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
26 RAPIDJSON_NAMESPACE_BEGIN
27 namespace internal {
28
29 #ifdef __GNUC__
30 RAPIDJSON_DIAG_PUSH
31 RAPIDJSON_DIAG_OFF(effc++)
32 #endif
33
GrisuRound(char * buffer,int len,uint64_t delta,uint64_t rest,uint64_t ten_kappa,uint64_t wp_w)34 inline void GrisuRound(char* buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w) {
35 while (rest < wp_w && delta - rest >= ten_kappa &&
36 (rest + ten_kappa < wp_w || /// closer
37 wp_w - rest > rest + ten_kappa - wp_w)) {
38 buffer[len - 1]--;
39 rest += ten_kappa;
40 }
41 }
42
CountDecimalDigit32(uint32_t n)43 inline unsigned CountDecimalDigit32(uint32_t n) {
44 // Simple pure C++ implementation was faster than __builtin_clz version in this situation.
45 if (n < 10) return 1;
46 if (n < 100) return 2;
47 if (n < 1000) return 3;
48 if (n < 10000) return 4;
49 if (n < 100000) return 5;
50 if (n < 1000000) return 6;
51 if (n < 10000000) return 7;
52 if (n < 100000000) return 8;
53 // Will not reach 10 digits in DigitGen()
54 //if (n < 1000000000) return 9;
55 //return 10;
56 return 9;
57 }
58
DigitGen(const DiyFp & W,const DiyFp & Mp,uint64_t delta,char * buffer,int * len,int * K)59 inline void DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, char* buffer, int* len, int* K) {
60 static const uint32_t kPow10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };
61 const DiyFp one(uint64_t(1) << -Mp.e, Mp.e);
62 const DiyFp wp_w = Mp - W;
63 uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e);
64 uint64_t p2 = Mp.f & (one.f - 1);
65 unsigned kappa = CountDecimalDigit32(p1); // kappa in [0, 9]
66 *len = 0;
67
68 while (kappa > 0) {
69 uint32_t d = 0;
70 switch (kappa) {
71 case 9: d = p1 / 100000000; p1 %= 100000000; break;
72 case 8: d = p1 / 10000000; p1 %= 10000000; break;
73 case 7: d = p1 / 1000000; p1 %= 1000000; break;
74 case 6: d = p1 / 100000; p1 %= 100000; break;
75 case 5: d = p1 / 10000; p1 %= 10000; break;
76 case 4: d = p1 / 1000; p1 %= 1000; break;
77 case 3: d = p1 / 100; p1 %= 100; break;
78 case 2: d = p1 / 10; p1 %= 10; break;
79 case 1: d = p1; p1 = 0; break;
80 default:;
81 }
82 if (d || *len)
83 buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d));
84 kappa--;
85 uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2;
86 if (tmp <= delta) {
87 *K += kappa;
88 GrisuRound(buffer, *len, delta, tmp, static_cast<uint64_t>(kPow10[kappa]) << -one.e, wp_w.f);
89 return;
90 }
91 }
92
93 // kappa = 0
94 for (;;) {
95 p2 *= 10;
96 delta *= 10;
97 char d = static_cast<char>(p2 >> -one.e);
98 if (d || *len)
99 buffer[(*len)++] = static_cast<char>('0' + d);
100 p2 &= one.f - 1;
101 kappa--;
102 if (p2 < delta) {
103 *K += kappa;
104 GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * kPow10[-static_cast<int>(kappa)]);
105 return;
106 }
107 }
108 }
109
Grisu2(double value,char * buffer,int * length,int * K)110 inline void Grisu2(double value, char* buffer, int* length, int* K) {
111 const DiyFp v(value);
112 DiyFp w_m, w_p;
113 v.NormalizedBoundaries(&w_m, &w_p);
114
115 const DiyFp c_mk = GetCachedPower(w_p.e, K);
116 const DiyFp W = v.Normalize() * c_mk;
117 DiyFp Wp = w_p * c_mk;
118 DiyFp Wm = w_m * c_mk;
119 Wm.f++;
120 Wp.f--;
121 DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
122 }
123
WriteExponent(int K,char * buffer)124 inline char* WriteExponent(int K, char* buffer) {
125 if (K < 0) {
126 *buffer++ = '-';
127 K = -K;
128 }
129
130 if (K >= 100) {
131 *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100));
132 K %= 100;
133 const char* d = GetDigitsLut() + K * 2;
134 *buffer++ = d[0];
135 *buffer++ = d[1];
136 }
137 else if (K >= 10) {
138 const char* d = GetDigitsLut() + K * 2;
139 *buffer++ = d[0];
140 *buffer++ = d[1];
141 }
142 else
143 *buffer++ = static_cast<char>('0' + static_cast<char>(K));
144
145 return buffer;
146 }
147
Prettify(char * buffer,int length,int k)148 inline char* Prettify(char* buffer, int length, int k) {
149 const int kk = length + k; // 10^(kk-1) <= v < 10^kk
150
151 if (length <= kk && kk <= 21) {
152 // 1234e7 -> 12340000000
153 for (int i = length; i < kk; i++)
154 buffer[i] = '0';
155 buffer[kk] = '.';
156 buffer[kk + 1] = '0';
157 return &buffer[kk + 2];
158 }
159 else if (0 < kk && kk <= 21) {
160 // 1234e-2 -> 12.34
161 std::memmove(&buffer[kk + 1], &buffer[kk], static_cast<size_t>(length - kk));
162 buffer[kk] = '.';
163 return &buffer[length + 1];
164 }
165 else if (-6 < kk && kk <= 0) {
166 // 1234e-6 -> 0.001234
167 const int offset = 2 - kk;
168 std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length));
169 buffer[0] = '0';
170 buffer[1] = '.';
171 for (int i = 2; i < offset; i++)
172 buffer[i] = '0';
173 return &buffer[length + offset];
174 }
175 else if (length == 1) {
176 // 1e30
177 buffer[1] = 'e';
178 return WriteExponent(kk - 1, &buffer[2]);
179 }
180 else {
181 // 1234e30 -> 1.234e33
182 std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1));
183 buffer[1] = '.';
184 buffer[length + 1] = 'e';
185 return WriteExponent(kk - 1, &buffer[0 + length + 2]);
186 }
187 }
188
dtoa(double value,char * buffer)189 inline char* dtoa(double value, char* buffer) {
190 Double d(value);
191 if (d.IsZero()) {
192 if (d.Sign())
193 *buffer++ = '-'; // -0.0, Issue #289
194 buffer[0] = '0';
195 buffer[1] = '.';
196 buffer[2] = '0';
197 return &buffer[3];
198 }
199 else {
200 if (value < 0) {
201 *buffer++ = '-';
202 value = -value;
203 }
204 int length, K;
205 Grisu2(value, buffer, &length, &K);
206 return Prettify(buffer, length, K);
207 }
208 }
209
210 #ifdef __GNUC__
211 RAPIDJSON_DIAG_POP
212 #endif
213
214 } // namespace internal
215 RAPIDJSON_NAMESPACE_END
216
217 #endif // RAPIDJSON_DTOA_
218