From 05abc262bac7dcee34a62737015ac67b32fc796e Mon Sep 17 00:00:00 2001 From: Christoph Oelckers Date: Tue, 14 Jul 2020 20:57:42 +0200 Subject: [PATCH] - removed libdivide for good and the unused C++ wrapper for fix16 along with it. --- source/CMakeLists.txt | 1 - source/blood/src/actor.cpp | 2 +- source/blood/src/fx.cpp | 4 +- source/blood/src/gib.cpp | 10 +- source/build/include/compat.h | 1 - source/build/include/pragmas.h | 18 - source/build/src/engine.cpp | 3 +- source/build/src/pragmas.cpp | 24 - source/thirdparty/include/fix16.h | 2 - source/thirdparty/include/fix16.hpp | 180 --- source/thirdparty/include/libdivide.h | 2087 ------------------------- 11 files changed, 9 insertions(+), 2323 deletions(-) delete mode 100644 source/build/src/pragmas.cpp delete mode 100644 source/thirdparty/include/fix16.hpp delete mode 100644 source/thirdparty/include/libdivide.h diff --git a/source/CMakeLists.txt b/source/CMakeLists.txt index 0aed88559..fcf1667d0 100644 --- a/source/CMakeLists.txt +++ b/source/CMakeLists.txt @@ -776,7 +776,6 @@ set (PCH_SOURCES build/src/mdsprite.cpp build/src/mhk.cpp build/src/polymost.cpp - build/src/pragmas.cpp build/src/scriptfile.cpp build/src/timer.cpp build/src/voxmodel.cpp diff --git a/source/blood/src/actor.cpp b/source/blood/src/actor.cpp index 574c03c2e..c87dc6bbe 100644 --- a/source/blood/src/actor.cpp +++ b/source/blood/src/actor.cpp @@ -5023,7 +5023,7 @@ void MoveDude(spritetype *pSprite) { xvel[pFX2->index] = Random2(0x6aaaa); yvel[pFX2->index] = Random2(0x6aaaa); - zvel[pFX2->index] = -Random(0xd5555); + zvel[pFX2->index] = -(int)Random(0xd5555); } } } diff --git a/source/blood/src/fx.cpp b/source/blood/src/fx.cpp index 7b628447b..8b576614a 100644 --- a/source/blood/src/fx.cpp +++ b/source/blood/src/fx.cpp @@ -288,7 +288,7 @@ void fxSpawnBlood(spritetype *pSprite, int a2) pBlood->ang = 1024; xvel[pBlood->index] = Random2(0x6aaaa); yvel[pBlood->index] = Random2(0x6aaaa); - zvel[pBlood->index] = -Random(0x10aaaa)-100; + zvel[pBlood->index] = -(int)Random(0x10aaaa)-100; evPost(pBlood->index, 3, 8, kCallbackFXBloodSpurt); } } @@ -313,7 +313,7 @@ void sub_746D4(spritetype *pSprite, int a2) pSpawn->ang = 1024; xvel[pSpawn->index] = Random2(0x6aaaa); yvel[pSpawn->index] = Random2(0x6aaaa); - zvel[pSpawn->index] = -Random(0x10aaaa)-100; + zvel[pSpawn->index] = -(int)Random(0x10aaaa)-100; evPost(pSpawn->index, 3, 8, kCallbackFXPodBloodSpray); } } diff --git a/source/blood/src/gib.cpp b/source/blood/src/gib.cpp index 059c40720..8fb0b6505 100644 --- a/source/blood/src/gib.cpp +++ b/source/blood/src/gib.cpp @@ -345,12 +345,12 @@ void GibFX(spritetype *pSprite, GIBFX *pGFX, CGibPosition *pPos, CGibVelocity *p } else if (dz2 > dz1 && dz1 < 0x4000) { - zvel[pFX->index] = -Random((klabs(pGFX->at11)<<18)/120); + zvel[pFX->index] = -(int)Random((klabs(pGFX->at11)<<18)/120); } else { if ((pGFX->at11<<18)/120 < 0) - zvel[pFX->index] = -Random((klabs(pGFX->at11)<<18)/120); + zvel[pFX->index] = -(int)Random((klabs(pGFX->at11)<<18)/120); else zvel[pFX->index] = Random2((pGFX->at11<<18)/120); } @@ -419,7 +419,7 @@ void GibThing(spritetype *pSprite, GIBTHING *pGThing, CGibPosition *pPos, CGibVe } else if (dz2 > dz1 && dz1 < 0x4000) { - zvel[pGib->index] = -Random((pGThing->at10<<18)/120); + zvel[pGib->index] = -(int)Random((pGThing->at10<<18)/120); } else { @@ -472,13 +472,13 @@ void GibFX(int nWall, GIBFX * pGFX, int a3, int a4, int a5, int a6, CGibVelocity { xvel[pGib->index] = Random2((pGFX->atd<<18)/120); yvel[pGib->index] = Random2((pGFX->atd<<18)/120); - zvel[pGib->index] = -Random((pGFX->at11<<18)/120); + zvel[pGib->index] = -(int)Random((pGFX->at11<<18)/120); } else { xvel[pGib->index] = Random2((pVel->vx<<18)/120); yvel[pGib->index] = Random2((pVel->vy<<18)/120); - zvel[pGib->index] = -Random((pVel->vz<<18)/120); + zvel[pGib->index] = -(int)Random((pVel->vz<<18)/120); } } } diff --git a/source/build/include/compat.h b/source/build/include/compat.h index e9a3774c6..360e87489 100644 --- a/source/build/include/compat.h +++ b/source/build/include/compat.h @@ -1017,7 +1017,6 @@ void *handle_memerr(void *); #define LIBDIVIDE_NONAMESPACE #define LIBDIVIDE_NOINLINE #include "fix16.h" -#include "libdivide.h" #include "vectors.h" using ClockTicks = int; diff --git a/source/build/include/pragmas.h b/source/build/include/pragmas.h index 88b716f8f..67aee9ff3 100644 --- a/source/build/include/pragmas.h +++ b/source/build/include/pragmas.h @@ -33,24 +33,6 @@ extern int32_t reciptable[2048]; #define DIVTABLESIZE 16384 -extern libdivide::libdivide_s64_t divtable64[DIVTABLESIZE]; -extern libdivide::libdivide_s32_t divtable32[DIVTABLESIZE]; -extern void initdivtables(void); - -static inline int64_t tabledivide64(int64_t const n, int64_t const d) -{ - static libdivide::libdivide_s64_t sdiv; - static int64_t lastd; - auto const dptr = ((uint64_t)d < DIVTABLESIZE) ? &divtable64[d] : &sdiv; - - if (d == lastd || dptr != &sdiv) - goto skip; - - sdiv = libdivide::libdivide_s64_gen((lastd = d)); -skip: - return libdivide::libdivide_s64_do(n, dptr); -} - static inline int32_t divscale(int32_t eax, int32_t ebx, int32_t ecx) { return (int64_t(eax) << ecx) / ebx; } static inline int64_t divscale64(int64_t eax, int64_t ebx, int64_t ecx) { return (eax << ecx) / ebx; } diff --git a/source/build/src/engine.cpp b/source/build/src/engine.cpp index a47434be6..ccc5e344e 100644 --- a/source/build/src/engine.cpp +++ b/source/build/src/engine.cpp @@ -568,7 +568,7 @@ static inline void initksqrt(void) temp = root*root-num; while (klabs(int32_t(temp-2*root+1)) < klabs(temp)) { - temp += -(2*root)+1; + temp += 1-int(2*root); root--; } while (klabs(int32_t(temp+2*root+1)) < klabs(temp)) @@ -1066,7 +1066,6 @@ static tspritetype tsprite_s[MAXSPRITESONSCREEN]; int32_t enginePreInit(void) { polymost_initosdfuncs(); - initdivtables(); #if !defined DEBUG_MAIN_ARRAYS sector = sector_s; diff --git a/source/build/src/pragmas.cpp b/source/build/src/pragmas.cpp deleted file mode 100644 index 6d199c47c..000000000 --- a/source/build/src/pragmas.cpp +++ /dev/null @@ -1,24 +0,0 @@ -// Function-wrapped Watcom pragmas -// by Jonathon Fowler (jf@jonof.id.au) -// -// These functions represent some of the more longer-winded pragmas -// from the original pragmas.h wrapped into functions for easier -// use since many jumps and whatnot make it harder to write macro- -// inline versions. I'll eventually convert these to macro-inline -// equivalents. --Jonathon - -#include "compat.h" -#include "pragmas.h" - -libdivide::libdivide_s64_t divtable64[DIVTABLESIZE]; -libdivide::libdivide_s32_t divtable32[DIVTABLESIZE]; - -void initdivtables(void) -{ - for (int i = 1; i < DIVTABLESIZE; ++i) - { - divtable64[i] = libdivide::libdivide_s64_gen(i); - divtable32[i] = libdivide::libdivide_s32_gen(i); - } -} - diff --git a/source/thirdparty/include/fix16.h b/source/thirdparty/include/fix16.h index c4a5ce408..7a377246e 100644 --- a/source/thirdparty/include/fix16.h +++ b/source/thirdparty/include/fix16.h @@ -297,6 +297,4 @@ extern fix16_t fix16_from_str(const char *buf); ) \ ) -#include "fix16.hpp" - #endif diff --git a/source/thirdparty/include/fix16.hpp b/source/thirdparty/include/fix16.hpp deleted file mode 100644 index dcba11d83..000000000 --- a/source/thirdparty/include/fix16.hpp +++ /dev/null @@ -1,180 +0,0 @@ -#ifndef __libfixmath_fix16_hpp__ -#define __libfixmath_fix16_hpp__ - -#include "fix16.h" - -class Fix16 { - public: - fix16_t value; - - Fix16() { value = 0; } - Fix16(const Fix16 &inValue) { value = inValue.value; } - Fix16(const fix16_t inValue) { value = inValue; } - Fix16(const float inValue) { value = fix16_from_float(inValue); } - Fix16(const double inValue) { value = fix16_from_dbl(inValue); } - Fix16(const int16_t inValue) { value = fix16_from_int(inValue); } - - operator fix16_t() const { return value; } - operator double() const { return fix16_to_dbl(value); } - operator float() const { return fix16_to_float(value); } - operator int16_t() const { return fix16_to_int(value); } - - Fix16 & operator=(const Fix16 &rhs) { value = rhs.value; return *this; } - Fix16 & operator=(const fix16_t rhs) { value = rhs; return *this; } - Fix16 & operator=(const double rhs) { value = fix16_from_dbl(rhs); return *this; } - Fix16 & operator=(const float rhs) { value = fix16_from_float(rhs); return *this; } - Fix16 & operator=(const int16_t rhs) { value = fix16_from_int(rhs); return *this; } - - Fix16 & operator+=(const Fix16 &rhs) { value += rhs.value; return *this; } - Fix16 & operator+=(const fix16_t rhs) { value += rhs; return *this; } - Fix16 & operator+=(const double rhs) { value += fix16_from_dbl(rhs); return *this; } - Fix16 & operator+=(const float rhs) { value += fix16_from_float(rhs); return *this; } - Fix16 & operator+=(const int16_t rhs) { value += fix16_from_int(rhs); return *this; } - - Fix16 & operator-=(const Fix16 &rhs) { value -= rhs.value; return *this; } - Fix16 & operator-=(const fix16_t rhs) { value -= rhs; return *this; } - Fix16 & operator-=(const double rhs) { value -= fix16_from_dbl(rhs); return *this; } - Fix16 & operator-=(const float rhs) { value -= fix16_from_float(rhs); return *this; } - Fix16 & operator-=(const int16_t rhs) { value -= fix16_from_int(rhs); return *this; } - - Fix16 & operator*=(const Fix16 &rhs) { value = fix16_mul(value, rhs.value); return *this; } - Fix16 & operator*=(const fix16_t rhs) { value = fix16_mul(value, rhs); return *this; } - Fix16 & operator*=(const double rhs) { value = fix16_mul(value, fix16_from_dbl(rhs)); return *this; } - Fix16 & operator*=(const float rhs) { value = fix16_mul(value, fix16_from_float(rhs)); return *this; } - Fix16 & operator*=(const int16_t rhs) { value *= rhs; return *this; } - - Fix16 & operator/=(const Fix16 &rhs) { value = fix16_div(value, rhs.value); return *this; } - Fix16 & operator/=(const fix16_t rhs) { value = fix16_div(value, rhs); return *this; } - Fix16 & operator/=(const double rhs) { value = fix16_div(value, fix16_from_dbl(rhs)); return *this; } - Fix16 & operator/=(const float rhs) { value = fix16_div(value, fix16_from_float(rhs)); return *this; } - Fix16 & operator/=(const int16_t rhs) { value /= rhs; return *this; } - - Fix16 & operator%=(const Fix16 &rhs) { value = fix16_mod(value, rhs.value); return *this; } - Fix16 & operator%=(const fix16_t rhs) { value = fix16_mod(value, rhs); return *this; } - Fix16 & operator%=(const double rhs) { value = fix16_mod(value, fix16_from_dbl(rhs)); return *this; } - Fix16 & operator%=(const float rhs) { value = fix16_mod(value, fix16_from_float(rhs)); return *this; } - Fix16 & operator%=(const int16_t rhs) { value %= rhs; return *this; } - - Fix16 & operator&=(const Fix16 &rhs) { value = fix16_from_int(fix16_to_int(value) & fix16_to_int(rhs.value)); return *this; } - Fix16 & operator&=(const fix16_t rhs) { value = fix16_from_int(fix16_to_int(value) & fix16_to_int(rhs)); return *this; } - Fix16 & operator&=(const int16_t rhs) { value = fix16_from_int(fix16_to_int(value) & rhs); return *this; } - - Fix16 & operator^=(const Fix16 &rhs) { value = fix16_from_int(fix16_to_int(value) ^ fix16_to_int(rhs.value)); return *this; } - Fix16 & operator^=(const fix16_t rhs) { value = fix16_from_int(fix16_to_int(value) ^ fix16_to_int(rhs)); return *this; } - Fix16 & operator^=(const int16_t rhs) { value = fix16_from_int(fix16_to_int(value) ^ rhs); return *this; } - - Fix16 & operator|=(const Fix16 &rhs) { value = fix16_from_int(fix16_to_int(value) | fix16_to_int(rhs.value)); return *this; } - Fix16 & operator|=(const fix16_t rhs) { value = fix16_from_int(fix16_to_int(value) | fix16_to_int(rhs)); return *this; } - Fix16 & operator|=(const int16_t rhs) { value = fix16_from_int(fix16_to_int(value) | rhs); return *this; } - - Fix16 & operator<<=(const Fix16 &rhs) { value <<= rhs.value; return *this; } - Fix16 & operator<<=(const fix16_t rhs) { value <<= rhs; return *this; } - Fix16 & operator<<=(const int16_t rhs) { value <<= fix16_from_int(rhs); return *this; } - - Fix16 & operator>>=(const Fix16 &rhs) { value >>= rhs.value; return *this; } - Fix16 & operator>>=(const fix16_t rhs) { value >>= rhs; return *this; } - Fix16 & operator>>=(const int16_t rhs) { value >>= fix16_from_int(rhs); return *this; } - - const Fix16 operator+(const Fix16 &other) const { Fix16 ret = *this; ret += other; return ret; } - const Fix16 operator+(const fix16_t other) const { Fix16 ret = *this; ret += other; return ret; } - const Fix16 operator+(const double other) const { Fix16 ret = *this; ret += other; return ret; } - const Fix16 operator+(const float other) const { Fix16 ret = *this; ret += other; return ret; } - const Fix16 operator+(const int16_t other) const { Fix16 ret = *this; ret += other; return ret; } - -#ifndef FIXMATH_NO_OVERFLOW - const Fix16 sadd(const Fix16 &other) const { Fix16 ret = fix16_sadd(value, other.value); return ret; } - const Fix16 sadd(const fix16_t other) const { Fix16 ret = fix16_sadd(value, other); return ret; } - const Fix16 sadd(const double other) const { Fix16 ret = fix16_sadd(value, fix16_from_dbl(other)); return ret; } - const Fix16 sadd(const float other) const { Fix16 ret = fix16_sadd(value, fix16_from_float(other)); return ret; } - const Fix16 sadd(const int16_t other) const { Fix16 ret = fix16_sadd(value, fix16_from_int(other)); return ret; } -#endif - - const Fix16 operator-(const Fix16 &other) const { Fix16 ret = *this; ret -= other; return ret; } - const Fix16 operator-(const fix16_t other) const { Fix16 ret = *this; ret -= other; return ret; } - const Fix16 operator-(const double other) const { Fix16 ret = *this; ret -= other; return ret; } - const Fix16 operator-(const float other) const { Fix16 ret = *this; ret -= other; return ret; } - const Fix16 operator-(const int16_t other) const { Fix16 ret = *this; ret -= other; return ret; } - -#ifndef FIXMATH_NO_OVERFLOW - const Fix16 ssub(const Fix16 &other) const { Fix16 ret = fix16_sadd(value, -other.value); return ret; } - const Fix16 ssub(const fix16_t other) const { Fix16 ret = fix16_sadd(value, -other); return ret; } - const Fix16 ssub(const double other) const { Fix16 ret = fix16_sadd(value, -fix16_from_dbl(other)); return ret; } - const Fix16 ssub(const float other) const { Fix16 ret = fix16_sadd(value, -fix16_from_float(other)); return ret; } - const Fix16 ssub(const int16_t other) const { Fix16 ret = fix16_sadd(value, -fix16_from_int(other)); return ret; } -#endif - - const Fix16 operator*(const Fix16 &other) const { Fix16 ret = *this; ret *= other; return ret; } - const Fix16 operator*(const fix16_t other) const { Fix16 ret = *this; ret *= other; return ret; } - const Fix16 operator*(const double other) const { Fix16 ret = *this; ret *= other; return ret; } - const Fix16 operator*(const float other) const { Fix16 ret = *this; ret *= other; return ret; } - const Fix16 operator*(const int16_t other) const { Fix16 ret = *this; ret *= other; return ret; } - -#ifndef FIXMATH_NO_OVERFLOW - const Fix16 smul(const Fix16 &other) const { Fix16 ret = fix16_smul(value, other.value); return ret; } - const Fix16 smul(const fix16_t other) const { Fix16 ret = fix16_smul(value, other); return ret; } - const Fix16 smul(const double other) const { Fix16 ret = fix16_smul(value, fix16_from_dbl(other)); return ret; } - const Fix16 smul(const float other) const { Fix16 ret = fix16_smul(value, fix16_from_float(other)); return ret; } - const Fix16 smul(const int16_t other) const { Fix16 ret = fix16_smul(value, fix16_from_int(other)); return ret; } -#endif - - const Fix16 operator/(const Fix16 &other) const { Fix16 ret = *this; ret /= other; return ret; } - const Fix16 operator/(const fix16_t other) const { Fix16 ret = *this; ret /= other; return ret; } - const Fix16 operator/(const double other) const { Fix16 ret = *this; ret /= other; return ret; } - const Fix16 operator/(const float other) const { Fix16 ret = *this; ret /= other; return ret; } - const Fix16 operator/(const int16_t other) const { Fix16 ret = *this; ret /= other; return ret; } - -#ifndef FIXMATH_NO_OVERFLOW - const Fix16 sdiv(const Fix16 &other) const { Fix16 ret = fix16_sdiv(value, other.value); return ret; } - const Fix16 sdiv(const fix16_t other) const { Fix16 ret = fix16_sdiv(value, other); return ret; } - const Fix16 sdiv(const double other) const { Fix16 ret = fix16_sdiv(value, fix16_from_dbl(other)); return ret; } - const Fix16 sdiv(const float other) const { Fix16 ret = fix16_sdiv(value, fix16_from_float(other)); return ret; } - const Fix16 sdiv(const int16_t other) const { Fix16 ret = fix16_sdiv(value, fix16_from_int(other)); return ret; } -#endif - - int operator==(const Fix16 &other) const { return (value == other.value); } - int operator==(const fix16_t other) const { return (value == other); } - int operator==(const double other) const { return (value == fix16_from_dbl(other)); } - int operator==(const float other) const { return (value == fix16_from_float(other)); } - int operator==(const int16_t other) const { return (value == fix16_from_int(other)); } - - int operator!=(const Fix16 &other) const { return (value != other.value); } - int operator!=(const fix16_t other) const { return (value != other); } - int operator!=(const double other) const { return (value != fix16_from_dbl(other)); } - int operator!=(const float other) const { return (value != fix16_from_float(other)); } - int operator!=(const int16_t other) const { return (value != fix16_from_int(other)); } - - int operator<=(const Fix16 &other) const { return (value <= other.value); } - int operator<=(const fix16_t other) const { return (value <= other); } - int operator<=(const double other) const { return (value <= fix16_from_dbl(other)); } - int operator<=(const float other) const { return (value <= fix16_from_float(other)); } - int operator<=(const int16_t other) const { return (value <= fix16_from_int(other)); } - - int operator>=(const Fix16 &other) const { return (value >= other.value); } - int operator>=(const fix16_t other) const { return (value >= other); } - int operator>=(const double other) const { return (value >= fix16_from_dbl(other)); } - int operator>=(const float other) const { return (value >= fix16_from_float(other)); } - int operator>=(const int16_t other) const { return (value >= fix16_from_int(other)); } - - int operator< (const Fix16 &other) const { return (value < other.value); } - int operator< (const fix16_t other) const { return (value < other); } - int operator< (const double other) const { return (value < fix16_from_dbl(other)); } - int operator< (const float other) const { return (value < fix16_from_float(other)); } - int operator< (const int16_t other) const { return (value < fix16_from_int(other)); } - - int operator> (const Fix16 &other) const { return (value > other.value); } - int operator> (const fix16_t other) const { return (value > other); } - int operator> (const double other) const { return (value > fix16_from_dbl(other)); } - int operator> (const float other) const { return (value > fix16_from_float(other)); } - int operator> (const int16_t other) const { return (value > fix16_from_int(other)); } - - Fix16 sin() const { return Fix16(fix16_sin(value)); } - Fix16 cos() const { return Fix16(fix16_cos(value)); } - Fix16 tan() const { return Fix16(fix16_tan(value)); } - Fix16 asin() const { return Fix16(fix16_asin(value)); } - Fix16 acos() const { return Fix16(fix16_acos(value)); } - Fix16 atan() const { return Fix16(fix16_atan(value)); } - Fix16 atan2(const Fix16 &inY) const { return Fix16(fix16_atan2(value, inY.value)); } - Fix16 sqrt() const { return Fix16(fix16_sqrt(value)); } -}; - -#endif diff --git a/source/thirdparty/include/libdivide.h b/source/thirdparty/include/libdivide.h deleted file mode 100644 index 204ce6556..000000000 --- a/source/thirdparty/include/libdivide.h +++ /dev/null @@ -1,2087 +0,0 @@ -// libdivide.h - Optimized integer division -// https://libdivide.com -// -// Copyright (C) 2010 - 2019 ridiculous_fish, -// Copyright (C) 2016 - 2019 Kim Walisch, -// -// libdivide is dual-licensed under the Boost or zlib licenses. -// You may use libdivide under the terms of either of these. -// See LICENSE.txt for more details. - -#ifndef LIBDIVIDE_H -#define LIBDIVIDE_H - -#define LIBDIVIDE_VERSION "3.0" -#define LIBDIVIDE_VERSION_MAJOR 3 -#define LIBDIVIDE_VERSION_MINOR 0 - -#include - -#if defined(__cplusplus) - #include - #include - #include -#else - #include - #include -#endif - -#if defined(__x86_64__) || defined(_M_X64) - #define LIBDIVIDE_X86_64 -#endif - -#if defined LIBDIVIDE_X86_64 || defined __SSE2__ || (defined _M_IX86_FP && _M_IX86_FP == 2) - #define LIBDIVIDE_SSE2 1 -#endif - -#if defined(LIBDIVIDE_AVX512) - #include -#elif defined(LIBDIVIDE_AVX2) - #include -#elif defined(LIBDIVIDE_SSE2) - #include -#endif - -#if defined(_MSC_VER) - #include - // disable warning C4146: unary minus operator applied - // to unsigned type, result still unsigned - #pragma warning(disable: 4146) - #define LIBDIVIDE_VC -#endif - -#if !defined(__has_builtin) - #define __has_builtin(x) 0 -#endif - -#if defined(__SIZEOF_INT128__) - #define HAS_INT128_T - // clang-cl on Windows does not yet support 128-bit division - #if !(defined(__clang__) && defined(LIBDIVIDE_VC)) - #define HAS_INT128_DIV - #endif -#endif - -#if defined(__i386__) - #define LIBDIVIDE_i386 -#endif - -#if defined(__GNUC__) || defined(__clang__) - #define LIBDIVIDE_GCC_STYLE_ASM -#endif - -#if defined(__cplusplus) || defined(LIBDIVIDE_VC) - #define LIBDIVIDE_FUNCTION __FUNCTION__ -#else - #define LIBDIVIDE_FUNCTION __func__ -#endif - -#if 0 - #define LIBDIVIDE_ERROR(msg) \ - do { \ - fprintf(stderr, "libdivide.h:%d: %s(): Error: %s\n", \ - __LINE__, LIBDIVIDE_FUNCTION, msg); \ - exit(-1); \ - } while (0) -#else - #define LIBDIVIDE_ERROR(msg) -#endif - -#if defined(LIBDIVIDE_ASSERTIONS_ON) - #define LIBDIVIDE_ASSERT(x) \ - do { \ - if (!