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 31typedef uint32_t rep_t; 32typedef int32_t srep_t; 33typedef float fp_t; 34#define REP_C UINT32_C 35#define significandBits 23 36 37static inline int rep_clz(rep_t a) { 38 return __builtin_clz(a); 39} 40 41// 32x32 --> 64 bit multiply 42static 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 50typedef uint64_t rep_t; 51typedef int64_t srep_t; 52typedef double fp_t; 53#define REP_C UINT64_C 54#define significandBits 52 55 56static 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. 73static 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 106static 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 111static 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 116static 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 122static inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) { 123 *hi = *hi << count | *lo >> (typeWidth - count); 124 *lo = *lo << count; 125} 126 127static inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, unsigned 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