@@ -203,9 +253,16 @@ Several modern C++20 libraries for sanely parsing Valve formats, rolled into one
\endhtmlonly
-(\*) Many text-based formats in Source are close to (if not identical to) KeyValues v1, such as [VDF](https://developer.valvesoftware.com/wiki/VDF), [VMT](https://developer.valvesoftware.com/wiki/VMT), and [VMF](https://developer.valvesoftware.com/wiki/VMF_(Valve_Map_Format)).
+(\*) These libraries are incomplete and still in development. Their interfaces are unstable and will likely change in the future.
+Libraries not starred should be considered stable, and their existing interfaces will not change much if at all. Note that wrappers
+only exist for stable libraries.
+
+(†) Many text-based formats in Source are close to (if not identical to) KeyValues v1, such as [VMT](https://developer.valvesoftware.com/wiki/VMT) and [VMF](https://developer.valvesoftware.com/wiki/VMF_(Valve_Map_Format)).
+
+## Wrappers
-(†) The MDL parser is not complete. It is usable in its current state, but it does not currently parse more complex components like animations. This parser is still in development.
+Wrappers for libraries considered complete exist for C, C#, and/or Python, depending on the library. The Python wrappers can be
+found on PyPI in the [sourcepp](https://pypi.org/project/sourcepp) package.
## Special Thanks
diff --git a/ext/_ext.cmake b/ext/_ext.cmake
index 54964b0b7..530c62412 100644
--- a/ext/_ext.cmake
+++ b/ext/_ext.cmake
@@ -21,6 +21,10 @@ if(NOT TARGET cryptopp::cryptopp)
endif()
+# half
+add_subdirectory("${CMAKE_CURRENT_LIST_DIR}/half")
+
+
# hat-trie
if(NOT TARGET tsl::hat_trie)
add_subdirectory("${CMAKE_CURRENT_LIST_DIR}/hat-trie")
@@ -38,11 +42,11 @@ endif()
# minizip-ng (guard this behind vpkpp because this is a big dependency)
-if(SOURCEPP_USE_VPKPP AND NOT TARGET MINIZIP::minizip)
+if((SOURCEPP_USE_VPKPP OR SOURCEPP_USE_VTFPP) AND NOT TARGET MINIZIP::minizip)
set(MZ_COMPAT OFF CACHE INTERNAL "")
# todo: guard liblzma/xz force-enable behind BSP compression option
set(MZ_LZMA ON CACHE INTERNAL "" FORCE)
- if(SOURCEPP_VPKPP_SUPPORT_VPK_V54)
+ if(SOURCEPP_USE_VTFPP OR SOURCEPP_VPKPP_SUPPORT_VPK_V54)
set(MZ_ZSTD ON CACHE INTERNAL "" FORCE)
endif()
set(MZ_FETCH_LIBS ON CACHE INTERNAL "" FORCE)
@@ -73,7 +77,7 @@ endif()
function(sourcepp_add_opencl TARGET)
if(SOURCEPP_BUILD_WITH_OPENCL)
- target_compile_definitions(${TARGET} PRIVATE SOURCEPP_BUILD_WITH_OPENCL)
+ target_compile_definitions(${TARGET} PUBLIC SOURCEPP_BUILD_WITH_OPENCL)
target_link_libraries(${TARGET} PRIVATE OpenCL::OpenCL)
endif()
endfunction()
@@ -83,10 +87,14 @@ endfunction()
add_subdirectory("${CMAKE_CURRENT_LIST_DIR}/stb")
-# TBB
+# tinyexr
+add_subdirectory("${CMAKE_CURRENT_LIST_DIR}/tinyexr")
+
+
+# tbb
function(sourcepp_add_tbb TARGET)
if(SOURCEPP_BUILD_WITH_TBB)
- target_compile_definitions(${TARGET} PRIVATE SOURCEPP_BUILD_WITH_TBB)
+ target_compile_definitions(${TARGET} PUBLIC SOURCEPP_BUILD_WITH_TBB)
if(NOT MSVC)
target_link_libraries(${TARGET} PRIVATE tbb)
endif()
@@ -106,7 +114,7 @@ endif()
function(sourcepp_add_threads TARGET)
if(SOURCEPP_BUILD_WITH_THREADS)
- target_compile_definitions(${TARGET} PRIVATE SOURCEPP_BUILD_WITH_THREADS)
+ target_compile_definitions(${TARGET} PUBLIC SOURCEPP_BUILD_WITH_THREADS)
target_link_libraries(${TARGET} PRIVATE Threads::Threads)
endif()
endfunction()
diff --git a/ext/bufferstream b/ext/bufferstream
index 689c50d56..fa4160118 160000
--- a/ext/bufferstream
+++ b/ext/bufferstream
@@ -1 +1 @@
-Subproject commit 689c50d56a0eefb066209c281eac99599845edb6
+Subproject commit fa4160118b06b84706a7a4766a3b487fd5c9a6d0
diff --git a/ext/compressonator/CMakeLists.txt b/ext/compressonator/CMakeLists.txt
index a4757f151..22cc64f15 100644
--- a/ext/compressonator/CMakeLists.txt
+++ b/ext/compressonator/CMakeLists.txt
@@ -1,4 +1,6 @@
-set(COMPRESSONATOR_DIR ${CMAKE_CURRENT_LIST_DIR} CACHE INTERNAL "")
+include_guard(GLOBAL)
+
+set(COMPRESSONATOR_DIR "${CMAKE_CURRENT_LIST_DIR}" CACHE INTERNAL "")
function(target_link_compressonator TARGET)
if(WIN32)
@@ -20,8 +22,8 @@ function(target_link_compressonator TARGET)
endif()
elseif(APPLE)
target_link_libraries(${TARGET} PRIVATE
- "${COMPRESSONATOR_DIR}/lib/macOS/libCompressonator$<$:d>.a"
- "${COMPRESSONATOR_DIR}/lib/macOS/libCMP_Core$<$:d>.a")
+ "${COMPRESSONATOR_DIR}/lib/macOS_arm64/libCompressonator$<$:d>.a"
+ "${COMPRESSONATOR_DIR}/lib/macOS_arm64/libCMP_Core$<$:d>.a")
elseif(UNIX)
target_link_libraries(${TARGET} PRIVATE
"${COMPRESSONATOR_DIR}/lib/linux_x86_64/libCompressonator$<$:d>.a"
diff --git a/ext/compressonator/lib/macOS/libCMP_Core.a b/ext/compressonator/lib/macOS_arm64/libCMP_Core.a
similarity index 98%
rename from ext/compressonator/lib/macOS/libCMP_Core.a
rename to ext/compressonator/lib/macOS_arm64/libCMP_Core.a
index b334e5f1f..69947a390 100644
Binary files a/ext/compressonator/lib/macOS/libCMP_Core.a and b/ext/compressonator/lib/macOS_arm64/libCMP_Core.a differ
diff --git a/ext/compressonator/lib/macOS/libCMP_Cored.a b/ext/compressonator/lib/macOS_arm64/libCMP_Cored.a
similarity index 51%
rename from ext/compressonator/lib/macOS/libCMP_Cored.a
rename to ext/compressonator/lib/macOS_arm64/libCMP_Cored.a
index 523764d44..68c2458ee 100644
Binary files a/ext/compressonator/lib/macOS/libCMP_Cored.a and b/ext/compressonator/lib/macOS_arm64/libCMP_Cored.a differ
diff --git a/ext/compressonator/lib/macOS/libCompressonator.a b/ext/compressonator/lib/macOS_arm64/libCompressonator.a
similarity index 89%
rename from ext/compressonator/lib/macOS/libCompressonator.a
rename to ext/compressonator/lib/macOS_arm64/libCompressonator.a
index 6ac269e9e..2fa0c0702 100644
Binary files a/ext/compressonator/lib/macOS/libCompressonator.a and b/ext/compressonator/lib/macOS_arm64/libCompressonator.a differ
diff --git a/ext/compressonator/lib/macOS/libCompressonatord.a b/ext/compressonator/lib/macOS_arm64/libCompressonatord.a
similarity index 61%
rename from ext/compressonator/lib/macOS/libCompressonatord.a
rename to ext/compressonator/lib/macOS_arm64/libCompressonatord.a
index 5c5e41bf9..203957a5b 100644
Binary files a/ext/compressonator/lib/macOS/libCompressonatord.a and b/ext/compressonator/lib/macOS_arm64/libCompressonatord.a differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MD.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MD.lib
index 0efe277be..9efa4b405 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MD.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MD.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX.lib
index b578fb151..4fc8a1a28 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512.lib
index c08519b47..25f22e752 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512d.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512d.lib
index 97202b42f..e10065294 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512d.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVX512d.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVXd.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVXd.lib
index 99a1b33cc..482bcc8e5 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVXd.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_AVXd.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSE.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSE.lib
index 014aebdd5..de5062d49 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSE.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSE.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSEd.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSEd.lib
index 61d410a9a..f3c42d72f 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSEd.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MD_SSEd.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MDd.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MDd.lib
index 95c3ef771..0d6f7aa66 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MDd.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MDd.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MT.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MT.lib
index 62660ca70..7a56db967 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MT.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MT.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX.lib
index 87defa8f6..f0b4cfc27 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512.lib
index 7a8681eff..3150b8ed9 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512d.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512d.lib
index 41ef859f2..af3fbcc5e 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512d.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVX512d.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVXd.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVXd.lib
index 9db8d8d7c..932ae1f1b 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVXd.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_AVXd.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSE.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSE.lib
index 2bf68a0ee..05f719b66 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSE.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSE.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSEd.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSEd.lib
index 538cee480..b720f1c7a 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSEd.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MT_SSEd.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/CMP_Core_MTd.lib b/ext/compressonator/lib/win_x86_64/CMP_Core_MTd.lib
index 1a21c9d03..5c19763da 100644
Binary files a/ext/compressonator/lib/win_x86_64/CMP_Core_MTd.lib and b/ext/compressonator/lib/win_x86_64/CMP_Core_MTd.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/Compressonator_MD.lib b/ext/compressonator/lib/win_x86_64/Compressonator_MD.lib
index 1c3f6b54c..f6cb96cda 100644
Binary files a/ext/compressonator/lib/win_x86_64/Compressonator_MD.lib and b/ext/compressonator/lib/win_x86_64/Compressonator_MD.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/Compressonator_MDd.lib b/ext/compressonator/lib/win_x86_64/Compressonator_MDd.lib
index 46aef8db7..79d3aad1c 100644
Binary files a/ext/compressonator/lib/win_x86_64/Compressonator_MDd.lib and b/ext/compressonator/lib/win_x86_64/Compressonator_MDd.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/Compressonator_MT.lib b/ext/compressonator/lib/win_x86_64/Compressonator_MT.lib
index 49197349a..9f7df3aae 100644
Binary files a/ext/compressonator/lib/win_x86_64/Compressonator_MT.lib and b/ext/compressonator/lib/win_x86_64/Compressonator_MT.lib differ
diff --git a/ext/compressonator/lib/win_x86_64/Compressonator_MTd.lib b/ext/compressonator/lib/win_x86_64/Compressonator_MTd.lib
index d863c69f8..2b3d81cc3 100644
Binary files a/ext/compressonator/lib/win_x86_64/Compressonator_MTd.lib and b/ext/compressonator/lib/win_x86_64/Compressonator_MTd.lib differ
diff --git a/ext/half/CMakeLists.txt b/ext/half/CMakeLists.txt
new file mode 100644
index 000000000..516cacabb
--- /dev/null
+++ b/ext/half/CMakeLists.txt
@@ -0,0 +1,11 @@
+cmake_minimum_required(VERSION 3.16)
+project(sourcepp_half)
+set(CMAKE_CXX_STANDARD 20)
+
+# Create library
+add_library(${PROJECT_NAME} INTERFACE
+ "${CMAKE_CURRENT_SOURCE_DIR}/include/half.hpp")
+
+target_include_directories(${PROJECT_NAME} INTERFACE
+ $
+ $)
diff --git a/ext/half/LICENSE b/ext/half/LICENSE
new file mode 100644
index 000000000..6023222b0
--- /dev/null
+++ b/ext/half/LICENSE
@@ -0,0 +1,21 @@
+The MIT License
+
+Copyright (c) 2012-2021 Christian Rau
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
diff --git a/ext/half/include/half.hpp b/ext/half/include/half.hpp
new file mode 100644
index 000000000..d0a882dd6
--- /dev/null
+++ b/ext/half/include/half.hpp
@@ -0,0 +1,4601 @@
+// half - IEEE 754-based half-precision floating-point library.
