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.
double_to_uint64(double d)14 inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
uint64_to_double(uint64_t d64)15 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
Double()28 Double() : d64_(0) {}
Double(double d)29 explicit Double(double d) : d64_(double_to_uint64(d)) {}
Double(uint64_t d64)30 explicit Double(uint64_t d64) : d64_(d64) {}
Double(DiyFp diy_fp)31 explicit Double(DiyFp diy_fp)
32 : 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(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(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 {
61 return d64_;
62 }
63
64 // Returns the next greater double. Returns +infinity on input +infinity.
NextDouble()65 double NextDouble() const {
66 if (d64_ == kInfinity) return Double(kInfinity).value();
67 if (Sign() < 0 && Significand() == 0) {
68 // -0.0
69 return 0.0;
70 }
71 if (Sign() < 0) {
72 return Double(d64_ - 1).value();
73 } else {
74 return Double(d64_ + 1).value();
75 }
76 }
77
Exponent()78 int Exponent() const {
79 if (IsDenormal()) return kDenormalExponent;
80
81 uint64_t d64 = AsUint64();
82 int biased_e =
83 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
84 return biased_e - kExponentBias;
85 }
86
Significand()87 uint64_t Significand() const {
88 uint64_t d64 = AsUint64();
89 uint64_t significand = d64 & kSignificandMask;
90 if (!IsDenormal()) {
91 return significand + kHiddenBit;
92 } else {
93 return significand;
94 }
95 }
96
97 // Returns true if the double is a denormal.
IsDenormal()98 bool IsDenormal() const {
99 uint64_t d64 = AsUint64();
100 return (d64 & kExponentMask) == 0;
101 }
102
103 // We consider denormals not to be special.
104 // Hence only Infinity and NaN are special.
IsSpecial()105 bool IsSpecial() const {
106 uint64_t d64 = AsUint64();
107 return (d64 & kExponentMask) == kExponentMask;
108 }
109
IsInfinite()110 bool IsInfinite() const {
111 uint64_t d64 = AsUint64();
112 return ((d64 & kExponentMask) == kExponentMask) &&
113 ((d64 & kSignificandMask) == 0);
114 }
115
Sign()116 int Sign() const {
117 uint64_t d64 = AsUint64();
118 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.
UpperBoundary()123 DiyFp UpperBoundary() const {
124 DCHECK(Sign() > 0);
125 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.
NormalizedBoundaries(DiyFp * out_m_minus,DiyFp * out_m_plus)132 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 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
137 DiyFp m_minus;
138 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 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
146 } else {
147 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
148 }
149 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
150 m_minus.set_e(m_plus.e());
151 *out_m_plus = m_plus;
152 *out_m_minus = m_minus;
153 }
154
value()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.
SignificandSizeForOrderOfMagnitude(int order)163 static int SignificandSizeForOrderOfMagnitude(int order) {
164 if (order >= (kDenormalExponent + kSignificandSize)) {
165 return kSignificandSize;
166 }
167 if (order <= kDenormalExponent) return 0;
168 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
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_DOUBLE_H_
211