298;
         }
+        if (estimator == EstimationMethod::Fundamental || estimator == EstimationMethod::Essential) {
+            lo_sample_size = 21;
+            lo_thr_multiplier = 10;
+        }
+        if (estimator == EstimationMethod::Homography)
+            maximum_thr = 8.;
         threshold = threshold_;
     }
     void setVerifier (VerificationMethod verifier_) override { verifier = verifier_; }
@@ -645,6 +688,7 @@ public:
     void setLOIterations (int iters) override { lo_inner_iterations = iters; }
     void setLOIterativeIters (int iters) override {lo_iterative_iterations = iters; }
     void setLOSampleSize (int lo_sample_size_) override { lo_sample_size = lo_sample_size_; }
+    void setThresholdMultiplierLO (double thr_mult) override { lo_thr_multiplier = (int) round(thr_mult); }
     void maskRequired (bool need_mask_) override { need_mask = need_mask_; }
     void setRandomGeneratorState (int state) override { random_generator_state = state; }
     bool isMaskRequired () const override { return need_mask; }
@@ -682,6 +726,7 @@ public:
     VerificationMethod getVerifier () const override { return verifier; }
     SamplingMethod getSampler () const override { return sampler; }
     int getRandomGeneratorState () const override { return random_generator_state; }
+    int getMaxItersBeforeLO () const override { return max_iters_before_LO; }
     double getSPRTdelta () const override { return sprt_delta; }
     double getSPRTepsilon () const override { return sprt_eps; }
     double getSPRTavgNumModels () const override { return avg_num_models; }
@@ -734,7 +779,9 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
             K1 = K1_.getMat(); K1.convertTo(K1, CV_64F);
             if (! dist_coeff1.empty()) {
                 // undistortPoints also calibrate points using K
-                undistortPoints(points1, undist_points1, K1_, dist_coeff1);
+                if (points1.isContinuous())
+                     undistortPoints(points1, undist_points1, K1_, dist_coeff1);
+                else undistortPoints(points1.getMat().clone(), undist_points1, K1_, dist_coeff1);
                 points_size = mergePoints(undist_points1, points2, points, true);
                 Utils::normalizeAndDecalibPointsPnP (K1, points, calib_points);
             } else {
@@ -750,8 +797,12 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
             K2 = K2_.getMat(); K2.convertTo(K2, CV_64F);
             if (! dist_coeff1.empty() || ! dist_coeff2.empty()) {
                 // undistortPoints also calibrate points using K
-                cv::undistortPoints(points1, undist_points1, K1_, dist_coeff1);
-                cv::undistortPoints(points2, undist_points2, K2_, dist_coeff2);
+                if (points1.isContinuous())
+                     undistortPoints(points1, undist_points1, K1_, dist_coeff1);
+                else undistortPoints(points1.getMat().clone(), undist_points1, K1_, dist_coeff1);
+                if (points2.isContinuous())
+                     undistortPoints(points2, undist_points2, K2_, dist_coeff2);
+                else undistortPoints(points2.getMat().clone(), undist_points2, K2_, dist_coeff2);
                 points_size = mergePoints(undist_points1, undist_points2, calib_points, false);
             } else {
                 points_size = mergePoints(points1, points2, points, false);
@@ -771,7 +822,7 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
         if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_GRID) {
             graph = GridNeighborhoodGraph::create(points, points_size,
                 params->getCellSize(), params->getCellSize(),
-                params->getCellSize(), params->getCellSize());
+                params->getCellSize(), params->getCellSize(), 10);
         } else if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_FLANN_KNN) {
             graph = FlannNeighborhoodGraph::create(points, points_size,params->getKNN(), false, 5, 1);
         } else if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_FLANN_RADIUS) {
@@ -802,7 +853,7 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
                         "Cell number in layers must be in decreasing order!");
             layers.emplace_back(GridNeighborhoodGraph::create(points, points_size,
           (int)(img1_width / (float)cell_number), (int)(img1_height / (float)cell_number),
-          (int)(img2_width / (float)cell_number), (int)(img2_height / (float)cell_number)));
+          (int)(img2_width / (float)cell_number), (int)(img2_height / (float)cell_number), 10));
         }
     }
 
@@ -811,8 +862,10 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
         points = calib_points;
         // if maximum calibrated threshold significanlty differs threshold then set upper bound
         if (max_thr > 10*threshold)
-            max_thr = 10*threshold;
+            max_thr = sqrt(10*threshold); // max thr will be squared after
     }
+    if (max_thr < threshold)
+        max_thr = threshold;
 
     switch (params->getError()) {
         case ErrorMetric::SYMM_REPR_ERR:
@@ -936,7 +989,8 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
                 lo = GraphCut::create(estimator, error, quality, graph, lo_sampler, threshold,
                    params->getGraphCutSpatialCoherenceTerm(), params->getLOInnerMaxIters()); break;
             case LocalOptimMethod::LOCAL_OPTIM_SIGMA:
-                lo = SigmaConsensus::create(estimator, error, quality, verifier, params->getLOSampleSize(), 1,
+                lo = SigmaConsensus::create(estimator, error, quality, verifier,
+                     params->getLOSampleSize(), params->getLOInnerMaxIters(),
                      params->getDegreesOfFreedom(), params->getSigmaQuantile(),
                      params->getUpperIncompleteOfSigmaQuantile(), params->getC(), max_thr); break;
             default: CV_Error(cv::Error::StsNotImplemented , "Local Optimization is not implemented!");

modules/calib3d/src/usac/sampler.cpp

@@ -256,8 +256,6 @@ public:
     }
 
     void generateSample (std::vector<int> &sample) override {
-        // std::cout << "PROSAC sampler, termination length " << termination_length << "\n";
-
         if (kth_sample_number > growth_max_samples) {
             // if PROSAC has not converged to solution then do uniform sampling.
             random_gen->generateUniqueRandomSet(sample, sample_size, points_size);

modules/calib3d/src/usac/utils.cpp

@@ -168,7 +168,7 @@ Vec3d Math::rotMat2RotVec (const Matx33d &R) {
 /*
  * Eliminate matrix of m rows and n columns to be upper triangular.
  */
-void Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
+bool Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
     for (int r = 0; r < m; r++){
         double pivot = a[r*n+r];
         int row_with_pivot = r;
@@ -182,7 +182,7 @@ void Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
 
         // if pivot value is 0 continue
         if (fabs(pivot) < DBL_EPSILON)
-            continue;
+            return false; // matrix is not full rank -> terminate
 
         // swap row with maximum pivot value with current row
         for (int c = r; c < n; c++)
@@ -190,11 +190,14 @@ void Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
 
         // eliminate other rows
         for (int j = r+1; j < m; j++){
-            const auto fac = a[j*n+r] / pivot;
-            for (int c = r; c < n; c++)
-                a[j*n+c] -= fac * a[r*n+c];
+            const int row_idx1 = j*n, row_idx2 = r*n;
+            const auto fac = a[row_idx1+r] / pivot;
+            a[row_idx1+r] = 0; // zero eliminated element
+            for (int c = r+1; c < n; c++)
+                a[row_idx1+c] -= fac * a[row_idx2+c];
         }
     }
+    return true;
 }
 
 //////////////////////////////////////// RANDOM GENERATOR /////////////////////////////
@@ -467,7 +470,8 @@ private:
     std::vector<std::vector<int>> graph;
 public:
     GridNeighborhoodGraphImpl (const Mat &container_, int points_size,
-          int cell_size_x_img1, int cell_size_y_img1, int cell_size_x_img2, int cell_size_y_img2) {
+          int cell_size_x_img1, int cell_size_y_img1, int cell_size_x_img2, int cell_size_y_img2,
+          int max_neighbors) {
 
         const auto * const container = (float *) container_.data;
         // <int, int, int, int> -> {neighbors set}
@@ -501,11 +505,14 @@ public:
             for (int v_in_cell : neighbors) {
                 // there is always at least one neighbor
                 auto &graph_row = graph[v_in_cell];
-                graph_row = std::vector<int>(neighbors_in_cell-1);
+                graph_row = std::vector<int>(std::min(max_neighbors, neighbors_in_cell-1));
                 int j = 0;
                 for (int n : neighbors)
-                    if (n != v_in_cell)
+                    if (n != v_in_cell){
                         graph_row[j++] = n;
+                        if (j >= max_neighbors)
+                            break;
+                    }
             }
         }
     }
@@ -519,8 +526,8 @@ public:
 
 Ptr<GridNeighborhoodGraph> GridNeighborhoodGraph::create(const Mat &points,
      int points_size, int cell_size_x_img1_, int cell_size_y_img1_,
-     int cell_size_x_img2_, int cell_size_y_img2_) {
+     int cell_size_x_img2_, int cell_size_y_img2_, int max_neighbors) {
     return makePtr<GridNeighborhoodGraphImpl>(points, points_size,
-      cell_size_x_img1_, cell_size_y_img1_, cell_size_x_img2_, cell_size_y_img2_);
+      cell_size_x_img1_, cell_size_y_img1_, cell_size_x_img2_, cell_size_y_img2_, max_neighbors);
 }
 }}

modules/calib3d/test/test_homography.cpp

@@ -63,6 +63,7 @@ namespace opencv_test { namespace {
 #define MESSAGE_RANSAC_DIFF "Reprojection error for current pair of points more than required."
 
 #define MAX_COUNT_OF_POINTS 303
+#define MIN_COUNT_OF_POINTS 4
 #define COUNT_NORM_TYPES 3
 #define METHODS_COUNT 4
 
@@ -249,7 +250,7 @@ void CV_HomographyTest::print_information_8(int _method, int j, int N, int k, in
 
 void CV_HomographyTest::run(int)
 {
-    for (int N = 4; N <= MAX_COUNT_OF_POINTS; ++N)
+    for (int N = MIN_COUNT_OF_POINTS; N <= MAX_COUNT_OF_POINTS; ++N)
     {
         RNG& rng = ts->get_rng();
 
@@ -711,4 +712,27 @@ TEST(Calib3d_Homography, fromImages)
     ASSERT_GE(ninliers1, 80);
 }
 
+TEST(Calib3d_Homography, minPoints)
+{
+    float pt1data[] =
+    {
+        2.80073029e+002f, 2.39591217e+002f, 2.21912201e+002f, 2.59783997e+002f
+    };
+
+    float pt2data[] =
+    {
+        1.84072723e+002f, 1.43591202e+002f, 1.25912483e+002f, 1.63783859e+002f
+    };
+
+    int npoints = (int)(sizeof(pt1data)/sizeof(pt1data[0])/2);
+    printf("npoints = %d\n", npoints);  // npoints = 2
+
+    Mat p1(1, npoints, CV_32FC2, pt1data);
+    Mat p2(1, npoints, CV_32FC2, pt2data);
+    Mat mask;
+
+    // findHomography should raise an error since npoints < MIN_COUNT_OF_POINTS
+    EXPECT_THROW(findHomography(p1, p2, RANSAC, 0.01, mask), cv::Exception);
+}
+
 }} // namespace

modules/core/CMakeLists.txt

@@ -80,6 +80,9 @@ endif()
 if(HAVE_MEMALIGN)
   ocv_append_source_file_compile_definitions(${CMAKE_CURRENT_SOURCE_DIR}/src/alloc.cpp "HAVE_MEMALIGN=1")
 endif()
+if(HAVE_VA_INTEL_OLD_HEADER)
+  ocv_append_source_file_compile_definitions("${CMAKE_CURRENT_LIST_DIR}/src/va_intel.cpp" "HAVE_VA_INTEL_OLD_HEADER")
+endif()
 
 option(OPENCV_ENABLE_ALLOCATOR_STATS "Enable Allocator metrics" ON)
 

modules/core/include/opencv2/core/check.hpp

@@ -63,7 +63,7 @@ struct CheckContext {
 #define CV__CHECK_LOCATION_VARNAME(id) CVAUX_CONCAT(CVAUX_CONCAT(__cv_check_, id), __LINE__)
 #define CV__DEFINE_CHECK_CONTEXT(id, message, testOp, p1_str, p2_str) \
     static const cv::detail::CheckContext CV__CHECK_LOCATION_VARNAME(id) = \
-            { CV__CHECK_FUNCTION, CV__CHECK_FILENAME, __LINE__, testOp, message, p1_str, p2_str }
+            { CV__CHECK_FUNCTION, CV__CHECK_FILENAME, __LINE__, testOp, "" message, "" p1_str, "" p2_str }
 
