1// Tencent is pleased to support the open source community by making RapidJSON available.
2//
3// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
4//
5// Licensed under the MIT License (the "License"); you may not use this file except
6// in compliance with the License. You may obtain a copy of the License at
7//
8// http://opensource.org/licenses/MIT
9//
10// Unless required by applicable law or agreed to in writing, software distributed
11// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
12// CONDITIONS OF ANY KIND, either express or implied. See the License for the
13// specific language governing permissions and limitations under the License.
14
15// This is a C++ header-only implementation of Grisu2 algorithm from the publication:
16// Loitsch, Florian. "Printing floating-point numbers quickly and accurately with
17// integers." ACM Sigplan Notices 45.6 (2010): 233-243.
18
19#ifndef RAPIDJSON_DTOA_
20#define RAPIDJSON_DTOA_
21
22#include "itoa.h" // GetDigitsLut()
23#include "diyfp.h"
24#include "ieee754.h"
25
26RAPIDJSON_NAMESPACE_BEGIN
27namespace internal {
28
29#ifdef __GNUC__
30RAPIDJSON_DIAG_PUSH
31RAPIDJSON_DIAG_OFF(effc++)
32RAPIDJSON_DIAG_OFF(array-bounds) // some gcc versions generate wrong warnings https://gcc.gnu.org/bugzilla/show_bug.cgi?id=59124
33#endif
34
35inline void GrisuRound(char* buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w) {
36 while (rest < wp_w && delta - rest >= ten_kappa &&
37 (rest + ten_kappa < wp_w || /// closer
38 wp_w - rest > rest + ten_kappa - wp_w)) {
39 buffer[len - 1]--;
40 rest += ten_kappa;
41 }
42}
43
44inline unsigned CountDecimalDigit32(uint32_t n) {
45 // Simple pure C++ implementation was faster than __builtin_clz version in this situation.
46 if (n < 10) return 1;
47 if (n < 100) return 2;
48 if (n < 1000) return 3;
49 if (n < 10000) return 4;
50 if (n < 100000) return 5;
51 if (n < 1000000) return 6;
52 if (n < 10000000) return 7;
53 if (n < 100000000) return 8;
54 // Will not reach 10 digits in DigitGen()
55 //if (n < 1000000000) return 9;
56 //return 10;
57 return 9;
58}
59
60inline void DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, char* buffer, int* len, int* K) {
61 static const uint32_t kPow10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };
62 const DiyFp one(uint64_t(1) << -Mp.e, Mp.e);
63 const DiyFp wp_w = Mp - W;
64 uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e);
65 uint64_t p2 = Mp.f & (one.f - 1);
66 unsigned kappa = CountDecimalDigit32(p1); // kappa in [0, 9]
67 *len = 0;
68
69 while (kappa > 0) {
70 uint32_t d = 0;
71 switch (kappa) {
72 case 9: d = p1 / 100000000; p1 %= 100000000; break;
73 case 8: d = p1 / 10000000; p1 %= 10000000; break;
74 case 7: d = p1 / 1000000; p1 %= 1000000; break;
75 case 6: d = p1 / 100000; p1 %= 100000; break;
76 case 5: d = p1 / 10000; p1 %= 10000; break;
77 case 4: d = p1 / 1000; p1 %= 1000; break;
78 case 3: d = p1 / 100; p1 %= 100; break;
79 case 2: d = p1 / 10; p1 %= 10; break;
80 case 1: d = p1; p1 = 0; break;
81 default:;
82 }
83 if (d || *len)
84 buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d));
85 kappa--;
86 uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2;
87 if (tmp <= delta) {
88 *K += kappa;
89 GrisuRound(buffer, *len, delta, tmp, static_cast<uint64_t>(kPow10[kappa]) << -one.e, wp_w.f);
90 return;
91 }
92 }
93
94 // kappa = 0
95 for (;;) {
96 p2 *= 10;
97 delta *= 10;
98 char d = static_cast<char>(p2 >> -one.e);
99 if (d || *len)
100 buffer[(*len)++] = static_cast<char>('0' + d);
101 p2 &= one.f - 1;
102 kappa--;
103 if (p2 < delta) {
104 *K += kappa;
105 int index = -static_cast<int>(kappa);
106 GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * (index < 9 ? kPow10[-static_cast<int>(kappa)] : 0));
