Line data Source code
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 :
11 : namespace v8 {
12 : namespace internal {
13 :
14 : // We assume that doubles and uint64_t have the same endianness.
15 : inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
16 : inline double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); }
17 :
18 : // Helper functions for doubles.
19 : class 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 5625792 : explicit Double(double d) : d64_(double_to_uint64(d)) {}
34 60 : explicit Double(uint64_t d64) : d64_(d64) {}
35 : explicit Double(DiyFp diy_fp)
36 45470 : : 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 3138736 : 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 3350442 : while ((f & kHiddenBit) == 0) {
54 105853 : f <<= 1;
55 105853 : e--;
56 : }
57 : // Do the final shifts in one go.
58 3138736 : f <<= DiyFp::kSignificandSize - kSignificandSize;
59 3138736 : e -= DiyFp::kSignificandSize - kSignificandSize;
60 3138736 : return DiyFp(f, e);
61 : }
62 :
63 : // Returns the double's bit as uint64.
64 : uint64_t AsUint64() const {
65 5279931 : return d64_;
66 : }
67 :
68 : // Returns the next greater double. Returns +infinity on input +infinity.
69 349990 : double NextDouble() const {
70 349990 : if (d64_ == kInfinity) return Double(kInfinity).value();
71 350015 : if (Sign() < 0 && Significand() == 0) {
72 : // -0.0
73 : return 0.0;
74 : }
75 349980 : if (Sign() < 0) {
76 15 : return Double(d64_ - 1).value();
77 : } else {
78 349965 : return Double(d64_ + 1).value();
79 : }
80 : }
81 :
82 : int Exponent() const {
83 12961847 : if (IsDenormal()) return kDenormalExponent;
84 :
85 : uint64_t d64 = AsUint64();
86 : int biased_e =
87 12950729 : static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
88 12950729 : return biased_e - kExponentBias;
89 : }
90 :
91 : uint64_t Significand() const {
92 : uint64_t d64 = AsUint64();
93 9536055 : uint64_t significand = d64 & kSignificandMask;
94 9536147 : if (!IsDenormal()) {
95 9526276 : 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 12501901 : 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 12458 : return ((d64 & kExponentMask) == kExponentMask) &&
117 : ((d64 & kSignificandMask) == 0);
118 : }
119 :
120 : int Sign() const {
121 : uint64_t d64 = AsUint64();
122 3580160 : 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);
129 478 : 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 2137126 : 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 2137126 : DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
141 : DiyFp m_minus;
142 2137126 : 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 114902 : m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
150 : } else {
151 2022224 : m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
152 : }
153 2137126 : m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
154 : m_minus.set_e(m_plus.e());
155 2137126 : *out_m_plus = m_plus;
156 2137126 : *out_m_minus = m_minus;
157 2137126 : }
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 45470 : if (order >= (kDenormalExponent + kSignificandSize)) {
169 : return kSignificandSize;
170 : }
171 203 : if (order <= kDenormalExponent) return 0;
172 146 : 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 45470 : static uint64_t DiyFpToUint64(DiyFp diy_fp) {
186 : uint64_t significand = diy_fp.f();
187 : int exponent = diy_fp.e();
188 45615 : while (significand > kHiddenBit + kSignificandMask) {
189 145 : significand >>= 1;
190 145 : exponent++;
191 : }
192 45470 : if (exponent >= kMaxExponent) {
193 : return kInfinity;
194 : }
195 45445 : if (exponent < kDenormalExponent) {
196 : return 0;
197 : }
198 45416 : while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
199 0 : significand <<= 1;
200 0 : exponent--;
201 : }
202 : uint64_t biased_exponent;
203 45416 : if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
204 : biased_exponent = 0;
205 : } else {
206 45242 : biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
207 : }
208 45416 : return (significand & kSignificandMask) |
209 45416 : (biased_exponent << kPhysicalSignificandSize);
210 : }
211 : };
212 :
213 : } // namespace internal
214 : } // namespace v8
215 :
216 : #endif // V8_DOUBLE_H_
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