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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 |
| (...skipping 16 matching lines...) Expand all Loading... |
| 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) { |
| 39 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64);
} | 39 return BitCast<uint64_t>(d); |
| 40 | 40 } |
| 41 // Helper functions for doubles. | 41 static double uint64_to_double(uint64_t d64) { |
| 42 class Double { | 42 return BitCast<double>(d64); |
| 43 public: | 43 } |
| 44 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); | 44 |
| 45 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 0000000
0); | 45 // Helper functions for doubles. |
| 46 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFF
FFFF); | 46 class Double { |
| 47 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); | 47 public: |
| 48 static const int kPhysicalSignificandSize = 52; // Excludes the hidden
bit. | 48 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); |
| 49 static const int kSignificandSize = 53; | 49 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000); |
| 50 | 50 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); |
| 51 Double() : d64_(0) {} | 51 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); |
| 52 explicit Double(double d) : d64_(double_to_uint64(d)) {} | 52 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. |
| 53 explicit Double(uint64_t d64) : d64_(d64) {} | 53 static const int kSignificandSize = 53; |
| 54 explicit Double(DiyFp diy_fp) | 54 |
| 55 : d64_(DiyFpToUint64(diy_fp)) {} | 55 Double() : d64_(0) {} |
| 56 | 56 explicit Double(double d) : d64_(double_to_uint64(d)) {} |
| 57 // The value encoded by this Double must be greater or equal to +0.0. | 57 explicit Double(uint64_t d64) : d64_(d64) {} |
| 58 // It must not be special (infinity, or NaN). | 58 explicit Double(DiyFp diy_fp) : d64_(DiyFpToUint64(diy_fp)) {} |
| 59 DiyFp AsDiyFp() const { | 59 |
| 60 ASSERT(Sign() > 0); | 60 // The value encoded by this Double must be greater or equal to +0.0. |
| 61 ASSERT(!IsSpecial()); | 61 // It must not be special (infinity, or NaN). |
| 62 return DiyFp(Significand(), Exponent()); | 62 DiyFp AsDiyFp() const { |
| 63 } | 63 ASSERT(Sign() > 0); |
| 64 | 64 ASSERT(!IsSpecial()); |
| 65 // The value encoded by this Double must be strictly greater than 0. | 65 return DiyFp(Significand(), Exponent()); |
| 66 DiyFp AsNormalizedDiyFp() const { | 66 } |
| 67 ASSERT(value() > 0.0); | 67 |
| 68 uint64_t f = Significand(); | 68 // The value encoded by this Double must be strictly greater than 0. |
| 69 int e = Exponent(); | 69 DiyFp AsNormalizedDiyFp() const { |
| 70 | 70 ASSERT(value() > 0.0); |
| 71 // The current double could be a denormal. | 71 uint64_t f = Significand(); |
| 72 while ((f & kHiddenBit) == 0) { | 72 int e = Exponent(); |
| 73 f <<= 1; | 73 |
| 74 e--; | 74 // The current double could be a denormal. |
| 75 } | 75 while ((f & kHiddenBit) == 0) { |
| 76 // Do the final shifts in one go. | 76 f <<= 1; |
| 77 f <<= DiyFp::kSignificandSize - kSignificandSize; | 77 e--; |
| 78 e -= DiyFp::kSignificandSize - kSignificandSize; | 78 } |
| 79 return DiyFp(f, e); | 79 // Do the final shifts in one go. |
| 80 } | 80 f <<= DiyFp::kSignificandSize - kSignificandSize; |
| 81 | 81 e -= DiyFp::kSignificandSize - kSignificandSize; |
| 82 // Returns the double's bit as uint64. | 82 return DiyFp(f, e); |
| 83 uint64_t AsUint64() const { | 83 } |
| 84 return d64_; | 84 |
| 85 } | 85 // Returns the double's bit as uint64. |
| 86 | 86 uint64_t AsUint64() const { return d64_; } |
| 87 // Returns the next greater double. Returns +infinity on input +infinity
. | 87 |
| 88 double NextDouble() const { | 88 // Returns the next greater double. Returns +infinity on input +infinity. |
| 89 if (d64_ == kInfinity) return Double(kInfinity).value(); | 89 double NextDouble() const { |
| 90 if (Sign() < 0 && Significand() == 0) { | 90 if (d64_ == kInfinity) |
| 91 // -0.0 | 91 return Double(kInfinity).value(); |
| 92 return 0.0; | 92 if (Sign() < 0 && Significand() == 0) { |
