1276789Sdim//===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===// 2276789Sdim// 3353358Sdim// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4353358Sdim// See https://llvm.org/LICENSE.txt for license information. 5353358Sdim// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6276789Sdim// 7276789Sdim//===----------------------------------------------------------------------===// 8276789Sdim// 9276789Sdim// This file is a configuration header for soft-float routines in compiler-rt. 10276789Sdim// This file does not provide any part of the compiler-rt interface, but defines 11276789Sdim// many useful constants and utility routines that are used in the 12276789Sdim// implementation of the soft-float routines in compiler-rt. 13276789Sdim// 14276789Sdim// Assumes that float, double and long double correspond to the IEEE-754 15276789Sdim// binary32, binary64 and binary 128 types, respectively, and that integer 16276789Sdim// endianness matches floating point endianness on the target platform. 17276789Sdim// 18276789Sdim//===----------------------------------------------------------------------===// 19276789Sdim 20276789Sdim#ifndef FP_LIB_HEADER 21276789Sdim#define FP_LIB_HEADER 22276789Sdim 23276789Sdim#include "int_lib.h" 24344779Sdim#include "int_math.h" 25353358Sdim#include <limits.h> 26353358Sdim#include <stdbool.h> 27353358Sdim#include <stdint.h> 28276789Sdim 29276789Sdim// x86_64 FreeBSD prior v9.3 define fixed-width types incorrectly in 30276789Sdim// 32-bit mode. 31276789Sdim#if defined(__FreeBSD__) && defined(__i386__) 32353358Sdim#include <sys/param.h> 33353358Sdim#if __FreeBSD_version < 903000 // v9.3 34353358Sdim#define uint64_t unsigned long long 35353358Sdim#define int64_t long long 36353358Sdim#undef UINT64_C 37353358Sdim#define UINT64_C(c) (c##ULL) 38276789Sdim#endif 39353358Sdim#endif 40276789Sdim 41276789Sdim#if defined SINGLE_PRECISION 42276789Sdim 43276789Sdimtypedef uint32_t rep_t; 44276789Sdimtypedef int32_t srep_t; 45276789Sdimtypedef float fp_t; 46276789Sdim#define REP_C UINT32_C 47276789Sdim#define significandBits 23 48276789Sdim 49353358Sdimstatic __inline int rep_clz(rep_t a) { return __builtin_clz(a); } 50276789Sdim 51276789Sdim// 32x32 --> 64 bit multiply 52296417Sdimstatic __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 53353358Sdim const uint64_t product = (uint64_t)a * b; 54353358Sdim *hi = product >> 32; 55353358Sdim *lo = product; 56276789Sdim} 57276789SdimCOMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b); 58276789Sdim 59276789Sdim#elif defined DOUBLE_PRECISION 60276789Sdim 61276789Sdimtypedef uint64_t rep_t; 62276789Sdimtypedef int64_t srep_t; 63276789Sdimtypedef double fp_t; 64276789Sdim#define REP_C UINT64_C 65276789Sdim#define significandBits 52 66276789Sdim 67296417Sdimstatic __inline int rep_clz(rep_t a) { 68276789Sdim#if defined __LP64__ 69353358Sdim return __builtin_clzl(a); 70276789Sdim#else 71353358Sdim if (a & REP_C(0xffffffff00000000)) 72353358Sdim return __builtin_clz(a >> 32); 73353358Sdim else 74353358Sdim return 32 + __builtin_clz(a & REP_C(0xffffffff)); 75276789Sdim#endif 76276789Sdim} 77276789Sdim 78276789Sdim#define loWord(a) (a & 0xffffffffU) 79276789Sdim#define hiWord(a) (a >> 32) 80276789Sdim 81276789Sdim// 64x64 -> 128 wide multiply for platforms that don't have such an operation; 82276789Sdim// many 64-bit platforms have this operation, but they tend to have hardware 83276789Sdim// floating-point, so we don't bother with a special case for them here. 