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mfbt/double-conversion/ieee.h

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1 // Copyright 2012 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 static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
39 static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }
40
41 // Helper functions for doubles.
42 class Double {
43 public:
44 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000);
45 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000);
46 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
47 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000);
48 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
49 static const int kSignificandSize = 53;
50
51 Double() : d64_(0) {}
52 explicit Double(double d) : d64_(double_to_uint64(d)) {}
53 explicit Double(uint64_t d64) : d64_(d64) {}
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).
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.
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.
83 uint64_t AsUint64() const {
84 return d64_;
85 }
86
87 // Returns the next greater double. Returns +infinity on input +infinity.
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
101 double PreviousDouble() const {
102 if (d64_ == (kInfinity | kSignMask)) return -Double::Infinity();
103 if (Sign() < 0) {
104 return Double(d64_ + 1).value();
105 } else {
106 if (Significand() == 0) return -0.0;
107 return Double(d64_ - 1).value();
108 }
109 }
110
111 int Exponent() const {
112 if (IsDenormal()) return kDenormalExponent;
113
114 uint64_t d64 = AsUint64();
115 int biased_e =
116 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
117 return biased_e - kExponentBias;
118 }
119
120 uint64_t Significand() const {
121 uint64_t d64 = AsUint64();
122 uint64_t significand = d64 & kSignificandMask;
123 if (!IsDenormal()) {
124 return significand + kHiddenBit;
125 } else {
126 return significand;
127 }
128 }
129
130 // Returns true if the double is a denormal.
131 bool IsDenormal() const {
132 uint64_t d64 = AsUint64();
133 return (d64 & kExponentMask) == 0;
134 }
135
136 // We consider denormals not to be special.
137 // Hence only Infinity and NaN are special.
138 bool IsSpecial() const {
139 uint64_t d64 = AsUint64();
140 return (d64 & kExponentMask) == kExponentMask;
141 }
142
143 bool IsNan() const {
144 uint64_t d64 = AsUint64();
145 return ((d64 & kExponentMask) == kExponentMask) &&
146 ((d64 & kSignificandMask) != 0);
147 }
148
149 bool IsInfinite() const {
150 uint64_t d64 = AsUint64();
151 return ((d64 & kExponentMask) == kExponentMask) &&
152 ((d64 & kSignificandMask) == 0);
153 }
154
155 int Sign() const {
156 uint64_t d64 = AsUint64();
157 return (d64 & kSignMask) == 0? 1: -1;
158 }
159
160 // Precondition: the value encoded by this Double must be greater or equal
161 // than +0.0.
162 DiyFp UpperBoundary() const {
163 ASSERT(Sign() > 0);
164 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
165 }
166
167 // Computes the two boundaries of this.
168 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
169 // exponent as m_plus.
170 // Precondition: the value encoded by this Double must be greater than 0.
171 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
172 ASSERT(value() > 0.0);
173 DiyFp v = this->AsDiyFp();
174 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
175 DiyFp m_minus;
176 if (LowerBoundaryIsCloser()) {
177 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
178 } else {
179 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
180 }
181 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
182 m_minus.set_e(m_plus.e());
183 *out_m_plus = m_plus;
184 *out_m_minus = m_minus;
185 }
186
187 bool LowerBoundaryIsCloser() const {
188 // The boundary is closer if the significand is of the form f == 2^p-1 then
189 // the lower boundary is closer.
190 // Think of v = 1000e10 and v- = 9999e9.
191 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
192 // at a distance of 1e8.
193 // The only exception is for the smallest normal: the largest denormal is
194 // at the same distance as its successor.
195 // Note: denormals have the same exponent as the smallest normals.
196 bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
197 return physical_significand_is_zero && (Exponent() != kDenormalExponent);
198 }
199
200 double value() const { return uint64_to_double(d64_); }
201
202 // Returns the significand size for a given order of magnitude.
203 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
204 // This function returns the number of significant binary digits v will have
205 // once it's encoded into a double. In almost all cases this is equal to
206 // kSignificandSize. The only exceptions are denormals. They start with
207 // leading zeroes and their effective significand-size is hence smaller.
208 static int SignificandSizeForOrderOfMagnitude(int order) {
209 if (order >= (kDenormalExponent + kSignificandSize)) {
210 return kSignificandSize;
211 }
212 if (order <= kDenormalExponent) return 0;
213 return order - kDenormalExponent;
214 }
215
216 static double Infinity() {
217 return Double(kInfinity).value();
218 }
219
220 static double NaN() {
221 return Double(kNaN).value();
222 }
223
224 private:
225 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
226 static const int kDenormalExponent = -kExponentBias + 1;
227 static const int kMaxExponent = 0x7FF - kExponentBias;
228 static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000);
229 static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000);
230
231 const uint64_t d64_;
232
233 static uint64_t DiyFpToUint64(DiyFp diy_fp) {
234 uint64_t significand = diy_fp.f();
235 int exponent = diy_fp.e();
236 while (significand > kHiddenBit + kSignificandMask) {
237 significand >>= 1;
238 exponent++;
239 }
240 if (exponent >= kMaxExponent) {
241 return kInfinity;
242 }
243 if (exponent < kDenormalExponent) {
244 return 0;
245 }
246 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
247 significand <<= 1;
248 exponent--;
249 }
250 uint64_t biased_exponent;
251 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
252 biased_exponent = 0;
253 } else {
254 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
255 }
256 return (significand & kSignificandMask) |
257 (biased_exponent << kPhysicalSignificandSize);
258 }
259 };
260
261 class Single {
262 public:
263 static const uint32_t kSignMask = 0x80000000;
264 static const uint32_t kExponentMask = 0x7F800000;
265 static const uint32_t kSignificandMask = 0x007FFFFF;
266 static const uint32_t kHiddenBit = 0x00800000;
267 static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit.
