diff --git a/mnn_demo/CMakeLists.txt b/mnn_demo/CMakeLists.txt new file mode 100644 index 0000000..0faf584 --- /dev/null +++ b/mnn_demo/CMakeLists.txt @@ -0,0 +1,70 @@ +cmake_minimum_required(VERSION 3.0) +project(mnn_demo) + +set(CMAKE_CXX_STANDARD 14) + +set(MNN_DIR /opt/soft/MNN) +set(FFMPEG_DIR /opt/soft/ffmpeg/ffmpeg) +set(LIBRARY_OUTPUT_PATH ${PROJECT_SOURCE_DIR}/lib) +IF (WIN32) + MESSAGE(STATUS "Now is windows") + set(MNN_DIR D:/soft/mnn/MNN) + set(FFMPEG_DIR D:/soft/ffmpeg/linux_ffmpeg) +ENDIF () + +# MNN +include_directories(${MNN_DIR}/include) +include_directories(${MNN_DIR}/include/MNN) + +# ffmpeg +include_directories(${FFMPEG_DIR}/include) + +# 项目头文件 +include_directories(inc src) +include_directories(ref) +include_directories(ref/av_waves/waves/inc) +include_directories(ref/av_resample/audio_resample/inc) +include_directories(ref/thread) +include_directories(third_party) + +# 第三方依赖 +add_subdirectory(ref) + +# 源数据 +FILE(GLOB SRC_DIR ${PROJECT_SOURCE_DIR}/src/*cpp) +FILE(GLOB THIRD_SRC_DIR ${PROJECT_SOURCE_DIR}/third_party/espyin-v1.0/*cpp) + +#add_library(svc_lite ${SRC_DIR}) +add_executable(mnn_demo main.cpp ${SRC_DIR} ${THIRD_SRC_DIR} + tests/test_flatbuffer.cpp) + + +#add_executable(test_circle_buffer tests/test_CRvcCircleBuffer.cpp src/CRvcCircleBuffer.cpp) +target_link_libraries(mnn_demo + /opt/soft/MNN/build/libMNN.a + ${LIBRARY_OUTPUT_PATH}/libwaves.a + ${LIBRARY_OUTPUT_PATH}/libthread.a + ${LIBRARY_OUTPUT_PATH}/libaudio_resample.a +) + +target_link_libraries(mnn_demo + ${FFMPEG_DIR}/lib/libavfilter.a + ${FFMPEG_DIR}/lib/libavformat.a + ${FFMPEG_DIR}/lib/libavcodec.a + ${FFMPEG_DIR}/lib/libswresample.a + ${FFMPEG_DIR}/lib/libswscale.a + ${FFMPEG_DIR}/lib/libavutil.a +) + + +# 测试代码 +#include_directories(${MNN_DIR}/tools) +#include_directories(${MNN_DIR}/3rd_party/flatbuffers/include) +# +#add_executable(test_flat_buffer tests/test_flatbuffer.cpp ${FLAT_SRC_DIR} +# ${MNN_DIR}/3rd_party/flatbuffers/src/code_generators.cpp +# ${MNN_DIR}/3rd_party/flatbuffers/src/idl_gen_text.cpp +# ${MNN_DIR}/3rd_party/flatbuffers/src/idl_parser.cpp +# ${MNN_DIR}/3rd_party/flatbuffers/src/util.cpp +# tests/half.hpp +#) \ No newline at end of file diff --git a/mnn_demo/build_android.sh b/mnn_demo/build_android.sh new file mode 100644 index 0000000..32ca240 --- /dev/null +++ b/mnn_demo/build_android.sh @@ -0,0 +1,64 @@ +#!/bin/sh + +# @Time : 2019-06-18 17:50 +# @Author : AlanWang +# @FileName: build_android.sh + +# MY_NDK 和 MY_CMAKE 需要改成自己对应的 ndk 中的目录 +MY_NDK="/mnt/d/soft/linux/android-ndk-r22b-linux-x86_64/android-ndk-r22b" +MY_CMAKE="/mnt/d/soft/linux/android_sdk/cmake/3.22.1/bin/cmake" + +if [ -z "$MY_NDK" ]; then + echo "Please set MY_NDK to the Android NDK folder" + exit 1 +fi + +if [ -z "$MY_CMAKE" ]; then + echo "Please set MY_CMAKE to the Android CMake folder" + exit 1 +fi + +OUTPUT_LIBS="./build/libs/android" +ANDROID_NATIVE_API_LEVEL="android-16" + +# arme_abis=(armeabi armeabi-v7a arm64-v8a x86 x86_64 mips mips64) +arme_abis=(armeabi-v7a arm64-v8a) + +function build_with_armeabi() { + ARME_ABI=$1 + echo ${ARME_ABI} + + BUILD_DIR="./build/android/${ARME_ABI}" + BUILD_REF_DIR="./build/android/${ARME_ABI}/ref" + OUTPUT_SO_DIR="${BUILD_DIR}/build/android/libs/${ARME_ABI}" + + PRE_EXE_DIR=$(pwd) + echo ${PRE_EXE_DIR} + + ${MY_CMAKE} \ + -H"./" \ + -B"${BUILD_DIR}" \ + -DANDROID_ABI="${ARME_ABI}" \ + -DANDROID_NDK="${MY_NDK}" \ + -DCMAKE_LIBRARY_OUTPUT_DIRECTORY="./build/android/libs/${ARME_ABI}" \ + -DCMAKE_BUILD_TYPE="Release" \ + -DCMAKE_TOOLCHAIN_FILE="${MY_NDK}/build/cmake/android.toolchain.cmake" \ + -DANDROID_NATIVE_API_LEVEL=${ANDROID_NATIVE_API_LEVEL} \ + -DANDROID_TOOLCHAIN="clang" \ + -DCMAKE_C_FLAGS="-fpic -fexceptions -frtti -Wno-narrowing" \ + -DCMAKE_CXX_FLAGS="-fpic -fexceptions -frtti -Wno-narrowing" \ + -DANDROID_STL="c++_static" \ + + + cd ${BUILD_DIR} + make + + cd ${PRE_EXE_DIR} + mkdir -p ${OUTPUT_LIBS}/${ARME_ABI}/ + mv ${PRE_EXE_DIR}/lib/* ${OUTPUT_LIBS}/${ARME_ABI}/ + rm -r ./build/android +} + +for i in ${arme_abis[@]}; do + build_with_armeabi $i +done diff --git a/mnn_demo/inc/CRvcLiteOnline.h b/mnn_demo/inc/CRvcLiteOnline.h new file mode 100644 index 0000000..f1c7677 --- /dev/null +++ b/mnn_demo/inc/CRvcLiteOnline.h @@ -0,0 +1,296 @@ +// +// Created by jianli.yang on 2023/11/29. +// + +#ifndef MNN_DEMO_CRVCLITEONLINE_H +#define MNN_DEMO_CRVCLITEONLINE_H + + +#define DEBUG + +#ifdef __ANDROID__ +#include + +#ifdef STRELEASE +#define LOGD(...) +#define LOGE(...) +#else +#define LOGD(TAG, ...) __android_log_print(ANDROID_LOG_DEBUG , TAG, __VA_ARGS__) +#define LOGE(TAG, ...) __android_log_print(ANDROID_LOG_ERROR , TAG, __VA_ARGS__) +#endif + +#else +#ifdef DEBUG +#define LOGD(TAG, ...) printf("\nDebug: %s",TAG);printf(__VA_ARGS__); +#define LOGE(TAG, ...) printf("\nError: %s",TAG);printf(__VA_ARGS__); +#else +#define LOGD(TAG, ...) +#define LOGE(TAG, ...) +#endif + +#endif + + +#include +#include +#include +#include +#include + +#define gs_src_samplerate 16000 +#define gs_dst_samplerate 32000 +#define gs_crossfade_time 0.08 // 单位是s +#define gs_block_time 1 +#define gs_extra_time 1 +#define gs_hubert_frame 206 // 和模型相关 +#define gs_hubert_dim 256 // 和模型相关 +#define gs_synth_input_frame 205 // 和模型相关 +#define gs_synth_input_dim 258 // 和模型相关 +#define gs_synth_output_frame 35840 // 和模型相关 + +enum { + ERR_RVC_LITE_SUCCESS = 0, + ERR_RVC_LITE_NOT_INIT = 1, + ERR_RVC_LITE_REINIT = 2, + ERR_RVC_LITE_RT_REINIT = 3, + ERR_RVC_LITE_RT_NOT_INIT = 4, + ERR_RVC_LITE_RT_NOT_ENOUGH_DATA = 5, + ERR_RVC_LITE_RT_INPUT_SAMPLE_ERR = 6, // 采样率小于16000 + ERR_RVC_LITE_RT_RESAMPLE_OUTBUF_SHORT = 7, // 重采样后的buf太短 +}; + + +class Hubert; + +class CSynthesizer; + +class ESPYIN; + +class CThreadPool; + +class CRvcCircleBuffer; + +class CFfmpegResampler; + +/** + * Rvc轻量化实时推理代码 + * 要求输入16k的音频数据，输出是目标采样率的数据 + */ +class CRvcLiteOnline { + +public: + CRvcLiteOnline(); + + ~CRvcLiteOnline(); + +private: + void uninit(); + + void get_f0_post(); + + void get_pyin_f0(); + + void init_variable(); + +public: + /** + * 初始化函数 + * @param hubert_model_path + * @param synth_model_path + * @return 0 表示正常 + */ + int init(const char *hubert_model_path, const char *synth_model_path); + + /** + * 换音色模型 + * @param synth_model_path + * @return + */ + int switch_synth_model(const char* synth_model_path); + + /** + * 处理定长的一帧数据 + * 要求输入单声道16k音频 + * @param in_buf + * @param in_len 长度小于等于gs_src_samplerate,最佳是gs_src_samplerate + * @param out_buf + * @param out_len 小于等于gs_dst_samplerate,最佳是gs_dst_samplerate[和输入有关,如果是32k，则恰好是输入的两倍] + * @return 0 表示正常 + */ + int process_block(float *in_buf, int in_len, float *out_buf, int out_len); + + /** + * 清空存储 + * @return + */ + void reset(); + + + /** + * 获取延迟时间 + * @return + */ + int get_latency_ms(); + + +private: + // 是否进行过init + bool m_init; + std::shared_ptr m_hubert_inst; + std::shared_ptr m_synthesizer_inst; + std::shared_ptr m_es_pyin; + + // 缓存使用的数据 + // 要求输入的时间片长度,采样点数 + int m_input_block_frame; + // 推理时额外需要的长度 + int m_input_extra_frame; + // 推理时使用的buffer长度 + int m_input_predict_buf_frame; + // 推理时使用的buffer + float *m_input_predict_buf; + + std::vector m_f0_data; + std::vector m_f0_coarse_data; + // 输出的情况 + int m_crossfade_frame; + int m_output_block_frame; + int m_output_cache_buf_frame; + float *m_crossfade_buf; + float *m_output_cache_buf; + + // 各个实例的返回结果 + std::vector>> m_hubert_ret; + std::vector>> m_synth_input; + std::vector>> m_synth_out; +}; + +class CResample { +public: + CResample(); + ~CResample(); +public: + int init(int in_samplerate, int out_samplerate, int in_channel=1, int out_channel=1); + // 返回的是单通道的采样点数 + int get_out_samples(int num); + int get_latency(); + void reset(); + // 不考虑让内部缓存的情况，有多少拿多少,in_num和out_num均是单通道采样点个数 + int resample(float * in_buf, int in_num, float * out_buf, int & out_num); + +private: + std::shared_ptr m_resample_inst; + int m_in_channel; + int m_out_channel; +}; + +/** + * 实时处理的类 + * 入一帧出一帧，允许非常短的帧做输入，延迟较高，在2s左右 + * 思路: + * 1. 构造函数设置变量 + * 2. init初始化环境，开启处理线程 + * 3. process，每次送一帧，触发一次判断逻辑 + * 4. flush函数将输入的未处理的数据全部处理一次，联合之前没有被取出的数据一起刷出来 + * 5. 析构时关闭处理线程，并释放所有空间 + */ +class CRvcLiteOnlineRealTime { +public: + CRvcLiteOnlineRealTime(); + + ~CRvcLiteOnlineRealTime(); + +private: + void init_variable(); + + void rvc_process(); + + void rvc_process_step(); + + void uninit(); + + void stop(); + +public: + + /** + * 初始化函数 + * @param hubert_model_path + * @param synth_model_path + * @param sample_rate + * @param channel + * @return + */ + int init(const char *hubert_model_path, const char *synth_model_path, int sample_rate, int channel); + + /** + * 切换音色 + * @param synth_model_path + * @return + */ + int switch_synth(const char *synth_model_path); + + /** + * 清空缓存 + */ + void reset(); + + /** + * 入一帧，出一帧，要求长度一致 + * 两者可以是同一块buffer + * @param in_buf + * @param in_len + * @param out_buf + * @param out_len + * @return + */ + int process(float *in_buf, int in_len, float *out_buf, int out_len); + + /** + * 将所有处理好的结果获取出来 + * 因为不确定还有多少，所以由内部来开辟空间,外部进行释放 + * @return + */ + void flush(float *&out_buf, int &len); + + /** + * 获取延迟时间 + */ + int get_latency_ms(); + +private: + int m_sample_rate; + int m_channel; + + std::shared_ptr m_resample_queue; + std::shared_ptr m_input_queue; + std::shared_ptr m_out_queue; + int m_input_tmp_buf_len; + int m_output_tmp_buf_len; + std::shared_ptr m_input_tmp_buf; + std::shared_ptr m_output_tmp_buf; + + std::shared_ptr m_rvc_inst; + std::shared_ptr m_thread_pool; + + // 逻辑变量 + bool m_init; + // 处理线程相关 + bool m_rvc_stop; + std::mutex m_rvc_mutex; + std::condition_variable m_rvc_cond; + + // 重采样相关 + std::shared_ptr m_resample16; + std::shared_ptr m_resample2src; + + int m_resample_buf_max_len; + std::shared_ptr m_resample_in_buf; + std::shared_ptr m_resample_out_buf; + + // 切换音色 + std::string m_synth_path; + std::string m_new_synth_path; +}; + +#endif //MNN_DEMO_CRVCLITEONLINE_H diff --git a/mnn_demo/main.cpp b/mnn_demo/main.cpp new file mode 100644 index 0000000..7b4f6dc --- /dev/null +++ b/mnn_demo/main.cpp @@ -0,0 +1,171 @@ +#include +#include +#include +#include "src/Hubert.h" +#include "src/CSynthesizer.h" + +int test_hubert() { + const char *hubert_model_path = "/mnt/d/dataset/svc/models/mnn/hubert_test_v1_fp16.mnn"; + Hubert hubert; + int err_code = hubert.init(hubert_model_path); + std::vector input(33280, 0.1); + std::vector>> ret; + ret.resize(1); + ret[0].resize(205); + for (int i = 0; i < 205; i++) { + ret[0][i].resize(256); + } + float time = hubert.process(input.data(), ret); + return 0; +} + +int test_contentvec() { + const char *contentvec_model_path = "/mnt/d/dataset/svc/models/mnn/contentvec_test_fp16.mnn"; + CSynthesizer contentVec; + int err_code = contentVec.init(contentvec_model_path); + std::vector>> input(1); + input[0].resize(205); + for (int i = 0; i < 205; i++) { + for (int j = 0; j < 258; j++) { + if (j == 256) { + input[0][i].push_back(0.2); + } else if (j == 257) { + input[0][i].push_back(1.0); + } else { + input[0][i].push_back(0.1); + } + } + } + + std::vector>> ret; + ret.resize(1); + for (int i = 0; i < 1; i++) { + ret[i].resize(1); + ret[i][0].resize(35840); + } + + float tot = 0.f; + for (int i = 0; i < 10; i++) { + float time = contentVec.process(input, ret); + tot += time; + } + printf("time: %f \n", tot / 100.f); + return 0; +} + +#include "CRvcLiteOnline.h" +#include "av_waves/waves/inc/STWaveFile.h" + +void test() { + const char *hubert_model_path = "/mnt/d/dataset/svc/models/mnn/hubert_test_v2_fp16.mnn"; + const char *contentvec_model_path = "/mnt/d/dataset/svc/models/mnn/contentvec_test_fp16.mnn"; + const char *in_wav = "/mnt/d/dataset/svc/dataset/tests/rainy_day321_01_16.wav"; +// const char *in_wav = "/mnt/d/code/develop/svc/Retrieval-based-Voice-Conversion-WebUI/online/1_1.wav"; + const char *out_wav = "/mnt/d/dataset/svc/dataset/tests/rainy_day321_01_cpp_v1.wav"; + + CRvcLiteOnline rvc_inst; + rvc_inst.init(hubert_model_path, contentvec_model_path); + + // 读取音频文件, 要求16k,单声道 + STCWaveFile wav_inst(in_wav, false); + int sample_rate = wav_inst.GetSampleRate(); + int channel = wav_inst.GetChannels(); + int len = wav_inst.GetTotalFrames() * channel; + float *data = new float[len]; + float *outdata = new float[len * 2]; + wav_inst.ReadFrameAsfloat(data, wav_inst.GetTotalFrames()); + int step = sample_rate; + printf("start ..\n"); + for (int i = 0; i < len; i += step) { + if (i + step > len) { + step = len - i; + } + struct timeval start; + struct timeval end; + gettimeofday(&start, NULL); + rvc_inst.process_block(data + i, step, outdata + 2 * i, 2 * step); + gettimeofday(&end, NULL); + printf("sp = %f ms\n", (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0); + } + STCWaveFile wav_out_inst(out_wav, true); + wav_out_inst.SetSampleRate(32000); + wav_out_inst.SetChannels(1); + wav_out_inst.SetSampleFormat(SF_IEEE_FLOAT); + wav_out_inst.SetupDone(); + wav_out_inst.WriteFrame(outdata, len * 2); + printf("finish2 ....\n"); +} + + +void test_rvc_lite_online() { +// const char *hubert_model_path = "/mnt/d/dataset/svc/models/mnn/hubert_test_v2_fp16.mnn"; +// const char *hubert_model_path = "/mnt/d/dataset/svc/models/layer6_bingxiao_v1/mnn/layers6_checkpoint_14_1660000_1_hubert.mnn"; + const char *hubert_model_path = "/mnt/d/dataset/svc/models/layers_3/layer3_contentvec.mnn"; +// const char *contentvec_model_path = "/mnt/d/dataset/svc/models/mnn/contentvec_test_fp16.mnn"; +// const char *syz_model = "/mnt/d/dataset/svc/models/layer6_bingxiao_v1/mnn/xusong_v1_6hubert_hifix_syz_base_vctk_kd_32k_hubert6_jianli_e225_s62775_205.mnn"; + const char *syz_model = "/mnt/d/dataset/svc/models/layers_3/layer3_xusong.mnn"; +// const char *contentvec_model_path = "/mnt/d/dataset/svc/models/layer6_bingxiao_v1/mnn/xiafan_fp16.mnn"; + + const char *in_wav = "/mnt/d/dataset/svc/dataset/tests/rainy_day321_01.wav"; +// const char* in_wav = "/mnt/d/dataset/svc/dataset/短数据样本/男声/qiankun.wav"; +// const char* in_wav = "/mnt/d/dataset/tmp/i.wav"; +// const char *in_wav = "/mnt/d/code/develop/svc/Retrieval-based-Voice-Conversion-WebUI/online/1_1.wav"; +// const char *out_wav = "/mnt/d/dataset/svc/dataset/tests/rainy_day321_01_cpp_v4.wav"; +// const char *out_wav = "/mnt/d/dataset/svc/dataset/tests/qiankun_412_v4.wav"; + const char *out_wav = "/mnt/d/dataset/tmp/i_out2.wav"; + + // 读取音频文件, 要求16k,单声道 + STCWaveFile wav_inst(in_wav, false); + int sample_rate = wav_inst.GetSampleRate(); + int channel = wav_inst.GetChannels(); + int len = wav_inst.GetTotalFrames() * channel; + float *data = new float[len]; + float *outdata = new float[len]; + + CRvcLiteOnlineRealTime rvc_inst; + rvc_inst.init(hubert_model_path, syz_model, sample_rate, channel); + + wav_inst.ReadFrameAsfloat(data, wav_inst.GetTotalFrames()); + int step = 1024; + printf("start ..\n"); + bool flag = true; + for (int i = 0; i < len; i += step) { + if (i + step > len) { + step = len - i; + } + struct timeval start; + struct timeval end; + gettimeofday(&start, NULL); + int ret = rvc_inst.process(data + i, step, outdata+i, step); + std::this_thread::sleep_for(std::chrono::milliseconds (15)); + gettimeofday(&end, NULL); + printf("ret = %d, sp = %f ms step=%d\n", ret, + (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0, step); + + if (flag && i >= len / 3) { + flag = false; + rvc_inst.switch_synth(syz_model); + } + } + STCWaveFile wav_out_inst(out_wav, true); + wav_out_inst.SetSampleRate(sample_rate); + wav_out_inst.SetChannels(channel); + wav_out_inst.SetSampleFormat(SF_IEEE_FLOAT); + wav_out_inst.SetupDone(); + wav_out_inst.WriteFrame(outdata, wav_inst.GetTotalFrames()); + + float* flush_data; + int flush_len; + rvc_inst.flush(flush_data, flush_len); + wav_out_inst.WriteFrame(flush_data, flush_len/channel); + printf("finish2 ....\n"); +} + +int main() { +// int ret_hubert = test_hubert(); +// int ret_contentvec = test_contentvec(); +// test(); +// test(); + test_rvc_lite_online(); + return 0; +} diff --git a/mnn_demo/readme.txt b/mnn_demo/readme.txt new file mode 100644 index 0000000..72c2565 --- /dev/null +++ b/mnn_demo/readme.txt @@ -0,0 +1,34 @@ +音色转换工具 + +环境要求: +MNN编译: https://mnn-docs.readthedocs.io/en/latest/compile/engine.html#linux-macos +编译完成后，修改CMakeLists.txt的MNN路径 +ffmpeg编译: https://phabricator.ushow.media/w/%E9%9F%B3%E8%A7%86%E9%A2%91%E7%BB%84%E6%96%87%E6%A1%A3/%E7%8E%AF%E5%A2%83%E5%AE%89%E8%A3%85/ffmpeg%E6%9C%8D%E5%8A%A1%E7%AB%AF%E5%AE%89%E8%A3%85%E8%84%9A%E6%9C%AC/ +编译完成后，修改CMakeLists.txt的ffmpeg路径 + +代码解释: + ---inc // 头文件 + ---src // 源代码位置 + ---ref // 依赖的代码 + ---av_resample // 重采样 + ---av_waves // 音频读取的模块 + ---thread // 多线程 + ---tests // 测试代码 + ---third_party // 第三方依赖的库 + ---main.cpp // 测试SVC的代码 + ---build_android.sh // 编译android的sh + ---readme.txt + +模型地址: +hubert模型: https://av-audit-sync-sg-1256122840.cos.ap-singapore.myqcloud.com/hub/models/svc_models/layer3_contentvec.mnn + +音色模型 +xusong模型: https://av-audit-sync-sg-1256122840.cos.ap-singapore.myqcloud.com/hub/models/svc_models/layer3_xusong.mnn +sunyanzi模型: https://av-audit-sync-sg-1256122840.cos.ap-singapore.myqcloud.com/hub/models/svc_models/layer3_syz.mnn +xiafan模型: https://av-audit-sync-sg-1256122840.cos.ap-singapore.myqcloud.com/hub/models/svc_models/layer3_xf_v1.mnn + +测试样本: +南拳妈妈: https://av-audit-sync-sg-1256122840.cos.ap-singapore.myqcloud.com/hub/models/svc_models/rainy_day321_01.wav + +快速使用： +下载上述hubert模型和一个音色模型以及测试音频，然后将其填写到main.cpp中，编译运行即可 diff --git a/mnn_demo/ref/CMakeLists.txt b/mnn_demo/ref/CMakeLists.txt new file mode 100644 index 0000000..d8500d8 --- /dev/null +++ b/mnn_demo/ref/CMakeLists.txt @@ -0,0 +1,3 @@ +add_subdirectory(av_resample/audio_resample) +add_subdirectory(av_waves/waves) +add_subdirectory(thread) \ No newline at end of file diff --git a/mnn_demo/ref/av_resample/.gitignore b/mnn_demo/ref/av_resample/.gitignore new file mode 100644 index 0000000..adda3fb --- /dev/null +++ b/mnn_demo/ref/av_resample/.gitignore @@ -0,0 +1,8 @@ +.DS_Store +cmake-build-debug/ +.idea/ +build/ +libs/ +objs/ +debug/ +resource/ diff --git a/mnn_demo/ref/av_resample/.gitmodules b/mnn_demo/ref/av_resample/.gitmodules new file mode 100644 index 0000000..f8fdb84 --- /dev/null +++ b/mnn_demo/ref/av_resample/.gitmodules @@ -0,0 +1,3 @@ +[submodule "audio_resample/third_party/av_waves"] + path = audio_resample/third_party/av_waves + url = ssh://git@phabricator.ushow.media/source/av_waves.git diff --git a/mnn_demo/ref/av_resample/audio_resample/CMakeLists.txt b/mnn_demo/ref/av_resample/audio_resample/CMakeLists.txt new file mode 100644 index 0000000..41605d2 --- /dev/null +++ b/mnn_demo/ref/av_resample/audio_resample/CMakeLists.txt @@ -0,0 +1,45 @@ + +if (CMAKE_SOURCE_DIR STREQUAL CMAKE_CURRENT_SOURCE_DIR) + cmake_minimum_required(VERSION 2.8) + project(audio_resampler) + set(LIBRARY_OUTPUT_PATH ${PROJECT_SOURCE_DIR}/lib) +endif () + +include_directories(./) +include_directories(inc src) + + +# ffmpeg-android +set(FFMPEG_DIR /opt/soft/ffmpeg/ffmpeg) +IF (WIN32) + MESSAGE(STATUS "Now is windows") + set(FFMPEG_DIR D:/soft/ffmpeg/linux_ffmpeg) +ENDIF () +include_directories(${FFMPEG_DIR}/include) +file(GLOB_RECURSE RESAMPLE_SRC_CPP src/*cpp) + +#add_subdirectory(third_party/av_waves/waves) +#include_directories(third_party/av_waves/waves/inc) +add_library(audio_resample ${RESAMPLE_SRC_CPP}) +#add_executable(test_audio_resample test/test_resample.cpp ${RESAMPLE_SRC_CPP}) +#target_link_libraries(test_audio_resample +# ${FFMPEG_LIB}/libavfilter.a +# ${FFMPEG_LIB}/libavformat.a +# ${FFMPEG_LIB}/libavcodec.a +# ${FFMPEG_LIB}/libswresample.a +# ${FFMPEG_LIB}/libswscale.a +# ${FFMPEG_LIB}/libavutil.a +# -lz -lbz2 -liconv -llzma +# "-framework VideoToolbox" +# "-framework Security" +# "-framework CoreFoundation" +# "-framework CoreMedia" +# "-framework CoreVideo" +# "-framework VideoDecodeAcceleration" +# "-framework AVFoundation" +# "-framework CoreGraphics" +# "-framework Foundation" +# "-framework CoreServices" +# +# ${LIBRARY_OUTPUT_PATH}/libwaves.a +# ) \ No newline at end of file diff --git a/mnn_demo/ref/av_resample/audio_resample/build_android.sh b/mnn_demo/ref/av_resample/audio_resample/build_android.sh new file mode 100644 index 0000000..822b8bc --- /dev/null +++ b/mnn_demo/ref/av_resample/audio_resample/build_android.sh @@ -0,0 +1,64 @@ +#!/bin/sh + +# @Time : 2019-06-18 17:50 +# @Author : AlanWang +# @FileName: build_android.sh + +# MY_NDK 和 MY_CMAKE 需要改成自己对应的 ndk 中的目录 +MY_NDK="/Users/yangjianli/Library/Android/sdk/ndk-bundle" +MY_CMAKE="/Users/yangjianli/Library/Android/sdk/cmake/3.6.4111459/bin/cmake" + +if [ -z "$MY_NDK" ]; then + echo "Please set MY_NDK to the Android NDK folder" + exit 1 +fi + +if [ -z "$MY_CMAKE" ]; then + echo "Please set MY_CMAKE to the Android CMake folder" + exit 1 +fi + +OUTPUT_LIBS="./build/libs/android" +ANDROID_NATIVE_API_LEVEL="android-16" + +# arme_abis=(armeabi armeabi-v7a arm64-v8a x86 x86_64 mips mips64) +arme_abis=(armeabi-v7a arm64-v8a) + +function build_with_armeabi() { + ARME_ABI=$1 + echo ${ARME_ABI} + + BUILD_DIR="./build/android/${ARME_ABI}" + BUILD_REF_DIR="./build/android/${ARME_ABI}/ref" + OUTPUT_SO_DIR="${BUILD_DIR}/build/android/libs/${ARME_ABI}" + + PRE_EXE_DIR=$(pwd) + echo ${PRE_EXE_DIR} + + ${MY_CMAKE} \ + -H"./" \ + -B"${BUILD_DIR}" \ + -DANDROID_ABI="${ARME_ABI}" \ + -DANDROID_NDK="${MY_NDK}" \ + -DCMAKE_LIBRARY_OUTPUT_DIRECTORY="./build/android/libs/${ARME_ABI}" \ + -DCMAKE_BUILD_TYPE="Release" \ + -DCMAKE_TOOLCHAIN_FILE="${MY_NDK}/build/cmake/android.toolchain.cmake" \ + -DANDROID_NATIVE_API_LEVEL=${ANDROID_NATIVE_API_LEVEL} \ + -DANDROID_TOOLCHAIN="clang" \ + -DCMAKE_C_FLAGS="-fpic -fexceptions -frtti -Wno-narrowing" \ + -DCMAKE_CXX_FLAGS="-fpic -fexceptions -frtti -Wno-narrowing" \ + -DANDROID_STL="c++_static" \ + + + cd ${BUILD_DIR} + make + + cd ${PRE_EXE_DIR} + mkdir -p ${OUTPUT_LIBS}/${ARME_ABI}/ + mv ${PRE_EXE_DIR}/lib/* ${OUTPUT_LIBS}/${ARME_ABI}/ + rm -r ./build/android +} + +for i in ${arme_abis[@]}; do + build_with_armeabi $i +done diff --git a/mnn_demo/ref/av_resample/audio_resample/inc/FfmpegResampler.h b/mnn_demo/ref/av_resample/audio_resample/inc/FfmpegResampler.h new file mode 100644 index 0000000..c39e185 --- /dev/null +++ b/mnn_demo/ref/av_resample/audio_resample/inc/FfmpegResampler.h @@ -0,0 +1,35 @@ +// +// Created by 杨将 on 2017/9/4. +// + +#ifndef __FFMPEGRESAMPLER_H__ +#define __FFMPEGRESAMPLER_H__ + +#include "IResampler.h" + +class SwrContext; + +class CFfmpegResampler : public IResampler +{ +public: + CFfmpegResampler(); + virtual ~CFfmpegResampler(); + +public: + virtual int init(int in_samplerate, int out_samplerate, int in_channel=1, int out_channel=1); + virtual int get_out_samples(int num); + virtual int get_latency(); + virtual void reset(); + virtual int resample(float * in_buf, int in_num, float * out_buf, int & out_num); + virtual void uninit(); + +private: + SwrContext * m_swr_context; + //重采样的buffer和长度 + unsigned char * m_swr_buffer; + int m_swr_bufsize; + int m_in_channel; + int m_out_channel; +}; + +#endif //__FFMPEGRESAMPLER_H__ diff --git a/mnn_demo/ref/av_resample/audio_resample/inc/IResampler.h b/mnn_demo/ref/av_resample/audio_resample/inc/IResampler.h new file mode 100644 index 0000000..93baf9b --- /dev/null +++ b/mnn_demo/ref/av_resample/audio_resample/inc/IResampler.h @@ -0,0 +1,67 @@ +// +// Created by 杨将 on 2017/9/4. +// +/** + * 基于ffmpeg的重采样模块 + */ +#ifndef __IRESAMPLER_H__ +#define __IRESAMPLER_H__ + +enum +{ + E_RESAMPLER_SUCCESS = 0, + E_RESAMPLER_NO_MEMORY = 10000, + E_RESAMPLER_NUM_ZERO, +}; +class IResampler +{ +public: + IResampler() { } + virtual ~IResampler() { } + +public: + /** + * 初始化函数 + * @param in_samplerate 输入数据的采样率 + * @param out_samplerate 输出数据的采样率 + * @param in_channel + * @param out_channel + * @return 0 表示正常 + */ + virtual int init(int in_samplerate, int out_samplerate, int in_channel=1, int out_channel=1) = 0; + + /** + * 当输入每个通道采样点数为num长度的数据时,从resample可以获取到的输出数据的最大长度 + * @param num 本次将要输入的数据长度[单通道采样点数量] + * @return 单通道采样点数量,负数表示异常 + */ + virtual int get_out_samples(int num) = 0; + + /** + * 获取延迟延迟时间,采样点级别 + * @return + */ + virtual int get_latency() = 0; + + /** + * 重设，清空内部缓存数据[当输入数据源切换时，需要进行设置] + */ + virtual void reset() = 0; + + /** + * 重采样函数 + * @param in_buf 输入数据[多通道时，交错方式的存储][in] + * @param in_num 输入数据单个通道的采样点数量[in] + * @param out_buf 输出数据[多通道时，交错方式的存储][in][注意:需要外部开辟好空间,可以使用get_out_samples获取需要开辟的最大长度] + * @param out_num 输出数据单个通道的采样点数量[out][注意: out_buf真实被写入的单通道采样点数量] + * @return 0表示正常 + */ + virtual int resample(float * in_buf, int in_num, float * out_buf, int & out_num) = 0; + + /** + * 销毁函数 + */ + virtual void uninit() = 0; +}; + +#endif //__IRESAMPLER_H__ diff --git a/mnn_demo/ref/av_resample/audio_resample/src/FfmpegResampler.cpp b/mnn_demo/ref/av_resample/audio_resample/src/FfmpegResampler.cpp new file mode 100644 index 0000000..3fb8d98 --- /dev/null +++ b/mnn_demo/ref/av_resample/audio_resample/src/FfmpegResampler.cpp @@ -0,0 +1,138 @@ +// +// Created by 杨将 on 2017/9/4. +// + +#include "FfmpegResampler.h" + +#ifdef __cplusplus +extern "C" { +#endif + +#include "libswresample/swresample.h" +#include "libavutil/channel_layout.h" + +#ifdef __cplusplus +}; +#endif + +CFfmpegResampler::CFfmpegResampler() +{ + m_swr_context = NULL; + m_swr_buffer = NULL; + m_swr_bufsize = 0; +} + +CFfmpegResampler::~CFfmpegResampler() +{ + uninit(); +} + +int CFfmpegResampler::init(int in_samplerate, int out_samplerate, int in_channel, int out_channel) +{ + if(in_samplerate != out_samplerate) + { + m_swr_context = swr_alloc_set_opts( + NULL, + av_get_default_channel_layout(out_channel), + AV_SAMPLE_FMT_FLT, + out_samplerate, + av_get_default_channel_layout(in_channel), + AV_SAMPLE_FMT_FLT, + in_samplerate, + 0, + NULL + ); + + if((NULL == m_swr_context) || swr_init(m_swr_context)) + { + return E_RESAMPLER_NO_MEMORY; + } + } + m_in_channel = in_channel; + m_out_channel = out_channel; + return E_RESAMPLER_SUCCESS; +} + +int CFfmpegResampler::get_out_samples(int num) +{ + if(m_swr_context) + { + return swr_get_out_samples(m_swr_context, num); + } + else + { + return num; + } +} + +int CFfmpegResampler::get_latency() +{ + return 0; +} + +void CFfmpegResampler::reset() +{ + if(m_swr_context && m_swr_buffer) + { + swr_convert(m_swr_context, &m_swr_buffer, m_swr_bufsize, 0, 0); + } +} + +int CFfmpegResampler::resample(float * in_buf, int in_num, float * out_buf, int & out_num) +{ + if(m_swr_context) + { + //看之前申请的内存空间是否足够，不足的话，就进行申请空间 + if(out_num > m_swr_bufsize) + { + unsigned char * buffer = NULL; + if(av_samples_alloc(&buffer, NULL, m_out_channel, out_num, AV_SAMPLE_FMT_FLT, 0) < 0) + { + return E_RESAMPLER_NO_MEMORY; + } + m_swr_bufsize = out_num; + if(m_swr_buffer) + { + av_freep(&m_swr_buffer); + } + m_swr_buffer = buffer; + } + + out_num = swr_convert( + m_swr_context, + &m_swr_buffer, + out_num, + (const uint8_t **)(&in_buf), + in_num + ); + if(out_num < 0) + { + out_num = 0; + return E_RESAMPLER_NUM_ZERO; + } + + memcpy(out_buf, m_swr_buffer, out_num * sizeof(float) * m_out_channel); + } + else if(in_buf == out_buf) + { + out_num = in_num; + } + else + { + memcpy(out_buf, in_buf, out_num * sizeof(float) * m_out_channel); + } + return