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
10namespace v8 {
11namespace internal {
12
13// We assume that doubles and uint64_t have the same endianness.
14inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
15inline double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); }
16
17// Helper functions for doubles.
18class 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 v8::internal
208
209#endif  // V8_DOUBLE_H_
210