lib/builtins/fp_lib.h

   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