315 lines
10 KiB
C
315 lines
10 KiB
C
/* clang-format off */
|
|
//===-- 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 "libc/literal.h"
|
|
#include "third_party/compiler_rt/int_lib.h"
|
|
#include "third_party/compiler_rt/int_math.h"
|
|
|
|
#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 ((1u << 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;
|
|
}
|
|
}
|
|
|
|
// Implements logb methods (logb, logbf, logbl) for IEEE-754. This avoids
|
|
// pulling in a libm dependency from compiler-rt, but is not meant to replace
|
|
// it (i.e. code calling logb() should get the one from libm, not this), hence
|
|
// the __compiler_rt prefix.
|
|
static __inline fp_t __compiler_rt_logbX(fp_t x) {
|
|
rep_t rep = toRep(x);
|
|
int exp = (rep & exponentMask) >> significandBits;
|
|
|
|
// Abnormal cases:
|
|
// 1) +/- inf returns +inf; NaN returns NaN
|
|
// 2) 0.0 returns -inf
|
|
if (exp == maxExponent) {
|
|
if (((rep & signBit) == 0) || (x != x)) {
|
|
return x; // NaN or +inf: return x
|
|
} else {
|
|
return -x; // -inf: return -x
|
|
}
|
|
} else if (x == 0.0) {
|
|
// 0.0: return -inf
|
|
return fromRep(infRep | signBit);
|
|
}
|
|
|
|
if (exp != 0) {
|
|
// Normal number
|
|
return exp - exponentBias; // Unbias exponent
|
|
} else {
|
|
// Subnormal number; normalize and repeat
|
|
rep &= absMask;
|
|
const int shift = 1 - normalize(&rep);
|
|
exp = (rep & exponentMask) >> significandBits;
|
|
return exp - exponentBias - shift; // Unbias exponent
|
|
}
|
|
}
|
|
#endif
|
|
|
|
#if defined(SINGLE_PRECISION)
|
|
static __inline fp_t __compiler_rt_logbf(fp_t x) {
|
|
return __compiler_rt_logbX(x);
|
|
}
|
|
#elif defined(DOUBLE_PRECISION)
|
|
static __inline fp_t __compiler_rt_logb(fp_t x) {
|
|
return __compiler_rt_logbX(x);
|
|
}
|
|
#elif defined(QUAD_PRECISION)
|
|
#if defined(CRT_LDBL_128BIT)
|
|
static __inline fp_t __compiler_rt_logbl(fp_t x) {
|
|
return __compiler_rt_logbX(x);
|
|
}
|
|
#else
|
|
// The generic implementation only works for ieee754 floating point. For other
|
|
// floating point types, continue to rely on the libm implementation for now.
|
|
static __inline long double __compiler_rt_logbl(long double x) {
|
|
return crt_logbl(x);
|
|
}
|
|
#endif
|
|
#endif
|
|
|
|
#endif // FP_LIB_HEADER
|