1 // Copyright 2011 the V8 project authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style license that can be 3 // found in the LICENSE file. 4 5 #ifndef V8_DOUBLE_H_ 6 #define V8_DOUBLE_H_ 7 8 #include "src/diy-fp.h" 9 10 namespace v8 { 11 namespace internal { 12 13 // We assume that doubles and uint64_t have the same endianness. 14 inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); } 15 inline double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); } 16 17 // Helper functions for doubles. 18 class Double { 19 public: 20 static const uint64_t kSignMask = V8_2PART_UINT64_C(0x80000000, 00000000); 21 static const uint64_t kExponentMask = V8_2PART_UINT64_C(0x7FF00000, 00000000); 22 static const uint64_t kSignificandMask = 23 V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF); 24 static const uint64_t kHiddenBit = V8_2PART_UINT64_C(0x00100000, 00000000); 25 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. 26 static const int kSignificandSize = 53; 27 28 Double() : d64_(0) {} 29 explicit Double(double d) : d64_(double_to_uint64(d)) {} 30 explicit Double(uint64_t d64) : d64_(d64) {} 31 explicit Double(DiyFp diy_fp) 32 : d64_(DiyFpToUint64(diy_fp)) {} 33 34 // The value encoded by this Double must be greater or equal to +0.0. 35 // It must not be special (infinity, or NaN). 36 DiyFp AsDiyFp() const { 37 DCHECK(Sign() > 0); 38 DCHECK(!IsSpecial()); 39 return DiyFp(Significand(), Exponent()); 40 } 41 42 // The value encoded by this Double must be strictly greater than 0. 43 DiyFp AsNormalizedDiyFp() const { 44 DCHECK(value() > 0.0); 45 uint64_t f = Significand(); 46 int e = Exponent(); 47 48 // The current double could be a denormal. 49 while ((f & kHiddenBit) == 0) { 50 f <<= 1; 51 e--; 52 } 53 // Do the final shifts in one go. 54 f <<= DiyFp::kSignificandSize - kSignificandSize; 55 e -= DiyFp::kSignificandSize - kSignificandSize; 56 return DiyFp(f, e); 57 } 58 59 // Returns the double's bit as uint64. 60 uint64_t AsUint64() const { 61 return d64_; 62 } 63 64 // Returns the next greater double. Returns +infinity on input +infinity. 65 double NextDouble() const { 66 if (d64_ == kInfinity) return Double(kInfinity).value(); 67 if (Sign() < 0 && Significand() == 0) { 68 // -0.0 69 return 0.0; 70 } 71 if (Sign() < 0) { 72 return Double(d64_ - 1).value(); 73 } else { 74 return Double(d64_ + 1).value(); 75 } 76 } 77 78 int Exponent() const { 79 if (IsDenormal()) return kDenormalExponent; 80 81 uint64_t d64 = AsUint64(); 82 int biased_e = 83 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); 84 return biased_e - kExponentBias; 85 } 86 87 uint64_t Significand() const { 88 uint64_t d64 = AsUint64(); 89 uint64_t significand = d64 & kSignificandMask; 90 if (!IsDenormal()) { 91 return significand + kHiddenBit; 92 } else { 93 return significand; 94 } 95 } 96 97 // Returns true if the double is a denormal. 98 bool IsDenormal() const { 99 uint64_t d64 = AsUint64(); 100 return (d64 & kExponentMask) == 0; 101 } 102 103 // We consider denormals not to be special. 104 // Hence only Infinity and NaN are special. 105 bool IsSpecial() const { 106 uint64_t d64 = AsUint64(); 107 return (d64 & kExponentMask) == kExponentMask; 108 } 109 110 bool IsInfinite() const { 111 uint64_t d64 = AsUint64(); 112 return ((d64 & kExponentMask) == kExponentMask) && 113 ((d64 & kSignificandMask) == 0); 114 } 115 116 int Sign() const { 117 uint64_t d64 = AsUint64(); 118 return (d64 & kSignMask) == 0? 1: -1; 119 } 120 121 // Precondition: the value encoded by this Double must be greater or equal 122 // than +0.0. 123 DiyFp UpperBoundary() const { 124 DCHECK(Sign() > 0); 125 return DiyFp(Significand() * 2 + 1, Exponent() - 1); 126 } 127 128 // Returns the two boundaries of this. 129 // The bigger boundary (m_plus) is normalized. The lower boundary has the same 130 // exponent as m_plus. 131 // Precondition: the value encoded by this Double must be greater than 0. 132 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { 133 DCHECK(value() > 0.0); 134 DiyFp v = this->AsDiyFp(); 135 bool significand_is_zero = (v.f() == kHiddenBit); 136 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); 137 DiyFp m_minus; 138 if (significand_is_zero && v.e() != kDenormalExponent) { 139 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. 140 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but 141 // at a distance of 1e8. 142 // The only exception is for the smallest normal: the largest denormal is 143 // at the same distance as its successor. 144 // Note: denormals have the same exponent as the smallest normals. 145 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); 146 } else { 147 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); 148 } 149 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); 150 m_minus.set_e(m_plus.e()); 151 *out_m_plus = m_plus; 152 *out_m_minus = m_minus; 153 } 154 155 double value() const { return uint64_to_double(d64_); } 156 157 // Returns the significand size for a given order of magnitude. 158 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. 159 // This function returns the number of significant binary digits v will have 160 // once its encoded into a double. In almost all cases this is equal to 161 // kSignificandSize. The only exception are denormals. They start with leading 162 // zeroes and their effective significand-size is hence smaller. 163 static int SignificandSizeForOrderOfMagnitude(int order) { 164 if (order >= (kDenormalExponent + kSignificandSize)) { 165 return kSignificandSize; 166 } 167 if (order <= kDenormalExponent) return 0; 168 return order - kDenormalExponent; 169 } 170 171 private: 172 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; 173 static const int kDenormalExponent = -kExponentBias + 1; 174 static const int kMaxExponent = 0x7FF - kExponentBias; 175 static const uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000); 176 177 const uint64_t d64_; 178 179 static uint64_t DiyFpToUint64(DiyFp diy_fp) { 180 uint64_t significand = diy_fp.f(); 181 int exponent = diy_fp.e(); 182 while (significand > kHiddenBit + kSignificandMask) { 183 significand >>= 1; 184 exponent++; 185 } 186 if (exponent >= kMaxExponent) { 187 return kInfinity; 188 } 189 if (exponent < kDenormalExponent) { 190 return 0; 191 } 192 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { 193 significand <<= 1; 194 exponent--; 195 } 196 uint64_t biased_exponent; 197 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { 198 biased_exponent = 0; 199 } else { 200 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); 201 } 202 return (significand & kSignificandMask) | 203 (biased_exponent << kPhysicalSignificandSize); 204 } 205 }; 206 207 } // namespace internal 208 } // namespace v8 209 210 #endif // V8_DOUBLE_H_ 211
