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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