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 "../rapidjson.h"
19 #include "ieee754.h"
20 #include "biginteger.h"
21 #include "diyfp.h"
22 #include "pow10.h"
23
24 RAPIDJSON_NAMESPACE_BEGIN
25 namespace internal {
26
FastPath(double significand,int exp)27 inline double FastPath(double significand, int exp) {
28 if (exp < -308)
29 return 0.0;
30 else if (exp >= 0)
31 return significand * internal::Pow10(exp);
32 else
33 return significand / internal::Pow10(-exp);
34 }
35
StrtodNormalPrecision(double d,int p)36 inline double StrtodNormalPrecision(double d, int p) {
37 if (p < -308) {
38 // Prevent expSum < -308, making Pow10(p) = 0
39 d = FastPath(d, -308);
40 d = FastPath(d, p + 308);
41 }
42 else
43 d = FastPath(d, p);
44 return d;
45 }
46
47 template <typename T>
Min3(T a,T b,T c)48 inline T Min3(T a, T b, T c) {
49 T m = a;
50 if (m > b) m = b;
51 if (m > c) m = c;
52 return m;
53 }
54
CheckWithinHalfULP(double b,const BigInteger & d,int dExp)55 inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
56 const Double db(b);
57 const uint64_t bInt = db.IntegerSignificand();
58 const int bExp = db.IntegerExponent();
59 const int hExp = bExp - 1;
60
61 int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
62
63 // Adjust for decimal exponent
64 if (dExp >= 0) {
65 dS_Exp2 += dExp;
66 dS_Exp5 += dExp;
67 }
68 else {
69 bS_Exp2 -= dExp;
70 bS_Exp5 -= dExp;
71 hS_Exp2 -= dExp;
72 hS_Exp5 -= dExp;
73 }
74
75 // Adjust for binary exponent
76 if (bExp >= 0)
77 bS_Exp2 += bExp;
78 else {
79 dS_Exp2 -= bExp;
80 hS_Exp2 -= bExp;
81 }
82
83 // Adjust for half ulp exponent
84 if (hExp >= 0)
85 hS_Exp2 += hExp;
86 else {
87 dS_Exp2 -= hExp;
88 bS_Exp2 -= hExp;
89 }
90
91 // Remove common power of two factor from all three scaled values
92 int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
93 dS_Exp2 -= common_Exp2;
94 bS_Exp2 -= common_Exp2;
95 hS_Exp2 -= common_Exp2;
96
97 BigInteger dS = d;
98 dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
99
100 BigInteger bS(bInt);
101 bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
102
103 BigInteger hS(1);
104 hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
105
106 BigInteger delta(0);
107 dS.Difference(bS, &delta);
108
109 return delta.Compare(hS);
110 }
111
StrtodFast(double d,int p,double * result)112 inline bool StrtodFast(double d, int p, double* result) {
113 // Use fast path for string-to-double conversion if possible
114 // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
115 if (p > 22 && p < 22 + 16) {
116 // Fast Path Cases In Disguise
117 d *= internal::Pow10(p - 22);
118 p = 22;
119 }
120
121 if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
122 *result = FastPath(d, p);
123 return true;
124 }
125 else
126 return false;
127 }
128
129 // Compute an approximation and see if it is within 1/2 ULP
StrtodDiyFp(const char * decimals,size_t length,size_t decimalPosition,int exp,double * result)130 inline bool StrtodDiyFp(const char* decimals, size_t length, size_t decimalPosition, int exp, double* result) {
131 uint64_t significand = 0;
132 size_t i = 0; // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
133 for (; i < length; i++) {
134 if (significand > RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
135 (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > '5'))
136 break;
137 significand = significand * 10u + static_cast<unsigned>(decimals[i] - '0');
138 }
139
140 if (i < length && decimals[i] >= '5') // Rounding
141 significand++;
142
143 size_t remaining = length - i;
144 const unsigned kUlpShift = 3;
145 const unsigned kUlp = 1 << kUlpShift;
146 int error = (remaining == 0) ? 0 : kUlp / 2;
147
148 DiyFp v(significand, 0);
149 v = v.Normalize();
150 error <<= -v.e;
151
152 const int dExp = (int)decimalPosition - (int)i + exp;
153
154 int actualExp;
155 DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
156 if (actualExp != dExp) {
157 static const DiyFp kPow10[] = {