+//
+// Copyright (c) 2012-2021 Christian Rau
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy,
+// modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+// Version 2.2.0
+
+/// \file
+/// Main header file for half-precision functionality.
+
+#ifndef HALF_HALF_HPP
+#define HALF_HALF_HPP
+
+#define HALF_GCC_VERSION (__GNUC__*100+__GNUC_MINOR__)
+
+#if defined(__INTEL_COMPILER)
+ #define HALF_ICC_VERSION __INTEL_COMPILER
+#elif defined(__ICC)
+ #define HALF_ICC_VERSION __ICC
+#elif defined(__ICL)
+ #define HALF_ICC_VERSION __ICL
+#else
+ #define HALF_ICC_VERSION 0
+#endif
+
+// check C++11 language features
+#if defined(__clang__) // clang
+ #if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+ #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+ #endif
+ #if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+ #define HALF_ENABLE_CPP11_CONSTEXPR 1
+ #endif
+ #if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+ #define HALF_ENABLE_CPP11_NOEXCEPT 1
+ #endif
+ #if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+ #define HALF_ENABLE_CPP11_USER_LITERALS 1
+ #endif
+ #if __has_feature(cxx_thread_local) && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+ #define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+ #endif
+ #if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+ #define HALF_ENABLE_CPP11_LONG_LONG 1
+ #endif
+#elif HALF_ICC_VERSION && defined(__INTEL_CXX11_MODE__) // Intel C++
+ #if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+ #define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+ #endif
+ #if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+ #define HALF_ENABLE_CPP11_USER_LITERALS 1
+ #endif
+ #if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+ #define HALF_ENABLE_CPP11_CONSTEXPR 1
+ #endif
+ #if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+ #define HALF_ENABLE_CPP11_NOEXCEPT 1
+ #endif
+ #if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+ #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+ #endif
+ #if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+ #define HALF_ENABLE_CPP11_LONG_LONG 1
+ #endif
+#elif defined(__GNUC__) // gcc
+ #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
+ #if HALF_GCC_VERSION >= 408 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+ #define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+ #endif
+ #if HALF_GCC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+ #define HALF_ENABLE_CPP11_USER_LITERALS 1
+ #endif
+ #if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+ #define HALF_ENABLE_CPP11_CONSTEXPR 1
+ #endif
+ #if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+ #define HALF_ENABLE_CPP11_NOEXCEPT 1
+ #endif
+ #if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+ #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+ #endif
+ #if !defined(HALF_ENABLE_CPP11_LONG_LONG)
+ #define HALF_ENABLE_CPP11_LONG_LONG 1
+ #endif
+ #endif
+ #define HALF_TWOS_COMPLEMENT_INT 1
+#elif defined(_MSC_VER) // Visual C++
+ #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+ #define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+ #endif
+ #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+ #define HALF_ENABLE_CPP11_USER_LITERALS 1
+ #endif
+ #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+ #define HALF_ENABLE_CPP11_CONSTEXPR 1
+ #endif
+ #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+ #define HALF_ENABLE_CPP11_NOEXCEPT 1
+ #endif
+ #if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+ #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+ #endif
+ #if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+ #define HALF_ENABLE_CPP11_LONG_LONG 1
+ #endif
+ #define HALF_TWOS_COMPLEMENT_INT 1
+ #define HALF_POP_WARNINGS 1
+ #pragma warning(push)
+ #pragma warning(disable : 4099 4127 4146) //struct vs class, constant in if, negative unsigned
+#endif
+
+// check C++11 library features
+#include
+#if defined(_LIBCPP_VERSION) // libc++
+ #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
+ #ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
+ #define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+ #endif
+ #ifndef HALF_ENABLE_CPP11_CSTDINT
+ #define HALF_ENABLE_CPP11_CSTDINT 1
+ #endif
+ #ifndef HALF_ENABLE_CPP11_CMATH
+ #define HALF_ENABLE_CPP11_CMATH 1
+ #endif
+ #ifndef HALF_ENABLE_CPP11_HASH
+ #define HALF_ENABLE_CPP11_HASH 1
+ #endif
+ #ifndef HALF_ENABLE_CPP11_CFENV
+ #define HALF_ENABLE_CPP11_CFENV 1
+ #endif
+ #endif
+#elif defined(__GLIBCXX__) // libstdc++
+ #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
+ #ifdef __clang__
+ #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+ #define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+ #endif
+ #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+ #define HALF_ENABLE_CPP11_CSTDINT 1
+ #endif
+ #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
+ #define HALF_ENABLE_CPP11_CMATH 1
+ #endif
+ #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
+ #define HALF_ENABLE_CPP11_HASH 1
+ #endif
+ #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CFENV)
+ #define HALF_ENABLE_CPP11_CFENV 1
+ #endif
+ #else
+ #if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+ #define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+ #endif
+ #if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+ #define HALF_ENABLE_CPP11_CSTDINT 1
+ #endif
+ #if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
+ #define HALF_ENABLE_CPP11_CMATH 1
+ #endif
+ #if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
+ #define HALF_ENABLE_CPP11_HASH 1
+ #endif
+ #if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CFENV)
+ #define HALF_ENABLE_CPP11_CFENV 1
+ #endif
+ #endif
+ #endif
+#elif defined(_CPPLIB_VER) // Dinkumware/Visual C++
+ #if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+ #define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+ #endif
+ #if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+ #define HALF_ENABLE_CPP11_CSTDINT 1
+ #endif
+ #if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_HASH)
+ #define HALF_ENABLE_CPP11_HASH 1
+ #endif
+ #if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CMATH)
+ #define HALF_ENABLE_CPP11_CMATH 1
+ #endif
+ #if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CFENV)
+ #define HALF_ENABLE_CPP11_CFENV 1
+ #endif
+#endif
+#undef HALF_GCC_VERSION
+#undef HALF_ICC_VERSION
+
+// any error throwing C++ exceptions?
+#if defined(HALF_ERRHANDLING_THROW_INVALID) || defined(HALF_ERRHANDLING_THROW_DIVBYZERO) || defined(HALF_ERRHANDLING_THROW_OVERFLOW) || defined(HALF_ERRHANDLING_THROW_UNDERFLOW) || defined(HALF_ERRHANDLING_THROW_INEXACT)
+#define HALF_ERRHANDLING_THROWS 1
+#endif
+
+// any error handling enabled?
+#define HALF_ERRHANDLING (HALF_ERRHANDLING_FLAGS||HALF_ERRHANDLING_ERRNO||HALF_ERRHANDLING_FENV||HALF_ERRHANDLING_THROWS)
+
+#if HALF_ERRHANDLING
+ #define HALF_UNUSED_NOERR(name) name
+#else
+ #define HALF_UNUSED_NOERR(name)
+#endif
+
+// support constexpr
+#if HALF_ENABLE_CPP11_CONSTEXPR
+ #define HALF_CONSTEXPR constexpr
+ #define HALF_CONSTEXPR_CONST constexpr
+ #if HALF_ERRHANDLING
+ #define HALF_CONSTEXPR_NOERR
+ #else
+ #define HALF_CONSTEXPR_NOERR constexpr
+ #endif
+#else
+ #define HALF_CONSTEXPR
+ #define HALF_CONSTEXPR_CONST const
+ #define HALF_CONSTEXPR_NOERR
+#endif
+
+// support noexcept
+#if HALF_ENABLE_CPP11_NOEXCEPT
+ #define HALF_NOEXCEPT noexcept
+ #define HALF_NOTHROW noexcept
+#else
+ #define HALF_NOEXCEPT
+ #define HALF_NOTHROW throw()
+#endif
+
+// support thread storage
+#if HALF_ENABLE_CPP11_THREAD_LOCAL
+ #define HALF_THREAD_LOCAL thread_local
+#else
+ #define HALF_THREAD_LOCAL static
+#endif
+
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+#if HALF_ENABLE_CPP11_TYPE_TRAITS
+ #include
+#endif
+#if HALF_ENABLE_CPP11_CSTDINT
+ #include
+#endif
+#if HALF_ERRHANDLING_ERRNO
+ #include
+#endif
+#if HALF_ENABLE_CPP11_CFENV
+ #include
+#endif
+#if HALF_ENABLE_CPP11_HASH
+ #include
+#endif
+
+
+#ifndef HALF_ENABLE_F16C_INTRINSICS
+ /// Enable F16C intruction set intrinsics.
+ /// Defining this to 1 enables the use of [F16C compiler intrinsics](https://en.wikipedia.org/wiki/F16C) for converting between
+ /// half-precision and single-precision values which may result in improved performance. This will not perform additional checks
+ /// for support of the F16C instruction set, so an appropriate target platform is required when enabling this feature.
+ ///
+ /// Unless predefined it will be enabled automatically when the `__F16C__` symbol is defined, which some compilers do on supporting platforms.
+ #define HALF_ENABLE_F16C_INTRINSICS __F16C__
+#endif
+#if HALF_ENABLE_F16C_INTRINSICS
+ #include
+#endif
+
+#ifdef HALF_DOXYGEN_ONLY
+/// Type for internal floating-point computations.
+/// This can be predefined to a built-in floating-point type (`float`, `double` or `long double`) to override the internal
+/// half-precision implementation to use this type for computing arithmetic operations and mathematical function (if available).
+/// This can result in improved performance for arithmetic operators and mathematical functions but might cause results to
+/// deviate from the specified half-precision rounding mode and inhibits proper detection of half-precision exceptions.
+#define HALF_ARITHMETIC_TYPE (undefined)
+
+/// Enable internal exception flags.
+/// Defining this to 1 causes operations on half-precision values to raise internal floating-point exception flags according to
+/// the IEEE 754 standard. These can then be cleared and checked with clearexcept(), testexcept().
+#define HALF_ERRHANDLING_FLAGS 0
+
+/// Enable exception propagation to `errno`.
+/// Defining this to 1 causes operations on half-precision values to propagate floating-point exceptions to
+/// [errno](https://en.cppreference.com/w/cpp/error/errno) from ``. Specifically this will propagate domain errors as
+/// [EDOM](https://en.cppreference.com/w/cpp/error/errno_macros) and pole, overflow and underflow errors as
+/// [ERANGE](https://en.cppreference.com/w/cpp/error/errno_macros). Inexact errors won't be propagated.
+#define HALF_ERRHANDLING_ERRNO 0
+
+/// Enable exception propagation to built-in floating-point platform.
+/// Defining this to 1 causes operations on half-precision values to propagate floating-point exceptions to the built-in
+/// single- and double-precision implementation's exception flags using the
+/// [C++11 floating-point environment control](https://en.cppreference.com/w/cpp/numeric/fenv) from ``. However, this
+/// does not work in reverse and single- or double-precision exceptions will not raise the corresponding half-precision
+/// exception flags, nor will explicitly clearing flags clear the corresponding built-in flags.
+#define HALF_ERRHANDLING_FENV 0
+
+/// Throw C++ exception on domain errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a
+/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified message on domain errors.
