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 "int_types.h" 26 #include <limits.h> 27 #include <stdbool.h> 28 #include <stdint.h> 29 30 #if defined SINGLE_PRECISION 31 32 typedef uint16_t half_rep_t; 33 typedef uint32_t rep_t; 34 typedef uint64_t twice_rep_t; 35 typedef int32_t srep_t; 36 typedef float fp_t; 37 #define HALF_REP_C UINT16_C 38 #define REP_C UINT32_C 39 #define significandBits 23 40 41 static __inline int rep_clz(rep_t a) { return clzsi(a); } 42 43 // 32x32 --> 64 bit multiply 44 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 45 const uint64_t product = (uint64_t)a * b; 46 *hi = product >> 32; 47 *lo = product; 48 } 49 COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b); 50 51 #elif defined DOUBLE_PRECISION 52 53 typedef uint32_t half_rep_t; 54 typedef uint64_t rep_t; 55 typedef int64_t srep_t; 56 typedef double fp_t; 57 #define HALF_REP_C UINT32_C 58 #define REP_C UINT64_C 59 #define significandBits 52 60 61 static __inline int rep_clz(rep_t a) { 62 #if defined __LP64__ 63 return __builtin_clzl(a); 64 #else 65 if (a & REP_C(0xffffffff00000000)) 66 return clzsi(a >> 32); 67 else 68 return 32 + clzsi(a & REP_C(0xffffffff)); 69 #endif 70 } 71 72 #define loWord(a) (a & 0xffffffffU) 73 #define hiWord(a) (a >> 32) 74 75 // 64x64 -> 128 wide multiply for platforms that don't have such an operation; 76 // many 64-bit platforms have this operation, but they tend to have hardware 77 // floating-point, so we don't bother with a special case for them here. 78 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 79 // Each of the component 32x32 -> 64 products 80 const uint64_t plolo = loWord(a) * loWord(b); 81 const uint64_t plohi = loWord(a) * hiWord(b); 82 const uint64_t philo = hiWord(a) * loWord(b); 83 const uint64_t phihi = hiWord(a) * hiWord(b); 84 // Sum terms that contribute to lo in a way that allows us to get the carry 85 const uint64_t r0 = loWord(plolo); 86 const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo); 87 *lo = r0 + (r1 << 32); 88 // Sum terms contributing to hi with the carry from lo 89 *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi; 90 } 91 #undef loWord 92 #undef hiWord 93 94 COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b); 95 96 #elif defined QUAD_PRECISION 97 #if defined(CRT_HAS_F128) && defined(CRT_HAS_128BIT) 98 typedef uint64_t half_rep_t; 99 typedef __uint128_t rep_t; 100 typedef __int128_t srep_t; 101 typedef tf_float fp_t; 102 #define HALF_REP_C UINT64_C 103 #define REP_C (__uint128_t) 104 #if defined(CRT_HAS_IEEE_TF) 105 // Note: Since there is no explicit way to tell compiler the constant is a 106 // 128-bit integer, we let the constant be casted to 128-bit integer 107 #define significandBits 112 108 #define TF_MANT_DIG (significandBits + 1) 109 110 static __inline int rep_clz(rep_t a) { 111 const union { 112 __uint128_t ll; 113 #if _YUGA_BIG_ENDIAN 114 struct { 115 uint64_t high, low; 116 } s; 117 #else 118 struct { 119 uint64_t low, high; 120 } s; 121 #endif 122 } uu = {.ll = a}; 123 124 uint64_t word; 125 uint64_t add; 126 127 if (uu.s.high) { 128 word = uu.s.high; 129 add = 0; 130 } else { 131 word = uu.s.low; 132 add = 64; 133 } 134 return __builtin_clzll(word) + add; 135 } 136 137 #define Word_LoMask UINT64_C(0x00000000ffffffff) 138 #define Word_HiMask UINT64_C(0xffffffff00000000) 139 #define Word_FullMask UINT64_C(0xffffffffffffffff) 140 #define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask) 