1//===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===// 2// 3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4// See https://llvm.org/LICENSE.txt for license information. 5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6// 7//===----------------------------------------------------------------------===// 8// 9// This file is a configuration header for soft-float routines in compiler-rt. 10// This file does not provide any part of the compiler-rt interface, but defines 11// many useful constants and utility routines that are used in the 12// implementation of the soft-float routines in compiler-rt. 13// 14// Assumes that float, double and long double correspond to the IEEE-754 15// binary32, binary64 and binary 128 types, respectively, and that integer 16// endianness matches floating point endianness on the target platform. 17// 18//===----------------------------------------------------------------------===// 19 20#ifndef FP_LIB_HEADER 21#define FP_LIB_HEADER 22 23#include "int_lib.h" 24#include "int_math.h" 25#include <limits.h> 26#include <stdbool.h> 27#include <stdint.h> 28 29// x86_64 FreeBSD prior v9.3 define fixed-width types incorrectly in 30// 32-bit mode. 31#if defined(__FreeBSD__) && defined(__i386__) 32#include <sys/param.h> 33#if __FreeBSD_version < 903000 // v9.3 34#define uint64_t unsigned long long 35#define int64_t long long 36#undef UINT64_C 37#define UINT64_C(c) (c##ULL) 38#endif 39#endif 40 41#if defined SINGLE_PRECISION 42 43typedef uint32_t rep_t; 44typedef int32_t srep_t; 45typedef float fp_t; 46#define REP_C UINT32_C 47#define significandBits 23 48 49static __inline int rep_clz(rep_t a) { return __builtin_clz(a); } 50 51// 32x32 --> 64 bit multiply 52static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 53 const uint64_t product = (uint64_t)a * b; 54 *hi = product >> 32; 55 *lo = product; 56} 57COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b); 58 59#elif defined DOUBLE_PRECISION 60 61typedef uint64_t rep_t; 62typedef int64_t srep_t; 63typedef double fp_t; 64#define REP_C UINT64_C 65#define significandBits 52 66 67static __inline int rep_clz(rep_t a) { 68#if defined __LP64__ 69 return __builtin_clzl(a); 70#else 71 if (a & REP_C(0xffffffff00000000)) 72 return __builtin_clz(a >> 32); 73 else 74 return 32 + __builtin_clz(a & REP_C(0xffffffff)); 75#endif 76} 77 78#define loWord(a) (a & 0xffffffffU) 79#define hiWord(a) (a >> 32) 80 81// 64x64 -> 128 wide multiply for platforms that don't have such an operation; 82// many 64-bit platforms have this operation, but they tend to have hardware 83// floating-point, so we don't bother with a special case for them here. 84static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 85 // Each of the component 32x32 -> 64 products 86 const uint64_t plolo = loWord(a) * loWord(b); 87 const uint64_t plohi = loWord(a) * hiWord(b); 88 const uint64_t philo = hiWord(a) * loWord(b); 89 const uint64_t phihi = hiWord(a) * hiWord(b); 90 // Sum terms that contribute to lo in a way that allows us to get the carry 91 const uint64_t r0 = loWord(plolo); 92 const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo); 93 *lo = r0 + (r1 << 32); 94 // Sum terms contributing to hi with the carry from lo 95 *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi; 96} 97#undef loWord 98#undef hiWord 99 100COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b); 101 102#elif defined QUAD_PRECISION 103#if __LDBL_MANT_DIG__ == 113 && defined(__SIZEOF_INT128__) 104#define CRT_LDBL_128BIT 105typedef __uint128_t rep_t; 106typedef __int128_t srep_t; 107typedef long double fp_t; 