E_RESAMPLER_SUCCESS; +} + +void CFfmpegResampler::uninit() +{ + if(m_swr_context) + { + swr_free(&m_swr_context); + } + if(m_swr_buffer) + { + av_freep(&m_swr_buffer); + } + m_swr_bufsize = 0; +} \ No newline at end of file diff --git a/mnn_demo/ref/av_resample/audio_resample/test/test_resample.cpp b/mnn_demo/ref/av_resample/audio_resample/test/test_resample.cpp new file mode 100644 index 0000000..fd914b8 --- /dev/null +++ b/mnn_demo/ref/av_resample/audio_resample/test/test_resample.cpp @@ -0,0 +1,60 @@ +// +// Created by yangjianli on 2021/1/20. +// +/** + * 将48k转码为16k,做测试 + */ +#include "STWaveFile.h" +#include "FfmpegResampler.h" +int main(int argc, char* argv[]) +{ + if (argc != 3) + { + printf("params is err! please input: infile outfile\n"); + return -1; + } + STCWaveFile infile(argv[1], false); + STCWaveFile outfile(argv[2], true); + outfile.SetSampleRate(8000); + outfile.SetChannels(2); + outfile.SetSampleFormat(SF_IEEE_FLOAT); + outfile.SetupDone(); + + // 载入数据 + float* inbuf = new float[infile.GetChannels() * infile.GetTotalFrames()]; + infile.ReadFrameAsfloat(inbuf, infile.GetTotalFrames()); + float* outbuf = NULL; + int outbuf_len = 0; + IResampler* resampler = new CFfmpegResampler(); + resampler->init(48000, 8000, infile.GetChannels(), outfile.GetChannels()); + int step = 1024 * infile.GetChannels(); + for(int i = 0; i < infile.GetTotalFrames() * infile.GetChannels(); i+=step) + { + int in_num = step; + if (i + in_num > infile.GetTotalFrames() * infile.GetChannels()) + { + in_num = infile.GetTotalFrames() * infile.GetChannels() - i; + } + int in_frame = in_num / infile.GetChannels(); + int out_frame = resampler->get_out_samples(in_frame); +// printf("%d\n", out_frame); + if (out_frame * outfile.GetChannels() > outbuf_len) + { + if(outbuf != NULL) + { + delete[] outbuf; + outbuf = NULL; + } + outbuf = new float[out_frame * outfile.GetChannels()]; + outbuf_len = out_frame * outfile.GetChannels(); + } + int err = resampler->resample(inbuf+i, in_frame, outbuf, out_frame); + if (err != E_RESAMPLER_SUCCESS) + { + printf("err=%d\n", err); + break; + } + outfile.WriteFrame(outbuf, out_frame); + } + return 0; +} diff --git a/mnn_demo/ref/av_waves/.gitignore b/mnn_demo/ref/av_waves/.gitignore new file mode 100644 index 0000000..e973be2 --- /dev/null +++ b/mnn_demo/ref/av_waves/.gitignore @@ -0,0 +1,9 @@ +.DS_Store +cmake-build-debug/ +.idea/ +build/ +libs/ +objs/ +debug/ +resource/ +lib/ diff --git a/mnn_demo/ref/av_waves/readme.txt b/mnn_demo/ref/av_waves/readme.txt new file mode 100644 index 0000000..a96559c --- /dev/null +++ b/mnn_demo/ref/av_waves/readme.txt @@ -0,0 +1,3 @@ +提供wave读写相关的第三方或者我们自己编写的依赖库 +介绍: + 每个子文件夹代表了一个实现的工程，工程中需要保证一个测试的demo，资源文件基本不需要，减少空间占用 diff --git a/mnn_demo/ref/av_waves/waves/CMakeLists.txt b/mnn_demo/ref/av_waves/waves/CMakeLists.txt new file mode 100644 index 0000000..4862f8d --- /dev/null +++ b/mnn_demo/ref/av_waves/waves/CMakeLists.txt @@ -0,0 +1,14 @@ +if(CMAKE_SOURCE_DIR STREQUAL CMAKE_CURRENT_SOURCE_DIR) + cmake_minimum_required(VERSION 2.8) + project(waves) + set(LIBRARY_OUTPUT_PATH ${PROJECT_SOURCE_DIR}/lib) +endif() + +include_directories(inc) +AUX_SOURCE_DIRECTORY(src DIR_WAVES_SRCS) +add_library(waves ${DIR_WAVES_SRCS}) + +if(CMAKE_SOURCE_DIR STREQUAL CMAKE_CURRENT_SOURCE_DIR) + add_executable(test_waves test_waves.cpp) + target_link_libraries(test_waves ${LIBRARY_OUTPUT_PATH}/libwaves.a) +endif() \ No newline at end of file diff --git a/mnn_demo/ref/av_waves/waves/inc/ExtraMono.h b/mnn_demo/ref/av_waves/waves/inc/ExtraMono.h new file mode 100644 index 0000000..280fab0 --- /dev/null +++ b/mnn_demo/ref/av_waves/waves/inc/ExtraMono.h @@ -0,0 +1,230 @@ + +#include +#include + +#define SIZE_LONG 4 +#define SIZE_SHORT 2 + +#define SIZE_FLAG 4 +#define FMT_TAG 0x0001 + +#define BITS_PER_BYTE 8 + +#ifndef AFS_CMPL_MAX_WAV +#define AFS_CMPL_MAX_WAV 15360000 // 时长16分（960*16000） +#endif + +//+---------------------------------------------------------------------------+ +//+ 从文件中读取一个32位数据 +//+---------------------------------------------------------------------------+ +unsigned long fa_read_u32(FILE* fp) +{ + unsigned long cx; + unsigned char temp[SIZE_LONG]; + + fread(temp, sizeof(unsigned char), SIZE_LONG, fp); + cx = (unsigned long)temp[0]; + cx |= (unsigned long)temp[1] << 8; + cx |= (unsigned long)temp[2] << 16; + cx |= (unsigned long)temp[3] << 24; + return cx; +} + +//+---------------------------------------------------------------------------+ +//+ 从文件中读取一个16位数据 +//+---------------------------------------------------------------------------+ +unsigned short fa_read_u16(FILE *fp) +{ + unsigned short cx; + unsigned char temp[SIZE_SHORT]; + + fread(temp, sizeof(unsigned char), SIZE_SHORT, fp); + cx = temp[0] | (temp[1] * 256); + return cx; +} + +int GetWaveHeadLen(const char* pszFile,unsigned short &channels, int &nPos, int& nLength) +{ + //+---------------------------------------------------------------------------+ + //+ 读取WAVE的头信息 + //+---------------------------------------------------------------------------+ + unsigned char temp[SIZE_FLAG]; + unsigned short bits_per_sample; + unsigned long x_size; + unsigned long n_skip; + + unsigned short format; + //unsigned short channels; + unsigned long sample_rate; + unsigned short block_align; + unsigned long data_size; + int nCnt = 0; + + /* 读取通用信息 */ + FILE* pWavFile = fopen(pszFile, "rb"); + if ( pWavFile == NULL ) + { + printf("Input file can not be opened!\n"); + return -1; + } + + fseek(pWavFile, 0, SEEK_END ); + nLength = ftell(pWavFile); + fseek(pWavFile, 0, SEEK_SET ); + + // 判断资源标识为"RIFF" + fread(temp, sizeof(unsigned char), SIZE_FLAG, pWavFile); + if ( memcmp(temp, "RIFF", (size_t)SIZE_FLAG) != 0 ) + { + fprintf(stderr, "Resource flag is not RIFF!\n"); + fclose(pWavFile); + + return -1; + } + nCnt += SIZE_FLAG; + + fseek(pWavFile, SIZE_LONG, SEEK_CUR); + nCnt += SIZE_LONG; + + // 判断文件标识为"WAVE" + fread(temp, sizeof(unsigned char), SIZE_FLAG, pWavFile); + if ( memcmp(temp, "WAVE", (size_t)SIZE_FLAG) != 0 ) + { + fprintf(stderr, "File flag is not WAVE\n"); + fclose(pWavFile); + + return -1; + } + nCnt += SIZE_FLAG; + + // 判断格式标识为"fmt " + fread(temp, sizeof(unsigned char), SIZE_FLAG, pWavFile); + if ( memcmp(temp, "fmt ", (size_t)SIZE_FLAG) != 0 ) + { + fprintf(stderr, "Format flag is not FMT!\n"); + fclose(pWavFile); + + return -1; + } + nCnt += SIZE_FLAG; + + x_size = fa_read_u32(pWavFile); + nCnt += SIZE_LONG; + + // 判断编码格式为0x0001 + format = fa_read_u16(pWavFile); + nCnt += SIZE_SHORT; + if ( format != FMT_TAG ) + { + fprintf(stderr, "Encoding format is not 0x0001!\n"); + fclose(pWavFile); + + return -1; + } + + // 读取声道数目和采样频率 + channels = fa_read_u16(pWavFile); + sample_rate = fa_read_u32(pWavFile); + + fseek(pWavFile, SIZE_LONG, SEEK_CUR); + + // 读取对齐单位和样本位数 + block_align = fa_read_u16(pWavFile); + bits_per_sample = fa_read_u16(pWavFile); + + /* 读取特殊信息 */ + x_size -= (4*SIZE_SHORT + 2*SIZE_LONG); + if ( x_size != 0 ) + { + fseek(pWavFile, x_size, SEEK_CUR); + } + + // 读取数据大小 + fread(temp, sizeof(unsigned char), SIZE_FLAG, pWavFile); + while ( memcmp(temp, "data", SIZE_FLAG) != 0 ) + { + n_skip = fa_read_u32(pWavFile); + fseek(pWavFile, n_skip, SEEK_CUR); + + fread(temp, sizeof(unsigned char), SIZE_FLAG, pWavFile); + } + + data_size = fa_read_u32(pWavFile); + fclose(pWavFile); + + //+---------------------------------------------------------------------------+ + //+ 返回WAVE的头长度 + //+---------------------------------------------------------------------------+ + nPos = nCnt; + int nHeadLength = nLength - data_size; + return nHeadLength; +} + +bool ExtraMono(const std::string &sInput, const std::string &sOutput) +{ + FILE *pFile = fopen(sInput.c_str(), "rb"); + if ( NULL == pFile ) + { + printf("Fopen Error %s", sInput.c_str()); + return false; + } + + FILE *pFile2 = fopen(sOutput.c_str(), "wb"); + if ( NULL == pFile2 ) + { + printf("Fopen2 Error %s", sOutput.c_str()); + return false; + } + + short *pBuf = new short[AFS_CMPL_MAX_WAV]; + int nLen = 0; + + nLen = fread(pBuf, sizeof(short), AFS_CMPL_MAX_WAV, pFile); + if ( nLen <= 0 ) + { + perror("Fread Error!"); + return false; + } + + unsigned short channels=0; + int nPos; + int nLength; + int nHeadByte = GetWaveHeadLen(sInput.c_str(),channels, nPos, nLength); + int nHeadShort = nHeadByte/2; + + if (channels==1) + { + fwrite(pBuf + nHeadShort, sizeof(short), nLen - nHeadShort, pFile2); + } + else + { + short *pBuf2 = new short[AFS_CMPL_MAX_WAV]; + memcpy( pBuf2, pBuf, nHeadShort*sizeof(short)); + pBuf2[nPos] = 1; + + unsigned char tmp[2]; + memcpy(tmp, &pBuf2[nPos], 2); + + pBuf2[nPos] = static_cast(tmp[0] | tmp[1]*256); + + short *pWav = pBuf + nHeadShort; + nLen -= nHeadShort; + + int halfnlen=nLen/2; + for (int i=0;i<=halfnlen;i++ ) + { + pBuf2[nHeadShort+i] = *(pWav+i*2); + } + fwrite(pBuf2, sizeof(short), nLen+nHeadShort, pFile2); + + delete []pBuf; + delete []pBuf2; + pBuf = NULL; + pBuf2 = NULL; + } + + + fclose(pFile); + fclose(pFile2); + return true; +} diff --git a/mnn_demo/ref/av_waves/waves/inc/STWaveFile.h b/mnn_demo/ref/av_waves/waves/inc/STWaveFile.h new file mode 100644 index 0000000..57920b1 --- /dev/null +++ b/mnn_demo/ref/av_waves/waves/inc/STWaveFile.h @@ -0,0 +1,75 @@ +#ifndef WAVE_FILE_H +#define WAVE_FILE_H + +#include +#include + + +typedef enum SAMPLE_FORMAT +{ + SF_U8 = 8, + SF_S16 = 16, + SF_S24 = 24, + SF_S32 = 32, + SF_IEEE_FLOAT = 0x100 + 32, + SF_IEEE_DOUBLE = 0x100 + 64, + SF_MAX, +} SAMPLE_FORMAT; + +/* 主处理对象 **/ +class STCWaveFile +{ +public: + /* 构造传入文件及 是读还是写 **/ + STCWaveFile(const char* Filename, bool Write); + virtual ~STCWaveFile(); + +public: + int GetChannels(); + int GetSampleRate(); + double GetDuration(); // in second + uint32_t GetChannelMask(); + void SetChannels(int Channels); + void SetSampleRate(int SampleRate); + void SetSampleFormat(SAMPLE_FORMAT Format); + void SetChannelMask(uint32_t Mask); + void Stat(); + void SetupDone(); + bool ReadFrameAsS16(short* FrameSamples, int Frames = 1); + bool ReadFrameAsDouble(double* FrameSamples, int Frames = 1); + bool ReadFrameAsfloat(float* FrameSamples, int Frames = 1); + void WriteRaw(void* Raw, int Size); + void WriteFrame(uint8_t* FrameSamples, int Frames = 1); + void WriteFrame(short* FrameSamples, int Frames = 1); + void WriteFrame(int32_t* FrameSamples, int Frames = 1); + void WriteFrameS24(int32_t* FrameSamples, int Frames = 1); + void WriteFrame(double* FrameSamples, int Frames = 1); + void WriteFrame(float* FrameSamples, int Frames=1); + void Seek(int FramePos, int Where = SEEK_SET); + bool GetStatus(); + SAMPLE_FORMAT GetFormat(); + int GetTotalFrames(); + int GetFramesRead(); + void WriteFramesDone(); + + +protected: + FILE* File; + int Channels; /* 通道数 **/ + int SampleRate; /* 采样率 **/ + SAMPLE_FORMAT Format; /* 采样精度 **/ + int SampleSize; // Measured in Bits + unsigned int FrameStartPos; /* 音频数据的起始位置 **/ + unsigned long TotalFrames; /* 总帧数，如果16bit，则一个short为一帧 **/ + unsigned long FramesRead; + double Duration; /* 时长 **/ + + bool ReadOnly; /* 是度还是写 **/ + + uint32_t ChannelMask; + + bool m_bOK; /* 文件是否已经被打开 **/ +}; + + +#endif \ No newline at end of file diff --git a/mnn_demo/ref/av_waves/waves/src/STWaveFile.cpp b/mnn_demo/ref/av_waves/waves/src/STWaveFile.cpp new file mode 100644 index 0000000..6e58f42 --- /dev/null +++ b/mnn_demo/ref/av_waves/waves/src/STWaveFile.cpp @@ -0,0 +1,816 @@ + +#include +#include +#include +#include + +#if WIN32 +#else +#include +#endif + +#include "STWaveFile.h" + +#define SPEAKER_FRONT_LEFT 0x1 +#define SPEAKER_FRONT_RIGHT 0x2 +#define SPEAKER_FRONT_CENTER 0x4 +#define SPEAKER_LOW_FREQUENCY 0x8 +#define SPEAKER_BACK_LEFT 0x10 +#define SPEAKER_BACK_RIGHT 0x20 +#define SPEAKER_FRONT_LEFT_OF_CENTER 0x40 +#define SPEAKER_FRONT_RIGHT_OF_CENTER 0x80 +#define SPEAKER_BACK_CENTER 0x100 +#define SPEAKER_SIDE_LEFT 0x200 +#define SPEAKER_SIDE_RIGHT 0x400 +#define SPEAKER_TOP_CENTER 0x800 +#define SPEAKER_TOP_FRONT_LEFT 0x1000 +#define SPEAKER_TOP_FRONT_CENTER 0x2000 +#define SPEAKER_TOP_FRONT_RIGHT 0x4000 +#define SPEAKER_TOP_BACK_LEFT 0x8000 +#define SPEAKER_TOP_BACK_CENTER 0x10000 +#define SPEAKER_TOP_BACK_RIGHT 0x20000 +#define SPEAKER_RESERVED 0x80000000 + + +#define SPEAKER_REAR_CENTER_SURROUND SPEAKER_BACK_CENTER + +#define DCA_MONO 0 +#define DCA_CHANNEL 1 +#define DCA_STEREO 2 +#define DCA_STEREO_SUMDIFF 3 +#define DCA_STEREO_TOTAL 4 +#define DCA_3F 5 +#define DCA_2F1R 6 +#define DCA_3F1R 7 +#define DCA_2F2R 8 +#define DCA_3F2R 9 +#define DCA_4F2R 10 + +#define DCA_DOLBY 101 /* FIXME */ + +#define DCA_CHANNEL_MAX DCA_3F2R /* We don't handle anything above that */ +#define DCA_CHANNEL_BITS 6 +#define DCA_CHANNEL_MASK 0x3F + +#define DCA_LFE 0x80 +#define DCA_ADJUST_LEVEL 0x100 + +#define WAVE_FORMAT_PCM 0x0001 +#define WAVE_FORMAT_IEEE_FLOAT 0x0003 +#define WAVE_FORMAT_EXTENSIBLE 0xFFFE + +static uint8_t wav_header[] = { + 'R', 'I', 'F', 'F', 0xfc, 0xff, 0xff, 0xff, 'W', 'A', 'V', 'E', + 'f', 'm', 't', ' ', 16, 0, 0, 0, + WAVE_FORMAT_PCM, WAVE_FORMAT_PCM >> 8, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, + 'd', 'a', 't', 'a', 0xd8, 0xff, 0xff, 0xff +}; + +static uint8_t wavmulti_header[] = { + 'R', 'I', 'F', 'F', 0xf0, 0xff, 0xff, 0xff, 'W', 'A', 'V', 'E', + 'f', 'm', 't', ' ', 40, 0, 0, 0, + (uint8_t)(WAVE_FORMAT_EXTENSIBLE & 0xFF), WAVE_FORMAT_EXTENSIBLE >> 8, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 22, 0, + 0, 0, 0, 0, 0, 0, + WAVE_FORMAT_IEEE_FLOAT, WAVE_FORMAT_IEEE_FLOAT >> 8, + 0, 0, 0, 0, 0x10, 0x00, 0x80, 0, 0, 0xaa, 0, 0x38, 0x9b, 0x71, + 'd', 'a', 't', 'a', 0xb4, 0xff, 0xff, 0xff +}; + +static void store4 (uint8_t * buf, int value) +{ + buf[0] = value; + buf[1] = value >> 8; + buf[2] = value >> 16; + buf[3] = value >> 24; +} + +static void store2 (uint8_t * buf, int value) +{ + buf[0] = value; + buf[1] = value >> 8; +} + + +static uint32_t find_chunk(FILE * file, const uint8_t chunk_id[4]) +{ + uint8_t buffer[8]; + while (1) { + size_t chunksize; + size_t s = fread(buffer, 1, 8, file); + if (s < 8) + return 0; + chunksize = (uint32_t)buffer[4] | ((uint32_t)buffer[5] << 8) | + ((uint32_t)buffer[6] << 16) | ((uint32_t)buffer[7] << 24); + if (!memcmp(buffer, chunk_id, 4)) + return chunksize; + fseek(file, chunksize, SEEK_CUR); + } +} + + +STCWaveFile::STCWaveFile(const char* Filename, bool Write) + : Duration(0), ReadOnly(false), m_bOK(false) +{ + Channels = 0; + + /* 打开文件 **/ + File = fopen(Filename, Write ? "wb":"rb"); + if ( !File ) + return; + + /* 设置写文件初始参数 **/ + if ( Write ) + { + SampleRate = 44100; + Channels = 2; + Format = SF_S16; + SampleSize = 16; + ChannelMask = 0; + m_bOK = true; + return; + } + + ReadOnly = true; + + size_t s; + uint8_t buffer[8]; + uint8_t *fmt = NULL; + uint32_t v; + uint32_t avg_bps; + uint32_t block_align; + unsigned short FormatType; + unsigned short SampleType; + + static const uint8_t riff[4] = { 'R', 'I', 'F', 'F' }; + static const uint8_t wave[4] = { 'W', 'A', 'V', 'E' }; + static const uint8_t fmt_[4] = { 'f', 'm', 't', ' ' }; + static const uint8_t data[4] = { 'd', 'a', 't', 'a' }; + + /* 前四个字节为 riff **/ + s = fread(buffer, 1, 8, File); + if (s < 8) + goto err2; + + if (memcmp(buffer, riff, 4)) + goto err2; + + /* 8~12为wave **/ + /* TODO: check size (in buffer[4..8]) */ + s = fread(buffer, 1, 4, File); + if (s < 4) + goto err2; + + if (memcmp(buffer, wave, 4)) + goto err2; + + s = find_chunk(File, fmt_); + if ( s != 16 && s != 18 && s != 40 ) + goto err2; + + fmt = (uint8_t*)malloc(s); + if (!fmt) + goto err2; + + if (fread(fmt, 1, s, File) != s) + goto err3; + + /* wFormatTag */ + v = (uint32_t)fmt[0] | ((uint32_t)fmt[1] << 8); + if (v != WAVE_FORMAT_PCM && v != WAVE_FORMAT_IEEE_FLOAT && v != WAVE_FORMAT_EXTENSIBLE) + goto err3; + + FormatType = v; + + if (s == 40 && 0xfffe == v) + { + // fmt begins at 0x14 of the wave file + v = *(unsigned short*)&fmt[0x2C - 0x14]; + } + + SampleType = v; + + /* wChannels */ + v = (uint32_t)fmt[2] | ((uint32_t)fmt[3] << 8); + + Channels = v; + + if (v < 1 || v > 32) + goto err3; + + /* dwSamplesPerSec */ + SampleRate = (uint32_t)fmt[4] | ((uint32_t)fmt[5] << 8) | + ((uint32_t)fmt[6] << 16) | ((uint32_t)fmt[7] << 24); + + /* dwAvgBytesPerSec */ + avg_bps = (uint32_t)fmt[8] | ((uint32_t)fmt[9] << 8) | + ((uint32_t)fmt[10] << 16) | ((uint32_t)fmt[11] << 24); + + /* wBlockAlign */ + block_align = (uint32_t)fmt[12] | ((uint32_t)fmt[13] << 8); + + /* wBitsPerSample */ + SampleSize = (uint32_t)fmt[14] | ((uint32_t)fmt[15] << 8); + if (SampleSize != 8 && SampleSize != 16 && SampleSize != 32 && SampleSize != 24 && SampleSize != 64) + goto err3; + + switch (SampleSize) + { + case 8: + Format = SF_U8; + break; + case 16: + Format = SF_S16; + break; + case 24: + Format = SF_S24; + break; + case 32: + { + if (SampleType == WAVE_FORMAT_IEEE_FLOAT) + Format = SF_IEEE_FLOAT; + else + Format = SF_S32; + + } + break; + case 64: + if (SampleType != WAVE_FORMAT_IEEE_FLOAT) + goto err3; + Format = SF_IEEE_DOUBLE; + break; + } + + + // Handle 24-bit samples individually +#if 0 + if (SampleSize == 24 && Channels <= 2) + { + int ba24 = Channels * (SampleSize / 8); // Align to 4x + + ba24 = (ba24 + 3) / 4 * 4; + + if (block_align != ba24) + goto err3; + } + else +#endif + { + if (block_align != Channels * (SampleSize / 8)) + goto err3; + } + + if (avg_bps != block_align * SampleRate) + goto err3; + + v = find_chunk(File, data); + + if (v == 0 || v % block_align != 0) + goto err3; + + TotalFrames = v / block_align; + + FramesRead = 0; + + if (FormatType == WAVE_FORMAT_EXTENSIBLE) + { + ChannelMask = *(unsigned int*)(&fmt[0x14]); + } + else + { + ChannelMask = 0; + } + + FrameStartPos = ftell(File); + + free(fmt); + m_bOK = true; + return; + +err3: + free(fmt); +err2: + fclose(File); + + File = NULL; +} + +bool STCWaveFile::GetStatus() +{ + return m_bOK; +} + +SAMPLE_FORMAT STCWaveFile::GetFormat() +{ + return Format; +} + +int STCWaveFile::GetTotalFrames() +{ + return TotalFrames; +} + +int STCWaveFile::GetFramesRead() +{ + return FramesRead; +} + +STCWaveFile::~STCWaveFile() +{ + WriteFramesDone(); +} + +int STCWaveFile::GetSampleRate() +{ + return SampleRate; +} + +void STCWaveFile::SetSampleRate(int SampleRate) +{ + this->SampleRate = SampleRate; +} + +void STCWaveFile::SetupDone() +{ + unsigned char Header[68]; + + fseek(File, 0, SEEK_SET); + + SampleSize = Format & 0xFF; + + if (ChannelMask) + { + memcpy(Header, wavmulti_header, sizeof(wavmulti_header)); + + if (Format < SF_IEEE_FLOAT) + { + // store2(Header + 20, WAVE_FORMAT_PCM); + store2(Header + 44, WAVE_FORMAT_PCM); + } + + store2(Header + 22, Channels); + store4(Header + 24, SampleRate); + store4(Header + 28, SampleSize / 8 * SampleRate * Channels); + store2(Header + 32, SampleSize / 8 * Channels); + store2(Header + 34, SampleSize / 8 * 8); + + store2(Header + 38, SampleSize / 8 * 8); + store4(Header + 40, ChannelMask); + + fwrite(Header, sizeof(wavmulti_header), 1, File); + } + else + { + memcpy(Header, wav_header, sizeof(wav_header)); + + if (Format >= SF_IEEE_FLOAT) + { + store2(Header + 20, WAVE_FORMAT_IEEE_FLOAT); + } + + store2(Header + 22, Channels); + store4(Header + 24, SampleRate); + store4(Header + 28, SampleSize / 8 * SampleRate * Channels); + store2(Header + 32, SampleSize / 8 * Channels); + store2(Header + 34, SampleSize / 8 * 8); + + fwrite(Header, sizeof(wav_header), 1, File); + } + + + FrameStartPos = ftell(File); +} + + +void STCWaveFile::Seek(int FramePos, int Where) +{ + // Ignoring Where + + fseek(File, FrameStartPos + FramePos * Channels* (SampleSize / 8), Where); + + FramesRead = FramePos; + +} + +int STCWaveFile::GetChannels() +{ + return Channels; +} + +void STCWaveFile::SetChannels(int Channels) +{ + this->Channels = Channels; +} + +void STCWaveFile::SetSampleFormat(SAMPLE_FORMAT Format) +{ + this->Format = Format; +} + +uint32_t STCWaveFile::GetChannelMask() +{ + return ChannelMask; +} + +void STCWaveFile::SetChannelMask(uint32_t Mask) +{ + ChannelMask = Mask; +} + +bool STCWaveFile::ReadFrameAsS16(short* FrameSamples, int Frames) +{ + if (FramesRead >= TotalFrames) + return false; + + FramesRead += Frames; + + switch (Format) + { + case SF_U8: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + short DirectSample = 0; + if (1 == fread(&DirectSample, 1, 1, File)) + { + FrameSamples[ch + frame*Channels] = (DirectSample - 128) << 8; + } + else + { + return false; + } + } + } + return true; + } + case SF_S16: + return Frames == fread(FrameSamples, sizeof(FrameSamples[0])*Channels, Frames, File); + case SF_S24: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + unsigned int DirectSample = 0; + if (1 == fread(&DirectSample, 3, 1, File)) + { + FrameSamples[ch + frame*Channels] = (short)(unsigned short)(DirectSample >> 8); // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_S32: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + unsigned int DirectSample = 0; + if (1 == fread(&DirectSample, 4, 1, File)) + { + FrameSamples[ch + frame*Channels] = (short)(unsigned short)(DirectSample >> 16); // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_IEEE_FLOAT: + { + float DirectSamples[32]; + + if (Frames == fread(DirectSamples, sizeof(DirectSamples[0]) * Channels, Frames, File)) + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + FrameSamples[ch + frame*Channels] = (short)(DirectSamples[ch + frame*Channels] * 32768); + } + } + return true; + } + return false; + } + case SF_IEEE_DOUBLE: + { + double DirectSamples[32]; + + if (Frames == fread(DirectSamples, sizeof(DirectSamples[0]) * Channels, Frames, File)) + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + FrameSamples[ch + frame*Channels] = (short)(DirectSamples[ch + frame*Channels] * 32768); + } + } + return true; + } + return false; + } + } + return false; +} + +bool STCWaveFile::ReadFrameAsfloat(float* FrameSamples, int Frames) +{ + if (FramesRead >= TotalFrames) + return false; + + FramesRead += Frames; + + switch (Format) + { + case SF_U8: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + short DirectSample = 0; + if (1 == fread(&DirectSample, 1, 1, File)) + { + FrameSamples[ch + frame*Channels] = (DirectSample - 128) / 128.0; // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_S16: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + short DirectSample = 0; + if (1 == fread(&DirectSample, 2, 1, File)) + { + FrameSamples[ch + frame*Channels] = DirectSample / 32768.0; // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_S24: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + uint32_t DirectSample = 0; + if (1 == fread(&DirectSample, 3, 1, File)) + { + FrameSamples[ch + frame*Channels] = ((int32_t)((uint32_t)(DirectSample << 8))) / + (double)(((uint32_t)(1 << 31))); // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_S32: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + uint32_t DirectSample = 0; + if (1 == fread(&DirectSample, 4, 1, File)) + { + FrameSamples[ch + frame*Channels] = ((int32_t)((uint32_t)(DirectSample))) / + (double)(((uint32_t)(1 << 31))); // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_IEEE_FLOAT: + { + if(fread(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File)) + { + return true; + } + return false; + } + case SF_IEEE_DOUBLE: + { + if (Frames == fread(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File)) + { + return true; + } + return false; + } + } + return false; +} + +bool STCWaveFile::ReadFrameAsDouble(double* FrameSamples, int Frames) +{ + if (FramesRead >= TotalFrames) + return false; + + FramesRead += Frames; + + switch (Format) + { + case SF_U8: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + short DirectSample = 0; + if (1 == fread(&DirectSample, 1, 1, File)) + { + FrameSamples[ch + frame*Channels] = (DirectSample - 128) / 128.0; // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_S16: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + short DirectSample = 0; + if (1 == fread(&DirectSample, 2, 1, File)) + { + FrameSamples[ch + frame*Channels] = DirectSample / 32768.0; // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_S24: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + uint32_t DirectSample = 0; + if (1 == fread(&DirectSample, 3, 1, File)) + { + FrameSamples[ch + frame*Channels] = ((int32_t)((uint32_t)(DirectSample << 8))) / + (double)(((uint32_t)(1 << 31))); // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_S32: + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + uint32_t DirectSample = 0; + if (1 == fread(&DirectSample, 4, 1, File)) + { + FrameSamples[ch + frame*Channels] = ((int32_t)((uint32_t)(DirectSample ))) / + (double)(((uint32_t)(1 << 31))); // (short)(DirectSample * 32767.0 / ((1 << 24) - 1)); + } + else + { + return false; + } + } + } + return true; + } + case SF_IEEE_FLOAT: + { + float DirectSamples[32]; + + if (Frames == fread(DirectSamples, sizeof(DirectSamples[0]) * Channels, Frames, File)) + { + for (int frame = 0; frame < Frames; frame++) + { + for (int ch = 0; ch < Channels; ch++) + { + FrameSamples[ch + frame*Channels] = (double)(DirectSamples[ch + frame*Channels]); + } + } + return true; + } + return false; + } + case SF_IEEE_DOUBLE: + { + if (Frames == fread(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File)) + { + return true; + } + return false; + } + } + return false; +} + +void STCWaveFile::WriteRaw(void* Raw, int Size) +{ + fwrite(Raw, Size, 1, File); +} + + +void STCWaveFile::WriteFrame(uint8_t* FrameSamples, int Frames) +{ + fwrite(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File); +} + +void STCWaveFile::WriteFrame(short* FrameSamples, int Frames) +{ + fwrite(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File); +} + +void STCWaveFile::WriteFrame(int32_t* FrameSamples, int Frames) +{ + fwrite(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File); +} + +void STCWaveFile::WriteFrameS24(int32_t* FrameSamples, int Frames) +{ + for (int c = 0; c < Channels; c++) + { + fwrite(&FrameSamples[c], 3, 1, File); + } +} + +void STCWaveFile::WriteFrame(double* FrameSamples, int Frames) +{ + fwrite(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File); +} + +void STCWaveFile::WriteFrame(float* FrameSamples, int Frames) +{ + fwrite(FrameSamples, sizeof(FrameSamples[0]) * Channels, Frames, File); +} + + +double STCWaveFile::GetDuration() +{ + return Duration; +} + + +void STCWaveFile::WriteFramesDone() +{ + if (File != NULL) + { + if (!ReadOnly) + { + unsigned int Size = ftell(File) - FrameStartPos;// 44; + + fseek(File, FrameStartPos - 4, SEEK_SET); + fwrite(&Size, 4, 1, File); + + Size += FrameStartPos - 8; + + fseek(File, 4, SEEK_SET); + fwrite(&Size, 4, 1, File); + } + + fclose(File); + File = NULL; + } +} diff --git a/mnn_demo/ref/av_waves/waves/test_waves.cpp b/mnn_demo/ref/av_waves/waves/test_waves.cpp new file mode 100644 index 0000000..0d855af --- /dev/null +++ b/mnn_demo/ref/av_waves/waves/test_waves.cpp @@ -0,0 +1,25 @@ +// +// Created by yangjianli on 2020/10/10. +// +#include "string" +#include "STWaveFile.h" +int main(int argc ,char* argv[]) +{ + std::string name = argv[1]; + STCWaveFile