 CV_EXPORTS void CV_NORETURN check_failed_auto(const int v1, const int v2, const CheckContext& ctx);
 CV_EXPORTS void CV_NORETURN check_failed_auto(const size_t v1, const size_t v2, const CheckContext& ctx);

modules/core/include/opencv2/core/eigen.hpp

@@ -58,11 +58,13 @@
 #pragma warning( disable: 4244 ) //conversion from '__int64' to 'int', possible loss of data
 #endif
 
+#if !defined(OPENCV_DISABLE_EIGEN_TENSOR_SUPPORT)
 #if EIGEN_WORLD_VERSION == 3 && EIGEN_MAJOR_VERSION >= 3 \
     && defined(CV_CXX11) && defined(CV_CXX_STD_ARRAY)
 #include <unsupported/Eigen/CXX11/Tensor>
-#define OPENCV_EIGEN_TENSOR_SUPPORT
-#endif // EIGEN_WORLD_VERSION == 3 && EIGEN_MAJOR_VERSION >= 3
+#define OPENCV_EIGEN_TENSOR_SUPPORT 1
+#endif  // EIGEN_WORLD_VERSION == 3 && EIGEN_MAJOR_VERSION >= 3
+#endif  // !defined(OPENCV_DISABLE_EIGEN_TENSOR_SUPPORT)
 
 namespace cv
 {

modules/core/include/opencv2/core/ocl.hpp

@@ -735,11 +735,11 @@ public:
     OpenCLExecutionContext() = default;
     ~OpenCLExecutionContext() = default;
 
-    OpenCLExecutionContext(const OpenCLExecutionContext& other) = default;
-    OpenCLExecutionContext(OpenCLExecutionContext&& other) = default;
+    OpenCLExecutionContext(const OpenCLExecutionContext&) = default;
+    OpenCLExecutionContext(OpenCLExecutionContext&&) = default;
 
-    OpenCLExecutionContext& operator=(const OpenCLExecutionContext& other) = default;
-    OpenCLExecutionContext& operator=(OpenCLExecutionContext&& other) = default;
+    OpenCLExecutionContext& operator=(const OpenCLExecutionContext&) = default;
+    OpenCLExecutionContext& operator=(OpenCLExecutionContext&&) = default;
 
     /** Get associated ocl::Context */
     Context& getContext() const;

modules/core/include/opencv2/core/va_intel.hpp

@@ -29,14 +29,11 @@ namespace cv { namespace va_intel {
 /** @addtogroup core_va_intel
 This section describes Intel VA-API/OpenCL (CL-VA) interoperability.
 
-To enable CL-VA interoperability support, configure OpenCV using CMake with WITH_VA_INTEL=ON . Currently VA-API is
-supported on Linux only. You should also install Intel Media Server Studio (MSS) to use this feature. You may
-have to specify the path(s) to MSS components for cmake in environment variables:
+To enable basic VA interoperability build OpenCV with libva library integration enabled: `-DWITH_VA=ON` (corresponding dev package should be installed).
 
-- VA_INTEL_IOCL_ROOT for Intel OpenCL (default is "/opt/intel/opencl").
+To enable advanced CL-VA interoperability support on Intel HW, enable option: `-DWITH_VA_INTEL=ON` (OpenCL integration should be enabled which is the default setting). Special runtime environment should be set up in order to use this feature: correct combination of [libva](https://github.com/intel/libva), [OpenCL runtime](https://github.com/intel/compute-runtime) and [media driver](https://github.com/intel/media-driver) should be installed.
 
-To use CL-VA interoperability you should first create VADisplay (libva), and then call initializeContextFromVA()
-function to create OpenCL context and set up interoperability.
+Check usage example for details: samples/va_intel/va_intel_interop.cpp
 */
 //! @{
 

modules/core/include/opencv2/core/version.hpp

@@ -8,7 +8,7 @@
 #define CV_VERSION_MAJOR    4
 #define CV_VERSION_MINOR    5
 #define CV_VERSION_REVISION 0
-#define CV_VERSION_STATUS   "-openvino"
+#define CV_VERSION_STATUS   ""
 
 #define CVAUX_STR_EXP(__A)  #__A
 #define CVAUX_STR(__A)      CVAUX_STR_EXP(__A)

modules/core/src/directx.cpp

@@ -459,7 +459,7 @@ Context& initializeContextFromD3D11Device(ID3D11Device* pD3D11Device)
     }
 
     cl_platform_id platform = platforms[found];
-    std::string platformName = PlatformInfo(platform).name();
+    std::string platformName = PlatformInfo(&platform).name();
 
     OpenCLExecutionContext clExecCtx;
     try
@@ -579,7 +579,7 @@ Context& initializeContextFromD3D10Device(ID3D10Device* pD3D10Device)
     }
 
     cl_platform_id platform = platforms[found];
-    std::string platformName = PlatformInfo(platform).name();
+    std::string platformName = PlatformInfo(&platform).name();
 
     OpenCLExecutionContext clExecCtx;
     try
@@ -701,7 +701,7 @@ Context& initializeContextFromDirect3DDevice9Ex(IDirect3DDevice9Ex* pDirect3DDev
     }
 
     cl_platform_id platform = platforms[found];
-    std::string platformName = PlatformInfo(platform).name();
+    std::string platformName = PlatformInfo(&platform).name();
 
     OpenCLExecutionContext clExecCtx;
     try
@@ -824,7 +824,7 @@ Context& initializeContextFromDirect3DDevice9(IDirect3DDevice9* pDirect3DDevice9
     }
 
     cl_platform_id platform = platforms[found];
-    std::string platformName = PlatformInfo(platform).name();
+    std::string platformName = PlatformInfo(&platform).name();
 
     OpenCLExecutionContext clExecCtx;
     try

modules/core/src/logger.cpp

@@ -94,8 +94,7 @@ LogLevel GlobalLoggingInitStruct::m_defaultUnconfiguredGlobalLevel = GlobalLoggi
 //
 static GlobalLoggingInitStruct& getGlobalLoggingInitStruct()
 {
-    static GlobalLoggingInitStruct globalLoggingInitInstance;
-    return globalLoggingInitInstance;
+    CV_SINGLETON_LAZY_INIT_REF(GlobalLoggingInitStruct, new GlobalLoggingInitStruct());
 }
 
 // To ensure that the combined struct defined above is initialized even

modules/core/src/matrix.cpp

@@ -237,12 +237,19 @@ void setSize( Mat& m, int _dims, const int* _sz, const size_t* _steps, bool auto
 
         if( _steps )
         {
-            if (_steps[i] % esz1 != 0)
+            if (i < _dims-1)
             {
-                CV_Error(Error::BadStep, "Step must be a multiple of esz1");
-            }
+                if (_steps[i] % esz1 != 0)
+                {
+                    CV_Error_(Error::BadStep, ("Step %zu for dimension %d must be a multiple of esz1 %zu", _steps[i], i, esz1));
+                }
 
-            m.step.p[i] = i < _dims-1 ? _steps[i] : esz;
+                m.step.p[i] = _steps[i];
+            }
+            else
+            {
+                m.step.p[i] = esz;
+            }
         }
         else if( autoSteps )
         {

modules/core/src/matrix_wrap.cpp

@@ -1248,6 +1248,7 @@ void _OutputArray::create(int d, const int* sizes, int mtype, int i,
     {
         CV_Assert( i < 0 );
         Mat& m = *(Mat*)obj;
+        CV_Assert(!(m.empty() && fixedType() && fixedSize()) && "Can't reallocate empty Mat with locked layout (probably due to misused 'const' modifier)");
         if (allowTransposed && !m.empty() &&
             d == 2 && m.dims == 2 &&
             m.type() == mtype && m.rows == sizes[1] && m.cols == sizes[0] &&
@@ -1261,13 +1262,13 @@ void _OutputArray::create(int d, const int* sizes, int mtype, int i,
             if(CV_MAT_CN(mtype) == m.channels() && ((1 << CV_MAT_TYPE(flags)) & fixedDepthMask) != 0 )
                 mtype = m.type();
             else
-                CV_CheckTypeEQ(m.type(), CV_MAT_TYPE(mtype), "");
+                CV_CheckTypeEQ(m.type(), CV_MAT_TYPE(mtype), "Can't reallocate Mat with locked type (probably due to misused 'const' modifier)");
         }
         if(fixedSize())
         {
-            CV_CheckEQ(m.dims, d, "");
+            CV_CheckEQ(m.dims, d, "Can't reallocate Mat with locked size (probably due to misused 'const' modifier)");
             for(int j = 0; j < d; ++j)
-                CV_CheckEQ(m.size[j], sizes[j], "");
+                CV_CheckEQ(m.size[j], sizes[j], "Can't reallocate Mat with locked size (probably due to misused 'const' modifier)");
         }
         m.create(d, sizes, mtype);
         return;
@@ -1277,6 +1278,7 @@ void _OutputArray::create(int d, const int* sizes, int mtype, int i,
     {
         CV_Assert( i < 0 );
         UMat& m = *(UMat*)obj;
+        CV_Assert(!(m.empty() && fixedType() && fixedSize()) && "Can't reallocate empty UMat with locked layout (probably due to misused 'const' modifier)");
         if (allowTransposed && !m.empty() &&
             d == 2 && m.dims == 2 &&
             m.type() == mtype && m.rows == sizes[1] && m.cols == sizes[0] &&
@@ -1290,13 +1292,13 @@ void _OutputArray::create(int d, const int* sizes, int mtype, int i,
             if(CV_MAT_CN(mtype) == m.channels() && ((1 << CV_MAT_TYPE(flags)) & fixedDepthMask) != 0 )
                 mtype = m.type();
             else
-                CV_CheckTypeEQ(m.type(), CV_MAT_TYPE(mtype), "");
+                CV_CheckTypeEQ(m.type(), CV_MAT_TYPE(mtype), "Can't reallocate UMat with locked type (probably due to misused 'const' modifier)");
         }
         if(fixedSize())
         {
-            CV_CheckEQ(m.dims, d, "");
+            CV_CheckEQ(m.dims, d, "Can't reallocate UMat with locked size (probably due to misused 'const' modifier)");
             for(int j = 0; j < d; ++j)
-                CV_CheckEQ(m.size[j], sizes[j], "");
+                CV_CheckEQ(m.size[j], sizes[j], "Can't reallocate UMat with locked size (probably due to misused 'const' modifier)");
         }
         m.create(d, sizes, mtype);
         return;

modules/core/src/ocl.cpp

@@ -3102,7 +3102,7 @@ void initializeContextFromHandle(Context& ctx, void* _platform, void* _context,
     cl_context context = (cl_context)_context;
     cl_device_id deviceID = (cl_device_id)_device;
 
-    std::string platformName = PlatformInfo(platformID).name();
+    std::string platformName = PlatformInfo(&platformID).name();
 
     auto clExecCtx = OpenCLExecutionContext::create(platformName, platformID, context, deviceID);
     CV_Assert(!clExecCtx.empty());
@@ -3311,7 +3311,7 @@ KernelArg KernelArg::Constant(const Mat& m)
 struct Kernel::Impl
 {
     Impl(const char* kname, const Program& prog) :
-        refcount(1), handle(NULL), isInProgress(false), nu(0)
+        refcount(1), handle(NULL), isInProgress(false), isAsyncRun(false), nu(0)
     {
         cl_program ph = (cl_program)prog.ptr();
         cl_int retval = 0;
@@ -3388,6 +3388,7 @@ struct Kernel::Impl
     enum { MAX_ARRS = 16 };
     UMatData* u[MAX_ARRS];
     bool isInProgress;
+    bool isAsyncRun;  // true if kernel was scheduled in async mode
     int nu;
     std::list<Image2D> images;
     bool haveTempDstUMats;
@@ -3667,13 +3668,45 @@ bool Kernel::run(int dims, size_t _globalsize[], size_t _localsize[],
 }
 
