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      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