diyfp.h

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// Tencent is pleased to support the open source community by making RapidJSON
// available.
//
// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All
// rights reserved.
//
// Licensed under the MIT License (the "License"); you may not use this file
// except in compliance with the License. You may obtain a copy of the License
// at
//
// http://opensource.org/licenses/MIT
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
// WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
// License for the specific language governing permissions and limitations under
// the License.

// This is a C++ header-only implementation of Grisu2 algorithm from the
// publication: Loitsch, Florian. "Printing floating-point numbers quickly and
// accurately with integers." ACM Sigplan Notices 45.6 (2010): 233-243.

#ifndef RAPIDJSON_DIYFP_H_
#define RAPIDJSON_DIYFP_H_

#include <limits>
#include "../rapidjson.h"
#include "clzll.h"

#if defined(_MSC_VER) && defined(_M_AMD64) && !defined(__INTEL_COMPILER)
#include <intrin.h>
#pragma intrinsic(_umul128)
#endif

RAPIDJSON_NAMESPACE_BEGIN
namespace internal {

#ifdef __GNUC__
RAPIDJSON_DIAG_PUSH
RAPIDJSON_DIAG_OFF(effc++)
#endif

#ifdef __clang__
RAPIDJSON_DIAG_PUSH
RAPIDJSON_DIAG_OFF(padded)
#endif

struct DiyFp {
  DiyFp() : f(), e() {}

  DiyFp(uint64_t fp, int exp) : f(fp), e(exp) {}

  explicit DiyFp(double d) {
    union {
      double d;
      uint64_t u64;
    } u = {d};

    int biased_e =
        static_cast<int>((u.u64 & kDpExponentMask) >> kDpSignificandSize);
    uint64_t significand = (u.u64 & kDpSignificandMask);
    if (biased_e != 0) {
      f = significand + kDpHiddenBit;
      e = biased_e - kDpExponentBias;
    } else {
      f = significand;
      e = kDpMinExponent + 1;
    }
  }

  DiyFp operator-(const DiyFp &rhs) const { return DiyFp(f - rhs.f, e); }

  DiyFp operator*(const DiyFp &rhs) const {
#if defined(_MSC_VER) && defined(_M_AMD64)
    uint64_t h;
    uint64_t l = _umul128(f, rhs.f, &h);
    if (l & (uint64_t(1) << 63))  // rounding
      h++;
    return DiyFp(h, e + rhs.e + 64);
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && \
    defined(__x86_64__)
    __extension__ typedef unsigned __int128 uint128;
    uint128 p = static_cast<uint128>(f) * static_cast<uint128>(rhs.f);
    uint64_t h = static_cast<uint64_t>(p >> 64);
    uint64_t l = static_cast<uint64_t>(p);
    if (l & (uint64_t(1) << 63))  // rounding
      h++;
    return DiyFp(h, e + rhs.e + 64);
#else
    const uint64_t M32 = 0xFFFFFFFF;
    const uint64_t a = f >> 32;
    const uint64_t b = f & M32;
    const uint64_t c = rhs.f >> 32;
    const uint64_t d = rhs.f & M32;
    const uint64_t ac = a * c;
    const uint64_t bc = b * c;
    const uint64_t ad = a * d;
    const uint64_t bd = b * d;
    uint64_t tmp = (bd >> 32) + (ad & M32) + (bc & M32);
    tmp += 1U << 31;  
    return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64);
#endif
  }

  DiyFp Normalize() const {
    int s = static_cast<int>(RAPIDJSON_CLZLL(f));
    return DiyFp(f << s, e - s);
  }