 
+static bool isRaiseErrorOnReuseAsyncKernel()
+{
+    static bool initialized = false;
+    static bool value = false;
+    if (!initialized)
+    {
+        value = cv::utils::getConfigurationParameterBool("OPENCV_OPENCL_RAISE_ERROR_REUSE_ASYNC_KERNEL", false);
+        initialized = true;
+    }
+    return value;
+}
+
 bool Kernel::Impl::run(int dims, size_t globalsize[], size_t localsize[],
         bool sync, int64* timeNS, const Queue& q)
 {
     CV_INSTRUMENT_REGION_OPENCL_RUN(name.c_str());
 
-    if (!handle || isInProgress)
+    if (!handle)
+    {
+        CV_LOG_ERROR(NULL, "OpenCL kernel has zero handle: " << name);
         return false;
+    }
+
+    if (isAsyncRun)
+    {
+        CV_LOG_ERROR(NULL, "OpenCL kernel can't be reused in async mode: " << name);
+        if (isRaiseErrorOnReuseAsyncKernel())
+            CV_Assert(0);
+        return false;  // OpenCV 5.0: raise error
+    }
+    isAsyncRun = !sync;
+
+    if (isInProgress)
+    {
+        CV_LOG_ERROR(NULL, "Previous OpenCL kernel launch is not finished: " << name);
+        if (isRaiseErrorOnReuseAsyncKernel())
+            CV_Assert(0);
+        return false;  // OpenCV 5.0: raise error
+    }
 
     cl_command_queue qq = getQueue(q);
     if (haveTempDstUMats)

modules/core/src/opencl/runtime/opencl_core.cpp

@@ -177,6 +177,55 @@ static void *GetHandle(const char *file)
     return handle;
 }
 
+#ifdef __ANDROID__
+
+static const char *defaultAndroidPaths[] = {
+    "libOpenCL.so",
+    "/system/lib64/libOpenCL.so",
+    "/system/vendor/lib64/libOpenCL.so",
+    "/system/vendor/lib64/egl/libGLES_mali.so",
+    "/system/vendor/lib64/libPVROCL.so",
+    "/data/data/org.pocl.libs/files/lib64/libpocl.so",
+    "/system/lib/libOpenCL.so",
+    "/system/vendor/lib/libOpenCL.so",
+    "/system/vendor/lib/egl/libGLES_mali.so",
+    "/system/vendor/lib/libPVROCL.so",
+    "/data/data/org.pocl.libs/files/lib/libpocl.so"
+};
+
+static void* GetProcAddress(const char* name)
+{
+    static bool initialized = false;
+    static void* handle = NULL;
+    if (!handle && !initialized)
+    {
+        cv::AutoLock lock(cv::getInitializationMutex());
+        if (!initialized)
+        {
+            bool foundOpenCL = false;
+            for (unsigned int i = 0; i < (sizeof(defaultAndroidPaths)/sizeof(char*)); i++)
+            {
+                const char* path = (i==0) ? getRuntimePath(defaultAndroidPaths[i]) : defaultAndroidPaths[i];
+                if (path) {
+                    handle = GetHandle(path);
+                    if (handle) {
+                        foundOpenCL = true;
+                        break;
+                    }
+                }
+            }
+            initialized = true;
+            if (!foundOpenCL)
+                fprintf(stderr, ERROR_MSG_CANT_LOAD);
+        }
+    }
+    if (!handle)
+        return NULL;
+    return dlsym(handle, name);
+}
+
+#else // NOT __ANDROID__
+
 static void* GetProcAddress(const char* name)
 {
     static bool initialized = false;
@@ -206,6 +255,8 @@ static void* GetProcAddress(const char* name)
         return NULL;
     return dlsym(handle, name);
 }
+#endif // __ANDROID__
+
 #define CV_CL_GET_PROC_ADDRESS(name) GetProcAddress(name)
 #endif
 

modules/core/src/opengl.cpp

@@ -1690,7 +1690,7 @@ Context& initializeContextFromGL()
         CV_Error(cv::Error::OpenCLInitError, "OpenCL: Can't create context for OpenGL interop");
 
     cl_platform_id platform = platforms[found];
-    std::string platformName = PlatformInfo(platform).name();
+    std::string platformName = PlatformInfo(&platform).name();
 
     OpenCLExecutionContext clExecCtx = OpenCLExecutionContext::create(platformName, platform, context, device);
     clReleaseDevice(device);

modules/core/src/parallel.cpp

@@ -54,7 +54,8 @@
 #endif
 
 #if defined __linux__ || defined __APPLE__ || defined __GLIBC__ \
-    || defined __HAIKU__ || defined __EMSCRIPTEN__ || defined __FreeBSD__
+    || defined __HAIKU__ || defined __EMSCRIPTEN__ || defined __FreeBSD__ \
+    || defined __OpenBSD__
     #include <unistd.h>
     #include <stdio.h>
     #include <sys/types.h>

modules/core/src/va_intel.cpp

@@ -25,13 +25,17 @@ using namespace cv;
 #  include "opencl_kernels_core.hpp"
 #endif // HAVE_OPENCL
 
-#if defined(HAVE_VA_INTEL) && defined(HAVE_OPENCL)
+#ifdef HAVE_VA_INTEL
+#ifdef HAVE_VA_INTEL_OLD_HEADER
 #  include <CL/va_ext.h>
-#endif // HAVE_VA_INTEL && HAVE_OPENCL
+#else
+#  include <CL/cl_va_api_media_sharing_intel.h>
+#endif
+#endif
 
 namespace cv { namespace va_intel {
 
-#if defined(HAVE_VA_INTEL) && defined(HAVE_OPENCL)
+#ifdef HAVE_VA_INTEL
 
 static clGetDeviceIDsFromVA_APIMediaAdapterINTEL_fn clGetDeviceIDsFromVA_APIMediaAdapterINTEL = NULL;
 static clCreateFromVA_APIMediaSurfaceINTEL_fn       clCreateFromVA_APIMediaSurfaceINTEL       = NULL;
@@ -40,7 +44,7 @@ static clEnqueueReleaseVA_APIMediaSurfacesINTEL_fn  clEnqueueReleaseVA_APIMediaS
 
 static bool contextInitialized = false;
 
-#endif // HAVE_VA_INTEL && HAVE_OPENCL
+#endif // HAVE_VA_INTEL
 
 namespace ocl {
 
@@ -50,7 +54,7 @@ Context& initializeContextFromVA(VADisplay display, bool tryInterop)
 #if !defined(HAVE_VA)
     NO_VA_SUPPORT_ERROR;
 #else  // !HAVE_VA
-# if (defined(HAVE_VA_INTEL) && defined(HAVE_OPENCL))
+#   ifdef HAVE_VA_INTEL
     contextInitialized = false;
     if (tryInterop)
     {
@@ -137,7 +141,7 @@ Context& initializeContextFromVA(VADisplay display, bool tryInterop)
             contextInitialized = true;
 
             cl_platform_id platform = platforms[found];
-            std::string platformName = PlatformInfo(platform).name();
+            std::string platformName = PlatformInfo(&platform).name();
 
             OpenCLExecutionContext clExecCtx;
             try
@@ -154,7 +158,7 @@ Context& initializeContextFromVA(VADisplay display, bool tryInterop)
             return const_cast<Context&>(clExecCtx.getContext());
         }
     }
-# endif // HAVE_VA_INTEL && HAVE_OPENCL
+# endif // HAVE_VA_INTEL
     {
         Context& ctx = Context::getDefault(true);
         return ctx;
@@ -162,7 +166,7 @@ Context& initializeContextFromVA(VADisplay display, bool tryInterop)
 #endif  // !HAVE_VA
 }
 
-#if defined(HAVE_VA_INTEL) && defined(HAVE_OPENCL)
+#ifdef HAVE_VA_INTEL
 static bool ocl_convert_nv12_to_bgr(cl_mem clImageY, cl_mem clImageUV, cl_mem clBuffer, int step, int cols, int rows)
 {
     ocl::Kernel k;
@@ -188,7 +192,7 @@ static bool ocl_convert_bgr_to_nv12(cl_mem clBuffer, int step, int cols, int row
     size_t globalsize[] = { (size_t)cols, (size_t)rows };
     return k.run(2, globalsize, 0, false);
 }
-#endif // HAVE_VA_INTEL && HAVE_OPENCL
+#endif // HAVE_VA_INTEL
 
 } // namespace cv::va_intel::ocl
 
@@ -511,7 +515,7 @@ void convertToVASurface(VADisplay display, InputArray src, VASurfaceID surface,
     Size srcSize = src.size();
     CV_Assert(srcSize.width == size.width && srcSize.height == size.height);
 
-# if (defined(HAVE_VA_INTEL) && defined(HAVE_OPENCL))
+#ifdef HAVE_VA_INTEL
     if (contextInitialized)
     {
         UMat u = src.getUMat();
@@ -559,7 +563,7 @@ void convertToVASurface(VADisplay display, InputArray src, VASurfaceID surface,
             CV_Error(cv::Error::OpenCLApiCallError, "OpenCL: clReleaseMem failed (UV plane)");
     }
     else
-# endif // HAVE_VA_INTEL && HAVE_OPENCL
+# endif // HAVE_VA_INTEL
     {
         Mat m = src.getMat();
 
@@ -612,7 +616,7 @@ void convertFromVASurface(VADisplay display, VASurfaceID surface, Size size, Out
     // TODO Need to specify ACCESS_WRITE here somehow to prevent useless data copying!
     dst.create(size, dtype);
 
-# if (defined(HAVE_VA_INTEL) && defined(HAVE_OPENCL))
+#ifdef HAVE_VA_INTEL
     if (contextInitialized)
     {
         UMat u = dst.getUMat();
@@ -660,7 +664,7 @@ void convertFromVASurface(VADisplay display, VASurfaceID surface, Size size, Out
             CV_Error(cv::Error::OpenCLApiCallError, "OpenCL: clReleaseMem failed (UV plane)");
     }
     else
-# endif // HAVE_VA_INTEL && HAVE_OPENCL
+# endif // HAVE_VA_INTEL
     {
         Mat m = dst.getMat();
 

modules/core/test/test_mat.cpp

@@ -2175,4 +2175,32 @@ TEST(Mat, empty_iterator_16855)
     EXPECT_TRUE(m.begin<uchar>() == m.end<uchar>());
 }
 
+
+TEST(Mat, regression_18473)
+{
+    std::vector<int> sizes(3);
+    sizes[0] = 20;
+    sizes[1] = 50;
+    sizes[2] = 100;
+#if 1  // with the fix
+    std::vector<size_t> steps(2);
+    steps[0] = 50*100*2;
+    steps[1] = 100*2;
+#else  // without the fix
+    std::vector<size_t> steps(3);
+    steps[0] = 50*100*2;
+    steps[1] = 100*2;
+    steps[2] = 2;
+#endif
+    std::vector<short> data(20*50*100, 0);  // 1Mb
+    data[data.size() - 1] = 5;
+
+    // param steps Array of ndims-1 steps
+    Mat m(sizes, CV_16SC1, (void*)data.data(), (const size_t*)steps.data());
+
+    ASSERT_FALSE(m.empty());
+    EXPECT_EQ((int)5, (int)m.at<short>(19, 49, 99));
+}
+
+
 }} // namespace

modules/dnn/CMakeLists.txt

@@ -128,18 +128,11 @@ else()
   set(sources_options ${sources_options} EXCLUDE_CUDA)
 endif()
 
-
 if(HAVE_TENGINE)
 	list(APPEND include_dirs ${TENGINE_INCLUDE_DIRS})
-	if(EXISTS ${TENGINE_LIBRARIES})
-		list(APPEND libs ${TENGINE_LIBRARIES})
-	else()
-		ocv_add_dependencies(opencv_dnn tengine)
-		list(APPEND libs ${TENGINE_LIBRARIES})
-	endif()
+	list(APPEND libs -Wl,--whole-archive ${TENGINE_LIBRARIES} -Wl,--no-whole-archive)
 endif()
 