+#define HALF_ERRHANDLING_THROW_INVALID (undefined)
+
+/// Throw C++ exception on pole errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a
+/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified message on pole errors.
+#define HALF_ERRHANDLING_THROW_DIVBYZERO (undefined)
+
+/// Throw C++ exception on overflow errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a
+/// [std::overflow_error](https://en.cppreference.com/w/cpp/error/overflow_error) with the specified message on overflows.
+#define HALF_ERRHANDLING_THROW_OVERFLOW (undefined)
+
+/// Throw C++ exception on underflow errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a
+/// [std::underflow_error](https://en.cppreference.com/w/cpp/error/underflow_error) with the specified message on underflows.
+#define HALF_ERRHANDLING_THROW_UNDERFLOW (undefined)
+
+/// Throw C++ exception on rounding errors.
+/// Defining this to 1 causes operations on half-precision values to throw a
+/// [std::range_error](https://en.cppreference.com/w/cpp/error/range_error) with the specified message on general rounding errors.
+#define HALF_ERRHANDLING_THROW_INEXACT (undefined)
+#endif
+
+#ifndef HALF_ERRHANDLING_OVERFLOW_TO_INEXACT
+/// Raise INEXACT exception on overflow.
+/// Defining this to 1 (default) causes overflow errors to automatically raise inexact exceptions in addition.
+/// These will be raised after any possible handling of the underflow exception.
+#define HALF_ERRHANDLING_OVERFLOW_TO_INEXACT 1
+#endif
+
+#ifndef HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
+/// Raise INEXACT exception on underflow.
+/// Defining this to 1 (default) causes underflow errors to automatically raise inexact exceptions in addition.
+/// These will be raised after any possible handling of the underflow exception.
+///
+/// **Note:** This will actually cause underflow (and the accompanying inexact) exceptions to be raised *only* when the result
+/// is inexact, while if disabled bare underflow errors will be raised for *any* (possibly exact) subnormal result.
+#define HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT 1
+#endif
+
+/// Default rounding mode.
+/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s and more precise types
+/// (unless using half_cast() and specifying the rounding mode directly) as well as in arithmetic operations and mathematical
+/// functions. It can be redefined (before including half.hpp) to one of the standard rounding modes using their respective
+/// constants or the equivalent values of
+/// [std::float_round_style](https://en.cppreference.com/w/cpp/types/numeric_limits/float_round_style):
+///
+/// `std::float_round_style` | value | rounding
+/// ---------------------------------|-------|-------------------------
+/// `std::round_indeterminate` | -1 | fastest
+/// `std::round_toward_zero` | 0 | toward zero
+/// `std::round_to_nearest` | 1 | to nearest (default)
+/// `std::round_toward_infinity` | 2 | toward positive infinity
+/// `std::round_toward_neg_infinity` | 3 | toward negative infinity
+///
+/// By default this is set to `1` (`std::round_to_nearest`), which rounds results to the nearest representable value. It can even
+/// be set to [std::numeric_limits::round_style](https://en.cppreference.com/w/cpp/types/numeric_limits/round_style) to synchronize
+/// the rounding mode with that of the built-in single-precision implementation (which is likely `std::round_to_nearest`, though).
+#ifndef HALF_ROUND_STYLE
+ #define HALF_ROUND_STYLE 1 // = std::round_to_nearest
+#endif
+
+/// Value signaling overflow.
+/// In correspondence with `HUGE_VAL[F|L]` from `` this symbol expands to a positive value signaling the overflow of an
+/// operation, in particular it just evaluates to positive infinity.
+///
+/// **See also:** Documentation for [HUGE_VAL](https://en.cppreference.com/w/cpp/numeric/math/HUGE_VAL)
+#define HUGE_VALH std::numeric_limits::infinity()
+
+/// Fast half-precision fma function.
+/// This symbol is defined if the fma() function generally executes as fast as, or faster than, a separate
+/// half-precision multiplication followed by an addition, which is always the case.
+///
+/// **See also:** Documentation for [FP_FAST_FMA](https://en.cppreference.com/w/cpp/numeric/math/fma)
+#define FP_FAST_FMAH 1
+
+/// Half rounding mode.
+/// In correspondence with `FLT_ROUNDS` from `` this symbol expands to the rounding mode used for
+/// half-precision operations. It is an alias for [HALF_ROUND_STYLE](\ref HALF_ROUND_STYLE).
+///
+/// **See also:** Documentation for [FLT_ROUNDS](https://en.cppreference.com/w/cpp/types/climits/FLT_ROUNDS)
+#define HLF_ROUNDS HALF_ROUND_STYLE
+
+#ifndef FP_ILOGB0
+ #define FP_ILOGB0 INT_MIN
+#endif
+#ifndef FP_ILOGBNAN
+ #define FP_ILOGBNAN INT_MAX
+#endif
+#ifndef FP_SUBNORMAL
+ #define FP_SUBNORMAL 0
+#endif
+#ifndef FP_ZERO
+ #define FP_ZERO 1
+#endif
+#ifndef FP_NAN
+ #define FP_NAN 2
+#endif
+#ifndef FP_INFINITE
+ #define FP_INFINITE 3
+#endif
+#ifndef FP_NORMAL
+ #define FP_NORMAL 4
+#endif
+
+#if !HALF_ENABLE_CPP11_CFENV && !defined(FE_ALL_EXCEPT)
+ #define FE_INVALID 0x10
+ #define FE_DIVBYZERO 0x08
+ #define FE_OVERFLOW 0x04
+ #define FE_UNDERFLOW 0x02
+ #define FE_INEXACT 0x01
+ #define FE_ALL_EXCEPT (FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT)
+#endif
+
+
+/// Main namespace for half-precision functionality.
+/// This namespace contains all the functionality provided by the library.
+namespace half_float
+{
+ class half;
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+ /// Library-defined half-precision literals.
+ /// Import this namespace to enable half-precision floating-point literals:
+ /// ~~~~{.cpp}
+ /// using namespace half_float::literal;
+ /// half_float::half = 4.2_h;
+ /// ~~~~
+ namespace literal
+ {
+ half operator "" _h(long double);
+ }
+#endif
+
+ /// \internal
+ /// \brief Implementation details.
+ namespace detail
+ {
+ #if HALF_ENABLE_CPP11_TYPE_TRAITS
+ /// Conditional type.
+ template struct conditional : std::conditional {};
+
+ /// Helper for tag dispatching.
+ template struct bool_type : std::integral_constant {};
+ using std::true_type;
+ using std::false_type;
+
+ /// Type traits for floating-point types.
+ template struct is_float : std::is_floating_point {};
+ #else
+ /// Conditional type.
+ template struct conditional { typedef T type; };
+ template struct conditional { typedef F type; };
+
+ /// Helper for tag dispatching.
+ template struct bool_type {};
+ typedef bool_type true_type;
+ typedef bool_type false_type;
+
+ /// Type traits for floating-point types.
+ template struct is_float : false_type {};
+ template struct is_float : is_float {};
+ template struct is_float : is_float {};
+ template struct is_float : is_float {};
+ template<> struct is_float : true_type {};
+ template<> struct is_float : true_type {};
+ template<> struct is_float : true_type {};
+ #endif
+
+ /// Type traits for floating-point bits.
+ template struct bits { typedef unsigned char type; };
+ template struct bits : bits {};
+ template struct bits : bits {};
+ template struct bits : bits {};
+
+ #if HALF_ENABLE_CPP11_CSTDINT
+ /// Unsigned integer of (at least) 16 bits width.
+ typedef std::uint_least16_t uint16;
+
+ /// Fastest unsigned integer of (at least) 32 bits width.
+ typedef std::uint_fast32_t uint32;
+
+ /// Fastest signed integer of (at least) 32 bits width.
+ typedef std::int_fast32_t int32;
+
+ /// Unsigned integer of (at least) 32 bits width.
+ template<> struct bits { typedef std::uint_least32_t type; };
+
+ /// Unsigned integer of (at least) 64 bits width.
+ template<> struct bits { typedef std::uint_least64_t type; };
+ #else
+ /// Unsigned integer of (at least) 16 bits width.
+ typedef unsigned short uint16;
+
+ /// Fastest unsigned integer of (at least) 32 bits width.
+ typedef unsigned long uint32;
+
+ /// Fastest unsigned integer of (at least) 32 bits width.
+ typedef long int32;
+
+ /// Unsigned integer of (at least) 32 bits width.
+ template<> struct bits : conditional::digits>=32,unsigned int,unsigned long> {};
+
+ #if HALF_ENABLE_CPP11_LONG_LONG
+ /// Unsigned integer of (at least) 64 bits width.
+ template<> struct bits : conditional::digits>=64,unsigned long,unsigned long long> {};
+ #else
+ /// Unsigned integer of (at least) 64 bits width.
+ template<> struct bits { typedef unsigned long type; };
+ #endif
+ #endif
+
+ #ifdef HALF_ARITHMETIC_TYPE
+ /// Type to use for arithmetic computations and mathematic functions internally.
+ typedef HALF_ARITHMETIC_TYPE internal_t;
+ #endif
+
+ /// Tag type for binary construction.
+ struct binary_t {};
+
+ /// Tag for binary construction.
+ HALF_CONSTEXPR_CONST binary_t binary = binary_t();
+
+ /// \name Implementation defined classification and arithmetic
+ /// \{
+
+ /// Check for infinity.
+ /// \tparam T argument type (builtin floating-point type)
+ /// \param arg value to query
+ /// \retval true if infinity
+ /// \retval false else
+ template bool builtin_isinf(T arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return std::isinf(arg);
+ #elif defined(_MSC_VER)
+ return !::_finite(static_cast(arg)) && !::_isnan(static_cast(arg));
+ #else
+ return arg == std::numeric_limits::infinity() || arg == -std::numeric_limits::infinity();
+ #endif
+ }
+
+ /// Check for NaN.
+ /// \tparam T argument type (builtin floating-point type)
+ /// \param arg value to query
+ /// \retval true if not a number
+ /// \retval false else
+ template bool builtin_isnan(T arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return std::isnan(arg);
+ #elif defined(_MSC_VER)
+ return ::_isnan(static_cast(arg)) != 0;
+ #else
+ return arg != arg;
+ #endif
+ }
+
+ /// Check sign.
+ /// \tparam T argument type (builtin floating-point type)
+ /// \param arg value to query
+ /// \retval true if signbit set
+ /// \retval false else
+ template bool builtin_signbit(T arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return std::signbit(arg);
+ #else
+ return arg < T() || (arg == T() && T(1)/arg < T());
+ #endif
+ }
+
+ /// Platform-independent sign mask.
+ /// \param arg integer value in two's complement
+ /// \retval -1 if \a arg negative
+ /// \retval 0 if \a arg positive
+ inline uint32 sign_mask(uint32 arg)
+ {
+ static const int N = std::numeric_limits::digits - 1;
+ #if HALF_TWOS_COMPLEMENT_INT
+ return static_cast(arg) >> N;
+ #else
+ return -((arg>>N)&1);
+ #endif
+ }
+
+ /// Platform-independent arithmetic right shift.
+ /// \param arg integer value in two's complement
+ /// \param i shift amount (at most 31)
+ /// \return \a arg right shifted for \a i bits with possible sign extension
+ inline uint32 arithmetic_shift(uint32 arg, int i)
+ {
+ #if HALF_TWOS_COMPLEMENT_INT
+ return static_cast(arg) >> i;
+ #else
+ return static_cast(arg)/(static_cast(1)<>(std::numeric_limits::digits-1))&1);
+ #endif
+ }
+
+ /// \}
+ /// \name Error handling
+ /// \{
+
+ /// Internal exception flags.
+ /// \return reference to global exception flags
+ inline int& errflags() { HALF_THREAD_LOCAL int flags = 0; return flags; }
+
+ /// Raise floating-point exception.
