1 //===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===// 2 // 3 // The LLVM Compiler Infrastructure 4 // 5 // This file is dual licensed under the MIT and the University of Illinois Open 6 // Source Licenses. See LICENSE.TXT for details. 7 // 8 //===----------------------------------------------------------------------===// 9 // 10 // This file is a configuration header for soft-float routines in compiler-rt. 11 // This file does not provide any part of the compiler-rt interface, but defines 12 // many useful constants and utility routines that are used in the 13 // implementation of the soft-float routines in compiler-rt. 14 // 15 // Assumes that float, double and long double correspond to the IEEE-754 16 // binary32, binary64 and binary 128 types, respectively, and that integer 17 // endianness matches floating point endianness on the target platform. 18 // 19 //===----------------------------------------------------------------------===// 20 21 #ifndef FP_LIB_HEADER 22 #define FP_LIB_HEADER 23 24 #include <stdint.h> 25 #include <stdbool.h> 26 #include <limits.h> 27 #include "int_lib.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 43 typedef uint32_t rep_t; 44 typedef int32_t srep_t; 45 typedef float fp_t; 46 #define REP_C UINT32_C 47 #define significandBits 23 48 49 static __inline int rep_clz(rep_t a) { 50 return __builtin_clz(a); 51 } 52 53 // 32x32 --> 64 bit multiply 54 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 55 const uint64_t product = (uint64_t)a*b; 56 *hi = product >> 32; 57 *lo = product; 58 } 59 COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b); 60 61 #elif defined DOUBLE_PRECISION 62 63 typedef uint64_t rep_t; 64 typedef int64_t srep_t; 65 typedef double fp_t; 66 #define REP_C UINT64_C 67 #define significandBits 52 68 69 static __inline int rep_clz(rep_t a) { 70 #if defined __LP64__ 71 return __builtin_clzl(a); 72 #else 73 if (a & REP_C(0xffffffff00000000)) 74 return __builtin_clz(a >> 32); 75 else 76 return 32 + __builtin_clz(a & REP_C(0xffffffff)); 77 #endif 78 } 79 80 #define loWord(a) (a & 0xffffffffU) 81 #define hiWord(a) (a >> 32) 82 83 // 64x64 -> 128 wide multiply for platforms that don't have such an operation; 84 // many 64-bit platforms have this operation, but they tend to have hardware 85 // floating-point, so we don't bother with a special case for them here. 86 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 87 // Each of the component 32x32 -> 64 products 88 const uint64_t plolo = loWord(a) * loWord(b); 89 const uint64_t plohi = loWord(a) * hiWord(b); 90 const uint64_t philo = hiWord(a) * loWord(b); 91 const uint64_t phihi = hiWord(a) * hiWord(b); 92 // Sum terms that contribute to lo in a way that allows us to get the carry 93 const uint64_t r0 = loWord(plolo); 94 const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo); 95 *lo = r0 + (r1 << 32); 96 // Sum terms contributing to hi with the carry from lo 97 *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi; 98 } 99 #undef loWord 100 #undef hiWord 101 102 COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b); 103 104 #elif defined QUAD_PRECISION 105 #if __LDBL_MANT_DIG__ == 113 106 #define CRT_LDBL_128BIT 107 typedef __uint128_t rep_t; 108 typedef __int128_t srep_t; 109 typedef long double fp_t; 110 #define REP_C (__uint128_t) 111 // Note: Since there is no explicit way to tell compiler the constant is a 112 // 128-bit integer, we let the constant be casted to 128-bit integer 113 #define significandBits 112 114 115 static __inline int rep_clz(rep_t a) { 116 const union 117 { 118 __uint128_t ll; 119 #if _YUGA_BIG_ENDIAN 120 struct { uint64_t high, low; } s; 121 #else 122 struct { uint64_t low, high; } s; 123 #endif 124 } uu = { .ll = a }; 125 126 uint64_t word; 127 uint64_t add; 128 129 if (uu.s.high){ 130 word = uu.s.high; 131 add = 0; 132 } 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. 