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 33namespace v8 { 34namespace internal { 35 36// We assume that doubles and uint64_t have the same endianness. 37inline uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } 38inline double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } 39 40// Helper functions for doubles. 41class 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 IsInfinite() const { 134 uint64_t d64 = AsUint64(); 135 return ((d64 & kExponentMask) == kExponentMask) && 136 ((d64 & kSignificandMask) == 0); 137 } 138 139 int Sign() const { 140 uint64_t d64 = AsUint64(); 141 return (d64 & kSignMask) == 0? 1: -1; 142 } 143 144 // Precondition: the value encoded by this Double must be greater or equal 145 // than +0.0. 146 DiyFp UpperBoundary() const { 147 ASSERT(Sign() > 0); 148 return DiyFp(Significand() * 2 + 1, Exponent() - 1); 149 } 150 151 // Returns the two boundaries of this. 152 // The bigger boundary (m_plus) is normalized. The lower boundary has the same 153 // exponent as m_plus. 154 // Precondition: the value encoded by this Double must be greater than 0. 155 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { 156 ASSERT(value() > 0.0); 157 DiyFp v = this->AsDiyFp(); 158 bool significand_is_zero = (v.f() == kHiddenBit); 159 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); 160 DiyFp m_minus; 161 if (significand_is_zero && v.e() != kDenormalExponent) { 162 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. 163 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but 164 // at a distance of 1e8. 165 // The only exception is for the smallest normal: the largest denormal is 166 // at the same distance as its successor. 167 // Note: denormals have the same exponent as the smallest normals. 168 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); 169 } else { 170 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); 171 } 172 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); 173 m_minus.set_e(m_plus.e()); 174 *out_m_plus = m_plus; 175 *out_m_minus = m_minus; 176 } 177 178 double value() const { return uint64_to_double(d64_); } 179 180 // Returns the significand size for a given order of magnitude. 181 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. 182 // This function returns the number of significant binary digits v will have 183 // once its encoded into a double. In almost all cases this is equal to 184 // kSignificandSize. The only exception are denormals. They start with leading 185 // zeroes and their effective significand-size is hence smaller. 186 static int SignificandSizeForOrderOfMagnitude(int order) { 187 if (order >= (kDenormalExponent + kSignificandSize)) { 188 return kSignificandSize; 189 } 190 if (order <= kDenormalExponent) return 0; 191 return order - kDenormalExponent; 192 } 193 194 private: 195 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; 196 static const int kDenormalExponent = -kExponentBias + 1; 197 static const int kMaxExponent = 0x7FF - kExponentBias; 198 static const uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000); 199 200 const uint64_t d64_; 201 202 static uint64_t DiyFpToUint64(DiyFp diy_fp) { 203 uint64_t significand = diy_fp.f(); 204 int exponent = diy_fp.e(); 205 while (significand > kHiddenBit + kSignificandMask) { 206 significand >>= 1; 207 exponent++; 208 } 209 if (exponent >= kMaxExponent) { 210 return kInfinity; 211 } 212 if (exponent < kDenormalExponent) { 213 return 0; 214 } 215 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { 216 significand <<= 1; 217 exponent--; 218 } 219 uint64_t biased_exponent; 220 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { 221 biased_exponent = 0; 222 } else { 223 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); 224 } 225 return (significand & kSignificandMask) | 226 (biased_exponent << kPhysicalSignificandSize); 227 } 228}; 229 230} } // namespace v8::internal 231 232#endif // V8_DOUBLE_H_ 233