+ /// \param flags exceptions to raise
+ /// \param cond condition to raise exceptions for
+ inline void raise(int HALF_UNUSED_NOERR(flags), bool HALF_UNUSED_NOERR(cond) = true)
+ {
+ #if HALF_ERRHANDLING
+ if(!cond)
+ return;
+ #if HALF_ERRHANDLING_FLAGS
+ errflags() |= flags;
+ #endif
+ #if HALF_ERRHANDLING_ERRNO
+ if(flags & FE_INVALID)
+ errno = EDOM;
+ else if(flags & (FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW))
+ errno = ERANGE;
+ #endif
+ #if HALF_ERRHANDLING_FENV && HALF_ENABLE_CPP11_CFENV
+ std::feraiseexcept(flags);
+ #endif
+ #ifdef HALF_ERRHANDLING_THROW_INVALID
+ if(flags & FE_INVALID)
+ throw std::domain_error(HALF_ERRHANDLING_THROW_INVALID);
+ #endif
+ #ifdef HALF_ERRHANDLING_THROW_DIVBYZERO
+ if(flags & FE_DIVBYZERO)
+ throw std::domain_error(HALF_ERRHANDLING_THROW_DIVBYZERO);
+ #endif
+ #ifdef HALF_ERRHANDLING_THROW_OVERFLOW
+ if(flags & FE_OVERFLOW)
+ throw std::overflow_error(HALF_ERRHANDLING_THROW_OVERFLOW);
+ #endif
+ #ifdef HALF_ERRHANDLING_THROW_UNDERFLOW
+ if(flags & FE_UNDERFLOW)
+ throw std::underflow_error(HALF_ERRHANDLING_THROW_UNDERFLOW);
+ #endif
+ #ifdef HALF_ERRHANDLING_THROW_INEXACT
+ if(flags & FE_INEXACT)
+ throw std::range_error(HALF_ERRHANDLING_THROW_INEXACT);
+ #endif
+ #if HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
+ if((flags & FE_UNDERFLOW) && !(flags & FE_INEXACT))
+ raise(FE_INEXACT);
+ #endif
+ #if HALF_ERRHANDLING_OVERFLOW_TO_INEXACT
+ if((flags & FE_OVERFLOW) && !(flags & FE_INEXACT))
+ raise(FE_INEXACT);
+ #endif
+ #endif
+ }
+
+ /// Check and signal for any NaN.
+ /// \param x first half-precision value to check
+ /// \param y second half-precision value to check
+ /// \retval true if either \a x or \a y is NaN
+ /// \retval false else
+ /// \exception FE_INVALID if \a x or \a y is NaN
+ inline HALF_CONSTEXPR_NOERR bool compsignal(unsigned int x, unsigned int y)
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_INVALID, (x&0x7FFF)>0x7C00 || (y&0x7FFF)>0x7C00);
+ #endif
+ return (x&0x7FFF) > 0x7C00 || (y&0x7FFF) > 0x7C00;
+ }
+
+ /// Signal and silence signaling NaN.
+ /// \param nan half-precision NaN value
+ /// \return quiet NaN
+ /// \exception FE_INVALID if \a nan is signaling NaN
+ inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int nan)
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_INVALID, !(nan&0x200));
+ #endif
+ return nan | 0x200;
+ }
+
+ /// Signal and silence signaling NaNs.
+ /// \param x first half-precision value to check
+ /// \param y second half-precision value to check
+ /// \return quiet NaN
+ /// \exception FE_INVALID if \a x or \a y is signaling NaN
+ inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y)
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_INVALID, ((x&0x7FFF)>0x7C00 && !(x&0x200)) || ((y&0x7FFF)>0x7C00 && !(y&0x200)));
+ #endif
+ return ((x&0x7FFF)>0x7C00) ? (x|0x200) : (y|0x200);
+ }
+
+ /// Signal and silence signaling NaNs.
+ /// \param x first half-precision value to check
+ /// \param y second half-precision value to check
+ /// \param z third half-precision value to check
+ /// \return quiet NaN
+ /// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN
+ inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y, unsigned int z)
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_INVALID, ((x&0x7FFF)>0x7C00 && !(x&0x200)) || ((y&0x7FFF)>0x7C00 && !(y&0x200)) || ((z&0x7FFF)>0x7C00 && !(z&0x200)));
+ #endif
+ return ((x&0x7FFF)>0x7C00) ? (x|0x200) : ((y&0x7FFF)>0x7C00) ? (y|0x200) : (z|0x200);
+ }
+
+ /// Select value or signaling NaN.
+ /// \param x preferred half-precision value
+ /// \param y ignored half-precision value except for signaling NaN
+ /// \return \a y if signaling NaN, \a x otherwise
+ /// \exception FE_INVALID if \a y is signaling NaN
+ inline HALF_CONSTEXPR_NOERR unsigned int select(unsigned int x, unsigned int HALF_UNUSED_NOERR(y))
+ {
+ #if HALF_ERRHANDLING
+ return (((y&0x7FFF)>0x7C00) && !(y&0x200)) ? signal(y) : x;
+ #else
+ return x;
+ #endif
+ }
+
+ /// Raise domain error and return NaN.
+ /// return quiet NaN
+ /// \exception FE_INVALID
+ inline HALF_CONSTEXPR_NOERR unsigned int invalid()
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_INVALID);
+ #endif
+ return 0x7FFF;
+ }
+
+ /// Raise pole error and return infinity.
+ /// \param sign half-precision value with sign bit only
+ /// \return half-precision infinity with sign of \a sign
+ /// \exception FE_DIVBYZERO
+ inline HALF_CONSTEXPR_NOERR unsigned int pole(unsigned int sign = 0)
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_DIVBYZERO);
+ #endif
+ return sign | 0x7C00;
+ }
+
+ /// Check value for underflow.
+ /// \param arg non-zero half-precision value to check
+ /// \return \a arg
+ /// \exception FE_UNDERFLOW if arg is subnormal
+ inline HALF_CONSTEXPR_NOERR unsigned int check_underflow(unsigned int arg)
+ {
+ #if HALF_ERRHANDLING && !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
+ raise(FE_UNDERFLOW, !(arg&0x7C00));
+ #endif
+ return arg;
+ }
+
+ /// \}
+ /// \name Conversion and rounding
+ /// \{
+
+ /// Half-precision overflow.
+ /// \tparam R rounding mode to use
+ /// \param sign half-precision value with sign bit only
+ /// \return rounded overflowing half-precision value
+ /// \exception FE_OVERFLOW
+ template HALF_CONSTEXPR_NOERR unsigned int overflow(unsigned int sign = 0)
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_OVERFLOW);
+ #endif
+ return (R==std::round_toward_infinity) ? (sign+0x7C00-(sign>>15)) :
+ (R==std::round_toward_neg_infinity) ? (sign+0x7BFF+(sign>>15)) :
+ (R==std::round_toward_zero) ? (sign|0x7BFF) :
+ (sign|0x7C00);
+ }
+
+ /// Half-precision underflow.
+ /// \tparam R rounding mode to use
+ /// \param sign half-precision value with sign bit only
+ /// \return rounded underflowing half-precision value
+ /// \exception FE_UNDERFLOW
+ template HALF_CONSTEXPR_NOERR unsigned int underflow(unsigned int sign = 0)
+ {
+ #if HALF_ERRHANDLING
+ raise(FE_UNDERFLOW);
+ #endif
+ return (R==std::round_toward_infinity) ? (sign+1-(sign>>15)) :
+ (R==std::round_toward_neg_infinity) ? (sign+(sign>>15)) :
+ sign;
+ }
+
+ /// Round half-precision number.
+ /// \tparam R rounding mode to use
+ /// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results
+ /// \param value finite half-precision number to round
+ /// \param g guard bit (most significant discarded bit)
+ /// \param s sticky bit (or of all but the most significant discarded bits)
+ /// \return rounded half-precision value
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if value had to be rounded or \a I is `true`
+ template HALF_CONSTEXPR_NOERR unsigned int rounded(unsigned int value, int g, int s)
+ {
+ #if HALF_ERRHANDLING
+ value += (R==std::round_to_nearest) ? (g&(s|value)) :
+ (R==std::round_toward_infinity) ? (~(value>>15)&(g|s)) :
+ (R==std::round_toward_neg_infinity) ? ((value>>15)&(g|s)) : 0;
+ if((value&0x7C00) == 0x7C00)
+ raise(FE_OVERFLOW);
+ else if(value & 0x7C00)
+ raise(FE_INEXACT, I || (g|s)!=0);
+ else
+ raise(FE_UNDERFLOW, !(HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT) || I || (g|s)!=0);
+ return value;
+ #else
+ return (R==std::round_to_nearest) ? (value+(g&(s|value))) :
+ (R==std::round_toward_infinity) ? (value+(~(value>>15)&(g|s))) :
+ (R==std::round_toward_neg_infinity) ? (value+((value>>15)&(g|s))) :
+ value;
+ #endif
+ }
+
+ /// Round half-precision number to nearest integer value.
+ /// \tparam R rounding mode to use
+ /// \tparam E `true` for round to even, `false` for round away from zero
+ /// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it
+ /// \param value half-precision value to round
+ /// \return half-precision bits for nearest integral value
+ /// \exception FE_INVALID for signaling NaN
+ /// \exception FE_INEXACT if value had to be rounded and \a I is `true`
+ template unsigned int integral(unsigned int value)
+ {
+ unsigned int abs = value & 0x7FFF;
+ if(abs < 0x3C00)
+ {
+ raise(FE_INEXACT, I);
+ return ((R==std::round_to_nearest) ? (0x3C00&-static_cast(abs>=(0x3800+E))) :
+ (R==std::round_toward_infinity) ? (0x3C00&-(~(value>>15)&(abs!=0))) :
+ (R==std::round_toward_neg_infinity) ? (0x3C00&-static_cast(value>0x8000)) :
+ 0) | (value&0x8000);
+ }
+ if(abs >= 0x6400)
+ return (abs>0x7C00) ? signal(value) : value;
+ unsigned int exp = 25 - (abs>>10), mask = (1<>exp)&E)) :
+ (R==std::round_toward_infinity) ? (mask&((value>>15)-1)) :
+ (R==std::round_toward_neg_infinity) ? (mask&-(value>>15)) :
+ 0) + value) & ~mask;
+ }
+
+ /// Convert fixed point to half-precision floating-point.
+ /// \tparam R rounding mode to use
+ /// \tparam F number of fractional bits in [11,31]
+ /// \tparam S `true` for signed, `false` for unsigned
+ /// \tparam N `true` for additional normalization step, `false` if already normalized to 1.F
+ /// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results
+ /// \param m mantissa in Q1.F fixed point format
+ /// \param exp biased exponent - 1
+ /// \param sign half-precision value with sign bit only
+ /// \param s sticky bit (or of all but the most significant already discarded bits)
+ /// \return value converted to half-precision
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if value had to be rounded or \a I is `true`
+ template unsigned int fixed2half(uint32 m, int exp = 14, unsigned int sign = 0, int s = 0)
+ {
+ if(S)
+ {
+ uint32 msign = sign_mask(m);
+ m = (m^msign) - msign;
+ sign = msign & 0x8000;
+ }
+ if(N)
+ for(; m<(static_cast(1)<(sign+(m>>(F-10-exp)), (m>>(F-11-exp))&1, s|((m&((static_cast(1)<<(F-11-exp))-1))!=0));
+ return rounded(sign+(exp<<10)+(m>>(F-10)), (m>>(F-11))&1, s|((m&((static_cast(1)<<(F-11))-1))!=0));
+ }
+
+ /// Convert IEEE single-precision to half-precision.
