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1 // Copyright 2010 the V8 project authors. All rights reserved. | 1 // Copyright 2010 the V8 project authors. All rights reserved. |
2 // Redistribution and use in source and binary forms, with or without | 2 // Redistribution and use in source and binary forms, with or without |
3 // modification, are permitted provided that the following conditions are | 3 // modification, are permitted provided that the following conditions are |
4 // met: | 4 // met: |
5 // | 5 // |
6 // * Redistributions of source code must retain the above copyright | 6 // * Redistributions of source code must retain the above copyright |
7 // notice, this list of conditions and the following disclaimer. | 7 // notice, this list of conditions and the following disclaimer. |
8 // * Redistributions in binary form must reproduce the above | 8 // * Redistributions in binary form must reproduce the above |
9 // copyright notice, this list of conditions and the following | 9 // copyright notice, this list of conditions and the following |
10 // disclaimer in the documentation and/or other materials provided | 10 // disclaimer in the documentation and/or other materials provided |
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26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | 26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
27 | 27 |
28 #ifndef DOUBLE_CONVERSION_DOUBLE_H_ | 28 #ifndef DOUBLE_CONVERSION_DOUBLE_H_ |
29 #define DOUBLE_CONVERSION_DOUBLE_H_ | 29 #define DOUBLE_CONVERSION_DOUBLE_H_ |
30 | 30 |
31 #include "diy-fp.h" | 31 #include "diy-fp.h" |
32 | 32 |
33 namespace WTF { | 33 namespace WTF { |
34 | 34 |
35 namespace double_conversion { | 35 namespace double_conversion { |
36 | 36 |
37 // We assume that doubles and uint64_t have the same endianness. | 37 // We assume that doubles and uint64_t have the same endianness. |
38 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } | 38 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } |
39 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64);
} | 39 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64);
} |
40 | 40 |
41 // Helper functions for doubles. | 41 // Helper functions for doubles. |
42 class Double { | 42 class Double { |
43 public: | 43 public: |
44 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); | 44 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); |
45 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 0000000
0); | 45 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 0000000
0); |
46 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFF
FFFF); | 46 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFF
FFFF); |
47 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); | 47 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); |
48 static const int kPhysicalSignificandSize = 52; // Excludes the hidden
bit. | 48 static const int kPhysicalSignificandSize = 52; // Excludes the hidden
bit. |
49 static const int kSignificandSize = 53; | 49 static const int kSignificandSize = 53; |
50 | 50 |
51 Double() : d64_(0) {} | 51 Double() : d64_(0) {} |
52 explicit Double(double d) : d64_(double_to_uint64(d)) {} | 52 explicit Double(double d) : d64_(double_to_uint64(d)) {} |
53 explicit Double(uint64_t d64) : d64_(d64) {} | 53 explicit Double(uint64_t d64) : d64_(d64) {} |
54 explicit Double(DiyFp diy_fp) | 54 explicit Double(DiyFp diy_fp) |
55 : d64_(DiyFpToUint64(diy_fp)) {} | 55 : d64_(DiyFpToUint64(diy_fp)) {} |
56 | 56 |
57 // The value encoded by this Double must be greater or equal to +0.0. | 57 // The value encoded by this Double must be greater or equal to +0.0. |
58 // It must not be special (infinity, or NaN). | 58 // It must not be special (infinity, or NaN). |
59 DiyFp AsDiyFp() const { | 59 DiyFp AsDiyFp() const { |
60 ASSERT(Sign() > 0); | 60 ASSERT(Sign() > 0); |
61 ASSERT(!IsSpecial()); | 61 ASSERT(!IsSpecial()); |
62 return DiyFp(Significand(), Exponent()); | 62 return DiyFp(Significand(), Exponent()); |
63 } | 63 } |
64 | 64 |
