third_party/WebKit/Source/wtf/dtoa/double.h

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  27
  28 #ifndef DOUBLE_CONVERSION_DOUBLE_H_
  29 #define DOUBLE_CONVERSION_DOUBLE_H_
  30
  31 #include "diy-fp.h"
  32
  33 namespace WTF {
  34
  35 namespace double_conversion {
  36
  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); }
  39     static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
  40
  41     // Helper functions for doubles.
  42     class Double {
  43     public:
  44         static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000);
  45         static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000);
  46         static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
  47         static const uint64_t kHiddenBit = UINT64_2PART_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         // Computes 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 it's encoded into a double. In almost all cases this is equal to
 190         // kSignificandSize. The only exceptions are denormals. They start with
 191         // leading 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         static double Infinity() {
 201             return Double(kInfinity).value();
 202         }
 203
 204         static double NaN() {
 205             return Double(kNaN).value();
 206         }
 207
 208     private:
 209         static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
 210         static const int kDenormalExponent = -kExponentBias + 1;
 211         static const int kMaxExponent = 0x7FF - kExponentBias;
 212         static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000);
 213         static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000);
 214
 215         const uint64_t d64_;
 216
 217         static uint64_t DiyFpToUint64(DiyFp diy_fp) {
 218             uint64_t significand = diy_fp.f();
 219             int exponent = diy_fp.e();
 220             while (significand > kHiddenBit + kSignificandMask) {
 221                 significand >>= 1;
 222                 exponent++;
 223             }
 224             if (exponent >= kMaxExponent) {
 225                 return kInfinity;
 226             }
 227             if (exponent < kDenormalExponent) {
 228                 return 0;
 229             }
 230             while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
 231                 significand <<= 1;
 232                 exponent--;
 233             }
 234             uint64_t biased_exponent;
 235             if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
 236                 biased_exponent = 0;
 237             } else {
 238                 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
 239             }
 240             return (significand & kSignificandMask) |
 241             (biased_exponent << kPhysicalSignificandSize);
 242         }
 243     };
 244
 245 }  // namespace double_conversion
 246
 247 } // namespace WTF
 248
 249 #endif  // DOUBLE_CONVERSION_DOUBLE_H_