+ /// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
+ /// \tparam R rounding mode to use
+ /// \param value single-precision value to convert
+ /// \return rounded half-precision value
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if value had to be rounded
+ template unsigned int float2half_impl(float value, true_type)
+ {
+ #if HALF_ENABLE_F16C_INTRINSICS
+ return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_set_ss(value),
+ (R==std::round_to_nearest) ? _MM_FROUND_TO_NEAREST_INT :
+ (R==std::round_toward_zero) ? _MM_FROUND_TO_ZERO :
+ (R==std::round_toward_infinity) ? _MM_FROUND_TO_POS_INF :
+ (R==std::round_toward_neg_infinity) ? _MM_FROUND_TO_NEG_INF :
+ _MM_FROUND_CUR_DIRECTION));
+ #else
+ bits::type fbits;
+ std::memcpy(&fbits, &value, sizeof(float));
+ #if 1
+ unsigned int sign = (fbits>>16) & 0x8000;
+ fbits &= 0x7FFFFFFF;
+ if(fbits >= 0x7F800000)
+ return sign | 0x7C00 | ((fbits>0x7F800000) ? (0x200|((fbits>>13)&0x3FF)) : 0);
+ if(fbits >= 0x47800000)
+ return overflow(sign);
+ if(fbits >= 0x38800000)
+ return rounded(sign|(((fbits>>23)-112)<<10)|((fbits>>13)&0x3FF), (fbits>>12)&1, (fbits&0xFFF)!=0);
+ if(fbits >= 0x33000000)
+ {
+ int i = 125 - (fbits>>23);
+ fbits = (fbits&0x7FFFFF) | 0x800000;
+ return rounded(sign|(fbits>>(i+1)), (fbits>>i)&1, (fbits&((static_cast(1)<(sign);
+ return sign;
+ #else
+ static const uint16 base_table[512] = {
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100,
+ 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00,
+ 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7BFF,
+ 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
+ 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
+ 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
+ 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
+ 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
+ 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
+ 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7C00,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100,
+ 0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00,
+ 0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFBFF,
+ 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
+ 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
+ 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
+ 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
+ 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
+ 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
+ 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFC00 };
+ static const unsigned char shift_table[256] = {
+ 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
+ 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
+ 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
+ 25, 25, 25, 25, 25, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 };
+ int sexp = fbits >> 23, exp = sexp & 0xFF, i = shift_table[exp];
+ fbits &= 0x7FFFFF;
+ uint32 m = (fbits|((exp!=0)<<23)) & -static_cast(exp!=0xFF);
+ return rounded(base_table[sexp]+(fbits>>i), (m>>(i-1))&1, (((static_cast(1)<<(i-1))-1)&m)!=0);
+ #endif
+ #endif
+ }
+
+ /// Convert IEEE double-precision to half-precision.
+ /// \tparam R rounding mode to use
+ /// \param value double-precision value to convert
+ /// \return rounded half-precision value
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if value had to be rounded
+ template unsigned int float2half_impl(double value, true_type)
+ {
+ #if HALF_ENABLE_F16C_INTRINSICS
+ if(R == std::round_indeterminate)
+ return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_cvtpd_ps(_mm_set_sd(value)), _MM_FROUND_CUR_DIRECTION));
+ #endif
+ bits::type dbits;
+ std::memcpy(&dbits, &value, sizeof(double));
+ uint32 hi = dbits >> 32, lo = dbits & 0xFFFFFFFF;
+ unsigned int sign = (hi>>16) & 0x8000;
+ hi &= 0x7FFFFFFF;
+ if(hi >= 0x7FF00000)
+ return sign | 0x7C00 | ((dbits&0xFFFFFFFFFFFFF) ? (0x200|((hi>>10)&0x3FF)) : 0);
+ if(hi >= 0x40F00000)
+ return overflow(sign);
+ if(hi >= 0x3F100000)
+ return rounded(sign|(((hi>>20)-1008)<<10)|((hi>>10)&0x3FF), (hi>>9)&1, ((hi&0x1FF)|lo)!=0);
+ if(hi >= 0x3E600000)
+ {
+ int i = 1018 - (hi>>20);
+ hi = (hi&0xFFFFF) | 0x100000;
+ return rounded(sign|(hi>>(i+1)), (hi>>i)&1, ((hi&((static_cast(1)<(sign);
+ return sign;
+ }
+
+ /// Convert non-IEEE floating-point to half-precision.
+ /// \tparam R rounding mode to use
+ /// \tparam T source type (builtin floating-point type)
+ /// \param value floating-point value to convert
+ /// \return rounded half-precision value
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if value had to be rounded
+ template unsigned int float2half_impl(T value, ...)
+ {
+ unsigned int hbits = static_cast(builtin_signbit(value)) << 15;
+ if(value == T())
+ return hbits;
+ if(builtin_isnan(value))
+ return hbits | 0x7FFF;
+ if(builtin_isinf(value))
+ return hbits | 0x7C00;
+ int exp;
+ std::frexp(value, &exp);
+ if(exp > 16)
+ return overflow(hbits);
+ if(exp < -13)
+ value = std::ldexp(value, 25);
+ else
+ {
+ value = std::ldexp(value, 12-exp);
+ hbits |= ((exp+13)<<10);
+ }
+ T ival, frac = std::modf(value, &ival);
+ int m = std::abs(static_cast(ival));
+ return rounded(hbits+(m>>1), m&1, frac!=T());
+ }
+
+ /// Convert floating-point to half-precision.
+ /// \tparam R rounding mode to use
+ /// \tparam T source type (builtin floating-point type)
+ /// \param value floating-point value to convert
+ /// \return rounded half-precision value
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if value had to be rounded
+ template unsigned int float2half(T value)
+ {
+ return float2half_impl(value, bool_type::is_iec559&&sizeof(typename bits::type)==sizeof(T)>());
+ }
+
+ /// Convert integer to half-precision floating-point.
+ /// \tparam R rounding mode to use
+ /// \tparam T type to convert (builtin integer type)
+ /// \param value integral value to convert
+ /// \return rounded half-precision value
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_INEXACT if value had to be rounded
+ template unsigned int int2half(T value)
+ {
+ unsigned int bits = static_cast(value<0) << 15;
+ if(!value)
+ return bits;
+ if(bits)
+ value = -value;
+ if(value > 0xFFFF)
+ return overflow(bits);
+ unsigned int m = static_cast(value), exp = 24;
+ for(; m<0x400; m<<=1,--exp) ;
+ for(; m>0x7FF; m>>=1,++exp) ;
+ bits |= (exp<<10) + m;
+ return (exp>24) ? rounded(bits, (value>>(exp-25))&1, (((1<<(exp-25))-1)&value)!=0) : bits;
+ }
+
+ /// Convert half-precision to IEEE single-precision.
+ /// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
+ /// \param value half-precision value to convert
+ /// \return single-precision value
+ inline float half2float_impl(unsigned int value, float, true_type)
+ {
+ #if HALF_ENABLE_F16C_INTRINSICS
+ return _mm_cvtss_f32(_mm_cvtph_ps(_mm_cvtsi32_si128(value)));
+ #else
+ #if 0
+ bits::type fbits = static_cast::type>(value&0x8000) << 16;
+ int abs = value & 0x7FFF;
+ if(abs)
+ {
+ fbits |= 0x38000000 << static_cast(abs>=0x7C00);
+ for(; abs<0x400; abs<<=1,fbits-=0x800000) ;
+ fbits += static_cast::type>(abs) << 13;
+ }
+ #else
+ static const bits::type mantissa_table[2048] = {
+ 0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000,
+ 0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000,
+ 0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000,
+ 0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000,
+ 0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000,
+ 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000,
+ 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000,
+ 0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000,
+ 0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000,
+ 0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000,
+ 0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000,
+ 0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000,
+ 0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000,
+ 0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000,
+ 0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000,
+ 0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000,
+ 0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000,
+ 0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000,
+ 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000,
+ 0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000,
+ 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000,
+ 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000,
+ 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000,
+ 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000,
+ 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000,
+ 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000,
+ 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000,
+ 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000,
+ 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000,
+ 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000,
+ 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000,
+ 0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000,
+ 0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000,
+ 0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000,
+ 0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000,
+ 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000,
+ 0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000,
+ 0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000,
+ 0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000,
+ 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000,
+ 0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000,
+ 0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000,
+ 0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000,
+ 0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000,
+ 0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000,
+ 0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000,
+ 0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000,
+ 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000,
+ 0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000,
+ 0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000,
+ 0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000,
+ 0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000,
+ 0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000,
+ 0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000,
+ 0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000,
+ 0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000,
+ 0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000,
+ 0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000,
+ 0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000,
+ 0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000,
+ 0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000,
+ 0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000,
+ 0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000,
+ 0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000,
+ 0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000,
+ 0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000,
+ 0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000,
+ 0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000,
+ 0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000,
+ 0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000,
+ 0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000,
+ 0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000,
+ 0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000,
+ 0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000,
+ 0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000,
+ 0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000,
+ 0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000,
+ 0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000,
+ 0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000,
+ 0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000,
+ 0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000,
+ 0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000,
+ 0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000,
+ 0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000,
+ 0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000,
+ 0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000,
+ 0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000,
+ 0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000,
+ 0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000,
+ 0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000,
+ 0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000,
+ 0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000,
+ 0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000,
+ 0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000,
+ 0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000,
+ 0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000,
+ 0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000,
+ 0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000,
+ 0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000,
+ 0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000,
+ 0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000,
+ 0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000,
+ 0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000,
+ 0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000,
+ 0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000,
+ 0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000,
+ 0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000,
+ 0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000,
+ 0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000,
+ 0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000,
+ 0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000,
+ 0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000,
+ 0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000,
+ 0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000,
+ 0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000,
+ 0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000,
+ 0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000,
+ 0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000,
+ 0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000,
+ 0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000,
+ 0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000,
+ 0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000,
+ 0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000,
+ 0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000,
+ 0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000,
+ 0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000,
+ 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000,
+ 0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 };
+ static const bits::type exponent_table[64] = {
+ 0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000,
+ 0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000,
+ 0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000,
+ 0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 };
+ static const unsigned short offset_table[64] = {
+ 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 };
+ bits::type fbits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10];
+ #endif
+ float out;
+ std::memcpy(&out, &fbits, sizeof(float));
+ return out;
+ #endif
+ }
+
+ /// Convert half-precision to IEEE double-precision.
+ /// \param value half-precision value to convert
+ /// \return double-precision value
+ inline double half2float_impl(unsigned int value, double, true_type)
+ {
+ #if HALF_ENABLE_F16C_INTRINSICS
+ return _mm_cvtsd_f64(_mm_cvtps_pd(_mm_cvtph_ps(_mm_cvtsi32_si128(value))));
+ #else
+ uint32 hi = static_cast(value&0x8000) << 16;
+ unsigned int abs = value & 0x7FFF;
+ if(abs)
+ {
+ hi |= 0x3F000000 << static_cast(abs>=0x7C00);
+ for(; abs<0x400; abs<<=1,hi-=0x100000) ;
+ hi += static_cast(abs) << 10;
+ }
+ bits::type dbits = static_cast::type>(hi) << 32;
+ double out;
+ std::memcpy(&out, &dbits, sizeof(double));
+ return out;
+ #endif
+ }
+
+ /// Convert half-precision to non-IEEE floating-point.
+ /// \tparam T type to convert to (builtin integer type)
+ /// \param value half-precision value to convert
+ /// \return floating-point value
+ template T half2float_impl(unsigned int value, T, ...)
