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_NUMBERS_DOUBLE_H_
6 #define V8_NUMBERS_DOUBLE_H_
7
8 #include "src/base/macros.h"
9 #include "src/numbers/diy-fp.h"
10
11 namespace v8 {
12 namespace internal {
13
14 // We assume that doubles and uint64_t have the same endianness.
double_to_uint64(double d)15 inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
uint64_to_double(uint64_t d64)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 = 0x8000'0000'0000'0000;
22 static constexpr uint64_t kExponentMask = 0x7FF0'0000'0000'0000;
23 static constexpr uint64_t kSignificandMask = 0x000F'FFFF'FFFF'FFFF;
24 static constexpr uint64_t kHiddenBit = 0x0010'0000'0000'0000;
25 static constexpr int kPhysicalSignificandSize =
26 52; // Excludes the hidden bit.
27 static constexpr int kSignificandSize = 53;
28
Double()29 Double() : d64_(0) {}
Double(double d)30 explicit Double(double d) : d64_(double_to_uint64(d)) {}
Double(uint64_t d64)31 explicit Double(uint64_t d64) : d64_(d64) {}
Double(DiyFp diy_fp)32 explicit Double(DiyFp diy_fp) : 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).
AsDiyFp()36 DiyFp AsDiyFp() const {
37 DCHECK_GT(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.
AsNormalizedDiyFp()43 DiyFp AsNormalizedDiyFp() const {
44 DCHECK_GT(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.
AsUint64()60 uint64_t AsUint64() const { return d64_; }
61
62 // Returns the next greater double. Returns +infinity on input +infinity.
NextDouble()63 double NextDouble() const {
64 if (d64_ == kInfinity) return Double(kInfinity).value();
65 if (Sign() < 0 && Significand() == 0) {
66 // -0.0
67 return 0.0;
68 }
69 if (Sign() < 0) {
70 return Double(d64_ - 1).value();
71 } else {
72 return Double(d64_ + 1).value();
73 }
74 }
75
Exponent()76 int Exponent() const {
77 if (IsDenormal()) return kDenormalExponent;
78
79 uint64_t d64 = AsUint64();
80 int biased_e =
81 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
82 return biased_e - kExponentBias;
83 }
84
Significand()85 uint64_t Significand() const {
86 uint64_t d64 = AsUint64();
87 uint64_t significand = d64 & kSignificandMask;
88 if (!IsDenormal()) {
89 return significand + kHiddenBit;
90 } else {
91 return significand;
92 }
93 }
94
95 // Returns true if the double is a denormal.
IsDenormal()96 bool IsDenormal() const {
97 uint64_t d64 = AsUint64();
98 return (d64 & kExponentMask) == 0;
99 }
100
101 // We consider denormals not to be special.
102 // Hence only Infinity and NaN are special.
IsSpecial()103 bool IsSpecial() const {
104 uint64_t d64 = AsUint64();
105 return (d64 & kExponentMask) == kExponentMask;
106 }
107
IsInfinite()108 bool IsInfinite() const {
109 uint64_t d64 = AsUint64();
110 return ((d64 & kExponentMask) == kExponentMask) &&
111 ((d64 & kSignificandMask) == 0);
112 }
113
Sign()114 int Sign() const {
115 uint64_t d64 = AsUint64();
116 return (d64 & kSignMask) == 0 ? 1 : -1;
117 }
118
119 // Precondition: the value encoded by this Double must be greater or equal
120 // than +0.0.
UpperBoundary()121 DiyFp UpperBoundary() const {
122 DCHECK_GT(Sign(), 0);
123 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
124 }
125
126 // Returns the two boundaries of this.
127 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
128 // exponent as m_plus.
129 // Precondition: the value encoded by this Double must be greater than 0.
NormalizedBoundaries(DiyFp * out_m_minus,DiyFp * out_m_plus)130 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
131 DCHECK_GT(value(), 0.0);
132 DiyFp v = this->AsDiyFp();
133 bool significand_is_zero = (v.f() == kHiddenBit);
134 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
135 DiyFp m_minus;
136 if (significand_is_zero && v.e() != kDenormalExponent) {
137 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
138 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
139 // at a distance of 1e8.
140 // The only exception is for the smallest normal: the largest denormal is
141 // at the same distance as its successor.
142 // Note: denormals have the same exponent as the smallest normals.
143 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
144 } else {
145 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
146 }
147 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
148 m_minus.set_e(m_plus.e());
149 *out_m_plus = m_plus;
150 *out_m_minus = m_minus;
151 }
152
value()153 double value() const { return uint64_to_double(d64_); }
154
155 // Returns the significand size for a given order of magnitude.
156 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
157 // This function returns the number of significant binary digits v will have
158 // once its encoded into a double. In almost all cases this is equal to
159 // kSignificandSize. The only exception are denormals. They start with leading
160 // zeroes and their effective significand-size is hence smaller.
SignificandSizeForOrderOfMagnitude(int order)161 static int SignificandSizeForOrderOfMagnitude(int order) {
162 if (order >= (kDenormalExponent + kSignificandSize)) {
163 return kSignificandSize;
164 }
165 if (order <= kDenormalExponent) return 0;
166 return order - kDenormalExponent;
167 }
168
169 private:
170 static constexpr int kExponentBias = 0x3FF + kPhysicalSignificandSize;
171 static constexpr int kDenormalExponent = -kExponentBias + 1;
172 static constexpr int kMaxExponent = 0x7FF - kExponentBias;
173 static constexpr uint64_t kInfinity = 0x7FF0'0000'0000'0000;
174
175 // The field d64_ is not marked as const to permit the usage of the copy
176 // constructor.
177 uint64_t d64_;
178
DiyFpToUint64(DiyFp diy_fp)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 internal
208 } // namespace v8
209
210 #endif // V8_NUMBERS_DOUBLE_H_
211