wave_read(name.c_str(), false); + if(wave_read.GetStatus()) + { + STCWaveFile wave_write((name + "_test.wav").c_str(), true); + wave_write.SetSampleRate(wave_read.GetSampleRate()); + wave_write.SetChannels(wave_read.GetChannels()); + wave_write.SetSampleFormat(SF_IEEE_FLOAT); + wave_write.SetupDone(); + + float* buf = new float[wave_read.GetChannels() * wave_read.GetTotalFrames()]; + wave_read.ReadFrameAsfloat(buf, wave_read.GetTotalFrames()); + wave_write.WriteFrame(buf, wave_read.GetTotalFrames()); + delete[] buf; + printf("%s ok\n", name.c_str()); + } + return 0; +} \ No newline at end of file diff --git a/mnn_demo/ref/thread/CMakeLists.txt b/mnn_demo/ref/thread/CMakeLists.txt new file mode 100644 index 0000000..5fc722b --- /dev/null +++ b/mnn_demo/ref/thread/CMakeLists.txt @@ -0,0 +1,3 @@ +include_directories(./) +AUX_SOURCE_DIRECTORY(./ DIR_THREAD_SRCS) +add_library(thread ${DIR_THREAD_SRCS}) \ No newline at end of file diff --git a/mnn_demo/ref/thread/Thread.cpp b/mnn_demo/ref/thread/Thread.cpp new file mode 100644 index 0000000..6eb6a31 --- /dev/null +++ b/mnn_demo/ref/thread/Thread.cpp @@ -0,0 +1,39 @@ +// +// Created by 杨将 on 2017/8/21. +// + +#include "Thread.h" + +CThread::CThread(const ThreadFunc & func) + : started_(false) + , joined_(false) + , func_(func) +{ + +} + +CThread::~CThread() +{ + if (started_ && !joined_) + { + pThread_->detach(); + } +} + +void CThread::start() +{ + if(!started_) + { + pThread_.reset(new std::thread(func_) ); + started_ = true; + } +} + +void CThread::join() +{ + if ( !joined_) + { + pThread_->join(); + joined_ = true; + } +} diff --git a/mnn_demo/ref/thread/Thread.h b/mnn_demo/ref/thread/Thread.h new file mode 100644 index 0000000..3554d05 --- /dev/null +++ b/mnn_demo/ref/thread/Thread.h @@ -0,0 +1,37 @@ +// +// Created by 杨将 on 2017/8/21. +// + +#ifndef __THREAD_H__ +#define __THREAD_H__ + +#include +#include +#include + +class CThread +{ +public: + typedef std::function ThreadFunc; + typedef std::shared_ptr ThreadPtr; + + explicit CThread(const ThreadFunc & func); + ~CThread(); + + void start(); + + void join(); + + bool started() const { return started_; } + +private: + bool started_; + bool joined_; + + ThreadFunc func_; + + ThreadPtr pThread_; + +}; + +#endif //__THREAD_H__ diff --git a/mnn_demo/ref/thread/ThreadPool.cpp b/mnn_demo/ref/thread/ThreadPool.cpp new file mode 100644 index 0000000..2659672 --- /dev/null +++ b/mnn_demo/ref/thread/ThreadPool.cpp @@ -0,0 +1,109 @@ +// +// Created by 杨将 on 2017/8/21. +// + +#include "ThreadPool.h" +#include + +CThreadPool::CThreadPool() + : mutex_() + , running_(false) +{ + threads_num_ = 0; +} + +CThreadPool::~CThreadPool() +{ + if (running_) + { + stop(); + } +} + +void CThreadPool::start(int32_t numThreads, bool bLoop) +{ + running_ = true; + loop_ = bLoop; + threads_.reserve((uint32_t)numThreads); + for (int32_t i = 0; i < numThreads; ++i) + { + threads_.emplace_back(new CThread( + std::bind(&CThreadPool::runInThread, this))); + threads_[i]->start(); + ++threads_num_; + } +} + +void CThreadPool::stop() +{ + { + std::lock_guard lock(mutex_); + running_ = false; + cond_.notify_all(); + } + for(auto & thr : threads_) + { + thr->join(); + } + threads_.clear(); +} + +void CThreadPool::run(const Task& task) +{ + if (threads_.empty()) + { + task(); + } + else + { + std::lock_guard lock(mutex_); + queue_.push_back(task); + cond_.notify_one(); + } +} + +CThreadPool::Task CThreadPool::take() +{ + std::unique_lock lock(mutex_); + + while (queue_.empty() && running_) + { + cond_.wait(lock); + } + Task task; + if(!queue_.empty()) + { + task = queue_.front(); + queue_.pop_front(); + if(loop_) + { + queue_.push_back(task); + } + } + return task; +} + +void CThreadPool::runInThread() +{ + while (running_) + { + Task task(take()); + + if (task) + { + task(); + } + } +} + +void CThreadPool::flush() +{ + std::lock_guard lock(mutex_); + queue_.clear(); +} + +int CThreadPool::getTaskQueueSize() +{ + std::lock_guard lock(mutex_); + return queue_.size(); +} diff --git a/mnn_demo/ref/thread/ThreadPool.h b/mnn_demo/ref/thread/ThreadPool.h new file mode 100644 index 0000000..d35ecf4 --- /dev/null +++ b/mnn_demo/ref/thread/ThreadPool.h @@ -0,0 +1,42 @@ +// +// Created by 杨将 on 2017/8/21. +// + +#ifndef __THREADPOOL_H__ +#define __THREADPOOL_H__ + +#include "Thread.h" +#include +#include +#include + +class CThreadPool +{ +public: + typedef std::function Task; + + explicit CThreadPool(); + ~CThreadPool(); + + void start(int32_t numThreads, bool bLoop = false); + void stop(); + + void run(const Task& f); + void flush(); + + int getTaskQueueSize(); + +private: + void runInThread(); + Task take(); + + size_t threads_num_; + std::mutex mutex_; + std::condition_variable cond_; + std::vector> threads_; + std::deque queue_; + bool running_; + bool loop_; +}; + +#endif //__THREADPOOL_H__ diff --git a/mnn_demo/src/CRvcCircleBuffer.cpp b/mnn_demo/src/CRvcCircleBuffer.cpp new file mode 100644 index 0000000..8419c38 --- /dev/null +++ b/mnn_demo/src/CRvcCircleBuffer.cpp @@ -0,0 +1,126 @@ +// +// Created by Administrator on 2023/11/30. +// + +#include +#include +#include "CRvcCircleBuffer.h" + +// 获取到大于等于x的2^n的数值 +// 用上述开辟空间，用于快速计算%, 因为n%x = n & (x - 1) +int32_t rvc_circle_buffer_next_power_2(int32_t x) { + if (x > 0) { + x--; + x |= x >> 1; + x |= x >> 2; + x |= x >> 4; + x |= x >> 8; + x |= x >> 16; + } + return x + 1; +} + +CRvcCircleBuffer::CRvcCircleBuffer(int size) { + m_cap = rvc_circle_buffer_next_power_2(size); + m_st_pos = 0; // 已经写入的数据 + m_ed_pos = 0; // 将要写入的数据 + m_buf = std::shared_ptr(new float[m_cap], std::default_delete()); +} + +CRvcCircleBuffer::~CRvcCircleBuffer() { + +} + +/*******************************对外函数*****************************************************/ + +int CRvcCircleBuffer::size() const { + return (m_ed_pos - m_st_pos + m_cap) & (m_cap - 1); +} + +void CRvcCircleBuffer::reset() +{ + m_st_pos = 0; + m_ed_pos = 0; +} + +void CRvcCircleBuffer::pop(float *buf, int &len) { + int cur_size = size(); + // 数据不够，则只允许取出所有的部分 + if (cur_size < len) + { + len = cur_size; + } + + if (cur_size == 0 || len == 0) + { + return; + } + + // 此时前置条件已经是: len <= cur_size + // 只有三种情况: + // 1. m_st_pos < m_ed_pos: + // copy: (m_st_pos, m_st_pos+len) + // 2. m_st_pos > m_ed_pos: + // 1. copy: m_st_pos, m_st_pos+len + // 2. copy: (m_st_pos, m_cap) + (0, len - (m_cap - m_st_pos)) + // 将前三个归纳为一种，后面单独归纳 +// int tail = std::min(m_cap - m_st_pos, len); + int tail = m_cap - m_st_pos; + if (tail > len) + { + tail = len; + } + int head = len - tail; + memcpy(buf, m_buf.get()+m_st_pos, sizeof(float) * tail); + if (head > 0) + { + memcpy(buf+tail, m_buf.get(), sizeof(float) * head); + } + m_st_pos = (m_st_pos + len) & (m_cap - 1); +} + +void CRvcCircleBuffer::push(float *buf, int len) { + + if(len == 0) + { + return; + } + + int cur_cap = m_cap - size(); + // 放不进去，则开空间 + if (cur_cap < len) + { + int cur_size = size(); + int new_cap = rvc_circle_buffer_next_power_2(m_cap + len); + float* new_buf = new float[new_cap]; + // 拷贝数据到新的空间 + if(m_ed_pos >= m_st_pos) + { + memcpy(new_buf, m_buf.get() + m_st_pos, sizeof(float) * (m_ed_pos - m_st_pos)); + } + else + { + // 拷贝两部分，一部分是st_pos到尾部，另一部分则是0到ed_pos + memcpy(new_buf, m_buf.get()+m_st_pos, sizeof(float) * (m_cap - m_st_pos)); + memcpy(new_buf+(m_cap - m_st_pos), m_buf.get(), sizeof(float) * m_ed_pos); + } + // 更新数据 + m_st_pos = 0; + m_ed_pos = cur_size; + m_cap = new_cap; + m_buf.reset(new_buf); + } + + // 拷贝数据到空间中 + if (m_cap - m_ed_pos > len) + { + memcpy(m_buf.get()+m_ed_pos, buf, sizeof(float) * len); + m_ed_pos += len; + } + else + { + memcpy(m_buf.get()+m_ed_pos, buf, sizeof(float) * (m_cap - m_ed_pos)); + memcpy(m_buf.get(), buf+(m_cap - m_ed_pos), sizeof(float) * (len - (m_cap - m_ed_pos))); + m_ed_pos = len - (m_cap - m_ed_pos); + } +} \ No newline at end of file diff --git a/mnn_demo/src/CRvcCircleBuffer.h b/mnn_demo/src/CRvcCircleBuffer.h new file mode 100644 index 0000000..347141d --- /dev/null +++ b/mnn_demo/src/CRvcCircleBuffer.h @@ -0,0 +1,52 @@ +// +// Created by jianli.yang on 2023/11/30. +// + +#ifndef MNN_DEMO_CRVCCIRCLEBUFFER_H +#define MNN_DEMO_CRVCCIRCLEBUFFER_H + +#include +#include + +class CRvcCircleBuffer { +public: + CRvcCircleBuffer(int size); + + ~CRvcCircleBuffer(); + +public: + /** + * 返回当前的数据长度 + * @return + */ + int size() const; + + /** + * 清空内部所有数据 + */ + void reset(); + + /** + * 给定buf,吐出数据 + * 调用之前可以先调用size，取得内部数据的长度 + * @param buf 目标写入的buf + * @param len 目标长度，调用函数之后，会修改本字段为真正写入的数据长度 + */ + void pop(float *buf, int &len); + + /** + * 塞入数据 + * @param buf + * @param len + */ + void push(float *buf, int len); + +private: + std::shared_ptr m_buf; + int m_cap; + int m_st_pos; + int m_ed_pos; +}; + + +#endif //MNN_DEMO_CRVCCIRCLEBUFFER_H diff --git a/mnn_demo/src/CRvcLiteOnline.cpp b/mnn_demo/src/CRvcLiteOnline.cpp new file mode 100644 index 0000000..3a08e27 --- /dev/null +++ b/mnn_demo/src/CRvcLiteOnline.cpp @@ -0,0 +1,633 @@ +// +// Created by Administrator on 2023/11/29. +// + +#include +#include +#include +#include "CRvcLiteOnline.h" +#include "Hubert.h" +#include "CSynthesizer.h" +#include "espyin-v1.0/ESPYIN.h" +#include "ThreadPool.h" +#include "CRvcCircleBuffer.h" +#include "FfmpegResampler.h" + +// size代表了buf的长度 +void stereo2mono(float *input, int size, float *output) { + for (int i = 0; i < size - 1; i += 2) { + output[i / 2] = (input[i] + input[i + 1]) / 2; + } +} + +void mono2stereo(float *input, int size, float *output) { + for (int i = 0; i < size; i++) { + output[2 * i] = input[i]; + output[2 * i + 1] = input[i]; + } +} + + +CRvcLiteOnline::CRvcLiteOnline() { + init_variable(); + m_init = false; + + // 输入部分需要的变量 + // 要求输入的时间片长度,采样点数 + m_input_block_frame = int(gs_block_time * gs_src_samplerate); + // 推理时额外需要的长度 + m_input_extra_frame = int(gs_extra_time * gs_src_samplerate); + int zc = gs_src_samplerate / 100; // 10ms的点数 + int input_corssfade_frame = int(gs_crossfade_time * gs_src_samplerate); + + // 推理时使用的buffer长度 + m_input_predict_buf_frame = int(ceil((m_input_extra_frame + input_corssfade_frame + m_input_block_frame) + * 1.0 / zc) * zc); + // 推理时使用的buffer + m_input_predict_buf = new float[m_input_predict_buf_frame]; + memset(m_input_predict_buf, 0, sizeof(float) * m_input_predict_buf_frame); + + // 输出部分需要的变量 + m_crossfade_frame = int(gs_crossfade_time * gs_dst_samplerate); + m_output_block_frame = int(gs_block_time * gs_dst_samplerate); + int output_extra_frame = int(gs_extra_time * gs_dst_samplerate); + zc = gs_dst_samplerate / 100; + m_output_cache_buf_frame = int(ceil((m_output_block_frame + m_crossfade_frame + output_extra_frame) + * 1.0 / zc) * zc); + m_output_cache_buf = new float[m_output_cache_buf_frame]; + memset(m_output_cache_buf, 0, sizeof(float) * m_output_cache_buf_frame); + m_crossfade_buf = new float[m_crossfade_frame]; + memset(m_crossfade_buf, 0, sizeof(float) * m_crossfade_frame); + + // 对于模型的输入和输出进行缓存 + // 此处是写死的和模型有关 + m_hubert_ret.resize(1); + m_hubert_ret[0].resize(gs_hubert_frame); + for (int i = 0; i < gs_hubert_frame; i++) { + m_hubert_ret[0][i].resize(gs_hubert_dim); + } + + // synth模型的输入 + m_synth_input.resize(1); + m_synth_input[0].resize(gs_synth_input_frame); + for (int i = 0; i < gs_synth_input_frame; i++) { + m_synth_input[0][i].resize(gs_synth_input_dim); + } + + m_synth_out.resize(1); + m_synth_out[0].resize(1); + m_synth_out[0][0].resize(gs_synth_output_frame); +} + +CRvcLiteOnline::~CRvcLiteOnline() { + uninit(); +} + +/**********************************对内函数*********************************************/ +void CRvcLiteOnline::uninit() { + if (m_input_predict_buf != NULL) { + delete[] m_input_predict_buf; + m_input_predict_buf = NULL; + } + if (m_output_cache_buf != NULL) { + delete[] m_output_cache_buf; + m_output_cache_buf = NULL; + } + if (m_crossfade_buf != NULL) { + delete[] m_crossfade_buf; + m_crossfade_buf = NULL; + } + init_variable(); +} + +void CRvcLiteOnline::get_pyin_f0() { + for (int i = 0; i < m_input_predict_buf_frame; i += 160) { + m_es_pyin->process(m_input_predict_buf + i); + } + m_f0_data.clear(); + ESFeatureSet feats = m_es_pyin->getRemainingFeatures(); + if (!feats.empty()) { + m_f0_data.resize(feats[4].size()); + for (size_t i = 0; i < feats[4].size(); ++i) { + // JL_DEBUG + m_f0_data[i] = feats[4][i].values[0]; + if (m_f0_data[i] < 0) { + m_f0_data[i] = 0; + } + } + } + m_es_pyin->reset(); + get_f0_post(); +} + +void CRvcLiteOnline::get_f0_post() { + int f0_min = 50; + int f0_max = 1100; + float f0_mel_min = 1127 * log2(1 + f0_min * 1.0 / 700); + float f0_mel_max = 1127 * log2(1 + f0_max * 1.0 / 700); + m_f0_coarse_data.clear(); + m_f0_coarse_data.resize(m_f0_data.size()); + for (int i = 0; i < m_f0_data.size(); i++) { + float f0_mel = 1127 * log2(1 + m_f0_data[i] / 700); + if (f0_mel > 0) { + f0_mel = (f0_mel - f0_mel_min) * 254.f / (f0_mel_max - f0_mel_min) + 1; + } + if (f0_mel <= 1) { + f0_mel = 1; + } else if (f0_mel > 255) { + f0_mel = 255; + } + m_f0_coarse_data[i] = float(int(f0_mel + 0.5)); + } +} + +void CRvcLiteOnline::init_variable() { + m_init = false; + // 缓存使用的数据 + // 要求输入的时间片长度,采样点数 + m_input_block_frame = 0; + m_input_extra_frame = 0; + m_input_predict_buf_frame = 0; + m_input_predict_buf = nullptr; + + m_f0_data.clear(); + m_f0_coarse_data.clear(); + + m_crossfade_frame = 0; + m_output_block_frame = 0; + m_output_cache_buf_frame = 0; + m_crossfade_buf = nullptr; + m_output_cache_buf = nullptr; + + // 各个实例的返回结果 + m_hubert_ret.clear(); + m_synth_input.clear(); + m_synth_out.clear(); +} + +/**********************************对外函数*********************************************/ +int CRvcLiteOnline::init(const char *hubert_model_path, const char *synth_model_path) { + if (m_init) { + return ERR_RVC_LITE_REINIT; + } + + m_hubert_inst = std::make_shared(); + m_synthesizer_inst = std::make_shared(); + m_hubert_inst->init(hubert_model_path); + m_synthesizer_inst->init(synth_model_path); + // 要求stepSize必须是2^n + m_es_pyin = std::make_shared(16000, 160, 1024, 50, 1100); + + m_init = true; + return ERR_RVC_LITE_SUCCESS; +} + +int CRvcLiteOnline::switch_synth_model(const char *synth_model_path) { + if (!m_init) { + return ERR_RVC_LITE_NOT_INIT; + } + + m_synthesizer_inst = std::make_shared(); + m_synthesizer_inst->init(synth_model_path); + return ERR_RVC_LITE_SUCCESS; +} + + +void CRvcLiteOnline::reset() { + memset(m_input_predict_buf, 0, sizeof(float) * m_input_predict_buf_frame); + memset(m_crossfade_buf, 0, sizeof(float) * m_crossfade_frame); + memset(m_output_cache_buf, 0, sizeof(float) * m_output_cache_buf_frame); +} + +int CRvcLiteOnline::process_block(float *in_buf, int in_len, float *out_buf, int out_len) { + if (!m_init) { + return ERR_RVC_LITE_NOT_INIT; + } + + // 剔除尾部的block的数据 + memcpy(m_input_predict_buf, m_input_predict_buf + in_len, + sizeof(float) * (m_input_predict_buf_frame - in_len)); + // 向尾部填充in_buf的数据 + memcpy(m_input_predict_buf + (m_input_predict_buf_frame - in_len), in_buf, + sizeof(float) * in_len); + + // 提取f0特征序列 + struct timeval start; + struct timeval end; + gettimeofday(&start, NULL); + get_pyin_f0(); + gettimeofday(&end, NULL); + LOGE("CRvcLiteOnline", "get pyin sp = %f ms\n", + (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0); + + // 推理hubert + gettimeofday(&start, NULL); + m_hubert_inst->process(m_input_predict_buf, m_hubert_ret); + gettimeofday(&end, NULL); + LOGE("CRvcLiteOnline", "m_hubert_inst sp = %f ms\n", + (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0); + + // 合成语音 + for (int i = 0; i < gs_synth_input_frame; i++) { + // 拷贝数据 1,gs_hubert_frame,258 + for (int j = 0; j < gs_hubert_dim; j++) { + m_synth_input[0][i][j] = m_hubert_ret[0][i][j]; + } + m_synth_input[0][i][256] = m_f0_coarse_data[i]; + m_synth_input[0][i][257] = m_f0_data[i]; + } + gettimeofday(&start, NULL); + m_synthesizer_inst->process(m_synth_input, m_synth_out); + gettimeofday(&end, NULL); + LOGE("CRvcLiteOnline", "m_synthesizer_inst sp = %f ms\n", + (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0); + + // 将结果全部放到缓存中 + memcpy(m_output_cache_buf, m_output_cache_buf + gs_synth_output_frame, + sizeof(float) * (m_output_cache_buf_frame - gs_synth_output_frame)); + memcpy(m_output_cache_buf + (m_output_cache_buf_frame - gs_synth_output_frame), + m_synth_out[0][0].data(), sizeof(float) * gs_synth_output_frame); + + int start_pos = m_output_cache_buf_frame - m_crossfade_frame - out_len; + memcpy(out_buf, m_output_cache_buf + start_pos, sizeof(float) * out_len); + // 对头部数据做fade_in以及fadeout + for (int i = 0; i < m_crossfade_frame; i++) { + float rate = float(i * 1.f / m_crossfade_frame); + out_buf[i] = rate * out_buf[i] + m_crossfade_buf[i] * (1 - rate); + } + memcpy(m_crossfade_buf, m_output_cache_buf + (m_output_cache_buf_frame - m_crossfade_frame), + sizeof(float) * m_crossfade_frame); + return 0; +} + +int CRvcLiteOnline::get_latency_ms() { + return gs_crossfade_time * 1000; +} + + + +/*******************************对内的类**************************************/ +CResample::CResample() +{ + m_resample_inst = nullptr; +} + +CResample::~CResample() +{ + +} + +int CResample::init(int in_samplerate, int out_samplerate, int in_channel, int out_channel) +{ + // 只是通道数不一致时走自驱逻辑 + m_in_channel = in_channel; + m_out_channel = out_channel; + if (in_samplerate == out_samplerate && in_channel != out_channel) { + m_resample_inst = nullptr; + } + else { + m_resample_inst = std::make_shared(); + return m_resample_inst->init(in_samplerate, out_samplerate, in_channel, out_channel); + } + return ERR_RVC_LITE_SUCCESS; +} + +int CResample::get_out_samples(int num) +{ + if (m_resample_inst) + { + return m_resample_inst->get_out_samples(num); + } + return num; +} + +void CResample::reset() +{ + if (m_resample_inst) + { + return m_resample_inst->reset(); + } +} + +int CResample::get_latency() +{ + if (m_resample_inst) + { + return m_resample_inst->get_latency(); + } + return 0; +} + +int CResample::resample(float *in_buf, int in_num, float *out_buf, int &out_num) { + if (m_resample_inst) { + return m_resample_inst->resample(in_buf, in_num, out_buf, out_num); + } + + if (m_in_channel == 2 && m_out_channel == 1) { + if (out_num < in_num) { + return ERR_RVC_LITE_RT_RESAMPLE_OUTBUF_SHORT; + } + stereo2mono(in_buf, in_num, out_buf); + return ERR_RVC_LITE_SUCCESS; + } + + if (m_in_channel == 1 && m_out_channel == 2) { + if (out_num < in_num) { + return ERR_RVC_LITE_RT_RESAMPLE_OUTBUF_SHORT; + } + mono2stereo(in_buf, in_num, out_buf); + return ERR_RVC_LITE_SUCCESS; + } + return ERR_RVC_LITE_SUCCESS; +} + +/*******************************对外的类***************************************/ + + + + +/*******************************对内函数***************************************/ +void CRvcLiteOnlineRealTime::init_variable() { + m_init = false; + m_rvc_stop = true; + m_sample_rate = 44100; + m_channel = 1; + m_synth_path = ""; + m_new_synth_path = ""; +} + +/*******************************对外函数***************************************/ +CRvcLiteOnlineRealTime::CRvcLiteOnlineRealTime() { + init_variable(); +} + +CRvcLiteOnlineRealTime::~CRvcLiteOnlineRealTime() { + uninit(); +} + +int CRvcLiteOnlineRealTime::init(const char *hubert_model_path, const char *synth_model_path, int sample_rate, + int channel) { + if (m_init) { + return ERR_RVC_LITE_RT_REINIT; + } + + if (sample_rate < 16000) { + return ERR_RVC_LITE_RT_INPUT_SAMPLE_ERR; + } + init_variable(); + m_sample_rate = sample_rate; + m_channel = channel; + m_synth_path = synth_model_path; + m_new_synth_path = synth_model_path; + int output_one_sec_number = m_sample_rate * m_channel; // 临时使用的数据 + CThreadPool::Task task = std::bind(&CRvcLiteOnlineRealTime::rvc_process, this); + + m_rvc_inst = std::make_shared(); + int err = m_rvc_inst->init(hubert_model_path, synth_model_path); + if (ERR_RVC_LITE_SUCCESS != err) { + goto exit; + } + + + // 重采样部分 + m_resample_queue = std::make_shared(sample_rate * 3 * m_channel); + m_resample16 = std::make_shared(); + err = m_resample16->init(m_sample_rate, gs_src_samplerate, m_channel, 1); + if (ERR_RVC_LITE_SUCCESS != err) { + goto exit; + } + + m_resample2src = std::make_shared(); + err = m_resample2src->init(gs_dst_samplerate, m_sample_rate, 1, m_channel); + if (ERR_RVC_LITE_SUCCESS != err) { + goto exit; + } + m_resample_buf_max_len = 2048; // 此时空间最大是2048，保证不超即可 + m_resample_in_buf = std::shared_ptr(new float[m_resample_buf_max_len], std::default_delete()); + m_resample_out_buf = std::shared_ptr(new float[m_resample_buf_max_len], std::default_delete()); + + // 核心处理部分 + m_input_tmp_buf_len = gs_src_samplerate; + m_output_tmp_buf_len = gs_dst_samplerate; + m_input_tmp_buf = std::shared_ptr(new float[m_input_tmp_buf_len], std::default_delete()); + m_output_tmp_buf = std::shared_ptr(new float[m_output_tmp_buf_len], std::default_delete()); + memset(m_input_tmp_buf.get(), 0, sizeof(float) * m_input_tmp_buf_len); + memset(m_output_tmp_buf.get(), 0, sizeof(float) * m_output_tmp_buf_len); + + // 循环buffer + m_input_queue = std::make_shared(m_input_tmp_buf_len * 3); + // 对外的是目标的采样率和通道数的数据 + m_out_queue = std::make_shared(output_one_sec_number * 3); + + // 提前塞入两组，保证延迟稳定在2s + for (int i = 0; i < 2; i++) { + // 塞入1s数据 + for (int j = 0; j < output_one_sec_number / m_output_tmp_buf_len; j++) { + m_out_queue->push(m_output_tmp_buf.get(), m_output_tmp_buf_len); + } + m_out_queue->push(m_output_tmp_buf.get(), output_one_sec_number % m_output_tmp_buf_len); + } + + // 开始处理线程 + m_thread_pool = std::make_shared(); + m_thread_pool->start(1); + m_rvc_stop = false; + m_thread_pool->run(task); + + m_init = true; + exit: + if (ERR_RVC_LITE_SUCCESS != err) { + m_init = true; + uninit(); + } + return err; +} + +int CRvcLiteOnlineRealTime::switch_synth(const char *synth_model_path) { + if (!m_init) { + return ERR_RVC_LITE_RT_NOT_INIT; + } + + { + std::unique_lock lock(m_rvc_mutex); + m_new_synth_path = synth_model_path; + } + return ERR_RVC_LITE_SUCCESS; +} + + +int CRvcLiteOnlineRealTime::process(float *in_buf, int in_len, float *out_buf, int out_len) { + if (!m_init) { + return ERR_RVC_LITE_RT_NOT_INIT; + } + + // 写入数据 + { + std::unique_lock lock(m_rvc_mutex); + m_resample_queue->push(in_buf, in_len); + m_rvc_cond.notify_all(); + } + memset(out_buf, 0, sizeof(float) * out_len); + int tmp_out_len = out_len; + + // 获取数据 + { + std::unique_lock lock(m_rvc_mutex); + m_out_queue->pop(out_buf, tmp_out_len); + } + + if (tmp_out_len != out_len) { + return ERR_RVC_LITE_RT_NOT_ENOUGH_DATA; + } + return ERR_RVC_LITE_SUCCESS; +} + +void CRvcLiteOnlineRealTime::reset() { + if (!m_init) { + return; + } + + { + std::unique_lock lock(m_rvc_mutex); + m_resample_queue->reset(); + m_resample16->reset(); + m_resample2src->reset(); + m_input_queue->reset(); + m_out_queue->reset(); + m_rvc_inst->reset(); + } +} + +void CRvcLiteOnlineRealTime::flush(float *&out_buf, int &len) { + // 将内部的所有的数据吐出来 + /** + * 先停止 + */ + stop(); + + // 先将重采样的部分走完 + int resample_in_len = 0; + int resample_out_len = 0; +// m_resample_queue->push(m_resample_in_buf.get(), m_resample_buf_max_len); + while (m_resample_queue->size() > 0) { + resample_in_len = m_resample_buf_max_len; + m_resample_queue->pop(m_resample_in_buf.get(), resample_in_len); + // 输入的数据需要考虑channel + resample_out_len = m_resample16->get_out_samples(resample_in_len / m_channel); + m_resample16->resample(m_resample_in_buf.get(), resample_in_len / m_channel, m_resample_out_buf.get(), + resample_out_len); + // 输出是16k单声道，不需要考虑 + m_input_queue->push(m_resample_out_buf.get(), resample_out_len); + } + memset(m_input_tmp_buf.get(), 0, sizeof(float) * m_input_tmp_buf_len); + int add_size = m_input_tmp_buf_len - m_input_queue->size() % m_input_tmp_buf_len; + if (add_size != 0 && add_size < m_input_tmp_buf_len) { + m_input_queue->push(m_input_tmp_buf.get(), add_size); + } + int num = m_input_queue->size() / m_input_tmp_buf_len; + for (int i = 0; i < num; i++) { + rvc_process_step(); + } + + // 将所有数据拷贝出来 + len = m_out_queue->size(); + out_buf = new float[len]; + m_out_queue->pop(out_buf, len); +} + +int CRvcLiteOnlineRealTime::get_latency_ms() { + return m_rvc_inst->get_latency_ms() + 2000; +} + +/*******************************对内函数***************************************/ +void CRvcLiteOnlineRealTime::uninit() { + if (!m_init) { + return; + } + stop(); +} + +void CRvcLiteOnlineRealTime::stop() { + // 释放thread_pool的数据,先通知一下rvc_process,防止是在等待中 + m_rvc_stop = true; + if (m_thread_pool) { + m_rvc_cond.notify_all(); + m_thread_pool->stop(); + } +} + +void CRvcLiteOnlineRealTime::rvc_process_step() { + + struct timeval start; + struct timeval end; + int sample_out_len = 0; + // 开始处理 + if (m_input_queue->size() < m_input_tmp_buf_len) { + return; + } + gettimeofday(&start, NULL); + m_input_queue->pop(m_input_tmp_buf.get(), m_input_tmp_buf_len); + m_rvc_inst->process_block(m_input_tmp_buf.get(), m_input_tmp_buf_len, + m_output_tmp_buf.get(), m_output_tmp_buf_len); + gettimeofday(&end, NULL); + LOGD("RvcLite", "rvc_process process sp %f ms", + (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0); + + // 重采样 + // 考虑到此处采样率变大，但是最多也不到两倍，但是通道数有可能扩展到两倍，所以按照1/4进行设置 + gettimeofday(&start, NULL); + int step = m_resample_buf_max_len / 4; + for (int i = 0; i < m_output_tmp_buf_len; i += step) { + if (i + step > m_output_tmp_buf_len) { + step = m_output_tmp_buf_len - i; + } + // 此时的输入是单声道，采样点数量和总长度一致 + sample_out_len = m_resample2src->get_out_samples(step); + m_resample2src->resample(m_output_tmp_buf.get() + i, step, m_resample_out_buf.get(), sample_out_len); + { + std::unique_lock lock(m_rvc_mutex); + m_out_queue->push(m_resample_out_buf.get(), sample_out_len * m_channel); + } + } + gettimeofday(&end, NULL); + LOGD("RvcLite", "rvc_process re_resample sp %f ms", + (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0); + printf("finish ...