dtoa.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_DTOA_
#define RAPIDJSON_DTOA_

#include "diyfp.h"
#include "ieee754.h"
#include "itoa.h"  // GetDigitsLut()

RAPIDJSON_NAMESPACE_BEGIN
namespace internal {

#ifdef __GNUC__
RAPIDJSON_DIAG_PUSH
RAPIDJSON_DIAG_OFF(effc++)
RAPIDJSON_DIAG_OFF(array - bounds)  // some gcc versions generate wrong warnings
// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=59124
#endif

inline void GrisuRound(char *buffer, int len, uint64_t delta, uint64_t rest,
                       uint64_t ten_kappa, uint64_t wp_w) {
  while (rest < wp_w && delta - rest >= ten_kappa &&
         (rest + ten_kappa < wp_w ||  
          wp_w - rest > rest + ten_kappa - wp_w)) {
    buffer[len - 1]--;
    rest += ten_kappa;
  }
}

inline int CountDecimalDigit32(uint32_t n) {
  // Simple pure C++ implementation was faster than __builtin_clz version in
  // this situation.
  if (n < 10) return 1;
  if (n < 100) return 2;
  if (n < 1000) return 3;
  if (n < 10000) return 4;
  if (n < 100000) return 5;
  if (n < 1000000) return 6;
  if (n < 10000000) return 7;
  if (n < 100000000) return 8;
  // Will not reach 10 digits in DigitGen()
  // if (n < 1000000000) return 9;
  // return 10;
  return 9;
}

inline void DigitGen(const DiyFp &W, const DiyFp &Mp, uint64_t delta,
                     char *buffer, int *len, int *K) {
  static const uint32_t kPow10[] = {1,         10,        100,     1000,
                                    10000,     100000,    1000000, 10000000,
                                    100000000, 1000000000};
  const DiyFp one(uint64_t(1) << -Mp.e, Mp.e);
  const DiyFp wp_w = Mp - W;
  uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e);
  uint64_t p2 = Mp.f & (one.f - 1);
  int kappa = CountDecimalDigit32(p1);  // kappa in [0, 9]
  *len = 0;

  while (kappa > 0) {
    uint32_t d = 0;
    switch (kappa) {
      case 9:
        d = p1 / 100000000;
        p1 %= 100000000;
        break;
      case 8:
        d = p1 / 10000000;
        p1 %= 10000000;
        break;
      case 7:
        d = p1 / 1000000;
        p1 %= 1000000;
        break;
      case 6:
        d = p1 / 100000;
        p1 %= 100000;
        break;
      case 5:
        d = p1 / 10000;
        p1 %= 10000;
        break;
      case 4:
        d = p1 / 1000;
        p1 %= 1000;
        break;
      case 3:
        d = p1 / 100;
        p1 %= 100;
        break;
      case 2:
        d = p1 / 10;
        p1 %= 10;
        break;
      case 1:
        d = p1;
        p1 = 0;
        break;
      default:;
    }
    if (d || *len)
      buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d));
    kappa--;
    uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2;
    if (tmp <= delta) {
      *K += kappa;
      GrisuRound(buffer, *len, delta, tmp,
                 static_cast<uint64_t>(kPow10[kappa]) << -one.e, wp_w.f);
      return;
    }
  }

  // kappa = 0
  for (;;) {
    p2 *= 10;
    delta *= 10;
    char d = static_cast<char>(p2 >> -one.e);
    if (d || *len) buffer[(*len)++] = static_cast<char>('0' + d);
    p2 &= one.f - 1;
    kappa--;
    if (p2 < delta) {
      *K += kappa;
      int index = -kappa;
      GrisuRound(buffer, *len, delta, p2, one.f,
                 wp_w.f * (index < 9 ? kPow10[index] : 0));
      return;
    }
  }
}

inline void Grisu2(double value, char *buffer, int *length, int *K) {
  const DiyFp v(value);
  DiyFp w_m, w_p;
  v.NormalizedBoundaries(&w_m, &w_p);