| 93 } | 93 // -0.0 |
| 94 if (Sign() < 0) { | 94 return 0.0; |
| 95 return Double(d64_ - 1).value(); | 95 } |
| 96 } else { | 96 if (Sign() < 0) { |
| 97 return Double(d64_ + 1).value(); | 97 return Double(d64_ - 1).value(); |
| 98 } | 98 } else { |
| 99 } | 99 return Double(d64_ + 1).value(); |
| 100 | 100 } |
| 101 int Exponent() const { | 101 } |
| 102 if (IsDenormal()) return kDenormalExponent; | 102 |
| 103 | 103 int Exponent() const { |
| 104 uint64_t d64 = AsUint64(); | 104 if (IsDenormal()) |
| 105 int biased_e = | 105 return kDenormalExponent; |
| 106 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); | 106 |
| 107 return biased_e - kExponentBias; | 107 uint64_t d64 = AsUint64(); |
| 108 } | 108 int biased_e = |
| 109 | 109 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); |
| 110 uint64_t Significand() const { | 110 return biased_e - kExponentBias; |
| 111 uint64_t d64 = AsUint64(); | 111 } |
| 112 uint64_t significand = d64 & kSignificandMask; | 112 |
| 113 if (!IsDenormal()) { | 113 uint64_t Significand() const { |
| 114 return significand + kHiddenBit; | 114 uint64_t d64 = AsUint64(); |
| 115 } else { | 115 uint64_t significand = d64 & kSignificandMask; |
| 116 return significand; | 116 if (!IsDenormal()) { |
| 117 } | 117 return significand + kHiddenBit; |
| 118 } | 118 } else { |
| 119 | 119 return significand; |
| 120 // Returns true if the double is a denormal. | 120 } |
| 121 bool IsDenormal() const { | 121 } |
| 122 uint64_t d64 = AsUint64(); | 122 |
| 123 return (d64 & kExponentMask) == 0; | 123 // Returns true if the double is a denormal. |
| 124 } | 124 bool IsDenormal() const { |
| 125 | 125 uint64_t d64 = AsUint64(); |
| 126 // We consider denormals not to be special. | 126 return (d64 & kExponentMask) == 0; |
| 127 // Hence only Infinity and NaN are special. | 127 } |
| 128 bool IsSpecial() const { | 128 |
| 129 uint64_t d64 = AsUint64(); | 129 // We consider denormals not to be special. |
| 130 return (d64 & kExponentMask) == kExponentMask; | 130 // Hence only Infinity and NaN are special. |
| 131 } | 131 bool IsSpecial() const { |
| 132 | 132 uint64_t d64 = AsUint64(); |
| 133 bool IsNan() const { | 133 return (d64 & kExponentMask) == kExponentMask; |
| 134 uint64_t d64 = AsUint64(); | 134 } |
| 135 return ((d64 & kExponentMask) == kExponentMask) && | 135 |
| 136 ((d64 & kSignificandMask) != 0); | 136 bool IsNan() const { |
| 137 } | 137 uint64_t d64 = AsUint64(); |
| 138 | 138 return ((d64 & kExponentMask) == kExponentMask) && |
| 139 bool IsInfinite() const { | 139 ((d64 & kSignificandMask) != 0); |
| 140 uint64_t d64 = AsUint64(); | 140 } |
| 141 return ((d64 & kExponentMask) == kExponentMask) && | 141 |
| 142 ((d64 & kSignificandMask) == 0); | 142 bool IsInfinite() const { |
| 143 } | 143 uint64_t d64 = AsUint64(); |
| 144 | 144 return ((d64 & kExponentMask) == kExponentMask) && |
| 145 int Sign() const { | 145 ((d64 & kSignificandMask) == 0); |
| 146 uint64_t d64 = AsUint64(); | 146 } |
| 147 return (d64 & kSignMask) == 0? 1: -1; | 147 |
| 148 } | 148 int Sign() const { |
| 149 | 149 uint64_t d64 = AsUint64(); |
| 150 // Precondition: the value encoded by this Double must be greater or equ
al | 150 return (d64 & kSignMask) == 0 ? 1 : -1; |
| 151 // than +0.0. | 151 } |
| 152 DiyFp UpperBoundary() const { | 152 |
| 153 ASSERT(Sign() > 0); | 153 // Precondition: the value encoded by this Double must be greater or equal |
| 154 return DiyFp(Significand() * 2 + 1, Exponent() - 1); | 154 // than +0.0. |
| 155 } | 155 DiyFp UpperBoundary() const { |
| 156 | 156 ASSERT(Sign() > 0); |
| 157 // Computes the two boundaries of this. | 157 return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
| 158 // The bigger boundary (m_plus) is normalized. The lower boundary has th
e same | 158 } |
| 159 // exponent as m_plus. | 159 |
| 160 // Precondition: the value encoded by this Double must be greater than 0
. | 160 // Computes the two boundaries of this. |
| 161 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { | 161 // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
