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#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
23RAPIDJSON_NAMESPACE_BEGIN
24namespace internal {
25
26inline double FastPath(double significand, int exp) {
27 if (exp < -308)
28 return 0.0;
29 else if (exp >= 0)
30 return significand * internal::Pow10(exp);
31 else
32 return significand / internal::Pow10(-exp);
33}
34
35inline double StrtodNormalPrecision(double d, int p) {
36 if (p < -308) {
37 // Prevent expSum < -308, making Pow10(p) = 0
38 d = FastPath(d, -308);
39 d = FastPath(d, p + 308);
40 }
41 else
42 d = FastPath(d, p);
43 return d;
44}
45
46template <typename T>
47inline T Min3(T a, T b, T c) {
48 T m = a;
49 if (m > b) m = b;
50 if (m > c) m = c;
51 return m;
52}
53
54inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
55 const Double db(b);
56 const uint64_t bInt = db.IntegerSignificand();
57 const int bExp = db.IntegerExponent();
58 const int hExp = bExp - 1;
59
60 int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
61
62 // Adjust for decimal exponent
63 if (dExp >= 0) {
64 dS_Exp2 += dExp;
65 dS_Exp5 += dExp;
66 }
67 else {
68 bS_Exp2 -= dExp;
69 bS_Exp5 -= dExp;
70 hS_Exp2 -= dExp;
71 hS_Exp5 -= dExp;
72 }
73
74 // Adjust for binary exponent
75 if (bExp >= 0)
76 bS_Exp2 += bExp;
77 else {
78 dS_Exp2 -= bExp;
79 hS_Exp2 -= bExp;
80 }
81
82 // Adjust for half ulp exponent
83 if (hExp >= 0)
84 hS_Exp2 += hExp;
85 else {
86 dS_Exp2 -= hExp;
87 bS_Exp2 -= hExp;
88 }
89
90 // Remove common power of two factor from all three scaled values
91 int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
92 dS_Exp2 -= common_Exp2;
93 bS_Exp2 -= common_Exp2;
94 hS_Exp2 -= common_Exp2;
95
96 BigInteger dS = d;
97 dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
98
99 BigInteger bS(bInt);
100 bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
101
102 BigInteger hS(1);
103 hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
104
105 BigInteger delta(0);
106 dS.Difference(bS, &delta);
107
108 return delta.Compare(hS);
109}
110
111inline bool StrtodFast(double d, int p, double* result) {
112 // Use fast path for string-to-double conversion if possible
113 // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
114 if (p > 22 && p < 22 + 16) {
115 // Fast Path Cases In Disguise
116 d *= internal::Pow10(p - 22);
117 p = 22;
118 }
119
120 if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
121 *result = FastPath(d, p);
122 return true;
123 }
124 else
125 return false;
126}
127
128// Compute an approximation and see if it is within 1/2 ULP
129inline bool StrtodDiyFp(const char* decimals, size_t length, size_t decimalPosition, int exp, double* result) {
130 uint64_t significand = 0;
131 size_t i = 0; // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
132 for (; i < length; i++) {
133 if (significand > RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
134 (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > '5'))
135 break;
136 significand = significand * 10u + static_cast<unsigned>(decimals[i] - '0');
137 }
138
139 if (i < length && decimals[i] >= '5') // Rounding
140 significand++;
141
142 size_t remaining = length - i;
143 const unsigned kUlpShift = 3;
144 const unsigned kUlp = 1 << kUlpShift;
145 int64_t error = (remaining == 0) ? 0 : kUlp / 2;
146
147 DiyFp v(significand, 0);
148 v = v.Normalize();
149 error <<= -v.e;
150
151 const int dExp = static_cast<int>(decimalPosition) - static_cast<int>(i) + exp;
152
153 int actualExp;
154 DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
155 if (actualExp != dExp) {
156 static const DiyFp kPow10[] = {
157 DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 00000000), -60), // 10^1
158 DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 00000000), -57), // 10^2
159 DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 00000000), -54), // 10^3
160 DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 00000000), -50), // 10^4
161 DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 00000000), -47), // 10^5
162 DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 00000000), -44), // 10^6
163 DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 00000000), -40) // 10^7
164 };
165 int adjustment = dExp - actualExp - 1;
166 RAPIDJSON_ASSERT(adjustment >= 0 && adjustment < 7);
167 v = v * kPow10[adjustment];
168 if (length + static_cast<unsigned>(adjustment)> 19u) // has more digits than decimal digits in 64-bit
169 error += kUlp / 2;
170 }
171
172 v = v * cachedPower;
173
174 error += kUlp + (error == 0 ? 0 : 1);
175
176 const int oldExp = v.e;
177 v = v.Normalize();
178 error <<= oldExp - v.e;
179
180 const unsigned effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
181 unsigned precisionSize = 64 - effectiveSignificandSize;
182 if (precisionSize + kUlpShift >= 64) {
183 unsigned scaleExp = (precisionSize + kUlpShift) - 63;
184 v.f >>= scaleExp;
185 v.e += scaleExp;
186 error = (error >> scaleExp) + 1 + static_cast<int>(kUlp);
187 precisionSize -= scaleExp;
188 }
189
190 DiyFp rounded(v.f >> precisionSize, v.e + static_cast<int>(precisionSize));
191 const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
192 const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
193 if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
194 rounded.f++;
195 if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
196 rounded.f >>= 1;
197 rounded.e++;
198 }
199 }
200
201 *result = rounded.ToDouble();
202
203 return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
204}
205
206inline double StrtodBigInteger(double approx, const char* decimals, size_t length, size_t decimalPosition, int exp) {
207 const BigInteger dInt(decimals, length);
208 const int dExp = static_cast<int>(decimalPosition) - static_cast<int>(length) + exp;
209 Double a(approx);
210 int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
211 if (cmp < 0)
212 return a.Value(); // within half ULP
213 else if (cmp == 0) {
214 // Round towards even
215 if (a.Significand() & 1)
216 return a.NextPositiveDouble();
217 else
218 return a.Value();
219 }
220 else // adjustment
221 return a.NextPositiveDouble();
222}
223
224inline double StrtodFullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
225 RAPIDJSON_ASSERT(d >= 0.0);
226 RAPIDJSON_ASSERT(length >= 1);
227
228 double result;
229 if (StrtodFast(d, p, &result))
230 return result;
231
232 // Trim leading zeros
233 while (*decimals == '0' && length > 1) {
234 length--;
235 decimals++;
236 decimalPosition--;
237 }
238
239 // Trim trailing zeros
240 while (decimals[length - 1] == '0' && length > 1) {
241 length--;
242 decimalPosition--;
243 exp++;
244 }
245
246 // Trim right-most digits
247 const int kMaxDecimalDigit = 780;
248 if (static_cast<int>(length) > kMaxDecimalDigit) {
249 int delta = (static_cast<int>(length) - kMaxDecimalDigit);
250 exp += delta;
251 decimalPosition -= static_cast<unsigned>(delta);
252 length = kMaxDecimalDigit;
253 }
254
255 // If too small, underflow to zero
256 if (int(length) + exp < -324)
257 return 0.0;
258
259 if (StrtodDiyFp(decimals, length, decimalPosition, exp, &result))
260 return result;
261
262 // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
263 return StrtodBigInteger(result, decimals, length, decimalPosition, exp);
264}
265
266} // namespace internal
267RAPIDJSON_NAMESPACE_END
268
269#endif // RAPIDJSON_STRTOD_
270