\n"); +} + +void CRvcLiteOnlineRealTime::rvc_process() { + int sample_in_len; + int sample_out_len = 0; + while (!m_rvc_stop) { + { + // 重采样 + std::unique_lock lock(m_rvc_mutex); + if (m_resample_queue->size() < m_resample_buf_max_len) { + // 睡眠前检查下情况 + if (m_rvc_stop) { + return; + } + m_rvc_cond.wait(lock); + continue; + } + sample_in_len = m_resample_buf_max_len; + m_resample_queue->pop(m_resample_in_buf.get(), sample_in_len); + } + + // 重采样到16k,此处采样率变低，所以不会出现sample_out_len > sample_in_len的情况 + sample_out_len = m_resample16->get_out_samples(sample_in_len / m_channel); + m_resample16->resample(m_resample_in_buf.get(), sample_in_len / m_channel, m_resample_out_buf.get(), + sample_out_len); + m_input_queue->push(m_resample_out_buf.get(), sample_out_len); + + // 开始变声 + if (m_synth_path != m_new_synth_path) { + { + std::unique_lock lock(m_rvc_mutex); + m_synth_path = m_new_synth_path; + } + m_rvc_inst->switch_synth_model(m_new_synth_path.c_str()); + } + rvc_process_step(); + } +} \ No newline at end of file diff --git a/mnn_demo/src/CSynthesizer.cpp b/mnn_demo/src/CSynthesizer.cpp new file mode 100644 index 0000000..2346fe9 --- /dev/null +++ b/mnn_demo/src/CSynthesizer.cpp @@ -0,0 +1,73 @@ +// +// Created by ZIHAO GUO on 2023/11/16. +// + +#include "CSynthesizer.h" +#include +#include + +CSynthesizer::CSynthesizer() = default; + +CSynthesizer::~CSynthesizer() { + uninit(); +} + +int CSynthesizer::init(const char *model_path) { + m_config.type = MNN_FORWARD_CPU; + m_runtime_info = MNN::Interpreter::createRuntime({m_config}); + m_net = std::shared_ptr(MNN::Interpreter::createFromFile(model_path)); + m_session = m_net->createSession(m_config, m_runtime_info); + m_input_tensor = m_net->getSessionInput(m_session, nullptr); + return 0; +} + +float CSynthesizer::process(std::vector>> &contentvec_input, std::vector>> &ret) { + std::vector input_dims{1, 205, 258}; + auto input_tensor = MNN::Tensor::create(input_dims, nullptr, MNN::Tensor::CAFFE); + auto input_data = input_tensor->host(); + auto input_size = input_tensor->size(); +// ::memcpy(input_data, contentvec_input.data(), input_size); + for (int i = 0; i < 205; i++) + { + std::memcpy(input_data+i*258, contentvec_input[0][i].data(), input_size / 205); + } + m_input_tensor->copyFromHostTensor(input_tensor); + delete input_tensor; + + struct timeval start; + struct timeval end; + gettimeofday(&start, NULL); + m_net->runSession(m_session); + gettimeofday(&end, NULL); + float time = (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0; + + auto output_tensor = m_net->getSessionOutput(m_session, nullptr); + std::vector shape = output_tensor->shape(); + auto output = MNN::Tensor::create(shape, nullptr, MNN::Tensor::CAFFE); + auto output_data = output->host(); + auto output_size = output->size(); + output_tensor->copyToHostTensor(output); + for (int i = 0; i < shape[0]; i++) + { + for (int j = 0; j < shape[1]; j++) + { + for (int k = 0; k < shape[2]; k++) + { + ret[i][j][k] = *(output_data + i * 35840 + k); + } + } + } + return time; +} + +void CSynthesizer::uninit() { + if (m_net != nullptr) + { + m_net->releaseModel(); + } + m_net = nullptr; + m_session = nullptr; + m_input_tensor = nullptr; +} + + diff --git a/mnn_demo/src/CSynthesizer.h b/mnn_demo/src/CSynthesizer.h new file mode 100644 index 0000000..64976de --- /dev/null +++ b/mnn_demo/src/CSynthesizer.h @@ -0,0 +1,33 @@ +// +// Created by ZIHAO GUO on 2023/11/16. +// + +#ifndef MNN_DEMO_CSYNTHESIZER_H +#define MNN_DEMO_CSYNTHESIZER_H + +#include "Interpreter.hpp" +#include "Tensor.hpp" +#include "MNNDefine.h" + +class CSynthesizer { +public: + CSynthesizer(); + ~CSynthesizer(); + +public: + int init(const char * model_path); + float process(std::vector>> & contentvec_input, std::vector>> & ret); + +private: + void uninit(); + +private: + MNN::RuntimeInfo m_runtime_info; + MNN::ScheduleConfig m_config; + std::shared_ptr m_net = nullptr; + MNN::Session * m_session = nullptr; + MNN::Tensor * m_input_tensor = nullptr; +}; + + +#endif //MNN_DEMO_CSYNTHESIZER_H diff --git a/mnn_demo/src/Hubert.cpp b/mnn_demo/src/Hubert.cpp new file mode 100644 index 0000000..d704de2 --- /dev/null +++ b/mnn_demo/src/Hubert.cpp @@ -0,0 +1,75 @@ +// +// Created by ZIHAO GUO on 2023/11/16. +// + +#include "Hubert.h" +#include +#include +#include +#include + +Hubert::Hubert() = default; + +Hubert::~Hubert() { + uninit(); +} + +int Hubert::init(const char *model_path) { + m_config.type = MNN_FORWARD_CPU; + m_runtime_info = MNN::Interpreter::createRuntime({m_config}); + m_net = std::shared_ptr(MNN::Interpreter::createFromFile(model_path)); + m_session = m_net->createSession(m_config, m_runtime_info); + m_input_tensor = m_net->getSessionInput(m_session, nullptr); + return 0; +} + + +float Hubert::process(float* hubert_input, std::vector>> & ret) { + std::vector input_dims{1, 33280}; + auto input_tensor = MNN::Tensor::create(input_dims, nullptr, MNN::Tensor::CAFFE); + auto input_data = input_tensor->host(); + auto input_size = input_tensor->size(); + std::memcpy(input_data, hubert_input, input_size); + m_input_tensor->copyFromHostTensor(input_tensor); + delete input_tensor; + +// m_net->resizeTensor(m_input_tensor, input_dims); +// m_net->resizeSession(m_session); + + struct timeval start; + struct timeval end; + gettimeofday(&start, NULL); + m_net->runSession(m_session); + + gettimeofday(&end, NULL); + float time = (end.tv_sec - start.tv_sec) * 1000.0 + (end.tv_usec - start.tv_usec) / 1000.0; + + auto output_tensor = m_net->getSessionOutput(m_session, nullptr); + std::vector shape = output_tensor->shape(); + auto output = MNN::Tensor::create(shape, nullptr, MNN::Tensor::CAFFE); + auto output_data = output->host(); + auto output_size = output->size(); + output_tensor->copyToHostTensor(output); + for (int i = 0; i < shape[0]; i++) + { + for (int j = 0; j < shape[1]; j++) + { + for (int k = 0; k < shape[2]; k++) + { + ret[i][j][k] = *(output_data + j * 256 + k); + } + } + } + return time; +} + + +void Hubert::uninit() { + if (m_net != nullptr) + { + m_net->releaseModel(); + } + m_net = nullptr; + m_session = nullptr; + m_input_tensor = nullptr; +} diff --git a/mnn_demo/src/Hubert.h b/mnn_demo/src/Hubert.h new file mode 100644 index 0000000..3064c7d --- /dev/null +++ b/mnn_demo/src/Hubert.h @@ -0,0 +1,33 @@ +// +// Created by ZIHAO GUO on 2023/11/16. +// + +#ifndef MNN_DEMO_HUBERT_H +#define MNN_DEMO_HUBERT_H + +#include "Interpreter.hpp" +#include "Tensor.hpp" +#include "MNNDefine.h" + +class Hubert { +public: + Hubert(); + ~Hubert(); + +public: + int init(const char * model_path); + float process(float* hubert_input, std::vector>> & ret); + +private: + void uninit(); + +private: + MNN::RuntimeInfo m_runtime_info; + MNN::ScheduleConfig m_config; + std::shared_ptr m_net = nullptr; + MNN::Session * m_session = nullptr; + MNN::Tensor * m_input_tensor = nullptr; +}; + + +#endif //MNN_DEMO_HUBERT_H diff --git a/mnn_demo/tests/half.hpp b/mnn_demo/tests/half.hpp new file mode 100644 index 0000000..5b2947a --- /dev/null +++ b/mnn_demo/tests/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; +#endif +#if HALF_ENABLE_CPP11_USER_LITERALS + friend half literal::operator "" _h(long double); +#endif +#endif + }; + +#if HALF_ENABLE_CPP11_USER_LITERALS + namespace literal + { + /// Half literal. + /// While this returns a properly rounded half-precision value, half literals can unfortunately not be constant + /// expressions due to rather involved conversions. So don't expect this to be a literal literal without involving + /// conversion operations at runtime. It is a convenience feature, not a performance optimization. + /// \param value literal value + /// \return half with of given value (possibly rounded) + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half operator "" _h(long double value) { return half(detail::binary, detail::float2half(value)); } + } +#endif + + namespace detail + { + /// Helper class for half casts. + /// This class template has to be specialized for all valid cast arguments to define an appropriate static + /// `cast` member function and a corresponding `type` member denoting its return type. + /// \tparam T destination type + /// \tparam U source type + /// \tparam R rounding mode to use + template struct half_caster {}; + template struct half_caster + { +#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast from non-arithmetic type unsupported"); +#endif + + static half cast(U arg) { return cast_impl(arg, is_float()); }; + + private: + static half cast_impl(U arg, true_type) { return half(binary, float2half(arg)); } + static half cast_impl(U arg, false_type) { return half(binary, int2half(arg)); } + }; + template struct half_caster + { +#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast to non-arithmetic type unsupported"); +#endif + + static T cast(half arg) { return cast_impl(arg, is_float()); } + + private: + static T cast_impl(half arg, true_type) { return half2float(arg.data_); } + static T cast_impl(half arg, false_type) { return half2int(arg.data_); } + }; + template struct half_caster + { + static half cast(half arg) { return arg; } + }; + } +} + +/// Extensions to the C++ standard library. +namespace std +{ + /// Numeric limits for half-precision floats. + /// **See also:** Documentation for [std::numeric_limits](https://en.cppreference.com/w/cpp/types/numeric_limits) + template<> class numeric_limits + { + public: + /// Is template specialization. + static HALF_CONSTEXPR_CONST bool is_specialized = true; + + /// Supports signed values. + static HALF_CONSTEXPR_CONST bool is_signed = true; + + /// Is not an integer type. + static HALF_CONSTEXPR_CONST bool is_integer = false; + + /// Is not exact. + static HALF_CONSTEXPR_CONST bool is_exact = false; + + /// Doesn't provide modulo arithmetic. + static HALF_CONSTEXPR_CONST bool is_modulo = false; + + /// Has a finite set of values. + static HALF_CONSTEXPR_CONST bool is_bounded = true; + + /// IEEE conformant. + static HALF_CONSTEXPR_CONST bool is_iec559 = true; + + /// Supports infinity. + static HALF_CONSTEXPR_CONST bool has_infinity = true; + + /// Supports quiet NaNs. + static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true; + + /// Supports signaling NaNs. + static HALF_CONSTEXPR_CONST bool has_signaling_NaN = true; + + /// Supports subnormal values. + static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present; + + /// Supports no denormalization detection. + static HALF_CONSTEXPR_CONST bool has_denorm_loss = false; + +#if HALF_ERRHANDLING_THROWS + static HALF_CONSTEXPR_CONST bool traps = true; +#else + /// Traps only if [HALF_ERRHANDLING_THROW_...](\ref HALF_ERRHANDLING_THROW_INVALID) is acitvated. + static HALF_CONSTEXPR_CONST bool traps = false; +#endif + + /// Does not support no pre-rounding underflow detection. + static HALF_CONSTEXPR_CONST bool tinyness_before = false; + + /// Rounding mode. + static HALF_CONSTEXPR_CONST float_round_style round_style = half_float::half::round_style; + + /// Significant digits. + static HALF_CONSTEXPR_CONST int digits = 11; + + /// Significant decimal digits. + static HALF_CONSTEXPR_CONST int digits10 = 3; + + /// Required decimal digits to represent all possible values. + static HALF_CONSTEXPR_CONST int max_digits10 = 5; + + /// Number base. + static HALF_CONSTEXPR_CONST int radix = 2; + + /// One more than smallest exponent. + static HALF_CONSTEXPR_CONST int min_exponent = -13; + + /// Smallest normalized representable power of 10. + static HALF_CONSTEXPR_CONST int min_exponent10 = -4; + + /// One more than largest exponent + static HALF_CONSTEXPR_CONST int max_exponent = 16; + + /// Largest finitely representable power of 10. + static HALF_CONSTEXPR_CONST int max_exponent10 = 4; + + /// Smallest positive normal value. + static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); } + + /// Smallest finite value. + static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); } + + /// Largest finite value. + static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); } + + /// Difference between 1 and next representable value. + static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x1400); } + + /// Maximum rounding error in ULP (units in the last place). + static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW + { return half_float::half(half_float::detail::binary, (round_style==std::round_to_nearest) ? 0x3800 : 0x3C00); } + + /// Positive infinity. + static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); } + + /// Quiet NaN. + static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); } + + /// Signaling NaN. + static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); } + + /// Smallest positive subnormal value. + static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); } + }; + +#if HALF_ENABLE_CPP11_HASH + /// Hash function for half-precision floats. + /// This is only defined if C++11 `std::hash` is supported and enabled. + /// + /// **See also:** Documentation for [std::hash](https://en.cppreference.com/w/cpp/utility/hash) + template<> struct hash + { + /// Type of function argument. + typedef half_float::half argument_type; + + /// Function return type. + typedef size_t result_type; + + /// Compute hash function. + /// \param arg half to hash + /// \return hash value + result_type operator()(argument_type arg) const { return hash()(arg.data_&-static_cast(arg.data_!=0x8000)); } + }; +#endif +} + +namespace half_float +{ + /// \anchor compop + /// \name Comparison operators + /// \{ + + /// Comparison for equality. + /// \param x first operand + /// \param y second operand + /// \retval true if operands equal + /// \retval false else + /// \exception FE_INVALID if \a x or \a y is NaN + inline HALF_CONSTEXPR_NOERR bool operator==(half x, half y) + { + return !detail::compsignal(x.data_, y.data_) && (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF)); + } + + /// Comparison for inequality. + /// \param x first operand + /// \param y second operand + /// \retval true if operands not equal + /// \retval false else + /// \exception FE_INVALID if \a x or \a y is NaN + inline HALF_CONSTEXPR_NOERR bool operator!=(half x, half y) + { + return detail::compsignal(x.data_, y.data_) || (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF)); + } + + /// Comparison for less than. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less than \a y + /// \retval false else + /// \exception FE_INVALID if \a x or \a y is NaN + inline HALF_CONSTEXPR_NOERR bool operator<(half x, half y) + { + return !detail::compsignal(x.data_, y.data_) && + ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) < ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)); + } + + /// Comparison for greater than. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater than \a y + /// \retval false else + /// \exception FE_INVALID if \a x or \a y is NaN + inline HALF_CONSTEXPR_NOERR bool operator>(half x, half y) + { + return !detail::compsignal(x.data_, y.data_) && + ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) > ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)); + } + + /// Comparison for less equal. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less equal \a y + /// \retval false else + /// \exception FE_INVALID if \a x or \a y is NaN + inline HALF_CONSTEXPR_NOERR bool operator<=(half x, half y) + { + return !detail::compsignal(x.data_, y.data_) && + ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) <= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)); + } + + /// Comparison for greater equal. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater equal \a y + /// \retval false else + /// \exception FE_INVALID if \a x or \a y is NaN + inline HALF_CONSTEXPR_NOERR bool operator>=(half x, half y) + { + return !detail::compsignal(x.data_, y.data_) && + ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) >= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)); + } + + /// \} + /// \anchor arithmetics + /// \name Arithmetic operators + /// \{ + + /// Identity. + /// \param arg operand + /// \return unchanged operand + inline HALF_CONSTEXPR half operator+(half arg) { return arg; } + + /// Negation. + /// \param arg operand + /// \return negated operand + inline HALF_CONSTEXPR half operator-(half arg) { return half(detail::binary, arg.data_^0x8000); } + + /// Addition. + /// This operation is exact to rounding for all rounding modes. + /// \param x left operand + /// \param y right operand + /// \return sum of half expressions + /// \exception FE_INVALID if \a x and \a y are infinities with different signs or signaling NaNs + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half operator+(half x, half y) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(detail::half2float(x.data_)+detail::half2float(y.data_))); +#else + int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF; + bool sub = ((x.data_^y.data_)&0x8000) != 0; + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : (absy!=0x7C00) ? x.data_ : + (sub && absx==0x7C00) ? detail::invalid() : y.data_); + if(!absx) + return absy ? y : half(detail::binary, (half::round_style==std::round_toward_neg_infinity) ? (x.data_|y.data_) : (x.data_&y.data_)); + if(!absy) + return x; + unsigned int sign = ((sub && absy>absx) ? y.data_ : x.data_) & 0x8000; + if(absy > absx) + std::swap(absx, absy); + int exp = (absx>>10) + (absx<=0x3FF), d = exp - (absy>>10) - (absy<=0x3FF), mx = ((absx&0x3FF)|((absx>0x3FF)<<10)) << 3, my; + if(d < 13) + { + my = ((absy&0x3FF)|((absy>0x3FF)<<10)) << 3; + my = (my>>d) | ((my&((1<(half::round_style==std::round_toward_neg_infinity)<<15); + for(; mx<0x2000 && exp>1; mx<<=1,--exp) ; + } + else + { + mx += my; + int i = mx >> 14; + if((exp+=i) > 30) + return half(detail::binary, detail::overflow(sign)); + mx = (mx>>i) | (mx&i); + } + return half(detail::binary, detail::rounded(sign+((exp-1)<<10)+(mx>>3), (mx>>2)&1, (mx&0x3)!=0)); +#endif + } + + /// Subtraction. + /// This operation is exact to rounding for all rounding modes. + /// \param x left operand + /// \param y right operand + /// \return difference of half expressions + /// \exception FE_INVALID if \a x and \a y are infinities with equal signs or signaling NaNs + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half operator-(half x, half y) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(detail::half2float(x.data_)-detail::half2float(y.data_))); +#else + return x + -y; +#endif + } + + /// Multiplication. + /// This operation is exact to rounding for all rounding modes. + /// \param x left operand + /// \param y right operand + /// \return product of half expressions + /// \exception FE_INVALID if multiplying 0 with infinity or if \a x or \a y is signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half operator*(half x, half y) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(detail::half2float(x.data_)*detail::half2float(y.data_))); +#else + int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -16; + unsigned int sign = (x.data_^y.data_) & 0x8000; + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : + ((absx==0x7C00 && !absy)||(absy==0x7C00 && !absx)) ? detail::invalid() : (sign|0x7C00)); + if(!absx || !absy) + return half(detail::binary, sign); + for(; absx<0x400; absx<<=1,--exp) ; + for(; absy<0x400; absy<<=1,--exp) ; + detail::uint32 m = static_cast((absx&0x3FF)|0x400) * static_cast((absy&0x3FF)|0x400); + int i = m >> 21, s = m & i; + exp += (absx>>10) + (absy>>10) + i; + if(exp > 29) + return half(detail::binary, detail::overflow(sign)); + else if(exp < -11) + return half(detail::binary, detail::underflow(sign)); + return half(detail::binary, detail::fixed2half(m>>i, exp, sign, s)); +#endif + } + + /// Division. + /// This operation is exact to rounding for all rounding modes. + /// \param x left operand + /// \param y right operand + /// \return quotient of half expressions + /// \exception FE_INVALID if dividing 0s or infinities with each other or if \a x or \a y is signaling NaN + /// \exception FE_DIVBYZERO if dividing finite value by 0 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half operator/(half x, half y) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(detail::half2float(x.data_)/detail::half2float(y.data_))); +#else + int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = 14; + unsigned int sign = (x.data_^y.data_) & 0x8000; + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : + (absx==absy) ? detail::invalid() : (sign|((absx==0x7C00) ? 0x7C00 : 0))); + if(!absx) + return half(detail::binary, absy ? sign : detail::invalid()); + if(!absy) + return half(detail::binary, detail::pole(sign)); + for(; absx<0x400; absx<<=1,--exp) ; + for(; absy<0x400; absy<<=1,++exp) ; + detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400; + int i = mx < my; + exp += (absx>>10) - (absy>>10) - i; + if(exp > 29) + return half(detail::binary, detail::overflow(sign)); + else if(exp < -11) + return half(detail::binary, detail::underflow(sign)); + mx <<= 12 + i; + my <<= 1; + return half(detail::binary, detail::fixed2half(mx/my, exp, sign, mx%my!=0)); +#endif + } + + /// \} + /// \anchor streaming + /// \name Input and output + /// \{ + + /// Output operator. + /// This uses the built-in functionality for streaming out floating-point numbers. + /// \param out output stream to write into + /// \param arg half expression to write + /// \return reference to output stream + template std::basic_ostream& operator<<(std::basic_ostream &out, half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return out << detail::half2float(arg.data_); +#else + return out << detail::half2float(arg.data_); +#endif + } + + /// Input operator. + /// This uses the built-in functionality for streaming in floating-point numbers, specifically double precision floating + /// point numbers (unless overridden with [HALF_ARITHMETIC_TYPE](\ref HALF_ARITHMETIC_TYPE)). So the input string is first + /// rounded to double precision using the underlying platform's current floating-point rounding mode before being rounded + /// to half-precision using the library's half-precision rounding mode. + /// \param in input stream to read from + /// \param arg half to read into + /// \return reference to input stream + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + template std::basic_istream& operator>>(std::basic_istream &in, half &arg) + { +#ifdef HALF_ARITHMETIC_TYPE + detail::internal_t f; +#else + double f; +#endif + if(in >> f) + arg.data_ = detail::float2half(f); + return in; + } + + /// \} + /// \anchor basic + /// \name Basic mathematical operations + /// \{ + + /// Absolute value. + /// **See also:** Documentation for [std::fabs](https://en.cppreference.com/w/cpp/numeric/math/fabs). + /// \param arg operand + /// \return absolute value of \a arg + inline HALF_CONSTEXPR half fabs(half arg) { return half(detail::binary, arg.data_&0x7FFF); } + + /// Absolute value. + /// **See also:** Documentation for [std::abs](https://en.cppreference.com/w/cpp/numeric/math/fabs). + /// \param arg operand + /// \return absolute value of \a arg + inline HALF_CONSTEXPR half abs(half arg) { return fabs(arg); } + + /// Remainder of division. + /// **See also:** Documentation for [std::fmod](https://en.cppreference.com/w/cpp/numeric/math/fmod). + /// \param x first operand + /// \param y second operand + /// \return remainder of floating-point division. + /// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN + inline half fmod(half x, half y) + { + unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000; + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : + (absx==0x7C00) ? detail::invalid() : x.data_); + if(!absy) + return half(detail::binary, detail::invalid()); + if(!absx) + return x; + if(absx == absy) + return half(detail::binary, sign); + return half(detail::binary, sign|detail::mod(absx, absy)); + } + + /// Remainder of division. + /// **See also:** Documentation for [std::remainder](https://en.cppreference.com/w/cpp/numeric/math/remainder). + /// \param x first operand + /// \param y second operand + /// \return remainder of floating-point division. + /// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN + inline half remainder(half x, half y) + { + unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000; + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : + (absx==0x7C00) ? detail::invalid() : x.data_); + if(!absy) + return half(detail::binary, detail::invalid()); + if(absx == absy) + return half(detail::binary, sign); + return half(detail::binary, sign^detail::mod(absx, absy)); + } + + /// Remainder of division. + /// **See also:** Documentation for [std::remquo](https://en.cppreference.com/w/cpp/numeric/math/remquo). + /// \param x first operand + /// \param y second operand + /// \param quo address to store some bits of quotient at + /// \return remainder of floating-point division. + /// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN + inline half remquo(half x, half y, int *quo) + { + unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, value = x.data_ & 0x8000; + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : + (absx==0x7C00) ? detail::invalid() : (*quo = 0, x.data_)); + if(!absy) + return half(detail::binary, detail::invalid()); + bool qsign = ((value^y.data_)&0x8000) != 0; + int q = 1; + if(absx != absy) + value ^= detail::mod(absx, absy, &q); + return *quo = qsign ? -q : q, half(detail::binary, value); + } + + /// Fused multiply add. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::fma](https://en.cppreference.com/w/cpp/numeric/math/fma). + /// \param x first operand + /// \param y second operand + /// \param z third operand + /// \return ( \a x * \a y ) + \a z rounded as one operation. + /// \exception FE_INVALID according to operator*() and operator+() unless any argument is a quiet NaN and no argument is a signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding the final addition + inline half fma(half x, half y, half z) + { +#ifdef HALF_ARITHMETIC_TYPE + detail::internal_t fx = detail::half2float(x.data_), fy = detail::half2float(y.data_), fz = detail::half2float(z.data_); + #if HALF_ENABLE_CPP11_CMATH && FP_FAST_FMA + return half(detail::binary, detail::float2half(std::fma(fx, fy, fz))); + #else + return half(detail::binary, detail::float2half(fx*fy+fz)); + #endif +#else + int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, exp = -15; + unsigned int sign = (x.data_^y.data_) & 0x8000; + bool sub = ((sign^z.data_)&0x8000) != 0; + if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00) + return (absx>0x7C00 || absy>0x7C00 || absz>0x7C00) ? half(detail::binary, detail::signal(x.data_, y.data_, z.data_)) : + (absx==0x7C00) ? half(detail::binary, (!absy || (sub && absz==0x7C00)) ? detail::invalid() : (sign|0x7C00)) : + (absy==0x7C00) ? half(detail::binary, (!absx || (sub && absz==0x7C00)) ? detail::invalid() : (sign|0x7C00)) : z; + if(!absx || !absy) + return absz ? z : half(detail::binary, (half::round_style==std::round_toward_neg_infinity) ? (z.data_|sign) : (z.data_&sign)); + for(; absx<0x400; absx<<=1,--exp) ; + for(; absy<0x400; absy<<=1,--exp) ; + detail::uint32 m = static_cast((absx&0x3FF)|0x400) * static_cast((absy&0x3FF)|0x400); + int i = m >> 21; + exp += (absx>>10) + (absy>>10) + i; + m <<= 3 - i; + if(absz) + { + int expz = 0; + for(; absz<0x400; absz<<=1,--expz) ; + expz += absz >> 10; + detail::uint32 mz = static_cast((absz&0x3FF)|0x400) << 13; + if(expz > exp || (expz == exp && mz > m)) + { + std::swap(m, mz); + std::swap(exp, expz); + if(sub) + sign = z.data_ & 0x8000; + } + int d = exp - expz; + mz = (d<23) ? ((mz>>d)|((mz&((static_cast(1)<(half::round_style==std::round_toward_neg_infinity)<<15); + for(; m<0x800000; m<<=1,--exp) ; + } + else + { + m += mz; + i = m >> 24; + m = (m>>i) | (m&i); + exp += i; + } + } + if(exp > 30) + return half(detail::binary, detail::overflow(sign)); + else if(exp < -10) + return half(detail::binary, detail::underflow(sign)); + return half(detail::binary, detail::fixed2half(m, exp-1, sign)); +#endif + } + + /// Maximum of half expressions. + /// **See also:** Documentation for [std::fmax](https://en.cppreference.com/w/cpp/numeric/math/fmax). + /// \param x first operand + /// \param y second operand + /// \return maximum of operands, ignoring quiet NaNs + /// \exception FE_INVALID if \a x or \a y is signaling NaN + inline HALF_CONSTEXPR_NOERR half fmax(half x, half y) + { + return half(detail::binary, (!isnan(y) && (isnan(x) || (x.data_^(0x8000|(0x8000-(x.data_>>15)))) < + (y.data_^(0x8000|(0x8000-(y.data_>>15)))))) ? detail::select(y.data_, x.data_) : detail::select(x.data_, y.data_)); + } + + /// Minimum of half expressions. + /// **See also:** Documentation for [std::fmin](https://en.cppreference.com/w/cpp/numeric/math/fmin). + /// \param x first operand + /// \param y second operand + /// \return minimum of operands, ignoring quiet NaNs + /// \exception FE_INVALID if \a x or \a y is signaling NaN + inline HALF_CONSTEXPR_NOERR half fmin(half x, half y) + { + return half(detail::binary, (!isnan(y) && (isnan(x) || (x.data_^(0x8000|(0x8000-(x.data_>>15)))) > + (y.data_^(0x8000|(0x8000-(y.data_>>15)))))) ? detail::select(y.data_, x.data_) : detail::select(x.data_, y.data_)); + } + + /// Positive difference. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::fdim](https://en.cppreference.com/w/cpp/numeric/math/fdim). + /// \param x first operand + /// \param y second operand + /// \return \a x - \a y or 0 if difference negative + /// \exception FE_... according to operator-(half,half) + inline half fdim(half x, half y) + { + if(isnan(x) || isnan(y)) + return half(detail::binary, detail::signal(x.data_, y.data_)); + return (x.data_^(0x8000|(0x8000-(x.data_>>15)))) <= (y.data_^(0x8000|(0x8000-(y.data_>>15)))) ? half(detail::binary, 0) : (x-y); + } + + /// Get NaN value. + /// **See also:** Documentation for [std::nan](https://en.cppreference.com/w/cpp/numeric/math/nan). + /// \param arg string code + /// \return quiet NaN + inline half nanh(const char *arg) + { + unsigned int value = 0x7FFF; + while(*arg) + value ^= static_cast(*arg++) & 0xFF; + return half(detail::binary, value); + } + + /// \} + /// \anchor exponential + /// \name Exponential functions + /// \{ + + /// Exponential function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::exp](https://en.cppreference.com/w/cpp/numeric/math/exp). + /// \param arg function argument + /// \return e raised to \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half exp(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::exp(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, e = (abs>>10) + (abs<=0x3FF), exp; + if(!abs) + return half(detail::binary, 0x3C00); + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? (0x7C00&((arg.data_>>15)-1U)) : detail::signal(arg.data_)); + if(abs >= 0x4C80) + return half(detail::binary, (arg.data_&0x8000) ? detail::underflow() : detail::overflow()); + detail::uint32 m = detail::multiply64(static_cast((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29); + if(e < 14) + { + exp = 0; + m >>= 14 - e; + } + else + { + exp = m >> (45-e); + m = (m<<(e-14)) & 0x7FFFFFFF; + } + return half(detail::binary, detail::exp2_post(m, exp, (arg.data_&0x8000)!=0, 0, 26)); +#endif + } + + /// Binary exponential. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::exp2](https://en.cppreference.com/w/cpp/numeric/math/exp2). + /// \param arg function argument + /// \return 2 raised to \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half exp2(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::exp2(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, e = (abs>>10) + (abs<=0x3FF), exp = (abs&0x3FF) + ((abs>0x3FF)<<10); + if(!abs) + return half(detail::binary, 0x3C00); + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? (0x7C00&((arg.data_>>15)-1U)) : detail::signal(arg.data_)); + if(abs >= 0x4E40) + return half(detail::binary, (arg.data_&0x8000) ? detail::underflow() : detail::overflow()); + return half(detail::binary, detail::exp2_post( + (static_cast(exp)<<(6+e))&0x7FFFFFFF, exp>>(25-e), (arg.data_&0x8000)!=0, 0, 28)); +#endif + } + + /// Exponential minus one. + /// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for `std::round_to_nearest` + /// and in <1% of inputs for any other rounding mode. + /// + /// **See also:** Documentation for [std::expm1](https://en.cppreference.com/w/cpp/numeric/math/expm1). + /// \param arg function argument + /// \return e raised to \a arg and subtracted by 1 + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half expm1(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::expm1(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000, e = (abs>>10) + (abs<=0x3FF), exp; + if(!abs) + return arg; + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? (0x7C00+(sign>>1)) : detail::signal(arg.data_)); + if(abs >= 0x4A00) + return half(detail::binary, (arg.data_&0x8000) ? detail::rounded(0xBBFF, 1, 1) : detail::overflow()); + detail::uint32 m = detail::multiply64(static_cast((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29); + if(e < 14) + { + exp = 0; + m >>= 14 - e; + } + else + { + exp = m >> (45-e); + m = (m<<(e-14)) & 0x7FFFFFFF; + } + m = detail::exp2(m); + if(sign) + { + int s = 0; + if(m > 0x80000000) + { + ++exp; + m = detail::divide64(0x80000000, m, s); + } + m = 0x80000000 - ((m>>exp)|((m&((static_cast(1)<>exp) : 1; + for(exp+=14; m<0x80000000 && exp; m<<=1,--exp) ; + if(exp > 29) + return half(detail::binary, detail::overflow()); + return half(detail::binary, detail::rounded(sign+(exp<<10)+(m>>21), (m>>20)&1, (m&0xFFFFF)!=0)); +#endif + } + + /// Natural logarithm. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::log](https://en.cppreference.com/w/cpp/numeric/math/log). + /// \param arg function argument + /// \return logarithm of \a arg to base e + /// \exception FE_INVALID for signaling NaN or negative argument + /// \exception FE_DIVBYZERO for 0 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half log(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::log(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp = -15; + if(!abs) + return half(detail::binary, detail::pole(0x8000)); + if(arg.data_ & 0x8000) + return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs >= 0x7C00) + return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); + for(; abs<0x400; abs<<=1,--exp) ; + exp += abs >> 10; + return half(detail::binary, detail::log2_post( + detail::log2(static_cast((abs&0x3FF)|0x400)<<20, 27)+8, exp, 17)); +#endif + } + + /// Common logarithm. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::log10](https://en.cppreference.com/w/cpp/numeric/math/log10). + /// \param arg function argument + /// \return logarithm of \a arg to base 10 + /// \exception FE_INVALID for signaling NaN or negative argument + /// \exception FE_DIVBYZERO for 0 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half log10(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::log10(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp = -15; + if(!abs) + return half(detail::binary, detail::pole(0x8000)); + if(arg.data_ & 0x8000) + return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs >= 0x7C00) + return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); + switch(abs) + { + case 0x4900: return half(detail::binary, 0x3C00); + case 0x5640: return half(detail::binary, 0x4000); + case 0x63D0: return half(detail::binary, 0x4200); + case 0x70E2: return half(detail::binary, 0x4400); + } + for(; abs<0x400; abs<<=1,--exp) ; + exp += abs >> 10; + return half(detail::binary, detail::log2_post( + detail::log2(static_cast((abs&0x3FF)|0x400)<<20, 27)+8, exp, 16)); +#endif + } + + /// Binary logarithm. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::log2](https://en.cppreference.com/w/cpp/numeric/math/log2). + /// \param arg function argument + /// \return logarithm of \a arg to base 2 + /// \exception FE_INVALID for signaling NaN or negative argument + /// \exception FE_DIVBYZERO for 0 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half log2(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::log2(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp = -15, s = 0; + if(!abs) + return half(detail::binary, detail::pole(0x8000)); + if(arg.data_ & 0x8000) + return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs >= 0x7C00) + return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); + if(abs == 0x3C00) + return half(detail::binary, 0); + for(; abs<0x400; abs<<=1,--exp) ; + exp += (abs>>10); + if(!(abs&0x3FF)) + { + unsigned int value = static_cast(exp<0) << 15, m = std::abs(exp) << 6; + for(exp=18; m<0x400; m<<=1,--exp) ; + return half(detail::binary, value+(exp<<10)+m); + } + detail::uint32 ilog = exp, sign = detail::sign_mask(ilog), m = + (((ilog<<27)+(detail::log2(static_cast((abs&0x3FF)|0x400)<<20, 28)>>4))^sign) - sign; + if(!m) + return half(detail::binary, 0); + for(exp=14; m<0x8000000 && exp; m<<=1,--exp) ; + for(; m>0xFFFFFFF; m>>=1,++exp) + s |= m & 1; + return half(detail::binary, detail::fixed2half(m, exp, sign&0x8000, s)); +#endif + } + + /// Natural logarithm plus one. + /// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for `std::round_to_nearest` + /// and in ~1% of inputs for any other rounding mode. + /// + /// **See also:** Documentation for [std::log1p](https://en.cppreference.com/w/cpp/numeric/math/log1p). + /// \param arg function argument + /// \return logarithm of \a arg plus 1 to base e + /// \exception FE_INVALID for signaling NaN or argument <-1 + /// \exception FE_DIVBYZERO for -1 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half log1p(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::log1p(detail::half2float(arg.data_)))); +#else + if(arg.data_ >= 0xBC00) + return half(detail::binary, (arg.data_==0xBC00) ? detail::pole(0x8000) : (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_)); + int abs = arg.data_ & 0x7FFF, exp = -15; + if(!abs || abs >= 0x7C00) + return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; + for(; abs<0x400; abs<<=1,--exp) ; + exp += abs >> 10; + detail::uint32 m = static_cast((abs&0x3FF)|0x400) << 20; + if(arg.data_ & 0x8000) + { + m = 0x40000000 - (m>>-exp); + for(exp=0; m<0x40000000; m<<=1,--exp) ; + } + else + { + if(exp < 0) + { + m = 0x40000000 + (m>>-exp); + exp = 0; + } + else + { + m += 0x40000000 >> exp; + int i = m >> 31; + m >>= i; + exp += i; + } + } + return half(detail::binary, detail::log2_post(detail::log2(m), exp, 17)); +#endif + } + + /// \} + /// \anchor power + /// \name Power functions + /// \{ + + /// Square root. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::sqrt](https://en.cppreference.com/w/cpp/numeric/math/sqrt). + /// \param arg function argument + /// \return square root of \a arg + /// \exception FE_INVALID for signaling NaN and negative arguments + /// \exception FE_INEXACT according to rounding + inline half sqrt(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::sqrt(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp = 15; + if(!abs || arg.data_ >= 0x7C00) + return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_>0x8000) ? detail::invalid() : arg.data_); + for(; abs<0x400; abs<<=1,--exp) ; + detail::uint32 r = static_cast((abs&0x3FF)|0x400) << 10, m = detail::sqrt<20>(r, exp+=abs>>10); + return half(detail::binary, detail::rounded((exp<<10)+(m&0x3FF), r>m, r!=0)); +#endif + } + + /// Inverse square root. + /// This function is exact to rounding for all rounding modes and thus generally more accurate than directly computing + /// 1 / sqrt(\a arg) in half-precision, in addition to also being faster. + /// \param arg function argument + /// \return reciprocal of square root of \a arg + /// \exception FE_INVALID for signaling NaN and negative arguments + /// \exception FE_INEXACT according to rounding + inline half rsqrt(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(detail::internal_t(1)/std::sqrt(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF, bias = 0x4000; + if(!abs || arg.data_ >= 0x7C00) + return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_>0x8000) ? + detail::invalid() : !abs ? detail::pole(arg.data_&0x8000) : 0); + for(; abs<0x400; abs<<=1,bias-=0x400) ; + unsigned int frac = (abs+=bias) & 0x7FF; + if(frac == 0x400) + return half(detail::binary, 0x7A00-(abs>>1)); + if((half::round_style == std::round_to_nearest && (frac == 0x3FE || frac == 0x76C)) || + (half::round_style != std::round_to_nearest && (frac == 0x15A || frac == 0x3FC || frac == 0x401 || frac == 0x402 || frac == 0x67B))) + return pow(arg, half(detail::binary, 0xB800)); + detail::uint32 f = 0x17376 - abs, mx = (abs&0x3FF) | 0x400, my = ((f>>1)&0x3FF) | 0x400, mz = my * my; + int expy = (f>>11) - 31, expx = 32 - (abs>>10), i = mz >> 21; + for(mz=0x60000000-(((mz>>i)*mx)>>(expx-2*expy-i)); mz<0x40000000; mz<<=1,--expy) ; + i = (my*=mz>>10) >> 31; + expy += i; + my = (my>>(20+i)) + 1; + i = (mz=my*my) >> 21; + for(mz=0x60000000-(((mz>>i)*mx)>>(expx-2*expy-i)); mz<0x40000000; mz<<=1,--expy) ; + i = (my*=(mz>>10)+1) >> 31; + return half(detail::binary, detail::fixed2half(my>>i, expy+i+14)); +#endif + } + + /// Cubic root. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::cbrt](https://en.cppreference.com/w/cpp/numeric/math/cbrt). + /// \param arg function argument + /// \return cubic root of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_INEXACT according to rounding + inline half cbrt(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::cbrt(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp = -15; + if(!abs || abs == 0x3C00 || abs >= 0x7C00) + return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; + for(; abs<0x400; abs<<=1, --exp); + detail::uint32 ilog = exp + (abs>>10), sign = detail::sign_mask(ilog), f, m = + (((ilog<<27)+(detail::log2(static_cast((abs&0x3FF)|0x400)<<20, 24)>>4))^sign) - sign; + for(exp=2; m<0x80000000; m<<=1,--exp) ; + m = detail::multiply64(m, 0xAAAAAAAB); + int i = m >> 31, s; + exp += i; + m <<= 1 - i; + if(exp < 0) + { + f = m >> -exp; + exp = 0; + } + else + { + f = (m<> (31-exp); + } + m = detail::exp2(f, (half::round_style==std::round_to_nearest) ? 29 : 26); + if(sign) + { + if(m > 0x80000000) + { + m = detail::divide64(0x80000000, m, s); + ++exp; + } + exp = -exp; + } + return half(detail::binary, (half::round_style==std::round_to_nearest) ? + detail::fixed2half(m, exp+14, arg.data_&0x8000) : + detail::fixed2half((m+0x80)>>8, exp+14, arg.data_&0x8000)); +#endif + } + + /// Hypotenuse function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot). + /// \param x first argument + /// \param y second argument + /// \return square root of sum of squares without internal over- or underflows + /// \exception FE_INVALID if \a x or \a y is signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root + inline half hypot(half x, half y) + { +#ifdef HALF_ARITHMETIC_TYPE + detail::internal_t fx = detail::half2float(x.data_), fy = detail::half2float(y.data_); + #if HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::hypot(fx, fy))); + #else + return half(detail::binary, detail::float2half(std::sqrt(fx*fx+fy*fy))); + #endif +#else + int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, expx = 0, expy = 0; + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx==0x7C00) ? detail::select(0x7C00, y.data_) : + (absy==0x7C00) ? detail::select(0x7C00, x.data_) : detail::signal(x.data_, y.data_)); + if(!absx) + return half(detail::binary, absy ? detail::check_underflow(absy) : 0); + if(!absy) + return half(detail::binary, detail::check_underflow(absx)); + if(absy > absx) + std::swap(absx, absy); + for(; absx<0x400; absx<<=1,--expx) ; + for(; absy<0x400; absy<<=1,--expy) ; + detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400; + mx *= mx; + my *= my; + int ix = mx >> 21, iy = my >> 21; + expx = 2*(expx+(absx>>10)) - 15 + ix; + expy = 2*(expy+(absy>>10)) - 15 + iy; + mx <<= 10 - ix; + my <<= 10 - iy; + int d = expx - expy; + my = (d<30) ? ((my>>d)|((my&((static_cast(1)<(mx+my, expx)); +#endif + } + + /// Hypotenuse function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot). + /// \param x first argument + /// \param y second argument + /// \param z third argument + /// \return square root of sum of squares without internal over- or underflows + /// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root + inline half hypot(half x, half y, half z) + { +#ifdef HALF_ARITHMETIC_TYPE + detail::internal_t fx = detail::half2float(x.data_), fy = detail::half2float(y.data_), fz = detail::half2float(z.data_); + return half(detail::binary, detail::float2half(std::sqrt(fx*fx+fy*fy+fz*fz))); +#else + int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, expx = 0, expy = 0, expz = 0; + if(!absx) + return hypot(y, z); + if(!absy) + return hypot(x, z); + if(!absz) + return hypot(x, y); + if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00) + return half(detail::binary, (absx==0x7C00) ? detail::select(0x7C00, detail::select(y.data_, z.data_)) : + (absy==0x7C00) ? detail::select(0x7C00, detail::select(x.data_, z.data_)) : + (absz==0x7C00) ? detail::select(0x7C00, detail::select(x.data_, y.data_)) : + detail::signal(x.data_, y.data_, z.data_)); + if(absz > absy) + std::swap(absy, absz); + if(absy > absx) + std::swap(absx, absy); + if(absz > absy) + std::swap(absy, absz); + for(; absx<0x400; absx<<=1,--expx) ; + for(; absy<0x400; absy<<=1,--expy) ; + for(; absz<0x400; absz<<=1,--expz) ; + detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400, mz = (absz&0x3FF) | 0x400; + mx *= mx; + my *= my; + mz *= mz; + int ix = mx >> 21, iy = my >> 21, iz = mz >> 21; + expx = 2*(expx+(absx>>10)) - 15 + ix; + expy = 2*(expy+(absy>>10)) - 15 + iy; + expz = 2*(expz+(absz>>10)) - 15 + iz; + mx <<= 10 - ix; + my <<= 10 - iy; + mz <<= 10 - iz; + int d = expy - expz; + mz = (d<30) ? ((mz>>d)|((mz&((static_cast(1)<>1) | (my&1); + if(++expy > expx) + { + std::swap(mx, my); + std::swap(expx, expy); + } + } + d = expx - expy; + my = (d<30) ? ((my>>d)|((my&((static_cast(1)<(mx+my, expx)); +#endif + } + + /// Power function. + /// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.00025% of inputs. + /// + /// **See also:** Documentation for [std::pow](https://en.cppreference.com/w/cpp/numeric/math/pow). + /// \param x base + /// \param y exponent + /// \return \a x raised to \a y + /// \exception FE_INVALID if \a x or \a y is signaling NaN or if \a x is finite an negative and \a y is finite and not integral + /// \exception FE_DIVBYZERO if \a x is 0 and \a y is negative + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half pow(half x, half y) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::pow(detail::half2float(x.data_), detail::half2float(y.data_)))); +#else + int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -15; + if(!absy || x.data_ == 0x3C00) + return half(detail::binary, detail::select(0x3C00, (x.data_==0x3C00) ? y.data_ : x.data_)); + bool is_int = absy >= 0x6400 || (absy>=0x3C00 && !(absy&((1<<(25-(absy>>10)))-1))); + unsigned int sign = x.data_ & (static_cast((absy<0x6800)&&is_int&&((absy>>(25-(absy>>10)))&1))<<15); + if(absx >= 0x7C00 || absy >= 0x7C00) + return half(detail::binary, (absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : + (absy==0x7C00) ? ((absx==0x3C00) ? 0x3C00 : (!absx && y.data_==0xFC00) ? detail::pole() : + (0x7C00&-((y.data_>>15)^(absx>0x3C00)))) : (sign|(0x7C00&((y.data_>>15)-1U)))); + if(!absx) + return half(detail::binary, (y.data_&0x8000) ? detail::pole(sign) : sign); + if((x.data_&0x8000) && !is_int) + return half(detail::binary, detail::invalid()); + if(x.data_ == 0xBC00) + return half(detail::binary, sign|0x3C00); + switch(y.data_) + { + case 0x3800: return sqrt(x); + case 0x3C00: return half(detail::binary, detail::check_underflow(x.data_)); + case 0x4000: return x * x; + case 0xBC00: return half(detail::binary, 0x3C00) / x; + } + for(; absx<0x400; absx<<=1,--exp) ; + detail::uint32 ilog = exp + (absx>>10), msign = detail::sign_mask(ilog), f, m = + (((ilog<<27)+((detail::log2(static_cast((absx&0x3FF)|0x400)<<20)+8)>>4))^msign) - msign; + for(exp=-11; m<0x80000000; m<<=1,--exp) ; + for(; absy<0x400; absy<<=1,--exp) ; + m = detail::multiply64(m, static_cast((absy&0x3FF)|0x400)<<21); + int i = m >> 31; + exp += (absy>>10) + i; + m <<= 1 - i; + if(exp < 0) + { + f = m >> -exp; + exp = 0; + } + else + { + f = (m<> (31-exp); + } + return half(detail::binary, detail::exp2_post(f, exp, ((msign&1)^(y.data_>>15))!=0, sign)); +#endif + } + + /// \} + /// \anchor trigonometric + /// \name Trigonometric functions + /// \{ + + /// Compute sine and cosine simultaneously. + /// This returns the same results as sin() and cos() but is faster than calling each function individually. + /// + /// This function is exact to rounding for all rounding modes. + /// \param arg function argument + /// \param sin variable to take sine of \a arg + /// \param cos variable to take cosine of \a arg + /// \exception FE_INVALID for signaling NaN or infinity + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline void sincos(half arg, half *sin, half *cos) + { +#ifdef HALF_ARITHMETIC_TYPE + detail::internal_t f = detail::half2float(arg.data_); + *sin = half(detail::binary, detail::float2half(std::sin(f))); + *cos = half(detail::binary, detail::float2half(std::cos(f))); +#else + int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15, k; + if(abs >= 0x7C00) + *sin = *cos = half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_)); + else if(!abs) + { + *sin = arg; + *cos = half(detail::binary, 0x3C00); + } + else if(abs < 0x2500) + { + *sin = half(detail::binary, detail::rounded(arg.data_-1, 1, 1)); + *cos = half(detail::binary, detail::rounded(0x3BFF, 1, 1)); + } + else + { + if(half::round_style != std::round_to_nearest) + { + switch(abs) + { + case 0x48B7: + *sin = half(detail::binary, detail::rounded((~arg.data_&0x8000)|0x1D07, 1, 1)); + *cos = half(detail::binary, detail::rounded(0xBBFF, 1, 1)); + return; + case 0x598C: + *sin = half(detail::binary, detail::rounded((arg.data_&0x8000)|0x3BFF, 1, 1)); + *cos = half(detail::binary, detail::rounded(0x80FC, 1, 1)); + return; + case 0x6A64: + *sin = half(detail::binary, detail::rounded((~arg.data_&0x8000)|0x3BFE, 1, 1)); + *cos = half(detail::binary, detail::rounded(0x27FF, 1, 1)); + return; + case 0x6D8C: + *sin = half(detail::binary, detail::rounded((arg.data_&0x8000)|0x0FE6, 1, 1)); + *cos = half(detail::binary, detail::rounded(0x3BFF, 1, 1)); + return; + } + } + std::pair sc = detail::sincos(detail::angle_arg(abs, k), 28); + switch(k & 3) + { + case 1: sc = std::make_pair(sc.second, -sc.first); break; + case 2: sc = std::make_pair(-sc.first, -sc.second); break; + case 3: sc = std::make_pair(-sc.second, sc.first); break; + } + *sin = half(detail::binary, detail::fixed2half((sc.first^-static_cast(sign))+sign)); + *cos = half(detail::binary, detail::fixed2half(sc.second)); + } +#endif + } + + /// Sine function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::sin](https://en.cppreference.com/w/cpp/numeric/math/sin). + /// \param arg function argument + /// \return sine value of \a arg + /// \exception FE_INVALID for signaling NaN or infinity + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half sin(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::sin(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, k; + if(!abs) + return arg; + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs < 0x2900) + return half(detail::binary, detail::rounded(arg.data_-1, 1, 1)); + if(half::round_style != std::round_to_nearest) + switch(abs) + { + case 0x48B7: return half(detail::binary, detail::rounded((~arg.data_&0x8000)|0x1D07, 1, 1)); + case 0x6A64: return half(detail::binary, detail::rounded((~arg.data_&0x8000)|0x3BFE, 1, 1)); + case 0x6D8C: return half(detail::binary, detail::rounded((arg.data_&0x8000)|0x0FE6, 1, 1)); + } + std::pair sc = detail::sincos(detail::angle_arg(abs, k), 28); + detail::uint32 sign = -static_cast(((k>>1)&1)^(arg.data_>>15)); + return half(detail::binary, detail::fixed2half((((k&1) ? sc.second : sc.first)^sign) - sign)); +#endif + } + + /// Cosine function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::cos](https://en.cppreference.com/w/cpp/numeric/math/cos). + /// \param arg function argument + /// \return cosine value of \a arg + /// \exception FE_INVALID for signaling NaN or infinity + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half cos(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::cos(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, k; + if(!abs) + return half(detail::binary, 0x3C00); + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs < 0x2500) + return half(detail::binary, detail::rounded(0x3BFF, 1, 1)); + if(half::round_style != std::round_to_nearest && abs == 0x598C) + return half(detail::binary, detail::rounded(0x80FC, 1, 1)); + std::pair sc = detail::sincos(detail::angle_arg(abs, k), 28); + detail::uint32 sign = -static_cast(((k>>1)^k)&1); + return half(detail::binary, detail::fixed2half((((k&1) ? sc.first : sc.second)^sign) - sign)); +#endif + } + + /// Tangent function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::tan](https://en.cppreference.com/w/cpp/numeric/math/tan). + /// \param arg function argument + /// \return tangent value of \a arg + /// \exception FE_INVALID for signaling NaN or infinity + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half tan(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::tan(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp = 13, k; + if(!abs) + return arg; + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs < 0x2700) + return half(detail::binary, detail::rounded(arg.data_, 0, 1)); + if(half::round_style != std::round_to_nearest) + switch(abs) + { + case 0x658C: return half(detail::binary, detail::rounded((arg.data_&0x8000)|0x07E6, 1, 1)); + case 0x7330: return half(detail::binary, detail::rounded((~arg.data_&0x8000)|0x4B62, 1, 1)); + } + std::pair sc = detail::sincos(detail::angle_arg(abs, k), 30); + if(k & 1) + sc = std::make_pair(-sc.second, sc.first); + detail::uint32 signy = detail::sign_mask(sc.first), signx = detail::sign_mask(sc.second); + detail::uint32 my = (sc.first^signy) - signy, mx = (sc.second^signx) - signx; + for(; my<0x80000000; my<<=1,--exp) ; + for(; mx<0x80000000; mx<<=1,++exp) ; + return half(detail::binary, detail::tangent_post(my, mx, exp, (signy^signx^arg.data_)&0x8000)); +#endif + } + + /// Arc sine. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::asin](https://en.cppreference.com/w/cpp/numeric/math/asin). + /// \param arg function argument + /// \return arc sine value of \a arg + /// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half asin(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::asin(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; + if(!abs) + return arg; + if(abs >= 0x3C00) + return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (abs>0x3C00) ? detail::invalid() : + detail::rounded(sign|0x3E48, 0, 1)); + if(abs < 0x2900) + return half(detail::binary, detail::rounded(arg.data_, 0, 1)); + if(half::round_style != std::round_to_nearest && (abs == 0x2B44 || abs == 0x2DC3)) + return half(detail::binary, detail::rounded(arg.data_+1, 1, 1)); + std::pair sc = detail::atan2_args(abs); + detail::uint32 m = detail::atan2(sc.first, sc.second, (half::round_style==std::round_to_nearest) ? 