//===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file is a configuration header for soft-float routines in compiler-rt.
// This file does not provide any part of the compiler-rt interface, but defines
// many useful constants and utility routines that are used in the
// implementation of the soft-float routines in compiler-rt.
//
// Assumes that float, double and long double correspond to the IEEE-754
// binary32, binary64 and binary 128 types, respectively, and that integer
// endianness matches floating point endianness on the target platform.
//
//===----------------------------------------------------------------------===//
#ifndef FP_LIB_HEADER
#define FP_LIB_HEADER
#include <stdint.h>
#include <stdbool.h>
#include <limits.h>
#include "int_lib.h"
// x86_64 FreeBSD prior v9.3 define fixed-width types incorrectly in
// 32-bit mode.
#if defined(__FreeBSD__) && defined(__i386__)
# include <sys/param.h>
# if __FreeBSD_version < 903000 // v9.3
# define uint64_t unsigned long long
# define int64_t long long
# undef UINT64_C
# define UINT64_C(c) (c ## ULL)
# endif
#endif
#if defined SINGLE_PRECISION
typedef uint32_t rep_t;
typedef int32_t srep_t;
typedef float fp_t;
#define REP_C UINT32_C
#define significandBits 23
static __inline int rep_clz(rep_t a) {
return __builtin_clz(a);
}
// 32x32 --> 64 bit multiply
static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
const uint64_t product = (uint64_t)a*b;
*hi = product >> 32;
*lo = product;
}
COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b);
#elif defined DOUBLE_PRECISION
typedef uint64_t rep_t;
typedef int64_t srep_t;
typedef double fp_t;
#define REP_C UINT64_C
#define significandBits 52
static __inline int rep_clz(rep_t a) {
#if defined __LP64__
return __builtin_clzl(a);
#else
if (a & REP_C(0xffffffff00000000))
return __builtin_clz(a >> 32);
else
return 32 + __builtin_clz(a & REP_C(0xffffffff));
#endif
}
#define loWord(a) (a & 0xffffffffU)
#define hiWord(a) (a >> 32)
// 64x64 -> 128 wide multiply for platforms that don't have such an operation;
// many 64-bit platforms have this operation, but they tend to have hardware
// floating-point, so we don't bother with a special case for them here.
static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
// Each of the component 32x32 -> 64 products
const uint64_t plolo = loWord(a) * loWord(b);
const uint64_t plohi = loWord(a) * hiWord(b);
const uint64_t philo = hiWord(a) * loWord(b);
const uint64_t phihi = hiWord(a) * hiWord(b);
// Sum terms that contribute to lo in a way that allows us to get the carry
const uint64_t r0 = loWord(plolo);
const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
*lo = r0 + (r1 << 32);
// Sum terms contributing to hi with the carry from lo
*hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
}
#undef loWord
#undef hiWord
COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b);
#elif defined QUAD_PRECISION
#if __LDBL_MANT_DIG__ == 113
#define CRT_LDBL_128BIT
typedef __uint128_t rep_t;
typedef __int128_t srep_t;
typedef long double fp_t;
#define REP_C (__uint128_t)
// Note: Since there is no explicit way to tell compiler the constant is a
// 128-bit integer, we let the constant be casted to 128-bit integer
#define significandBits 112
static __inline int rep_clz(rep_t a) {
const union
{
__uint128_t ll;
#if _YUGA_BIG_ENDIAN
struct { uint64_t high, low; } s;
#else
struct { uint64_t low, high; } s;
#endif
} uu = { .ll = a };
uint64_t word;
uint64_t add;
if (uu.s.high){
word = uu.s.high;
add = 0;
}
else{
word = uu.s.low;
add = 64;
}
return __builtin_clzll(word) + add;
}
#define Word_LoMask UINT64_C(0x00000000ffffffff)
#define Word_HiMask UINT64_C(0xffffffff00000000)
#define Word_FullMask UINT64_C(0xffffffffffffffff)
#define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask)
#define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask)
#define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask)
#define Word_4(a) (uint64_t)(a & Word_LoMask)
// 128x128 -> 256 wide multiply for platforms that don't have such an operation;
// many 64-bit platforms have this operation, but they tend to have hardware
// floating-point, so we don't bother with a special case for them here.
