compiler-rt/lib/builtins/fp_lib.h

   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
  43 typedef uint16_t half_rep_t;
  44 typedef uint32_t rep_t;
  45 typedef uint64_t twice_rep_t;
  46 typedef int32_t srep_t;
  47 typedef float fp_t;
  48 #define HALF_REP_C UINT16_C
  49 #define REP_C UINT32_C
  50 #define significandBits 23
  51
  52 static __inline int rep_clz(rep_t a) { return clzsi(a); }
  53
  54 // 32x32 --> 64 bit multiply
  55 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
  56   const uint64_t product = (uint64_t)a * b;
  57   *hi = product >> 32;
  58   *lo = product;
  59 }
  60 COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b);
  61
  62 #elif defined DOUBLE_PRECISION
  63
  64 typedef uint32_t half_rep_t;
  65 typedef uint64_t rep_t;
  66 typedef int64_t srep_t;
  67 typedef double fp_t;
  68 #define HALF_REP_C UINT32_C
  69 #define REP_C UINT64_C
  70 #define significandBits 52
  71
  72 static __inline int rep_clz(rep_t a) {
  73 #if defined __LP64__
  74   return __builtin_clzl(a);
  75 #else
  76   if (a & REP_C(0xffffffff00000000))
  77     return clzsi(a >> 32);
  78   else
  79     return 32 + clzsi(a & REP_C(0xffffffff));
  80 #endif
  81 }
  82
  83 #define loWord(a) (a & 0xffffffffU)
  84 #define hiWord(a) (a >> 32)
  85
  86 // 64x64 -> 128 wide multiply for platforms that don't have such an operation;
  87 // many 64-bit platforms have this operation, but they tend to have hardware
  88 // floating-point, so we don't bother with a special case for them here.
  89 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
  90   // Each of the component 32x32 -> 64 products
  91   const uint64_t plolo = loWord(a) * loWord(b);
  92   const uint64_t plohi = loWord(a) * hiWord(b);
  93   const uint64_t philo = hiWord(a) * loWord(b);
  94   const uint64_t phihi = hiWord(a) * hiWord(b);
  95   // Sum terms that contribute to lo in a way that allows us to get the carry
  96   const uint64_t r0 = loWord(plolo);
  97   const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
  98   *lo = r0 + (r1 << 32);
  99   // Sum terms contributing to hi with the carry from lo
 100   *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
 101 }
 102 #undef loWord
 103 #undef hiWord
 104
 105 COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b);
 106
 107 #elif defined QUAD_PRECISION
 108 #if __LDBL_MANT_DIG__ == 113 && defined(__SIZEOF_INT128__)
 109 #define CRT_LDBL_128BIT
 110 typedef uint64_t half_rep_t;
 111 typedef __uint128_t rep_t;
 112 typedef __int128_t srep_t;
 113 typedef long double fp_t;
 114 #define HALF_REP_C UINT64_C
 115 #define REP_C (__uint128_t)
 116 // Note: Since there is no explicit way to tell compiler the constant is a
 117 // 128-bit integer, we let the constant be casted to 128-bit integer
 118 #define significandBits 112
 119
 120 static __inline int rep_clz(rep_t a) {
 121   const union {
 122     __uint128_t ll;
 123 #if _YUGA_BIG_ENDIAN
 124     struct {
 125       uint64_t high, low;
 126     } s;
 127 #else
 128     struct {
 129       uint64_t low, high;
 130     } s;
 131 #endif
 132   } uu = {.ll = a};
 133
 134   uint64_t word;
 135   uint64_t add;
 136
 137   if (uu.s.high) {
 138     word = uu.s.high;
 139     add = 0;
 140   } else {
 141     word = uu.s.low;
 142     add = 64;
 143   }
 144   return __builtin_clzll(word) + add;
 145 }
 146
 147 #define Word_LoMask UINT64_C(0x00000000ffffffff)
 148 #define Word_HiMask UINT64_C(0xffffffff00000000)
 149 #define Word_FullMask UINT64_C(0xffffffffffffffff)
 150 #define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask)
 151 #define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask)
 152 #define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask)
 153 #define Word_4(a) (uint64_t)(a & Word_LoMask)
 154
 155 // 128x128 -> 256 wide multiply for platforms that don't have such an operation;
 156 // many 64-bit platforms have this operation, but they tend to have hardware
 157 // floating-point, so we don't bother with a special case for them here.