-
 ocv_module_include_directories(${include_dirs})
 if(CMAKE_CXX_COMPILER_ID STREQUAL "GNU")
   ocv_append_source_files_cxx_compiler_options(fw_srcs "-Wno-suggest-override")  # GCC

modules/dnn/perf/perf_net.cpp

@@ -111,6 +111,10 @@ PERF_TEST_P_(DNNTestNetwork, ENet)
     if ((backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU) ||
         (backend == DNN_BACKEND_OPENCV && target == DNN_TARGET_OPENCL_FP16))
         throw SkipTestException("");
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2021010000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+        throw SkipTestException("");
+#endif
     processNet("dnn/Enet-model-best.net", "", "enet.yml",
             Mat(cv::Size(512, 256), CV_32FC3));
 }
@@ -202,6 +206,10 @@ PERF_TEST_P_(DNNTestNetwork, YOLOv3)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_OPENCL_FP16)
         throw SkipTestException("Test is disabled in OpenVINO 2020.4");
 #endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021010000)  // nGraph compilation failure
+    if (target == DNN_TARGET_MYRIAD)
+        throw SkipTestException("");
+#endif
 
     Mat sample = imread(findDataFile("dnn/dog416.png"));
     cvtColor(sample, sample, COLOR_BGR2RGB);
@@ -214,7 +222,7 @@ PERF_TEST_P_(DNNTestNetwork, YOLOv4)
 {
     if (backend == DNN_BACKEND_HALIDE)
         throw SkipTestException("");
-    if (target == DNN_TARGET_MYRIAD)
+    if (target == DNN_TARGET_MYRIAD)  // not enough resources
         throw SkipTestException("");
 #if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2020040000)  // nGraph compilation failure
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_OPENCL)
@@ -233,6 +241,10 @@ PERF_TEST_P_(DNNTestNetwork, YOLOv4_tiny)
 {
     if (backend == DNN_BACKEND_HALIDE)
         throw SkipTestException("");
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021010000)  // nGraph compilation failure
+    if (target == DNN_TARGET_MYRIAD)
+        throw SkipTestException("");
+#endif
     Mat sample = imread(findDataFile("dnn/dog416.png"));
     cvtColor(sample, sample, COLOR_BGR2RGB);
     Mat inp;
@@ -263,6 +275,10 @@ PERF_TEST_P_(DNNTestNetwork, Inception_v2_Faster_RCNN)
 #if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2019020000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
         throw SkipTestException("Test is disabled in OpenVINO 2019R2");
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021010000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_MYRIAD)
+        throw SkipTestException("Test is disabled in OpenVINO 2021.1 / MYRIAD");
 #endif
     if (backend == DNN_BACKEND_HALIDE ||
         (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target != DNN_TARGET_CPU) ||

modules/dnn/src/cuda4dnn/init.hpp

@@ -57,6 +57,9 @@ namespace cv { namespace dnn { namespace cuda4dnn {
 
     bool isDeviceCompatible()
     {
+        if (getDeviceCount() <= 0)
+            return false;
+
         int device_id = getDevice();
         if (device_id < 0)
             return false;
@@ -77,6 +80,9 @@ namespace cv { namespace dnn { namespace cuda4dnn {
 
     bool doesDeviceSupportFP16()
     {
+        if (getDeviceCount() <= 0)
+            return false;
+
         int device_id = getDevice();
         if (device_id < 0)
             return false;

modules/dnn/src/darknet/darknet_io.cpp

@@ -984,8 +984,8 @@ namespace cv {
                     }
 
                     std::string activation = getParam<std::string>(layer_params, "activation", "linear");
-                    if(activation == "leaky" || activation == "swish" || activation == "mish" || activation == "logistic")
-                        ++cv_layers_counter;  // For ReLU, Swish, Mish, Sigmoid
+                    if (activation != "linear")
+                        ++cv_layers_counter;  // For ReLU, Swish, Mish, Sigmoid, etc
 
                     if(!darknet_layers_counter)
                         tensor_shape.resize(1);

modules/dnn/src/dnn.cpp

@@ -1585,7 +1585,9 @@ struct Net::Impl : public detail::NetImplBase
     {
         CV_TRACE_FUNCTION();
         if (preferableBackend == DNN_BACKEND_OPENCV)
+        {
             CV_Assert(preferableTarget == DNN_TARGET_CPU || IS_DNN_OPENCL_TARGET(preferableTarget));
+        }
         else if (preferableBackend == DNN_BACKEND_HALIDE)
             initHalideBackend();
         else if (preferableBackend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
@@ -2652,12 +2654,15 @@ struct Net::Impl : public detail::NetImplBase
 
                 // OpenCL: fuse convolution layer followed by eltwise + relu
                 // CUDA: fuse convolution layer followed by eltwise (and optional activation)
-                if ((IS_DNN_OPENCL_TARGET(preferableTarget) || IS_DNN_CUDA_TARGET(preferableTarget)) &&
-                    ld.layerInstance->type == "Convolution" )
+                while (nextData &&
+                    (IS_DNN_OPENCL_TARGET(preferableTarget) || IS_DNN_CUDA_TARGET(preferableTarget)) &&
+                    ld.layerInstance->type == "Convolution"
+                )  // semantic of 'if'
                 {
-                    Ptr<EltwiseLayer> nextEltwiseLayer;
-                    if( nextData )
-                        nextEltwiseLayer = nextData->layerInstance.dynamicCast<EltwiseLayer>();
+                    Ptr<EltwiseLayer> nextEltwiseLayer = nextData->layerInstance.dynamicCast<EltwiseLayer>();
+                    if (nextEltwiseLayer.empty())
+                        break;
+
 #ifdef HAVE_CUDA
                     // CUDA backend supports fusion with eltwise sum (without variable channels)
                     // `nextEltwiseLayer` is reset if eltwise layer doesn't have a compatible configuration for fusion
@@ -2673,7 +2678,37 @@ struct Net::Impl : public detail::NetImplBase
                             nextEltwiseLayer = Ptr<EltwiseLayer>();
                     }
 #endif
-                    if (!nextEltwiseLayer.empty() && nextData && nextData->inputBlobsId.size() == 2)
+
+                    if (pinsToKeep.count(lpNext) != 0)
+                        break;
+                    if (nextData->inputBlobsId.size() != 2)
+                        break;
+
+                    if (!nextData->params.has("operation") || toLowerCase(nextData->params.get<String>("operation")) == "sum")
+                    {
+                        if (nextData->params.has("coeff"))
+                        {
+                            DictValue paramCoeff = nextData->params.get("coeff");
+                            int n = paramCoeff.size();
+                            bool isCoeffOneOne = (n == 2);
+                            for (int i = 0; isCoeffOneOne && i < n; i++)
+                            {
+                                float c = paramCoeff.get<float>(i);
+                                isCoeffOneOne &= (c == 1.0f);
+                            }
+                            if (!isCoeffOneOne)
+                            {
+                                CV_LOG_DEBUG(NULL, "DNN/OpenCL: fusion of 'Sum' without coeffs (or {1.0, 1.0}) is supported only");
+                                break;
+                            }
+                        }
+                    }
+                    else
+                    {
+                        CV_LOG_DEBUG(NULL, "DNN/OpenCL: fusion with eltwise operation is not supported: " << nextData->params.get<String>("operation"));
+                        break;
+                    }
+
                     {
                         LayerData *eltwiseData = nextData;
 
@@ -2730,11 +2765,13 @@ struct Net::Impl : public detail::NetImplBase
                                 // we need to check them separately; hence, the fuse variables
                                 bool fuse_eltwise = false, fuse_activation = false;
 
+                                Ptr<PowerLayer> activ_power;
                                 if (IS_DNN_OPENCL_TARGET(preferableTarget) && !nextFusabeleActivLayer.empty() &&
                                     nextData &&
                                     (!nextData->type.compare("ReLU") ||
                                      !nextData->type.compare("ChannelsPReLU") ||
-                                     !nextData->type.compare("Power")) &&
+                                     (!nextData->type.compare("Power") && (activ_power = nextFusabeleActivLayer.dynamicCast<PowerLayer>()) && activ_power->scale == 1.0f)
+                                    ) &&
                                     currLayer->setActivation(nextFusabeleActivLayer))
                                 {
                                     fuse_eltwise = true;
@@ -2866,6 +2903,8 @@ struct Net::Impl : public detail::NetImplBase
                             }
                         }
                     }
+
+                    break;
                 }
             }
 
@@ -3105,11 +3144,11 @@ struct Net::Impl : public detail::NetImplBase
 
         Ptr<Layer> layer = ld.layerInstance;
 
-        TickMeter tm;
-        tm.start();
-
         if( !ld.skip )
         {
+            TickMeter tm;
+            tm.start();
+
             std::map<int, Ptr<BackendNode> >::iterator it = ld.backendNodes.find(preferableBackend);
             if (preferableBackend == DNN_BACKEND_OPENCV || it == ld.backendNodes.end() || it->second.empty())
             {
@@ -3318,12 +3357,15 @@ struct Net::Impl : public detail::NetImplBase
                     CV_Error(Error::StsNotImplemented, "Unknown backend identifier");
                 }
             }
+
+            tm.stop();
+            int64 t = tm.getTimeTicks();
+            layersTimings[ld.id] = (t > 0) ? t : t + 1;  // zero for skipped layers only
         }
         else
-            tm.reset();
-
-        tm.stop();
-        layersTimings[ld.id] = tm.getTimeTicks();
+        {
+            layersTimings[ld.id] = 0;
+        }
 
         ld.flag = 1;
     }
@@ -3932,11 +3974,16 @@ void Net::connect(String _outPin, String _inPin)
 Mat Net::forward(const String& outputName)
 {
     CV_TRACE_FUNCTION();
+    CV_Assert(!empty());
 
     String layerName = outputName;
 
     if (layerName.empty())
-        layerName = getLayerNames().back();
+    {
+        std::vector<String> layerNames = getLayerNames();
+        CV_Assert(!layerNames.empty());
+        layerName = layerNames.back();
+    }
 
     std::vector<LayerPin> pins(1, impl->getPinByAlias(layerName));
     impl->setUpNet(pins);
@@ -3948,11 +3995,17 @@ Mat Net::forward(const String& outputName)
 AsyncArray Net::forwardAsync(const String& outputName)
 {
     CV_TRACE_FUNCTION();
+    CV_Assert(!empty());
+
 #ifdef CV_CXX11
     String layerName = outputName;
 
     if (layerName.empty())
-        layerName = getLayerNames().back();
+    {
+        std::vector<String> layerNames = getLayerNames();
+        CV_Assert(!layerNames.empty());
+        layerName = layerNames.back();
+    }
 
     std::vector<LayerPin> pins(1, impl->getPinByAlias(layerName));
     impl->setUpNet(pins);
@@ -3973,11 +4026,16 @@ AsyncArray Net::forwardAsync(const String& outputName)
 void Net::forward(OutputArrayOfArrays outputBlobs, const String& outputName)
 {
     CV_TRACE_FUNCTION();
+    CV_Assert(!empty());
 
     String layerName = outputName;
 
     if (layerName.empty())
-        layerName = getLayerNames().back();
+    {
+        std::vector<String> layerNames = getLayerNames();
+        CV_Assert(!layerNames.empty());
+        layerName = layerNames.back();
+    }
 
     std::vector<LayerPin> pins(1, impl->getPinByAlias(layerName));
     impl->setUpNet(pins);
@@ -4569,6 +4627,8 @@ std::vector<Ptr<Layer> > Net::getLayerInputs(LayerId layerId)
 
 std::vector<String> Net::getLayerNames() const
 {
+    CV_TRACE_FUNCTION();
+
     std::vector<String> res;
     res.reserve(impl->layers.size());
 

modules/dnn/src/layers/convolution_layer.cpp

@@ -48,6 +48,8 @@
 #include "../ie_ngraph.hpp"
 #include "../op_vkcom.hpp"
 
