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strtod.h
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3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
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5 // Licensed under the MIT License (the "License"); you may not use this file except
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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 
25 namespace internal {
26 
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 
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>
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 
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(dS_Exp5) <<= dS_Exp2;
99 
100  BigInteger bS(bInt);
101  bS.MultiplyPow5(bS_Exp5) <<= bS_Exp2;
102 
103  BigInteger hS(1);
104  hS.MultiplyPow5(hS_Exp5) <<= hS_Exp2;
105 
106  BigInteger delta(0);
107  dS.Difference(bS, &delta);
108 
109  return delta.Compare(hS);
110 }
111 
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
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 * 10 + (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 + adjustment > 19) // 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 + kUlp;
188  precisionSize -= scaleExp;
189  }
190 
191  DiyFp rounded(v.f >> precisionSize, v.e + 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 + 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 - error >= precisionBits || precisionBits >= halfWay + error;
205 }
206 
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 
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 -= 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
269 
270 #endif // RAPIDJSON_STRTOD_
Quat exp(const Quat &q)
Definition: Quat.h:729
double StrtodFullPrecision(double d, int p, const char *decimals, size_t length, size_t decimalPosition, int exp)
Definition: strtod.h:225
static unsigned EffectiveSignificandSize(int order)
Definition: ieee754.h:50
#define RAPIDJSON_ASSERT(x)
Assertion.
Definition: rapidjson.h:344
#define RAPIDJSON_UINT64_C2(high32, low32)
Construct a 64-bit literal by a pair of 32-bit integer.
Definition: rapidjson.h:261
#define RAPIDJSON_NAMESPACE_END
provide custom rapidjson namespace (closing expression)
Definition: rapidjson.h:119
uint64_t Significand() const
Definition: ieee754.h:38
DiyFp GetCachedPower10(int exp, int *outExp)
Definition: diyfp.h:234
int Compare(const BigInteger &rhs) const
Definition: biginteger.h:198
#define RAPIDJSON_NAMESPACE_BEGIN
provide custom rapidjson namespace (opening expression)
Definition: rapidjson.h:116
DiyFp Normalize() const
Definition: diyfp.h:95
double Value() const
Definition: ieee754.h:29
double NextPositiveDouble() const
Definition: ieee754.h:32
bool StrtodFast(double d, int p, double *result)
Definition: strtod.h:112
Definition: diyfp.h:37
double StrtodNormalPrecision(double d, int p)
Definition: strtod.h:36
int CheckWithinHalfULP(double b, const BigInteger &d, int dExp)
Definition: strtod.h:55
double StrtodBigInteger(double approx, const char *decimals, size_t length, size_t decimalPosition, int exp)
Definition: strtod.h:207
double ToDouble() const
Definition: diyfp.h:133
unsigned __int64 uint64_t
Definition: stdint.h:90
uint64_t f
Definition: diyfp.h:154
uint64_t IntegerSignificand() const
Definition: ieee754.h:46
float length(float v)
Definition: vectorMath.h:208
Definition: document.h:390
double Pow10(int n)
Computes integer powers of 10 in double (10.0^n).
Definition: pow10.h:28
int IntegerExponent() const
Definition: ieee754.h:47
Definition: ieee754.h:23
T Min3(T a, T b, T c)
Definition: strtod.h:48
bool StrtodDiyFp(const char *decimals, size_t length, size_t decimalPosition, int exp, double *result)
Definition: strtod.h:130
int e
Definition: diyfp.h:155
Definition: biginteger.h:27
BigInteger & MultiplyPow5(unsigned exp)
Definition: biginteger.h:152
static const uint64_t kDpHiddenBit
Definition: diyfp.h:152
double FastPath(double significand, int exp)
Definition: strtod.h:27
bool Difference(const BigInteger &rhs, BigInteger *out) const
Definition: biginteger.h:176