 158 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
 159
 160   const uint64_t product11 = Word_1(a) * Word_1(b);
 161   const uint64_t product12 = Word_1(a) * Word_2(b);
 162   const uint64_t product13 = Word_1(a) * Word_3(b);
 163   const uint64_t product14 = Word_1(a) * Word_4(b);
 164   const uint64_t product21 = Word_2(a) * Word_1(b);
 165   const uint64_t product22 = Word_2(a) * Word_2(b);
 166   const uint64_t product23 = Word_2(a) * Word_3(b);
 167   const uint64_t product24 = Word_2(a) * Word_4(b);
 168   const uint64_t product31 = Word_3(a) * Word_1(b);
 169   const uint64_t product32 = Word_3(a) * Word_2(b);
 170   const uint64_t product33 = Word_3(a) * Word_3(b);
 171   const uint64_t product34 = Word_3(a) * Word_4(b);
 172   const uint64_t product41 = Word_4(a) * Word_1(b);
 173   const uint64_t product42 = Word_4(a) * Word_2(b);
 174   const uint64_t product43 = Word_4(a) * Word_3(b);
 175   const uint64_t product44 = Word_4(a) * Word_4(b);
 176
 177   const __uint128_t sum0 = (__uint128_t)product44;
 178   const __uint128_t sum1 = (__uint128_t)product34 + (__uint128_t)product43;
 179   const __uint128_t sum2 =
 180       (__uint128_t)product24 + (__uint128_t)product33 + (__uint128_t)product42;
 181   const __uint128_t sum3 = (__uint128_t)product14 + (__uint128_t)product23 +
 182                            (__uint128_t)product32 + (__uint128_t)product41;
 183   const __uint128_t sum4 =
 184       (__uint128_t)product13 + (__uint128_t)product22 + (__uint128_t)product31;
 185   const __uint128_t sum5 = (__uint128_t)product12 + (__uint128_t)product21;
 186   const __uint128_t sum6 = (__uint128_t)product11;
 187
 188   const __uint128_t r0 = (sum0 & Word_FullMask) + ((sum1 & Word_LoMask) << 32);
 189   const __uint128_t r1 = (sum0 >> 64) + ((sum1 >> 32) & Word_FullMask) +
 190                          (sum2 & Word_FullMask) + ((sum3 << 32) & Word_HiMask);
 191
 192   *lo = r0 + (r1 << 64);
 193   *hi = (r1 >> 64) + (sum1 >> 96) + (sum2 >> 64) + (sum3 >> 32) + sum4 +
 194         (sum5 << 32) + (sum6 << 64);
 195 }
 196 #undef Word_1
 197 #undef Word_2
 198 #undef Word_3
 199 #undef Word_4
 200 #undef Word_HiMask
 201 #undef Word_LoMask
 202 #undef Word_FullMask
 203 #endif // __LDBL_MANT_DIG__ == 113 && __SIZEOF_INT128__
 204 #else
 205 #error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined.
