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/base/macros.h"
9#include "src/diy-fp.h"
10
11namespace v8 {
12namespace internal {
13
14// We assume that doubles and uint64_t have the same endianness.
15inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
16inline double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); }
17
18// Helper functions for doubles.
19class Double {
20 public:
21 static constexpr uint64_t kSignMask = V8_2PART_UINT64_C(0x80000000, 00000000);
22 static constexpr uint64_t kExponentMask =
23 V8_2PART_UINT64_C(0x7FF00000, 00000000);
24 static constexpr uint64_t kSignificandMask =
25 V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
26 static constexpr uint64_t kHiddenBit =
27 V8_2PART_UINT64_C(0x00100000, 00000000);
28 static constexpr int kPhysicalSignificandSize =
29 52; // Excludes the hidden bit.
30 static constexpr int kSignificandSize = 53;
31
32 Double() : d64_(0) {}
33 explicit Double(double d) : d64_(double_to_uint64(d)) {}
34 explicit Double(uint64_t d64) : d64_(d64) {}
35 explicit Double(DiyFp diy_fp)
36 : d64_(DiyFpToUint64(diy_fp)) {}
37
38 // The value encoded by this Double must be greater or equal to +0.0.
39 // It must not be special (infinity, or NaN).
40 DiyFp AsDiyFp() const {
41 DCHECK_GT(Sign(), 0);
42 DCHECK(!IsSpecial());
43 return DiyFp(Significand(), Exponent());
44 }
45
46 // The value encoded by this Double must be strictly greater than 0.
47 DiyFp AsNormalizedDiyFp() const {
48 DCHECK_GT(value(), 0.0);
49 uint64_t f = Significand();
50 int e = Exponent();
51
52 // The current double could be a denormal.
53 while ((f & kHiddenBit) == 0) {
54 f <<= 1;
55 e--;
56 }
57 // Do the final shifts in one go.
58 f <<= DiyFp::kSignificandSize - kSignificandSize;
59 e -= DiyFp::kSignificandSize - kSignificandSize;
60 return DiyFp(f, e);
61 }
62
63 // Returns the double's bit as uint64.
64 uint64_t AsUint64() const {
65 return d64_;
66 }
67
68 // Returns the next greater double. Returns +infinity on input +infinity.
69 double NextDouble() const {
70 if (d64_ == kInfinity) return Double(kInfinity).value();
71 if (Sign() < 0 && Significand() == 0) {
72 // -0.0
73 return 0.0;
74 }
75 if (Sign() < 0) {
76 return Double(d64_ - 1).value();
77 } else {
78 return Double(d64_ + 1).value();
79 }
80 }
81
82 int Exponent() const {
83 if (IsDenormal()) return kDenormalExponent;
84
85 uint64_t d64 = AsUint64();
86 int biased_e =
87 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
88 return biased_e - kExponentBias;
89 }
90
91 uint64_t Significand() const {
92 uint64_t d64 = AsUint64();
93 uint64_t significand = d64 & kSignificandMask;
94 if (!IsDenormal()) {
95 return significand + kHiddenBit;
96 } else {
97 return significand;
98 }
99 }
100
101 // Returns true if the double is a denormal.
102 bool IsDenormal() const {
103 uint64_t d64 = AsUint64();
104 return (d64 & kExponentMask) == 0;
105 }
106
107 // We consider denormals not to be special.
108 // Hence only Infinity and NaN are special.
109 bool IsSpecial() const {
110 uint64_t d64 = AsUint64();
111 return (d64 & kExponentMask) == kExponentMask;
112 }
113
114 bool IsInfinite() const {
115 uint64_t d64 = AsUint64();
116 return ((d64 & kExponentMask) == kExponentMask) &&
117 ((d64 & kSignificandMask) == 0);
118 }
119
120 int Sign() const {
121 uint64_t d64 = AsUint64();
122 return (d64 & kSignMask) == 0? 1: -1;
123 }
124
125 // Precondition: the value encoded by this Double must be greater or equal
126 // than +0.0.
127 DiyFp UpperBoundary() const {
128 DCHECK_GT(Sign(), 0);
129 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
130 }
131
132 // Returns the two boundaries of this.
133 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
134 // exponent as m_plus.
135 // Precondition: the value encoded by this Double must be greater than 0.
136 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
137 DCHECK_GT(value(), 0.0);
138 DiyFp v = this->AsDiyFp();
139 bool significand_is_zero = (v.f() == kHiddenBit);
140 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
141 DiyFp m_minus;
142 if (significand_is_zero && v.e() != kDenormalExponent) {
143 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
144 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
145 // at a distance of 1e8.
146 // The only exception is for the smallest normal: the largest denormal is
147 // at the same distance as its successor.
148 // Note: denormals have the same exponent as the smallest normals.
149 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
150 } else {
151 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
152 }
153 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
154 m_minus.set_e(m_plus.e());
155 *out_m_plus = m_plus;
156 *out_m_minus = m_minus;
157 }
158
159 double value() const { return uint64_to_double(d64_); }
160
161 // Returns the significand size for a given order of magnitude.
162 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
163 // This function returns the number of significant binary digits v will have
164 // once its encoded into a double. In almost all cases this is equal to
165 // kSignificandSize. The only exception are denormals. They start with leading
166 // zeroes and their effective significand-size is hence smaller.
167 static int SignificandSizeForOrderOfMagnitude(int order) {
168 if (order >= (kDenormalExponent + kSignificandSize)) {
169 return kSignificandSize;
170 }
171 if (order <= kDenormalExponent) return 0;
172 return order - kDenormalExponent;
173 }
174
175 private:
176 static constexpr int kExponentBias = 0x3FF + kPhysicalSignificandSize;
177 static constexpr int kDenormalExponent = -kExponentBias + 1;
178 static constexpr int kMaxExponent = 0x7FF - kExponentBias;
179 static constexpr uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000);
180
181 // The field d64_ is not marked as const to permit the usage of the copy
182 // constructor.
183 uint64_t d64_;
184
185 static uint64_t DiyFpToUint64(DiyFp diy_fp) {
186 uint64_t significand = diy_fp.f();
187 int exponent = diy_fp.e();
188 while (significand > kHiddenBit + kSignificandMask) {
189 significand >>= 1;
190 exponent++;
191 }
192 if (exponent >= kMaxExponent) {
193 return kInfinity;
194 }
195 if (exponent < kDenormalExponent) {
196 return 0;
197 }
198 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
199 significand <<= 1;
200 exponent--;
201 }
202 uint64_t biased_exponent;
203 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
204 biased_exponent = 0;
205 } else {
206 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
207 }
208 return (significand & kSignificandMask) |
209 (biased_exponent << kPhysicalSignificandSize);
210 }
211};
212
213} // namespace internal
214} // namespace v8
215
216#endif // V8_DOUBLE_H_
217