84296417Sdimstatic __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 85353358Sdim // Each of the component 32x32 -> 64 products 86353358Sdim const uint64_t plolo = loWord(a) * loWord(b); 87353358Sdim const uint64_t plohi = loWord(a) * hiWord(b); 88353358Sdim const uint64_t philo = hiWord(a) * loWord(b); 89353358Sdim const uint64_t phihi = hiWord(a) * hiWord(b); 90353358Sdim // Sum terms that contribute to lo in a way that allows us to get the carry 91353358Sdim const uint64_t r0 = loWord(plolo); 92353358Sdim const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo); 93353358Sdim *lo = r0 + (r1 << 32); 94353358Sdim // Sum terms contributing to hi with the carry from lo 95353358Sdim *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi; 96276789Sdim} 97276789Sdim#undef loWord 98276789Sdim#undef hiWord 99276789Sdim 100276789SdimCOMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b); 101276789Sdim 102276789Sdim#elif defined QUAD_PRECISION 103353358Sdim#if __LDBL_MANT_DIG__ == 113 && defined(__SIZEOF_INT128__) 104276789Sdim#define CRT_LDBL_128BIT 105276789Sdimtypedef __uint128_t rep_t; 106276789Sdimtypedef __int128_t srep_t; 107276789Sdimtypedef long double fp_t; 108276789Sdim#define REP_C (__uint128_t) 109276789Sdim// Note: Since there is no explicit way to tell compiler the constant is a 110276789Sdim// 128-bit integer, we let the constant be casted to 128-bit integer 111276789Sdim#define significandBits 112 112276789Sdim 113296417Sdimstatic __inline int rep_clz(rep_t a) { 114353358Sdim const union { 115353358Sdim __uint128_t ll; 116276789Sdim#if _YUGA_BIG_ENDIAN 117353358Sdim struct { 118353358Sdim uint64_t high, low; 119353358Sdim } s; 120276789Sdim#else 121353358Sdim struct { 122353358Sdim uint64_t low, high; 123353358Sdim } s; 124276789Sdim#endif 125353358Sdim } uu = {.ll = a}; 126276789Sdim 127353358Sdim uint64_t word; 128353358Sdim uint64_t add; 129276789Sdim 130353358Sdim if (uu.s.high) { 131353358Sdim word = uu.s.high; 132353358Sdim add = 0; 133353358Sdim } else { 134353358Sdim word = uu.s.low; 135353358Sdim add = 64; 136353358Sdim } 137353358Sdim return __builtin_clzll(word) + add; 138276789Sdim} 139276789Sdim 140353358Sdim#define Word_LoMask UINT64_C(0x00000000ffffffff) 141353358Sdim#define Word_HiMask UINT64_C(0xffffffff00000000) 142276789Sdim#define Word_FullMask UINT64_C(0xffffffffffffffff) 143276789Sdim#define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask) 144276789Sdim#define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask) 145276789Sdim#define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask) 146276789Sdim#define Word_4(a) (uint64_t)(a & Word_LoMask) 147276789Sdim 148276789Sdim// 128x128 -> 256 wide multiply for platforms that don't have such an operation; 149276789Sdim// many 64-bit platforms have this operation, but they tend to have hardware 150276789Sdim// floating-point, so we don't bother with a special case for them here. 151296417Sdimstatic __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 152276789Sdim 153353358Sdim const uint64_t product11 = Word_1(a) * Word_1(b); 154353358Sdim const uint64_t product12 = Word_1(a) * Word_2(b); 155353358Sdim const uint64_t product13 = Word_1(a) * Word_3(b); 156353358Sdim const uint64_t product14 = Word_1(a) * Word_4(b); 157353358Sdim const uint64_t product21 = Word_2(a) * Word_1(b); 158353358Sdim const uint64_t product22 = Word_2(a) * Word_2(b); 159353358Sdim const uint64_t product23 = Word_2(a) * Word_3(b); 160353358Sdim const uint64_t product24 = Word_2(a) * Word_4(b); 161353358Sdim const uint64_t product31 = Word_3(a) * Word_1(b); 162353358Sdim const uint64_t product32 = Word_3(a) * Word_2(b); 163353358Sdim const uint64_t product33 = Word_3(a) * Word_3(b); 164353358Sdim const uint64_t product34 = Word_3(a) * Word_4(b); 165353358Sdim const uint64_t product41 = Word_4(a) * Word_1(b); 166353358Sdim const uint64_t product42 = Word_4(a) * Word_2(b); 167353358Sdim const uint64_t product43 = Word_4(a) * Word_3(b); 168353358Sdim const uint64_t product44 = Word_4(a) * Word_4(b); 169276789Sdim 170353358Sdim const __uint128_t sum0 = (__uint128_t)product44; 171353358Sdim const __uint128_t sum1 = (__uint128_t)product34 + (__uint128_t)product43; 172353358Sdim const __uint128_t sum2 = 173353358Sdim (__uint128_t)product24 + (__uint128_t)product33 + (__uint128_t)product42; 174353358Sdim const __uint128_t sum3 = (__uint128_t)product14 + (__uint128_t)product23 + 175353358Sdim (__uint128_t)product32 + (__uint128_t)product41; 176353358Sdim const __uint128_t sum4 = 177353358Sdim (__uint128_t)product13 + (__uint128_t)product22 + (__uint128_t)product31; 178353358Sdim const __uint128_t sum5 = (__uint128_t)product12 + (__uint128_t)product21; 179353358Sdim const __uint128_t sum6 = (__uint128_t)product11; 180276789Sdim 181353358Sdim const __uint128_t r0 = (sum0 & Word_FullMask) + ((sum1 & Word_LoMask) << 32); 182353358Sdim const __uint128_t r1 = (sum0 >> 64) + ((sum1 >> 32) & Word_FullMask) + 183353358Sdim (sum2 & Word_FullMask) + ((sum3 << 32) & Word_HiMask); 184276789Sdim 185353358Sdim *lo = r0 + (r1 << 64); 186353358Sdim *hi = (r1 >> 64) + (sum1 >> 96) + (sum2 >> 64) + (sum3 >> 32) + sum4 + 187353358Sdim (sum5 << 32) + (sum6 << 64); 188276789Sdim} 189276789Sdim#undef Word_1 190276789Sdim#undef Word_2 191276789Sdim#undef Word_3 192276789Sdim#undef Word_4 193276789Sdim#undef Word_HiMask 194276789Sdim#undef Word_LoMask 195276789Sdim#undef Word_FullMask 196353358Sdim#endif // __LDBL_MANT_DIG__ == 113 && __SIZEOF_INT128__ 197276789Sdim#else 198276789Sdim#error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined. 199276789Sdim#endif 200276789Sdim 201353358Sdim#if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || \ 202353358Sdim defined(CRT_LDBL_128BIT) 203353358Sdim#define typeWidth (sizeof(rep_t) * CHAR_BIT) 204353358Sdim#define exponentBits (typeWidth - significandBits - 1) 205353358Sdim#define maxExponent ((1 << exponentBits) - 1) 206353358Sdim#define exponentBias (maxExponent >> 1) 207276789Sdim 208353358Sdim#define implicitBit (REP_C(1) << significandBits) 209276789Sdim#define significandMask (implicitBit - 1U) 210353358Sdim#define signBit (REP_C(1) << (significandBits + exponentBits)) 211353358Sdim#define absMask (signBit - 1U) 212353358Sdim#define exponentMask (absMask ^ significandMask) 213353358Sdim#define oneRep ((rep_t)exponentBias << significandBits) 214353358Sdim#define infRep exponentMask 215353358Sdim#define quietBit (implicitBit >> 1) 216353358Sdim#define qnanRep (exponentMask | quietBit) 217276789Sdim 218296417Sdimstatic __inline rep_t toRep(fp_t x) { 219353358Sdim const union { 220353358Sdim fp_t f; 221353358Sdim rep_t i; 222353358Sdim } rep = {.f = x}; 223353358Sdim return rep.i; 224276789Sdim} 225276789Sdim 226296417Sdimstatic __inline fp_t fromRep(rep_t x) { 227353358Sdim const union { 228353358Sdim fp_t f; 229353358Sdim rep_t i; 230353358Sdim } rep = {.i = x}; 231353358Sdim return rep.f; 232276789Sdim} 233276789Sdim 234296417Sdimstatic __inline int normalize(rep_t *significand) { 235353358Sdim