+#include <opencv2/core/utils/logger.hpp>
+
 #include "opencv2/core/hal/hal.hpp"
 #include "opencv2/core/hal/intrin.hpp"
 #include <iostream>
@@ -248,6 +250,10 @@ public:
     float power;
 #endif
 
+#ifdef HAVE_TENGINE
+    teng_graph_t tengine_graph;
+#endif
+
 #ifdef HAVE_CUDA
     cuda4dnn::ConvolutionConfiguration::FusionMode cudaFusionMode;
     cuda4dnn::ConvolutionConfiguration::ActivationType cudaActType;
@@ -266,8 +272,20 @@ public:
 #ifdef HAVE_CUDA
         cudaFusionMode = cuda4dnn::ConvolutionConfiguration::FusionMode::NONE;
         cudaActType = cuda4dnn::ConvolutionConfiguration::ActivationType::IDENTITY;
+#endif
+#ifdef HAVE_TENGINE
+        tengine_graph=NULL;
 #endif
     }
+#ifdef HAVE_TENGINE
+    ~ConvolutionLayerImpl()
+    {
+        if(NULL != tengine_graph )
+        {
+            tengine_release(tengine_graph);
+        }
+    }
+#endif
 
     MatShape computeColRowShape(const MatShape &inpShape, const MatShape &outShape) const CV_OVERRIDE
     {
@@ -391,6 +409,13 @@ public:
             for(int i = 0; i < numOutput; i++ )
                 biasvec[i] = biasMat.at<float>(i);
         }
+#ifdef HAVE_TENGINE
+        if(NULL != tengine_graph )
+        {
+            tengine_release(tengine_graph);
+            tengine_graph = NULL ;
+        }
+#endif
 #ifdef HAVE_OPENCL
         convolutionOp.release();
 #endif
@@ -413,6 +438,14 @@ public:
             Ptr<PowerLayer> activ_power = activ.dynamicCast<PowerLayer>();
             if (!activ_power.empty())
             {
+                if (activ_power->scale != 1.0f)  // not supported well by implementation, #17964
+                {
+                    // FIXIT no way to check number of blobs (like, eltwise input)
+                    CV_LOG_DEBUG(NULL, "DNN/OpenCL: can't configure Power activation (scale != 1.0f)");
+                    activ.release();
+                    newActiv = false;
+                    return false;
+                }
                 if (activ_power->scale != 1.f || activ_power->shift != 0.f)
                 {
                     const int outCh = blobs[0].size[0];
@@ -1765,26 +1798,50 @@ public:
         }
 
 #ifdef HAVE_TENGINE
-        int inch = inputs[0].size[1]; 		// inch
-        int in_h = inputs[0].size[2]; 		// in_h
-        int in_w = inputs[0].size[3]; 		// in_w
+        bool tengine_ret = false; ;
 
-        int out_b = outputs[0].size[0];     // out batch size
-        int outch = outputs[0].size[1]; 	// outch
-        int out_h = outputs[0].size[2]; 	// out_h
-        int out_w = outputs[0].size[3]; 	// out_w
+        std::vector<Mat> teng_in, teng_out;
+        inputs_arr.getMatVector(teng_in);
+        outputs_arr.getMatVector(teng_out);
 
-        float *input_  = inputs[0].ptr<float>();
-        float *output_ = outputs[0].ptr<float>();
+        int inch = teng_in[0].size[1];    // inch
+        int in_h = teng_in[0].size[2];    // in_h
+        int in_w = teng_in[0].size[3];    // in_w
+
+        int out_b = teng_out[0].size[0];  // out batch size
+        int outch = teng_out[0].size[1];  // outch
+        int out_h = teng_out[0].size[2];  // out_h
+        int out_w = teng_out[0].size[3];  // out_w
+
+        float *input_  = teng_in[0].ptr<float>();
+        float *output_ = teng_out[0].ptr<float>();
         float *kernel_ = weightsMat.ptr<float>();
         float *teg_bias = &biasvec[0];
 
-        bool tengine_ret = tengine_forward(input_, inch, ngroups, in_h, in_w,
-                                    output_, out_b, outch, out_h, out_w,
-                                    kernel_, kernel_size.size(), kernel.height, kernel.width,
-                                    teg_bias, stride.height, stride.width,
-                                    pad.height,  pad.width, dilation.height, dilation.width,
-                                    weightsMat.step1(), padMode);
+        int nstripes = std::max(getNumThreads(), 1);
+
+        /* tengine_init will run when first time. */
+        if(NULL == tengine_graph)
+        {
+            tengine_graph = tengine_init(name.c_str(), input_, inch, ngroups, in_h, in_w,
+                                         output_, out_b, outch, out_h, out_w,
+                                         kernel_, kernel_size.size(), kernel.height, kernel.width,
+                                         teg_bias, stride.height, stride.width,
+                                         pad.height,  pad.width, dilation.height, dilation.width,
+                                         weightsMat.step1(), padMode, tengine_graph, nstripes);
+            /*printf("Init(%s):  input=%p(%d %d %d %d ),output=%p(%d %d %d %d ),kernel=%p(%ld %d %d ), bias=%p ,"
+                   "stride(%d %d), pad(%d %d), dilation(%d %d) ,weightsMat=%ld, padMode=%s ,tengine_graph = %p \n",
+                   name.c_str(),input_, inch, ngroups, in_h, in_w,
+                   output_, out_b, outch, out_h, out_w,
+                   kernel_, kernel_size.size(), kernel.height, kernel.width,
+                   teg_bias, stride.height, stride.width,
+                   pad.height,  pad.width, dilation.height, dilation.width,
+                   weightsMat.step1(), padMode.c_str() ,tengine_graph);*/
+        }
+        if(NULL != tengine_graph)
+        {
+            tengine_ret = tengine_forward(tengine_graph);
+        }
         /* activation */
         if((true == tengine_ret) && activ )
         {

modules/dnn/src/layers/resize_layer.cpp

@@ -45,7 +45,7 @@ public:
             CV_Assert(params.has("zoom_factor_x") && params.has("zoom_factor_y"));
         }
         interpolation = params.get<String>("interpolation");
-        CV_Assert(interpolation == "nearest" || interpolation == "opencv_linear" || interpolation == "bilinear");
+        CV_Check(interpolation, interpolation == "nearest" || interpolation == "opencv_linear" || interpolation == "bilinear", "");
 
         alignCorners = params.get<bool>("align_corners", false);
     }

modules/dnn/src/ocl4dnn/src/math_functions.cpp

@@ -46,6 +46,8 @@
 #include <vector>
 #include "opencl_kernels_dnn.hpp"
 
+#include "opencv2/core/utils/logger.hpp"
+
 namespace cv { namespace dnn { namespace ocl4dnn {
 
 enum gemm_data_type_t
@@ -238,10 +240,6 @@ static bool ocl4dnnFastImageGEMM(const CBLAS_TRANSPOSE TransA,
         kernel_name += "_float";
     }
 
-    ocl::Kernel oclk_gemm_float(kernel_name.c_str(), ocl::dnn::gemm_image_oclsrc, opts);
-    if (oclk_gemm_float.empty())
-        return false;
-
     while (C_start_y < M)
     {
         blockC_width = std::min(static_cast<int>(N) - C_start_x, blocksize);
@@ -348,6 +346,10 @@ static bool ocl4dnnFastImageGEMM(const CBLAS_TRANSPOSE TransA,
             }
             local[1] = 1;
 
+            ocl::Kernel oclk_gemm_float(kernel_name.c_str(), ocl::dnn::gemm_image_oclsrc, opts);
+            if (oclk_gemm_float.empty())
+                return false;
+
             cl_uint arg_idx = 0;
             if (is_image_a)
                 oclk_gemm_float.set(arg_idx++, ocl::KernelArg::PtrReadOnly(A));
@@ -378,7 +380,10 @@ static bool ocl4dnnFastImageGEMM(const CBLAS_TRANSPOSE TransA,
             oclk_gemm_float.set(arg_idx++, isFirstColBlock);
 
             if (!oclk_gemm_float.run(2, global, local, false))
+            {
+                CV_LOG_WARNING(NULL, "OpenCL kernel enqueue failed: " << kernel_name);
                 return false;
+            }
 
             if (TransA == CblasNoTrans)
                 A_start_x += blockA_width;

modules/dnn/src/ocl4dnn/src/ocl4dnn_conv_spatial.cpp

@@ -607,6 +607,7 @@ void OCL4DNNConvSpatial<Dtype>::calculateBenchmark(const UMat &bottom, UMat &ver
 {
     options_.str(""); options_.clear(); // clear contents and state flags
     createBasicKernel(1, 1, 1);
+    CV_Assert(!kernelQueue.empty());  // basic kernel must be available
     kernel_index_ = kernelQueue.size() - 1;
     convolve(bottom, verifyTop, weight, bias, numImages, kernelQueue[kernel_index_]);
     CV_Assert(phash.find(kernelQueue[kernel_index_]->kernelName) != phash.end());
@@ -1713,6 +1714,7 @@ void OCL4DNNConvSpatial<float>::useFirstAvailable(const UMat &bottom,
                                     tunerItems[i]->blockHeight,
                                     tunerItems[i]->blockDepth))
         {
+            CV_Assert(!kernelQueue.empty());  // basic kernel must be available
             int kernelIdx = kernelQueue.size() - 1;
             kernelConfig* config = kernelQueue[kernelIdx].get();
             bool failed = false;
@@ -1883,6 +1885,7 @@ void OCL4DNNConvSpatial<float>::setupConvolution(const UMat &bottom,
         CV_LOG_INFO(NULL, "fallback to basic kernel");
         options_.str(""); options_.clear(); // clear contents and state flags
         createBasicKernel(1, 1, 1);
+        CV_Assert(!kernelQueue.empty());  // basic kernel must be available
         kernel_index_ = kernelQueue.size() - 1;
     }
     this->bestKernelConfig = kernelQueue[kernel_index_];

modules/dnn/src/opencl/conv_layer_spatial.cl

@@ -205,7 +205,7 @@ __kernel void ConvolveBasic(
 #if APPLY_BIAS
                 ACTIVATION_FUNCTION(convolved_image, offset, sum[kern] + bias[biasIndex + kern], biasIndex + kern);
 #else
-                ACTIVATION_FUNCTION(convolved_image, offset, sum[kern], biasIndex + kern);
+                ACTIVATION_FUNCTION(convolved_image, offset, sum[kern], kernelNum + kern);
 #endif
             }
         }

modules/dnn/src/opencl/ocl4dnn_lrn.cl

@@ -83,7 +83,7 @@ __kernel void TEMPLATE(lrn_full_no_scale,Dtype)(const int nthreads, __global con
             * in_off[(head - size) * step];
       }
       scale_val = k + accum_scale * alpha_over_size;
-      out_off[(head - post_pad) * step] = in_off[(head - post_pad) * step] * (Dtype)native_powr((Dtype)scale_val, (Dtype)negative_beta);
+      out_off[(head - post_pad) * step] = in_off[(head - post_pad) * step] * (Dtype)native_powr(scale_val, negative_beta);
       ++head;
     }
     // subtract only
@@ -93,7 +93,7 @@ __kernel void TEMPLATE(lrn_full_no_scale,Dtype)(const int nthreads, __global con
             * in_off[(head - size) * step];
       }
       scale_val = k + accum_scale * alpha_over_size;
-      out_off[(head - post_pad) * step] = in_off[(head - post_pad) * step] * (Dtype)native_powr((Dtype)scale_val, (Dtype)negative_beta);
+      out_off[(head - post_pad) * step] = in_off[(head - post_pad) * step] * (Dtype)native_powr(scale_val, negative_beta);
       ++head;
     }
   }

modules/dnn/src/opencl/prior_box.cl

@@ -114,6 +114,6 @@ __kernel void clip(const int nthreads,
     for (int index = get_global_id(0); index < nthreads; index += get_global_size(0))
     {
         Dtype4 vec = vload4(index, dst);
-        vstore4(clamp(vec, 0.0f, 1.0f), index, dst);
+        vstore4(clamp(vec, (Dtype)0.0f, (Dtype)1.0f), index, dst);
     }
 }