65 // The value encoded by this Double must be strictly greater than 0. | 65 // The value encoded by this Double must be strictly greater than 0. |
66 DiyFp AsNormalizedDiyFp() const { | 66 DiyFp AsNormalizedDiyFp() const { |
67 ASSERT(value() > 0.0); | 67 ASSERT(value() > 0.0); |
68 uint64_t f = Significand(); | 68 uint64_t f = Significand(); |
69 int e = Exponent(); | 69 int e = Exponent(); |
70 | 70 |
71 // The current double could be a denormal. | 71 // The current double could be a denormal. |
72 while ((f & kHiddenBit) == 0) { | 72 while ((f & kHiddenBit) == 0) { |
73 f <<= 1; | 73 f <<= 1; |
74 e--; | 74 e--; |
75 } | 75 } |
76 // Do the final shifts in one go. | 76 // Do the final shifts in one go. |
77 f <<= DiyFp::kSignificandSize - kSignificandSize; | 77 f <<= DiyFp::kSignificandSize - kSignificandSize; |
78 e -= DiyFp::kSignificandSize - kSignificandSize; | 78 e -= DiyFp::kSignificandSize - kSignificandSize; |
79 return DiyFp(f, e); | 79 return DiyFp(f, e); |
80 } | 80 } |
81 | 81 |
82 // Returns the double's bit as uint64. | 82 // Returns the double's bit as uint64. |
83 uint64_t AsUint64() const { | 83 uint64_t AsUint64() const { |
84 return d64_; | 84 return d64_; |
85 } | 85 } |
86 | 86 |
87 // Returns the next greater double. Returns +infinity on input +infinity
. | 87 // Returns the next greater double. Returns +infinity on input +infinity
. |
88 double NextDouble() const { | 88 double NextDouble() const { |
89 if (d64_ == kInfinity) return Double(kInfinity).value(); | 89 if (d64_ == kInfinity) return Double(kInfinity).value(); |
90 if (Sign() < 0 && Significand() == 0) { | 90 if (Sign() < 0 && Significand() == 0) { |
91 // -0.0 | 91 // -0.0 |
92 return 0.0; | 92 return 0.0; |
93 } | 93 } |
94 if (Sign() < 0) { | 94 if (Sign() < 0) { |
95 return Double(d64_ - 1).value(); | 95 return Double(d64_ - 1).value(); |
96 } else { | 96 } else { |
97 return Double(d64_ + 1).value(); | 97 return Double(d64_ + 1).value(); |
98 } | 98 } |
99 } | 99 } |
100 | 100 |
101 int Exponent() const { | 101 int Exponent() const { |
102 if (IsDenormal()) return kDenormalExponent; | 102 if (IsDenormal()) return kDenormalExponent; |
103 | 103 |
104 uint64_t d64 = AsUint64(); | 104 uint64_t d64 = AsUint64(); |
105 int biased_e = | 105 int biased_e = |
106 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); | 106 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); |
107 return biased_e - kExponentBias; | 107 return biased_e - kExponentBias; |
108 } | 108 } |
109 | 109 |
110 uint64_t Significand() const { | 110 uint64_t Significand() const { |
111 uint64_t d64 = AsUint64(); | 111 uint64_t d64 = AsUint64(); |
112 uint64_t significand = d64 & kSignificandMask; | 112 uint64_t significand = d64 & kSignificandMask; |
113 if (!IsDenormal()) { | 113 if (!IsDenormal()) { |
114 return significand + kHiddenBit; | 114 return significand + kHiddenBit; |
115 } else { | 115 } else { |
116 return significand; | 116 return significand; |
117 } | 117 } |
118 } | 118 } |
119 | 119 |
120 // Returns true if the double is a denormal. | 120 // Returns true if the double is a denormal. |
121 bool IsDenormal() const { | 121 bool IsDenormal() const { |
122 uint64_t d64 = AsUint64(); | 122 uint64_t d64 = AsUint64(); |
123 return (d64 & kExponentMask) == 0; | 123 return (d64 & kExponentMask) == 0; |
124 } | 124 } |
125 | 125 |
126 // We consider denormals not to be special. | 126 // We consider denormals not to be special. |
127 // Hence only Infinity and NaN are special. | 127 // Hence only Infinity and NaN are special. |
128 bool IsSpecial() const { | 128 bool IsSpecial() const { |
129 uint64_t d64 = AsUint64(); | 129 uint64_t d64 = AsUint64(); |
130 return (d64 & kExponentMask) == kExponentMask; | 130 return (d64 & kExponentMask) == kExponentMask; |
131 } | 131 } |
132 | 132 |
133 bool IsNan() const { | 133 bool IsNan() const { |
134 uint64_t d64 = AsUint64(); | 134 uint64_t d64 = AsUint64(); |
135 return ((d64 & kExponentMask) == kExponentMask) && | 135 return ((d64 & kExponentMask) == kExponentMask) && |
136 ((d64 & kSignificandMask) != 0); | 136 ((d64 & kSignificandMask) != 0); |
137 } | 137 } |
138 | 138 |
