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1 // Copyright 2010 the V8 project authors. All rights reserved. | |
2 // Redistribution and use in source and binary forms, with or without | |
3 // modification, are permitted provided that the following conditions are | |
4 // met: | |
5 // | |
6 // * Redistributions of source code must retain the above copyright | |
7 // notice, this list of conditions and the following disclaimer. | |
8 // * Redistributions in binary form must reproduce the above | |
9 // copyright notice, this list of conditions and the following | |
10 // disclaimer in the documentation and/or other materials provided | |
11 // with the distribution. | |
12 // * Neither the name of Google Inc. nor the names of its | |
13 // contributors may be used to endorse or promote products derived | |
14 // from this software without specific prior written permission. | |
15 // | |
16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | |
20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | |
22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | |
23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | |
24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | |
25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | |
26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
27 | |
28 #ifndef DOUBLE_CONVERSION_DOUBLE_H_ | |
29 #define DOUBLE_CONVERSION_DOUBLE_H_ | |
30 | |
31 #include "diy-fp.h" | |
32 | |
33 namespace double_conversion { | |
34 | |
35 // We assume that doubles and uint64_t have the same endianness. | |
36 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } | |
37 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } | |
38 | |
39 // Helper functions for doubles. | |
40 class Double { | |
41 public: | |
42 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); | |
43 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000); | |
44 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); | |
45 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); | |
46 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. | |
47 static const int kSignificandSize = 53; | |
48 | |
49 Double() : d64_(0) {} | |
50 explicit Double(double d) : d64_(double_to_uint64(d)) {} | |
51 explicit Double(uint64_t d64) : d64_(d64) {} | |
52 explicit Double(DiyFp diy_fp) | |
53 : d64_(DiyFpToUint64(diy_fp)) {} | |
54 | |
55 // The value encoded by this Double must be greater or equal to +0.0. | |
56 // It must not be special (infinity, or NaN). | |
57 DiyFp AsDiyFp() const { | |
58 ASSERT(Sign() > 0); | |
59 ASSERT(!IsSpecial()); | |
60 return DiyFp(Significand(), Exponent()); | |
61 } | |
62 | |
63 // The value encoded by this Double must be strictly greater than 0. | |
64 DiyFp AsNormalizedDiyFp() const { | |
65 ASSERT(value() > 0.0); | |
66 uint64_t f = Significand(); | |
67 int e = Exponent(); | |
68 | |
69 // The current double could be a denormal. | |
70 while ((f & kHiddenBit) == 0) { | |
71 f <<= 1; | |
72 e--; | |
73 } | |
74 // Do the final shifts in one go. | |
75 f <<= DiyFp::kSignificandSize - kSignificandSize; | |
76 e -= DiyFp::kSignificandSize - kSignificandSize; | |
77 return DiyFp(f, e); | |
78 } | |
79 | |
80 // Returns the double's bit as uint64. | |
81 uint64_t AsUint64() const { | |
82 return d64_; | |
83 } | |
84 | |
85 // Returns the next greater double. Returns +infinity on input +infinity. | |
86 double NextDouble() const { | |
87 if (d64_ == kInfinity) return Double(kInfinity).value(); | |
88 if (Sign() < 0 && Significand() == 0) { | |
89 // -0.0 | |
90 return 0.0; | |
91 } | |
92 if (Sign() < 0) { | |
93 return Double(d64_ - 1).value(); | |
94 } else { | |
95 return Double(d64_ + 1).value(); | |
96 } | |
97 } | |
98 | |
99 int Exponent() const { | |
100 if (IsDenormal()) return kDenormalExponent; | |
101 | |
102 uint64_t d64 = AsUint64(); | |
103 int biased_e = | |
104 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); | |
105 return biased_e - kExponentBias; | |
106 } | |
107 | |
108 uint64_t Significand() const { | |
109 uint64_t d64 = AsUint64(); | |
110 uint64_t significand = d64 & kSignificandMask; | |
111 if (!IsDenormal()) { | |
112 return significand + kHiddenBit; | |
113 } else { | |
114 return significand; | |
115 } | |
116 } | |
117 | |
118 // Returns true if the double is a denormal. | |
119 bool IsDenormal() const { | |
120 uint64_t d64 = AsUint64(); | |
121 return (d64 & kExponentMask) == 0; | |
122 } | |
123 | |
124 // We consider denormals not to be special. | |
125 // Hence only Infinity and NaN are special. | |