+ {
+ T out;
+ unsigned int abs = value & 0x7FFF;
+ if(abs > 0x7C00)
+ out = (std::numeric_limits::has_signaling_NaN && !(abs&0x200)) ? std::numeric_limits::signaling_NaN() :
+ std::numeric_limits::has_quiet_NaN ? std::numeric_limits::quiet_NaN() : T();
+ else if(abs == 0x7C00)
+ out = std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : std::numeric_limits::max();
+ else if(abs > 0x3FF)
+ out = std::ldexp(static_cast((abs&0x3FF)|0x400), (abs>>10)-25);
+ else
+ out = std::ldexp(static_cast(abs), -24);
+ return (value&0x8000) ? -out : out;
+ }
+
+ /// Convert half-precision to floating-point.
+ /// \tparam T type to convert to (builtin integer type)
+ /// \param value half-precision value to convert
+ /// \return floating-point value
+ template T half2float(unsigned int value)
+ {
+ return half2float_impl(value, T(), bool_type::is_iec559&&sizeof(typename bits::type)==sizeof(T)>());
+ }
+
+ /// Convert half-precision floating-point to integer.
+ /// \tparam R rounding mode to use
+ /// \tparam E `true` for round to even, `false` for round away from zero
+ /// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it
+ /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
+ /// \param value half-precision value to convert
+ /// \return rounded integer value
+ /// \exception FE_INVALID if value is not representable in type \a T
+ /// \exception FE_INEXACT if value had to be rounded and \a I is `true`
+ template T half2int(unsigned int value)
+ {
+ unsigned int abs = value & 0x7FFF;
+ if(abs >= 0x7C00)
+ {
+ raise(FE_INVALID);
+ return (value&0x8000) ? std::numeric_limits::min() : std::numeric_limits::max();
+ }
+ if(abs < 0x3800)
+ {
+ raise(FE_INEXACT, I);
+ return (R==std::round_toward_infinity) ? T(~(value>>15)&(abs!=0)) :
+ (R==std::round_toward_neg_infinity) ? -T(value>0x8000) :
+ T();
+ }
+ int exp = 25 - (abs>>10);
+ unsigned int m = (value&0x3FF) | 0x400;
+ int32 i = static_cast((exp<=0) ? (m<<-exp) : ((m+(
+ (R==std::round_to_nearest) ? ((1<<(exp-1))-(~(m>>exp)&E)) :
+ (R==std::round_toward_infinity) ? (((1<>15)-1)) :
+ (R==std::round_toward_neg_infinity) ? (((1<>15)) : 0))>>exp));
+ if((!std::numeric_limits::is_signed && (value&0x8000)) || (std::numeric_limits::digits<16 &&
+ ((value&0x8000) ? (-i::min()) : (i>std::numeric_limits::max()))))
+ raise(FE_INVALID);
+ else if(I && exp > 0 && (m&((1<((value&0x8000) ? -i : i);
+ }
+
+ /// \}
+ /// \name Mathematics
+ /// \{
+
+ /// upper part of 64-bit multiplication.
+ /// \tparam R rounding mode to use
+ /// \param x first factor
+ /// \param y second factor
+ /// \return upper 32 bit of \a x * \a y
+ template uint32 mulhi(uint32 x, uint32 y)
+ {
+ uint32 xy = (x>>16) * (y&0xFFFF), yx = (x&0xFFFF) * (y>>16), c = (xy&0xFFFF) + (yx&0xFFFF) + (((x&0xFFFF)*(y&0xFFFF))>>16);
+ return (x>>16)*(y>>16) + (xy>>16) + (yx>>16) + (c>>16) +
+ ((R==std::round_to_nearest) ? ((c>>15)&1) : (R==std::round_toward_infinity) ? ((c&0xFFFF)!=0) : 0);
+ }
+
+ /// 64-bit multiplication.
+ /// \param x first factor
+ /// \param y second factor
+ /// \return upper 32 bit of \a x * \a y rounded to nearest
+ inline uint32 multiply64(uint32 x, uint32 y)
+ {
+ #if HALF_ENABLE_CPP11_LONG_LONG
+ return static_cast((static_cast(x)*static_cast(y)+0x80000000)>>32);
+ #else
+ return mulhi(x, y);
+ #endif
+ }
+
+ /// 64-bit division.
+ /// \param x upper 32 bit of dividend
+ /// \param y divisor
+ /// \param s variable to store sticky bit for rounding
+ /// \return (\a x << 32) / \a y
+ inline uint32 divide64(uint32 x, uint32 y, int &s)
+ {
+ #if HALF_ENABLE_CPP11_LONG_LONG
+ unsigned long long xx = static_cast(x) << 32;
+ return s = (xx%y!=0), static_cast(xx/y);
+ #else
+ y >>= 1;
+ uint32 rem = x, div = 0;
+ for(unsigned int i=0; i<32; ++i)
+ {
+ div <<= 1;
+ if(rem >= y)
+ {
+ rem -= y;
+ div |= 1;
+ }
+ rem <<= 1;
+ }
+ return s = rem > 1, div;
+ #endif
+ }
+
+ /// Half precision positive modulus.
+ /// \tparam Q `true` to compute full quotient, `false` else
+ /// \tparam R `true` to compute signed remainder, `false` for positive remainder
+ /// \param x first operand as positive finite half-precision value
+ /// \param y second operand as positive finite half-precision value
+ /// \param quo adress to store quotient at, `nullptr` if \a Q `false`
+ /// \return modulus of \a x / \a y
+ template unsigned int mod(unsigned int x, unsigned int y, int *quo = NULL)
+ {
+ unsigned int q = 0;
+ if(x > y)
+ {
+ int absx = x, absy = y, expx = 0, expy = 0;
+ for(; absx<0x400; absx<<=1,--expx) ;
+ for(; absy<0x400; absy<<=1,--expy) ;
+ expx += absx >> 10;
+ expy += absy >> 10;
+ int mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;
+ for(int d=expx-expy; d; --d)
+ {
+ if(!Q && mx == my)
+ return 0;
+ if(mx >= my)
+ {
+ mx -= my;
+ q += Q;
+ }
+ mx <<= 1;
+ q <<= static_cast(Q);
+ }
+ if(!Q && mx == my)
+ return 0;
+ if(mx >= my)
+ {
+ mx -= my;
+ ++q;
+ }
+ if(Q)
+ {
+ q &= (1<<(std::numeric_limits::digits-1)) - 1;
+ if(!mx)
+ return *quo = q, 0;
+ }
+ for(; mx<0x400; mx<<=1,--expy) ;
+ x = (expy>0) ? ((expy<<10)|(mx&0x3FF)) : (mx>>(1-expy));
+ }
+ if(R)
+ {
+ unsigned int a, b;
+ if(y < 0x800)
+ {
+ a = (x<0x400) ? (x<<1) : (x+0x400);
+ b = y;
+ }
+ else
+ {
+ a = x;
+ b = y - 0x400;
+ }
+ if(a > b || (a == b && (q&1)))
+ {
+ int exp = (y>>10) + (y<=0x3FF), d = exp - (x>>10) - (x<=0x3FF);
+ int m = (((y&0x3FF)|((y>0x3FF)<<10))<<1) - (((x&0x3FF)|((x>0x3FF)<<10))<<(1-d));
+ for(; m<0x800 && exp>1; m<<=1,--exp) ;
+ x = 0x8000 + ((exp-1)<<10) + (m>>1);
+ q += Q;
+ }
+ }
+ if(Q)
+ *quo = q;
+ return x;
+ }
+
+ /// Fixed point square root.
+ /// \tparam F number of fractional bits
+ /// \param r radicand in Q1.F fixed point format
+ /// \param exp exponent
+ /// \return square root as Q1.F/2
+ template uint32 sqrt(uint32 &r, int &exp)
+ {
+ int i = exp & 1;
+ r <<= i;
+ exp = (exp-i) / 2;
+ uint32 m = 0;
+ for(uint32 bit=static_cast(1)<>=2)
+ {
+ if(r < m+bit)
+ m >>= 1;
+ else
+ {
+ r -= m + bit;
+ m = (m>>1) + bit;
+ }
+ }
+ return m;
+ }
+
+ /// Fixed point binary exponential.
+ /// This uses the BKM algorithm in E-mode.
+ /// \param m exponent in [0,1) as Q0.31
+ /// \param n number of iterations (at most 32)
+ /// \return 2 ^ \a m as Q1.31
+ inline uint32 exp2(uint32 m, unsigned int n = 32)
+ {
+ static const uint32 logs[] = {
+ 0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, 0x016FE50B,
+ 0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3, 0x00017153,
+ 0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,
+ 0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };
+ if(!m)
+ return 0x80000000;
+ uint32 mx = 0x80000000, my = 0;
+ for(unsigned int i=1; i> i;
+ }
+ }
+ return mx;
+ }
+
+ /// Fixed point binary logarithm.
+ /// This uses the BKM algorithm in L-mode.
+ /// \param m mantissa in [1,2) as Q1.30
+ /// \param n number of iterations (at most 32)
+ /// \return log2(\a m) as Q0.31
+ inline uint32 log2(uint32 m, unsigned int n = 32)
+ {
+ static const uint32 logs[] = {
+ 0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, 0x016FE50B,
+ 0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3, 0x00017153,
+ 0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,
+ 0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };
+ if(m == 0x40000000)
+ return 0;
+ uint32 mx = 0x40000000, my = 0;
+ for(unsigned int i=1; i>i);
+ if(mz <= m)
+ {
+ mx = mz;
+ my += logs[i];
+ }
+ }
+ return my;
+ }
+
+ /// Fixed point sine and cosine.
+ /// This uses the CORDIC algorithm in rotation mode.
+ /// \param mz angle in [-pi/2,pi/2] as Q1.30
+ /// \param n number of iterations (at most 31)
+ /// \return sine and cosine of \a mz as Q1.30
+ inline std::pair sincos(uint32 mz, unsigned int n = 31)
+ {
+ static const uint32 angles[] = {
+ 0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C, 0x00FFFAAB, 0x007FFF55,
+ 0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, 0x00010000, 0x00008000,
+ 0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, 0x00000200, 0x00000100, 0x00000080,
+ 0x00000040, 0x00000020, 0x00000010, 0x00000008, 0x00000004, 0x00000002, 0x00000001 };
+ uint32 mx = 0x26DD3B6A, my = 0;
+ for(unsigned int i=0; i0x3FF)<<10);
+ int exp = (abs>>10) + (abs<=0x3FF) - 15;
+ if(abs < 0x3A48)
+ return k = 0, m << (exp+20);
+ #if HALF_ENABLE_CPP11_LONG_LONG
+ unsigned long long y = m * 0xA2F9836E4E442, mask = (1ULL<<(62-exp)) - 1, yi = (y+(mask>>1)) & ~mask, f = y - yi;
+ uint32 sign = -static_cast(f>>63);
+ k = static_cast(yi>>(62-exp));
+ return (multiply64(static_cast((sign ? -f : f)>>(31-exp)), 0xC90FDAA2)^sign) - sign;
+ #else
+ uint32 yh = m*0xA2F98 + mulhi(m, 0x36E4E442), yl = (m*0x36E4E442) & 0xFFFFFFFF;
+ uint32 mask = (static_cast(1)<<(30-exp)) - 1, yi = (yh+(mask>>1)) & ~mask, sign = -static_cast(yi>yh);
+ k = static_cast(yi>>(30-exp));
+ uint32 fh = (yh^sign) + (yi^~sign) - ~sign, fl = (yl^sign) - sign;
+ return (multiply64((exp>-1) ? (((fh<<(1+exp))&0xFFFFFFFF)|((fl&0xFFFFFFFF)>>(31-exp))) : fh, 0xC90FDAA2)^sign) - sign;
+ #endif
+ }
+
+ /// Get arguments for atan2 function.
