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strtod.h
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#ifndef RAPIDJSON_STRTOD_
16#define RAPIDJSON_STRTOD_
17
18#include "ieee754.h"
19#include "biginteger.h"
20#include "diyfp.h"
21#include "pow10.h"
22#include <climits>
23#include <limits>
24
25RAPIDJSON_NAMESPACE_BEGIN
26namespace internal {
27
28inline double FastPath(double significand, int exp) {
29 if (exp < -308)
30 return 0.0;
31 else if (exp >= 0)
32 return significand * internal::Pow10(exp);
33 else
34 return significand / internal::Pow10(-exp);
35}
36
37inline double StrtodNormalPrecision(double d, int p) {
38 if (p < -308) {
39 // Prevent expSum < -308, making Pow10(p) = 0
40 d = FastPath(d, -308);
41 d = FastPath(d, p + 308);
42 }
43 else
44 d = FastPath(d, p);
45 return d;
46}
47
48template <typename T>
49inline T Min3(T a, T b, T c) {
50 T m = a;
51 if (m > b) m = b;
52 if (m > c) m = c;
53 return m;
54}
55
56inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
57 const Double db(b);
58 const uint64_t bInt = db.IntegerSignificand();
59 const int bExp = db.IntegerExponent();
60 const int hExp = bExp - 1;
61
62 int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
63
64 // Adjust for decimal exponent
65 if (dExp >= 0) {
66 dS_Exp2 += dExp;
67 dS_Exp5 += dExp;
68 }
69 else {
70 bS_Exp2 -= dExp;
71 bS_Exp5 -= dExp;
72 hS_Exp2 -= dExp;
73 hS_Exp5 -= dExp;
74 }
75
76 // Adjust for binary exponent
77 if (bExp >= 0)
78 bS_Exp2 += bExp;
79 else {
80 dS_Exp2 -= bExp;
81 hS_Exp2 -= bExp;
82 }
83
84 // Adjust for half ulp exponent
85 if (hExp >= 0)
86 hS_Exp2 += hExp;
87 else {
88 dS_Exp2 -= hExp;
89 bS_Exp2 -= hExp;
90 }
91
92 // Remove common power of two factor from all three scaled values
93 int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
94 dS_Exp2 -= common_Exp2;
95 bS_Exp2 -= common_Exp2;
96 hS_Exp2 -= common_Exp2;
97
98 BigInteger dS = d;
99 dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
100
101 BigInteger bS(bInt);
102 bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
103
104 BigInteger hS(1);
105 hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
106
107 BigInteger delta(0);
108 dS.Difference(bS, &delta);
109
110 return delta.Compare(hS);
111}
112
113inline bool StrtodFast(double d, int p, double* result) {
114 // Use fast path for string-to-double conversion if possible
115 // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
116 if (p > 22 && p < 22 + 16) {
117 // Fast Path Cases In Disguise
118 d *= internal::Pow10(p - 22);
119 p = 22;
120 }
121
122 if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
123 *result = FastPath(d, p);
124 return true;
125 }
126 else
127 return false;
128}
129
130// Compute an approximation and see if it is within 1/2 ULP
131template<typename Ch>
132inline bool StrtodDiyFp(const Ch* decimals, int dLen, int dExp, double* result) {
133 uint64_t significand = 0;
134 int i = 0; // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
135 for (; i < dLen; i++) {
136 if (significand > RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
137 (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > Ch('5')))
138 break;
139 significand = significand * 10u + static_cast<unsigned>(decimals[i] - Ch('0'));
140 }
141
142 if (i < dLen && decimals[i] >= Ch('5')) // Rounding
143 significand++;
144
145 int remaining = dLen - i;
146 const int kUlpShift = 3;
147 const int kUlp = 1 << kUlpShift;
148 int64_t error = (remaining == 0) ? 0 : kUlp / 2;
149
150 DiyFp v(significand, 0);
151 v = v.Normalize();
152 error <<= -v.e;
153
154 dExp += remaining;
155
156 int actualExp;
157 DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
158 if (actualExp != dExp) {
159 static const DiyFp kPow10[] = {
160 DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 0x00000000), -60), // 10^1
161 DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 0x00000000), -57), // 10^2
162 DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 0x00000000), -54), // 10^3
163 DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), -50), // 10^4
