fp_lib.h

//===-- 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"
#include "int_math.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;
    }
}

// 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