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 | // |
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8 | // * Redistributions in binary form must reproduce the above |
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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 = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000); |
45 | static const uint64_t kExponentMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000); |
46 | static const uint64_t kSignificandMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x000FFFFF, FFFFFFFF); |
47 | static const uint64_t kHiddenBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00100000, 00000000); |
48 | static const uint64_t kQuietNanBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00080000, 00000000); |
49 | static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. |
50 | static const int kSignificandSize = 53; |
51 | static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; |
52 | static const int kMaxExponent = 0x7FF - kExponentBias; |
53 | |
54 | Double() : d64_(0) {} |
55 | explicit Double(double d) : d64_(double_to_uint64(d)) {} |
56 | explicit Double(uint64_t d64) : d64_(d64) {} |
57 | explicit Double(DiyFp diy_fp) |
58 | : d64_(DiyFpToUint64(diy_fp)) {} |
59 | |
60 | // The value encoded by this Double must be greater or equal to +0.0. |
61 | // It must not be special (infinity, or NaN). |
62 | DiyFp AsDiyFp() const { |
63 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
64 | DOUBLE_CONVERSION_ASSERT(!IsSpecial()); |
65 | return DiyFp(Significand(), Exponent()); |
66 | } |
67 | |
68 | // The value encoded by this Double must be strictly greater than 0. |
69 | DiyFp AsNormalizedDiyFp() const { |
70 | DOUBLE_CONVERSION_ASSERT(value() > 0.0); |
71 | uint64_t f = Significand(); |
72 | int e = Exponent(); |
73 | |
74 | // The current double could be a denormal. |
75 | while ((f & kHiddenBit) == 0) { |
76 | f <<= 1; |
77 | e--; |
78 | } |
79 | // Do the final shifts in one go. |
80 | f <<= DiyFp::kSignificandSize - kSignificandSize; |
81 | e -= DiyFp::kSignificandSize - kSignificandSize; |
82 | return DiyFp(f, e); |
83 | } |
84 | |
85 | // Returns the double's bit as uint64. |
86 | uint64_t AsUint64() const { |
87 | return d64_; |
88 | } |
89 | |
90 | // Returns the next greater double. Returns +infinity on input +infinity. |
91 | double NextDouble() const { |
92 | if (d64_ == kInfinity) return Double(kInfinity).value(); |
93 | if (Sign() < 0 && Significand() == 0) { |
94 | // -0.0 |
95 | return 0.0; |
96 | } |
97 | if (Sign() < 0) { |
98 | return Double(d64_ - 1).value(); |
99 | } else { |
100 | return Double(d64_ + 1).value(); |
101 | } |
102 | } |
103 | |
104 | double PreviousDouble() const { |
105 | if (d64_ == (kInfinity | kSignMask)) return -Infinity(); |
106 | if (Sign() < 0) { |
107 | return Double(d64_ + 1).value(); |
108 | } else { |
109 | if (Significand() == 0) return -0.0; |
110 | return Double(d64_ - 1).value(); |
111 | } |
112 | } |
113 | |
114 | int Exponent() const { |
115 | if (IsDenormal()) return kDenormalExponent; |
116 | |
117 | uint64_t d64 = AsUint64(); |
118 | int biased_e = |
119 | static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); |
120 | return biased_e - kExponentBias; |
121 | } |
122 | |
123 | uint64_t Significand() const { |
124 | uint64_t d64 = AsUint64(); |
125 | uint64_t significand = d64 & kSignificandMask; |
126 | if (!IsDenormal()) { |
127 | return significand + kHiddenBit; |
128 | } else { |
129 | return significand; |
130 | } |
131 | } |
132 | |
133 | // Returns true if the double is a denormal. |
134 | bool IsDenormal() const { |
135 | uint64_t d64 = AsUint64(); |
136 | return (d64 & kExponentMask) == 0; |
137 | } |
138 | |
139 | // We consider denormals not to be special. |
140 | // Hence only Infinity and NaN are special. |
141 | bool IsSpecial() const { |
142 | uint64_t d64 = AsUint64(); |
143 | return (d64 & kExponentMask) == kExponentMask; |
144 | } |
145 | |
146 | bool IsNan() const { |
147 | uint64_t d64 = AsUint64(); |
148 | return ((d64 & kExponentMask) == kExponentMask) && |
149 | ((d64 & kSignificandMask) != 0); |
150 | } |
151 | |
152 | bool IsQuietNan() const { |
153 | #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__) |
154 | return IsNan() && ((AsUint64() & kQuietNanBit) == 0); |
155 | #else |
156 | return IsNan() && ((AsUint64() & kQuietNanBit) != 0); |
157 | #endif |
158 | } |
159 | |
160 | bool IsSignalingNan() const { |
161 | #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__) |
162 | return IsNan() && ((AsUint64() & kQuietNanBit) != 0); |
163 | #else |
164 | return IsNan() && ((AsUint64() & kQuietNanBit) == 0); |
165 | #endif |
166 | } |
167 | |
168 | |
169 | bool IsInfinite() const { |
170 | uint64_t d64 = AsUint64(); |
171 | return ((d64 & kExponentMask) == kExponentMask) && |
172 | ((d64 & kSignificandMask) == 0); |
173 | } |
174 | |
175 | int Sign() const { |
176 | uint64_t d64 = AsUint64(); |
177 | return (d64 & kSignMask) == 0? 1: -1; |
178 | } |
179 | |
