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 #include <climits>
23 #include <limits>
24 
25 RAPIDJSON_NAMESPACE_BEGIN
26 namespace internal {
27 
28 inline double FastPath(double significand, int exp) {
29  if (exp < -308)
30  return 0.0;
31  else if (exp >= 0)
32  return significand * internal::Pow10(exp);
33  else
34  return significand / internal::Pow10(-exp);
35 }
36 
37 inline double StrtodNormalPrecision(double d, int p) {
38  if (p < -308) {
39  // Prevent expSum < -308, making Pow10(p) = 0
40  d = FastPath(d, -308);
41  d = FastPath(d, p + 308);
42  }
43  else
44  d = FastPath(d, p);
45  return d;
46 }
47 
48 template <typename T>
49 inline T Min3(T a, T b, T c) {
50  T m = a;
51  if (m > b) m = b;
52  if (m > c) m = c;
53  return m;
54 }
55 
56 inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
57  const Double db(b);
58  const uint64_t bInt = db.IntegerSignificand();
59  const int bExp = db.IntegerExponent();
60  const int hExp = bExp - 1;
61 
62  int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
63 
64  // Adjust for decimal exponent
65  if (dExp >= 0) {
66  dS_Exp2 += dExp;
67  dS_Exp5 += dExp;
68  }
69  else {
70  bS_Exp2 -= dExp;
71  bS_Exp5 -= dExp;
72  hS_Exp2 -= dExp;
73  hS_Exp5 -= dExp;
74  }
75 
76  // Adjust for binary exponent
77  if (bExp >= 0)
78  bS_Exp2 += bExp;
79  else {
80  dS_Exp2 -= bExp;
81  hS_Exp2 -= bExp;
82  }
83 
84  // Adjust for half ulp exponent
85  if (hExp >= 0)
86  hS_Exp2 += hExp;
87  else {
88  dS_Exp2 -= hExp;
89  bS_Exp2 -= hExp;
90  }
91 
92  // Remove common power of two factor from all three scaled values
93  int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
94  dS_Exp2 -= common_Exp2;
95  bS_Exp2 -= common_Exp2;
96  hS_Exp2 -= common_Exp2;
97 
98  BigInteger dS = d;
99  dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
100 
101  BigInteger bS(bInt);
102  bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
103 
104  BigInteger hS(1);
105  hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
106 
107  BigInteger delta(0);
108  dS.Difference(bS, &delta);
109 
110  return delta.Compare(hS);
111 }
112 
113 inline bool StrtodFast(double d, int p, double* result) {
114  // Use fast path for string-to-double conversion if possible
115  // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
116  if (p > 22 && p < 22 + 16) {
117  // Fast Path Cases In Disguise
118  d *= internal::Pow10(p - 22);
119  p = 22;
120  }
121 
122  if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
123  *result = FastPath(d, p);
124  return true;
125  }
126  else
127  return false;
128 }
129 
130 // Compute an approximation and see if it is within 1/2 ULP
131 inline bool StrtodDiyFp(const char* decimals, int dLen, int dExp, double* result) {
132  uint64_t significand = 0;
133  int i = 0; // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
134  for (; i < dLen; i++) {
135  if (significand > RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
136  (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > '5'))
137  break;
138  significand = significand * 10u + static_cast<unsigned>(decimals[i] - '0');
139  }
140 
141  if (i < dLen && decimals[i] >= '5') // Rounding
142  significand++;
143 
144  int remaining = dLen - i;
145  const int kUlpShift = 3;
146  const int kUlp = 1 << kUlpShift;
147  int64_t error = (remaining == 0) ? 0 : kUlp / 2;
148 
149  DiyFp v(significand, 0);
150  v = v.Normalize();
151  error <<= -v.e;
152 
153  dExp += remaining;
154 
155  int actualExp;
156  DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
157  if (actualExp != dExp) {
158  static const DiyFp kPow10[] = {
159  DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 0x00000000), -60), // 10^1
160  DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 0x00000000), -57), // 10^2
161  DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 0x00000000), -54), // 10^3
162  DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), -50), // 10^4
163  DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 0x00000000), -47), // 10^5
