1 // Copyright 2010 the V8 project authors. All rights reserved.
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3 // modification, are permitted provided that the following conditions are
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5 //
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15 //
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27
28 #ifndef V8_DOUBLE_H_
29 #define V8_DOUBLE_H_
30
31 #include "diy-fp.h"
32
33 namespace v8 {
34 namespace internal {
35
36 // We assume that doubles and uint64_t have the same endianness.
double_to_uint64(double d)37 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
uint64_to_double(uint64_t d64)38 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
39
40 // Helper functions for doubles.
41 class Double {
42 public:
43 static const uint64_t kSignMask = V8_2PART_UINT64_C(0x80000000, 00000000);
44 static const uint64_t kExponentMask = V8_2PART_UINT64_C(0x7FF00000, 00000000);
45 static const uint64_t kSignificandMask =
46 V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
47 static const uint64_t kHiddenBit = V8_2PART_UINT64_C(0x00100000, 00000000);
48 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
49 static const int kSignificandSize = 53;
50
Double()51 Double() : d64_(0) {}
Double(double d)52 explicit Double(double d) : d64_(double_to_uint64(d)) {}
Double(uint64_t d64)53 explicit Double(uint64_t d64) : d64_(d64) {}
Double(DiyFp diy_fp)54 explicit Double(DiyFp diy_fp)
55 : d64_(DiyFpToUint64(diy_fp)) {}
56
57 // The value encoded by this Double must be greater or equal to +0.0.
58 // It must not be special (infinity, or NaN).
AsDiyFp()59 DiyFp AsDiyFp() const {
60 ASSERT(Sign() > 0);
61 ASSERT(!IsSpecial());
62 return DiyFp(Significand(), Exponent());
63 }
64
65 // The value encoded by this Double must be strictly greater than 0.
AsNormalizedDiyFp()66 DiyFp AsNormalizedDiyFp() const {
67 ASSERT(value() > 0.0);
68 uint64_t f = Significand();
69 int e = Exponent();
70
71 // The current double could be a denormal.
72 while ((f & kHiddenBit) == 0) {
73 f <<= 1;
74 e--;
75 }
76 // Do the final shifts in one go.
77 f <<= DiyFp::kSignificandSize - kSignificandSize;
78 e -= DiyFp::kSignificandSize - kSignificandSize;
79 return DiyFp(f, e);
80 }
81
82 // Returns the double's bit as uint64.
AsUint64()83 uint64_t AsUint64() const {
84 return d64_;
85 }
86
87 // Returns the next greater double. Returns +infinity on input +infinity.
NextDouble()88 double NextDouble() const {
89 if (d64_ == kInfinity) return Double(kInfinity).value();
90 if (Sign() < 0 && Significand() == 0) {
91 // -0.0
92 return 0.0;
93 }
94 if (Sign() < 0) {
95 return Double(d64_ - 1).value();
96 } else {
97 return Double(d64_ + 1).value();
98 }
99 }
100
Exponent()101 int Exponent() const {
102 if (IsDenormal()) return kDenormalExponent;
103
104 uint64_t d64 = AsUint64();
105 int biased_e =
106 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
107 return biased_e - kExponentBias;
108 }
109
Significand()110 uint64_t Significand() const {
111 uint64_t d64 = AsUint64();
112 uint64_t significand = d64 & kSignificandMask;
113 if (!IsDenormal()) {
114 return significand + kHiddenBit;
115 } else {
116 return significand;
117 }
118 }
119
120 // Returns true if the double is a denormal.
IsDenormal()121 bool IsDenormal() const {
122 uint64_t d64 = AsUint64();
123 return (d64 & kExponentMask) == 0;
124 }
125
126 // We consider denormals not to be special.
127 // Hence only Infinity and NaN are special.
IsSpecial()128 bool IsSpecial() const {
129 uint64_t d64 = AsUint64();
130 return (d64 & kExponentMask) == kExponentMask;
131 }
132
IsNan()133 bool IsNan() const {
134 uint64_t d64 = AsUint64();
135 return ((d64 & kExponentMask) == kExponentMask) &&
136 ((d64 & kSignificandMask) != 0);
137 }
138
IsInfinite()139 bool IsInfinite() const {
140 uint64_t d64 = AsUint64();
141 return ((d64 & kExponentMask) == kExponentMask) &&
142 ((d64 & kSignificandMask) == 0);
143 }
144
Sign()145 int Sign() const {
146 uint64_t d64 = AsUint64();
147 return (d64 & kSignMask) == 0? 1: -1;
148 }
149
150 // Precondition: the value encoded by this Double must be greater or equal
151 // than +0.0.
UpperBoundary()152 DiyFp UpperBoundary() const {
153 ASSERT(Sign() > 0);
154 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
155 }
156
157 // Returns the two boundaries of this.
158 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
159 // exponent as m_plus.
160 // Precondition: the value encoded by this Double must be greater than 0.
NormalizedBoundaries(DiyFp * out_m_minus,DiyFp * out_m_plus)161 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
162 ASSERT(value() > 0.0);
163 DiyFp v = this->AsDiyFp();
164 bool significand_is_zero = (v.f() == kHiddenBit);
165 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
166 DiyFp m_minus;
167 if (significand_is_zero && v.e() != kDenormalExponent) {
168 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
169 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
170 // at a distance of 1e8.
171 // The only exception is for the smallest normal: the largest denormal is
172 // at the same distance as its successor.
173 // Note: denormals have the same exponent as the smallest normals.
174 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
175 } else {
176 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
177 }
178 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
179 m_minus.set_e(m_plus.e());
180 *out_m_plus = m_plus;
181 *out_m_minus = m_minus;
182 }
183
value()184 double value() const { return uint64_to_double(d64_); }
185
186 // Returns the significand size for a given order of magnitude.
187 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
188 // This function returns the number of significant binary digits v will have
189 // once its encoded into a double. In almost all cases this is equal to
190 // kSignificandSize. The only exception are denormals. They start with leading
191 // zeroes and their effective significand-size is hence smaller.
SignificandSizeForOrderOfMagnitude(int order)192 static int SignificandSizeForOrderOfMagnitude(int order) {
193 if (order >= (kDenormalExponent + kSignificandSize)) {
194 return kSignificandSize;
195 }
196 if (order <= kDenormalExponent) return 0;
197 return order - kDenormalExponent;
198 }
199
200 private:
201 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
202 static const int kDenormalExponent = -kExponentBias + 1;
203 static const int kMaxExponent = 0x7FF - kExponentBias;
204 static const uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000);
205
206 const uint64_t d64_;
207
DiyFpToUint64(DiyFp diy_fp)208 static uint64_t DiyFpToUint64(DiyFp diy_fp) {
209 uint64_t significand = diy_fp.f();
210 int exponent = diy_fp.e();
211 while (significand > kHiddenBit + kSignificandMask) {
212 significand >>= 1;
213 exponent++;
214 }
215 if (exponent >= kMaxExponent) {
216 return kInfinity;
217 }
218 if (exponent < kDenormalExponent) {
219 return 0;
220 }
221 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
222 significand <<= 1;
223 exponent--;
224 }
225 uint64_t biased_exponent;
226 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
227 biased_exponent = 0;
228 } else {
229 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
230 }
231 return (significand & kSignificandMask) |
232 (biased_exponent << kPhysicalSignificandSize);
233 }
234 };
235
236 } } // namespace v8::internal
237
238 #endif // V8_DOUBLE_H_
239