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_