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| 1 // Copyright 2010 the V8 project authors. All rights reserved. |
| 2 // Redistribution and use in source and binary forms, with or without |
| 3 // modification, are permitted provided that the following conditions are |
| 4 // met: |
| 5 // |
| 6 // * Redistributions of source code must retain the above copyright |
| 7 // notice, this list of conditions and the following disclaimer. |
| 8 // * Redistributions in binary form must reproduce the above |
| 9 // copyright notice, this list of conditions and the following |
| 10 // disclaimer in the documentation and/or other materials provided |
| 11 // with the distribution. |
| 12 // * Neither the name of Google Inc. nor the names of its |
| 13 // contributors may be used to endorse or promote products derived |
| 14 // from this software without specific prior written permission. |
| 15 // |
| 16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| 17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| 18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| 19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| 20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| 22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| 23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| 24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| 26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 27 |
| 28 #ifndef DOUBLE_CONVERSION_DOUBLE_H_ |
| 29 #define DOUBLE_CONVERSION_DOUBLE_H_ |
| 30 |
| 31 #include "diy-fp.h" |
| 32 |
| 33 namespace double_conversion { |
| 34 |
| 35 // We assume that doubles and uint64_t have the same endianness. |
| 36 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } |
| 37 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } |
| 38 |
| 39 // Helper functions for doubles. |
| 40 class Double { |
| 41 public: |
| 42 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); |
| 43 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000); |
| 44 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); |
| 45 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); |
| 46 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. |
| 47 static const int kSignificandSize = 53; |
| 48 |
| 49 Double() : d64_(0) {} |
| 50 explicit Double(double d) : d64_(double_to_uint64(d)) {} |
| 51 explicit Double(uint64_t d64) : d64_(d64) {} |
| 52 explicit Double(DiyFp diy_fp) |
| 53 : d64_(DiyFpToUint64(diy_fp)) {} |
| 54 |
| 55 // The value encoded by this Double must be greater or equal to +0.0. |
| 56 // It must not be special (infinity, or NaN). |
| 57 DiyFp AsDiyFp() const { |
| 58 ASSERT(Sign() > 0); |
| 59 ASSERT(!IsSpecial()); |
| 60 return DiyFp(Significand(), Exponent()); |
| 61 } |
| 62 |
| 63 // The value encoded by this Double must be strictly greater than 0. |
| 64 DiyFp AsNormalizedDiyFp() const { |
| 65 ASSERT(value() > 0.0); |
| 66 uint64_t f = Significand(); |
| 67 int e = Exponent(); |
| 68 |
| 69 // The current double could be a denormal. |
| 70 while ((f & kHiddenBit) == 0) { |
| 71 f <<= 1; |
| 72 e--; |
| 73 } |
| 74 // Do the final shifts in one go. |
| 75 f <<= DiyFp::kSignificandSize - kSignificandSize; |
| 76 e -= DiyFp::kSignificandSize - kSignificandSize; |
| 77 return DiyFp(f, e); |
| 78 } |
| 79 |
| 80 // Returns the double's bit as uint64. |
| 81 uint64_t AsUint64() const { |
| 82 return d64_; |
| 83 } |
| 84 |
| 85 // Returns the next greater double. Returns +infinity on input +infinity. |
| 86 double NextDouble() const { |
| 87 if (d64_ == kInfinity) return Double(kInfinity).value(); |
| 88 if (Sign() < 0 && Significand() == 0) { |
| 89 // -0.0 |
| 90 return 0.0; |
| 91 } |
| 92 if (Sign() < 0) { |
| 93 return Double(d64_ - 1).value(); |
| 94 } else { |
| 95 return Double(d64_ + 1).value(); |
| 96 } |
| 97 } |
| 98 |
| 99 int Exponent() const { |
| 100 if (IsDenormal()) return kDenormalExponent; |
| 101 |
| 102 uint64_t d64 = AsUint64(); |
| 103 int biased_e = |
| 104 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); |
| 105 return biased_e - kExponentBias; |
| 106 } |
| 107 |
| 108 uint64_t Significand() const { |
| 109 uint64_t d64 = AsUint64(); |
| 110 uint64_t significand = d64 & kSignificandMask; |
| 111 if (!IsDenormal()) { |
| 112 return significand + kHiddenBit; |
| 113 } else { |
| 114 return significand; |
| 115 } |
| 116 } |
| 117 |
| 118 // Returns true if the double is a denormal. |
| 119 bool IsDenormal() const { |
| 120 uint64_t d64 = AsUint64(); |
| 121 return (d64 & kExponentMask) == 0; |
| 122 } |
| 123 |
| 124 // We consider denormals not to be special. |