139 bool IsInfinite() const { | 139 bool IsInfinite() const { |
140 uint64_t d64 = AsUint64(); | 140 uint64_t d64 = AsUint64(); |
141 return ((d64 & kExponentMask) == kExponentMask) && | 141 return ((d64 & kExponentMask) == kExponentMask) && |
142 ((d64 & kSignificandMask) == 0); | 142 ((d64 & kSignificandMask) == 0); |
143 } | 143 } |
144 | 144 |
145 int Sign() const { | 145 int Sign() const { |
146 uint64_t d64 = AsUint64(); | 146 uint64_t d64 = AsUint64(); |
147 return (d64 & kSignMask) == 0? 1: -1; | 147 return (d64 & kSignMask) == 0? 1: -1; |
148 } | 148 } |
149 | 149 |
150 // Precondition: the value encoded by this Double must be greater or equ
al | 150 // Precondition: the value encoded by this Double must be greater or equ
al |
151 // than +0.0. | 151 // than +0.0. |
152 DiyFp UpperBoundary() const { | 152 DiyFp UpperBoundary() const { |
153 ASSERT(Sign() > 0); | 153 ASSERT(Sign() > 0); |
154 return DiyFp(Significand() * 2 + 1, Exponent() - 1); | 154 return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
155 } | 155 } |
156 | 156 |
157 // Computes the two boundaries of this. | 157 // Computes the two boundaries of this. |
158 // The bigger boundary (m_plus) is normalized. The lower boundary has th
e same | 158 // The bigger boundary (m_plus) is normalized. The lower boundary has th
e same |
159 // exponent as m_plus. | 159 // exponent as m_plus. |
160 // Precondition: the value encoded by this Double must be greater than 0
. | 160 // Precondition: the value encoded by this Double must be greater than 0
. |
161 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { | 161 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
162 ASSERT(value() > 0.0); | 162 ASSERT(value() > 0.0); |
163 DiyFp v = this->AsDiyFp(); | 163 DiyFp v = this->AsDiyFp(); |
164 bool significand_is_zero = (v.f() == kHiddenBit); | 164 bool significand_is_zero = (v.f() == kHiddenBit); |
165 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); | 165 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
166 DiyFp m_minus; | 166 DiyFp m_minus; |
167 if (significand_is_zero && v.e() != kDenormalExponent) { | 167 if (significand_is_zero && v.e() != kDenormalExponent) { |
168 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. | 168 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. |
169 // Then the boundary (== (v - v-)/2) is not just at a distance o
f 1e9 but | 169 // Then the boundary (== (v - v-)/2) is not just at a distance o
f 1e9 but |
170 // at a distance of 1e8. | 170 // at a distance of 1e8. |
171 // The only exception is for the smallest normal: the largest de
normal is | 171 // The only exception is for the smallest normal: the largest de
normal is |
172 // at the same distance as its successor. | 172 // at the same distance as its successor. |
173 // Note: denormals have the same exponent as the smallest normal
s. | 173 // Note: denormals have the same exponent as the smallest normal
s. |
174 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); | 174 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
175 } else { | 175 } else { |
176 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); | 176 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
177 } | 177 } |
178 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); | 178 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
179 m_minus.set_e(m_plus.e()); | 179 m_minus.set_e(m_plus.e()); |
180 *out_m_plus = m_plus; | 180 *out_m_plus = m_plus; |
181 *out_m_minus = m_minus; | 181 *out_m_minus = m_minus; |
182 } | 182 } |
183 | 183 |
184 double value() const { return uint64_to_double(d64_); } | 184 double value() const { return uint64_to_double(d64_); } |
185 | 185 |
186 // Returns the significand size for a given order of magnitude. | 186 // Returns the significand size for a given order of magnitude. |
187 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitud
e. | 187 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitud
e. |
188 // This function returns the number of significant binary digits v will
have | 188 // This function returns the number of significant binary digits v will