141 #define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask) 142 #define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask) 143 #define Word_4(a) (uint64_t)(a & Word_LoMask) 144 145 // 128x128 -> 256 wide multiply for platforms that don't have such an operation; 146 // many 64-bit platforms have this operation, but they tend to have hardware 147 // floating-point, so we don't bother with a special case for them here. 148 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) { 149 150 const uint64_t product11 = Word_1(a) * Word_1(b); 151 const uint64_t product12 = Word_1(a) * Word_2(b); 152 const uint64_t product13 = Word_1(a) * Word_3(b); 153 const uint64_t product14 = Word_1(a) * Word_4(b); 154 const uint64_t product21 = Word_2(a) * Word_1(b); 155 const uint64_t product22 = Word_2(a) * Word_2(b); 156 const uint64_t product23 = Word_2(a) * Word_3(b); 157 const uint64_t product24 = Word_2(a) * Word_4(b); 158 const uint64_t product31 = Word_3(a) * Word_1(b); 159 const uint64_t product32 = Word_3(a) * Word_2(b); 160 const uint64_t product33 = Word_3(a) * Word_3(b); 161 const uint64_t product34 = Word_3(a) * Word_4(b); 162 const uint64_t product41 = Word_4(a) * Word_1(b); 163 const uint64_t product42 = Word_4(a) * Word_2(b); 164 const uint64_t product43 = Word_4(a) * Word_3(b); 165 const uint64_t product44 = Word_4(a) * Word_4(b); 166 167 const __uint128_t sum0 = (__uint128_t)product44; 168 const __uint128_t sum1 = (__uint128_t)product34 + (__uint128_t)product43; 169 const __uint128_t sum2 = 170 (__uint128_t)product24 + (__uint128_t)product33 + (__uint128_t)product42; 171 const __uint128_t sum3 = (__uint128_t)product14 + (__uint128_t)product23 + 172 (__uint128_t)product32 + (__uint128_t)product41; 173 const __uint128_t sum4 = 174 (__uint128_t)product13 + (__uint128_t)product22 + (__uint128_t)product31; 175 const __uint128_t sum5 = (__uint128_t)product12 + (__uint128_t)product21; 176 const __uint128_t sum6 = (__uint128_t)product11; 177 178 const __uint128_t r0 = (sum0 & Word_FullMask) + ((sum1 & Word_LoMask) << 32); 179 const __uint128_t r1 = (sum0 >> 64) + ((sum1 >> 32) & Word_FullMask) + 180 (sum2 & Word_FullMask) + ((sum3 << 32) & Word_HiMask); 181 182 *lo = r0 + (r1 << 64); 183 *hi = (r1 >> 64) + (sum1 >> 96) + (sum2 >> 64) + (sum3 >> 32) + sum4 + 184 (sum5 << 32) + (sum6 << 64); 185 } 186 #undef Word_1 187 #undef Word_2 188 #undef Word_3 189 #undef Word_4 190 #undef Word_HiMask 191 #undef Word_LoMask 192 #undef Word_FullMask 193 #endif // defined(CRT_HAS_IEEE_TF) 194 #else 195 typedef long double fp_t; 196 #endif // defined(CRT_HAS_F128) && defined(CRT_HAS_128BIT) 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(QUAD_PRECISION) && defined(CRT_HAS_TF_MODE)) 203 #define typeWidth (sizeof(rep_t) * CHAR_BIT) 204 205 static __inline rep_t toRep(fp_t x) { 206 const union { 207 fp_t f; 208 rep_t i; 209 } rep = {.f = x}; 210 return rep.i; 211 } 212 213 static __inline fp_t fromRep(rep_t x) { 214 const union { 215 fp_t f; 216 rep_t i; 217 } rep = {.i = x}; 218 return rep.f; 219 } 220 221 #if !defined(QUAD_PRECISION) || defined(CRT_HAS_IEEE_TF) 222 #define exponentBits (typeWidth - significandBits - 1) 223 #define maxExponent ((1 << exponentBits) - 1) 224 #define exponentBias (maxExponent >> 1) 225 226 #define implicitBit (REP_C(1) << significandBits) 227 #define significandMask (implicitBit - 1U) 228 #define signBit (REP_C(1) << (significandBits + exponentBits)) 