164  DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 0x00000000), -44), // 10^6
165  DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 0x00000000), -40) // 10^7
166  };
167  int adjustment = dExp - actualExp;
168  RAPIDJSON_ASSERT(adjustment >= 1 && adjustment < 8);
169  v = v * kPow10[adjustment - 1];
170  if (dLen + adjustment > 19) // has more digits than decimal digits in 64-bit
171  error += kUlp / 2;
172  }
173 
174  v = v * cachedPower;
175 
176  error += kUlp + (error == 0 ? 0 : 1);
177 
178  const int oldExp = v.e;
179  v = v.Normalize();
180  error <<= oldExp - v.e;
181 
182  const int effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
183  int precisionSize = 64 - effectiveSignificandSize;
184  if (precisionSize + kUlpShift >= 64) {
185  int scaleExp = (precisionSize + kUlpShift) - 63;
186  v.f >>= scaleExp;
187  v.e += scaleExp;
188  error = (error >> scaleExp) + 1 + kUlp;
189  precisionSize -= scaleExp;
190  }
191 
192  DiyFp rounded(v.f >> precisionSize, v.e + precisionSize);
193  const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
194  const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
195  if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
196  rounded.f++;
197  if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
198  rounded.f >>= 1;
199  rounded.e++;
200  }
201  }
202 
203  *result = rounded.ToDouble();
204 
205  return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
206 }
207 
208 inline double StrtodBigInteger(double approx, const char* decimals, int dLen, int dExp) {
209  RAPIDJSON_ASSERT(dLen >= 0);
210  const BigInteger dInt(decimals, static_cast<unsigned>(dLen));
211  Double a(approx);
212  int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
213  if (cmp < 0)
214  return a.Value(); // within half ULP
215  else if (cmp == 0) {
216  // Round towards even
217  if (a.Significand() & 1)
218  return a.NextPositiveDouble();
219  else
220  return a.Value();
221  }
222  else // adjustment
223  return a.NextPositiveDouble();
224 }
225 
226 inline double StrtodFullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
227  RAPIDJSON_ASSERT(d >= 0.0);
228  RAPIDJSON_ASSERT(length >= 1);
229 
230  double result = 0.0;
231  if (StrtodFast(d, p, &result))
232  return result;
233 
234  RAPIDJSON_ASSERT(length <= INT_MAX);
235  int dLen = static_cast<int>(length);
236 
237  RAPIDJSON_ASSERT(length >= decimalPosition);
238  RAPIDJSON_ASSERT(length - decimalPosition <= INT_MAX);
239  int dExpAdjust = static_cast<int>(length - decimalPosition);
240 
241  RAPIDJSON_ASSERT(exp >= INT_MIN + dExpAdjust);
242  int dExp = exp - dExpAdjust;
243 
244  // Make sure length+dExp does not overflow
245  RAPIDJSON_ASSERT(dExp <= INT_MAX - dLen);
246 
247  // Trim leading zeros
248  while (dLen > 0 && *decimals == '0') {
249  dLen--;
250  decimals++;
251  }
252 
253  // Trim trailing zeros
254  while (dLen > 0 && decimals[dLen - 1] == '0') {
255  dLen--;
256  dExp++;
257  }
258 
259  if (dLen == 0) { // Buffer only contains zeros.
260  return 0.0;
261  }
262 
263  // Trim right-most digits
264  const int kMaxDecimalDigit = 767 + 1;
265  if (dLen > kMaxDecimalDigit) {
266  dExp += dLen - kMaxDecimalDigit;
267  dLen = kMaxDecimalDigit;
268  }
269 
270  // If too small, underflow to zero.
271  // Any x <= 10^-324 is interpreted as zero.
272  if (dLen + dExp <= -324)
273  return 0.0;
274 
275  // If too large, overflow to infinity.
276  // Any x >= 10^309 is interpreted as +infinity.
277  if (dLen + dExp > 309)
278  return std::numeric_limits<double>::infinity();
279 
280  if (StrtodDiyFp(decimals, dLen, dExp, &result))
281  return result;
282 
283  // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
284  return StrtodBigInteger(result, decimals, dLen, dExp);
285 }
286 
287 } // namespace internal
288 RAPIDJSON_NAMESPACE_END
289 
290 #endif // RAPIDJSON_STRTOD_
RAPIDJSON_ASSERT
#define RAPIDJSON_ASSERT(x)
Assertion.
Definition: rapidjson.h:437
RAPIDJSON_UINT64_C2
#define RAPIDJSON_UINT64_C2(high32, low32)
Construct a 64-bit literal by a pair of 32-bit integer.
Definition: rapidjson.h:320