158 DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 00000000), -60), // 10^1
159 DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 00000000), -57), // 10^2
160 DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 00000000), -54), // 10^3
161 DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 00000000), -50), // 10^4
162 DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 00000000), -47), // 10^5
163 DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 00000000), -44), // 10^6
164 DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 00000000), -40) // 10^7
165 };
166 int adjustment = dExp - actualExp - 1;
167 RAPIDJSON_ASSERT(adjustment >= 0 && adjustment < 7);
168 v = v * kPow10[adjustment];
169 if (length + static_cast<unsigned>(adjustment)> 19u) // has more digits than decimal digits in 64-bit
170 error += kUlp / 2;
171 }
172
173 v = v * cachedPower;
174
175 error += kUlp + (error == 0 ? 0 : 1);
176
177 const int oldExp = v.e;
178 v = v.Normalize();
179 error <<= oldExp - v.e;
180
181 const unsigned effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
182 unsigned precisionSize = 64 - effectiveSignificandSize;
183 if (precisionSize + kUlpShift >= 64) {
184 unsigned scaleExp = (precisionSize + kUlpShift) - 63;
185 v.f >>= scaleExp;
186 v.e += scaleExp;
187 error = (error >> scaleExp) + 1 + static_cast<int>(kUlp);
188 precisionSize -= scaleExp;
189 }
190
191 DiyFp rounded(v.f >> precisionSize, v.e + static_cast<int>(precisionSize));
192 const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
193 const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
194 if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
195 rounded.f++;
196 if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
197 rounded.f >>= 1;
198 rounded.e++;
199 }
200 }
201
202 *result = rounded.ToDouble();
203
204 return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
205 }
206
StrtodBigInteger(double approx,const char * decimals,size_t length,size_t decimalPosition,int exp)207 inline double StrtodBigInteger(double approx, const char* decimals, size_t length, size_t decimalPosition, int exp) {
208 const BigInteger dInt(decimals, length);
209 const int dExp = (int)decimalPosition - (int)length + exp;
210 Double a(approx);
211 int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
212 if (cmp < 0)
213 return a.Value(); // within half ULP
214 else if (cmp == 0) {
215 // Round towards even
216 if (a.Significand() & 1)
217 return a.NextPositiveDouble();
218 else
219 return a.Value();
220 }
221 else // adjustment
222 return a.NextPositiveDouble();
223 }
224
StrtodFullPrecision(double d,int p,const char * decimals,size_t length,size_t decimalPosition,int exp)225 inline double StrtodFullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
226 RAPIDJSON_ASSERT(d >= 0.0);
227 RAPIDJSON_ASSERT(length >= 1);
228
229 double result;
230 if (StrtodFast(d, p, &result))
231 return result;
232
233 // Trim leading zeros
234 while (*decimals == '0' && length > 1) {
235 length--;
236 decimals++;
237 decimalPosition--;
238 }
239
240 // Trim trailing zeros
241 while (decimals[length - 1] == '0' && length > 1) {
242 length--;
243 decimalPosition--;
244 exp++;
245 }
246
247 // Trim right-most digits
248 const int kMaxDecimalDigit = 780;
249 if ((int)length > kMaxDecimalDigit) {
250 int delta = (int(length) - kMaxDecimalDigit);
251 exp += delta;
252 decimalPosition -= static_cast<unsigned>(delta);
253 length = kMaxDecimalDigit;
254 }
255
256 // If too small, underflow to zero
257 if (int(length) + exp < -324)
258 return 0.0;
259
260 if (StrtodDiyFp(decimals, length, decimalPosition, exp, &result))
261 return result;
262
263 // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
264 return StrtodBigInteger(result, decimals, length, decimalPosition, exp);
265 }
266
267 } // namespace internal
268 RAPIDJSON_NAMESPACE_END
269
270 #endif // RAPIDJSON_STRTOD_
271