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

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 unsigned 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);
 unsigned 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 = -static_cast<int>(kappa);
 GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * (index < 9 ? kPow10[-static_cast<int>(kappa)] : 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_