27 : 26); + return half(detail::binary, detail::fixed2half(m, 14, sign)); +#endif + } + + /// Arc cosine function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::acos](https://en.cppreference.com/w/cpp/numeric/math/acos). + /// \param arg function argument + /// \return arc cosine value of \a arg + /// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half acos(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::acos(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15; + if(!abs) + return half(detail::binary, detail::rounded(0x3E48, 0, 1)); + if(abs >= 0x3C00) + return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (abs>0x3C00) ? detail::invalid() : + sign ? detail::rounded(0x4248, 0, 1) : 0); + std::pair cs = detail::atan2_args(abs); + detail::uint32 m = detail::atan2(cs.second, cs.first, 28); + return half(detail::binary, detail::fixed2half(sign ? (0xC90FDAA2-m) : m, 15, 0, sign)); +#endif + } + + /// Arc tangent function. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::atan](https://en.cppreference.com/w/cpp/numeric/math/atan). + /// \param arg function argument + /// \return arc tangent value of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half atan(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::atan(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; + if(!abs) + return arg; + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? detail::rounded(sign|0x3E48, 0, 1) : detail::signal(arg.data_)); + if(abs <= 0x2700) + return half(detail::binary, detail::rounded(arg.data_-1, 1, 1)); + int exp = (abs>>10) + (abs<=0x3FF); + detail::uint32 my = (abs&0x3FF) | ((abs>0x3FF)<<10); + detail::uint32 m = (exp>15) ? detail::atan2(my<<19, 0x20000000>>(exp-15), (half::round_style==std::round_to_nearest) ? 26 : 24) : + detail::atan2(my<<(exp+4), 0x20000000, (half::round_style==std::round_to_nearest) ? 30 : 28); + return half(detail::binary, detail::fixed2half(m, 14, sign)); +#endif + } + + /// Arc tangent function. + /// This function may be 1 ULP off the correctly rounded exact result in ~0.005% of inputs for `std::round_to_nearest`, + /// in ~0.1% of inputs for `std::round_toward_zero` and in ~0.02% of inputs for any other rounding mode. + /// + /// **See also:** Documentation for [std::atan2](https://en.cppreference.com/w/cpp/numeric/math/atan2). + /// \param y numerator + /// \param x denominator + /// \return arc tangent value + /// \exception FE_INVALID if \a x or \a y is signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half atan2(half y, half x) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::atan2(detail::half2float(y.data_), detail::half2float(x.data_)))); +#else + unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, signx = x.data_ >> 15, signy = y.data_ & 0x8000; + if(absx >= 0x7C00 || absy >= 0x7C00) + { + if(absx > 0x7C00 || absy > 0x7C00) + return half(detail::binary, detail::signal(x.data_, y.data_)); + if(absy == 0x7C00) + return half(detail::binary, (absx<0x7C00) ? detail::rounded(signy|0x3E48, 0, 1) : + signx ? detail::rounded(signy|0x40B6, 0, 1) : + detail::rounded(signy|0x3A48, 0, 1)); + return (x.data_==0x7C00) ? half(detail::binary, signy) : half(detail::binary, detail::rounded(signy|0x4248, 0, 1)); + } + if(!absy) + return signx ? half(detail::binary, detail::rounded(signy|0x4248, 0, 1)) : y; + if(!absx) + return half(detail::binary, detail::rounded(signy|0x3E48, 0, 1)); + int d = (absy>>10) + (absy<=0x3FF) - (absx>>10) - (absx<=0x3FF); + if(d > (signx ? 18 : 12)) + return half(detail::binary, detail::rounded(signy|0x3E48, 0, 1)); + if(signx && d < -11) + return half(detail::binary, detail::rounded(signy|0x4248, 0, 1)); + if(!signx && d < ((half::round_style==std::round_toward_zero) ? -15 : -9)) + { + for(; absy<0x400; absy<<=1,--d) ; + detail::uint32 mx = ((absx<<1)&0x7FF) | 0x800, my = ((absy<<1)&0x7FF) | 0x800; + int i = my < mx; + d -= i; + if(d < -25) + return half(detail::binary, detail::underflow(signy)); + my <<= 11 + i; + return half(detail::binary, detail::fixed2half(my/mx, d+14, signy, my%mx!=0)); + } + detail::uint32 m = detail::atan2( ((absy&0x3FF)|((absy>0x3FF)<<10))<<(19+((d<0) ? d : (d>0) ? 0 : -1)), + ((absx&0x3FF)|((absx>0x3FF)<<10))<<(19-((d>0) ? d : (d<0) ? 0 : 1))); + return half(detail::binary, detail::fixed2half(signx ? (0xC90FDAA2-m) : m, 15, signy, signx)); +#endif + } + + /// \} + /// \anchor hyperbolic + /// \name Hyperbolic functions + /// \{ + + /// Hyperbolic sine. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::sinh](https://en.cppreference.com/w/cpp/numeric/math/sinh). + /// \param arg function argument + /// \return hyperbolic sine value of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half sinh(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::sinh(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp; + if(!abs || abs >= 0x7C00) + return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; + if(abs <= 0x2900) + return half(detail::binary, detail::rounded(arg.data_, 0, 1)); + std::pair mm = detail::hyperbolic_args(abs, exp, (half::round_style==std::round_to_nearest) ? 29 : 27); + detail::uint32 m = mm.first - mm.second; + for(exp+=13; m<0x80000000 && exp; m<<=1,--exp) ; + unsigned int sign = arg.data_ & 0x8000; + if(exp > 29) + return half(detail::binary, detail::overflow(sign)); + return half(detail::binary, detail::fixed2half(m, exp, sign)); +#endif + } + + /// Hyperbolic cosine. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::cosh](https://en.cppreference.com/w/cpp/numeric/math/cosh). + /// \param arg function argument + /// \return hyperbolic cosine value of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half cosh(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::cosh(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp; + if(!abs) + return half(detail::binary, 0x3C00); + if(abs >= 0x7C00) + return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : 0x7C00); + std::pair mm = detail::hyperbolic_args(abs, exp, (half::round_style==std::round_to_nearest) ? 23 : 26); + detail::uint32 m = mm.first + mm.second, i = (~m&0xFFFFFFFF) >> 31; + m = (m>>i) | (m&i) | 0x80000000; + if((exp+=13+i) > 29) + return half(detail::binary, detail::overflow()); + return half(detail::binary, detail::fixed2half(m, exp)); +#endif + } + + /// Hyperbolic tangent. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::tanh](https://en.cppreference.com/w/cpp/numeric/math/tanh). + /// \param arg function argument + /// \return hyperbolic tangent value of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half tanh(half arg) + { +#ifdef HALF_ARITHMETIC_TYPE + return half(detail::binary, detail::float2half(std::tanh(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp; + if(!abs) + return arg; + if(abs >= 0x7C00) + return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_-0x4000)); + if(abs >= 0x4500) + return half(detail::binary, detail::rounded((arg.data_&0x8000)|0x3BFF, 1, 1)); + if(abs < 0x2700) + return half(detail::binary, detail::rounded(arg.data_-1, 1, 1)); + if(half::round_style != std::round_to_nearest && abs == 0x2D3F) + return half(detail::binary, detail::rounded(arg.data_-3, 0, 1)); + std::pair mm = detail::hyperbolic_args(abs, exp, 27); + detail::uint32 my = mm.first - mm.second - (half::round_style!=std::round_to_nearest), mx = mm.first + mm.second, i = (~mx&0xFFFFFFFF) >> 31; + for(exp=13; my<0x80000000; my<<=1,--exp) ; + mx = (mx>>i) | 0x80000000; + return half(detail::binary, detail::tangent_post(my, mx, exp-i, arg.data_&0x8000)); +#endif + } + + /// Hyperbolic area sine. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::asinh](https://en.cppreference.com/w/cpp/numeric/math/asinh). + /// \param arg function argument + /// \return area sine value of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half asinh(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::asinh(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF; + if(!abs || abs >= 0x7C00) + return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; + if(abs <= 0x2900) + return half(detail::binary, detail::rounded(arg.data_-1, 1, 1)); + if(half::round_style != std::round_to_nearest) + switch(abs) + { + case 0x32D4: return half(detail::binary, detail::rounded(arg.data_-13, 1, 1)); + case 0x3B5B: return half(detail::binary, detail::rounded(arg.data_-197, 1, 1)); + } + return half(detail::binary, detail::area(arg.data_)); +#endif + } + + /// Hyperbolic area cosine. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::acosh](https://en.cppreference.com/w/cpp/numeric/math/acosh). + /// \param arg function argument + /// \return area cosine value of \a arg + /// \exception FE_INVALID for signaling NaN or arguments <1 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half acosh(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::acosh(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF; + if((arg.data_&0x8000) || abs < 0x3C00) + return half(detail::binary, (abs<=0x7C00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs == 0x3C00) + return half(detail::binary, 0); + if(arg.data_ >= 0x7C00) + return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; + return half(detail::binary, detail::area(arg.data_)); +#endif + } + + /// Hyperbolic area tangent. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::atanh](https://en.cppreference.com/w/cpp/numeric/math/atanh). + /// \param arg function argument + /// \return area tangent value of \a arg + /// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1 + /// \exception FE_DIVBYZERO for +/-1 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half atanh(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::atanh(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF, exp = 0; + if(!abs) + return arg; + if(abs >= 0x3C00) + return half(detail::binary, (abs==0x3C00) ? detail::pole(arg.data_&0x8000) : (abs<=0x7C00) ? detail::invalid() : detail::signal(arg.data_)); + if(abs < 0x2700) + return half(detail::binary, detail::rounded(arg.data_, 0, 1)); + detail::uint32 m = static_cast((abs&0x3FF)|((abs>0x3FF)<<10)) << ((abs>>10)+(abs<=0x3FF)+6), my = 0x80000000 + m, mx = 0x80000000 - m; + for(; mx<0x80000000; mx<<=1,++exp) ; + int i = my >= mx, s; + return half(detail::binary, detail::log2_post(detail::log2( + (detail::divide64(my>>i, mx, s)+1)>>1, 27)+0x10, exp+i-1, 16, arg.data_&0x8000)); +#endif + } + + /// \} + /// \anchor special + /// \name Error and gamma functions + /// \{ + + /// Error function. + /// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs. + /// + /// **See also:** Documentation for [std::erf](https://en.cppreference.com/w/cpp/numeric/math/erf). + /// \param arg function argument + /// \return error function value of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half erf(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::erf(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF; + if(!abs || abs >= 0x7C00) + return (abs>=0x7C00) ? half(detail::binary, (abs==0x7C00) ? (arg.data_-0x4000) : detail::signal(arg.data_)) : arg; + if(abs >= 0x4200) + return half(detail::binary, detail::rounded((arg.data_&0x8000)|0x3BFF, 1, 1)); + return half(detail::binary, detail::erf(arg.data_)); +#endif + } + + /// Complementary error function. + /// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs. + /// + /// **See also:** Documentation for [std::erfc](https://en.cppreference.com/w/cpp/numeric/math/erfc). + /// \param arg function argument + /// \return 1 minus error function value of \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half erfc(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::erfc(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; + if(abs >= 0x7C00) + return (abs>=0x7C00) ? half(detail::binary, (abs==0x7C00) ? (sign>>1) : detail::signal(arg.data_)) : arg; + if(!abs) + return half(detail::binary, 0x3C00); + if(abs >= 0x4400) + return half(detail::binary, detail::rounded((sign>>1)-(sign>>15), sign>>15, 1)); + return half(detail::binary, detail::erf(arg.data_)); +#endif + } + + /// Natural logarithm of gamma function. + /// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.025% of inputs. + /// + /// **See also:** Documentation for [std::lgamma](https://en.cppreference.com/w/cpp/numeric/math/lgamma). + /// \param arg function argument + /// \return natural logarith of gamma function for \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_DIVBYZERO for 0 or negative integer arguments + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half lgamma(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::lgamma(detail::half2float(arg.data_)))); +#else + int abs = arg.data_ & 0x7FFF; + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? 0x7C00 : detail::signal(arg.data_)); + if(!abs || arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs&((1<<(25-(abs>>10)))-1)))) + return half(detail::binary, detail::pole()); + if(arg.data_ == 0x3C00 || arg.data_ == 0x4000) + return half(detail::binary, 0); + return half(detail::binary, detail::gamma(arg.data_)); +#endif + } + + /// Gamma function. + /// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.25% of inputs. + /// + /// **See also:** Documentation for [std::tgamma](https://en.cppreference.com/w/cpp/numeric/math/tgamma). + /// \param arg function argument + /// \return gamma function value of \a arg + /// \exception FE_INVALID for signaling NaN, negative infinity or negative integer arguments + /// \exception FE_DIVBYZERO for 0 + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half tgamma(half arg) + { +#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH + return half(detail::binary, detail::float2half(std::tgamma(detail::half2float(arg.data_)))); +#else + unsigned int abs = arg.data_ & 0x7FFF; + if(!abs) + return half(detail::binary, detail::pole(arg.data_)); + if(abs >= 0x7C00) + return (arg.data_==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); + if(arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs&((1<<(25-(abs>>10)))-1)))) + return half(detail::binary, detail::invalid()); + if(arg.data_ >= 0xCA80) + return half(detail::binary, detail::underflow((1-((abs>>(25-(abs>>10)))&1))<<15)); + if(arg.data_ <= 0x100 || (arg.data_ >= 0x4900 && arg.data_ < 0x8000)) + return half(detail::binary, detail::overflow()); + if(arg.data_ == 0x3C00) + return arg; + return half(detail::binary, detail::gamma(arg.data_)); +#endif + } + + /// \} + /// \anchor rounding + /// \name Rounding + /// \{ + + /// Nearest integer not less than half value. + /// **See also:** Documentation for [std::ceil](https://en.cppreference.com/w/cpp/numeric/math/ceil). + /// \param arg half to round + /// \return nearest integer not less than \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_INEXACT if value had to be rounded + inline half ceil(half arg) { return half(detail::binary, detail::integral(arg.data_)); } + + /// Nearest integer not greater than half value. + /// **See also:** Documentation for [std::floor](https://en.cppreference.com/w/cpp/numeric/math/floor). + /// \param arg half to round + /// \return nearest integer not greater than \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_INEXACT if value had to be rounded + inline half floor(half arg) { return half(detail::binary, detail::integral(arg.data_)); } + + /// Nearest integer not greater in magnitude than half value. + /// **See also:** Documentation for [std::trunc](https://en.cppreference.com/w/cpp/numeric/math/trunc). + /// \param arg half to round + /// \return nearest integer not greater in magnitude than \a arg + /// \exception FE_INVALID for signaling NaN + /// \exception FE_INEXACT if value had to be rounded + inline half trunc(half arg) { return half(detail::binary, detail::integral(arg.data_)); } + + /// Nearest integer. + /// **See also:** Documentation for [std::round](https://en.cppreference.com/w/cpp/numeric/math/round). + /// \param arg half to round + /// \return nearest integer, rounded away from zero in half-way cases + /// \exception FE_INVALID for signaling NaN + /// \exception FE_INEXACT if value had to be rounded + inline half round(half arg) { return half(detail::binary, detail::integral(arg.data_)); } + + /// Nearest integer. + /// **See also:** Documentation for [std::lround](https://en.cppreference.com/w/cpp/numeric/math/round). + /// \param arg half to round + /// \return nearest integer, rounded away from zero in half-way cases + /// \exception FE_INVALID if value is not representable as `long` + inline long lround(half arg) { return detail::half2int(arg.data_); } + + /// Nearest integer using half's internal rounding mode. + /// **See also:** Documentation for [std::rint](https://en.cppreference.com/w/cpp/numeric/math/rint). + /// \param arg half expression to round + /// \return nearest integer using default rounding mode + /// \exception FE_INVALID for signaling NaN + /// \exception FE_INEXACT if value had to be rounded + inline half rint(half arg) { return half(detail::binary, detail::integral(arg.data_)); } + + /// Nearest integer using half's internal rounding mode. + /// **See also:** Documentation for [std::lrint](https://en.cppreference.com/w/cpp/numeric/math/rint). + /// \param arg half expression to round + /// \return nearest integer using default rounding mode + /// \exception FE_INVALID if value is not representable as `long` + /// \exception FE_INEXACT if value had to be rounded + inline long lrint(half arg) { return detail::half2int(arg.data_); } + + /// Nearest integer using half's internal rounding mode. + /// **See also:** Documentation for [std::nearbyint](https://en.cppreference.com/w/cpp/numeric/math/nearbyint). + /// \param arg half expression to round + /// \return nearest integer using default rounding mode + /// \exception FE_INVALID for signaling NaN + inline half nearbyint(half arg) { return half(detail::binary, detail::integral(arg.data_)); } +#if HALF_ENABLE_CPP11_LONG_LONG + /// Nearest integer. + /// **See also:** Documentation for [std::llround](https://en.cppreference.com/w/cpp/numeric/math/round). + /// \param arg half to round + /// \return nearest integer, rounded away from zero in half-way cases + /// \exception FE_INVALID if value is not representable as `long long` + inline long long llround(half arg) { return detail::half2int(arg.data_); } + + /// Nearest integer using half's internal rounding mode. + /// **See also:** Documentation for [std::llrint](https://en.cppreference.com/w/cpp/numeric/math/rint). + /// \param arg half expression to round + /// \return nearest integer using default rounding mode + /// \exception FE_INVALID if value is not representable as `long long` + /// \exception FE_INEXACT if value had to be rounded + inline long long llrint(half arg) { return detail::half2int(arg.data_); } +#endif + + /// \} + /// \anchor float + /// \name Floating point manipulation + /// \{ + + /// Decompress floating-point number. + /// **See also:** Documentation for [std::frexp](https://en.cppreference.com/w/cpp/numeric/math/frexp). + /// \param arg number to decompress + /// \param exp address to store exponent at + /// \return significant in range [0.5, 1) + /// \exception FE_INVALID for signaling NaN + inline half frexp(half arg, int *exp) + { + *exp = 0; + unsigned int abs = arg.data_ & 0x7FFF; + if(abs >= 0x7C00 || !abs) + return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; + for(; abs<0x400; abs<<=1,--*exp) ; + *exp += (abs>>10) - 14; + return half(detail::binary, (arg.data_&0x8000)|0x3800|(abs&0x3FF)); + } + + /// Multiply by power of two. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::scalbln](https://en.cppreference.com/w/cpp/numeric/math/scalbn). + /// \param arg number to modify + /// \param exp power of two to multiply with + /// \return \a arg multplied by 2 raised to \a exp + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half scalbln(half arg, long exp) + { + unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; + if(abs >= 0x7C00 || !abs) + return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; + for(; abs<0x400; abs<<=1,--exp) ; + exp += abs >> 10; + if(exp > 30) + return half(detail::binary, detail::overflow(sign)); + else if(exp < -10) + return half(detail::binary, detail::underflow(sign)); + else if(exp > 0) + return half(detail::binary, sign|(exp<<10)|(abs&0x3FF)); + unsigned int m = (abs&0x3FF) | 0x400; + return half(detail::binary, detail::rounded(sign|(m>>(1-exp)), (m>>-exp)&1, (m&((1<<-exp)-1))!=0)); + } + + /// Multiply by power of two. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::scalbn](https://en.cppreference.com/w/cpp/numeric/math/scalbn). + /// \param arg number to modify + /// \param exp power of two to multiply with + /// \return \a arg multplied by 2 raised to \a exp + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half scalbn(half arg, int exp) { return scalbln(arg, exp); } + + /// Multiply by power of two. + /// This function is exact to rounding for all rounding modes. + /// + /// **See also:** Documentation for [std::ldexp](https://en.cppreference.com/w/cpp/numeric/math/ldexp). + /// \param arg number to modify + /// \param exp power of two to multiply with + /// \return \a arg multplied by 2 raised to \a exp + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + inline half ldexp(half arg, int exp) { return scalbln(arg, exp); } + + /// Extract integer and fractional parts. + /// **See also:** Documentation for [std::modf](https://en.cppreference.com/w/cpp/numeric/math/modf). + /// \param arg number to decompress + /// \param iptr address to store integer part at + /// \return fractional part + /// \exception FE_INVALID for signaling NaN + inline half modf(half arg, half *iptr) + { + unsigned int abs = arg.data_ & 0x7FFF; + if(abs > 0x7C00) + { + arg = half(detail::binary, detail::signal(arg.data_)); + return *iptr = arg, arg; + } + if(abs >= 0x6400) + return *iptr = arg, half(detail::binary, arg.data_&0x8000); + if(abs < 0x3C00) + return iptr->data_ = arg.data_ & 0x8000, arg; + unsigned int exp = abs >> 10, mask = (1<<(25-exp)) - 1, m = arg.data_ & mask; + iptr->data_ = arg.data_ & ~mask; + if(!m) + return half(detail::binary, arg.data_&0x8000); + for(; m<0x400; m<<=1,--exp) ; + return half(detail::binary, (arg.data_&0x8000)|(exp<<10)|(m&0x3FF)); + } + + /// Extract exponent. + /// **See also:** Documentation for [std::ilogb](https://en.cppreference.com/w/cpp/numeric/math/ilogb). + /// \param arg number to query + /// \return floating-point exponent + /// \retval FP_ILOGB0 for zero + /// \retval FP_ILOGBNAN for NaN + /// \retval INT_MAX for infinity + /// \exception FE_INVALID for 0 or infinite values + inline int ilogb(half arg) + { + int abs = arg.data_ & 0x7FFF, exp; + if(!abs || abs >= 0x7C00) + { + detail::raise(FE_INVALID); + return !abs ? FP_ILOGB0 : (abs==0x7C00) ? INT_MAX : FP_ILOGBNAN; + } + for(exp=(abs>>10)-15; abs<0x200; abs<<=1,--exp) ; + return exp; + } + + /// Extract exponent. + /// **See also:** Documentation for [std::logb](https://en.cppreference.com/w/cpp/numeric/math/logb). + /// \param arg number to query + /// \return floating-point exponent + /// \exception FE_INVALID for signaling NaN + /// \exception FE_DIVBYZERO for 0 + inline half logb(half arg) + { + int abs = arg.data_ & 0x7FFF, exp; + if(!abs) + return half(detail::binary, detail::pole(0x8000)); + if(abs >= 0x7C00) + return half(detail::binary, (abs==0x7C00) ? 0x7C00 : detail::signal(arg.data_)); + for(exp=(abs>>10)-15; abs<0x200; abs<<=1,--exp) ; + unsigned int value = static_cast(exp<0) << 15; + if(exp) + { + unsigned int m = std::abs(exp) << 6; + for(exp=18; m<0x400; m<<=1,--exp) ; + value |= (exp<<10) + m; + } + return half(detail::binary, value); + } + + /// Next representable value. + /// **See also:** Documentation for [std::nextafter](https://en.cppreference.com/w/cpp/numeric/math/nextafter). + /// \param from value to compute next representable value for + /// \param to direction towards which to compute next value + /// \return next representable value after \a from in direction towards \a to + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW for infinite result from finite argument + /// \exception FE_UNDERFLOW for subnormal result + inline half nextafter(half from, half to) + { + int fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF; + if(fabs > 0x7C00 || tabs > 0x7C00) + return half(detail::binary, detail::signal(from.data_, to.data_)); + if(from.data_ == to.data_ || !