(x)) { \ - fprintf(stderr, "libdivide.h:%d: %s(): Assertion failed: %s\n", \ - __LINE__, LIBDIVIDE_FUNCTION, #x); \ - exit(-1); \ - } \ - } while (0) -#else - #define LIBDIVIDE_ASSERT(x) -#endif - -#ifdef __cplusplus -namespace libdivide { -#endif - -// pack divider structs to prevent compilers from padding. -// This reduces memory usage by up to 43% when using a large -// array of libdivide dividers and improves performance -// by up to 10% because of reduced memory bandwidth. -#pragma pack(push, 1) - -struct libdivide_u32_t { - uint32_t magic; - uint8_t more; -}; - -struct libdivide_s32_t { - int32_t magic; - uint8_t more; -}; - -struct libdivide_u64_t { - uint64_t magic; - uint8_t more; -}; - -struct libdivide_s64_t { - int64_t magic; - uint8_t more; -}; - -struct libdivide_u32_branchfree_t { - uint32_t magic; - uint8_t more; -}; - -struct libdivide_s32_branchfree_t { - int32_t magic; - uint8_t more; -}; - -struct libdivide_u64_branchfree_t { - uint64_t magic; - uint8_t more; -}; - -struct libdivide_s64_branchfree_t { - int64_t magic; - uint8_t more; -}; - -#pragma pack(pop) - -// Explanation of the "more" field: -// -// * Bits 0-5 is the shift value (for shift path or mult path). -// * Bit 6 is the add indicator for mult path. -// * Bit 7 is set if the divisor is negative. We use bit 7 as the negative -// divisor indicator so that we can efficiently use sign extension to -// create a bitmask with all bits set to 1 (if the divisor is negative) -// or 0 (if the divisor is positive). -// -// u32: [0-4] shift value -// [5] ignored -// [6] add indicator -// magic number of 0 indicates shift path -// -// s32: [0-4] shift value -// [5] ignored -// [6] add indicator -// [7] indicates negative divisor -// magic number of 0 indicates shift path -// -// u64: [0-5] shift value -// [6] add indicator -// magic number of 0 indicates shift path -// -// s64: [0-5] shift value -// [6] add indicator -// [7] indicates negative divisor -// magic number of 0 indicates shift path -// -// In s32 and s64 branchfree modes, the magic number is negated according to -// whether the divisor is negated. In branchfree strategy, it is not negated. - -enum { - LIBDIVIDE_32_SHIFT_MASK = 0x1F, - LIBDIVIDE_64_SHIFT_MASK = 0x3F, - LIBDIVIDE_ADD_MARKER = 0x40, - LIBDIVIDE_NEGATIVE_DIVISOR = 0x80 -}; - -static inline struct libdivide_s32_t libdivide_s32_gen(int32_t d); -static inline struct libdivide_u32_t libdivide_u32_gen(uint32_t d); -static inline struct libdivide_s64_t libdivide_s64_gen(int64_t d); -static inline struct libdivide_u64_t libdivide_u64_gen(uint64_t d); - -static inline struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d); -static inline struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d); -static inline struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d); -static inline struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d); - -static inline int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom); -static inline uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom); -static inline int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom); -static inline uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom); - -static inline int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom); -static inline uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom); -static inline int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom); -static inline uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom); - -static inline int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom); -static inline uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom); -static inline int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom); -static inline uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom); - -static inline int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom); -static inline uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom); -static inline int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom); -static inline uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom); - -//////// Internal Utility Functions - -static inline uint32_t libdivide_mullhi_u32(uint32_t x, uint32_t y) { - uint64_t xl = x, yl = y; - uint64_t rl = xl * yl; - return (uint32_t)(rl >> 32); -} - -static inline int32_t libdivide_mullhi_s32(int32_t x, int32_t y) { - int64_t xl = x, yl = y; - int64_t rl = xl * yl; - // needs to be arithmetic shift - return (int32_t)(rl >> 32); -} - -static inline uint64_t libdivide_mullhi_u64(uint64_t x, uint64_t y) { -#if defined(LIBDIVIDE_VC) && \ - defined(LIBDIVIDE_X86_64) - return __umulh(x, y); -#elif defined(HAS_INT128_T) - __uint128_t xl = x, yl = y; - __uint128_t rl = xl * yl; - return (uint64_t)(rl >> 64); -#else - // full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64) - uint32_t mask = 0xFFFFFFFF; - uint32_t x0 = (uint32_t)(x & mask); - uint32_t x1 = (uint32_t)(x >> 32); - uint32_t y0 = (uint32_t)(y & mask); - uint32_t y1 = (uint32_t)(y >> 32); - uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0); - uint64_t x0y1 = x0 * (uint64_t)y1; - uint64_t x1y0 = x1 * (uint64_t)y0; - uint64_t x1y1 = x1 * (uint64_t)y1; - uint64_t temp = x1y0 + x0y0_hi; - uint64_t temp_lo = temp & mask; - uint64_t temp_hi = temp >> 32; - - return x1y1 + temp_hi + ((temp_lo + x0y1) >> 32); -#endif -} - -static inline int64_t libdivide_mullhi_s64(int64_t x, int64_t y) { -#if defined(LIBDIVIDE_VC) && \ - defined(LIBDIVIDE_X86_64) - return __mulh(x, y); -#elif defined(HAS_INT128_T) - __int128_t xl = x, yl = y; - __int128_t rl = xl * yl; - return (int64_t)(rl >> 64); -#else - // full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64) - uint32_t mask = 0xFFFFFFFF; - uint32_t x0 = (uint32_t)(x & mask); - uint32_t y0 = (uint32_t)(y & mask); - int32_t x1 = (int32_t)(x >> 32); - int32_t y1 = (int32_t)(y >> 32); - uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0); - int64_t t = x1 * (int64_t)y0 + x0y0_hi; - int64_t w1 = x0 * (int64_t)y1 + (t & mask); - - return x1 * (int64_t)y1 + (t >> 32) + (w1 >> 32); -#endif -} - -static inline int32_t libdivide_count_leading_zeros32(uint32_t val) { -#if defined(__GNUC__) || \ - __has_builtin(__builtin_clz) - // Fast way to count leading zeros - return __builtin_clz(val); -#elif defined(LIBDIVIDE_VC) - unsigned long result; - if (_BitScanReverse(&result, val)) { - return 31 - result; - } - return 0; -#else - if (val == 0) - return 32; - int32_t result = 8; - uint32_t hi = 0xFFU << 24; - while ((val & hi) == 0) { - hi >>= 8; - result += 8; - } - while (val & hi) { - result -= 1; - hi <<= 1; - } - return result; -#endif -} - -static inline int32_t libdivide_count_leading_zeros64(uint64_t val) { -#if defined(__GNUC__) || \ - __has_builtin(__builtin_clzll) - // Fast way to count leading zeros - return __builtin_clzll(val); -#elif defined(LIBDIVIDE_VC) && defined(_WIN64) - unsigned long result; - if (_BitScanReverse64(&result, val)) { - return 63 - result; - } - return 0; -#else - uint32_t hi = val >> 32; - uint32_t lo = val & 0xFFFFFFFF; - if (hi != 0) return libdivide_count_leading_zeros32(hi); - return 32 + libdivide_count_leading_zeros32(lo); -#endif -} - -// libdivide_64_div_32_to_32: divides a 64-bit uint {u1, u0} by a 32-bit -// uint {v}. The result must fit in 32 bits. -// Returns the quotient directly and the remainder in *r -static inline uint32_t libdivide_64_div_32_to_32(uint32_t u1, uint32_t u0, uint32_t v, uint32_t *r) { -#if (defined(LIBDIVIDE_i386) || defined(LIBDIVIDE_X86_64)) && \ - defined(LIBDIVIDE_GCC_STYLE_ASM) - uint32_t result; - __asm__("divl %[v]" - : "=a"(result), "=d"(*r) - : [v] "r"(v), "a"(u0), "d"(u1) - ); - return result; -#else - uint64_t n = ((uint64_t)u1 << 32) | u0; - uint32_t result = (uint32_t)(n / v); - *r = (uint32_t)(n - result * (uint64_t)v); - return result; -#endif -} - -// libdivide_128_div_64_to_64: divides a 128-bit uint {u1, u0} by a 64-bit -// uint {v}. The result must fit in 64 bits. -// Returns the quotient directly and the remainder in *r -static uint64_t libdivide_128_div_64_to_64(uint64_t u1, uint64_t u0, uint64_t v, uint64_t *r) { -#if defined(LIBDIVIDE_X86_64) && \ - defined(LIBDIVIDE_GCC_STYLE_ASM) - uint64_t result; - __asm__("divq %[v]" - : "=a"(result), "=d"(*r) - : [v] "r"(v), "a"(u0), "d"(u1) - ); - return result; -#elif defined(HAS_INT128_T) && \ - defined(HAS_INT128_DIV) - __uint128_t n = ((__uint128_t)u1 << 64) | u0; - uint64_t result = (uint64_t)(n / v); - *r = (uint64_t)(n - result * (__uint128_t)v); - return result; -#else - // Code taken from Hacker's Delight: - // http://www.hackersdelight.org/HDcode/divlu.c. - // License permits inclusion here per: - // http://www.hackersdelight.org/permissions.htm - - const uint64_t b = (1ULL << 32); // Number base (32 bits) - uint64_t un1, un0; // Norm. dividend LSD's - uint64_t vn1, vn0; // Norm. divisor digits - uint64_t q1, q0; // Quotient digits - uint64_t un64, un21, un10; // Dividend digit pairs - uint64_t rhat; // A remainder - int32_t s; // Shift amount for norm - - // If overflow, set rem. to an impossible value, - // and return the largest possible quotient - if (EDUKE32_PREDICT_FALSE(u1 >= v)) { - *r = (uint64_t) -1; - return (uint64_t) -1; - } - - // count leading zeros - s = libdivide_count_leading_zeros64(v); - if (s > 0) { - // Normalize divisor - v = v << s; - un64 = (u1 << s) | (u0 >> (64 - s)); - un10 = u0 << s; // Shift dividend left - } else { - // Avoid undefined behavior of (u0 >> 64). - // The behavior is undefined if the right operand is - // negative, or greater than or equal to the length - // in bits of the promoted left operand. - un64 = u1; - un10 = u0; - } - - // Break divisor up into two 32-bit digits - vn1 = v >> 32; - vn0 = v & 0xFFFFFFFF; - - // Break right half of dividend into two digits - un1 = un10 >> 32; - un0 = un10 & 0xFFFFFFFF; - - // Compute the first quotient digit, q1 - q1 = un64 / vn1; - rhat = un64 - q1 * vn1; - - while (q1 >= b || q1 * vn0 > b * rhat + un1) { - q1 = q1 - 1; - rhat = rhat + vn1; - if (rhat >= b) - break; - } - - // Multiply and subtract - un21 = un64 * b + un1 - q1 * v; - - // Compute the second quotient digit - q0 = un21 / vn1; - rhat = un21 - q0 * vn1; - - while (q0 >= b || q0 * vn0 > b * rhat + un0) { - q0 = q0 - 1; - rhat = rhat + vn1; - if (rhat >= b) - break; - } - - *r = (un21 * b + un0 - q0 * v) >> s; - return q1 * b + q0; -#endif -} - -// Bitshift a u128 in place, left (signed_shift > 0) or right (signed_shift < 0) -static inline void libdivide_u128_shift(uint64_t *u1, uint64_t *u0, int32_t signed_shift) { - if (signed_shift > 0) { - uint32_t shift = signed_shift; - *u1 <<= shift; - *u1 |= *u0 >> (64 - shift); - *u0 <<= shift; - } - else if (signed_shift < 0) { - uint32_t shift = -signed_shift; - *u0 >>= shift; - *u0 |= *u1 << (64 - shift); - *u1 >>= shift; - } -} - -// Computes a 128 / 128 -> 64 bit division, with a 128 bit remainder. -static uint64_t libdivide_128_div_128_to_64(uint64_t u_hi, uint64_t u_lo, uint64_t v_hi, uint64_t v_lo, uint64_t *r_hi, uint64_t *r_lo) { -#if defined(HAS_INT128_T) && \ - defined(HAS_INT128_DIV) - __uint128_t ufull = u_hi; - __uint128_t