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.
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 RAPIDJSON_DIAG_OFF(array-bounds) // some gcc versions generate wrong warnings https://gcc.gnu.org/bugzilla/show_bug.cgi?id=59124
33 #endif
34
GrisuRound(char * buffer,int len,uint64_t delta,uint64_t rest,uint64_t ten_kappa,uint64_t wp_w)35 inline 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
CountDecimalDigit32(uint32_t n)44 inline int 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
DigitGen(const DiyFp & W,const DiyFp & Mp,uint64_t delta,char * buffer,int * len,int * K)60 inline void DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, char* buffer, int* len, int* K) {
61 static const uint64_t kPow10[] = { 1ULL, 10ULL, 100ULL, 1000ULL, 10000ULL, 100000ULL, 1000000ULL, 10000000ULL, 100000000ULL,
62 1000000000ULL, 10000000000ULL, 100000000000ULL, 1000000000000ULL,
63 10000000000000ULL, 100000000000000ULL, 1000000000000000ULL,
64 10000000000000000ULL, 100000000000000000ULL, 1000000000000000000ULL,
65 10000000000000000000ULL };
66 const DiyFp one(uint64_t(1) << -Mp.e, Mp.e);
67 const DiyFp wp_w = Mp - W;
68 uint32_t p1 = static_cast<uint32_t>(Mp.f >> -one.e);
69 uint64_t p2 = Mp.f & (one.f - 1);
70 int kappa = CountDecimalDigit32(p1); // kappa in [0, 9]
71 *len = 0;
72
73 while (kappa > 0) {
74 uint32_t d = 0;
75 switch (kappa) {
76 case 9: d = p1 / 100000000; p1 %= 100000000; break;
77 case 8: d = p1 / 10000000; p1 %= 10000000; break;
78 case 7: d = p1 / 1000000; p1 %= 1000000; break;
79 case 6: d = p1 / 100000; p1 %= 100000; break;
80 case 5: d = p1 / 10000; p1 %= 10000; break;
81 case 4: d = p1 / 1000; p1 %= 1000; break;
82 case 3: d = p1 / 100; p1 %= 100; break;
83 case 2: d = p1 / 10; p1 %= 10; break;
84 case 1: d = p1; p1 = 0; break;
85 default:;
86 }
87 if (d || *len)
88 buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d));
89 kappa--;
90 uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2;
91 if (tmp <= delta) {
92 *K += kappa;
93 GrisuRound(buffer, *len, delta, tmp, kPow10[kappa] << -one.e, wp_w.f);
94 return;
95 }
96 }
97
98 // kappa = 0
99 for (;;) {
100 p2 *= 10;
101 delta *= 10;
102 char d = static_cast<char>(p2 >> -one.e);
103 if (d || *len)
104 buffer[(*len)++] = static_cast<char>('0' + d);
105 p2 &= one.f - 1;
106 kappa--;
107 if (p2 < delta) {
108 *K += kappa;
109 int index = -kappa;
110 GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * (index < 20 ? kPow10[index] : 0));
111 return;
112 }
113 }
114 }
115
Grisu2(double value,char * buffer,int * length,int * K)116 inline void Grisu2(double value, char* buffer, int* length, int* K) {
117 const DiyFp v(value);
118 DiyFp w_m, w_p;
119 v.NormalizedBoundaries(&w_m, &w_p);
120
121 const DiyFp c_mk = GetCachedPower(w_p.e, K);
122 const DiyFp W = v.Normalize() * c_mk;
123 DiyFp Wp = w_p * c_mk;
124 DiyFp Wm = w_m * c_mk;
125 Wm.f++;
126 Wp.f--;
127 DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
128 }
129
WriteExponent(int K,char * buffer)130 inline char* WriteExponent(int K, char* buffer) {
131 if (K < 0) {
132 *buffer++ = '-';
133 K = -K;
134 }
135
136 if (K >= 100) {