  DiyFp NormalizeBoundary() const {
    DiyFp res = *this;
    while (!(res.f & (kDpHiddenBit << 1))) {
      res.f <<= 1;
      res.e--;
    }
    res.f <<= (kDiySignificandSize - kDpSignificandSize - 2);
    res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 2);
    return res;
  }

  void NormalizedBoundaries(DiyFp *minus, DiyFp *plus) const {
    DiyFp pl = DiyFp((f << 1) + 1, e - 1).NormalizeBoundary();
    DiyFp mi = (f == kDpHiddenBit) ? DiyFp((f << 2) - 1, e - 2)
                                   : DiyFp((f << 1) - 1, e - 1);
    mi.f <<= mi.e - pl.e;
    mi.e = pl.e;
    *plus = pl;
    *minus = mi;
  }

  double ToDouble() const {
    union {
      double d;
      uint64_t u64;
    } u;
    RAPIDJSON_ASSERT(f <= kDpHiddenBit + kDpSignificandMask);
    if (e < kDpDenormalExponent) {
      // Underflow.
      return 0.0;
    }
    if (e >= kDpMaxExponent) {
      // Overflow.
      return std::numeric_limits<double>::infinity();
    }
    const uint64_t be = (e == kDpDenormalExponent && (f & kDpHiddenBit) == 0)
                            ? 0
                            : static_cast<uint64_t>(e + kDpExponentBias);
    u.u64 = (f & kDpSignificandMask) | (be << kDpSignificandSize);
    return u.d;
  }

  static const int kDiySignificandSize = 64;
  static const int kDpSignificandSize = 52;
  static const int kDpExponentBias = 0x3FF + kDpSignificandSize;
  static const int kDpMaxExponent = 0x7FF - kDpExponentBias;
  static const int kDpMinExponent = -kDpExponentBias;
  static const int kDpDenormalExponent = -kDpExponentBias + 1;
  static const uint64_t kDpExponentMask =
      RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000);
  static const uint64_t kDpSignificandMask =
      RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
  static const uint64_t kDpHiddenBit =
      RAPIDJSON_UINT64_C2(0x00100000, 0x00000000);

  uint64_t f;
  int e;
};