 206 #endif
 207
 208 #if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) ||                  \
 209     defined(CRT_LDBL_128BIT)
 210 #define typeWidth (sizeof(rep_t) * CHAR_BIT)
 211 #define exponentBits (typeWidth - significandBits - 1)
 212 #define maxExponent ((1 << exponentBits) - 1)
 213 #define exponentBias (maxExponent >> 1)
 214
 215 #define implicitBit (REP_C(1) << significandBits)
 216 #define significandMask (implicitBit - 1U)
 217 #define signBit (REP_C(1) << (significandBits + exponentBits))
 218 #define absMask (signBit - 1U)
 219 #define exponentMask (absMask ^ significandMask)
 220 #define oneRep ((rep_t)exponentBias << significandBits)
 221 #define infRep exponentMask
 222 #define quietBit (implicitBit >> 1)
 223 #define qnanRep (exponentMask | quietBit)
 224
 225 static __inline rep_t toRep(fp_t x) {
 226   const union {
 227     fp_t f;
 228     rep_t i;
 229   } rep = {.f = x};
 230   return rep.i;
 231 }
 232
 233 static __inline fp_t fromRep(rep_t x) {
 234   const union {
 235     fp_t f;
 236     rep_t i;
 237   } 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,
 253                                               unsigned int count) {
 254   if (count < typeWidth) {
 255     const bool sticky = (*lo << (typeWidth - count)) != 0;
 256     *lo = *hi << (typeWidth - count) | *lo >> count | sticky;
 257     *hi = *hi >> count;
 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
 269 // Implements logb methods (logb, logbf, logbl) for IEEE-754. This avoids
 270 // pulling in a libm dependency from compiler-rt, but is not meant to replace
 271 // it (i.e. code calling logb() should get the one from libm, not this), hence
 272 // the __compiler_rt prefix.
 273 static __inline fp_t __compiler_rt_logbX(fp_t x) {
 274   rep_t rep = toRep(x);
 275   int exp = (rep & exponentMask) >> significandBits;
 276
 277   // Abnormal cases:
 278   // 1) +/- inf returns +inf; NaN returns NaN
 279   // 2) 0.0 returns -inf
 280   if (exp == maxExponent) {
 281     if (((rep & signBit) == 0) || (x != x)) {
 282       return x; // NaN or +inf: return x
 283     } else {
 284       return -x; // -inf: return -x
 285     }
 286   } else if (x == 0.0) {
 287     // 0.0: return -inf
 288     return fromRep(infRep | signBit);
 289   }
 290
 291   if (exp != 0) {
 292     // Normal number
 293     return exp - exponentBias; // Unbias exponent
 294   } else {
 295     // Subnormal number; normalize and repeat
 296     rep &= absMask;
 297     const int shift = 1 - normalize(&rep);
 298     exp = (rep & exponentMask) >> significandBits;
 299     return exp - exponentBias - shift; // Unbias exponent
 300   }
 301 }
 302
 303 // Avoid using scalbn from libm. Unlike libc/libm scalbn, this function never
 304 // sets errno on underflow/overflow.
 305 static __inline fp_t __compiler_rt_scalbnX(fp_t x, int y) {
 306   const rep_t rep = toRep(x);
 307   int exp = (rep & exponentMask) >> significandBits;
 308
 309   if (x == 0.0 || exp == maxExponent)
 310     return x; // +/- 0.0, NaN, or inf: return x
 311
 312   // Normalize subnormal input.
 313   rep_t sig = rep & significandMask;
 314   if (exp == 0) {
 315     exp += normalize(&sig);
 316     sig &= ~implicitBit; // clear the implicit bit again
 317   }
 318
 319   if (__builtin_sadd_overflow(exp, y, &exp)) {
 320     // Saturate the exponent, which will guarantee an underflow/overflow below.
 321     exp = (y >= 0) ? INT_MAX : INT_MIN;
 322   }
 323
 324   // Return this value: [+/-] 1.sig * 2 ** (exp - exponentBias).
 325   const rep_t sign = rep & signBit;
 326   if (exp >= maxExponent) {
 327     // Overflow, which could produce infinity or the largest-magnitude value,
 328     // depending on the rounding mode.