268 static const int kSignificandSize = 24;
269
270 Single() : d32_(0) {}
271 explicit Single(float f) : d32_(float_to_uint32(f)) {}
272 explicit Single(uint32_t d32) : d32_(d32) {}
273
274 // The value encoded by this Single must be greater or equal to +0.0.
275 // It must not be special (infinity, or NaN).
276 DiyFp AsDiyFp() const {
277 ASSERT(Sign() > 0);
278 ASSERT(!IsSpecial());
279 return DiyFp(Significand(), Exponent());
280 }
281
282 // Returns the single's bit as uint64.
283 uint32_t AsUint32() const {
284 return d32_;
285 }
286
287 int Exponent() const {
288 if (IsDenormal()) return kDenormalExponent;
289
290 uint32_t d32 = AsUint32();
291 int biased_e =
292 static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize);
293 return biased_e - kExponentBias;
294 }
295
296 uint32_t Significand() const {
297 uint32_t d32 = AsUint32();
298 uint32_t significand = d32 & kSignificandMask;
299 if (!IsDenormal()) {
300 return significand + kHiddenBit;
301 } else {
302 return significand;
303 }
304 }
305
306 // Returns true if the single is a denormal.
307 bool IsDenormal() const {
308 uint32_t d32 = AsUint32();
309 return (d32 & kExponentMask) == 0;
310 }
311
312 // We consider denormals not to be special.
313 // Hence only Infinity and NaN are special.
314 bool IsSpecial() const {
315 uint32_t d32 = AsUint32();
316 return (d32 & kExponentMask) == kExponentMask;
317 }
318
319 bool IsNan() const {
320 uint32_t d32 = AsUint32();
321 return ((d32 & kExponentMask) == kExponentMask) &&
322 ((d32 & kSignificandMask) != 0);
323 }
324
325 bool IsInfinite() const {
326 uint32_t d32 = AsUint32();
327 return ((d32 & kExponentMask) == kExponentMask) &&
328 ((d32 & kSignificandMask) == 0);
329 }
330
331 int Sign() const {
332 uint32_t d32 = AsUint32();
333 return (d32 & kSignMask) == 0? 1: -1;
334 }
335
336 // Computes the two boundaries of this.
337 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
338 // exponent as m_plus.
339 // Precondition: the value encoded by this Single must be greater than 0.
340 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
341 ASSERT(value() > 0.0);
342 DiyFp v = this->AsDiyFp();
343 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
344 DiyFp m_minus;
345 if (LowerBoundaryIsCloser()) {
346 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
347 } else {
348 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
349 }
350 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
351 m_minus.set_e(m_plus.e());
352 *out_m_plus = m_plus;
353 *out_m_minus = m_minus;
354 }
355
356 // Precondition: the value encoded by this Single must be greater or equal
357 // than +0.0.
358 DiyFp UpperBoundary() const {
359 ASSERT(Sign() > 0);
360 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
361 }
362
363 bool LowerBoundaryIsCloser() const {
364 // The boundary is closer if the significand is of the form f == 2^p-1 then
365 // the lower boundary is closer.
366 // Think of v = 1000e10 and v- = 9999e9.
367 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
368 // at a distance of 1e8.
369 // The only exception is for the smallest normal: the largest denormal is
370 // at the same distance as its successor.
371 // Note: denormals have the same exponent as the smallest normals.
372 bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0);
373 return physical_significand_is_zero && (Exponent() != kDenormalExponent);
374 }
375
376 float value() const { return uint32_to_float(d32_); }
377
378 static float Infinity() {
379 return Single(kInfinity).value();
380 }
381
382 static float NaN() {
383 return Single(kNaN).value();
384 }
385
386 private:
387 static const int kExponentBias = 0x7F + kPhysicalSignificandSize;
388 static const int kDenormalExponent = -kExponentBias + 1;
389 static const int kMaxExponent = 0xFF - kExponentBias;
390 static const uint32_t kInfinity = 0x7F800000;
391 static const uint32_t kNaN = 0x7FC00000;
392
393 const uint32_t d32_;
394 };
395
396 } // namespace double_conversion
397
398 #endif // DOUBLE_CONVERSION_DOUBLE_H_

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