const int shift = rep_clz(*significand) - rep_clz(implicitBit); 236353358Sdim *significand <<= shift; 237353358Sdim return 1 - shift; 238276789Sdim} 239276789Sdim 240296417Sdimstatic __inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) { 241353358Sdim *hi = *hi << count | *lo >> (typeWidth - count); 242353358Sdim *lo = *lo << count; 243276789Sdim} 244276789Sdim 245353358Sdimstatic __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, 246353358Sdim unsigned int count) { 247353358Sdim if (count < typeWidth) { 248360784Sdim const bool sticky = (*lo << (typeWidth - count)) != 0; 249353358Sdim *lo = *hi << (typeWidth - count) | *lo >> count | sticky; 250353358Sdim *hi = *hi >> count; 251353358Sdim } else if (count < 2 * typeWidth) { 252353358Sdim const bool sticky = *hi << (2 * typeWidth - count) | *lo; 253353358Sdim *lo = *hi >> (count - typeWidth) | sticky; 254353358Sdim *hi = 0; 255353358Sdim } else { 256353358Sdim const bool sticky = *hi | *lo; 257353358Sdim *lo = sticky; 258353358Sdim *hi = 0; 259353358Sdim } 260276789Sdim} 261344779Sdim 262344779Sdim// Implements logb methods (logb, logbf, logbl) for IEEE-754. This avoids 263344779Sdim// pulling in a libm dependency from compiler-rt, but is not meant to replace 264344779Sdim// it (i.e. code calling logb() should get the one from libm, not this), hence 265344779Sdim// the __compiler_rt prefix. 266344779Sdimstatic __inline fp_t __compiler_rt_logbX(fp_t x) { 267344779Sdim rep_t rep = toRep(x); 268344779Sdim int exp = (rep & exponentMask) >> significandBits; 269344779Sdim 270344779Sdim // Abnormal cases: 271344779Sdim // 1) +/- inf returns +inf; NaN returns NaN 272344779Sdim // 2) 0.0 returns -inf 273344779Sdim if (exp == maxExponent) { 274344779Sdim if (((rep & signBit) == 0) || (x != x)) { 275353358Sdim return x; // NaN or +inf: return x 276344779Sdim } else { 277353358Sdim return -x; // -inf: return -x 278344779Sdim } 279344779Sdim } else if (x == 0.0) { 280344779Sdim // 0.0: return -inf 281344779Sdim return fromRep(infRep | signBit); 282344779Sdim } 283344779Sdim 284344779Sdim if (exp != 0) { 285344779Sdim // Normal number 286353358Sdim return exp - exponentBias; // Unbias exponent 287344779Sdim } else { 288344779Sdim // Subnormal number; normalize and repeat 289344779Sdim rep &= absMask; 290344779Sdim const int shift = 1 - normalize(&rep); 291344779Sdim exp = (rep & exponentMask) >> significandBits; 292353358Sdim return exp - exponentBias - shift; // Unbias exponent 293344779Sdim } 294344779Sdim} 295276789Sdim#endif 296276789Sdim 297344779Sdim#if defined(SINGLE_PRECISION) 298344779Sdimstatic __inline fp_t __compiler_rt_logbf(fp_t x) { 299344779Sdim return __compiler_rt_logbX(x); 300344779Sdim} 301344779Sdim#elif defined(DOUBLE_PRECISION) 302344779Sdimstatic __inline fp_t __compiler_rt_logb(fp_t x) { 303344779Sdim return __compiler_rt_logbX(x); 304344779Sdim} 305344779Sdim#elif defined(QUAD_PRECISION) 306353358Sdim#if defined(CRT_LDBL_128BIT) 307344779Sdimstatic __inline fp_t __compiler_rt_logbl(fp_t x) { 308344779Sdim return __compiler_rt_logbX(x); 309344779Sdim} 310353358Sdim#else 311344779Sdim// The generic implementation only works for ieee754 floating point. For other 312344779Sdim// floating point types, continue to rely on the libm implementation for now. 313344779Sdimstatic __inline long double __compiler_rt_logbl(long double x) { 314344779Sdim return crt_logbl(x); 315344779Sdim} 316344779Sdim#endif 317353358Sdim#endif 318344779Sdim 319276789Sdim#endif // FP_LIB_HEADER 320