108#define REP_C (__uint128_t) 109// Note: Since there is no explicit way to tell compiler the constant is a 110// 128-bit integer, we let the constant be casted to 128-bit integer 111#define significandBits 112 112 113static __inline int rep_clz(rep_t a) { 114 const union { 115 __uint128_t ll; 116#if _YUGA_BIG_ENDIAN 117 struct { 118 uint64_t high, low; 119 } s; 120#else 121 struct { 122 uint64_t low, high; 123 } s; 124#endif 125 } uu = {.ll = a}; 126 127 uint64_t word; 128 uint64_t add; 129 130 if (uu.s.high) { 131 word = uu.s.high; 132 add = 0; 133 } else { 134 word = uu.s.low; 135 add = 64; 136 } 137 return __builtin_clzll(word) + add; 138} 139 140#define Word_LoMask UINT64_C(0x00000000ffffffff) 141#define Word_HiMask UINT64_C(0xffffffff00000000) 142#define Word_FullMask UINT64_C(0xffffffffffffffff) 143#define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask) 144#define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask) 145#define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask) 146#define Word_4(a) (uint64_t)(a & Word_LoMask) 147 148// 128x128 -> 256 wide multiply for platforms that don't have such an operation; 149// many 64-bit platforms have this operation, but they tend to have hardware 150// floating-point, so we don't bother with a special case for them here. 151static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 152 153 const uint64_t product11 = Word_1(a) * Word_1(b); 154 const uint64_t product12 = Word_1(a) * Word_2(b); 155 const uint64_t product13 = Word_1(a) * Word_3(b); 156 const uint64_t product14 = Word_1(a) * Word_4(b); 157 const uint64_t product21 = Word_2(a) * Word_1(b); 158 const uint64_t product22 = Word_2(a) * Word_2(b); 159 const uint64_t product23 = Word_2(a) * Word_3(b); 160 const uint64_t product24 = Word_2(a) * Word_4(b); 161 const uint64_t product31 = Word_3(a) * Word_1(b); 162 const uint64_t product32 = Word_3(a) * Word_2(b); 163 const uint64_t product33 = Word_3(a) * Word_3(b); 164 const uint64_t product34 = Word_3(a) * Word_4(b); 165 const uint64_t product41 = Word_4(a) * Word_1(b); 166 const uint64_t product42 = Word_4(a) * Word_2(b); 167 const uint64_t product43 = Word_4(a) * Word_3(b); 168 const uint64_t product44 = Word_4(a) * Word_4(b); 169 170 const __uint128_t sum0 = (__uint128_t)product44; 171 const __uint128_t sum1 = (__uint128_t)product34 + (__uint128_t)product43; 172 const __uint128_t sum2 = 173 (__uint128_t)product24 + (__uint128_t)product33 + (__uint128_t)product42; 174 const __uint128_t sum3 = (__uint128_t)product14 + (__uint128_t)product23 + 175 (__uint128_t)product32 + (__uint128_t)product41; 176 const __uint128_t sum4 = 177 (__uint128_t)product13 + (__uint128_t)product22 + (__uint128_t)product31; 178 const __uint128_t sum5 = (__uint128_t)product12 + (__uint128_t)product21; 179 const __uint128_t sum6 = (__uint128_t)product11; 180 181 const __uint128_t r0 = (sum0 & Word_FullMask) + ((sum1 & Word_LoMask) << 32); 182 const __uint128_t r1 = (sum0 >> 64) + ((sum1 >> 32) & Word_FullMask) + 183 (sum2 & Word_FullMask) + ((sum3 << 32) & Word_HiMask); 184 185 *lo = r0 + (r1 << 64); 186 *hi = (r1 >> 64) + (sum1 >> 96) + (sum2 >> 64) + (sum3 >> 32) + sum4 + 187 (sum5 << 32) + (sum6 << 64); 188} 189#undef Word_1 190#undef Word_2 191#undef Word_3 192#undef Word_4 193#undef Word_HiMask 194#undef Word_LoMask 195#undef Word_FullMask 196#endif // __LDBL_MANT_DIG__ == 113 && __SIZEOF_INT128__ 197#else 198#error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined. 199#endif 200 201#if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || \ 202 defined(CRT_LDBL_128BIT) 203#define