164 DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 0x00000000), -47), // 10^5
165 DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 0x00000000), -44), // 10^6
166 DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 0x00000000), -40) // 10^7
167 };
168 int adjustment = dExp - actualExp;
169 RAPIDJSON_ASSERT(adjustment >= 1 && adjustment < 8);
170 v = v * kPow10[adjustment - 1];
171 if (dLen + adjustment > 19) // has more digits than decimal digits in 64-bit
172 error += kUlp / 2;
173 }
174
175 v = v * cachedPower;
176
177 error += kUlp + (error == 0 ? 0 : 1);
178
179 const int oldExp = v.e;
180 v = v.Normalize();
181 error <<= oldExp - v.e;
182
183 const int effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
184 int precisionSize = 64 - effectiveSignificandSize;
185 if (precisionSize + kUlpShift >= 64) {
186 int scaleExp = (precisionSize + kUlpShift) - 63;
187 v.f >>= scaleExp;
188 v.e += scaleExp;
189 error = (error >> scaleExp) + 1 + kUlp;
190 precisionSize -= scaleExp;
191 }
192
193 DiyFp rounded(v.f >> precisionSize, v.e + precisionSize);
194 const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
195 const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
196 if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
197 rounded.f++;
198 if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
199 rounded.f >>= 1;
200 rounded.e++;
201 }
202 }
203
204 *result = rounded.ToDouble();
205
206 return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
207}
208
209template<typename Ch>
210inline double StrtodBigInteger(double approx, const Ch* decimals, int dLen, int dExp) {
211 RAPIDJSON_ASSERT(dLen >= 0);
212 const BigInteger dInt(decimals, static_cast<unsigned>(dLen));
213 Double a(approx);
214 int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
215 if (cmp < 0)
216 return a.Value(); // within half ULP
217 else if (cmp == 0) {
218 // Round towards even
219 if (a.Significand() & 1)
220 return a.NextPositiveDouble();
221 else
222 return a.Value();
223 }
224 else // adjustment
225 return a.NextPositiveDouble();
226}
227
228template<typename Ch>
229inline double StrtodFullPrecision(double d, int p, const Ch* decimals, size_t length, size_t decimalPosition, int exp) {
230 RAPIDJSON_ASSERT(d >= 0.0);
231 RAPIDJSON_ASSERT(length >= 1);
232
233 double result = 0.0;
234 if (StrtodFast(d, p, &result))
235 return result;
236
237 RAPIDJSON_ASSERT(length <= INT_MAX);
238 int dLen = static_cast<int>(length);
239
240 RAPIDJSON_ASSERT(length >= decimalPosition);
241 RAPIDJSON_ASSERT(length - decimalPosition <= INT_MAX);
242 int dExpAdjust = static_cast<int>(length - decimalPosition);
243
244 RAPIDJSON_ASSERT(exp >= INT_MIN + dExpAdjust);
245 int dExp = exp - dExpAdjust;
246
247 // Make sure length+dExp does not overflow
248 RAPIDJSON_ASSERT(dExp <= INT_MAX - dLen);
249
250 // Trim leading zeros
251 while (dLen > 0 && *decimals == '0') {
252 dLen--;
253 decimals++;
254 }
255
256 // Trim trailing zeros
257 while (dLen > 0 && decimals[dLen - 1] == '0') {
258 dLen--;
259 dExp++;
260 }
261
262 if (dLen == 0) { // Buffer only contains zeros.
263 return 0.0;
264 }
265
266 // Trim right-most digits
267 const int kMaxDecimalDigit = 767 + 1;
268 if (dLen > kMaxDecimalDigit) {
269 dExp += dLen - kMaxDecimalDigit;
270 dLen = kMaxDecimalDigit;
271 }
272
273 // If too small, underflow to zero.
274 // Any x <= 10^-324 is interpreted as zero.
275 if (dLen + dExp <= -324)
276 return 0.0;
277
278 // If too large, overflow to infinity.
279 // Any x >= 10^309 is interpreted as +infinity.
280 if (dLen + dExp > 309)
281 return std::numeric_limits<double>::infinity();
282
283 if (StrtodDiyFp(decimals, dLen, dExp, &result))
284 return result;
285
286 // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
287 return StrtodBigInteger(result, decimals, dLen, dExp);
288}
289
290} // namespace internal
291RAPIDJSON_NAMESPACE_END
292
293#endif // RAPIDJSON_STRTOD_
#define RAPIDJSON_ASSERT(x)
Assertion.
定义 rapidjson.h:437
#define RAPIDJSON_UINT64_C2(high32, low32)
Construct a 64-bit literal by a pair of 32-bit integer.
定义 rapidjson.h:320