180 | // Precondition: the value encoded by this Double must be greater or equal |
181 | // than +0.0. |
182 | DiyFp UpperBoundary() const { |
183 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
184 | return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
185 | } |
186 | |
187 | // Computes the two boundaries of this. |
188 | // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
189 | // exponent as m_plus. |
190 | // Precondition: the value encoded by this Double must be greater than 0. |
191 | void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
192 | DOUBLE_CONVERSION_ASSERT(value() > 0.0); |
193 | DiyFp v = this->AsDiyFp(); |
194 | DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
195 | DiyFp m_minus; |
196 | if (LowerBoundaryIsCloser()) { |
197 | m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
198 | } else { |
199 | m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
200 | } |
201 | m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
202 | m_minus.set_e(m_plus.e()); |
203 | *out_m_plus = m_plus; |
204 | *out_m_minus = m_minus; |
205 | } |
206 | |
207 | bool LowerBoundaryIsCloser() const { |
208 | // The boundary is closer if the significand is of the form f == 2^p-1 then |
209 | // the lower boundary is closer. |
210 | // Think of v = 1000e10 and v- = 9999e9. |
211 | // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
212 | // at a distance of 1e8. |
213 | // The only exception is for the smallest normal: the largest denormal is |
214 | // at the same distance as its successor. |
215 | // Note: denormals have the same exponent as the smallest normals. |
216 | bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0); |
217 | return physical_significand_is_zero && (Exponent() != kDenormalExponent); |
218 | } |
219 | |
220 | double value() const { return uint64_to_double(d64_); } |
221 | |
222 | // Returns the significand size for a given order of magnitude. |
223 | // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. |
224 | // This function returns the number of significant binary digits v will have |
225 | // once it's encoded into a double. In almost all cases this is equal to |
226 | // kSignificandSize. The only exceptions are denormals. They start with |
227 | // leading zeroes and their effective significand-size is hence smaller. |
228 | static int SignificandSizeForOrderOfMagnitude(int order) { |
229 | if (order >= (kDenormalExponent + kSignificandSize)) { |
230 | return kSignificandSize; |
231 | } |
232 | if (order <= kDenormalExponent) return 0; |
233 | return order - kDenormalExponent; |
234 | } |
235 | |
236 | static double Infinity() { |
237 | return Double(kInfinity).value(); |
238 | } |
239 | |
240 | static double NaN() { |
241 | return Double(kNaN).value(); |
242 | } |
243 | |
244 | private: |
245 | static const int kDenormalExponent = -kExponentBias + 1; |
246 | static const uint64_t kInfinity = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000); |
247 | #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__) |
248 | static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF7FFFF, FFFFFFFF); |
249 | #else |
250 | static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF80000, 00000000); |
251 | #endif |
252 | |
253 | |
254 | const uint64_t d64_; |
255 | |
256 | static uint64_t DiyFpToUint64(DiyFp diy_fp) { |
257 | uint64_t significand = diy_fp.f(); |
258 | int exponent = diy_fp.e(); |
259 | while (significand > kHiddenBit + kSignificandMask) { |
260 | significand >>= 1; |
261 | exponent++; |
262 | } |
263 | if (exponent >= kMaxExponent) { |
264 | return kInfinity; |
265 | } |
266 | if (exponent < kDenormalExponent) { |
267 | return 0; |
268 | } |
269 | while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { |
270 | significand <<= 1; |
271 | exponent--; |
272 | } |
273 | uint64_t biased_exponent; |
274 | if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { |
275 | biased_exponent = 0; |
276 | } else { |
277 | biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); |
278 | } |
279 | return (significand & kSignificandMask) | |
280 | (biased_exponent << kPhysicalSignificandSize); |
281 | } |
282 | |
283 | DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Double); |
284 | }; |
285 | |
286 | class Single { |
287 | public: |
288 | static const uint32_t kSignMask = 0x80000000; |
289 | static const uint32_t kExponentMask = 0x7F800000; |
290 | static const uint32_t kSignificandMask = 0x007FFFFF; |
291 | static const uint32_t kHiddenBit = 0x00800000; |
292 | static const uint32_t kQuietNanBit = 0x00400000; |
293 | static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit. |
294 | static const int kSignificandSize = 24; |
295 | |
296 | Single() : d32_(0) {} |
297 | explicit Single(float f) : d32_(float_to_uint32(f)) {} |
298 | explicit Single(uint32_t d32) : d32_(d32) {} |
299 | |
300 | // The value encoded by this Single must be greater or equal to +0.0. |
301 | // It must not be special (infinity, or NaN). |
302 | DiyFp AsDiyFp() const { |
303 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