107 return;
108 }
109 }
110}
111
112inline void Grisu2(double value, char* buffer, int* length, int* K) {
113 const DiyFp v(value);
114 DiyFp w_m, w_p;
115 v.NormalizedBoundaries(&w_m, &w_p);
116
117 const DiyFp c_mk = GetCachedPower(w_p.e, K);
118 const DiyFp W = v.Normalize() * c_mk;
119 DiyFp Wp = w_p * c_mk;
120 DiyFp Wm = w_m * c_mk;
121 Wm.f++;
122 Wp.f--;
123 DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
124}
125
126inline char* WriteExponent(int K, char* buffer) {
127 if (K < 0) {
128 *buffer++ = '-';
129 K = -K;
130 }
131
132 if (K >= 100) {
133 *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100));
134 K %= 100;
135 const char* d = GetDigitsLut() + K * 2;
136 *buffer++ = d[0];
137 *buffer++ = d[1];
138 }
139 else if (K >= 10) {
140 const char* d = GetDigitsLut() + K * 2;
141 *buffer++ = d[0];
142 *buffer++ = d[1];
143 }
144 else
145 *buffer++ = static_cast<char>('0' + static_cast<char>(K));
146
147 return buffer;
148}
149
150inline char* Prettify(char* buffer, int length, int k, int maxDecimalPlaces) {
151 const int kk = length + k; // 10^(kk-1) <= v < 10^kk
152
153 if (0 <= k && kk <= 21) {
154 // 1234e7 -> 12340000000
155 for (int i = length; i < kk; i++)
156 buffer[i] = '0';
157 buffer[kk] = '.';
158 buffer[kk + 1] = '0';
159 return &buffer[kk + 2];
160 }
161 else if (0 < kk && kk <= 21) {
162 // 1234e-2 -> 12.34
163 std::memmove(&buffer[kk + 1], &buffer[kk], static_cast<size_t>(length - kk));
164 buffer[kk] = '.';
165 if (0 > k + maxDecimalPlaces) {
166 // When maxDecimalPlaces = 2, 1.2345 -> 1.23, 1.102 -> 1.1
167 // Remove extra trailing zeros (at least one) after truncation.
168 for (int i = kk + maxDecimalPlaces; i > kk + 1; i--)
169 if (buffer[i] != '0')
170 return &buffer[i + 1];
171 return &buffer[kk + 2]; // Reserve one zero
172 }
173 else
174 return &buffer[length + 1];
175 }
176 else if (-6 < kk && kk <= 0) {
177 // 1234e-6 -> 0.001234
178 const int offset = 2 - kk;
179 std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length));
180 buffer[0] = '0';
181 buffer[1] = '.';
182 for (int i = 2; i < offset; i++)
183 buffer[i] = '0';
184 if (length - kk > maxDecimalPlaces) {
185 // When maxDecimalPlaces = 2, 0.123 -> 0.12, 0.102 -> 0.1
186 // Remove extra trailing zeros (at least one) after truncation.
187 for (int i = maxDecimalPlaces + 1; i > 2; i--)
188 if (buffer[i] != '0')
189 return &buffer[i + 1];
190 return &buffer[3]; // Reserve one zero
191 }
192 else
193 return &buffer[length + offset];
194 }
195 else if (kk < -maxDecimalPlaces) {
196 // Truncate to zero
197 buffer[0] = '0';
198 buffer[1] = '.';
199 buffer[2] = '0';
200 return &buffer[3];
201 }
202 else if (length == 1) {
203 // 1e30
204 buffer[1] = 'e';
205 return WriteExponent(kk - 1, &buffer[2]);
206 }
207 else {
208 // 1234e30 -> 1.234e33
209 std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1));
210 buffer[1] = '.';
211 buffer[length + 1] = 'e';
212 return WriteExponent(kk - 1, &buffer[0 + length + 2]);
213 }
214}
215
216inline char* dtoa(double value, char* buffer, int maxDecimalPlaces = 324) {
217 RAPIDJSON_ASSERT(maxDecimalPlaces >= 1);
218 Double d(value);
219 if (d.IsZero()) {
220 if (d.Sign())
221 *buffer++ = '-'; // -0.0, Issue #289
222 buffer[0] = '0';
223 buffer[1] = '.';
224 buffer[2] = '0';
225 return &buffer[3];
226 }
227 else {
228 if (value < 0) {
229 *buffer++ = '-';
230 value = -value;
231 }
232 int length, K;
233 Grisu2(value, buffer, &length, &K);
234 return Prettify(buffer, length, K, maxDecimalPlaces);
235 }
236}
237
238#ifdef __GNUC__
239RAPIDJSON_DIAG_POP
240#endif
241
242} // namespace internal
243RAPIDJSON_NAMESPACE_END
244
245#endif // RAPIDJSON_DTOA_
246