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