(fabs|tabs)) + return to; + if(!fabs) + { + detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT); + return half(detail::binary, (to.data_&0x8000)+1); + } + unsigned int out = from.data_ + (((from.data_>>15)^static_cast( + (from.data_^(0x8000|(0x8000-(from.data_>>15))))<(to.data_^(0x8000|(0x8000-(to.data_>>15))))))<<1) - 1; + detail::raise(FE_OVERFLOW, fabs<0x7C00 && (out&0x7C00)==0x7C00); + detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out&0x7C00)<0x400); + return half(detail::binary, out); + } + + /// Next representable value. + /// **See also:** Documentation for [std::nexttoward](https://en.cppreference.com/w/cpp/numeric/math/nexttoward). + /// \param from value to compute next representable value for + /// \param to direction towards which to compute next value + /// \return next representable value after \a from in direction towards \a to + /// \exception FE_INVALID for signaling NaN + /// \exception FE_OVERFLOW for infinite result from finite argument + /// \exception FE_UNDERFLOW for subnormal result + inline half nexttoward(half from, long double to) + { + int fabs = from.data_ & 0x7FFF; + if(fabs > 0x7C00) + return half(detail::binary, detail::signal(from.data_)); + long double lfrom = static_cast(from); + if(detail::builtin_isnan(to) || lfrom == to) + return half(static_cast(to)); + if(!fabs) + { + detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT); + return half(detail::binary, (static_cast(detail::builtin_signbit(to))<<15)+1); + } + unsigned int out = from.data_ + (((from.data_>>15)^static_cast(lfrom 0x7C00; } + + /// Check if normal number. + /// **See also:** Documentation for [std::isnormal](https://en.cppreference.com/w/cpp/numeric/math/isnormal). + /// \param arg number to check + /// \retval true if normal number + /// \retval false if either subnormal, zero, infinity or NaN + inline HALF_CONSTEXPR bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); } + + /// Check sign. + /// **See also:** Documentation for [std::signbit](https://en.cppreference.com/w/cpp/numeric/math/signbit). + /// \param arg number to check + /// \retval true for negative number + /// \retval false for positive number + inline HALF_CONSTEXPR bool signbit(half arg) { return (arg.data_&0x8000) != 0; } + + /// \} + /// \anchor compfunc + /// \name Comparison + /// \{ + + /// Quiet comparison for greater than. + /// **See also:** Documentation for [std::isgreater](https://en.cppreference.com/w/cpp/numeric/math/isgreater). + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater than \a y + /// \retval false else + inline HALF_CONSTEXPR bool isgreater(half x, half y) + { + return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) > ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y); + } + + /// Quiet comparison for greater equal. + /// **See also:** Documentation for [std::isgreaterequal](https://en.cppreference.com/w/cpp/numeric/math/isgreaterequal). + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater equal \a y + /// \retval false else + inline HALF_CONSTEXPR bool isgreaterequal(half x, half y) + { + return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) >= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y); + } + + /// Quiet comparison for less than. + /// **See also:** Documentation for [std::isless](https://en.cppreference.com/w/cpp/numeric/math/isless). + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less than \a y + /// \retval false else + inline HALF_CONSTEXPR bool isless(half x, half y) + { + return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) < ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y); + } + + /// Quiet comparison for less equal. + /// **See also:** Documentation for [std::islessequal](https://en.cppreference.com/w/cpp/numeric/math/islessequal). + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less equal \a y + /// \retval false else + inline HALF_CONSTEXPR bool islessequal(half x, half y) + { + return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) <= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y); + } + + /// Quiet comarison for less or greater. + /// **See also:** Documentation for [std::islessgreater](https://en.cppreference.com/w/cpp/numeric/math/islessgreater). + /// \param x first operand + /// \param y second operand + /// \retval true if either less or greater + /// \retval false else + inline HALF_CONSTEXPR bool islessgreater(half x, half y) + { + return x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF) && !isnan(x) && !isnan(y); + } + + /// Quiet check if unordered. + /// **See also:** Documentation for [std::isunordered](https://en.cppreference.com/w/cpp/numeric/math/isunordered). + /// \param x first operand + /// \param y second operand + /// \retval true if unordered (one or two NaN operands) + /// \retval false else + inline HALF_CONSTEXPR bool isunordered(half x, half y) { return isnan(x) || isnan(y); } + + /// \} + /// \anchor casting + /// \name Casting + /// \{ + + /// Cast to or from half-precision floating-point number. + /// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted + /// directly using the default rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do. + /// + /// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types + /// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler + /// error and casting between [half](\ref half_float::half)s returns the argument unmodified. + /// \tparam T destination type (half or built-in arithmetic type) + /// \tparam U source type (half or built-in arithmetic type) + /// \param arg value to cast + /// \return \a arg converted to destination type + /// \exception FE_INVALID if \a T is integer type and result is not representable as \a T + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + template T half_cast(U arg) { return detail::half_caster::cast(arg); } + + /// Cast to or from half-precision floating-point number. + /// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted + /// directly using the specified rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do. + /// + /// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types + /// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler + /// error and casting between [half](\ref half_float::half)s returns the argument unmodified. + /// \tparam T destination type (half or built-in arithmetic type) + /// \tparam R rounding mode to use. + /// \tparam U source type (half or built-in arithmetic type) + /// \param arg value to cast + /// \return \a arg converted to destination type + /// \exception FE_INVALID if \a T is integer type and result is not representable as \a T + /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding + template T half_cast(U arg) { return detail::half_caster::cast(arg); } + /// \} + + /// \} + /// \anchor errors + /// \name Error handling + /// \{ + + /// Clear exception flags. + /// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, + /// but in that case manual flag management is the only way to raise flags. + /// + /// **See also:** Documentation for [std::feclearexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feclearexcept). + /// \param excepts OR of exceptions to clear + /// \retval 0 all selected flags cleared successfully + inline int feclearexcept(int excepts) { detail::errflags() &= ~excepts; return 0; } + + /// Test exception flags. + /// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, + /// but in that case manual flag management is the only way to raise flags. + /// + /// **See also:** Documentation for [std::fetestexcept](https://en.cppreference.com/w/cpp/numeric/fenv/fetestexcept). + /// \param excepts OR of exceptions to test + /// \return OR of selected exceptions if raised + inline int fetestexcept(int excepts) { return detail::errflags() & excepts; } + + /// Raise exception flags. + /// This raises the specified floating point exceptions and also invokes any additional automatic exception handling as + /// configured with the [HALF_ERRHANDLIG_...](\ref HALF_ERRHANDLING_ERRNO) preprocessor symbols. + /// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, + /// but in that case manual flag management is the only way to raise flags. + /// + /// **See also:** Documentation for [std::feraiseexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feraiseexcept). + /// \param excepts OR of exceptions to raise + /// \retval 0 all selected exceptions raised successfully + inline int feraiseexcept(int excepts) { detail::errflags() |= excepts; detail::raise(excepts); return 0; } + + /// Save exception flags. + /// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, + /// but in that case manual flag management is the only way to raise flags. + /// + /// **See also:** Documentation for [std::fegetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag). + /// \param flagp adress to store flag state at + /// \param excepts OR of flags to save + /// \retval 0 for success + inline int fegetexceptflag(int *flagp, int excepts) { *flagp = detail::errflags() & excepts; return 0; } + + /// Restore exception flags. + /// This only copies the specified exception state (including unset flags) without incurring any additional exception handling. + /// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, + /// but in that case manual flag management is the only way to raise flags. + /// + /// **See also:** Documentation for [std::fesetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag). + /// \param flagp adress to take flag state from + /// \param excepts OR of flags to restore + /// \retval 0 for success + inline int fesetexceptflag(const int *flagp, int excepts) { detail::errflags() = (detail::errflags()|(*flagp&excepts)) & (*flagp|~excepts); return 0; } + + /// Throw C++ exceptions based on set exception flags. + /// This function manually throws a corresponding C++ exception if one of the specified flags is set, + /// no matter if automatic throwing (via [HALF_ERRHANDLING_THROW_...](\ref HALF_ERRHANDLING_THROW_INVALID)) is enabled or not. + /// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, + /// but in that case manual flag management is the only way to raise flags. + /// \param excepts OR of exceptions to test + /// \param msg error message to use for exception description + /// \throw std::domain_error if `FE_INVALID` or `FE_DIVBYZERO` is selected and set + /// \throw std::overflow_error if `FE_OVERFLOW` is selected and set + /// \throw std::underflow_error if `FE_UNDERFLOW` is selected and set + /// \throw std::range_error if `FE_INEXACT` is selected and set + inline void fethrowexcept(int excepts, const char *msg = "") + { + excepts &= detail::errflags(); + if(excepts & (FE_INVALID|FE_DIVBYZERO)) + throw std::domain_error(msg); + if(excepts & FE_OVERFLOW) + throw std::overflow_error(msg); + if(excepts & FE_UNDERFLOW) + throw std::underflow_error(msg); + if(excepts & FE_INEXACT) + throw std::range_error(msg); + } + /// \} +} + + +#undef HALF_UNUSED_NOERR +#undef HALF_CONSTEXPR +#undef HALF_CONSTEXPR_CONST +#undef HALF_CONSTEXPR_NOERR +#undef HALF_NOEXCEPT +#undef HALF_NOTHROW +#undef HALF_THREAD_LOCAL +#undef HALF_TWOS_COMPLEMENT_INT +#ifdef HALF_POP_WARNINGS +#pragma warning(pop) + #undef HALF_POP_WARNINGS +#endif + +#endif diff --git a/mnn_demo/tests/test_CRvcCircleBuffer.cpp b/mnn_demo/tests/test_CRvcCircleBuffer.cpp new file mode 100644 index 0000000..d006f19 --- /dev/null +++ b/mnn_demo/tests/test_CRvcCircleBuffer.cpp @@ -0,0 +1,85 @@ +// +// Created by jianli.yang on 2023/11/30. +// + +// 测试循环buffer +#include "CRvcCircleBuffer.h" +#include +#include +int main() +{ + /** + * 测试包含: + * 1. 开辟空间情况 + * 2. 塞数据情况 + * 3. 取数据情况 + */ + for(int i = 0; i < 10000000; i++) + { + CRvcCircleBuffer circle_buffer(1000000 * 40); + printf("%d\n", circle_buffer.size()); // 目标输出 0 + // 此时理论上可以塞入4个数据，到第五个的时候才会开辟空间 + float* buf = new float[1000000]{1,2,3,4,5}; + float* buf2 = new float[5]{0,0,0,0,0}; + circle_buffer.push(buf, 5); + printf("%d\n", circle_buffer.size()); // 目标输出 5 // 测试开辟空间情况 + int buf2_len = 5; + circle_buffer.pop(buf2, buf2_len); + printf("%d,%d:", circle_buffer.size(), buf2_len); + for(int i = 0; i < buf2_len; i++) + { + if(i > 0) printf(","); + printf("%f", buf2[i]); + } + printf("\n"); // 目标: 0, 5: 1,2,3,4,5 + + // 第二遍 + circle_buffer.push(buf, 5); + memset(buf2, 0, sizeof(float) * 5); + buf2_len = 3; + circle_buffer.pop(buf2, buf2_len); + printf("%d,%d:", circle_buffer.size(), buf2_len); + for(int i = 0; i < buf2_len; i++) + { + if(i > 0) printf(","); + printf("%f", buf2[i]); + } + printf("\n"); // 目标: 2, 3: 1,2,3 + + // 第三遍 + circle_buffer.push(buf, 5); + circle_buffer.push(buf, 5); + buf2_len = 5; + circle_buffer.pop(buf2, buf2_len); + printf("%d,%d:", circle_buffer.size(), buf2_len); + for(int i = 0; i < buf2_len; i++) + { + if(i > 0) printf(","); + printf("%f", buf2[i]); + } + printf("\n"); // 目标: 7,5:4,5,1,2,3 + + // 第四遍 + buf2_len = 5; + circle_buffer.pop(buf2, buf2_len); + printf("%d,%d:", circle_buffer.size(), buf2_len); + for(int i = 0; i < buf2_len; i++) + { + if(i > 0) printf(","); + printf("%f", buf2[i]); + } + printf("\n"); // 目标: 2,5:4,5,1,2,3 + buf2_len = 5; + circle_buffer.pop(buf2, buf2_len); + printf("%d,%d:", circle_buffer.size(), buf2_len); + for(int i = 0; i < buf2_len; i++) + { + if(i > 0) printf(","); + printf("%f", buf2[i]); + } + printf("\n"); // 目标: 0,2:4,5 + delete buf; + delete buf2; + } + return 0; +} \ No newline at end of file diff --git a/mnn_demo/tests/test_flatbuffer.cpp b/mnn_demo/tests/test_flatbuffer.cpp new file mode 100644 index 0000000..a631a3c --- /dev/null +++ b/mnn_demo/tests/test_flatbuffer.cpp @@ -0,0 +1,67 @@ +// +// Created by Administrator on 2023/12/20. +// +#include +#include +#include +#include "flatbuffers/idl.h" +#include "flatbuffers/util.h" +#include "half.hpp" + +int main() { + + std::ifstream infile; + infile.open("mobilenet_v1.mnn", std::ios::binary | std::ios::in); +// infile.open("D:/dataset/svc/models/layers_3/layer3_syz.mnn", std::ios::binary | std::ios::in); + infile.seekg(0, std::ios::end); + int length = infile.tellg(); + infile.seekg(0, std::ios::beg); + char *buffer_pointer = new char[length]; + infile.read(buffer_pointer, length); + infile.close(); + + std::string MNN_text; + std::string base_dir = "D:/simple_work/mnn_ops/default"; + flatbuffers::LoadFile((base_dir + "/MNN.fbs").c_str(), false, &MNN_text); + printf("start parser\n"); + flatbuffers::Parser parser; + const char **path = new const char *[2]; + path[0] = base_dir.c_str(); + parser.Parse(MNN_text.c_str(), path, "MNN.fbs"); + std::string output_text; + flatbuffers::GenerateText(parser, buffer_pointer, &output_text); + std::ofstream os; + os.open("mobilenet-v2.txt"); + os << output_text; + os.close(); + + +// float mm = 200; +// int8_t * aa = (int8_t*)&mm; +// for(int i = 0; i < 4; i++) +// { +// printf("%d\n", aa[i]); +// } +// // -0.011971, 0.118042 +// char aa2[4] = {33, -94, -114, 47}; +//// char aa2[4] = {33, 0, 0, -94}; +//// short* as = (short*)(aa2); +//// printf("%d, %d\n", as[0], as[1]); +//// float* as = (float*)(aa2); +//// printf("%f\n", as[0]); +// +// using half_float::half; +// half* aa = (half_float::half*) aa2; +// float* a2 = new float[2]; +// for(int i = 0; i < 2; i++) { +// a2[i] = aa[i]; +// } +// printf("%f, %f\n", a2[0], a2[1]); +// std::cout << aa[0] << std::endl; +// half a(3.4), b(5); +// half c = a * b; +// c += 3; +// if(c > a) + + +} \ No newline at end of file diff --git a/mnn_demo/third_party/espyin-v1.0/ESFFTimpl.cpp b/mnn_demo/third_party/espyin-v1.0/ESFFTimpl.cpp new file mode 100644 index 0000000..e83685f --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESFFTimpl.cpp @@ -0,0 +1,120 @@ + +/* Public domain FFT implementation from Don Cross. */ + +#include + +#define M_PI 3.14159 + +static void +esfft(unsigned int n, bool inverse, + const double *ri, const double *ii, + double *ro, double *io) +{ + if (!ri || !ro || !io) return; + + unsigned int bits; + unsigned int i, j, k, m; + unsigned int blockSize, blockEnd; + + double tr, ti; + + if (n < 2) return; + if (n & (n-1)) return; + + double angle = 2.0 * M_PI; + if (inverse) angle = -angle; + + for (i = 0; ; ++i) { + if (n & (1 << i)) { + bits = i; + break; + } + } + +#ifdef _MSC_VER + int *table = (int *)malloc(n * sizeof(int)); +#else + int table[n]; +#endif + + for (i = 0; i < n; ++i) { + m = i; + for (j = k = 0; j < bits; ++j) { + k = (k << 1) | (m & 1); + m >>= 1; + } + table[i] = k; + } + + if (ii) { + for (i = 0; i < n; ++i) { + ro[table[i]] = ri[i]; + io[table[i]] = ii[i]; + } + } else { + for (i = 0; i < n; ++i) { + ro[table[i]] = ri[i]; + io[table[i]] = 0.0; + } + } + + blockEnd = 1; + + for (blockSize = 2; blockSize <= n; blockSize <<= 1) { + + double delta = angle / (double)blockSize; + double sm2 = -sin(-2 * delta); + double sm1 = -sin(-delta); + double cm2 = cos(-2 * delta); + double cm1 = cos(-delta); + double w = 2 * cm1; + double ar[3], ai[3]; + + for (i = 0; i < n; i += blockSize) { + + ar[2] = cm2; + ar[1] = cm1; + + ai[2] = sm2; + ai[1] = sm1; + + for (j = i, m = 0; m < blockEnd; j++, m++) { + + ar[0] = w * ar[1] - ar[2]; + ar[2] = ar[1]; + ar[1] = ar[0]; + + ai[0] = w * ai[1] - ai[2]; + ai[2] = ai[1]; + ai[1] = ai[0]; + + k = j + blockEnd; + tr = ar[0] * ro[k] - ai[0] * io[k]; + ti = ar[0] * io[k] + ai[0] * ro[k]; + + ro[k] = ro[j] - tr; + io[k] = io[j] - ti; + + ro[j] += tr; + io[j] += ti; + } + } + + blockEnd = blockSize; + } + + if (inverse) { + + double denom = (double)n; + + for (i = 0; i < n; i++) { + ro[i] /= denom; + io[i] /= denom; + } + } + +#ifdef _MSC_VER + free(table); +#endif +} + diff --git a/mnn_demo/third_party/espyin-v1.0/ESMonoPitch.cpp b/mnn_demo/third_party/espyin-v1.0/ESMonoPitch.cpp new file mode 100644 index 0000000..fef43de --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESMonoPitch.cpp @@ -0,0 +1,87 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#include "ESMonoPitch.h" +#include "ESMonoPitchHMM.h" +#include + +#include +#include +#include + +using std::vector; +using std::pair; + +ESMonoPitch::ESMonoPitch(int reso_type) : + hmm(reso_type) +{ +} + +ESMonoPitch::~ESMonoPitch() +{ +} + +const vector +ESMonoPitch::process(const vector > > pitchProb) +{ + // std::cerr << "before observation prob calculation" << std::endl; + vector > obsProb; + for (size_t iFrame = 0; iFrame < pitchProb.size(); ++iFrame) + { + obsProb.push_back(hmm.calculateObsProb(pitchProb[iFrame])); + } + for (size_t i = 0; i < obsProb[0].size(); ++i) { + obsProb[0][i] = 0; + } + obsProb[0][obsProb[0].size()-1] = 1; + + // std::cerr << "after observation prob calculation" << std::endl; + + vector *scale = new vector(pitchProb.size()); + + vector out; + + // std::cerr << "before Viterbi decoding" << obsProb.size() << "ng" << obsProb[1].size() << std::endl; + vector path = hmm.decodeViterbi(obsProb, scale); + // std::cerr << "after Viterbi decoding" << std::endl; + + for (size_t iFrame = 0; iFrame < path.size(); ++iFrame) + { + // std::cerr << path[iFrame] << " " << hmm.m_freqs[path[iFrame]] << std::endl; + float hmmFreq = hmm.m_freqs[path[iFrame]]; + float bestFreq = 0; + float leastDist = 10000; + if (hmmFreq > 0) + { + // This was a Yin estimate, so try to get original pitch estimate back + // ... a bit hacky, since we could have direclty saved the frequency + // that was assigned to the HMM bin in hmm.calculateObsProb -- but would + // have had to rethink the interface of that method. + for (size_t iPitch = 0; iPitch < pitchProb[iFrame].size(); ++iPitch) + { + float freq = 440. * std::pow(2, (pitchProb[iFrame][iPitch].first - 69)/12); + float dist = std::abs(hmmFreq-freq); + if (dist < leastDist) + { + leastDist = dist; + bestFreq = freq; + } + } + } else { + bestFreq = hmmFreq; + } + out.push_back(bestFreq); + } + delete scale; + return(out); +} diff --git a/mnn_demo/third_party/espyin-v1.0/ESMonoPitch.h b/mnn_demo/third_party/espyin-v1.0/ESMonoPitch.h new file mode 100644 index 0000000..2ca39f5 --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESMonoPitch.h @@ -0,0 +1,37 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#ifndef _ESMONOPITCH_H_ +#define _ESMONOPITCH_H_ + +#include "ESMonoPitchHMM.h" + +#include +#include +#include + +using std::vector; +using std::pair; + +class ESMonoPitch { +public: + ESMonoPitch(int reso_type=1); + virtual ~ESMonoPitch(); + + // pitchProb is a frame-wise vector carrying a vector of pitch-probability pairs + const vector process(const vector > > pitchProb); +private: + ESMonoPitchHMM hmm; +}; + +#endif diff --git a/mnn_demo/third_party/espyin-v1.0/ESMonoPitchHMM.cpp b/mnn_demo/third_party/espyin-v1.0/ESMonoPitchHMM.cpp new file mode 100644 index 0000000..3fdebc0 --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESMonoPitchHMM.cpp @@ -0,0 +1,174 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#include "ESMonoPitchHMM.h" + +#include +#include + +using std::vector; +using std::pair; + +ESMonoPitchHMM::ESMonoPitchHMM(int reso_type) : +m_minFreq(55), +m_nBPS(10), +m_nPitch(0), +m_transitionWidth(0), +m_selfTrans(0.99), +m_yinTrust(.5), +m_freqs(0) +{ + int size = 0; + if (reso_type == 1) { + size = 51592; + m_transitionWidth = 5*(m_nBPS/2) + 1; + } else { + size = 14416; + m_minFreq = 80; + m_nBPS = 5; + m_transitionWidth = 5 * (int(m_nBPS / 2)) + 4; + } + + m_nPitch = 48 * m_nBPS; + m_freqs = vector(2*m_nPitch+1); + for (size_t iPitch = 0; iPitch < m_nPitch; ++iPitch) + { + m_freqs[iPitch] = m_minFreq * std::pow(2, iPitch * 1.0 / (12 * m_nBPS)); + // m_freqs[iPitch+m_nPitch] = -2; + m_freqs[iPitch+m_nPitch] = -m_freqs[iPitch]; + // std::cerr << "pitch " << iPitch << " = " << m_freqs[iPitch] << std::endl; + } + m_freqs[2*m_nPitch] = -1; + + from.resize(size, 0); + to.resize(size, 0); + transProb.resize(size, 0); + + build(); +} + +const vector +ESMonoPitchHMM::calculateObsProb(const vector > pitchProb) +{ + vector out = vector(2*m_nPitch+1); + double probYinPitched = 0; + // BIN THE PITCHES + for (size_t iPair = 0; iPair < pitchProb.size(); ++iPair) + { + double freq = 440. * std::pow(2, (pitchProb[iPair].first - 69)/12); + if (freq <= m_minFreq) continue; + double d = 0; + double oldd = 1000; + for (size_t iPitch = 0; iPitch < m_nPitch; ++iPitch) + { + d = std::abs(freq-m_freqs[iPitch]); + if (oldd < d && iPitch > 0) + { + // previous bin must have been the closest + out[iPitch-1] = pitchProb[iPair].second; + probYinPitched += out[iPitch-1]; + break; + } + oldd = d; + } + } + + double probReallyPitched = m_yinTrust * probYinPitched; + for (size_t iPitch = 0; iPitch < m_nPitch; ++iPitch) + { + if (probYinPitched > 0) out[iPitch] *= (probReallyPitched/probYinPitched) ; + out[iPitch+m_nPitch] = (1 - probReallyPitched) / m_nPitch; + } + // out[2*m_nPitch] = m_yinTrust * (1 - probYinPitched); + return(out); +} + +void +ESMonoPitchHMM::build() +{ + int idx = 0; + // INITIAL VECTOR + init = vector(2*m_nPitch+1); + init[2*m_nPitch] = 1; // force first frame to be unvoiced. + + // TRANSITIONS + for (size_t iPitch = 0; iPitch < m_nPitch; ++iPitch) + { + int theoreticalMinNextPitch = static_cast(iPitch)-static_cast(m_transitionWidth/2); + int minNextPitch = iPitch>m_transitionWidth/2 ? iPitch-m_transitionWidth/2 : 0; + int maxNextPitch = iPitch weights; + for (size_t i = minNextPitch; i <= maxNextPitch; ++i) + { + if (i <= iPitch) + { + weights.push_back(i-theoreticalMinNextPitch+1); + // weights.push_back(i-theoreticalMinNextPitch+1+m_transitionWidth/2); + } else { + weights.push_back(iPitch-theoreticalMinNextPitch+1-(i-iPitch)); + // weights.push_back(iPitch-theoreticalMinNextPitch+1-(i-iPitch)+m_transitionWidth/2); + } + weightSum += weights[weights.size()-1]; + } + + // std::cerr << minNextPitch << " " << maxNextPitch << std::endl; + // TRANSITIONS TO CLOSE PITCH + for (size_t i = minNextPitch; i <= maxNextPitch; ++i) + { + from[idx] = iPitch; + to[idx] = i; + transProb[idx] = weights[i-minNextPitch] / weightSum * m_selfTrans; + ++idx; + + from[idx] = iPitch; + to[idx] = i+m_nPitch; + transProb[idx] = weights[i-minNextPitch] / weightSum * (1-m_selfTrans); + ++idx; + + from[idx] = iPitch+m_nPitch; + to[idx] = i+m_nPitch; + transProb[idx] = weights[i-minNextPitch] / weightSum * m_selfTrans; + ++idx; + // transProb.push_back(weights[i-minNextPitch] / weightSum * 0.5); + + from[idx] = iPitch+m_nPitch; + to[idx] = i; + transProb[idx] = weights[i-minNextPitch] / weightSum * (1-m_selfTrans); + ++idx; + // transProb.push_back(weights[i-minNextPitch] / weightSum * 0.5); + } + + // TRANSITION TO UNVOICED + // from.push_back(iPitch+m_nPitch); + // to.push_back(2*m_nPitch); + // transProb.push_back(1-m_selfTrans); + + // TRANSITION FROM UNVOICED TO PITCH + from[idx] = 2*m_nPitch; + to[idx] = iPitch+m_nPitch; + transProb[idx] = 1.0/m_nPitch; + ++idx; + } + // UNVOICED SELFTRANSITION + // from.push_back(2*m_nPitch); + // to.push_back(2*m_nPitch); + // transProb.push_back(m_selfTrans); + + // for (size_t i = 0; i < from.size(); ++i) { + // std::cerr << "P(["<< from[i] << " --> " << to[i] << "]) = " << transProb[i] << std::endl; + // } + +} diff --git a/mnn_demo/third_party/espyin-v1.0/ESMonoPitchHMM.h b/mnn_demo/third_party/espyin-v1.0/ESMonoPitchHMM.h new file mode 100644 index 0000000..d34648a --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESMonoPitchHMM.h @@ -0,0 +1,40 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#ifndef _ESMONOPITCHHMM_H_ +#define _ESMONOPITCHHMM_H_ + +#include "ESSparseHMM.h" +#include +#include + +using std::vector; + +class ESMonoPitchHMM : public ESSparseHMM +{ +public: + ESMonoPitchHMM(int reso_type=1); + const std::vector calculateObsProb(const vector >); + // double getMidiPitch(size_t index); + // double getFrequency(size_t index); + void build(); + double m_minFreq; // 82.40689f/2 + size_t m_nBPS; + size_t m_nPitch; + size_t m_transitionWidth; + double m_selfTrans; + double m_yinTrust; + vector m_freqs; +}; + +#endif diff --git a/mnn_demo/third_party/espyin-v1.0/ESPYIN.cpp b/mnn_demo/third_party/espyin-v1.0/ESPYIN.cpp new file mode 100644 index 0000000..a0c762d --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESPYIN.cpp @@ -0,0 +1,163 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#include "ESPYIN.h" +#include "ESMonoPitch.h" + +#include +#include + +#include +#include +#include + +using std::string; +using std::vector; + +ESPYIN::ESPYIN(float inputSampleRate, size_t stepSize, size_t blockSize, size_t fmin, size_t fmax) : + m_stepSize(stepSize), + m_blockSize(blockSize), + m_fmin(fmin), + m_fmax(fmax), + m_yin(blockSize, inputSampleRate, 0.0), + m_oF0Candidates(0), + m_oF0Probs(1), + m_oVoicedProb(2), + m_oCandidateSalience(3), + m_oSmoothedPitchTrack(4), + m_threshDistr(2.0f), + m_outputUnvoiced(2.0f), + m_pitchProb(0) +{ + reset(); +} + +ESPYIN::~ESPYIN() +{ +} + +void +ESPYIN::reset() +{ + m_yin.setThresholdDistr(m_threshDistr); + m_yin.setFrameSize(m_blockSize); + + m_pitchProb.clear(); +} + +void +ESPYIN::updata(int reserve_frame_num) +{ + vector > > temp_pitchProb(m_pitchProb); + + if (!temp_pitchProb.empty()) { + int frame_num = int(temp_pitchProb.size()); + + if (reserve_frame_num <= 0 || reserve_frame_num > frame_num) { + return; + } + + for (int i = 0; i < reserve_frame_num; ++i) { + temp_pitchProb[i] = temp_pitchProb[frame_num - reserve_frame_num + i]; + } + + temp_pitchProb.resize(reserve_frame_num); + m_pitchProb = temp_pitchProb; + } +} + +ESFeatureSet +ESPYIN::process(const float * const inputBuffers) +{ + ESFeatureSet fs; + double *dInputBuffers = new double[m_blockSize]; + for (size_t i = 0; i < m_blockSize; ++i) dInputBuffers[i] = inputBuffers[i]; + ESYin::YinOutput yo = m_yin.processProbabilisticYin(dInputBuffers); + ESFeature f; + for (size_t i = 0; i < yo.freqProb.size(); ++i) + { + f.values.push_back(yo.freqProb[i].first); + } + fs[m_oF0Candidates].push_back(f); + f.values.clear(); + float voicedProb = 0; + for (size_t i = 0; i < yo.freqProb.size(); ++i) + { + f.values.push_back(yo.freqProb[i].second); + voicedProb += yo.freqProb[i].second; + } + fs[m_oF0Probs].push_back(f); + + f.values.clear(); + f.values.push_back(voicedProb); + fs[m_oVoicedProb].push_back(f); + + f.values.clear(); + float salienceSum = 0; + for (size_t iBin = 0; iBin < yo.salience.size(); ++iBin) + { + f.values.push_back(yo.salience[iBin]); + salienceSum += yo.salience[iBin]; + } + fs[m_oCandidateSalience].push_back(f); + delete [] dInputBuffers; + + vector > tempPitchProb; + for (size_t iCandidate = 0; iCandidate < yo.freqProb.size(); ++iCandidate) + { + double tempPitch = 12 * std::log(yo.freqProb[iCandidate].first/440)/std::log(2.) + 69; + tempPitchProb.push_back(pair + (tempPitch, yo.freqProb[iCandidate].second)); + } + m_pitchProb.push_back(tempPitchProb); + + return fs; +} + +ESFeatureSet +ESPYIN::getRemainingFeatures(int reso_type) +{ + ESFeatureSet fs; + ESFeature f; + vector > > temp_pitchProb(m_pitchProb); + + if (temp_pitchProb.empty()) { + return fs; + } + + // MONO-PITCH STUFF + ESMonoPitch mp(reso_type); +// std::cerr << "before viterbi" << std::endl; + vector mpOut = mp.process(temp_pitchProb); + // std::cerr << "after viterbi " << mpOut.size() << " "<< m_timestamp.size() << std::endl; + for (size_t iFrame = 0; iFrame < mpOut.size(); ++iFrame) + { + if (mpOut[iFrame] < 0 && (m_outputUnvoiced==0)) continue; + f.values.clear(); + if (m_outputUnvoiced == 1) + { + f.values.push_back(abs(mpOut[iFrame])); + } else { + f.values.push_back(mpOut[iFrame]); + } + + fs[m_oSmoothedPitchTrack].push_back(f); + } + + return fs; +} + +int +ESPYIN::getFrames() { + return