vfull = v_hi; - ufull = (ufull << 64) | u_lo; - vfull = (vfull << 64) | v_lo; - uint64_t res = (uint64_t)(ufull / vfull); - __uint128_t remainder = ufull - (vfull * res); - *r_lo = (uint64_t)remainder; - *r_hi = (uint64_t)(remainder >> 64); - return res; -#else - // Adapted from "Unsigned Doubleword Division" in Hacker's Delight - // We want to compute u / v - typedef struct { uint64_t hi; uint64_t lo; } u128_t; - u128_t u = {u_hi, u_lo}; - u128_t v = {v_hi, v_lo}; - - if (v.hi == 0) { - // divisor v is a 64 bit value, so we just need one 128/64 division - // Note that we are simpler than Hacker's Delight here, because we know - // the quotient fits in 64 bits whereas Hacker's Delight demands a full - // 128 bit quotient - *r_hi = 0; - return libdivide_128_div_64_to_64(u.hi, u.lo, v.lo, r_lo); - } - // Here v >= 2**64 - // We know that v.hi != 0, so count leading zeros is OK - // We have 0 <= n <= 63 - uint32_t n = libdivide_count_leading_zeros64(v.hi); - - // Normalize the divisor so its MSB is 1 - u128_t v1t = v; - libdivide_u128_shift(&v1t.hi, &v1t.lo, n); - uint64_t v1 = v1t.hi; // i.e. v1 = v1t >> 64 - - // To ensure no overflow - u128_t u1 = u; - libdivide_u128_shift(&u1.hi, &u1.lo, -1); - - // Get quotient from divide unsigned insn. - uint64_t rem_ignored; - uint64_t q1 = libdivide_128_div_64_to_64(u1.hi, u1.lo, v1, &rem_ignored); - - // Undo normalization and division of u by 2. - u128_t q0 = {0, q1}; - libdivide_u128_shift(&q0.hi, &q0.lo, n); - libdivide_u128_shift(&q0.hi, &q0.lo, -63); - - // Make q0 correct or too small by 1 - // Equivalent to `if (q0 != 0) q0 = q0 - 1;` - if (q0.hi != 0 || q0.lo != 0) { - q0.hi -= (q0.lo == 0); // borrow - q0.lo -= 1; - } - - // Now q0 is correct. - // Compute q0 * v as q0v - // = (q0.hi << 64 + q0.lo) * (v.hi << 64 + v.lo) - // = (q0.hi * v.hi << 128) + (q0.hi * v.lo << 64) + - // (q0.lo * v.hi << 64) + q0.lo * v.lo) - // Each term is 128 bit - // High half of full product (upper 128 bits!) are dropped - u128_t q0v = {0, 0}; - q0v.hi = q0.hi*v.lo + q0.lo*v.hi + libdivide_mullhi_u64(q0.lo, v.lo); - q0v.lo = q0.lo*v.lo; - - // Compute u - q0v as u_q0v - // This is the remainder - u128_t u_q0v = u; - u_q0v.hi -= q0v.hi + (u.lo < q0v.lo); // second term is borrow - u_q0v.lo -= q0v.lo; - - // Check if u_q0v >= v - // This checks if our remainder is larger than the divisor - if ((u_q0v.hi > v.hi) || - (u_q0v.hi == v.hi && u_q0v.lo >= v.lo)) { - // Increment q0 - q0.lo += 1; - q0.hi += (q0.lo == 0); // carry - - // Subtract v from remainder - u_q0v.hi -= v.hi + (u_q0v.lo < v.lo); - u_q0v.lo -= v.lo; - } - - *r_hi = u_q0v.hi; - *r_lo = u_q0v.lo; - - LIBDIVIDE_ASSERT(q0.hi == 0); - return q0.lo; -#endif -} - -////////// UINT32 - -static inline struct libdivide_u32_t libdivide_internal_u32_gen(uint32_t d, int branchfree) { - if (d == 0) { - LIBDIVIDE_ERROR("divider must be != 0"); - } - - struct libdivide_u32_t result; - uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(d); - - // Power of 2 - if ((d & (d - 1)) == 0) { - // We need to subtract 1 from the shift value in case of an unsigned - // branchfree divider because there is a hardcoded right shift by 1 - // in its division algorithm. Because of this we also need to add back - // 1 in its recovery algorithm. - result.magic = 0; - result.more = (uint8_t)(floor_log_2_d - (branchfree != 0)); - } else { - uint8_t more; - uint32_t rem, proposed_m; - proposed_m = libdivide_64_div_32_to_32(1U << floor_log_2_d, 0, d, &rem); - - LIBDIVIDE_ASSERT(rem > 0 && rem < d); - const uint32_t e = d - rem; - - // This power works if e < 2**floor_log_2_d. - if (!branchfree && (e < (1U << floor_log_2_d))) { - // This power works - more = floor_log_2_d; - } else { - // We have to use the general 33-bit algorithm. We need to compute - // (2**power) / d. However, we already have (2**(power-1))/d and - // its remainder. By doubling both, and then correcting the - // remainder, we can compute the larger division. - // don't care about overflow here - in fact, we expect it - proposed_m += proposed_m; - const uint32_t twice_rem = rem + rem; - if (twice_rem >= d || twice_rem < rem) proposed_m += 1; - more = floor_log_2_d | LIBDIVIDE_ADD_MARKER; - } - result.magic = 1 + proposed_m; - result.more = more; - // result.more's shift should in general be ceil_log_2_d. But if we - // used the smaller power, we subtract one from the shift because we're - // using the smaller power. If we're using the larger power, we - // subtract one from the shift because it's taken care of by the add - // indicator. So floor_log_2_d happens to be correct in both cases. - } - return result; -} - -struct libdivide_u32_t libdivide_u32_gen(uint32_t d) { - return libdivide_internal_u32_gen(d, 0); -} - -struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d) { - if (d == 1) { - LIBDIVIDE_ERROR("branchfree divider must be != 1"); - } - struct libdivide_u32_t tmp = libdivide_internal_u32_gen(d, 1); - struct libdivide_u32_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_32_SHIFT_MASK)}; - return ret; -} - -uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return numer >> more; - } - else { - uint32_t q = libdivide_mullhi_u32(denom->magic, numer); - if (more & LIBDIVIDE_ADD_MARKER) { - uint32_t t = ((numer - q) >> 1) + q; - return t >> (more & LIBDIVIDE_32_SHIFT_MASK); - } - else { - // All upper bits are 0, - // don't need to mask them off. - return q >> more; - } - } -} - -uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom) { - uint32_t q = libdivide_mullhi_u32(denom->magic, numer); - uint32_t t = ((numer - q) >> 1) + q; - return t >> denom->more; -} - -uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - - if (!denom->magic) { - return 1U << shift; - } else if (!(more & LIBDIVIDE_ADD_MARKER)) { - // We compute q = n/d = n*m / 2^(32 + shift) - // Therefore we have d = 2^(32 + shift) / m - // We need to ceil it. - // We know d is not a power of 2, so m is not a power of 2, - // so we can just add 1 to the floor - uint32_t hi_dividend = 1U << shift; - uint32_t rem_ignored; - return 1 + libdivide_64_div_32_to_32(hi_dividend, 0, denom->magic, &rem_ignored); - } else { - // Here we wish to compute d = 2^(32+shift+1)/(m+2^32). - // Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now - // Also note that shift may be as high as 31, so shift + 1 will - // overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and - // then double the quotient and remainder. - uint64_t half_n = 1ULL << (32 + shift); - uint64_t d = (1ULL << 32) | denom->magic; - // Note that the quotient is guaranteed <= 32 bits, but the remainder - // may need 33! - uint32_t half_q = (uint32_t)(half_n / d); - uint64_t rem = half_n % d; - // We computed 2^(32+shift)/(m+2^32) - // Need to double it, and then add 1 to the quotient if doubling th - // remainder would increase the quotient. - // Note that rem<<1 cannot overflow, since rem < d and d is 33 bits - uint32_t full_q = half_q + half_q + ((rem<<1) >= d); - - // We rounded down in gen (hence +1) - return full_q + 1; - } -} - -uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - - if (!denom->magic) { - return 1U << (shift + 1); - } else { - // Here we wish to compute d = 2^(32+shift+1)/(m+2^32). - // Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now - // Also note that shift may be as high as 31, so shift + 1 will - // overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and - // then double the quotient and remainder. - uint64_t half_n = 1ULL << (32 + shift); - uint64_t d = (1ULL << 32) | denom->magic; - // Note that the quotient is guaranteed <= 32 bits, but the remainder - // may need 33! - uint32_t half_q = (uint32_t)(half_n / d); - uint64_t rem = half_n % d; - // We computed 2^(32+shift)/(m+2^32) - // Need to double it, and then add 1 to the quotient if doubling th - // remainder would increase the quotient. - // Note that rem<<1 cannot overflow, since rem < d and d is 33 bits - uint32_t full_q = half_q + half_q + ((rem<<1) >= d); - - // We rounded down in gen (hence +1) - return full_q + 1; - } -} - -/////////// UINT64 - -static inline struct libdivide_u64_t libdivide_internal_u64_gen(uint64_t d, int branchfree) { - if (d == 0) { - LIBDIVIDE_ERROR("divider must be != 0"); - } - - struct libdivide_u64_t result; - uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(d); - - // Power of 2 - if ((d & (d - 1)) == 0) { - // We need to subtract 1 from the shift value in case of an unsigned - // branchfree divider because there is a hardcoded right shift by 1 - // in its division algorithm. Because of this we also need to add back - // 1 in its recovery algorithm. - result.magic = 0; - result.more = (uint8_t)(floor_log_2_d - (branchfree != 0)); - } else { - uint64_t proposed_m, rem; - uint8_t more; - // (1 << (64 + floor_log_2_d)) / d - proposed_m = libdivide_128_div_64_to_64(1ULL << floor_log_2_d, 0, d, &rem); - - LIBDIVIDE_ASSERT(rem > 0 && rem < d); - const uint64_t e = d - rem; - - // This power works if e < 2**floor_log_2_d. - if (!branchfree && e < (1ULL << floor_log_2_d)) { - // This power works - more = floor_log_2_d; - } else { - // We have to use the general 65-bit algorithm. We need to compute - // (2**power) / d. However, we already have (2**(power-1))/d and - // its remainder. By doubling both, and then correcting the - // remainder, we can compute the larger division. - // don't care about overflow here - in fact, we expect it - proposed_m += proposed_m; - const uint64_t twice_rem = rem + rem; - if (twice_rem >= d || twice_rem < rem) proposed_m += 1; - more = floor_log_2_d | LIBDIVIDE_ADD_MARKER; - } - result.magic = 1 + proposed_m; - result.more = more; - // result.more's shift should in general be ceil_log_2_d. But if we - // used the smaller power, we subtract one from the shift because we're - // using the smaller power. If we're using the larger power, we - // subtract one from the shift because it's taken care of by the add - // indicator. So floor_log_2_d happens to be correct in both cases, - // which is why we do it outside of the if statement. - } - return result; -} - -struct libdivide_u64_t libdivide_u64_gen(uint64_t d) { - return libdivide_internal_u64_gen(d, 0); -} - -struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d) { - if (d == 1) { - LIBDIVIDE_ERROR("branchfree divider must be != 1"); - } - struct libdivide_u64_t tmp = libdivide_internal_u64_gen(d, 1); - struct libdivide_u64_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_64_SHIFT_MASK)}; - return ret; -} - -uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return numer >> more; - } - else { - uint64_t q = libdivide_mullhi_u64(denom->magic, numer); - if (more & LIBDIVIDE_ADD_MARKER) { - uint64_t t = ((numer - q) >> 1) + q; - return t >> (more & LIBDIVIDE_64_SHIFT_MASK); - } - else { - // All upper bits are 0, - // don't need to mask them off. - return q >> more; - } - } -} - -uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom) { - uint64_t q = libdivide_mullhi_u64(denom->magic, numer); - uint64_t t = ((numer - q) >> 1) + q; - return t >> denom->more; -} - -uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - - if (!denom->magic) { - return 1ULL << shift; - } else if (!