StdLib/LibC/Main/Arm/fp_lib.h

/**
University of Illinois/NCSA
Open Source License

Copyright (c) 2009-2014 by the contributors listed in CREDITS.TXT

All rights reserved.

Developed by:

    LLVM Team

    University of Illinois at Urbana-Champaign

    http://llvm.org

Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal with
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:

    * Redistributions of source code must retain the above copyright notice,
      this list of conditions and the following disclaimers.

    * Redistributions in binary form must reproduce the above copyright notice,
      this list of conditions and the following disclaimers in the
      documentation and/or other materials provided with the distribution.

    * Neither the names of the LLVM Team, University of Illinois at
      Urbana-Champaign, nor the names of its contributors may be used to
      endorse or promote products derived from this Software without specific
      prior written permission.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL THE
CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
**/

#ifndef FP_LIB_HEADER
#define FP_LIB_HEADER

#include <stdint.h>
#include <stdbool.h>
#include <limits.h>
#include "int_lib.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     ((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