modules/dnn/src/tengine4dnn/include/tengine_graph_convolution.hpp

@@ -26,17 +26,24 @@
 #define TENGINE_GRAPH_CONVOLUTION_HPP
 
 #define FLOAT_TO_REALSIZE (4)
+#ifdef HAVE_TENGINE
+
+#include "tengine_c_api.h"
 
 namespace cv
 {
 namespace dnn
 {
-bool tengine_forward(float *input_, int inch, int group, int in_h, int in_w,
+teng_graph_t  tengine_init(const char* name , float* input_, int inch, int group, int in_h, int in_w,
                         float *output_, int out_b, int outch, int out_h, int out_w,
                         float *kernel_,int kernel_s , int kernel_h, int kernel_w,
                         float *teg_bias, int stride_h,int stride_w,
                         int pad_h, int pad_w,  int dilation_h, int dilation_w,
-                        size_t wstep, const std::string padMode) ;
+                        size_t wstep, const std::string padMode , teng_graph_t& graph, int nstripes) ;
+
+bool tengine_forward(teng_graph_t& graph) ;
+bool tengine_release(teng_graph_t& graph) ;
 }
 }
-#endif /* TENGINE_GRAPH_CONVOLUTION_HPP */
+#endif
+#endif /* TENGINE_GRAPH_CONVOLUTION_HPP */

modules/dnn/src/tengine4dnn/src/tengine_graph_convolution.cpp

@@ -34,80 +34,78 @@
 #ifdef HAVE_TENGINE
 
 #include "tengine_c_api.h"
-#include "tengine_c_compat.h"
-#include "tengine_operations.h"
+
 
 namespace cv
 {
 namespace dnn
 {
-
-int create_input_node(graph_t graph, const char* node_name, int inch, int in_h, int in_w)
+static int create_input_node(teng_graph_t graph, const char* node_name, int inch, int in_h, int in_w)
 {
-    node_t node     = create_graph_node(graph, node_name, "InputOp");
-    tensor_t tensor = create_graph_tensor(graph, node_name, TENGINE_DT_FP32);
-    set_node_output_tensor(node, 0, tensor, TENSOR_TYPE_INPUT);
+    node_t node     = teng_create_graph_node(graph, node_name, "InputOp");
+    tensor_t tensor = teng_create_graph_tensor(graph, node_name, TENGINE_DT_FP32);
+    teng_set_node_output_tensor(node, 0, tensor, TENSOR_TYPE_INPUT);
 
     int dims[4] = {1, inch, in_h, in_w};
-    set_tensor_shape(tensor, dims, 4);
+    teng_set_tensor_shape(tensor, dims, 4);
 
-    release_graph_tensor(tensor);
-    release_graph_node(node);
+    teng_release_graph_tensor(tensor);
+    teng_release_graph_node(node);
 
     return 0;
 }
 
-int create_conv_node(graph_t graph, const char* node_name, const char* input_name, int in_h, int in_w, int out_h, int out_w,
+static int create_conv_node(teng_graph_t graph, const char* node_name, const char* input_name, int in_h, int in_w, int out_h, int out_w,
     int kernel_h, int kernel_w, int stride_h, int stride_w, int pad_h, int pad_w, int inch, int outch, int group,
     int dilation_h, int dilation_w, int activation, std::string padMode)
 {
-    node_t conv_node      = create_graph_node(graph, node_name, "Convolution");
-    tensor_t input_tensor = get_graph_tensor(graph, input_name);
+    node_t conv_node      = teng_create_graph_node(graph, node_name, "Convolution");
+    tensor_t input_tensor = teng_get_graph_tensor(graph, input_name);
 
     if (input_tensor == NULL)
     {
-        CV_LOG_WARNING(NULL,"Tengine :input_tensor is NULL . " );
+        CV_LOG_WARNING(NULL,"Tengine: input_tensor is NULL." );
         return -1;
     }
 
-    set_node_input_tensor(conv_node, 0, input_tensor);
-    release_graph_tensor(input_tensor);
+    teng_set_node_input_tensor(conv_node, 0, input_tensor);
+    teng_release_graph_tensor(input_tensor);
 
     /* output */
-    tensor_t output_tensor = create_graph_tensor(graph, node_name, TENGINE_DT_FP32);
+    tensor_t output_tensor = teng_create_graph_tensor(graph, node_name, TENGINE_DT_FP32);
 
-    set_node_output_tensor(conv_node, 0, output_tensor, TENSOR_TYPE_VAR);
-    release_graph_tensor(output_tensor);
+    teng_set_node_output_tensor(conv_node, 0, output_tensor, TENSOR_TYPE_VAR);
+    teng_release_graph_tensor(output_tensor);
 
     /* weight */
     std::string weight_name(node_name);
     weight_name += "/weight";
 
-    node_t w_node = create_graph_node(graph, weight_name.c_str(), "Const");
-    tensor_t w_tensor = create_graph_tensor(graph, weight_name.c_str(), TENGINE_DT_FP32);
-    set_node_output_tensor(w_node, 0, w_tensor, TENSOR_TYPE_CONST);
-    set_node_input_tensor(conv_node, 1, w_tensor);
+    node_t w_node = teng_create_graph_node(graph, weight_name.c_str(), "Const");
+    tensor_t w_tensor = teng_create_graph_tensor(graph, weight_name.c_str(), TENGINE_DT_FP32);
+    teng_set_node_output_tensor(w_node, 0, w_tensor, TENSOR_TYPE_CONST);
+    teng_set_node_input_tensor(conv_node, 1, w_tensor);
     int w_dims[] = {outch, inch / group, kernel_h, kernel_w};
 
-    set_tensor_shape(w_tensor, w_dims, 4);
+    teng_set_tensor_shape(w_tensor, w_dims, 4);
 
-    release_graph_node(w_node);
-    release_graph_tensor(w_tensor);
+    teng_release_graph_node(w_node);
+    teng_release_graph_tensor(w_tensor);
 
     /* bias */
     std::string bias_name(node_name);
     bias_name += "/bias";
 
-    node_t b_node = create_graph_node(graph, bias_name.c_str(), "Const");
-    tensor_t b_tensor = create_graph_tensor(graph, bias_name.c_str(), TENGINE_DT_FP32);
-    set_node_output_tensor(b_node, 0, b_tensor, TENSOR_TYPE_CONST);
+    node_t b_node = teng_create_graph_node(graph, bias_name.c_str(), "Const");
+    tensor_t b_tensor = teng_create_graph_tensor(graph, bias_name.c_str(), TENGINE_DT_FP32);
+    teng_set_node_output_tensor(b_node, 0, b_tensor, TENSOR_TYPE_CONST);
     int b_dims[] = {outch};
 
-    set_tensor_shape(b_tensor, b_dims, 1);
+    teng_set_tensor_shape(b_tensor, b_dims, 1);
 
-    set_node_input_tensor(conv_node, 2, b_tensor);
-    release_graph_node(b_node);
-    release_graph_tensor(b_tensor);
+    teng_set_node_input_tensor(conv_node, 2, b_tensor);
+    teng_release_graph_node(b_node);
+    teng_release_graph_tensor(b_tensor);
 
     int pad_h1 = pad_h;
     int pad_w1 = pad_w;
@@ -127,31 +125,32 @@ int create_conv_node(graph_t graph, const char* node_name, const char* input_nam
     }
 
     /* attr */
-    set_node_attr_int(conv_node, "kernel_h", &kernel_h);
-    set_node_attr_int(conv_node, "kernel_w", &kernel_w);
-    set_node_attr_int(conv_node, "stride_h", &stride_h);
-    set_node_attr_int(conv_node, "stride_w", &stride_w);
-    set_node_attr_int(conv_node, "pad_h0", &pad_h);
-    set_node_attr_int(conv_node, "pad_w0", &pad_w);
-    set_node_attr_int(conv_node, "pad_h1", &pad_h1);
-    set_node_attr_int(conv_node, "pad_w1", &pad_w1);
-    set_node_attr_int(conv_node, "output_channel", &outch);
-    set_node_attr_int(conv_node, "group", &group);
-    set_node_attr_int(conv_node, "dilation_h", &dilation_h);
-    set_node_attr_int(conv_node, "dilation_w", &dilation_w);
-    set_node_attr_int(conv_node, "activation", &activation);
+    teng_set_node_attr_int(conv_node, "kernel_h", &kernel_h);
+    teng_set_node_attr_int(conv_node, "kernel_w", &kernel_w);
+    teng_set_node_attr_int(conv_node, "stride_h", &stride_h);
+    teng_set_node_attr_int(conv_node, "stride_w", &stride_w);
+    teng_set_node_attr_int(conv_node, "pad_h0", &pad_h);
+    teng_set_node_attr_int(conv_node, "pad_w0", &pad_w);
+    teng_set_node_attr_int(conv_node, "pad_h1", &pad_h1);
+    teng_set_node_attr_int(conv_node, "pad_w1", &pad_w1);
+    teng_set_node_attr_int(conv_node, "output_channel", &outch);
+    teng_set_node_attr_int(conv_node, "input_channel", &inch);
+    teng_set_node_attr_int(conv_node, "group", &group);
+    teng_set_node_attr_int(conv_node, "dilation_h", &dilation_h);
+    teng_set_node_attr_int(conv_node, "dilation_w", &dilation_w);
+  //  set_node_attr_int(conv_node, "activation", &activation);
 
-    release_graph_node(conv_node);
+    teng_release_graph_node(conv_node);
 
     return 0;
 }
 
-graph_t create_conv_graph(float *input_data, int inch, int group, int in_h, int in_w,
-                        float *output_data, int outch, int out_h, int out_w,
+static teng_graph_t create_conv_graph(const char* layer_name, float* input_data, int inch, int group, int in_h, int in_w,
+                        float* output_data, int outch, int out_h, int out_w,
                         int kernel_h, int kernel_w,
                         int stride_h,int stride_w,
                         int pad_h, int pad_w,  int dilation_h, int dilation_w, int activation,
-                        float * teg_weight , float * teg_bias , std::string padMode)
+                        float* teg_weight, float* teg_bias, std::string padMode, int nstripes)
 {
     node_t    conv_node     = NULL;
 
@@ -170,28 +169,28 @@ graph_t create_conv_graph(float *input_data, int inch, int group, int in_h, int
     int input_num = 0;
 
     /* create graph */
-    graph_t graph = create_graph(NULL, NULL, NULL);
+    teng_graph_t graph = teng_create_graph(NULL, NULL, NULL);
     bool ok = true;
 
     if(graph == NULL)
     {
-        CV_LOG_WARNING(NULL,"Tengine :create_graph failed . " );
+        CV_LOG_WARNING(NULL,"Tengine: create_graph failed." );
         ok = false;
     }
 
     const char* input_name = "data";
-    const char* conv_name  = "conv";
+    const char* conv_name  = layer_name;
 
     if (ok && create_input_node(graph, input_name, inch, in_h, in_w) < 0)
     {
-        CV_LOG_WARNING(NULL,"Tengine :create_input_node failed. " );
+        CV_LOG_WARNING(NULL,"Tengine: create_input_node failed." );
         ok = false;
     }
 
     if (ok && create_conv_node(graph, conv_name, input_name, in_h, in_w, out_h, out_w, kernel_h, kernel_w,
         stride_h, stride_w, pad_h, pad_w, inch, outch, group, dilation_h, dilation_w, activation, padMode) < 0)
     {
-        CV_LOG_WARNING(NULL,"Tengine :create conv node failed. " );
+        CV_LOG_WARNING(NULL,"Tengine: create conv node failed." );
         ok = false;
     }
 
@@ -199,94 +198,101 @@ graph_t create_conv_graph(float *input_data, int inch, int group, int in_h, int
     const char* inputs_name[]  = {input_name};
     const char* outputs_name[] = {conv_name};
 