(more & LIBDIVIDE_ADD_MARKER)) { - // We compute q = n/d = n*m / 2^(64 + shift) - // Therefore we have d = 2^(64 + shift) / m - // We need to ceil it. - // We know d is not a power of 2, so m is not a power of 2, - // so we can just add 1 to the floor - uint64_t hi_dividend = 1ULL << shift; - uint64_t rem_ignored; - return 1 + libdivide_128_div_64_to_64(hi_dividend, 0, denom->magic, &rem_ignored); - } else { - // Here we wish to compute d = 2^(64+shift+1)/(m+2^64). - // Notice (m + 2^64) is a 65 bit number. This gets hairy. See - // libdivide_u32_recover for more on what we do here. - // TODO: do something better than 128 bit math - - // Full n is a (potentially) 129 bit value - // half_n is a 128 bit value - // Compute the hi half of half_n. Low half is 0. - uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0; - // d is a 65 bit value. The high bit is always set to 1. - const uint64_t d_hi = 1, d_lo = denom->magic; - // Note that the quotient is guaranteed <= 64 bits, - // but the remainder may need 65! - uint64_t r_hi, r_lo; - uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo); - // We computed 2^(64+shift)/(m+2^64) - // Double the remainder ('dr') and check if that is larger than d - // Note that d is a 65 bit value, so r1 is small and so r1 + r1 - // cannot overflow - uint64_t dr_lo = r_lo + r_lo; - uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry - int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo); - uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0); - return full_q + 1; - } -} - -uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - - if (!denom->magic) { - return 1ULL << (shift + 1); - } else { - // Here we wish to compute d = 2^(64+shift+1)/(m+2^64). - // Notice (m + 2^64) is a 65 bit number. This gets hairy. See - // libdivide_u32_recover for more on what we do here. - // TODO: do something better than 128 bit math - - // Full n is a (potentially) 129 bit value - // half_n is a 128 bit value - // Compute the hi half of half_n. Low half is 0. - uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0; - // d is a 65 bit value. The high bit is always set to 1. - const uint64_t d_hi = 1, d_lo = denom->magic; - // Note that the quotient is guaranteed <= 64 bits, - // but the remainder may need 65! - uint64_t r_hi, r_lo; - uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo); - // We computed 2^(64+shift)/(m+2^64) - // Double the remainder ('dr') and check if that is larger than d - // Note that d is a 65 bit value, so r1 is small and so r1 + r1 - // cannot overflow - uint64_t dr_lo = r_lo + r_lo; - uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry - int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo); - uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0); - return full_q + 1; - } -} - -/////////// SINT32 - -static inline struct libdivide_s32_t libdivide_internal_s32_gen(int32_t d, int branchfree) { - if (d == 0) { - LIBDIVIDE_ERROR("divider must be != 0"); - } - - struct libdivide_s32_t result; - - // If d is a power of 2, or negative a power of 2, we have to use a shift. - // This is especially important because the magic algorithm fails for -1. - // To check if d is a power of 2 or its inverse, it suffices to check - // whether its absolute value has exactly one bit set. This works even for - // INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set - // and is a power of 2. - uint32_t ud = (uint32_t)d; - uint32_t absD = (d < 0) ? -ud : ud; - uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(absD); - // check if exactly one bit is set, - // don't care if absD is 0 since that's divide by zero - if ((absD & (absD - 1)) == 0) { - // Branchfree and normal paths are exactly the same - result.magic = 0; - result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0); - } else { - LIBDIVIDE_ASSERT(floor_log_2_d >= 1); - - uint8_t more; - // the dividend here is 2**(floor_log_2_d + 31), so the low 32 bit word - // is 0 and the high word is floor_log_2_d - 1 - uint32_t rem, proposed_m; - proposed_m = libdivide_64_div_32_to_32(1U << (floor_log_2_d - 1), 0, absD, &rem); - const uint32_t e = absD - rem; - - // We are going to start with a power of floor_log_2_d - 1. - // This works if works if e < 2**floor_log_2_d. - if (!branchfree && e < (1U << floor_log_2_d)) { - // This power works - more = floor_log_2_d - 1; - } else { - // We need to go one higher. This should not make proposed_m - // overflow, but it will make it negative when interpreted as an - // int32_t. - proposed_m += proposed_m; - const uint32_t twice_rem = rem + rem; - if (twice_rem >= absD || twice_rem < rem) proposed_m += 1; - more = floor_log_2_d | LIBDIVIDE_ADD_MARKER; - } - - proposed_m += 1; - int32_t magic = (int32_t)proposed_m; - - // Mark if we are negative. Note we only negate the magic number in the - // branchfull case. - if (d < 0) { - more |= LIBDIVIDE_NEGATIVE_DIVISOR; - if (!branchfree) { - magic = -magic; - } - } - - result.more = more; - result.magic = magic; - } - return result; -} - -struct libdivide_s32_t libdivide_s32_gen(int32_t d) { - return libdivide_internal_s32_gen(d, 0); -} - -struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d) { - struct libdivide_s32_t tmp = libdivide_internal_s32_gen(d, 1); - struct libdivide_s32_branchfree_t result = {tmp.magic, tmp.more}; - return result; -} - -int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - - if (!denom->magic) { - uint32_t sign = (int8_t)more >> 7; - uint32_t mask = (1U << shift) - 1; - uint32_t uq = numer + ((numer >> 31) & mask); - int32_t q = (int32_t)uq; - q >>= shift; - q = (q ^ sign) - sign; - return q; - } else { - uint32_t uq = (uint32_t)libdivide_mullhi_s32(denom->magic, numer); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift and then sign extend - int32_t sign = (int8_t)more >> 7; - // q += (more < 0 ? -numer : numer) - // cast required to avoid UB - uq += ((uint32_t)numer ^ sign) - sign; - } - int32_t q = (int32_t)uq; - q >>= shift; - q += (q < 0); - return q; - } -} - -int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - // must be arithmetic shift and then sign extend - int32_t sign = (int8_t)more >> 7; - int32_t magic = denom->magic; - int32_t q = libdivide_mullhi_s32(magic, numer); - q += numer; - - // If q is non-negative, we have nothing to do - // If q is negative, we want to add either (2**shift)-1 if d is a power of - // 2, or (2**shift) if it is not a power of 2 - uint32_t is_power_of_2 = (magic == 0); - uint32_t q_sign = (uint32_t)(q >> 31); - q += q_sign & ((1U << shift) - is_power_of_2); - - // Now arithmetic right shift - q >>= shift; - // Negate if needed - q = (q ^ sign) - sign; - - return q; -} - -int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - if (!denom->magic) { - uint32_t absD = 1U << shift; - if (more & LIBDIVIDE_NEGATIVE_DIVISOR) { - absD = -absD; - } - return (int32_t)absD; - } else { - // Unsigned math is much easier - // We negate the magic number only in the branchfull case, and we don't - // know which case we're in. However we have enough information to - // determine the correct sign of the magic number. The divisor was - // negative if LIBDIVIDE_NEGATIVE_DIVISOR is set. If ADD_MARKER is set, - // the magic number's sign is opposite that of the divisor. - // We want to compute the positive magic number. - int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR); - int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER) - ? denom->magic > 0 : denom->magic < 0; - - // Handle the power of 2 case (including branchfree) - if (denom->magic == 0) { - int32_t result = 1U << shift; - return negative_divisor ? -result : result; - } - - uint32_t d = (uint32_t)(magic_was_negated ? -denom->magic : denom->magic); - uint64_t n = 1ULL << (32 + shift); // this shift cannot exceed 30 - uint32_t q = (uint32_t)(n / d); - int32_t result = (int32_t)q; - result += 1; - return negative_divisor ? -result : result; - } -} - -int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom) { - return libdivide_s32_recover((const struct libdivide_s32_t *)denom); -} - -///////////// SINT64 - -static inline struct libdivide_s64_t libdivide_internal_s64_gen(int64_t d, int branchfree) { - if (d == 0) { - LIBDIVIDE_ERROR("divider must be != 0"); - } - - struct libdivide_s64_t result; - - // If d is a power of 2, or negative a power of 2, we have to use a shift. - // This is especially important because the magic algorithm fails for -1. - // To check if d is a power of 2 or its inverse, it suffices to check - // whether its absolute value has exactly one bit set. This works even for - // INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set - // and is a power of 2. - uint64_t ud = (uint64_t)d; - uint64_t absD = (d < 0) ? -ud : ud; - uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(absD); - // check if exactly one bit is set, - // don't care if absD is 0 since that's divide by zero - if ((absD & (absD - 1)) == 0) { - // Branchfree and non-branchfree cases are the same - result.magic = 0; - result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0); - } else { - // the dividend here is 2**(floor_log_2_d + 63), so the low 64 bit word - // is 0 and the high word is floor_log_2_d - 1 - uint8_t more; - uint64_t rem, proposed_m; - proposed_m = libdivide_128_div_64_to_64(1ULL << (floor_log_2_d - 1), 0, absD, &rem); - const uint64_t e = absD - rem; - - // We are going to start with a power of floor_log_2_d - 1. - // This works if works if e < 2**floor_log_2_d. - if (!branchfree && e < (1ULL << floor_log_2_d)) { - // This power works - more = floor_log_2_d - 1; - } else { - // We need to go one higher. This should not make proposed_m - // overflow, but it will make it negative when interpreted as an - // int32_t. - proposed_m += proposed_m; - const uint64_t twice_rem = rem + rem; - if (twice_rem >= absD || twice_rem < rem) proposed_m += 1; - // note that we only set the LIBDIVIDE_NEGATIVE_DIVISOR bit if we - // also set ADD_MARKER this is an annoying optimization that - // enables algorithm #4 to avoid the mask. However we always set it - // in the branchfree case - more = floor_log_2_d | LIBDIVIDE_ADD_MARKER; - } - proposed_m += 1; - int64_t magic = (int64_t)proposed_m; - - // Mark if we are negative - if (d < 0) { - more |= LIBDIVIDE_NEGATIVE_DIVISOR; - if (!branchfree) { - magic = -magic; - } - } - - result.more = more; - result.magic = magic; - } - return result; -} - -struct libdivide_s64_t libdivide_s64_gen(int64_t d) { - return libdivide_internal_s64_gen(d, 0); -} - -struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d) { - struct libdivide_s64_t tmp = libdivide_internal_s64_gen(d, 1); - struct libdivide_s64_branchfree_t ret = {tmp.magic, tmp.more}; - return ret; -} - -int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - - if (!denom->magic) { // shift path - uint64_t mask = (1ULL << shift) - 1; - uint64_t uq = numer + ((numer >> 63) & mask); - int64_t q = (int64_t)uq; - q >>= shift; - // must be arithmetic shift and then sign-extend - int64_t sign = (int8_t)more >> 7; - q = (q ^ sign) - sign; - return q; - } else { - uint64_t uq = (uint64_t)libdivide_mullhi_s64(denom->magic, numer); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift and then sign extend - int64_t sign = (int8_t)more >> 7; - // q += (more < 0 ? -numer : numer) - // cast required to avoid UB - uq += ((uint64_t)numer ^ sign) - sign; - } - int64_t q = (int64_t)uq; - q >>= shift; - q += (q < 0); - return q; - } -} - -int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - // must be arithmetic shift and then sign extend - int64_t sign = (int8_t)more >> 7; - int64_t magic = denom->magic; - int64_t q = libdivide_mullhi_s64(magic, numer); - q += numer; - - // If q is non-negative, we have nothing to do. - // If q is negative, we want to add either (2**shift)-1 if d is a power of - // 2, or (2**shift) if it is not a power of 2. - uint64_t is_power_of_2 = (magic == 0); - uint64_t q_sign = (uint64_t)(q >> 63); - q += q_sign & ((1ULL << shift) - is_power_of_2); - - // Arithmetic right shift - q >>= shift; - // Negate if needed - q = (q ^ sign) - sign; - - return q; -} - -int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom) { - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - if (denom->magic == 0) { // shift path - uint64_t absD = 1ULL << shift; - if (more & LIBDIVIDE_NEGATIVE_DIVISOR) { - absD = -absD; - } - return (int64_t)absD; - } else { - // Unsigned math is much easier - int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR); - int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER) - ? denom->magic > 0 : denom->magic < 0; - - uint64_t d = (uint64_t)(magic_was_negated ? -denom->magic : denom->magic); - uint64_t n_hi = 1ULL << shift, n_lo = 0; - uint64_t rem_ignored; - uint64_t q = libdivide_128_div_64_to_64(n_hi, n_lo, d, &rem_ignored); - int64_t result = (int64_t)(q + 1); - if (negative_divisor) { - result = -result; - } - return result; - } -} - -int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom) { - return libdivide_s64_recover((const struct libdivide_s64_t *)denom); -} - -#if defined(LIBDIVIDE_AVX512) - -static inline __m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom); -static inline __m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom); -static inline __m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom); -static inline __m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom); - -static inline __m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom); -static inline __m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom); -static inline __m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom); -static inline __m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom); - -//////// Internal Utility Functions - -static inline __m512i libdivide_s64_signbits(__m512i v) {; - return _mm512_srai_epi64(v, 63); -} - -static inline __m512i libdivide_s64_shift_right_vector(__m512i v, int amt) { - return _mm512_srai_epi64(v, amt); -} - -// Here, b is assumed to contain one 32-bit value repeated. -static inline __m512i libdivide_mullhi_u32_vector(__m512i a, __m512i b) { - __m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epu32(a, b), 32); - __m512i a1X3X = _mm512_srli_epi64(a, 32); - __m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0); - __m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epu32(a1X3X, b), mask); - return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3); -} - -// b is one 32-bit value repeated. -static inline __m512i libdivide_mullhi_s32_vector(__m512i a, __m512i b) { - __m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epi32(a, b), 32); - __m512i a1X3X = _mm512_srli_epi64(a, 32); - __m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0); - __m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epi32(a1X3X, b), mask); - return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3); -} - -// Here, y is assumed to contain one 64-bit value repeated. -// https://stackoverflow.com/a/28827013 -static inline __m512i libdivide_mullhi_u64_vector(__m512i x, __m512i y) { - __m512i lomask = _mm512_set1_epi64(0xffffffff); - __m512i xh = _mm512_shuffle_epi32(x, (_MM_PERM_ENUM) 0xB1); - __m512i yh = _mm512_shuffle_epi32(y, (_MM_PERM_ENUM) 0xB1); - __m512i w0 = _mm512_mul_epu32(x, y); - __m512i w1 = _mm512_mul_epu32(x, yh); - __m512i w2 = _mm512_mul_epu32(xh, y); - __m512i w3 = _mm512_mul_epu32(xh, yh); - __m512i w0h = _mm512_srli_epi64(w0, 32); - __m512i s1 = _mm512_add_epi64(w1, w0h); - __m512i s1l = _mm512_and_si512(s1, lomask); - __m512i s1h = _mm512_srli_epi64(s1, 32); - __m512i s2 = _mm512_add_epi64(w2, s1l); - __m512i s2h = _mm512_srli_epi64(s2, 32); - __m512i hi = _mm512_add_epi64(w3, s1h); - hi = _mm512_add_epi64(hi, s2h); - - return hi; -} - -// y is one 64-bit value repeated. -static inline __m512i libdivide_mullhi_s64_vector(__m512i x, __m512i y) { - __m512i p = libdivide_mullhi_u64_vector(x, y); - __m512i t1 = _mm512_and_si512(libdivide_s64_signbits(x), y); - __m512i t2 = _mm512_and_si512(libdivide_s64_signbits(y), x); - p = _mm512_sub_epi64(p, t1); - p = _mm512_sub_epi64(p, t2); - return p; -} - -////////// UINT32 - -__m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return _mm512_srli_epi32(numers, more); - } - else { - __m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // uint32_t t = ((numer - q) >> 1) + q; - // return t >> denom->shift; - uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - __m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q); - return _mm512_srli_epi32(t, shift); - } - else { - return _mm512_srli_epi32(q, more); - } - } -} - -__m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom) { - __m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic)); - __m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q); - return _mm512_srli_epi32(t, denom->more); -} - -////////// UINT64 - -__m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return _mm512_srli_epi64(numers, more); - } - else { - __m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // uint32_t t = ((numer - q) >> 1) + q; - // return t >> denom->shift; - uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - __m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q); - return _mm512_srli_epi64(t, shift); - } - else { - return _mm512_srli_epi64(q, more); - } - } -} - -__m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom) { - __m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic)); - __m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q); - return _mm512_srli_epi64(t, denom->more); -} - -////////// SINT32 - -__m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - uint32_t mask = (1U << shift) - 1; - __m512i roundToZeroTweak = _mm512_set1_epi32(mask); - // q = numer + ((numer >> 31) & roundToZeroTweak); - __m512i q = _mm512_add_epi32(numers, _mm512_and_si512(_mm512_srai_epi32(numers, 31), roundToZeroTweak)); - q = _mm512_srai_epi32(q, shift); - __m512i sign = _mm512_set1_epi32((int8_t)more >> 7); - // q = (q ^ sign) - sign; - q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign); - return q; - } - else { - __m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift - __m512i sign = _mm512_set1_epi32((int8_t)more >> 7); - // q += ((numer ^ sign) - sign); - q = _mm512_add_epi32(q, _mm512_sub_epi32(_mm512_xor_si512(numers, sign), sign)); - } - // q >>= shift - q = _mm512_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK); - q = _mm512_add_epi32(q, _mm512_srli_epi32(q, 31)); // q += (q < 0) - return q; - } -} - -__m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom) { - int32_t magic = denom->magic; - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - // must be arithmetic shift - __m512i sign = _mm512_set1_epi32((int8_t)more >> 7); - __m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(magic)); - q = _mm512_add_epi32(q, numers); // q += numers - - // If q is non-negative, we have nothing to do - // If q is negative, we want to add either (2**shift)-1 if d is - // a power of 2, or (2**shift) if it is not a power of 2 - uint32_t is_power_of_2 = (magic == 0); - __m512i q_sign = _mm512_srai_epi32(q, 31); // q_sign = q >> 31 - __m512i mask = _mm512_set1_epi32((1U << shift) - is_power_of_2); - q = _mm512_add_epi32(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask) - q = _mm512_srai_epi32(q, shift); // q >>= shift - q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign - return q; -} - -////////// SINT64 - -__m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom) { - uint8_t more = denom->more; - int64_t magic = denom->magic; - if (magic == 0) { // shift path - uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - uint64_t mask = (1ULL << shift) - 1; - __m512i roundToZeroTweak = _mm512_set1_epi64(mask); - // q = numer + ((numer >> 63) & roundToZeroTweak); - __m512i q = _mm512_add_epi64(numers, _mm512_and_si512(libdivide_s64_signbits(numers), roundToZeroTweak)); - q = libdivide_s64_shift_right_vector(q, shift); - __m512i sign = _mm512_set1_epi32((int8_t)more >> 7); - // q = (q ^ sign) - sign; - q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign); - return q; - } - else { - __m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift - __m512i sign = _mm512_set1_epi32((int8_t)more >> 7); - // q += ((numer ^ sign) - sign); - q = _mm512_add_epi64(q, _mm512_sub_epi64(_mm512_xor_si512(numers, sign), sign)); - } - // q >>= denom->mult_path.shift - q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK); - q = _mm512_add_epi64(q, _mm512_srli_epi64(q, 63)); // q += (q < 0) - return q; - } -} - -__m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom) { - int64_t magic = denom->magic; - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - // must be arithmetic shift - __m512i sign = _mm512_set1_epi32((int8_t)more >> 7); - - // libdivide_mullhi_s64(numers, magic); - __m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic)); - q = _mm512_add_epi64(q, numers); // q += numers - - // If q is non-negative, we have nothing to do. - // If q is negative, we want to add either (2**shift)-1 if d is - // a power of 2, or (2**shift) if it is not a power of 2. - uint32_t is_power_of_2 = (magic == 0); - __m512i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63 - __m512i mask = _mm512_set1_epi64((1ULL << shift) - is_power_of_2); - q = _mm512_add_epi64(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask) - q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift - q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign - return q; -} - -#elif defined(LIBDIVIDE_AVX2) - -static inline __m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom); -static inline __m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom); -static inline __m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom); -static