137 *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100));
138 K %= 100;
139 const char* d = GetDigitsLut() + K * 2;
140 *buffer++ = d[0];
141 *buffer++ = d[1];
142 }
143 else if (K >= 10) {
144 const char* d = GetDigitsLut() + K * 2;
145 *buffer++ = d[0];
146 *buffer++ = d[1];
147 }
148 else
149 *buffer++ = static_cast<char>('0' + static_cast<char>(K));
150
151 return buffer;
152 }
153
Prettify(char * buffer,int length,int k,int maxDecimalPlaces)154 inline char* Prettify(char* buffer, int length, int k, int maxDecimalPlaces) {
155 const int kk = length + k; // 10^(kk-1) <= v < 10^kk
156
157 if (0 <= k && kk <= 21) {
158 // 1234e7 -> 12340000000
159 for (int i = length; i < kk; i++)
160 buffer[i] = '0';
161 buffer[kk] = '.';
162 buffer[kk + 1] = '0';
163 return &buffer[kk + 2];
164 }
165 else if (0 < kk && kk <= 21) {
166 // 1234e-2 -> 12.34
167 std::memmove(&buffer[kk + 1], &buffer[kk], static_cast<size_t>(length - kk));
168 buffer[kk] = '.';
169 if (0 > k + maxDecimalPlaces) {
170 // When maxDecimalPlaces = 2, 1.2345 -> 1.23, 1.102 -> 1.1
171 // Remove extra trailing zeros (at least one) after truncation.
172 for (int i = kk + maxDecimalPlaces; i > kk + 1; i--)
173 if (buffer[i] != '0')
174 return &buffer[i + 1];
175 return &buffer[kk + 2]; // Reserve one zero
176 }
177 else
178 return &buffer[length + 1];
179 }
180 else if (-6 < kk && kk <= 0) {
181 // 1234e-6 -> 0.001234
182 const int offset = 2 - kk;
183 std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length));
184 buffer[0] = '0';
185 buffer[1] = '.';
186 for (int i = 2; i < offset; i++)
187 buffer[i] = '0';
188 if (length - kk > maxDecimalPlaces) {
189 // When maxDecimalPlaces = 2, 0.123 -> 0.12, 0.102 -> 0.1
190 // Remove extra trailing zeros (at least one) after truncation.
191 for (int i = maxDecimalPlaces + 1; i > 2; i--)
192 if (buffer[i] != '0')
193 return &buffer[i + 1];
194 return &buffer[3]; // Reserve one zero
195 }
196 else
197 return &buffer[length + offset];
198 }
199 else if (kk < -maxDecimalPlaces) {
200 // Truncate to zero
201 buffer[0] = '0';
202 buffer[1] = '.';
203 buffer[2] = '0';
204 return &buffer[3];
205 }
206 else if (length == 1) {
207 // 1e30
208 buffer[1] = 'e';
209 return WriteExponent(kk - 1, &buffer[2]);
210 }
211 else {
212 // 1234e30 -> 1.234e33
213 std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1));
214 buffer[1] = '.';
215 buffer[length + 1] = 'e';
216 return WriteExponent(kk - 1, &buffer[0 + length + 2]);
217 }
218 }
219
220 inline char* dtoa(double value, char* buffer, int maxDecimalPlaces = 324) {
221 RAPIDJSON_ASSERT(maxDecimalPlaces >= 1);
222 Double d(value);
223 if (d.IsZero()) {
224 if (d.Sign())
225 *buffer++ = '-'; // -0.0, Issue #289
226 buffer[0] = '0';
227 buffer[1] = '.';
228 buffer[2] = '0';
229 return &buffer[3];
230 }
231 else {
232 if (value < 0) {
233 *buffer++ = '-';
234 value = -value;
235 }
236 int length, K;
237 Grisu2(value, buffer, &length, &K);
238 return Prettify(buffer, length, K, maxDecimalPlaces);
239 }
240 }
241
242 #ifdef __GNUC__
243 RAPIDJSON_DIAG_POP
244 #endif
245
246 } // namespace internal
247 RAPIDJSON_NAMESPACE_END
248
249 #endif // RAPIDJSON_DTOA_
250