229 #define absMask (signBit - 1U) 230 #define exponentMask (absMask ^ significandMask) 231 #define oneRep ((rep_t)exponentBias << significandBits) 232 #define infRep exponentMask 233 #define quietBit (implicitBit >> 1) 234 #define qnanRep (exponentMask | quietBit) 235 236 static __inline int normalize(rep_t *significand) { 237 const int shift = rep_clz(*significand) - rep_clz(implicitBit); 238 *significand <<= shift; 239 return 1 - shift; 240 } 241 242 static __inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) { 243 *hi = *hi << count | *lo >> (typeWidth - count); 244 *lo = *lo << count; 245 } 246 247 static __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, 248 unsigned int count) { 249 if (count < typeWidth) { 250 const bool sticky = (*lo << (typeWidth - count)) != 0; 251 *lo = *hi << (typeWidth - count) | *lo >> count | sticky; 252 *hi = *hi >> count; 253 } else if (count < 2 * typeWidth) { 254 const bool sticky = *hi << (2 * typeWidth - count) | *lo; 255 *lo = *hi >> (count - typeWidth) | sticky; 256 *hi = 0; 257 } else { 258 const bool sticky = *hi | *lo; 259 *lo = sticky; 260 *hi = 0; 261 } 262 } 263 264 // Implements logb methods (logb, logbf, logbl) for IEEE-754. This avoids 265 // pulling in a libm dependency from compiler-rt, but is not meant to replace 266 // it (i.e. code calling logb() should get the one from libm, not this), hence 267 // the __compiler_rt prefix. 268 static __inline fp_t __compiler_rt_logbX(fp_t x) { 269 rep_t rep = toRep(x); 270 int exp = (rep & exponentMask) >> significandBits; 271 272 // Abnormal cases: 273 // 1) +/- inf returns +inf; NaN returns NaN 274 // 2) 0.0 returns -inf 275 if (exp == maxExponent) { 276 if (((rep & signBit) == 0) || (x != x)) { 277 return x; // NaN or +inf: return x 278 } else { 279 return -x; // -inf: return -x 280 } 281 } else if (x == 0.0) { 282 // 0.0: return -inf 283 return fromRep(infRep | signBit); 284 } 285 286 if (exp != 0) { 287 // Normal number 288 return exp - exponentBias; // Unbias exponent 289 } else { 290 // Subnormal number; normalize and repeat 291 rep &= absMask; 292 const int shift = 1 - normalize(&rep); 293 exp = (rep & exponentMask) >> significandBits; 294 return exp - exponentBias - shift; // Unbias exponent 295 } 296 } 297 298 // Avoid using scalbn from libm. Unlike libc/libm scalbn, this function never 299 // sets errno on underflow/overflow. 300 static __inline fp_t __compiler_rt_scalbnX(fp_t x, int y) { 301 const rep_t rep = toRep(x); 302 int exp = (rep & exponentMask) >> significandBits; 303 304 if (x == 0.0 || exp == maxExponent) 305 return x; // +/- 0.0, NaN, or inf: return x 306 307 // Normalize subnormal input. 308 rep_t sig = rep & significandMask; 309 if (exp == 0) { 310 exp += normalize(&sig); 311 sig &= ~implicitBit; // clear the implicit bit again 312 } 313 314 if (__builtin_sadd_overflow(exp, y, &exp)) { 315 // Saturate the exponent, which will guarantee an underflow/overflow below. 316 exp = (y >= 0) ? INT_MAX : INT_MIN; 317 } 318 319 // Return this value: [+/-] 1.sig * 2 ** (exp - exponentBias). 320 const rep_t sign = rep & signBit; 321 if (exp >= maxExponent) { 322 // Overflow, which could produce infinity or the largest-magnitude value, 323 // depending on the rounding mode. 324 return fromRep(sign | ((rep_t)(maxExponent - 1) << significandBits)) * 2.0f; 325 } else if (exp <= 0) { 326 // Subnormal or underflow. Use floating-point multiply to handle truncation 327 // correctly. 