static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
const uint64_t product11 = Word_1(a) * Word_1(b);
const uint64_t product12 = Word_1(a) * Word_2(b);
const uint64_t product13 = Word_1(a) * Word_3(b);
const uint64_t product14 = Word_1(a) * Word_4(b);
const uint64_t product21 = Word_2(a) * Word_1(b);
const uint64_t product22 = Word_2(a) * Word_2(b);
const uint64_t product23 = Word_2(a) * Word_3(b);
const uint64_t product24 = Word_2(a) * Word_4(b);
const uint64_t product31 = Word_3(a) * Word_1(b);
const uint64_t product32 = Word_3(a) * Word_2(b);
const uint64_t product33 = Word_3(a) * Word_3(b);
const uint64_t product34 = Word_3(a) * Word_4(b);
const uint64_t product41 = Word_4(a) * Word_1(b);
const uint64_t product42 = Word_4(a) * Word_2(b);
const uint64_t product43 = Word_4(a) * Word_3(b);
const uint64_t product44 = Word_4(a) * Word_4(b);
const __uint128_t sum0 = (__uint128_t)product44;
const __uint128_t sum1 = (__uint128_t)product34 +
(__uint128_t)product43;
const __uint128_t sum2 = (__uint128_t)product24 +
(__uint128_t)product33 +
(__uint128_t)product42;
const __uint128_t sum3 = (__uint128_t)product14 +
(__uint128_t)product23 +
(__uint128_t)product32 +
(__uint128_t)product41;
const __uint128_t sum4 = (__uint128_t)product13 +
(__uint128_t)product22 +
(__uint128_t)product31;
const __uint128_t sum5 = (__uint128_t)product12 +
(__uint128_t)product21;
const __uint128_t sum6 = (__uint128_t)product11;
const __uint128_t r0 = (sum0 & Word_FullMask) +
((sum1 & Word_LoMask) << 32);
const __uint128_t r1 = (sum0 >> 64) +
((sum1 >> 32) & Word_FullMask) +
(sum2 & Word_FullMask) +
((sum3 << 32) & Word_HiMask);
*lo = r0 + (r1 << 64);
*hi = (r1 >> 64) +
(sum1 >> 96) +
(sum2 >> 64) +
(sum3 >> 32) +
sum4 +
(sum5 << 32) +
(sum6 << 64);
}
#undef Word_1
#undef Word_2
#undef Word_3
#undef Word_4
#undef Word_HiMask
#undef Word_LoMask
#undef Word_FullMask
#endif // __LDBL_MANT_DIG__ == 113
#else
#error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined.
#endif
#if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || defined(CRT_LDBL_128BIT)
#define typeWidth (sizeof(rep_t)*CHAR_BIT)
#define exponentBits (typeWidth - significandBits - 1)
#define maxExponent ((1 << exponentBits) - 1)
#define exponentBias (maxExponent >> 1)
#define implicitBit (REP_C(1) << significandBits)
#define significandMask (implicitBit - 1U)
#define signBit (REP_C(1) << (significandBits + exponentBits))
#define absMask (signBit - 1U)
#define exponentMask (absMask ^ significandMask)
#define oneRep ((rep_t)exponentBias << significandBits)
#define infRep exponentMask
#define quietBit (implicitBit >> 1)
#define qnanRep (exponentMask | quietBit)
static __inline rep_t toRep(fp_t x) {
const union { fp_t f; rep_t i; } rep = {.f = x};
return rep.i;
}
static __inline fp_t fromRep(rep_t x) {
const union { fp_t f; rep_t i; } rep = {.i = x};
return rep.f;
}
static __inline int normalize(rep_t *significand) {
const int shift = rep_clz(*significand) - rep_clz(implicitBit);
*significand <<= shift;
return 1 - shift;
}
static __inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) {
*hi = *hi << count | *lo >> (typeWidth - count);
*lo = *lo << count;
}
static __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, unsigned int count) {
if (count < typeWidth) {
const bool sticky = *lo << (typeWidth - count);
*lo = *hi << (typeWidth - count) | *lo >> count | sticky;
*hi = *hi >> count;
}
else if (count < 2*typeWidth) {
const bool sticky = *hi << (2*typeWidth - count) | *lo;
*lo = *hi >> (count - typeWidth) | sticky;
*hi = 0;
} else {
const bool sticky = *hi | *lo;
*lo = sticky;
*hi = 0;
}
}
#endif
#endif // FP_LIB_HEADER