inline __m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom); - -static inline __m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom); -static inline __m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom); -static inline __m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom); -static inline __m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom); - -//////// Internal Utility Functions - -// Implementation of _mm256_srai_epi64(v, 63) (from AVX512). -static inline __m256i libdivide_s64_signbits(__m256i v) { - __m256i hiBitsDuped = _mm256_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1)); - __m256i signBits = _mm256_srai_epi32(hiBitsDuped, 31); - return signBits; -} - -// Implementation of _mm256_srai_epi64 (from AVX512). -static inline __m256i libdivide_s64_shift_right_vector(__m256i v, int amt) { - const int b = 64 - amt; - __m256i m = _mm256_set1_epi64x(1ULL << (b - 1)); - __m256i x = _mm256_srli_epi64(v, amt); - __m256i result = _mm256_sub_epi64(_mm256_xor_si256(x, m), m); - return result; -} - -// Here, b is assumed to contain one 32-bit value repeated. -static inline __m256i libdivide_mullhi_u32_vector(__m256i a, __m256i b) { - __m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epu32(a, b), 32); - __m256i a1X3X = _mm256_srli_epi64(a, 32); - __m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0); - __m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epu32(a1X3X, b), mask); - return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3); -} - -// b is one 32-bit value repeated. -static inline __m256i libdivide_mullhi_s32_vector(__m256i a, __m256i b) { - __m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epi32(a, b), 32); - __m256i a1X3X = _mm256_srli_epi64(a, 32); - __m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0); - __m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epi32(a1X3X, b), mask); - return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3); -} - -// Here, y is assumed to contain one 64-bit value repeated. -// https://stackoverflow.com/a/28827013 -static inline __m256i libdivide_mullhi_u64_vector(__m256i x, __m256i y) { - __m256i lomask = _mm256_set1_epi64x(0xffffffff); - __m256i xh = _mm256_shuffle_epi32(x, 0xB1); // x0l, x0h, x1l, x1h - __m256i yh = _mm256_shuffle_epi32(y, 0xB1); // y0l, y0h, y1l, y1h - __m256i w0 = _mm256_mul_epu32(x, y); // x0l*y0l, x1l*y1l - __m256i w1 = _mm256_mul_epu32(x, yh); // x0l*y0h, x1l*y1h - __m256i w2 = _mm256_mul_epu32(xh, y); // x0h*y0l, x1h*y0l - __m256i w3 = _mm256_mul_epu32(xh, yh); // x0h*y0h, x1h*y1h - __m256i w0h = _mm256_srli_epi64(w0, 32); - __m256i s1 = _mm256_add_epi64(w1, w0h); - __m256i s1l = _mm256_and_si256(s1, lomask); - __m256i s1h = _mm256_srli_epi64(s1, 32); - __m256i s2 = _mm256_add_epi64(w2, s1l); - __m256i s2h = _mm256_srli_epi64(s2, 32); - __m256i hi = _mm256_add_epi64(w3, s1h); - hi = _mm256_add_epi64(hi, s2h); - - return hi; -} - -// y is one 64-bit value repeated. -static inline __m256i libdivide_mullhi_s64_vector(__m256i x, __m256i y) { - __m256i p = libdivide_mullhi_u64_vector(x, y); - __m256i t1 = _mm256_and_si256(libdivide_s64_signbits(x), y); - __m256i t2 = _mm256_and_si256(libdivide_s64_signbits(y), x); - p = _mm256_sub_epi64(p, t1); - p = _mm256_sub_epi64(p, t2); - return p; -} - -////////// UINT32 - -__m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return _mm256_srli_epi32(numers, more); - } - else { - __m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // uint32_t t = ((numer - q) >> 1) + q; - // return t >> denom->shift; - uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - __m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q); - return _mm256_srli_epi32(t, shift); - } - else { - return _mm256_srli_epi32(q, more); - } - } -} - -__m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom) { - __m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic)); - __m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q); - return _mm256_srli_epi32(t, denom->more); -} - -////////// UINT64 - -__m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return _mm256_srli_epi64(numers, more); - } - else { - __m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // uint32_t t = ((numer - q) >> 1) + q; - // return t >> denom->shift; - uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - __m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q); - return _mm256_srli_epi64(t, shift); - } - else { - return _mm256_srli_epi64(q, more); - } - } -} - -__m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom) { - __m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic)); - __m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q); - return _mm256_srli_epi64(t, denom->more); -} - -////////// SINT32 - -__m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - uint32_t mask = (1U << shift) - 1; - __m256i roundToZeroTweak = _mm256_set1_epi32(mask); - // q = numer + ((numer >> 31) & roundToZeroTweak); - __m256i q = _mm256_add_epi32(numers, _mm256_and_si256(_mm256_srai_epi32(numers, 31), roundToZeroTweak)); - q = _mm256_srai_epi32(q, shift); - __m256i sign = _mm256_set1_epi32((int8_t)more >> 7); - // q = (q ^ sign) - sign; - q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign); - return q; - } - else { - __m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift - __m256i sign = _mm256_set1_epi32((int8_t)more >> 7); - // q += ((numer ^ sign) - sign); - q = _mm256_add_epi32(q, _mm256_sub_epi32(_mm256_xor_si256(numers, sign), sign)); - } - // q >>= shift - q = _mm256_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK); - q = _mm256_add_epi32(q, _mm256_srli_epi32(q, 31)); // q += (q < 0) - return q; - } -} - -__m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom) { - int32_t magic = denom->magic; - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - // must be arithmetic shift - __m256i sign = _mm256_set1_epi32((int8_t)more >> 7); - __m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(magic)); - q = _mm256_add_epi32(q, numers); // q += numers - - // If q is non-negative, we have nothing to do - // If q is negative, we want to add either (2**shift)-1 if d is - // a power of 2, or (2**shift) if it is not a power of 2 - uint32_t is_power_of_2 = (magic == 0); - __m256i q_sign = _mm256_srai_epi32(q, 31); // q_sign = q >> 31 - __m256i mask = _mm256_set1_epi32((1U << shift) - is_power_of_2); - q = _mm256_add_epi32(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask) - q = _mm256_srai_epi32(q, shift); // q >>= shift - q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign - return q; -} - -////////// SINT64 - -__m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom) { - uint8_t more = denom->more; - int64_t magic = denom->magic; - if (magic == 0) { // shift path - uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - uint64_t mask = (1ULL << shift) - 1; - __m256i roundToZeroTweak = _mm256_set1_epi64x(mask); - // q = numer + ((numer >> 63) & roundToZeroTweak); - __m256i q = _mm256_add_epi64(numers, _mm256_and_si256(libdivide_s64_signbits(numers), roundToZeroTweak)); - q = libdivide_s64_shift_right_vector(q, shift); - __m256i sign = _mm256_set1_epi32((int8_t)more >> 7); - // q = (q ^ sign) - sign; - q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign); - return q; - } - else { - __m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift - __m256i sign = _mm256_set1_epi32((int8_t)more >> 7); - // q += ((numer ^ sign) - sign); - q = _mm256_add_epi64(q, _mm256_sub_epi64(_mm256_xor_si256(numers, sign), sign)); - } - // q >>= denom->mult_path.shift - q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK); - q = _mm256_add_epi64(q, _mm256_srli_epi64(q, 63)); // q += (q < 0) - return q; - } -} - -__m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom) { - int64_t magic = denom->magic; - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - // must be arithmetic shift - __m256i sign = _mm256_set1_epi32((int8_t)more >> 7); - - // libdivide_mullhi_s64(numers, magic); - __m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic)); - q = _mm256_add_epi64(q, numers); // q += numers - - // If q is non-negative, we have nothing to do. - // If q is negative, we want to add either (2**shift)-1 if d is - // a power of 2, or (2**shift) if it is not a power of 2. - uint32_t is_power_of_2 = (magic == 0); - __m256i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63 - __m256i mask = _mm256_set1_epi64x((1ULL << shift) - is_power_of_2); - q = _mm256_add_epi64(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask) - q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift - q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign - return q; -} - -#elif defined(LIBDIVIDE_SSE2) - -static inline __m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom); -static inline __m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom); -static inline __m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom); -static inline __m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom); - -static inline __m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom); -static inline __m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom); -static inline __m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom); -static inline __m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom); - -//////// Internal Utility Functions - -// Implementation of _mm_srai_epi64(v, 63) (from AVX512). -static inline __m128i libdivide_s64_signbits(__m128i v) { - __m128i hiBitsDuped = _mm_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1)); - __m128i signBits = _mm_srai_epi32(hiBitsDuped, 31); - return signBits; -} - -// Implementation of _mm_srai_epi64 (from AVX512). -static inline __m128i libdivide_s64_shift_right_vector(__m128i v, int amt) { - const int b = 64 - amt; - __m128i m = _mm_set1_epi64x(1ULL << (b - 1)); - __m128i x = _mm_srli_epi64(v, amt); - __m128i result = _mm_sub_epi64(_mm_xor_si128(x, m), m); - return result; -} - -// Here, b is assumed to contain one 32-bit value repeated. -static inline __m128i libdivide_mullhi_u32_vector(__m128i a, __m128i b) { - __m128i hi_product_0Z2Z = _mm_srli_epi64(_mm_mul_epu32(a, b), 32); - __m128i a1X3X = _mm_srli_epi64(a, 32); - __m128i mask = _mm_set_epi32(-1, 0, -1, 0); - __m128i hi_product_Z1Z3 = _mm_and_si128(_mm_mul_epu32(a1X3X, b), mask); - return _mm_or_si128(hi_product_0Z2Z, hi_product_Z1Z3); -} - -// SSE2 does not have a signed multiplication instruction, but we can convert -// unsigned to signed pretty efficiently. Again, b is just a 32 bit value -// repeated four times. -static inline __m128i libdivide_mullhi_s32_vector(__m128i a, __m128i b) { - __m128i p = libdivide_mullhi_u32_vector(a, b); - // t1 = (a >> 31) & y, arithmetic shift - __m128i t1 = _mm_and_si128(_mm_srai_epi32(a, 31), b); - __m128i t2 = _mm_and_si128(_mm_srai_epi32(b, 31), a); - p = _mm_sub_epi32(p, t1); - p = _mm_sub_epi32(p, t2); - return p; -} - -// Here, y is assumed to contain one 