328 fp_t tmp = fromRep(sign | (REP_C(1) << significandBits) | sig); 329 exp += exponentBias - 1; 330 if (exp < 1) 331 exp = 1; 332 tmp *= fromRep((rep_t)exp << significandBits); 333 return tmp; 334 } else 335 return fromRep(sign | ((rep_t)exp << significandBits) | sig); 336 } 337 338 #endif // !defined(QUAD_PRECISION) || defined(CRT_HAS_IEEE_TF) 339 340 // Avoid using fmax from libm. 341 static __inline fp_t __compiler_rt_fmaxX(fp_t x, fp_t y) { 342 // If either argument is NaN, return the other argument. If both are NaN, 343 // arbitrarily return the second one. Otherwise, if both arguments are +/-0, 344 // arbitrarily return the first one. 345 return (crt_isnan(x) || x < y) ? y : x; 346 } 347 348 #endif 349 350 #if defined(SINGLE_PRECISION) 351 352 static __inline fp_t __compiler_rt_logbf(fp_t x) { 353 return __compiler_rt_logbX(x); 354 } 355 static __inline fp_t __compiler_rt_scalbnf(fp_t x, int y) { 356 return __compiler_rt_scalbnX(x, y); 357 } 358 static __inline fp_t __compiler_rt_fmaxf(fp_t x, fp_t y) { 359 #if defined(__aarch64__) 360 // Use __builtin_fmaxf which turns into an fmaxnm instruction on AArch64. 361 return __builtin_fmaxf(x, y); 362 #else 363 // __builtin_fmaxf frequently turns into a libm call, so inline the function. 364 return __compiler_rt_fmaxX(x, y); 365 #endif 366 } 367 368 #elif defined(DOUBLE_PRECISION) 369 370 static __inline fp_t __compiler_rt_logb(fp_t x) { 371 return __compiler_rt_logbX(x); 372 } 373 static __inline fp_t __compiler_rt_scalbn(fp_t x, int y) { 374 return __compiler_rt_scalbnX(x, y); 375 } 376 static __inline fp_t __compiler_rt_fmax(fp_t x, fp_t y) { 377 #if defined(__aarch64__) 378 // Use __builtin_fmax which turns into an fmaxnm instruction on AArch64. 379 return __builtin_fmax(x, y); 380 #else 381 // __builtin_fmax frequently turns into a libm call, so inline the function. 382 return __compiler_rt_fmaxX(x, y); 383 #endif 384 } 385 386 #elif defined(QUAD_PRECISION) && defined(CRT_HAS_TF_MODE) 387 // The generic implementation only works for ieee754 floating point. For other 388 // floating point types, continue to rely on the libm implementation for now. 389 #if defined(CRT_HAS_IEEE_TF) 390 static __inline tf_float __compiler_rt_logbtf(tf_float x) { 391 return __compiler_rt_logbX(x); 392 } 393 static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) { 394 return __compiler_rt_scalbnX(x, y); 395 } 396 static __inline tf_float __compiler_rt_fmaxtf(tf_float x, tf_float y) { 397 return __compiler_rt_fmaxX(x, y); 398 } 399 #define __compiler_rt_logbl __compiler_rt_logbtf 400 #define __compiler_rt_scalbnl __compiler_rt_scalbntf 401 #define __compiler_rt_fmaxl __compiler_rt_fmaxtf 402 #define crt_fabstf crt_fabsf128 403 #define crt_copysigntf crt_copysignf128 404 #elif defined(CRT_LDBL_128BIT) 405 static __inline tf_float __compiler_rt_logbtf(tf_float x) { 406 return crt_logbl(x); 407 } 408 static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) { 409 return crt_scalbnl(x, y); 410 } 411 static __inline tf_float __compiler_rt_fmaxtf(tf_float x, tf_float y) { 412 return crt_fmaxl(x, y); 413 } 414 #define __compiler_rt_logbl crt_logbl 415 #define __compiler_rt_scalbnl crt_scalbnl 416 #define __compiler_rt_fmaxl crt_fmaxl 417 #define crt_fabstf crt_fabsl 418 #define crt_copysigntf crt_copysignl 419 #else 420 #error Unsupported TF mode type 421 #endif 422 423 #endif // *_PRECISION 424 425 #endif // FP_LIB_HEADER 426