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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 and double correspond to the IEEE-754 binary32 and
     16 // binary64 types, respectively, and that integer endianness matches floating
     17 // 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 #if defined SINGLE_PRECISION
     30 
     31 typedef uint32_t rep_t;
     32 typedef int32_t srep_t;
     33 typedef float fp_t;
     34 #define REP_C UINT32_C
     35 #define significandBits 23
     36 
     37 static inline int rep_clz(rep_t a) {
     38     return __builtin_clz(a);
     39 }
     40 
     41 // 32x32 --> 64 bit multiply
     42 static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
     43     const uint64_t product = (uint64_t)a*b;
     44     *hi = product >> 32;
     45     *lo = product;
     46 }
     47 
     48 #elif defined DOUBLE_PRECISION
     49 
     50 typedef uint64_t rep_t;
     51 typedef int64_t srep_t;
     52 typedef double fp_t;
     53 #define REP_C UINT64_C
     54 #define significandBits 52
     55 
     56 static inline int rep_clz(rep_t a) {
     57 #if defined __LP64__
     58     return __builtin_clzl(a);
     59 #else
     60     if (a & REP_C(0xffffffff00000000))
     61         return __builtin_clz(a >> 32);
     62     else
     63         return 32 + __builtin_clz(a & REP_C(0xffffffff));
     64 #endif
     65 }
     66 
     67 #define loWord(a) (a & 0xffffffffU)
     68 #define hiWord(a) (a >> 32)
     69 
     70 // 64x64 -> 128 wide multiply for platforms that don't have such an operation;
     71 // many 64-bit platforms have this operation, but they tend to have hardware
     72 // floating-point, so we don't bother with a special case for them here.
     73 static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
     74     // Each of the component 32x32 -> 64 products
     75     const uint64_t plolo = loWord(a) * loWord(b);
     76     const uint64_t plohi = loWord(a) * hiWord(b);
     77     const uint64_t philo = hiWord(a) * loWord(b);
     78     const uint64_t phihi = hiWord(a) * hiWord(b);
     79     // Sum terms that contribute to lo in a way that allows us to get the carry
     80     const uint64_t r0 = loWord(plolo);
     81     const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
     82     *lo = r0 + (r1 << 32);
     83     // Sum terms contributing to hi with the carry from lo
     84     *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
     85 }
     86 
     87 #else
     88 #error Either SINGLE_PRECISION or DOUBLE_PRECISION must be defined.
     89 #endif
     90 
     91 #define typeWidth       (sizeof(rep_t)*CHAR_BIT)
     92 #define exponentBits    (typeWidth - significandBits - 1)
     93 #define maxExponent     ((1 << exponentBits) - 1)
     94 #define exponentBias    (maxExponent >> 1)
     95 
     96 #define implicitBit     (REP_C(1) << significandBits)
     97 #define significandMask (implicitBit - 1U)
     98 #define signBit         (REP_C(1) << (significandBits + exponentBits))
     99 #define absMask         (signBit - 1U)
    100 #define exponentMask    (absMask ^ significandMask)
    101 #define oneRep          ((rep_t)exponentBias << significandBits)
    102 #define infRep          exponentMask
    103 #define quietBit        (implicitBit >> 1)
    104 #define qnanRep         (exponentMask | quietBit)
    105 
    106 static inline rep_t toRep(fp_t x) {
    107     const union { fp_t f; rep_t i; } rep = {.f = x};
    108     return rep.i;
    109 }
    110 
    111 static inline fp_t fromRep(rep_t x) {
    112     const union { fp_t f; rep_t i; } rep = {.i = x};
    113     return rep.f;
    114 }
    115 
    116 static inline int normalize(rep_t *significand) {
    117     const int shift = rep_clz(*significand) - rep_clz(implicitBit);
    118     *significand <<= shift;
    119     return 1 - shift;
    120 }
    121 
    122 static inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) {
    123     *hi = *hi << count | *lo >> (typeWidth - count);
    124     *lo = *lo << count;
    125 }
    126 
    127 static inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, int count) {
    128     if (count < typeWidth) {
    129         const bool sticky = *lo << (typeWidth - count);
    130         *lo = *hi << (typeWidth - count) | *lo >> count | sticky;
    131         *hi = *hi >> count;
    132     }
    133     else if (count < 2*typeWidth) {
    134         const bool sticky = *hi << (2*typeWidth - count) | *lo;
    135         *lo = *hi >> (count - typeWidth) | sticky;
    136         *hi = 0;
    137     } else {
    138         const bool sticky = *hi | *lo;
    139         *lo = sticky;
    140         *hi = 0;
    141     }
    142 }
    143 
    144 #endif // FP_LIB_HEADER
    145