//===-- 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 #include #include #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 # 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