-    if (ok && set_graph_input_node(graph, inputs_name, sizeof(inputs_name) / sizeof(char*)) < 0)
+    if (ok && teng_set_graph_input_node(graph, inputs_name, sizeof(inputs_name) / sizeof(char*)) < 0)
     {
-        CV_LOG_WARNING(NULL,"Tengine :set inputs failed . " );
+        CV_LOG_WARNING(NULL,"Tengine: set inputs failed." );
         ok = false;
     }
 
-    if (ok && set_graph_output_node(graph, outputs_name, sizeof(outputs_name) / sizeof(char*)) < 0)
+    if (ok && teng_set_graph_output_node(graph, outputs_name, sizeof(outputs_name) / sizeof(char*)) < 0)
     {
-        CV_LOG_WARNING(NULL,"Tengine :set outputs failed . " );
+        CV_LOG_WARNING(NULL,"Tengine: set outputs failed." );
         ok = false;
     }
 
     /* set input data */
     if (ok)
     {
-        input_tensor = get_graph_input_tensor(graph, 0, 0);
-        buf_size     = get_tensor_buffer_size(input_tensor);
+        input_tensor = teng_get_graph_input_tensor(graph, 0, 0);
+        buf_size     = teng_get_tensor_buffer_size(input_tensor);
         if (buf_size != in_size * FLOAT_TO_REALSIZE)
         {
-            CV_LOG_WARNING(NULL,"Tengine :Input data size check failed . ");
+            CV_LOG_WARNING(NULL,"Tengine: Input data size check failed.");
             ok = false;
         }
     }
 
     if (ok)
     {
-        set_tensor_buffer(input_tensor, (float *)input_data, buf_size);
-        release_graph_tensor(input_tensor);
+        teng_set_tensor_buffer(input_tensor, (float *)input_data, buf_size);
+        teng_release_graph_tensor(input_tensor);
 
         /* create convolution node */
         /* set weight node */
-        conv_node     = get_graph_node(graph, "conv");
-        weight_tensor = get_node_input_tensor(conv_node, 1);
-        buf_size      = get_tensor_buffer_size(weight_tensor);
+        conv_node     = teng_get_graph_node(graph, conv_name);
+        weight_tensor = teng_get_node_input_tensor(conv_node, 1);
+        buf_size      = teng_get_tensor_buffer_size(weight_tensor);
 
         if (buf_size != weight_size * FLOAT_TO_REALSIZE)
         {
-            CV_LOG_WARNING(NULL,"Input weight size check failed . ");
+            CV_LOG_WARNING(NULL,"Tengine: Input weight size check failed.");
             ok = false;
         }
     }
 
     if (ok)
     {
-        set_tensor_buffer(weight_tensor, teg_weight, buf_size);
+        teng_set_tensor_buffer(weight_tensor, teg_weight, buf_size);
 
         /* set bias node */
-        input_num = get_node_input_number(conv_node);
+        input_num = teng_get_node_input_number(conv_node);
         if (input_num > 2)
         {
-            bias_tensor = get_node_input_tensor(conv_node, 2);
-            buf_size    = get_tensor_buffer_size(bias_tensor);
+            bias_tensor = teng_get_node_input_tensor(conv_node, 2);
+            buf_size    = teng_get_tensor_buffer_size(bias_tensor);
             if (buf_size != bias_size * FLOAT_TO_REALSIZE)
             {
-                CV_LOG_WARNING(NULL,"Tengine :Input bias size check failed . ");
+                CV_LOG_WARNING(NULL,"Tengine: Input bias size check failed.");
                 ok = false;
             }
-            else set_tensor_buffer(bias_tensor, teg_bias, buf_size);
+            else teng_set_tensor_buffer(bias_tensor, teg_bias, buf_size);
         }
     }
 
+    /* prerun */
+    if (ok && teng_prerun_graph_multithread(graph, TENGINE_CLUSTER_BIG, nstripes) < 0)
+    {
+        CV_LOG_WARNING(NULL, "Tengine: prerun_graph failed.");
+        ok = false;
+    }
+
     if (ok)
     {
         /* set output data */
-        output_tensor = get_node_output_tensor(conv_node, 0);
-        int ret = set_tensor_buffer(output_tensor, output_data, out_size * FLOAT_TO_REALSIZE);
+        output_tensor = teng_get_node_output_tensor(conv_node, 0);
+        int ret = teng_set_tensor_buffer(output_tensor, output_data, out_size * FLOAT_TO_REALSIZE);
         if(ret)
         {
-            CV_LOG_WARNING(NULL,"Tengine :Set output tensor buffer failed . " );
+            CV_LOG_WARNING(NULL,"Tengine: Set output tensor buffer failed." );
+            ok = false;
         }
     }
 
-    if (!ok)
+    if (false == ok)
     {
-        destroy_graph(graph);
-        return NULL;
+        teng_destroy_graph(graph) ;
+        return NULL ;
     }
     return graph;
 }
-
-bool tengine_forward(float *input_, int inch, int group, int in_h, int in_w,
+static bool tengine_init_flag = false;
+teng_graph_t tengine_init(const char* layer_name, float* input_, int inch, int group, int in_h, int in_w,
                         float *output_, int out_b, int outch, int out_h, int out_w,
                         float *kernel_, int kernel_s ,int kernel_h, int kernel_w,
                         float *teg_bias, int stride_h,int stride_w,
                         int pad_h, int pad_w,  int dilation_h, int dilation_w,
-                        size_t wstep,const std::string padMode)
+                        size_t wstep, const std::string padMode, teng_graph_t &graph, int nstripes)
 {
-    graph_t graph = NULL;
     std::vector<float> teg_weight_vec;
     float *teg_weight = NULL;
     int kernel_inwh = (inch / group) * kernel_w * kernel_h;
@@ -296,17 +302,20 @@ bool tengine_forward(float *input_, int inch, int group, int in_h, int in_w,
     if (!(kernel_s == 2 && kernel_h == kernel_w && pad_h == pad_w
         && dilation_h == dilation_w && stride_h == stride_w
         && out_b == 1 && pad_h < 10)) // just for Conv2D
-        return false;
+    {
+       // printf("return : just for Conv2D\n");
+        return NULL;
+    }
 
     {
-        /*printf("Tengine: input (1 x %d x %d x %d),output (%d x %d x %d x %d), kernel (%d x %d), stride (%d x %d), dilation (%d x %d), pad (%d x %d).\n",
-               inch, in_h, in_w,
-               out_b,outch,out_h,out_w,
+      /*   printf("Tengine(%s): input (1 x %d x %d x %d),output (%d x %d x %d x %d), kernel (%d x %d), stride (%d x %d), dilation (%d x %d), pad (%d x %d).\n",
+               layer_name, inch, in_h, in_w,
+               out_b, outch, out_h, out_w,
                kernel_w, kernel_h,
                stride_w, stride_h,
                dilation_w, dilation_h,
-               pad_w,pad_h);*/
-
+               pad_w, pad_h);
+     */
         // weight
         if (kernel_inwh != wstep)
         {
@@ -323,35 +332,42 @@ bool tengine_forward(float *input_, int inch, int group, int in_h, int in_w,
         }
 
         /* initial the resoruce of tengine */
-        init_tengine();
+        if(false == tengine_init_flag)
+        {
+            init_tengine();
+            tengine_init_flag = true;
+        }
 
         /* create the convolution graph */
-        graph = create_conv_graph( input_, inch, group, in_h, in_w,
+        graph = create_conv_graph(layer_name, input_, inch, group, in_h, in_w,
                                     output_, outch, out_h, out_w,
                                     kernel_h, kernel_w, stride_h,stride_w,
                                     pad_h, pad_w, dilation_h, dilation_w, activation,
-                                    teg_weight , teg_bias , padMode);
-
-        /* prerun */
-        if(prerun_graph(graph) < 0)
+                                    teg_weight, teg_bias, padMode, nstripes);
+        if(NULL == graph )
         {
-            CV_LOG_WARNING(NULL, "Tengine :prerun_graph failed .");
-            return false ;
+            return NULL;
         }
-
-        /* run */
-        if(run_graph(graph, 1) < 0)
-        {
-            CV_LOG_WARNING(NULL,"Tengine :run_graph failed .");
-            return false ;
-        }
-
-        postrun_graph(graph);
-        destroy_graph(graph);
     }
-    return true ;
+    return graph ;
 }
 
+bool tengine_forward(teng_graph_t &graph)
+{
+    /* run */
+    if(teng_run_graph(graph, 1) < 0)
+    {
+        CV_LOG_WARNING(NULL,"Tengine: run_graph failed.");
+        return false ;
+    }
+    return true;
+}
+bool tengine_release(teng_graph_t &graph)
+{
+    teng_postrun_graph(graph);
+    teng_destroy_graph(graph);
+    return true;
+}
 }
 }
 #endif

modules/dnn/test/test_common.impl.hpp

@@ -67,10 +67,10 @@ void normAssert(
         double l1 /*= 0.00001*/, double lInf /*= 0.0001*/)
 {
     double normL1 = cvtest::norm(ref, test, cv::NORM_L1) / ref.getMat().total();
-    EXPECT_LE(normL1, l1) << comment;
+    EXPECT_LE(normL1, l1) << comment << "  |ref| = " << cvtest::norm(ref, cv::NORM_INF);
 
     double normInf = cvtest::norm(ref, test, cv::NORM_INF);
-    EXPECT_LE(normInf, lInf) << comment;
+    EXPECT_LE(normInf, lInf) << comment << "  |ref| = " << cvtest::norm(ref, cv::NORM_INF);
 }
 
 std::vector<cv::Rect2d> matToBoxes(const cv::Mat& m)

modules/dnn/test/test_darknet_importer.cpp

@@ -656,6 +656,11 @@ TEST_P(Test_Darknet_nets, YOLOv4_tiny)
         target == DNN_TARGET_CPU ? CV_TEST_TAG_MEMORY_512MB : CV_TEST_TAG_MEMORY_1GB
     );
 
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2021010000)  // nGraph compilation failure
+    if (target == DNN_TARGET_MYRIAD)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_VERSION);
+#endif
+
     const double confThreshold = 0.5;
     // batchId, classId, confidence, left, top, right, bottom
     const int N0 = 2;

modules/dnn/test/test_ie_models.cpp

@@ -103,11 +103,15 @@ static const std::map<std::string, OpenVINOModelTestCaseInfo>& getOpenVINOTestMo
 #if INF_ENGINE_RELEASE >= 2020010000
         // Downloaded using these parameters for Open Model Zoo downloader (2020.1):
         // ./downloader.py -o ${OPENCV_DNN_TEST_DATA_PATH}/omz_intel_models --cache_dir ${OPENCV_DNN_TEST_DATA_PATH}/.omz_cache/ \
-        //     --name person-detection-retail-0013
+        //     --name person-detection-retail-0013,age-gender-recognition-retail-0013
         { "person-detection-retail-0013", {  // IRv10
             "intel/person-detection-retail-0013/FP32/person-detection-retail-0013",
             "intel/person-detection-retail-0013/FP16/person-detection-retail-0013"
         }},
+        { "age-gender-recognition-retail-0013", {
+            "intel/age-gender-recognition-retail-0013/FP16/age-gender-recognition-retail-0013",
+            "intel/age-gender-recognition-retail-0013/FP32/age-gender-recognition-retail-0013"
+        }},
 #endif
     };
 
@@ -123,6 +127,21 @@ static const std::vector<std::string> getOpenVINOTestModelsList()
     return result;
 }
 
+inline static std::string getOpenVINOModel(const std::string &modelName, bool isFP16)
+{
+    const std::map<std::string, OpenVINOModelTestCaseInfo>& models = getOpenVINOTestModels();
+    const auto it = models.find(modelName);
+    if (it != models.end())
+    {
+        OpenVINOModelTestCaseInfo modelInfo = it->second;
+        if (isFP16 && modelInfo.modelPathFP16)
+            return std::string(modelInfo.modelPathFP16);
+        else if (!isFP16 && modelInfo.modelPathFP32)
+            return std::string(modelInfo.modelPathFP32);
+    }
+    return std::string();
+}
+
 static inline void genData(const InferenceEngine::TensorDesc& desc, Mat& m, Blob::Ptr& dataPtr)
 {
     const std::vector<size_t>& dims = desc.getDims();
@@ -310,11 +329,8 @@ TEST_P(DNNTestOpenVINO, models)
 
     bool isFP16 = (targetId == DNN_TARGET_OPENCL_FP16 || targetId == DNN_TARGET_MYRIAD);
 
