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/diy-fp.h"
9 :
10 : namespace v8 {
11 : namespace internal {
12 :
13 : // We assume that doubles and uint64_t have the same endianness.
14 2176008 : inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
15 2182576 : inline double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); }
16 :
17 : // Helper functions for doubles.
18 : class 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 9576597 : explicit Double(double d) : d64_(double_to_uint64(d)) {}
30 : explicit Double(uint64_t d64) : d64_(d64) {}
31 : explicit Double(DiyFp diy_fp)
32 67435 : : 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 5275791 : 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 10725806 : while ((f & kHiddenBit) == 0) {
50 174224 : f <<= 1;
51 174224 : e--;
52 : }
53 : // Do the final shifts in one go.
54 5275791 : f <<= DiyFp::kSignificandSize - kSignificandSize;
55 5275791 : e -= DiyFp::kSignificandSize - kSignificandSize;
56 5275791 : return DiyFp(f, e);
57 : }
58 :
59 : // Returns the double's bit as uint64.
60 : uint64_t AsUint64() const {
61 9242641 : return d64_;
62 : }
63 :
64 : // Returns the next greater double. Returns +infinity on input +infinity.
65 333956 : double NextDouble() const {
66 333956 : if (d64_ == kInfinity) return Double(kInfinity).value();
67 333956 : if (Sign() < 0 && Significand() == 0) {
68 : // -0.0
69 : return 0.0;
70 : }
71 333956 : if (Sign() < 0) {
72 0 : return Double(d64_ - 1).value();
73 : } else {
74 333956 : return Double(d64_ + 1).value();
75 : }
76 : }
77 :
78 : int Exponent() const {
79 19167876 : if (IsDenormal()) return kDenormalExponent;
80 :
81 : uint64_t d64 = AsUint64();
82 : int biased_e =
83 19150553 : static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
84 19150553 : return biased_e - kExponentBias;
85 : }
86 :
87 : uint64_t Significand() const {
88 : uint64_t d64 = AsUint64();
89 14549416 : uint64_t significand = d64 & kSignificandMask;
90 14549541 : if (!IsDenormal()) {
91 14534272 : 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 18608359 : 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 12659 : return ((d64 & kExponentMask) == kExponentMask) &&
113 : ((d64 & kSignificandMask) == 0);
114 : }
115 :
116 : int Sign() const {
117 : uint64_t d64 = AsUint64();
118 5534063 : 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);
125 682 : 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 3966850 : 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 3966850 : DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
137 : DiyFp m_minus;
138 3966850 : 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 260597 : m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
146 : } else {
147 3706253 : m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
148 : }
149 3966850 : m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
150 : m_minus.set_e(m_plus.e());
151 3966850 : *out_m_plus = m_plus;
152 3966850 : *out_m_minus = m_minus;
153 3966850 : }
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 67435 : if (order >= (kDenormalExponent + kSignificandSize)) {
165 : return kSignificandSize;
166 : }
167 196 : if (order <= kDenormalExponent) return 0;
168 110 : 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 67435 : static uint64_t DiyFpToUint64(DiyFp diy_fp) {
180 67435 : uint64_t significand = diy_fp.f();
181 67435 : int exponent = diy_fp.e();
182 67442 : while (significand > kHiddenBit + kSignificandMask) {
183 7 : significand >>= 1;
184 7 : exponent++;
185 : }
186 67435 : if (exponent >= kMaxExponent) {
187 : return kInfinity;
188 : }
189 67400 : if (exponent < kDenormalExponent) {
190 : return 0;
191 : }
192 67357 : while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
193 0 : significand <<= 1;
194 0 : exponent--;
195 : }
196 : uint64_t biased_exponent;
197 67357 : if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
198 : biased_exponent = 0;
199 : } else {
200 67204 : biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
201 : }
202 67357 : return (significand & kSignificandMask) |
203 67357 : (biased_exponent << kPhysicalSignificandSize);
204 : }
205 : };
206 :
207 : } // namespace internal
208 : } // namespace v8
209 :
210 : #endif // V8_DOUBLE_H_
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