1 // Copyright 2011 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 V8_DOUBLE_H_ 29 #define V8_DOUBLE_H_ 30 31 #include "diy-fp.h" 32 33 namespace v8 { 34 namespace internal { 35 36 // We assume that doubles and uint64_t have the same endianness. 37 inline uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } 38 inline double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } 39 40 // Helper functions for doubles. 41 class Double { 42 public: 43 static const uint64_t kSignMask = V8_2PART_UINT64_C(0x80000000, 00000000); 44 static const uint64_t kExponentMask = V8_2PART_UINT64_C(0x7FF00000, 00000000); 45 static const uint64_t kSignificandMask = 46 V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF); 47 static const uint64_t kHiddenBit = V8_2PART_UINT64_C(0x00100000, 00000000); 48 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. 49 static const int kSignificandSize = 53; 50 51 Double() : d64_(0) {} 52 explicit Double(double d) : d64_(double_to_uint64(d)) {} 53 explicit Double(uint64_t d64) : d64_(d64) {} 54 explicit Double(DiyFp diy_fp) 55 : d64_(DiyFpToUint64(diy_fp)) {} 56 57 // The value encoded by this Double must be greater or equal to +0.0. 58 // It must not be special (infinity, or NaN). 59 DiyFp AsDiyFp() const { 60 ASSERT(Sign() > 0); 61 ASSERT(!IsSpecial()); 62 return DiyFp(Significand(), Exponent()); 63 } 64 65 // The value encoded by this Double must be strictly greater than 0. 66 DiyFp AsNormalizedDiyFp() const { 67 ASSERT(value() > 0.0); 68 uint64_t f = Significand(); 69 int e = Exponent(); 70 71 // The current double could be a denormal. 72 while ((f & kHiddenBit) == 0) { 73 f <<= 1; 74 e--; 75 } 76 // Do the final shifts in one go. 77 f <<= DiyFp::kSignificandSize - kSignificandSize; 78 e -= DiyFp::kSignificandSize - kSignificandSize; 79 return DiyFp(f, e); 80 } 81 82 // Returns the double's bit as uint64. 83 uint64_t AsUint64() const { 84 return d64_; 85 } 86 87 // Returns the next greater double. Returns +infinity on input +infinity. 88 double NextDouble() const { 89 if (d64_ == kInfinity) return Double(kInfinity).value(); 90 if (Sign() < 0 && Significand() == 0) { 91 // -0.0 92 return 0.0; 93 } 94 if (Sign() < 0) { 95 return Double(d64_ - 1).value(); 96 } else { 97 return Double(d64_ + 1).value(); 98 } 99 } 100 101 int Exponent() const { 102 if (IsDenormal()) return kDenormalExponent; 103 104 uint64_t d64 = AsUint64(); 105 int biased_e = 106 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); 107 return biased_e - kExponentBias; 108 } 109 110 uint64_t Significand() const { 111 uint64_t d64 = AsUint64(); 112 uint64_t significand = d64 & kSignificandMask; 113 if (!IsDenormal()) { 114 return significand + kHiddenBit; 115 } else { 116 return significand; 117 } 118 } 119 120 // Returns true if the double is a denormal. 121 bool IsDenormal() const { 122 uint64_t d64 = AsUint64(); 123 return (d64 & kExponentMask) == 0; 124 } 125 126 // We consider denormals not to be special. 127 // Hence only Infinity and NaN are special. 128 bool IsSpecial() const { 129 uint64_t d64 = AsUint64(); 130 return (d64 & kExponentMask) == kExponentMask; 131 } 132 133 bool IsNan() const { 134 uint64_t d64 = AsUint64(); 135 return ((d64 & kExponentMask) == kExponentMask) && 136 ((d64 & kSignificandMask) != 0); 137 } 138 139 bool IsInfinite() const { 140 uint64_t d64 = AsUint64(); 141 return ((d64 & kExponentMask) == kExponentMask) && 142 ((d64 & kSignificandMask) == 0); 143 } 144 145 int Sign() const { 146 uint64_t d64 = AsUint64(); 147 return (d64 & kSignMask) == 0? 1: -1; 148 } 149 150 // Precondition: the value encoded by this Double must be greater or equal 151 // than +0.0. 152 DiyFp UpperBoundary() const { 153 ASSERT(Sign() > 0); 154 return DiyFp(Significand() * 2 + 1, Exponent() - 1); 155 } 156 157 // Returns the two boundaries of this. 158 // The bigger boundary (m_plus) is normalized. The lower boundary has the same 159 // exponent as m_plus. 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 { 162 ASSERT(value() > 0.0); 163 DiyFp v = this->AsDiyFp(); 164 bool significand_is_zero = (v.f() == kHiddenBit); 165 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); 166 DiyFp m_minus; 167 if (significand_is_zero && v.e() != kDenormalExponent) { 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 of 1e9 but 170 // at a distance of 1e8. 171 // The only exception is for the smallest normal: the largest denormal is 172 // at the same distance as its successor. 173 // Note: denormals have the same exponent as the smallest normals. 174 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); 175 } else { 176 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); 177 } 178 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); 179 m_minus.set_e(m_plus.e()); 180 *out_m_plus = m_plus; 181 *out_m_minus = m_minus; 182 } 183 184 double value() const { return uint64_to_double(d64_); } 185 186 // 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 magnitude. 188 // This function returns the number of significant binary digits v will have 189 // once its encoded into a double. In almost all cases this is equal to 190 // kSignificandSize. The only exception are denormals. They start with leading 191 // zeroes and their effective significand-size is hence smaller. 192 static int SignificandSizeForOrderOfMagnitude(int order) { 193 if (order >= (kDenormalExponent + kSignificandSize)) { 194 return kSignificandSize; 195 } 196 if (order <= kDenormalExponent) return 0; 197 return order - kDenormalExponent; 198 } 199 200 private: 201 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; 202 static const int kDenormalExponent = -kExponentBias + 1; 203 static const int kMaxExponent = 0x7FF - kExponentBias; 204 static const uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000); 205 206 const uint64_t d64_; 207 208 static uint64_t DiyFpToUint64(DiyFp diy_fp) { 209 uint64_t significand = diy_fp.f(); 210 int exponent = diy_fp.e(); 211 while (significand > kHiddenBit + kSignificandMask) { 212 significand >>= 1; 213 exponent++; 214 } 215 if (exponent >= kMaxExponent) { 216 return kInfinity; 217 } 218 if (exponent < kDenormalExponent) { 219 return 0; 220 } 221 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { 222 significand <<= 1; 223 exponent--; 224 } 225 uint64_t biased_exponent; 226 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { 227 biased_exponent = 0; 228 } else { 229 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); 230 } 231 return (significand & kSignificandMask) | 232 (biased_exponent << kPhysicalSignificandSize); 233 } 234 }; 235 236 } } // namespace v8::internal 237 238 #endif // V8_DOUBLE_H_ 239
