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double.h
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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.
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.
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.
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_
uint64_t Significand() const
Definition: double.h:110
double NextDouble() const
Definition: double.h:88
static const uint64_t kExponentMask
Definition: double.h:44
static const int kSignificandSize
Definition: diy-fp.h:41
uint64_t double_to_uint64(double d)
Definition: double.h:37
void set_f(uint64_t new_value)
Definition: diy-fp.h:105
DiyFp UpperBoundary() const
Definition: double.h:146
static const uint64_t kHiddenBit
Definition: double.h:47
int Exponent() const
Definition: double.h:101
uint64_t f() const
Definition: diy-fp.h:102
static int SignificandSizeForOrderOfMagnitude(int order)
Definition: double.h:186
#define ASSERT(condition)
Definition: checks.h:329
DiyFp AsDiyFp() const
Definition: double.h:59
static const int kSignificandSize
Definition: double.h:49
bool IsInfinite() const
Definition: double.h:133
static const uint64_t kSignMask
Definition: double.h:43
int e() const
Definition: diy-fp.h:103
double uint64_to_double(uint64_t d64)
Definition: double.h:38
Double(uint64_t d64)
Definition: double.h:53
#define V8_2PART_UINT64_C(a, b)
Definition: globals.h:226
DiyFp AsNormalizedDiyFp() const
Definition: double.h:66
static const uint64_t kSignificandMask
Definition: double.h:45
bool IsSpecial() const
Definition: double.h:128
uint64_t AsUint64() const
Definition: double.h:83
void set_e(int new_value)
Definition: diy-fp.h:106
Double(double d)
Definition: double.h:52
void Normalize()
Definition: diy-fp.h:76
Double(DiyFp diy_fp)
Definition: double.h:54
double value() const
Definition: double.h:178
bool IsDenormal() const
Definition: double.h:121
void NormalizedBoundaries(DiyFp *out_m_minus, DiyFp *out_m_plus) const
Definition: double.h:155
int Sign() const
Definition: double.h:139
static const int kPhysicalSignificandSize
Definition: double.h:48