-    const std::map<std::string, OpenVINOModelTestCaseInfo>& models = getOpenVINOTestModels();
-    const auto it = models.find(modelName);
-    ASSERT_TRUE(it != models.end()) << modelName;
-    OpenVINOModelTestCaseInfo modelInfo = it->second;
-    std::string modelPath = isFP16 ? modelInfo.modelPathFP16 : modelInfo.modelPathFP32;
+    const std::string modelPath = getOpenVINOModel(modelName, isFP16);
+    ASSERT_FALSE(modelPath.empty()) << modelName;
 
     std::string xmlPath = findDataFile(modelPath + ".xml", false);
     std::string binPath = findDataFile(modelPath + ".bin", false);
@@ -358,10 +374,9 @@ TEST_P(DNNTestHighLevelAPI, predict)
 
     Target target = (dnn::Target)(int)GetParam();
     bool isFP16 = (target == DNN_TARGET_OPENCL_FP16 || target == DNN_TARGET_MYRIAD);
-
-    OpenVINOModelTestCaseInfo modelInfo = getOpenVINOTestModels().find("age-gender-recognition-retail-0013")->second;
-
-    std::string modelPath = isFP16 ? modelInfo.modelPathFP16 : modelInfo.modelPathFP32;
+    const std::string modelName = "age-gender-recognition-retail-0013";
+    const std::string modelPath = getOpenVINOModel(modelName, isFP16);
+    ASSERT_FALSE(modelPath.empty()) << modelName;
 
     std::string xmlPath = findDataFile(modelPath + ".xml");
     std::string binPath = findDataFile(modelPath + ".bin");

modules/dnn/test/test_layers.cpp

@@ -2264,17 +2264,6 @@ TEST_P(ConvolutionActivationFusion, Accuracy)
     Backend backendId = get<0>(get<2>(GetParam()));
     Target targetId = get<1>(get<2>(GetParam()));
 
-    // bug: https://github.com/opencv/opencv/issues/17964
-    if (actType == "Power" && backendId == DNN_BACKEND_OPENCV && (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16))
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL);
-
-    // bug: https://github.com/opencv/opencv/issues/17953
-    if (actType == "ChannelsPReLU" && bias_term == false &&
-        backendId == DNN_BACKEND_OPENCV && (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16))
-    {
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL);
-    }
-
     Net net;
     int convId = net.addLayer(convParams.name, convParams.type, convParams);
     int activId = net.addLayerToPrev(activationParams.name, activationParams.type, activationParams);
@@ -2287,7 +2276,7 @@ TEST_P(ConvolutionActivationFusion, Accuracy)
             expectedFusedLayers.push_back(activId); // all activations are fused
         else if (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16)
         {
-            if (actType == "ReLU" || actType == "ChannelsPReLU" || actType == "ReLU6" || actType == "TanH" || actType == "Power")
+            if (actType == "ReLU" || actType == "ChannelsPReLU" || actType == "ReLU6" || actType == "TanH" /*|| actType == "Power"*/)
                 expectedFusedLayers.push_back(activId);
         }
     }
@@ -2397,21 +2386,6 @@ TEST_P(ConvolutionEltwiseActivationFusion, Accuracy)
     Backend backendId = get<0>(get<4>(GetParam()));
     Target targetId = get<1>(get<4>(GetParam()));
 
-    // bug: https://github.com/opencv/opencv/issues/17945
-    if ((eltwiseOp != "sum" || weightedEltwise) && backendId == DNN_BACKEND_OPENCV && (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16))
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL);
-
-    // bug: https://github.com/opencv/opencv/issues/17953
-    if (eltwiseOp == "sum" && actType == "ChannelsPReLU" && bias_term == false &&
-        backendId == DNN_BACKEND_OPENCV && (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16))
-    {
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL);
-    }
-
-    // bug: https://github.com/opencv/opencv/issues/17964
-    if (actType == "Power" && backendId == DNN_BACKEND_OPENCV && (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16))
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL);
-
     Net net;
     int convId = net.addLayer(convParams.name, convParams.type, convParams);
     int eltwiseId = net.addLayer(eltwiseParams.name, eltwiseParams.type, eltwiseParams);
@@ -2428,7 +2402,9 @@ TEST_P(ConvolutionEltwiseActivationFusion, Accuracy)
             expectedFusedLayers.push_back(activId); // activation is fused with eltwise layer
         else if (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16)
         {
-            if (actType == "ReLU" || actType == "ChannelsPReLU" || actType == "Power")
+            if (eltwiseOp == "sum" && !weightedEltwise &&
+                (actType == "ReLU" || actType == "ChannelsPReLU" /*|| actType == "Power"*/)
+            )
             {
                 expectedFusedLayers.push_back(eltwiseId);
                 expectedFusedLayers.push_back(activId);
@@ -2490,17 +2466,6 @@ TEST_P(ConvolutionActivationEltwiseFusion, Accuracy)
     Backend backendId = get<0>(get<4>(GetParam()));
     Target targetId = get<1>(get<4>(GetParam()));
 
-    // bug: https://github.com/opencv/opencv/issues/17964
-    if (actType == "Power" && backendId == DNN_BACKEND_OPENCV && (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16))
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL);
-
-    // bug: https://github.com/opencv/opencv/issues/17953
-    if (actType == "ChannelsPReLU" && bias_term == false &&
-        backendId == DNN_BACKEND_OPENCV && (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16))
-    {
-        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL);
-    }
-
     Net net;
     int convId = net.addLayer(convParams.name, convParams.type, convParams);
     int activId = net.addLayer(activationParams.name, activationParams.type, activationParams);
@@ -2517,7 +2482,7 @@ TEST_P(ConvolutionActivationEltwiseFusion, Accuracy)
             expectedFusedLayers.push_back(activId); // activation fused with convolution
         else if (targetId == DNN_TARGET_OPENCL || targetId == DNN_TARGET_OPENCL_FP16)
         {
-            if (actType == "ReLU" || actType == "ChannelsPReLU" || actType == "ReLU6" || actType == "TanH" || actType == "Power")
+            if (actType == "ReLU" || actType == "ChannelsPReLU" || actType == "ReLU6" || actType == "TanH" /*|| actType == "Power"*/)
                 expectedFusedLayers.push_back(activId); // activation fused with convolution
         }
     }

modules/dnn/test/test_misc.cpp

@@ -99,6 +99,15 @@ TEST(readNet, do_not_call_setInput)  // https://github.com/opencv/opencv/issues/
     EXPECT_TRUE(res.empty()) << res.size;
 }
 
+TEST(Net, empty_forward_18392)
+{
+    cv::dnn::Net net;
+    Mat image(Size(512, 512), CV_8UC3, Scalar::all(0));
+    Mat inputBlob = cv::dnn::blobFromImage(image, 1.0, Size(512, 512), Scalar(0,0,0), true, false);
+    net.setInput(inputBlob);
+    EXPECT_ANY_THROW(Mat output = net.forward());
+}
+
 #ifdef HAVE_INF_ENGINE
 static
 void test_readNet_IE_do_not_call_setInput(Backend backendId)

modules/dnn/test/test_model.cpp

@@ -363,7 +363,7 @@ TEST_P(Test_Model, Detection_normalized)
         scoreDiff = 5e-3;
         iouDiff = 0.09;
     }
-#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_EQ(2020040000)
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2020040000)
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target == DNN_TARGET_MYRIAD)
     {
         iouDiff = 0.095f;

modules/dnn/test/test_onnx_importer.cpp

@@ -275,6 +275,18 @@ TEST_P(Test_ONNX_layers, ReduceSum)
     testONNXModels("reduce_sum");
 }
 
+TEST_P(Test_ONNX_layers, ReduceMaxGlobal)
+{
+    testONNXModels("reduce_max");
+}
+
+TEST_P(Test_ONNX_layers, Scale)
+{
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
+    testONNXModels("scale");
+}
+
 TEST_P(Test_ONNX_layers, ReduceMean3D)
 {
     if (backend == DNN_BACKEND_CUDA)
@@ -664,6 +676,11 @@ TEST_P(Test_ONNX_layers, MatmulWithTwoInputs)
     testONNXModels("matmul_with_two_inputs");
 }
 
+TEST_P(Test_ONNX_layers, ResizeOpset11_Torch1_6)
+{
+    testONNXModels("resize_opset11_torch1.6");
+}
+
 INSTANTIATE_TEST_CASE_P(/*nothing*/, Test_ONNX_layers, dnnBackendsAndTargets());
 
 class Test_ONNX_nets : public Test_ONNX_layers

modules/dnn/test/test_torch_importer.cpp

@@ -116,7 +116,7 @@ TEST_P(Test_Torch_layers, run_convolution)
     if (target == DNN_TARGET_OPENCL_FP16 || target == DNN_TARGET_MYRIAD)
     {
         l1 = 0.08;
-        lInf = 0.42;
+        lInf = 0.43;
     }
     else if (target == DNN_TARGET_CUDA_FP16)
     {
@@ -187,7 +187,7 @@ TEST_P(Test_Torch_layers, run_depth_concat)
     double lInf = 0.0;
     if (target == DNN_TARGET_OPENCL_FP16)
     {
-        lInf = 0.021;
+        lInf = 0.032;
     }
     else if (target == DNN_TARGET_CUDA_FP16)
     {
@@ -409,6 +409,10 @@ TEST_P(Test_Torch_nets, ENet_accuracy)
         if (target == DNN_TARGET_MYRIAD)      applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
         throw SkipTestException("");
     }
+#endif
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_GE(2021010000)
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_NGRAPH);
 #endif
     if (backend == DNN_BACKEND_INFERENCE_ENGINE_NGRAPH && target != DNN_TARGET_CPU)
     {

modules/gapi/CMakeLists.txt

@@ -49,6 +49,7 @@ file(GLOB gapi_ext_hdrs
     "${CMAKE_CURRENT_LIST_DIR}/include/opencv2/${name}/ocl/*.hpp"
     "${CMAKE_CURRENT_LIST_DIR}/include/opencv2/${name}/own/*.hpp"
     "${CMAKE_CURRENT_LIST_DIR}/include/opencv2/${name}/render/*.hpp"
+    "${CMAKE_CURRENT_LIST_DIR}/include/opencv2/${name}/s11n/*.hpp"
     "${CMAKE_CURRENT_LIST_DIR}/include/opencv2/${name}/streaming/*.hpp"
     "${CMAKE_CURRENT_LIST_DIR}/include/opencv2/${name}/plaidml/*.hpp"
     "${CMAKE_CURRENT_LIST_DIR}/include/opencv2/${name}/util/*.hpp"
@@ -61,6 +62,7 @@ set(gapi_srcs
     src/api/garray.cpp
     src/api/gopaque.cpp
     src/api/gscalar.cpp
+    src/api/gframe.cpp
     src/api/gkernel.cpp
     src/api/gbackend.cpp
     src/api/gproto.cpp
@@ -71,10 +73,13 @@ set(gapi_srcs
     src/api/kernels_core.cpp
     src/api/kernels_imgproc.cpp
     src/api/kernels_video.cpp
+    src/api/kernels_nnparsers.cpp
     src/api/render.cpp
     src/api/render_ocv.cpp
     src/api/ginfer.cpp
     src/api/ft_render.cpp
+    src/api/media.cpp
+    src/api/rmat.cpp
 
     # Compiler part
     src/compiler/gmodel.cpp
@@ -105,6 +110,7 @@ set(gapi_srcs
     src/backends/cpu/gcpuimgproc.cpp
     src/backends/cpu/gcpuvideo.cpp
     src/backends/cpu/gcpucore.cpp
+    src/backends/cpu/gnnparsers.cpp
 
     # Fluid Backend (also built-in, FIXME:move away)
     src/backends/fluid/gfluidbuffer.cpp