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dtoa.h
// 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 || /// closer
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_
RAPIDJSON_ASSERT
#define RAPIDJSON_ASSERT(x)
Assertion.
Definition rapidjson.h:402