64-bit value repeated. -// https://stackoverflow.com/a/28827013 -static inline __m128i libdivide_mullhi_u64_vector(__m128i x, __m128i y) { - __m128i lomask = _mm_set1_epi64x(0xffffffff); - __m128i xh = _mm_shuffle_epi32(x, 0xB1); // x0l, x0h, x1l, x1h - __m128i yh = _mm_shuffle_epi32(y, 0xB1); // y0l, y0h, y1l, y1h - __m128i w0 = _mm_mul_epu32(x, y); // x0l*y0l, x1l*y1l - __m128i w1 = _mm_mul_epu32(x, yh); // x0l*y0h, x1l*y1h - __m128i w2 = _mm_mul_epu32(xh, y); // x0h*y0l, x1h*y0l - __m128i w3 = _mm_mul_epu32(xh, yh); // x0h*y0h, x1h*y1h - __m128i w0h = _mm_srli_epi64(w0, 32); - __m128i s1 = _mm_add_epi64(w1, w0h); - __m128i s1l = _mm_and_si128(s1, lomask); - __m128i s1h = _mm_srli_epi64(s1, 32); - __m128i s2 = _mm_add_epi64(w2, s1l); - __m128i s2h = _mm_srli_epi64(s2, 32); - __m128i hi = _mm_add_epi64(w3, s1h); - hi = _mm_add_epi64(hi, s2h); - - return hi; -} - -// y is one 64-bit value repeated. -static inline __m128i libdivide_mullhi_s64_vector(__m128i x, __m128i y) { - __m128i p = libdivide_mullhi_u64_vector(x, y); - __m128i t1 = _mm_and_si128(libdivide_s64_signbits(x), y); - __m128i t2 = _mm_and_si128(libdivide_s64_signbits(y), x); - p = _mm_sub_epi64(p, t1); - p = _mm_sub_epi64(p, t2); - return p; -} - -////////// UINT32 - -__m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return _mm_srli_epi32(numers, more); - } - else { - __m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // uint32_t t = ((numer - q) >> 1) + q; - // return t >> denom->shift; - uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - __m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q); - return _mm_srli_epi32(t, shift); - } - else { - return _mm_srli_epi32(q, more); - } - } -} - -__m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom) { - __m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic)); - __m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q); - return _mm_srli_epi32(t, denom->more); -} - -////////// UINT64 - -__m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - return _mm_srli_epi64(numers, more); - } - else { - __m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // uint32_t t = ((numer - q) >> 1) + q; - // return t >> denom->shift; - uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - __m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q); - return _mm_srli_epi64(t, shift); - } - else { - return _mm_srli_epi64(q, more); - } - } -} - -__m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom) { - __m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic)); - __m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q); - return _mm_srli_epi64(t, denom->more); -} - -////////// SINT32 - -__m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom) { - uint8_t more = denom->more; - if (!denom->magic) { - uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - uint32_t mask = (1U << shift) - 1; - __m128i roundToZeroTweak = _mm_set1_epi32(mask); - // q = numer + ((numer >> 31) & roundToZeroTweak); - __m128i q = _mm_add_epi32(numers, _mm_and_si128(_mm_srai_epi32(numers, 31), roundToZeroTweak)); - q = _mm_srai_epi32(q, shift); - __m128i sign = _mm_set1_epi32((int8_t)more >> 7); - // q = (q ^ sign) - sign; - q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign); - return q; - } - else { - __m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(denom->magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift - __m128i sign = _mm_set1_epi32((int8_t)more >> 7); - // q += ((numer ^ sign) - sign); - q = _mm_add_epi32(q, _mm_sub_epi32(_mm_xor_si128(numers, sign), sign)); - } - // q >>= shift - q = _mm_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK); - q = _mm_add_epi32(q, _mm_srli_epi32(q, 31)); // q += (q < 0) - return q; - } -} - -__m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom) { - int32_t magic = denom->magic; - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK; - // must be arithmetic shift - __m128i sign = _mm_set1_epi32((int8_t)more >> 7); - __m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(magic)); - q = _mm_add_epi32(q, numers); // q += numers - - // If q is non-negative, we have nothing to do - // If q is negative, we want to add either (2**shift)-1 if d is - // a power of 2, or (2**shift) if it is not a power of 2 - uint32_t is_power_of_2 = (magic == 0); - __m128i q_sign = _mm_srai_epi32(q, 31); // q_sign = q >> 31 - __m128i mask = _mm_set1_epi32((1U << shift) - is_power_of_2); - q = _mm_add_epi32(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask) - q = _mm_srai_epi32(q, shift); // q >>= shift - q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign - return q; -} - -////////// SINT64 - -__m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom) { - uint8_t more = denom->more; - int64_t magic = denom->magic; - if (magic == 0) { // shift path - uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - uint64_t mask = (1ULL << shift) - 1; - __m128i roundToZeroTweak = _mm_set1_epi64x(mask); - // q = numer + ((numer >> 63) & roundToZeroTweak); - __m128i q = _mm_add_epi64(numers, _mm_and_si128(libdivide_s64_signbits(numers), roundToZeroTweak)); - q = libdivide_s64_shift_right_vector(q, shift); - __m128i sign = _mm_set1_epi32((int8_t)more >> 7); - // q = (q ^ sign) - sign; - q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign); - return q; - } - else { - __m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic)); - if (more & LIBDIVIDE_ADD_MARKER) { - // must be arithmetic shift - __m128i sign = _mm_set1_epi32((int8_t)more >> 7); - // q += ((numer ^ sign) - sign); - q = _mm_add_epi64(q, _mm_sub_epi64(_mm_xor_si128(numers, sign), sign)); - } - // q >>= denom->mult_path.shift - q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK); - q = _mm_add_epi64(q, _mm_srli_epi64(q, 63)); // q += (q < 0) - return q; - } -} - -__m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom) { - int64_t magic = denom->magic; - uint8_t more = denom->more; - uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK; - // must be arithmetic shift - __m128i sign = _mm_set1_epi32((int8_t)more >> 7); - - // libdivide_mullhi_s64(numers, magic); - __m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic)); - q = _mm_add_epi64(q, numers); // q += numers - - // If q is non-negative, we have nothing to do. - // If q is negative, we want to add either (2**shift)-1 if d is - // a power of 2, or (2**shift) if it is not a power of 2. - uint32_t is_power_of_2 = (magic == 0); - __m128i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63 - __m128i mask = _mm_set1_epi64x((1ULL << shift) - is_power_of_2); - q = _mm_add_epi64(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask) - q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift - q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign - return q; -} - -#endif - -/////////// C++ stuff - -#ifdef __cplusplus - -// The C++ divider class is templated on both an integer type -// (like uint64_t) and an algorithm type. -// * BRANCHFULL is the default algorithm type. -// * BRANCHFREE is the branchfree algorithm type. -enum { - BRANCHFULL, - BRANCHFREE -}; - -#if defined(LIBDIVIDE_AVX512) - #define LIBDIVIDE_VECTOR_TYPE __m512i -#elif defined(LIBDIVIDE_AVX2) - #define LIBDIVIDE_VECTOR_TYPE __m256i -#elif defined(LIBDIVIDE_SSE2) - #define LIBDIVIDE_VECTOR_TYPE __m128i -#endif - -#if !defined(LIBDIVIDE_VECTOR_TYPE) - #define LIBDIVIDE_DIVIDE_VECTOR(ALGO) -#else - #define LIBDIVIDE_DIVIDE_VECTOR(ALGO) \ - LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const { \ - return libdivide_##ALGO##_do_vector(n, &denom); \ - } -#endif - -// The DISPATCHER_GEN() macro generates C++ methods (for the given integer -// and algorithm types) that redirect to libdivide's C API. -#define DISPATCHER_GEN(T, ALGO) \ - libdivide_##ALGO##_t denom; \ - dispatcher() { } \ - dispatcher(T d) \ - : denom(libdivide_##ALGO##_gen(d)) \ - { } \ - T divide(T n) const { \ - return libdivide_##ALGO##_do(n, &denom); \ - } \ - LIBDIVIDE_DIVIDE_VECTOR(ALGO) \ - T recover() const { \ - return libdivide_##ALGO##_recover(&denom); \ - } - -// The dispatcher selects a specific division algorithm for a given -// type and ALGO using partial template specialization. -template struct dispatcher { }; - -template<> struct dispatcher { DISPATCHER_GEN(int32_t, s32) }; -template<> struct dispatcher { DISPATCHER_GEN(int32_t, s32_branchfree) }; -template<> struct dispatcher { DISPATCHER_GEN(uint32_t, u32) }; -template<> struct dispatcher { DISPATCHER_GEN(uint32_t, u32_branchfree) }; -template<> struct dispatcher { DISPATCHER_GEN(int64_t, s64) }; -template<> struct dispatcher { DISPATCHER_GEN(int64_t, s64_branchfree) }; -template<> struct dispatcher { DISPATCHER_GEN(uint64_t, u64) }; -template<> struct dispatcher { DISPATCHER_GEN(uint64_t, u64_branchfree) }; - -// This is the main divider class for use by the user (C++ API). -// The actual division algorithm is selected using the dispatcher struct -// based on the integer and algorithm template parameters. -template -class divider { -public: - // We leave the default constructor empty so that creating - // an array of dividers and then initializing them - // later doesn't slow us down. - divider() { } - - // Constructor that takes the divisor as a parameter - divider(T d) : div(d) { } - - // Divides n by the divisor - T divide(T n) const { - return div.divide(n); - } - - // Recovers the divisor, returns the value that was - // used to initialize this divider object. - T recover() const { - return div.recover(); - } - - bool operator==(const divider& other) const { - return div.denom.magic == other.denom.magic && - div.denom.more == other.denom.more; - } - - bool operator!=(const divider& other) const { - return !(*this == other); - } - -#if defined(LIBDIVIDE_VECTOR_TYPE) - // Treats the vector as packed integer values with the same type as - // the divider (e.g. s32, u32, s64, u64) and divides each of - // them by the divider, returning the packed quotients. - LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const { - return div.divide(n); - } -#endif - -private: - // Storage for the actual divisor - dispatcher::value, - std::is_signed::value, sizeof(T), ALGO> div; -}; - -// Overload of operator / for scalar division -template -T operator/(T n, const divider& div) { - return div.divide(n); -} - -// Overload of operator /= for scalar division -template -T& operator/=(T& n, const divider& div) { - n = div.divide(n); - return n; -} - -#if defined(LIBDIVIDE_VECTOR_TYPE) - // Overload of operator / for vector division - template - LIBDIVIDE_VECTOR_TYPE operator/(LIBDIVIDE_VECTOR_TYPE n, const divider& div) { - return div.divide(n); - } - // Overload of operator /= for vector division - template - LIBDIVIDE_VECTOR_TYPE& operator/=(LIBDIVIDE_VECTOR_TYPE& n, const divider& div) { - n = div.divide(n); - return n; - } -#endif - -// libdivdie::branchfree_divider -template -using branchfree_divider = divider; - -} // namespace libdivide - -#endif // __cplusplus - -#endif // LIBDIVIDE_H