+ /// \param abs half-precision floating-point value
+ /// \return \a abs and sqrt(1 - \a abs^2) as Q0.30
+ inline std::pair atan2_args(unsigned int abs)
+ {
+ int exp = -15;
+ for(; abs<0x400; abs<<=1,--exp) ;
+ exp += abs >> 10;
+ uint32 my = ((abs&0x3FF)|0x400) << 5, r = my * my;
+ int rexp = 2 * exp;
+ r = 0x40000000 - ((rexp>-31) ? ((r>>-rexp)|((r&((static_cast(1)<<-rexp)-1))!=0)) : 1);
+ for(rexp=0; r<0x40000000; r<<=1,--rexp) ;
+ uint32 mx = sqrt<30>(r, rexp);
+ int d = exp - rexp;
+ if(d < 0)
+ return std::make_pair((d<-14) ? ((my>>(-d-14))+((my>>(-d-15))&1)) : (my<<(14+d)), (mx<<14)+(r<<13)/mx);
+ if(d > 0)
+ return std::make_pair(my<<14, (d>14) ? ((mx>>(d-14))+((mx>>(d-15))&1)) : ((d==14) ? mx : ((mx<<(14-d))+(r<<(13-d))/mx)));
+ return std::make_pair(my<<13, (mx<<13)+(r<<12)/mx);
+ }
+
+ /// Get exponentials for hyperbolic computation
+ /// \param abs half-precision floating-point value
+ /// \param exp variable to take unbiased exponent of larger result
+ /// \param n number of BKM iterations (at most 32)
+ /// \return exp(abs) and exp(-\a abs) as Q1.31 with same exponent
+ inline std::pair hyperbolic_args(unsigned int abs, int &exp, unsigned int n = 32)
+ {
+ uint32 mx = detail::multiply64(static_cast((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29), my;
+ int e = (abs>>10) + (abs<=0x3FF);
+ if(e < 14)
+ {
+ exp = 0;
+ mx >>= 14 - e;
+ }
+ else
+ {
+ exp = mx >> (45-e);
+ mx = (mx<<(e-14)) & 0x7FFFFFFF;
+ }
+ mx = exp2(mx, n);
+ int d = exp << 1, s;
+ if(mx > 0x80000000)
+ {
+ my = divide64(0x80000000, mx, s);
+ my |= s;
+ ++d;
+ }
+ else
+ my = mx;
+ return std::make_pair(mx, (d<31) ? ((my>>d)|((my&((static_cast(1)< unsigned int exp2_post(uint32 m, int exp, bool esign, unsigned int sign = 0, unsigned int n = 32)
+ {
+ if(esign)
+ {
+ exp = -exp - (m!=0);
+ if(exp < -25)
+ return underflow(sign);
+ else if(exp == -25)
+ return rounded(sign, 1, m!=0);
+ }
+ else if(exp > 15)
+ return overflow(sign);
+ if(!m)
+ return sign | (((exp+=15)>0) ? (exp<<10) : check_underflow(0x200>>-exp));
+ m = exp2(m, n);
+ int s = 0;
+ if(esign)
+ m = divide64(0x80000000, m, s);
+ return fixed2half(m, exp+14, sign, s);
+ }
+
+ /// Postprocessing for binary logarithm.
+ /// \tparam R rounding mode to use
+ /// \tparam L logarithm for base transformation as Q1.31
+ /// \param m fractional part of logarithm as Q0.31
+ /// \param ilog signed integer part of logarithm
+ /// \param exp biased exponent of result
+ /// \param sign sign bit of result
+ /// \return value base-transformed and converted to half-precision
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if no other exception occurred
+ template unsigned int log2_post(uint32 m, int ilog, int exp, unsigned int sign = 0)
+ {
+ uint32 msign = sign_mask(ilog);
+ m = (((static_cast(ilog)<<27)+(m>>4))^msign) - msign;
+ if(!m)
+ return 0;
+ for(; m<0x80000000; m<<=1,--exp) ;
+ int i = m >= L, s;
+ exp += i;
+ m >>= 1 + i;
+ sign ^= msign & 0x8000;
+ if(exp < -11)
+ return underflow(sign);
+ m = divide64(m, L, s);
+ return fixed2half(m, exp, sign, 1);
+ }
+
+ /// Hypotenuse square root and postprocessing.
+ /// \tparam R rounding mode to use
+ /// \param r mantissa as Q2.30
+ /// \param exp biased exponent
+ /// \return square root converted to half-precision
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if value had to be rounded
+ template unsigned int hypot_post(uint32 r, int exp)
+ {
+ int i = r >> 31;
+ if((exp+=i) > 46)
+ return overflow();
+ if(exp < -34)
+ return underflow();
+ r = (r>>i) | (r&i);
+ uint32 m = sqrt<30>(r, exp+=15);
+ return fixed2half(m, exp-1, 0, r!=0);
+ }
+
+ /// Division and postprocessing for tangents.
+ /// \tparam R rounding mode to use
+ /// \param my dividend as Q1.31
+ /// \param mx divisor as Q1.31
+ /// \param exp biased exponent of result
+ /// \param sign sign bit of result
+ /// \return quotient converted to half-precision
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if no other exception occurred
+ template unsigned int tangent_post(uint32 my, uint32 mx, int exp, unsigned int sign = 0)
+ {
+ int i = my >= mx, s;
+ exp += i;
+ if(exp > 29)
+ return overflow(sign);
+ if(exp < -11)
+ return underflow(sign);
+ uint32 m = divide64(my>>(i+1), mx, s);
+ return fixed2half(m, exp, sign, s);
+ }
+
+ /// Area function and postprocessing.
+ /// This computes the value directly in Q2.30 using the representation `asinh|acosh(x) = log(x+sqrt(x^2+|-1))`.
+ /// \tparam R rounding mode to use
+ /// \tparam S `true` for asinh, `false` for acosh
+ /// \param arg half-precision argument
+ /// \return asinh|acosh(\a arg) converted to half-precision
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if no other exception occurred
+ template unsigned int area(unsigned int arg)
+ {
+ int abs = arg & 0x7FFF, expx = (abs>>10) + (abs<=0x3FF) - 15, expy = -15, ilog, i;
+ uint32 mx = static_cast((abs&0x3FF)|((abs>0x3FF)<<10)) << 20, my, r;
+ for(; abs<0x400; abs<<=1,--expy) ;
+ expy += abs >> 10;
+ r = ((abs&0x3FF)|0x400) << 5;
+ r *= r;
+ i = r >> 31;
+ expy = 2*expy + i;
+ r >>= i;
+ if(S)
+ {
+ if(expy < 0)
+ {
+ r = 0x40000000 + ((expy>-30) ? ((r>>-expy)|((r&((static_cast(1)<<-expy)-1))!=0)) : 1);
+ expy = 0;
+ }
+ else
+ {
+ r += 0x40000000 >> expy;
+ i = r >> 31;
+ r = (r>>i) | (r&i);
+ expy += i;
+ }
+ }
+ else
+ {
+ r -= 0x40000000 >> expy;
+ for(; r<0x40000000; r<<=1,--expy) ;
+ }
+ my = sqrt<30>(r, expy);
+ my = (my<<15) + (r<<14)/my;
+ if(S)
+ {
+ mx >>= expy - expx;
+ ilog = expy;
+ }
+ else
+ {
+ my >>= expx - expy;
+ ilog = expx;
+ }
+ my += mx;
+ i = my >> 31;
+ static const int G = S && (R==std::round_to_nearest);
+ return log2_post(log2(my>>i, 26+S+G)+(G<<3), ilog+i, 17, arg&(static_cast(S)<<15));
+ }
+
+ /// Class for 1.31 unsigned floating-point computation
+ struct f31
+ {
+ /// Constructor.
+ /// \param mant mantissa as 1.31
+ /// \param e exponent
+ HALF_CONSTEXPR f31(uint32 mant, int e) : m(mant), exp(e) {}
+
+ /// Constructor.
+ /// \param abs unsigned half-precision value
+ f31(unsigned int abs) : exp(-15)
+ {
+ for(; abs<0x400; abs<<=1,--exp) ;
+ m = static_cast((abs&0x3FF)|0x400) << 21;
+ exp += (abs>>10);
+ }
+
+ /// Addition operator.
+ /// \param a first operand
+ /// \param b second operand
+ /// \return \a a + \a b
+ friend f31 operator+(f31 a, f31 b)
+ {
+ if(b.exp > a.exp)
+ std::swap(a, b);
+ int d = a.exp - b.exp;
+ uint32 m = a.m + ((d<32) ? (b.m>>d) : 0);
+ int i = (m&0xFFFFFFFF) < a.m;
+ return f31(((m+i)>>i)|0x80000000, a.exp+i);
+ }
+
+ /// Subtraction operator.
+ /// \param a first operand
+ /// \param b second operand
+ /// \return \a a - \a b
+ friend f31 operator-(f31 a, f31 b)
+ {
+ int d = a.exp - b.exp, exp = a.exp;
+ uint32 m = a.m - ((d<32) ? (b.m>>d) : 0);
+ if(!m)
+ return f31(0, -32);
+ for(; m<0x80000000; m<<=1,--exp) ;
+ return f31(m, exp);
+ }
+
+ /// Multiplication operator.
+ /// \param a first operand
+ /// \param b second operand
+ /// \return \a a * \a b
+ friend f31 operator*(f31 a, f31 b)
+ {
+ uint32 m = multiply64(a.m, b.m);
+ int i = m >> 31;
+ return f31(m<<(1-i), a.exp + b.exp + i);
+ }
+
+ /// Division operator.
+ /// \param a first operand
+ /// \param b second operand
+ /// \return \a a / \a b
+ friend f31 operator/(f31 a, f31 b)
+ {
+ int i = a.m >= b.m, s;
+ uint32 m = divide64((a.m+i)>>i, b.m, s);
+ return f31(m, a.exp - b.exp + i - 1);
+ }
+
+ uint32 m; ///< mantissa as 1.31.
+ int exp; ///< exponent.
+ };
+
+ /// Error function and postprocessing.
+ /// This computes the value directly in Q1.31 using the approximations given
+ /// [here](https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions).
+ /// \tparam R rounding mode to use
+ /// \tparam C `true` for comlementary error function, `false` else
+ /// \param arg half-precision function argument
+ /// \return approximated value of error function in half-precision
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if no other exception occurred
+ template unsigned int erf(unsigned int arg)
+ {
+ unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;
+ f31 x(abs), x2 = x * x * f31(0xB8AA3B29, 0), t = f31(0x80000000, 0) / (f31(0x80000000, 0)+f31(0xA7BA054A, -2)*x), t2 = t * t;
+ f31 e = ((f31(0x87DC2213, 0)*t2+f31(0xB5F0E2AE, 0))*t2+f31(0x82790637, -2)-(f31(0xBA00E2B8, 0)*t2+f31(0x91A98E62, -2))*t) * t /
+ ((x2.exp<0) ? f31(exp2((x2.exp>-32) ? (x2.m>>-x2.exp) : 0, 30), 0) : f31(exp2((x2.m<>(31-x2.exp)));
+ return (!C || sign) ? fixed2half(0x80000000-(e.m>>(C-e.exp)), 14+C, sign&(C-1U)) :
+ (e.exp<-25) ? underflow() : fixed2half(e.m>>1, e.exp+14, 0, e.m&1);
+ }
+
+ /// Gamma function and postprocessing.
+ /// This approximates the value of either the gamma function or its logarithm directly in Q1.31.
