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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 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