text: //===-- 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);
      *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
  