  const DiyFp c_mk = GetCachedPower(w_p.e, K);
  const DiyFp W = v.Normalize() * c_mk;
  DiyFp Wp = w_p * c_mk;
  DiyFp Wm = w_m * c_mk;
  Wm.f++;
  Wp.f--;
  DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
}

inline char *WriteExponent(int K, char *buffer) {
  if (K < 0) {
    *buffer++ = '-';
    K = -K;
  }

  if (K >= 100) {
    *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100));
    K %= 100;
    const char *d = GetDigitsLut() + K * 2;
    *buffer++ = d[0];
    *buffer++ = d[1];
  } else if (K >= 10) {
    const char *d = GetDigitsLut() + K * 2;
    *buffer++ = d[0];
    *buffer++ = d[1];
  } else
    *buffer++ = static_cast<char>('0' + static_cast<char>(K));

  return buffer;
}

inline char *Prettify(char *buffer, int length, int k, int maxDecimalPlaces) {
  const int kk = length + k;  // 10^(kk-1) <= v < 10^kk

  if (0 <= k && kk <= 21) {
    // 1234e7 -> 12340000000
    for (int i = length; i < kk; i++) buffer[i] = '0';
    buffer[kk] = '.';
    buffer[kk + 1] = '0';
    return &buffer[kk + 2];
  } else if (0 < kk && kk <= 21) {
    // 1234e-2 -> 12.34
    std::memmove(&buffer[kk + 1], &buffer[kk],
                 static_cast<size_t>(length - kk));
    buffer[kk] = '.';
    if (0 > k + maxDecimalPlaces) {
      // When maxDecimalPlaces = 2, 1.2345 -> 1.23, 1.102 -> 1.1
      // Remove extra trailing zeros (at least one) after truncation.
      for (int i = kk + maxDecimalPlaces; i > kk + 1; i--)
        if (buffer[i] != '0') return &buffer[i + 1];
      return &buffer[kk + 2];  // Reserve one zero
    } else
      return &buffer[length + 1];
  } else if (-6 < kk && kk <= 0) {
    // 1234e-6 -> 0.001234
    const int offset = 2 - kk;
    std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length));
    buffer[0] = '0';
    buffer[1] = '.';
    for (int i = 2; i < offset; i++) buffer[i] = '0';
    if (length - kk > maxDecimalPlaces) {
      // When maxDecimalPlaces = 2, 0.123 -> 0.12, 0.102 -> 0.1
      // Remove extra trailing zeros (at least one) after truncation.
      for (int i = maxDecimalPlaces + 1; i > 2; i--)
        if (buffer[i] != '0') return &buffer[i + 1];
      return &buffer[3];  // Reserve one zero
    } else
      return &buffer[length + offset];
  } else if (kk < -maxDecimalPlaces) {
    // Truncate to zero
    buffer[0] = '0';
    buffer[1] = '.';
    buffer[2] = '0';
    return &buffer[3];
  } else if (length == 1) {
    // 1e30
    buffer[1] = 'e';
    return WriteExponent(kk - 1, &buffer[2]);
  } else {
    // 1234e30 -> 1.234e33
    std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1));
    buffer[1] = '.';
    buffer[length + 1] = 'e';
    return WriteExponent(kk - 1, &buffer[0 + length + 2]);
  }
}

inline char *dtoa(double value, char *buffer, int maxDecimalPlaces = 324) {
  RAPIDJSON_ASSERT(maxDecimalPlaces >= 1);
  Double d(value);
  if (d.IsZero()) {
    if (d.Sign()) *buffer++ = '-';  // -0.0, Issue #289
    buffer[0] = '0';
    buffer[1] = '.';
    buffer[2] = '0';
    return &buffer[3];
  } else {
    if (value < 0) {
      *buffer++ = '-';
      value = -value;
    }
    int length, K;
    Grisu2(value, buffer, &length, &K);
    return Prettify(buffer, length, K, maxDecimalPlaces);
  }
}

#ifdef __GNUC__
RAPIDJSON_DIAG_POP
#endif

}  // namespace internal
RAPIDJSON_NAMESPACE_END

#endif  // RAPIDJSON_DTOA_