304 | DOUBLE_CONVERSION_ASSERT(!IsSpecial()); |
305 | return DiyFp(Significand(), Exponent()); |
306 | } |
307 | |
308 | // Returns the single's bit as uint64. |
309 | uint32_t AsUint32() const { |
310 | return d32_; |
311 | } |
312 | |
313 | int Exponent() const { |
314 | if (IsDenormal()) return kDenormalExponent; |
315 | |
316 | uint32_t d32 = AsUint32(); |
317 | int biased_e = |
318 | static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize); |
319 | return biased_e - kExponentBias; |
320 | } |
321 | |
322 | uint32_t Significand() const { |
323 | uint32_t d32 = AsUint32(); |
324 | uint32_t significand = d32 & kSignificandMask; |
325 | if (!IsDenormal()) { |
326 | return significand + kHiddenBit; |
327 | } else { |
328 | return significand; |
329 | } |
330 | } |
331 | |
332 | // Returns true if the single is a denormal. |
333 | bool IsDenormal() const { |
334 | uint32_t d32 = AsUint32(); |
335 | return (d32 & kExponentMask) == 0; |
336 | } |
337 | |
338 | // We consider denormals not to be special. |
339 | // Hence only Infinity and NaN are special. |
340 | bool IsSpecial() const { |
341 | uint32_t d32 = AsUint32(); |
342 | return (d32 & kExponentMask) == kExponentMask; |
343 | } |
344 | |
345 | bool IsNan() const { |
346 | uint32_t d32 = AsUint32(); |
347 | return ((d32 & kExponentMask) == kExponentMask) && |
348 | ((d32 & kSignificandMask) != 0); |
349 | } |
350 | |
351 | bool IsQuietNan() const { |
352 | #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__) |
353 | return IsNan() && ((AsUint32() & kQuietNanBit) == 0); |
354 | #else |
355 | return IsNan() && ((AsUint32() & kQuietNanBit) != 0); |
356 | #endif |
357 | } |
358 | |
359 | bool IsSignalingNan() const { |
360 | #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__) |
361 | return IsNan() && ((AsUint32() & kQuietNanBit) != 0); |
362 | #else |
363 | return IsNan() && ((AsUint32() & kQuietNanBit) == 0); |
364 | #endif |
365 | } |
366 | |
367 | |
368 | bool IsInfinite() const { |
369 | uint32_t d32 = AsUint32(); |
370 | return ((d32 & kExponentMask) == kExponentMask) && |
371 | ((d32 & kSignificandMask) == 0); |
372 | } |
373 | |
374 | int Sign() const { |
375 | uint32_t d32 = AsUint32(); |
376 | return (d32 & kSignMask) == 0? 1: -1; |
377 | } |
378 | |
379 | // Computes the two boundaries of this. |
380 | // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
381 | // exponent as m_plus. |
382 | // Precondition: the value encoded by this Single must be greater than 0. |
383 | void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
384 | DOUBLE_CONVERSION_ASSERT(value() > 0.0); |
385 | DiyFp v = this->AsDiyFp(); |
386 | DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
387 | DiyFp m_minus; |
388 | if (LowerBoundaryIsCloser()) { |
389 | m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
390 | } else { |
391 | m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
392 | } |
393 | m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
394 | m_minus.set_e(m_plus.e()); |
395 | *out_m_plus = m_plus; |
396 | *out_m_minus = m_minus; |
397 | } |
398 | |
399 | // Precondition: the value encoded by this Single must be greater or equal |
400 | // than +0.0. |
401 | DiyFp UpperBoundary() const { |
402 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
403 | return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
404 | } |
405 | |
406 | bool LowerBoundaryIsCloser() const { |
407 | // The boundary is closer if the significand is of the form f == 2^p-1 then |
408 | // the lower boundary is closer. |
409 | // Think of v = 1000e10 and v- = 9999e9. |
410 | // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
411 | // at a distance of 1e8. |
412 | // The only exception is for the smallest normal: the largest denormal is |
413 | // at the same distance as its successor. |
414 | // Note: denormals have the same exponent as the smallest normals. |
415 | bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0); |
416 | return physical_significand_is_zero && (Exponent() != kDenormalExponent); |
417 | } |
418 | |
419 | float value() const { return uint32_to_float(d32_); } |
420 | |
421 | static float Infinity() { |
422 | return Single(kInfinity).value(); |
423 | } |
424 | |
425 | static float NaN() { |
426 | return Single(kNaN).value(); |
427 | } |
428 | |
429 | private: |
430 | static const int kExponentBias = 0x7F + kPhysicalSignificandSize; |
431 | static const int kDenormalExponent = -kExponentBias + 1; |
432 | static const int kMaxExponent = 0xFF - kExponentBias; |
433 | static const uint32_t kInfinity = 0x7F800000; |
434 | #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__) |
435 | static const uint32_t kNaN = 0x7FBFFFFF; |
436 | #else |
437 | static const uint32_t kNaN = 0x7FC00000; |
438 | #endif |
439 | |
440 | const uint32_t d32_; |
441 | |
442 | DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Single); |
443 | }; |
444 | |
445 | } // namespace double_conversion |
446 | |
447 | #endif // DOUBLE_CONVERSION_DOUBLE_H_ |
448 | |