 329     return fromRep(sign | ((rep_t)(maxExponent - 1) << significandBits)) * 2.0f;
 330   } else if (exp <= 0) {
 331     // Subnormal or underflow. Use floating-point multiply to handle truncation
 332     // correctly.
 333     fp_t tmp = fromRep(sign | (REP_C(1) << significandBits) | sig);
 334     exp += exponentBias - 1;
 335     if (exp < 1)
 336       exp = 1;
 337     tmp *= fromRep((rep_t)exp << significandBits);
 338     return tmp;
 339   } else
 340     return fromRep(sign | ((rep_t)exp << significandBits) | sig);
 341 }
 342
 343 // Avoid using fmax from libm.
 344 static __inline fp_t __compiler_rt_fmaxX(fp_t x, fp_t y) {
 345   // If either argument is NaN, return the other argument. If both are NaN,
 346   // arbitrarily return the second one. Otherwise, if both arguments are +/-0,
 347   // arbitrarily return the first one.
 348   return (crt_isnan(x) || x < y) ? y : x;
 349 }
 350
 351 #endif
 352
 353 #if defined(SINGLE_PRECISION)
 354
 355 static __inline fp_t __compiler_rt_logbf(fp_t x) {
 356   return __compiler_rt_logbX(x);
 357 }
 358 static __inline fp_t __compiler_rt_scalbnf(fp_t x, int y) {
 359   return __compiler_rt_scalbnX(x, y);
 360 }
 361 static __inline fp_t __compiler_rt_fmaxf(fp_t x, fp_t y) {
 362 #if defined(__aarch64__)
 363   // Use __builtin_fmaxf which turns into an fmaxnm instruction on AArch64.
 364   return __builtin_fmaxf(x, y);
 365 #else
 366   // __builtin_fmaxf frequently turns into a libm call, so inline the function.
 367   return __compiler_rt_fmaxX(x, y);
 368 #endif
 369 }
 370
 371 #elif defined(DOUBLE_PRECISION)
 372
 373 static __inline fp_t __compiler_rt_logb(fp_t x) {
 374   return __compiler_rt_logbX(x);
 375 }
 376 static __inline fp_t __compiler_rt_scalbn(fp_t x, int y) {
 377   return __compiler_rt_scalbnX(x, y);
 378 }
 379 static __inline fp_t __compiler_rt_fmax(fp_t x, fp_t y) {
 380 #if defined(__aarch64__)
 381   // Use __builtin_fmax which turns into an fmaxnm instruction on AArch64.
 382   return __builtin_fmax(x, y);
 383 #else
 384   // __builtin_fmax frequently turns into a libm call, so inline the function.
 385   return __compiler_rt_fmaxX(x, y);
 386 #endif
 387 }
 388
 389 #elif defined(QUAD_PRECISION)
 390
 391 #if defined(CRT_LDBL_128BIT)
 392 static __inline fp_t __compiler_rt_logbl(fp_t x) {
 393   return __compiler_rt_logbX(x);
 394 }
 395 static __inline fp_t __compiler_rt_scalbnl(fp_t x, int y) {
 396   return __compiler_rt_scalbnX(x, y);
 397 }
 398 static __inline fp_t __compiler_rt_fmaxl(fp_t x, fp_t y) {
 399   return __compiler_rt_fmaxX(x, y);
 400 }
 401 #else
 402 // The generic implementation only works for ieee754 floating point. For other
 403 // floating point types, continue to rely on the libm implementation for now.
 404 static __inline long double __compiler_rt_logbl(long double x) {
 405   return crt_logbl(x);
 406 }
 407 static __inline long double __compiler_rt_scalbnl(long double x, int y) {
 408   return crt_scalbnl(x, y);
 409 }
 410 static __inline long double __compiler_rt_fmaxl(long double x, long double y) {
 411   return crt_fmaxl(x, y);
 412 }
 413 #endif // CRT_LDBL_128BIT
 414
 415 #endif // *_PRECISION
 416
 417 #endif // FP_LIB_HEADER