inline DiyFp GetCachedPowerByIndex(size_t index) {
  // 10^-348, 10^-340, ..., 10^340
  static const uint64_t kCachedPowers_F[] = {
      RAPIDJSON_UINT64_C2(0xfa8fd5a0, 0x081c0288),
      RAPIDJSON_UINT64_C2(0xbaaee17f, 0xa23ebf76),
      RAPIDJSON_UINT64_C2(0x8b16fb20, 0x3055ac76),
      RAPIDJSON_UINT64_C2(0xcf42894a, 0x5dce35ea),
      RAPIDJSON_UINT64_C2(0x9a6bb0aa, 0x55653b2d),
      RAPIDJSON_UINT64_C2(0xe61acf03, 0x3d1a45df),
      RAPIDJSON_UINT64_C2(0xab70fe17, 0xc79ac6ca),
      RAPIDJSON_UINT64_C2(0xff77b1fc, 0xbebcdc4f),
      RAPIDJSON_UINT64_C2(0xbe5691ef, 0x416bd60c),
      RAPIDJSON_UINT64_C2(0x8dd01fad, 0x907ffc3c),
      RAPIDJSON_UINT64_C2(0xd3515c28, 0x31559a83),
      RAPIDJSON_UINT64_C2(0x9d71ac8f, 0xada6c9b5),
      RAPIDJSON_UINT64_C2(0xea9c2277, 0x23ee8bcb),
      RAPIDJSON_UINT64_C2(0xaecc4991, 0x4078536d),
      RAPIDJSON_UINT64_C2(0x823c1279, 0x5db6ce57),
      RAPIDJSON_UINT64_C2(0xc2109436, 0x4dfb5637),
      RAPIDJSON_UINT64_C2(0x9096ea6f, 0x3848984f),
      RAPIDJSON_UINT64_C2(0xd77485cb, 0x25823ac7),
      RAPIDJSON_UINT64_C2(0xa086cfcd, 0x97bf97f4),
      RAPIDJSON_UINT64_C2(0xef340a98, 0x172aace5),
      RAPIDJSON_UINT64_C2(0xb23867fb, 0x2a35b28e),
      RAPIDJSON_UINT64_C2(0x84c8d4df, 0xd2c63f3b),
      RAPIDJSON_UINT64_C2(0xc5dd4427, 0x1ad3cdba),
      RAPIDJSON_UINT64_C2(0x936b9fce, 0xbb25c996),
      RAPIDJSON_UINT64_C2(0xdbac6c24, 0x7d62a584),
      RAPIDJSON_UINT64_C2(0xa3ab6658, 0x0d5fdaf6),
      RAPIDJSON_UINT64_C2(0xf3e2f893, 0xdec3f126),
      RAPIDJSON_UINT64_C2(0xb5b5ada8, 0xaaff80b8),
      RAPIDJSON_UINT64_C2(0x87625f05, 0x6c7c4a8b),
      RAPIDJSON_UINT64_C2(0xc9bcff60, 0x34c13053),
      RAPIDJSON_UINT64_C2(0x964e858c, 0x91ba2655),
      RAPIDJSON_UINT64_C2(0xdff97724, 0x70297ebd),
      RAPIDJSON_UINT64_C2(0xa6dfbd9f, 0xb8e5b88f),
      RAPIDJSON_UINT64_C2(0xf8a95fcf, 0x88747d94),
      RAPIDJSON_UINT64_C2(0xb9447093, 0x8fa89bcf),
      RAPIDJSON_UINT64_C2(0x8a08f0f8, 0xbf0f156b),
      RAPIDJSON_UINT64_C2(0xcdb02555, 0x653131b6),
      RAPIDJSON_UINT64_C2(0x993fe2c6, 0xd07b7fac),
      RAPIDJSON_UINT64_C2(0xe45c10c4, 0x2a2b3b06),
      RAPIDJSON_UINT64_C2(0xaa242499, 0x697392d3),
      RAPIDJSON_UINT64_C2(0xfd87b5f2, 0x8300ca0e),
      RAPIDJSON_UINT64_C2(0xbce50864, 0x92111aeb),
      RAPIDJSON_UINT64_C2(0x8cbccc09, 0x6f5088cc),
      RAPIDJSON_UINT64_C2(0xd1b71758, 0xe219652c),
      RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000),
      RAPIDJSON_UINT64_C2(0xe8d4a510, 0x00000000),
      RAPIDJSON_UINT64_C2(0xad78ebc5, 0xac620000),
      RAPIDJSON_UINT64_C2(0x813f3978, 0xf8940984),
      RAPIDJSON_UINT64_C2(0xc097ce7b, 0xc90715b3),
      RAPIDJSON_UINT64_C2(0x8f7e32ce, 0x7bea5c70),
      RAPIDJSON_UINT64_C2(0xd5d238a4, 0xabe98068),
      RAPIDJSON_UINT64_C2(0x9f4f2726, 0x179a2245),
      RAPIDJSON_UINT64_C2(0xed63a231, 0xd4c4fb27),
      RAPIDJSON_UINT64_C2(0xb0de6538, 0x8cc8ada8),
      RAPIDJSON_UINT64_C2(0x83c7088e, 0x1aab65db),
      RAPIDJSON_UINT64_C2(0xc45d1df9, 0x42711d9a),
      RAPIDJSON_UINT64_C2(0x924d692c, 0xa61be758),
      RAPIDJSON_UINT64_C2(0xda01ee64, 0x1a708dea),
      RAPIDJSON_UINT64_C2(0xa26da399, 0x9aef774a),
