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+//===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// 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 "int_lib.h"
+#include "int_math.h"
+#include <limits.h>
+#include <stdbool.h>
+#include <stdint.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 && defined(__SIZEOF_INT128__)
+#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 && __SIZEOF_INT128__
+#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)) != 0;
+ *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