126 bool IsSpecial() const { | |
127 uint64_t d64 = AsUint64(); | |
128 return (d64 & kExponentMask) == kExponentMask; | |
129 } | |
130 | |
131 bool IsNan() const { | |
132 uint64_t d64 = AsUint64(); | |
133 return ((d64 & kExponentMask) == kExponentMask) && | |
134 ((d64 & kSignificandMask) != 0); | |
135 } | |
136 | |
137 bool IsInfinite() const { | |
138 uint64_t d64 = AsUint64(); | |
139 return ((d64 & kExponentMask) == kExponentMask) && | |
140 ((d64 & kSignificandMask) == 0); | |
141 } | |
142 | |
143 int Sign() const { | |
144 uint64_t d64 = AsUint64(); | |
145 return (d64 & kSignMask) == 0? 1: -1; | |
146 } | |
147 | |
148 // Precondition: the value encoded by this Double must be greater or equal | |
149 // than +0.0. | |
150 DiyFp UpperBoundary() const { | |
151 ASSERT(Sign() > 0); | |
152 return DiyFp(Significand() * 2 + 1, Exponent() - 1); | |
153 } | |
154 | |
155 // Computes the two boundaries of this. | |
156 // The bigger boundary (m_plus) is normalized. The lower boundary has the same | |
157 // exponent as m_plus. | |
158 // Precondition: the value encoded by this Double must be greater than 0. | |
159 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { | |
160 ASSERT(value() > 0.0); | |
161 DiyFp v = this->AsDiyFp(); | |
162 bool significand_is_zero = (v.f() == kHiddenBit); | |
163 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); | |
164 DiyFp m_minus; | |
165 if (significand_is_zero && v.e() != kDenormalExponent) { | |
166 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9. | |
167 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but | |
168 // at a distance of 1e8. | |
169 // The only exception is for the smallest normal: the largest denormal is | |
170 // at the same distance as its successor. | |
171 // Note: denormals have the same exponent as the smallest normals. | |
172 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); | |
173 } else { | |
174 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); | |
175 } | |
176 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); | |
177 m_minus.set_e(m_plus.e()); | |
178 *out_m_plus = m_plus; | |
179 *out_m_minus = m_minus; | |
180 } | |
181 | |
182 double value() const { return uint64_to_double(d64_); } | |
183 | |
184 // Returns the significand size for a given order of magnitude. | |
185 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. | |
186 // This function returns the number of significant binary digits v will have | |
187 // once it's encoded into a double. In almost all cases this is equal to | |
188 // kSignificandSize. The only exceptions are denormals. They start with | |
189 // leading zeroes and their effective significand-size is hence smaller. | |
190 static int SignificandSizeForOrderOfMagnitude(int order) { | |
191 if (order >= (kDenormalExponent + kSignificandSize)) { | |
192 return kSignificandSize; | |
193 } | |
194 if (order <= kDenormalExponent) return 0; | |
195 return order - kDenormalExponent; | |
196 } | |
197 | |
198 static double Infinity() { | |
199 return Double(kInfinity).value(); | |
200 } | |
201 | |
202 static double NaN() { | |
203 return Double(kNaN).value(); | |
204 } | |
205 | |
206 private: | |
207 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; | |
208 static const int kDenormalExponent = -kExponentBias + 1; | |
209 static const int kMaxExponent = 0x7FF - kExponentBias; | |
210 static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000); | |
211 static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000); | |
212 | |
213 const uint64_t d64_; | |
214 | |
215 static uint64_t DiyFpToUint64(DiyFp diy_fp) { | |
216 uint64_t significand = diy_fp.f(); | |
217 int exponent = diy_fp.e(); | |
218 while (significand > kHiddenBit + kSignificandMask) { | |
219 significand >>= 1; | |
220 exponent++; | |
221 } | |
222 if (exponent >= kMaxExponent) { | |
223 return kInfinity; | |
224 } | |
225 if (exponent < kDenormalExponent) { | |
226 return 0; | |
227 } | |
228 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { | |
229 significand <<= 1; | |
230 exponent--; | |
231 } | |
232 uint64_t biased_exponent; | |
233 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { | |
234 biased_exponent = 0; | |
235 } else { | |
236 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); | |
237 } | |
238 return (significand & kSignificandMask) | | |
239 (biased_exponent << kPhysicalSignificandSize); | |
240 } | |
241 }; | |
242 | |
243 } // namespace double_conversion | |
244 | |
245 #endif // DOUBLE_CONVERSION_DOUBLE_H_ | |
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