| 162 ASSERT(value() > 0.0); | 162 // exponent as m_plus. |
| 163 DiyFp v = this->AsDiyFp(); | 163 // Precondition: the value encoded by this Double must be greater than 0. |
| 164 bool significand_is_zero = (v.f() == kHiddenBit); | 164 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
| 165 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); | 165 ASSERT(value() > 0.0); |
| 166 DiyFp m_minus; | 166 DiyFp v = this->AsDiyFp(); |
| 167 if (significand_is_zero && v.e() != kDenormalExponent) { | 167 bool significand_is_zero = (v.f() == kHiddenBit); |
| 168 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. | 168 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
| 169 // Then the boundary (== (v - v-)/2) is not just at a distance o
f 1e9 but | 169 DiyFp m_minus; |
| 170 // at a distance of 1e8. | 170 if (significand_is_zero && v.e() != kDenormalExponent) { |
| 171 // The only exception is for the smallest normal: the largest de
normal is | 171 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. |
| 172 // at the same distance as its successor. | 172 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
| 173 // Note: denormals have the same exponent as the smallest normal
s. | 173 // at a distance of 1e8. |
| 174 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); | 174 // The only exception is for the smallest normal: the largest denormal is |
| 175 } else { | 175 // at the same distance as its successor. |
| 176 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); | 176 // Note: denormals have the same exponent as the smallest normals. |
| 177 } | 177 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
| 178 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); | 178 } else { |
| 179 m_minus.set_e(m_plus.e()); | 179 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
| 180 *out_m_plus = m_plus; | 180 } |
| 181 *out_m_minus = m_minus; | 181 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
| 182 } | 182 m_minus.set_e(m_plus.e()); |
| 183 | 183 *out_m_plus = m_plus; |
| 184 double value() const { return uint64_to_double(d64_); } | 184 *out_m_minus = m_minus; |
| 185 | 185 } |
| 186 // Returns the significand size for a given order of magnitude. | 186 |
| 187 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitud
e. | 187 double value() const { return uint64_to_double(d64_); } |
| 188 // This function returns the number of significant binary digits v will
have | 188 |
| 189 // once it's encoded into a double. In almost all cases this is equal to | 189 // Returns the significand size for a given order of magnitude. |
| 190 // kSignificandSize. The only exceptions are denormals. They start with | 190 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. |
| 191 // leading zeroes and their effective significand-size is hence smaller. | 191 // This function returns the number of significant binary digits v will have |
| 192 static int SignificandSizeForOrderOfMagnitude(int order) { | 192 // once it's encoded into a double. In almost all cases this is equal to |
| 193 if (order >= (kDenormalExponent + kSignificandSize)) { | 193 // kSignificandSize. The only exceptions are denormals. They start with |
| 194 return kSignificandSize; | 194 // leading zeroes and their effective significand-size is hence smaller. |
| 195 } | 195 static int SignificandSizeForOrderOfMagnitude(int order) { |
| 196 if (order <= kDenormalExponent) return 0; | 196 if (order >= (kDenormalExponent + kSignificandSize)) { |
| 197 return order - kDenormalExponent; | 197 return kSignificandSize; |
| 198 } | 198 } |
| 199 | 199 if (order <= kDenormalExponent) |
| 200 static double Infinity() { | 200 return 0; |
| 201 return Double(kInfinity).value(); | 201 return order - kDenormalExponent; |
| 202 } | 202 } |
| 203 | 203 |
| 204 static double NaN() { | 204 static double Infinity() { return Double(kInfinity).value(); } |
| 205 return Double(kNaN).value(); | 205 |
| 206 } | 206 static double NaN() { return Double(kNaN).value(); } |
| 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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