| 125 // Hence only Infinity and NaN are special. |
| 126 bool IsSpecial() const { |
| 127 uint64_t d64 = AsUint64(); |
| 128 return (d64 & kExponentMask) == kExponentMask; |
| 129 } |
| 130 |
| 131 bool IsNan() const { |
| 132 uint64_t d64 = AsUint64(); |
| 133 return ((d64 & kExponentMask) == kExponentMask) && |
| 134 ((d64 & kSignificandMask) != 0); |
| 135 } |
| 136 |
| 137 bool IsInfinite() const { |
| 138 uint64_t d64 = AsUint64(); |
| 139 return ((d64 & kExponentMask) == kExponentMask) && |
| 140 ((d64 & kSignificandMask) == 0); |
| 141 } |
| 142 |
| 143 int Sign() const { |
| 144 uint64_t d64 = AsUint64(); |
| 145 return (d64 & kSignMask) == 0? 1: -1; |
| 146 } |
| 147 |
| 148 // Precondition: the value encoded by this Double must be greater or equal |
| 149 // than +0.0. |
| 150 DiyFp UpperBoundary() const { |
| 151 ASSERT(Sign() > 0); |
| 152 return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
| 153 } |
| 154 |
| 155 // Computes the two boundaries of this. |
| 156 // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
| 157 // exponent as m_plus. |
| 158 // Precondition: the value encoded by this Double must be greater than 0. |
| 159 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
| 160 ASSERT(value() > 0.0); |
| 161 DiyFp v = this->AsDiyFp(); |
| 162 bool significand_is_zero = (v.f() == kHiddenBit); |
| 163 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
| 164 DiyFp m_minus; |
| 165 if (significand_is_zero && v.e() != kDenormalExponent) { |
| 166 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. |
| 167 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
| 168 // at a distance of 1e8. |
| 169 // The only exception is for the smallest normal: the largest denormal is |
| 170 // at the same distance as its successor. |
| 171 // Note: denormals have the same exponent as the smallest normals. |
| 172 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
| 173 } else { |
| 174 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
| 175 } |
| 176 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
| 177 m_minus.set_e(m_plus.e()); |
| 178 *out_m_plus = m_plus; |
| 179 *out_m_minus = m_minus; |
| 180 } |
| 181 |
| 182 double value() const { return uint64_to_double(d64_); } |
| 183 |
| 184 // Returns the significand size for a given order of magnitude. |
| 185 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. |
| 186 // This function returns the number of significant binary digits v will have |
| 187 // once it's encoded into a double. In almost all cases this is equal to |
| 188 // kSignificandSize. The only exceptions are denormals. They start with |
| 189 // leading zeroes and their effective significand-size is hence smaller. |
| 190 static int SignificandSizeForOrderOfMagnitude(int order) { |
| 191 if (order >= (kDenormalExponent + kSignificandSize)) { |
| 192 return kSignificandSize; |
| 193 } |
| 194 if (order <= kDenormalExponent) return 0; |
| 195 return order - kDenormalExponent; |
| 196 } |
| 197 |
| 198 static double Infinity() { |
| 199 return Double(kInfinity).value(); |
| 200 } |
| 201 |
| 202 static double NaN() { |
| 203 return Double(kNaN).value(); |
| 204 } |
| 205 |
| 206 private: |
| 207 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; |
| 208 static const int kDenormalExponent = -kExponentBias + 1; |
| 209 static const int kMaxExponent = 0x7FF - kExponentBias; |
| 210 static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000); |
| 211 static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000); |
| 212 |
| 213 const uint64_t d64_; |
| 214 |
| 215 static uint64_t DiyFpToUint64(DiyFp diy_fp) { |
| 216 uint64_t significand = diy_fp.f(); |
| 217 int exponent = diy_fp.e(); |
| 218 while (significand > kHiddenBit + kSignificandMask) { |
| 219 significand >>= 1; |
| 220 exponent++; |
| 221 } |
| 222 if (exponent >= kMaxExponent) { |
| 223 return kInfinity; |
| 224 } |
| 225 if (exponent < kDenormalExponent) { |
| 226 return 0; |
| 227 } |
| 228 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { |
| 229 significand <<= 1; |
| 230 exponent--; |
| 231 } |
| 232 uint64_t biased_exponent; |
| 233 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { |
| 234 biased_exponent = 0; |
| 235 } else { |
| 236 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); |
| 237 } |
| 238 return (significand & kSignificandMask) | |
| 239 (biased_exponent << kPhysicalSignificandSize); |
| 240 } |
| 241 }; |
| 242 |
| 243 } // namespace double_conversion |
| 244 |
| 245 #endif // DOUBLE_CONVERSION_DOUBLE_H_ |
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