      RAPIDJSON_UINT64_C2(0xf209787b, 0xb47d6b85),
      RAPIDJSON_UINT64_C2(0xb454e4a1, 0x79dd1877),
      RAPIDJSON_UINT64_C2(0x865b8692, 0x5b9bc5c2),
      RAPIDJSON_UINT64_C2(0xc83553c5, 0xc8965d3d),
      RAPIDJSON_UINT64_C2(0x952ab45c, 0xfa97a0b3),
      RAPIDJSON_UINT64_C2(0xde469fbd, 0x99a05fe3),
      RAPIDJSON_UINT64_C2(0xa59bc234, 0xdb398c25),
      RAPIDJSON_UINT64_C2(0xf6c69a72, 0xa3989f5c),
      RAPIDJSON_UINT64_C2(0xb7dcbf53, 0x54e9bece),
      RAPIDJSON_UINT64_C2(0x88fcf317, 0xf22241e2),
      RAPIDJSON_UINT64_C2(0xcc20ce9b, 0xd35c78a5),
      RAPIDJSON_UINT64_C2(0x98165af3, 0x7b2153df),
      RAPIDJSON_UINT64_C2(0xe2a0b5dc, 0x971f303a),
      RAPIDJSON_UINT64_C2(0xa8d9d153, 0x5ce3b396),
      RAPIDJSON_UINT64_C2(0xfb9b7cd9, 0xa4a7443c),
      RAPIDJSON_UINT64_C2(0xbb764c4c, 0xa7a44410),
      RAPIDJSON_UINT64_C2(0x8bab8eef, 0xb6409c1a),
      RAPIDJSON_UINT64_C2(0xd01fef10, 0xa657842c),
      RAPIDJSON_UINT64_C2(0x9b10a4e5, 0xe9913129),
      RAPIDJSON_UINT64_C2(0xe7109bfb, 0xa19c0c9d),
      RAPIDJSON_UINT64_C2(0xac2820d9, 0x623bf429),
      RAPIDJSON_UINT64_C2(0x80444b5e, 0x7aa7cf85),
      RAPIDJSON_UINT64_C2(0xbf21e440, 0x03acdd2d),
      RAPIDJSON_UINT64_C2(0x8e679c2f, 0x5e44ff8f),
      RAPIDJSON_UINT64_C2(0xd433179d, 0x9c8cb841),
      RAPIDJSON_UINT64_C2(0x9e19db92, 0xb4e31ba9),
      RAPIDJSON_UINT64_C2(0xeb96bf6e, 0xbadf77d9),
      RAPIDJSON_UINT64_C2(0xaf87023b, 0x9bf0ee6b)};
  static const int16_t kCachedPowers_E[] = {
      -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980, -954,
      -927,  -901,  -874,  -847,  -821,  -794,  -768,  -741,  -715,  -688, -661,
      -635,  -608,  -582,  -555,  -529,  -502,  -475,  -449,  -422,  -396, -369,
      -343,  -316,  -289,  -263,  -236,  -210,  -183,  -157,  -130,  -103, -77,
      -50,   -24,   3,     30,    56,    83,    109,   136,   162,   189,  216,
      242,   269,   295,   322,   348,   375,   402,   428,   455,   481,  508,
      534,   561,   588,   614,   641,   667,   694,   720,   747,   774,  800,
      827,   853,   880,   907,   933,   960,   986,   1013,  1039,  1066};
  RAPIDJSON_ASSERT(index < 87);
  return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
}

inline DiyFp GetCachedPower(int e, int *K) {
  // int k = static_cast<int>(ceil((-61 - e) * 0.30102999566398114)) + 374;
  double dk = (-61 - e) * 0.30102999566398114 +
              347;  // dk must be positive, so can do ceiling in positive
  int k = static_cast<int>(dk);
  if (dk - k > 0.0) k++;

  unsigned index = static_cast<unsigned>((k >> 3) + 1);
  *K = -(-348 + static_cast<int>(
                    index << 3));  // decimal exponent no need lookup table

  return GetCachedPowerByIndex(index);
}

inline DiyFp GetCachedPower10(int exp, int *outExp) {
  RAPIDJSON_ASSERT(exp >= -348);
  unsigned index = static_cast<unsigned>(exp + 348) / 8u;
  *outExp = -348 + static_cast<int>(index) * 8;
  return GetCachedPowerByIndex(index);
}

#ifdef __GNUC__
RAPIDJSON_DIAG_POP
#endif

#ifdef __clang__
RAPIDJSON_DIAG_POP
RAPIDJSON_DIAG_OFF(padded)
#endif

}  // namespace internal
RAPIDJSON_NAMESPACE_END

#endif  // RAPIDJSON_DIYFP_H_