151 static __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 + 172 (__uint128_t)product43; 173 const __uint128_t sum2 = (__uint128_t)product24 + 174 (__uint128_t)product33 + 175 (__uint128_t)product42; 176 const __uint128_t sum3 = (__uint128_t)product14 + 177 (__uint128_t)product23 + 178 (__uint128_t)product32 + 179 (__uint128_t)product41; 180 const __uint128_t sum4 = (__uint128_t)product13 + 181 (__uint128_t)product22 + 182 (__uint128_t)product31; 183 const __uint128_t sum5 = (__uint128_t)product12 + 184 (__uint128_t)product21; 185 const __uint128_t sum6 = (__uint128_t)product11; 186 187 const __uint128_t r0 = (sum0 & Word_FullMask) + 188 ((sum1 & Word_LoMask) << 32); 189 const __uint128_t r1 = (sum0 >> 64) + 190 ((sum1 >> 32) & Word_FullMask) + 191 (sum2 & Word_FullMask) + 192 ((sum3 << 32) & Word_HiMask); 193 194 *lo = r0 + (r1 << 64); 195 *hi = (r1 >> 64) + 196 (sum1 >> 96) + 197 (sum2 >> 64) + 198 (sum3 >> 32) + 199 sum4 + 200 (sum5 << 32) + 201 (sum6 << 64); 202 } 203 #undef Word_1 204 #undef Word_2 205 #undef Word_3 206 #undef Word_4 207 #undef Word_HiMask 208 #undef Word_LoMask 209 #undef Word_FullMask 210 #endif // __LDBL_MANT_DIG__ == 113 211 #else 212 #error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined. 213 #endif 214 215 #if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || defined(CRT_LDBL_128BIT) 216 #define typeWidth (sizeof(rep_t)*CHAR_BIT) 217 #define exponentBits (typeWidth - significandBits - 1) 218 #define maxExponent ((1 << exponentBits) - 1) 219 #define exponentBias (maxExponent >> 1) 220 221 #define implicitBit (REP_C(1) << significandBits) 222 #define significandMask (implicitBit - 1U) 223 #define signBit (REP_C(1) << (significandBits + exponentBits)) 224 #define absMask (signBit - 1U) 225 #define exponentMask (absMask ^ significandMask) 226 #define oneRep ((rep_t)exponentBias << significandBits) 227 #define infRep exponentMask 228 #define quietBit (implicitBit >> 1) 229 #define qnanRep (exponentMask | quietBit) 230 231 static __inline rep_t toRep(fp_t x) { 232 const union { fp_t f; rep_t i; } rep = {.f = x}; 233 return rep.i; 234 } 235 236 static __inline fp_t fromRep(rep_t x) { 237 const union { fp_t f; rep_t i; } rep = {.i = x}; 238 return rep.f; 239 } 240 241 static __inline int normalize(rep_t *significand) { 242 const int shift = rep_clz(*significand) - rep_clz(implicitBit); 243 *significand <<= shift; 244 return 1 - shift; 245 } 246 247 static __inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) { 248 *hi = *hi << count | *lo >> (typeWidth - count); 249 *lo = *lo << count; 250 } 251 252 static __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, unsigned int count) { 253 if (count < typeWidth) { 254 const bool sticky = *lo << (typeWidth - count); 255 *lo = *hi << (typeWidth - count) | *lo >> count | sticky; 256 *hi = *hi >> count; 257 } 258 else if (count < 2*typeWidth) { 259 const bool sticky = *hi << (2*typeWidth - count) | *lo; 260 *lo = *hi >> (count - typeWidth) | sticky; 261 *hi = 0; 262 } else { 263 const bool sticky = *hi | *lo; 264 *lo = sticky; 265 *hi = 0; 266 } 267 } 268 #endif 269 270 #endif // FP_LIB_HEADER 271