+ /// \tparam R rounding mode to use
+ /// \tparam L `true` for lograithm of gamma function, `false` for gamma function
+ /// \param arg half-precision floating-point value
+ /// \return lgamma/tgamma(\a arg) in half-precision
+ /// \exception FE_OVERFLOW on overflows
+ /// \exception FE_UNDERFLOW on underflows
+ /// \exception FE_INEXACT if \a arg is not a positive integer
+ template unsigned int gamma(unsigned int arg)
+ {
+/* static const double p[] ={ 2.50662827563479526904, 225.525584619175212544, -268.295973841304927459, 80.9030806934622512966, -5.00757863970517583837, 0.0114684895434781459556 };
+ double t = arg + 4.65, s = p[0];
+ for(unsigned int i=0; i<5; ++i)
+ s += p[i+1] / (arg+i);
+ return std::log(s) + (arg-0.5)*std::log(t) - t;
+*/ static const f31 pi(0xC90FDAA2, 1), lbe(0xB8AA3B29, 0);
+ unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;
+ bool bsign = sign != 0;
+ f31 z(abs), x = sign ? (z+f31(0x80000000, 0)) : z, t = x + f31(0x94CCCCCD, 2), s =
+ f31(0xA06C9901, 1) + f31(0xBBE654E2, -7)/(x+f31(0x80000000, 2)) + f31(0xA1CE6098, 6)/(x+f31(0x80000000, 1))
+ + f31(0xE1868CB7, 7)/x - f31(0x8625E279, 8)/(x+f31(0x80000000, 0)) - f31(0xA03E158F, 2)/(x+f31(0xC0000000, 1));
+ int i = (s.exp>=2) + (s.exp>=4) + (s.exp>=8) + (s.exp>=16);
+ s = f31((static_cast(s.exp)<<(31-i))+(log2(s.m>>1, 28)>>i), i) / lbe;
+ if(x.exp != -1 || x.m != 0x80000000)
+ {
+ i = (t.exp>=2) + (t.exp>=4) + (t.exp>=8);
+ f31 l = f31((static_cast(t.exp)<<(31-i))+(log2(t.m>>1, 30)>>i), i) / lbe;
+ s = (x.exp<-1) ? (s-(f31(0x80000000, -1)-x)*l) : (s+(x-f31(0x80000000, -1))*l);
+ }
+ s = x.exp ? (s-t) : (t-s);
+ if(bsign)
+ {
+ if(z.exp >= 0)
+ {
+ sign &= (L|((z.m>>(31-z.exp))&1)) - 1;
+ for(z=f31((z.m<<(1+z.exp))&0xFFFFFFFF, -1); z.m<0x80000000; z.m<<=1,--z.exp) ;
+ }
+ if(z.exp == -1)
+ z = f31(0x80000000, 0) - z;
+ if(z.exp < -1)
+ {
+ z = z * pi;
+ z.m = sincos(z.m>>(1-z.exp), 30).first;
+ for(z.exp=1; z.m<0x80000000; z.m<<=1,--z.exp) ;
+ }
+ else
+ z = f31(0x80000000, 0);
+ }
+ if(L)
+ {
+ if(bsign)
+ {
+ f31 l(0x92868247, 0);
+ if(z.exp < 0)
+ {
+ uint32 m = log2((z.m+1)>>1, 27);
+ z = f31(-((static_cast(z.exp)<<26)+(m>>5)), 5);
+ for(; z.m<0x80000000; z.m<<=1,--z.exp) ;
+ l = l + z / lbe;
+ }
+ sign = static_cast(x.exp&&(l.exp(x.exp==0) << 15;
+ if(s.exp < -24)
+ return underflow(sign);
+ if(s.exp > 15)
+ return overflow(sign);
+ }
+ }
+ else
+ {
+ s = s * lbe;
+ uint32 m;
+ if(s.exp < 0)
+ {
+ m = s.m >> -s.exp;
+ s.exp = 0;
+ }
+ else
+ {
+ m = (s.m<>(31-s.exp));
+ }
+ s.m = exp2(m, 27);
+ if(!x.exp)
+ s = f31(0x80000000, 0) / s;
+ if(bsign)
+ {
+ if(z.exp < 0)
+ s = s * z;
+ s = pi / s;
+ if(s.exp < -24)
+ return underflow(sign);
+ }
+ else if(z.exp > 0 && !(z.m&((1<<(31-z.exp))-1)))
+ return ((s.exp+14)<<10) + (s.m>>21);
+ if(s.exp > 15)
+ return overflow(sign);
+ }
+ return fixed2half(s.m, s.exp+14, sign);
+ }
+ /// \}
+
+ template struct half_caster;
+ }
+
+ /// Half-precision floating-point type.
+ /// This class implements an IEEE-conformant half-precision floating-point type with the usual arithmetic
+ /// operators and conversions. It is implicitly convertible to single-precision floating-point, which makes artihmetic
+ /// expressions and functions with mixed-type operands to be of the most precise operand type.
+ ///
+ /// According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and
+ /// extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which
+ /// means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the
+ /// actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be of
+ /// exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will most
+ /// probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying 16-bit
+ /// IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16 bits if
+ /// your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the case on
+ /// nearly any reasonable platform.
+ ///
+ /// So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable
+ /// assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation.
+ class half
+ {
+ public:
+ /// \name Construction and assignment
+ /// \{
+
+ /// Default constructor.
+ /// This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics
+ /// and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics.
+ HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {}
+
+ /// Conversion constructor.
+ /// \param rhs float to convert
+ /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+ explicit half(float rhs) : data_(static_cast(detail::float2half(rhs))) {}
+
+ /// Conversion to single-precision.
+ /// \return single precision value representing expression value
+ operator float() const { return detail::half2float(data_); }
+
+ /// Assignment operator.
+ /// \param rhs single-precision value to copy from
+ /// \return reference to this half
+ /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+ half& operator=(float rhs) { data_ = static_cast(detail::float2half(rhs)); return *this; }
+
+ /// \}
+ /// \name Arithmetic updates
+ /// \{
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to add
+ /// \return reference to this half
+ /// \exception FE_... according to operator+(half,half)
+ half& operator+=(half rhs) { return *this = *this + rhs; }
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to subtract
+ /// \return reference to this half
+ /// \exception FE_... according to operator-(half,half)
+ half& operator-=(half rhs) { return *this = *this - rhs; }
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to multiply with
+ /// \return reference to this half
+ /// \exception FE_... according to operator*(half,half)
+ half& operator*=(half rhs) { return *this = *this * rhs; }
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to divide by
+ /// \return reference to this half
+ /// \exception FE_... according to operator/(half,half)
+ half& operator/=(half rhs) { return *this = *this / rhs; }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to add
+ /// \return reference to this half
+ /// \exception FE_... according to operator=()
+ half& operator+=(float rhs) { return *this = *this + rhs; }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to subtract
+ /// \return reference to this half
+ /// \exception FE_... according to operator=()
+ half& operator-=(float rhs) { return *this = *this - rhs; }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to multiply with
+ /// \return reference to this half
+ /// \exception FE_... according to operator=()
+ half& operator*=(float rhs) { return *this = *this * rhs; }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to divide by
+ /// \return reference to this half
+ /// \exception FE_... according to operator=()
+ half& operator/=(float rhs) { return *this = *this / rhs; }
+
+ /// \}
+ /// \name Increment and decrement
+ /// \{
+
+ /// Prefix increment.
+ /// \return incremented half value
+ /// \exception FE_... according to operator+(half,half)
+ half& operator++() { return *this = *this + half(detail::binary, 0x3C00); }
+
+ /// Prefix decrement.
+ /// \return decremented half value
+ /// \exception FE_... according to operator-(half,half)
+ half& operator--() { return *this = *this + half(detail::binary, 0xBC00); }
+
+ /// Postfix increment.
+ /// \return non-incremented half value
+ /// \exception FE_... according to operator+(half,half)
+ half operator++(int) { half out(*this); ++*this; return out; }
+
+ /// Postfix decrement.
+ /// \return non-decremented half value
+ /// \exception FE_... according to operator-(half,half)
+ half operator--(int) { half out(*this); --*this; return out; }
+ /// \}
+
+ private:
+ /// Rounding mode to use
+ static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);
+
+ /// Constructor.
+ /// \param bits binary representation to set half to
+ HALF_CONSTEXPR half(detail::binary_t, unsigned int bits) HALF_NOEXCEPT : data_(static_cast(bits)) {}
+
+ /// Internal binary representation
+ detail::uint16 data_;
+
+ #ifndef HALF_DOXYGEN_ONLY
+ friend HALF_CONSTEXPR_NOERR bool operator==(half, half);
+ friend HALF_CONSTEXPR_NOERR bool operator!=(half, half);
+ friend HALF_CONSTEXPR_NOERR bool operator<(half, half);
+ friend HALF_CONSTEXPR_NOERR bool operator>(half, half);
+ friend HALF_CONSTEXPR_NOERR bool operator<=(half, half);
+ friend HALF_CONSTEXPR_NOERR bool operator>=(half, half);
+ friend HALF_CONSTEXPR half operator-(half);
+ friend half operator+(half, half);
+ friend half operator-(half, half);
+ friend half operator*(half, half);
+ friend half operator/(half, half);
+ template friend std::basic_ostream& operator<<(std::basic_ostream&, half);
+ template friend std::basic_istream& operator>>(std::basic_istream&, half&);
+ friend HALF_CONSTEXPR half fabs(half);
+ friend half fmod(half, half);
+ friend half remainder(half, half);
+ friend half remquo(half, half, int*);
+ friend half fma(half, half, half);
+ friend HALF_CONSTEXPR_NOERR half fmax(half, half);
+ friend HALF_CONSTEXPR_NOERR half fmin(half, half);
+ friend half fdim(half, half);
+ friend half nanh(const char*);
+ friend half exp(half);
+ friend half exp2(half);
+ friend half expm1(half);
+ friend half log(half);
+ friend half log10(half);
+ friend half log2(half);
+ friend half log1p(half);
+ friend half sqrt(half);
+ friend half rsqrt(half);
+ friend half cbrt(half);
+ friend half hypot(half, half);
+ friend half hypot(half, half, half);
+ friend half pow(half, half);
+ friend void sincos(half, half*, half*);
+ friend half sin(half);
+ friend half cos(half);
+ friend half tan(half);
+ friend half asin(half);
+ friend half acos(half);
+ friend half atan(half);
+ friend half atan2(half, half);
+ friend half sinh(half);
+ friend half cosh(half);
+ friend half tanh(half);
+ friend half asinh(half);
+ friend half acosh(half);
+ friend half atanh(half);
+ friend half erf(half);
+ friend half erfc(half);
+ friend half lgamma(half);
+ friend half tgamma(half);
+ friend half ceil(half);
+ friend half floor(half);
+ friend half trunc(half);
+ friend half round(half);
+ friend long lround(half);
+ friend half rint(half);
+ friend long lrint(half);
+ friend half nearbyint(half);
+ #ifdef HALF_ENABLE_CPP11_LONG_LONG
+ friend long long llround(half);
+ friend long long llrint(half);
+ #endif
+ friend half frexp(half, int*);
+ friend half scalbln(half, long);
+ friend half modf(half, half*);
+ friend int ilogb(half);
+ friend half logb(half);
+ friend half nextafter(half, half);
+ friend half nexttoward(half, long double);
+ friend HALF_CONSTEXPR half copysign(half, half);
+ friend HALF_CONSTEXPR int fpclassify(half);
+ friend HALF_CONSTEXPR bool isfinite(half);
+ friend HALF_CONSTEXPR bool isinf(half);
+ friend HALF_CONSTEXPR bool isnan(half);
+ friend HALF_CONSTEXPR bool isnormal(half);
+ friend HALF_CONSTEXPR bool signbit(half);
+ friend HALF_CONSTEXPR bool isgreater(half, half);
+ friend HALF_CONSTEXPR bool isgreaterequal(half, half);
+ friend HALF_CONSTEXPR bool isless(half, half);
+ friend HALF_CONSTEXPR bool islessequal(half, half);
+ friend HALF_CONSTEXPR bool islessgreater(half, half);
+ template friend struct detail::half_caster;
+ friend class std::numeric_limits;
+ #if HALF_ENABLE_CPP11_HASH
+ friend struct std::hash |