typeWidth (sizeof(rep_t) * CHAR_BIT) 204#define exponentBits (typeWidth - significandBits - 1) 205#define maxExponent ((1 << exponentBits) - 1) 206#define exponentBias (maxExponent >> 1) 207 208#define implicitBit (REP_C(1) << significandBits) 209#define significandMask (implicitBit - 1U) 210#define signBit (REP_C(1) << (significandBits + exponentBits)) 211#define absMask (signBit - 1U) 212#define exponentMask (absMask ^ significandMask) 213#define oneRep ((rep_t)exponentBias << significandBits) 214#define infRep exponentMask 215#define quietBit (implicitBit >> 1) 216#define qnanRep (exponentMask | quietBit) 217 218static __inline rep_t toRep(fp_t x) { 219 const union { 220 fp_t f; 221 rep_t i; 222 } rep = {.f = x}; 223 return rep.i; 224} 225 226static __inline fp_t fromRep(rep_t x) { 227 const union { 228 fp_t f; 229 rep_t i; 230 } rep = {.i = x}; 231 return rep.f; 232} 233 234static __inline int normalize(rep_t *significand) { 235 const int shift = rep_clz(*significand) - rep_clz(implicitBit); 236 *significand <<= shift; 237 return 1 - shift; 238} 239 240static __inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) { 241 *hi = *hi << count | *lo >> (typeWidth - count); 242 *lo = *lo << count; 243} 244 245static __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, 246 unsigned int count) { 247 if (count < typeWidth) { 248 const bool sticky = (*lo << (typeWidth - count)) != 0; 249 *lo = *hi << (typeWidth - count) | *lo >> count | sticky; 250 *hi = *hi >> count; 251 } else if (count < 2 * typeWidth) { 252 const bool sticky = *hi << (2 * typeWidth - count) | *lo; 253 *lo = *hi >> (count - typeWidth) | sticky; 254 *hi = 0; 255 } else { 256 const bool sticky = *hi | *lo; 257 *lo = sticky; 258 *hi = 0; 259 } 260} 261 262// Implements logb methods (logb, logbf, logbl) for IEEE-754. This avoids 263// pulling in a libm dependency from compiler-rt, but is not meant to replace 264// it (i.e. code calling logb() should get the one from libm, not this), hence 265// the __compiler_rt prefix. 266static __inline fp_t __compiler_rt_logbX(fp_t x) { 267 rep_t rep = toRep(x); 268 int exp = (rep & exponentMask) >> significandBits; 269 270 // Abnormal cases: 271 // 1) +/- inf returns +inf; NaN returns NaN 272 // 2) 0.0 returns -inf 273 if (exp == maxExponent) { 274 if (((rep & signBit) == 0) || (x != x)) { 275 return x; // NaN or +inf: return x 276 } else { 277 return -x; // -inf: return -x 278 } 279 } else if (x == 0.0) { 280 // 0.0: return -inf 281 return fromRep(infRep | signBit); 282 } 283 284 if (exp != 0) { 285 // Normal number 286 return exp - exponentBias; // Unbias exponent 287 } else { 288 // Subnormal number; normalize and repeat 289 rep &= absMask; 290 const int shift = 1 - normalize(&rep); 291 exp = (rep & exponentMask) >> significandBits; 292 return exp - exponentBias - shift; // Unbias exponent 293 } 294} 295#endif 296 297#if defined(SINGLE_PRECISION) 298static __inline fp_t __compiler_rt_logbf(fp_t x) { 299 return __compiler_rt_logbX(x); 300} 301#elif defined(DOUBLE_PRECISION) 302static __inline fp_t __compiler_rt_logb(fp_t x) { 303 return __compiler_rt_logbX(x); 304} 305#elif defined(QUAD_PRECISION) 306#if defined(CRT_LDBL_128BIT) 307static __inline fp_t __compiler_rt_logbl(fp_t x) { 308 return __compiler_rt_logbX(x); 309} 310#else 311// The generic implementation only works for ieee754 floating point. For other 312// floating point types, continue to rely on the libm implementation for now. 313static __inline long double __compiler_rt_logbl(long double x) { 314 return crt_logbl(x); 315} 316#endif 317#endif 318 319#endif // FP_LIB_HEADER 320