int(m_pitchProb.size()); +} diff --git a/mnn_demo/third_party/espyin-v1.0/ESPYIN.h b/mnn_demo/third_party/espyin-v1.0/ESPYIN.h new file mode 100644 index 0000000..b3c57ef --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESPYIN.h @@ -0,0 +1,65 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#ifndef _ESPYIN_H_ +#define _ESPYIN_H_ + +#include "ESYin.h" +#include + +using std::map; + +struct ESFeature +{ + std::vector values; +}; + +typedef std::vector ESFeatureList; + +typedef std::map ESFeatureSet; + +class ESPYIN +{ +public: + ESPYIN(float inputSampleRate, size_t stepSize, size_t blockSize, size_t fmin, size_t fmax); + virtual ~ESPYIN(); + + void reset(); + + void updata(int reserve_frame_num); + + ESFeatureSet process(const float * const inputBuffers); + + ESFeatureSet getRemainingFeatures(int reso_type=1); + + int getFrames(); + +protected: + size_t m_stepSize; + size_t m_blockSize; + float m_fmin; + float m_fmax; + ESYin m_yin; + + mutable int m_oF0Candidates; + mutable int m_oF0Probs; + mutable int m_oVoicedProb; + mutable int m_oCandidateSalience; + mutable int m_oSmoothedPitchTrack; + + float m_threshDistr; + float m_outputUnvoiced; + vector > > m_pitchProb; +}; + +#endif diff --git a/mnn_demo/third_party/espyin-v1.0/ESSparseHMM.cpp b/mnn_demo/third_party/espyin-v1.0/ESSparseHMM.cpp new file mode 100644 index 0000000..fd2cf1c --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESSparseHMM.cpp @@ -0,0 +1,141 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#include "ESSparseHMM.h" +#include +#include +#include + +using std::vector; +using std::pair; + +const vector +ESSparseHMM::calculateObsProb(const vector > data) +{ + // dummy (virtual?) implementation to be overloaded + return(vector()); +} + +const std::vector +ESSparseHMM::decodeViterbi(std::vector > obsProb, + vector *scale) +{ + size_t nState = init.size(); + size_t nFrame = obsProb.size(); + + // check for consistency + size_t nTrans = transProb.size(); + + // declaring variables + std::vector delta = std::vector(nState); + std::vector oldDelta = std::vector(nState); + vector > psi; // "matrix" of remembered indices of the best transitions + vector path = vector(nFrame, nState-1); // the final output path (current assignment arbitrary, makes sense only for Chordino, where nChord-1 is the "no chord" label) + + double deltasum = 0; + + // initialise first frame + for (size_t iState = 0; iState < nState; ++iState) + { + oldDelta[iState] = init[iState] * obsProb[0][iState]; + // std::cerr << iState << " ----- " << init[iState] << std::endl; + deltasum += oldDelta[iState]; + } + + for (size_t iState = 0; iState < nState; ++iState) + { + oldDelta[iState] /= deltasum; // normalise (scale) + // std::cerr << oldDelta[iState] << std::endl; + } + + scale->push_back(1.0/deltasum); + psi.push_back(vector(nState,0)); + + // rest of forward step + for (size_t iFrame = 1; iFrame < nFrame; ++iFrame) + { + deltasum = 0; + psi.push_back(vector(nState,0)); + + // calculate best previous state for every current state + size_t fromState; + size_t toState; + double currentTransProb; + double currentValue; + + // this is the "sparse" loop + for (size_t iTrans = 0; iTrans < nTrans; ++iTrans) + { + fromState = from[iTrans]; + toState = to[iTrans]; + currentTransProb = transProb[iTrans]; + + currentValue = oldDelta[fromState] * currentTransProb; + if (currentValue > delta[toState]) + { + delta[toState] = currentValue; // will be multiplied by the right obs later! + psi[iFrame][toState] = fromState; + } + } + + for (size_t jState = 0; jState < nState; ++jState) + { + delta[jState] *= obsProb[iFrame][jState]; + deltasum += delta[jState]; + } + + if (deltasum > 0) + { + for (size_t iState = 0; iState < nState; ++iState) + { + oldDelta[iState] = delta[iState] / deltasum; // normalise (scale) + delta[iState] = 0; + } + scale->push_back(1.0/deltasum); + } else + { + std::cerr << "WARNING: Viterbi has been fed some zero probabilities, at least they become zero in combination with the model." << std::endl; + for (size_t iState = 0; iState < nState; ++iState) + { + oldDelta[iState] = 1.0/nState; + delta[iState] = 0; + } + scale->push_back(1.0); + } + } + + // initialise backward step + double bestValue = 0; + for (size_t iState = 0; iState < nState; ++iState) + { + double currentValue = oldDelta[iState]; + if (currentValue > bestValue) + { + bestValue = currentValue; + path[nFrame-1] = iState; + } + } + + // rest of backward step + for (int iFrame = nFrame-2; iFrame != -1; --iFrame) + { + path[iFrame] = psi[iFrame+1][path[iFrame+1]]; + } + + for (size_t iState = 0; iState < nState; ++iState) + { + // std::cerr << psi[2][iState] << std::endl; + } + + return path; +} diff --git a/mnn_demo/third_party/espyin-v1.0/ESSparseHMM.h b/mnn_demo/third_party/espyin-v1.0/ESSparseHMM.h new file mode 100644 index 0000000..228f532 --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESSparseHMM.h @@ -0,0 +1,35 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#ifndef _ESSPARSEHMM_H_ +#define _ESSPARSEHMM_H_ + +#include +#include + +using std::vector; +using std::pair; + +class ESSparseHMM +{ +public: + virtual const std::vector calculateObsProb(const vector >); + const std::vector decodeViterbi(std::vector > obs, + vector *scale); + vector init; + vector from; + vector to; + vector transProb; +}; + +#endif diff --git a/mnn_demo/third_party/espyin-v1.0/ESYin.cpp b/mnn_demo/third_party/espyin-v1.0/ESYin.cpp new file mode 100644 index 0000000..cb0f7e1 --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESYin.cpp @@ -0,0 +1,145 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#include "ESYin.h" + + + +#include "ESYinUtil.h" + +#include +#include +#include +#include +#include + +using std::vector; + +ESYin::ESYin(size_t frameSize, size_t inputSampleRate, double thresh) : + m_frameSize(frameSize), + m_inputSampleRate(inputSampleRate), + m_thresh(thresh), + m_threshDistr(2), + m_yinBufferSize(frameSize/2) +{ + if (frameSize & (frameSize-1)) { + throw "N must be a power of two"; + } +} + +ESYin::~ESYin() +{ +} + +ESYin::YinOutput +ESYin::process(const double *in) const { + + double* yinBuffer = new double[m_yinBufferSize]; + + // calculate aperiodicity function for all periods + ESYinUtil::fastDifference(in, yinBuffer, m_yinBufferSize); + ESYinUtil::cumulativeDifference(yinBuffer, m_yinBufferSize); + + int tau = 0; + tau = ESYinUtil::absoluteThreshold(yinBuffer, m_yinBufferSize, m_thresh); + + double interpolatedTau; + double aperiodicity; + double f0; + + if (tau!=0) + { + interpolatedTau = ESYinUtil::parabolicInterpolation(yinBuffer, abs(tau), m_yinBufferSize); + f0 = m_inputSampleRate * (1.0 / interpolatedTau); + } else { + interpolatedTau = 0; + f0 = 0; + } + double rms = std::sqrt(ESYinUtil::sumSquare(in, 0, m_yinBufferSize)/m_yinBufferSize); + aperiodicity = yinBuffer[abs(tau)]; + // std::cerr << aperiodicity << std::endl; + if (tau < 0) f0 = -f0; + + ESYin::YinOutput yo(f0, 1-aperiodicity, rms); + for (size_t iBuf = 0; iBuf < m_yinBufferSize; ++iBuf) + { + yo.salience.push_back(yinBuffer[iBuf] < 1 ? 1-yinBuffer[iBuf] : 0); // why are the values sometimes < 0 if I don't check? + } + + delete [] yinBuffer; + return yo; +} + +ESYin::YinOutput +ESYin::processProbabilisticYin(const double *in) const { + double* yinBuffer = new double[m_yinBufferSize]; + // calculate aperiodicity function for all periods + ESYinUtil::fastDifference(in, yinBuffer, m_yinBufferSize); + ESYinUtil::cumulativeDifference(yinBuffer, m_yinBufferSize); + vector peakProbability = ESYinUtil::yinProb(yinBuffer, m_threshDistr, m_yinBufferSize); + + // calculate overall "probability" from peak probability + double probSum = 0; + for (size_t iBin = 0; iBin < m_yinBufferSize; ++iBin) + { + probSum += peakProbability[iBin]; + } + + ESYin::YinOutput yo(0,0,0); + for (size_t iBuf = 0; iBuf < m_yinBufferSize; ++iBuf) + { + yo.salience.push_back(peakProbability[iBuf]); + if (peakProbability[iBuf] > 0) + { + double currentF0 = + m_inputSampleRate * (1.0 / + ESYinUtil::parabolicInterpolation(yinBuffer, iBuf, m_yinBufferSize)); + yo.freqProb.push_back(pair(currentF0, peakProbability[iBuf])); + } + } + + // std::cerr << yo.freqProb.size() << std::endl; + + delete [] yinBuffer; + return yo; +} + + +int +ESYin::setThreshold(double parameter) +{ + m_thresh = static_cast(parameter); + return 0; +} + +int +ESYin::setThresholdDistr(float parameter) +{ + m_threshDistr = static_cast(parameter); + return 0; +} + +int +ESYin::setFrameSize(size_t parameter) +{ + m_frameSize = parameter; + m_yinBufferSize = m_frameSize/2; + return 0; +} + +// int +// Yin::setRemoveUnvoiced(bool parameter) +// { +// m_removeUnvoiced = parameter; +// return 0; +// } diff --git a/mnn_demo/third_party/espyin-v1.0/ESYin.h b/mnn_demo/third_party/espyin-v1.0/ESYin.h new file mode 100644 index 0000000..5ce2fdd --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESYin.h @@ -0,0 +1,69 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#ifndef _ESYIN_H_ +#define _ESYIN_H_ + + + + +#include + +#include +#include +#include + +using std::vector; +using std::pair; + + + +class ESYin +{ +public: + ESYin(size_t frameSize, size_t inputSampleRate, double thresh = 0.2); + virtual ~ESYin(); + + struct YinOutput { + double f0; + double periodicity; + double rms; + vector salience; + vector > freqProb; + YinOutput() : f0(0), periodicity(0), rms(0), + salience(vector(0)), freqProb(vector >(0)) { } + YinOutput(double _f, double _p, double _r) : + f0(_f), periodicity(_p), rms(_r), + salience(vector(0)), freqProb(vector >(0)) { } + YinOutput(double _f, double _p, double _r, vector _salience) : + f0(_f), periodicity(_p), rms(_r), salience(_salience), + freqProb(vector >(0)) { } + }; + + int setThreshold(double parameter); + int setThresholdDistr(float parameter); + int setFrameSize(size_t frameSize); + // int setRemoveUnvoiced(bool frameSize); + YinOutput process(const double *in) const; + YinOutput processProbabilisticYin(const double *in) const; + +private: + mutable size_t m_frameSize; + mutable size_t m_inputSampleRate; + mutable double m_thresh; + mutable size_t m_threshDistr; + mutable size_t m_yinBufferSize; + // mutable bool m_removeUnvoiced; +}; + +#endif diff --git a/mnn_demo/third_party/espyin-v1.0/ESYinUtil.cpp b/mnn_demo/third_party/espyin-v1.0/ESYinUtil.cpp new file mode 100644 index 0000000..6bacdbf --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESYinUtil.cpp @@ -0,0 +1,346 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#include "ESYinUtil.h" +#include "ESFFTimpl.cpp" + +#include + +#include +#include +#include + +void +ESYinUtil::fastDifference(const double *in, double *yinBuffer, const size_t yinBufferSize) +{ + + // DECLARE AND INITIALISE + // initialisation of most of the arrays here was done in a separate function, + // with all the arrays as members of the class... moved them back here. + + size_t frameSize = 2 * yinBufferSize; + + for (size_t j = 0; j < yinBufferSize; ++j) + { + yinBuffer[j] = 0.; + } + + double *audioTransformedReal = new double[frameSize]; + double *audioTransformedImag = new double[frameSize]; + double *nullImag = new double[frameSize]; + double *kernel = new double[frameSize]; + double *kernelTransformedReal = new double[frameSize]; + double *kernelTransformedImag = new double[frameSize]; + double *yinStyleACFReal = new double[frameSize]; + double *yinStyleACFImag = new double[frameSize]; + double *powerTerms = new double[yinBufferSize]; + + for (size_t j = 0; j < yinBufferSize; ++j) + { + powerTerms[j] = 0.; + } + + for (size_t j = 0; j < frameSize; ++j) + { + nullImag[j] = 0.; + audioTransformedReal[j] = 0.; + audioTransformedImag[j] = 0.; + kernel[j] = 0.; + kernelTransformedReal[j] = 0.; + kernelTransformedImag[j] = 0.; + yinStyleACFReal[j] = 0.; + yinStyleACFImag[j] = 0.; + } + + // POWER TERM CALCULATION + // ... for the power terms in equation (7) in the Yin paper + powerTerms[0] = 0.0; + for (size_t j = 0; j < yinBufferSize; ++j) { + powerTerms[0] += in[j] * in[j]; + } + + // now iteratively calculate all others (saves a few multiplications) + for (size_t tau = 1; tau < yinBufferSize; ++tau) { + powerTerms[tau] = powerTerms[tau-1] - in[tau-1] * in[tau-1] + in[tau+yinBufferSize] * in[tau+yinBufferSize]; + } + + // YIN-STYLE AUTOCORRELATION via FFT + // 1. data + esfft(uint(frameSize), false, in, nullImag, audioTransformedReal, audioTransformedImag); + + // 2. half of the data, disguised as a convolution kernel + for (size_t j = 0; j < yinBufferSize; ++j) { + kernel[j] = in[yinBufferSize-1-j]; + kernel[j+yinBufferSize] = 0; + } + esfft(uint(frameSize), false, kernel, nullImag, kernelTransformedReal, kernelTransformedImag); + + // 3. convolution via complex multiplication -- written into + for (size_t j = 0; j < frameSize; ++j) { + yinStyleACFReal[j] = audioTransformedReal[j]*kernelTransformedReal[j] - audioTransformedImag[j]*kernelTransformedImag[j]; // real + yinStyleACFImag[j] = audioTransformedReal[j]*kernelTransformedImag[j] + audioTransformedImag[j]*kernelTransformedReal[j]; // imaginary + } + esfft(uint(frameSize), true, yinStyleACFReal, yinStyleACFImag, audioTransformedReal, audioTransformedImag); + + // CALCULATION OF difference function + // ... according to (7) in the Yin paper. + for (size_t j = 0; j < yinBufferSize; ++j) { + // taking only the real part + yinBuffer[j] = powerTerms[0] + powerTerms[j] - 2 * audioTransformedReal[j+yinBufferSize-1]; + } + delete [] audioTransformedReal; + delete [] audioTransformedImag; + delete [] nullImag; + delete [] kernel; + delete [] kernelTransformedReal; + delete [] kernelTransformedImag; + delete [] yinStyleACFReal; + delete [] yinStyleACFImag; + delete [] powerTerms; +} + +void +ESYinUtil::cumulativeDifference(double *yinBuffer, const size_t yinBufferSize) +{ + size_t tau; + + yinBuffer[0] = 1; + + double runningSum = 0; + + for (tau = 1; tau < yinBufferSize; ++tau) { + runningSum += yinBuffer[tau]; + if (runningSum == 0) + { + yinBuffer[tau] = 1; + } else { + yinBuffer[tau] *= tau / runningSum; + } + } +} + +int +ESYinUtil::absoluteThreshold(const double *yinBuffer, const size_t yinBufferSize, const double thresh) +{ + size_t tau; + size_t minTau = 0; + double minVal = 1000.; + + // using Joren Six's "loop construct" from TarsosDSP + tau = 2; + while (tau < yinBufferSize) + { + if (yinBuffer[tau] < thresh) + { + while (tau+1 < yinBufferSize && yinBuffer[tau+1] < yinBuffer[tau]) + { + ++tau; + } + return tau; + } else { + if (yinBuffer[tau] < minVal) + { + minVal = yinBuffer[tau]; + minTau = tau; + } + } + ++tau; + } + if (minTau > 0) + { + return -minTau; + } + return 0; +} + + +std::vector +ESYinUtil::yinProb(const double *yinBuffer, const size_t prior, const size_t yinBufferSize) +{ + double minWeight = 0.01; + size_t tau; + std::vector thresholds; + std::vector distribution; + std::vector peakProb = std::vector(yinBufferSize); + // TODO: make the distributions below part of a class, so they don't have to + // be allocated every time. + float uniformDist[100] = {0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000,0.0100000}; + float betaDist1[100] = {0.028911,0.048656,0.061306,0.068539,0.071703,0.071877,0.069915,0.066489,0.062117,0.057199,0.052034,0.046844,0.041786,0.036971,0.032470,0.028323,0.024549,0.021153,0.018124,0.015446,0.013096,0.011048,0.009275,0.007750,0.006445,0.005336,0.004397,0.003606,0.002945,0.002394,0.001937,0.001560,0.001250,0.000998,0.000792,0.000626,0.000492,0.000385,0.000300,0.000232,0.000179,0.000137,0.000104,0.000079,0.000060,0.000045,0.000033,0.000024,0.000018,0.000013,0.000009,0.000007,0.000005,0.000003,0.000002,0.000002,0.000001,0.000001,0.000001,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000}; + float betaDist2[100] = {0.012614,0.022715,0.030646,0.036712,0.041184,0.044301,0.046277,0.047298,0.047528,0.047110,0.046171,0.044817,0.043144,0.041231,0.039147,0.036950,0.034690,0.032406,0.030133,0.027898,0.025722,0.023624,0.021614,0.019704,0.017900,0.016205,0.014621,0.013148,0.011785,0.010530,0.009377,0.008324,0.007366,0.006497,0.005712,0.005005,0.004372,0.003806,0.003302,0.002855,0.002460,0.002112,0.001806,0.001539,0.001307,0.001105,0.000931,0.000781,0.000652,0.000542,0.000449,0.000370,0.000303,0.000247,0.000201,0.000162,0.000130,0.000104,0.000082,0.000065,0.000051,0.000039,0.000030,0.000023,0.000018,0.000013,0.000010,0.000007,0.000005,0.000004,0.000003,0.000002,0.000001,0.000001,0.000001,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000}; + float betaDist3[100] = {0.006715,0.012509,0.017463,0.021655,0.025155,0.028031,0.030344,0.032151,0.033506,0.034458,0.035052,0.035331,0.035332,0.035092,0.034643,0.034015,0.033234,0.032327,0.031314,0.030217,0.029054,0.027841,0.026592,0.025322,0.024042,0.022761,0.021489,0.020234,0.019002,0.017799,0.016630,0.015499,0.014409,0.013362,0.012361,0.011407,0.010500,0.009641,0.008830,0.008067,0.007351,0.006681,0.006056,0.005475,0.004936,0.004437,0.003978,0.003555,0.003168,0.002814,0.002492,0.002199,0.001934,0.001695,0.001481,0.001288,0.001116,0.000963,0.000828,0.000708,0.000603,0.000511,0.000431,0.000361,0.000301,0.000250,0.000206,0.000168,0.000137,0.000110,0.000088,0.000070,0.000055,0.000043,0.000033,0.000025,0.000019,0.000014,0.000010,0.000007,0.000005,0.000004,0.000002,0.000002,0.000001,0.000001,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000}; + float betaDist4[100] = {0.003996,0.007596,0.010824,0.013703,0.016255,0.018501,0.020460,0.022153,0.023597,0.024809,0.025807,0.026607,0.027223,0.027671,0.027963,0.028114,0.028135,0.028038,0.027834,0.027535,0.027149,0.026687,0.026157,0.025567,0.024926,0.024240,0.023517,0.022763,0.021983,0.021184,0.020371,0.019548,0.018719,0.017890,0.017062,0.016241,0.015428,0.014627,0.013839,0.013068,0.012315,0.011582,0.010870,0.010181,0.009515,0.008874,0.008258,0.007668,0.007103,0.006565,0.006053,0.005567,0.005107,0.004673,0.004264,0.003880,0.003521,0.003185,0.002872,0.002581,0.002312,0.002064,0.001835,0.001626,0.001434,0.001260,0.001102,0.000959,0.000830,0.000715,0.000612,0.000521,0.000440,0.000369,0.000308,0.000254,0.000208,0.000169,0.000136,0.000108,0.000084,0.000065,0.000050,0.000037,0.000027,0.000019,0.000014,0.000009,0.000006,0.000004,0.000002,0.000001,0.000001,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000}; + float single10[100] = {0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,1.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000}; + float single15[100] = {0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,1.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000}; + float single20[100] = {0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,1.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000,0.00000}; + + size_t nThreshold = 100; + int nThresholdInt = nThreshold; + + for (int i = 0; i < nThresholdInt; ++i) + { + switch (prior) { + case 0: + distribution.push_back(uniformDist[i]); + break; + case 1: + distribution.push_back(betaDist1[i]); + break; + case 2: + distribution.push_back(betaDist2[i]); + break; + case 3: + distribution.push_back(betaDist3[i]); + break; + case 4: + distribution.push_back(betaDist4[i]); + break; + case 5: + distribution.push_back(single10[i]); + break; + case 6: + distribution.push_back(single15[i]); + break; + case 7: + distribution.push_back(single20[i]); + break; + default: + distribution.push_back(uniformDist[i]); + } + thresholds.push_back(0.01 + i*0.01); + } + + // double minYin = 2936; + // for (size_t i = 2; i < yinBufferSize; ++i) + // { + // if (yinBuffer[i] < minYin) + // { + // minYin = yinBuffer[i]; + // } + // } + // if (minYin < 0.01) std::cerr << "min Yin buffer element: " << minYin << std::endl; + + + int currThreshInd = nThreshold-1; + tau = 2; + + // double factor = 1.0 / (0.25 * (nThresholdInt+1) * (nThresholdInt + 1)); // factor to scale down triangular weight + size_t minInd = 0; + float minVal = 42.f; + while (currThreshInd != -1 && tau < yinBufferSize) + { + if (yinBuffer[tau] < thresholds[currThreshInd]) + { + while (tau + 1 < yinBufferSize && yinBuffer[tau+1] < yinBuffer[tau]) + { + tau++; + } + // tau is now local minimum + // std::cerr << tau << " " << currThreshInd << " "<< thresholds[currThreshInd] << " " << distribution[currThreshInd] << std::endl; + if (yinBuffer[tau] < minVal && tau > 2){ + minVal = yinBuffer[tau]; + minInd = tau; + } + peakProb[tau] += distribution[currThreshInd]; + currThreshInd--; + } else { + tau++; + } + } + double nonPeakProb = 1; + for (size_t i = 0; i < yinBufferSize; ++i) + { + nonPeakProb -= peakProb[i]; + } + // std::cerr << nonPeakProb << std::endl; + if (minInd > 0) + { + // std::cerr << "min set " << minVal << " " << minInd << " " << nonPeakProb << std::endl; + peakProb[minInd] += nonPeakProb * minWeight; + } + + return peakProb; +} + +double +ESYinUtil::parabolicInterpolation(const double *yinBuffer, const size_t tau, const size_t yinBufferSize) +{ + // this is taken almost literally from Joren Six's Java implementation + if (tau == yinBufferSize) // not valid anyway. + { + return static_cast(tau); + } + + double betterTau = 0.0; + size_t x0; + size_t x2; + + if (tau < 1) + { + x0 = tau; + } else { + x0 = tau - 1; + } + + if (tau + 1 < yinBufferSize) + { + x2 = tau + 1; + } else { + x2 = tau; + } + + if (x0 == tau) + { + if (yinBuffer[tau] <= yinBuffer[x2]) + { + betterTau = tau; + } else { + betterTau = x2; + } + } + else if (x2 == tau) + { + if (yinBuffer[tau] <= yinBuffer[x0]) + { + betterTau = tau; + } + else + { + betterTau = x0; + } + } + else + { + float s0, s1, s2; + s0 = yinBuffer[x0]; + s1 = yinBuffer[tau]; + s2 = yinBuffer[x2]; + // fixed AUBIO implementation, thanks to Karl Helgason: + // (2.0f * s1 - s2 - s0) was incorrectly multiplied with -1 + betterTau = tau + (s2 - s0) / (2 * (2 * s1 - s2 - s0)); + + // std::cerr << tau << " --> " << betterTau << std::endl; + + } + return betterTau; +} + +double +ESYinUtil::sumSquare(const double *in, const size_t start, const size_t end) +{ + double out = 0; + for (size_t i = start; i < end; ++i) + { + out += in[i] * in[i]; + } + return out; +} diff --git a/mnn_demo/third_party/espyin-v1.0/ESYinUtil.h b/mnn_demo/third_party/espyin-v1.0/ESYinUtil.h new file mode 100644 index 0000000..6236b57 --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/ESYinUtil.h @@ -0,0 +1,41 @@ +/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */ + +/* + pYIN - A fundamental frequency estimator for monophonic audio + Centre for Digital Music, Queen Mary, University of London. + + This program is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. See the file + COPYING included with this distribution for more information. +*/ + +#ifndef _ESYINUTIL_H_ +#define _ESYINUTIL_H_ + + + + +#include + +#include +#include +#include + +using std::vector; + +class ESYinUtil +{ +public: + static double sumSquare(const double *in, const size_t startInd, const size_t endInd); + static void difference(const double *in, double *yinBuffer, const size_t yinBufferSize); + static void fastDifference(const double *in, double *yinBuffer, const size_t yinBufferSize); + static void cumulativeDifference(double *yinBuffer, const size_t yinBufferSize); + static int absoluteThreshold(const double *yinBuffer, const size_t yinBufferSize, const double thresh); + static vector yinProb(const double *yinBuffer, const size_t prior, const size_t yinBufferSize); + static double parabolicInterpolation(const double *yinBuffer, const size_t tau, + const size_t yinBufferSize); +}; + +#endif diff --git a/mnn_demo/third_party/espyin-v1.0/README b/mnn_demo/third_party/espyin-v1.0/README new file mode 100644 index 0000000..1235faa --- /dev/null +++ b/mnn_demo/third_party/espyin-v1.0/README @@ -0,0 +1,85 @@ + +pYIN +==== + +pYIN is a modification of the well-loved YIN algorithm for fundamental +frequency (F0) estimation in monophonic audio. + +This is a Vamp plugin (http://vamp-plugins.org) implementation of +pYIN, as well as the original YIN method. The plugin can be used by +any Vamp host such as Sonic Visualiser and Sonic Annotator. + + +Method +====== + +The pYIN method is a modification of the method known as YIN (De +Cheveigné, Alain, and Hideki Kawahara. "YIN, a fundamental frequency +estimator for speech and music." The Journal of the Acoustical Society +of America 111 (2002)). + +The original YIN has one threshold parameter. In pYIN this parameter +is replaced by a parameter distribution, and for every frame several +fundamental frequency candidates obtained, conditional on this prior +parameter distribution. In the second phase, a hidden Markov model +(HMM) is Viterbi-decoded to find a "smooth" path through the +fundamental frequency candidates. Note that this smoothed path is not +smudging or averaging pitch estimates: any pitch estimate contains +only fundamental frequency estimates that are genuine estimates of the +original YIN method for some threshold parameter. + +The note estimator is a post-processing step on the pYIN pitch track, +also performed as Viterbi decoding of an HMM. + + +Limitations +=========== + +The pYIN method is designed to reliably extract the fundamental +frequency of audio recordings of a monophonic, harmonic instrument +such as the human voice. Being based on YIN means that pYIN exploits +the periodicity of the signal. In some circumstances it will not be +reliable. Such circumstances occur, e.g. + + ... if the source audio is not monophonic, e.g. a singer with + accompanying instruments, + + ... if the recording has reverb/echo (this essentially makes it + polyphonic), + + ... if, in a stringed instrument such as the cello, one string + keeps ringing while the melody turns to a different pitch. + + +Authors, Citation, License and Use +================================== + +pYIN was written by Matthias Mauch. Copyright 2012-2013 Matthias Mauch +and Queen Mary, University of London. + +The YIN code was drawn from the Java implementation in the TarsosDSP +library by Joren Six. + +If you make use of this software for any public or commercial purpose, +we ask you to kindly mention the authors and Queen Mary, University of +London in your user-visible documentation. We're very happy to see +this sort of use but would much appreciate being credited, separately +from the requirements of the software license itself (see below). + +If you make use of this software for academic purposes, please cite +one of the publications indicated on the Publications page: + +https://code.soundsoftware.ac.uk/publications?project_id=pyin + +This program is free software: you can redistribute it and/or modify +it under the terms of the GNU General Public License as published by +the Free Software Foundation, either version 2 of the License, or (at +your option) any later version. + +This program is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A ARTICULAR PURPOSE. See the GNU +General Public License for more details. You should have received a +copy of the GNU General Public License along with this program. If +not, see http://www.gnu.org/licenses/. +