have |
189 // once it's encoded into a double. In almost all cases this is equal to | 189 // once it's encoded into a double. In almost all cases this is equal to |
190 // kSignificandSize. The only exceptions are denormals. They start with | 190 // kSignificandSize. The only exceptions are denormals. They start with |
191 // leading zeroes and their effective significand-size is hence smaller. | 191 // leading zeroes and their effective significand-size is hence smaller. |
192 static int SignificandSizeForOrderOfMagnitude(int order) { | 192 static int SignificandSizeForOrderOfMagnitude(int order) { |
193 if (order >= (kDenormalExponent + kSignificandSize)) { | 193 if (order >= (kDenormalExponent + kSignificandSize)) { |
194 return kSignificandSize; | 194 return kSignificandSize; |
195 } | 195 } |
196 if (order <= kDenormalExponent) return 0; | 196 if (order <= kDenormalExponent) return 0; |
197 return order - kDenormalExponent; | 197 return order - kDenormalExponent; |
198 } | 198 } |
199 | 199 |
200 static double Infinity() { | 200 static double Infinity() { |
201 return Double(kInfinity).value(); | 201 return Double(kInfinity).value(); |
202 } | 202 } |
203 | 203 |
204 static double NaN() { | 204 static double NaN() { |
205 return Double(kNaN).value(); | 205 return Double(kNaN).value(); |
206 } | 206 } |
207 | 207 |
208 private: | 208 private: |
209 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; | 209 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; |
210 static const int kDenormalExponent = -kExponentBias + 1; | 210 static const int kDenormalExponent = -kExponentBias + 1; |
211 static const int kMaxExponent = 0x7FF - kExponentBias; | 211 static const int kMaxExponent = 0x7FF - kExponentBias; |
212 static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000); | 212 static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000); |
213 static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000); | 213 static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000); |
214 | 214 |
215 const uint64_t d64_; | 215 const uint64_t d64_; |
216 | 216 |
217 static uint64_t DiyFpToUint64(DiyFp diy_fp) { | 217 static uint64_t DiyFpToUint64(DiyFp diy_fp) { |
218 uint64_t significand = diy_fp.f(); | 218 uint64_t significand = diy_fp.f(); |
219 int exponent = diy_fp.e(); | 219 int exponent = diy_fp.e(); |
220 while (significand > kHiddenBit + kSignificandMask) { | 220 while (significand > kHiddenBit + kSignificandMask) { |
221 significand >>= 1; | 221 significand >>= 1; |
222 exponent++; | 222 exponent++; |
223 } | 223 } |
224 if (exponent >= kMaxExponent) { | 224 if (exponent >= kMaxExponent) { |
225 return kInfinity; | 225 return kInfinity; |
226 } | 226 } |
227 if (exponent < kDenormalExponent) { | 227 if (exponent < kDenormalExponent) { |
228 return 0; | 228 return 0; |
229 } | 229 } |
230 while (exponent > kDenormalExponent && (significand & kHiddenBit) ==
0) { | 230 while (exponent > kDenormalExponent && (significand & kHiddenBit) ==
0) { |
231 significand <<= 1; | 231 significand <<= 1; |
232 exponent--; | 232 exponent--; |
233 } | 233 } |
234 uint64_t biased_exponent; | 234 uint64_t biased_exponent; |
235 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0
) { | 235 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0
) { |
236 biased_exponent = 0; | 236 biased_exponent = 0; |
237 } else { | 237 } else { |
238 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias
); | 238 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias
); |
239 } | 239 } |
240 return (significand & kSignificandMask) | | 240 return (significand & kSignificandMask) | |
241 (biased_exponent << kPhysicalSignificandSize); | 241 (biased_exponent << kPhysicalSignificandSize); |
242 } | 242 } |
243 }; | 243 }; |
244 | 244 |
245 } // namespace double_conversion | 245 } // namespace double_conversion |
246 | 246 |
247 } // namespace WTF | 247 } // namespace WTF |
248 | 248 |
249 #endif // DOUBLE_CONVERSION_DOUBLE_H_ | 249 #endif // DOUBLE_CONVERSION_DOUBLE_H_ |
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