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strtod.h
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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 
24 namespace internal {
25 
26 inline 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 
35 inline 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 
46 template <typename T>
47 inline 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 
54 inline 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 
111 inline 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
129 inline 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 
206 inline 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 
224 inline 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
268 
269 #endif // RAPIDJSON_STRTOD_
uint64_t f
Definition: diyfp.h:160
double StrtodFullPrecision(double d, int p, const char *decimals, size_t length, size_t decimalPosition, int exp)
Definition: strtod.h:224
double FastPath(double significand, int exp)
Definition: strtod.h:26
static unsigned EffectiveSignificandSize(int order)
Definition: ieee754.h:51
uint64_t IntegerSignificand() const
Definition: ieee754.h:47
double Pow10(int n)
Computes integer powers of 10 in double (10.0^n).
Definition: pow10.h:28
Definition: biginteger.h:28
#define T(x)
bool Difference(const BigInteger &rhs, BigInteger *out) const
Definition: biginteger.h:186
int e
Definition: diyfp.h:161
bool StrtodDiyFp(const char *decimals, size_t length, size_t decimalPosition, int exp, double *result)
Definition: strtod.h:129
#define exp(a)
Definition: math.h:32
#define RAPIDJSON_NAMESPACE_END
provide custom rapidjson namespace (closing expression)
Definition: rapidjson.h:119
const GLubyte * c
Definition: glext.h:9812
GLboolean GLboolean GLboolean b
Definition: glext.h:6844
int IntegerExponent() const
Definition: ieee754.h:48
DiyFp GetCachedPower10(int exp, int *outExp)
Definition: diyfp.h:240
double StrtodNormalPrecision(double d, int p)
Definition: strtod.h:35
double StrtodBigInteger(double approx, const char *decimals, size_t length, size_t decimalPosition, int exp)
Definition: strtod.h:206
static l_noret error(LoadState *S, const char *why)
Definition: lundump.c:39
#define RAPIDJSON_ASSERT(x)
Assertion.
Definition: rapidjson.h:402
GLuint64EXT * result
Definition: glext.h:12211
Definition: document.h:391
static const uint64_t kDpHiddenBit
Definition: diyfp.h:158
GLfloat GLfloat p
Definition: glext.h:9809
BigInteger & MultiplyPow5(unsigned exp)
Definition: biginteger.h:162
const GLdouble * v
Definition: glext.h:6391
#define RAPIDJSON_NAMESPACE_BEGIN
provide custom rapidjson namespace (opening expression)
Definition: rapidjson.h:116
Definition: ieee754.h:23
signed __int64 int64_t
Definition: stdint.h:135
bool StrtodFast(double d, int p, double *result)
Definition: strtod.h:111
int CheckWithinHalfULP(double b, const BigInteger &d, int dExp)
Definition: strtod.h:54
int Compare(const BigInteger &rhs) const
Definition: biginteger.h:208
#define RAPIDJSON_UINT64_C2(high32, low32)
Construct a 64-bit literal by a pair of 32-bit integer.
Definition: rapidjson.h:289
unsigned __int64 uint64_t
Definition: stdint.h:136
GLenum GLuint GLenum GLsizei length
Definition: glext.h:6233
const GLfloat * m
Definition: glext.h:11755
double ToDouble() const
Definition: diyfp.h:139
GLboolean GLboolean GLboolean GLboolean a
Definition: glext.h:6844
Definition: diyfp.h:43
T Min3(T a, T b, T c)
Definition: strtod.h:47