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27
28#ifndef DOUBLE_CONVERSION_DOUBLE_H_
29#define DOUBLE_CONVERSION_DOUBLE_H_
30
31#include <double-conversion/diy-fp.h>
32
33namespace double_conversion {
34
35// We assume that doubles and uint64_t have the same endianness.
36static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
37static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
38static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
39static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }
40
41// Helper functions for doubles.
42class 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 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
51 static const int kMaxExponent = 0x7FF - kExponentBias;
52
53 Double() : d64_(0) {}
54 explicit Double(double d) : d64_(double_to_uint64(d)) {}
55 explicit Double(uint64_t d64) : d64_(d64) {}
56 explicit Double(DiyFp diy_fp)
57 : d64_(DiyFpToUint64(diy_fp)) {}
58
59 // The value encoded by this Double must be greater or equal to +0.0.
60 // It must not be special (infinity, or NaN).
61 DiyFp AsDiyFp() const {
62 ASSERT(Sign() > 0);
63 ASSERT(!IsSpecial());
64 return DiyFp(Significand(), Exponent());
65 }
66
67 // The value encoded by this Double must be strictly greater than 0.
68 DiyFp AsNormalizedDiyFp() const {
69 ASSERT(value() > 0.0);
70 uint64_t f = Significand();
71 int e = Exponent();
72
73 // The current double could be a denormal.
74 while ((f & kHiddenBit) == 0) {
75 f <<= 1;
76 e--;
77 }
78 // Do the final shifts in one go.
79 f <<= DiyFp::kSignificandSize - kSignificandSize;
80 e -= DiyFp::kSignificandSize - kSignificandSize;
81 return DiyFp(f, e);
82 }
83
84 // Returns the double's bit as uint64.
85 uint64_t AsUint64() const {
86 return d64_;
87 }
88
89 // Returns the next greater double. Returns +infinity on input +infinity.
90 double NextDouble() const {
91 if (d64_ == kInfinity) return Double(kInfinity).value();
92 if (Sign() < 0 && Significand() == 0) {
93 // -0.0
94 return 0.0;
95 }
96 if (Sign() < 0) {
97 return Double(d64_ - 1).value();
98 } else {
99 return Double(d64_ + 1).value();
100 }
101 }
102
103 double PreviousDouble() const {
104 if (d64_ == (kInfinity | kSignMask)) return -Infinity();
105 if (Sign() < 0) {
106 return Double(d64_ + 1).value();
107 } else {
108 if (Significand() == 0) return -0.0;
109 return Double(d64_ - 1).value();
110 }
111 }
112
113 int Exponent() const {
114 if (IsDenormal()) return kDenormalExponent;
115
116 uint64_t d64 = AsUint64();
117 int biased_e =
118 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
119 return biased_e - kExponentBias;
120 }
121
122 uint64_t Significand() const {
123 uint64_t d64 = AsUint64();
124 uint64_t significand = d64 & kSignificandMask;
125 if (!IsDenormal()) {
126 return significand + kHiddenBit;
127 } else {
128 return significand;
129 }
130 }
131
132 // Returns true if the double is a denormal.
133 bool IsDenormal() const {
134 uint64_t d64 = AsUint64();
135 return (d64 & kExponentMask) == 0;
136 }
137
138 // We consider denormals not to be special.
139 // Hence only Infinity and NaN are special.
140 bool IsSpecial() const {
141 uint64_t d64 = AsUint64();
142 return (d64 & kExponentMask) == kExponentMask;
143 }
144
145 bool IsNan() const {
146 uint64_t d64 = AsUint64();
147 return ((d64 & kExponentMask) == kExponentMask) &&
148 ((d64 & kSignificandMask) != 0);
149 }
150
151 bool IsInfinite() const {
152 uint64_t d64 = AsUint64();
153 return ((d64 & kExponentMask) == kExponentMask) &&
154 ((d64 & kSignificandMask) == 0);
155 }
156
157 int Sign() const {
158 uint64_t d64 = AsUint64();
159 return (d64 & kSignMask) == 0? 1: -1;
160 }
161
162 // Precondition: the value encoded by this Double must be greater or equal
163 // than +0.0.
164 DiyFp UpperBoundary() const {
165 ASSERT(Sign() > 0);
166 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
167 }
168
169 // Computes the two boundaries of this.
170 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
171 // exponent as m_plus.
172 // Precondition: the value encoded by this Double must be greater than 0.
173 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
174 ASSERT(value() > 0.0);
175 DiyFp v = this->AsDiyFp();
176 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
177 DiyFp m_minus;
178 if (LowerBoundaryIsCloser()) {
179 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
180 } else {
181 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
182 }
183 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
184 m_minus.set_e(m_plus.e());
185 *out_m_plus = m_plus;
186 *out_m_minus = m_minus;
187 }
188
189 bool LowerBoundaryIsCloser() const {
190 // The boundary is closer if the significand is of the form f == 2^p-1 then
191 // the lower boundary is closer.
192 // Think of v = 1000e10 and v- = 9999e9.
193 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
194 // at a distance of 1e8.
195 // The only exception is for the smallest normal: the largest denormal is
196 // at the same distance as its successor.
197 // Note: denormals have the same exponent as the smallest normals.
198 bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
199 return physical_significand_is_zero && (Exponent() != kDenormalExponent);
200 }
201
202 double value() const { return uint64_to_double(d64_); }
203
204 // Returns the significand size for a given order of magnitude.
205 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
206 // This function returns the number of significant binary digits v will have
207 // once it's encoded into a double. In almost all cases this is equal to
208 // kSignificandSize. The only exceptions are denormals. They start with
209 // leading zeroes and their effective significand-size is hence smaller.
210 static int SignificandSizeForOrderOfMagnitude(int order) {
211 if (order >= (kDenormalExponent + kSignificandSize)) {
212 return kSignificandSize;
213 }
214 if (order <= kDenormalExponent) return 0;
215 return order - kDenormalExponent;
216 }
217
218 static double Infinity() {
219 return Double(kInfinity).value();
220 }
221
222 static double NaN() {
223 return Double(kNaN).value();
224 }
225
226 private:
227 static const int kDenormalExponent = -kExponentBias + 1;
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 DC_DISALLOW_COPY_AND_ASSIGN(Double);
261};
262
263class Single {
264 public:
265 static const uint32_t kSignMask = 0x80000000;
266 static const uint32_t kExponentMask = 0x7F800000;
267 static const uint32_t kSignificandMask = 0x007FFFFF;
268 static const uint32_t kHiddenBit = 0x00800000;
269 static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit.
270 static const int kSignificandSize = 24;
271
272 Single() : d32_(0) {}
273 explicit Single(float f) : d32_(float_to_uint32(f)) {}
274 explicit Single(uint32_t d32) : d32_(d32) {}
275
276 // The value encoded by this Single must be greater or equal to +0.0.
277 // It must not be special (infinity, or NaN).
278 DiyFp AsDiyFp() const {
279 ASSERT(Sign() > 0);
280 ASSERT(!IsSpecial());
281 return DiyFp(Significand(), Exponent());
282 }
283
284 // Returns the single's bit as uint64.
285 uint32_t AsUint32() const {
286 return d32_;
287 }
288
289 int Exponent() const {
290 if (IsDenormal()) return kDenormalExponent;
291
292 uint32_t d32 = AsUint32();
293 int biased_e =
294 static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize);
295 return biased_e - kExponentBias;
296 }
297
298 uint32_t Significand() const {
299 uint32_t d32 = AsUint32();
300 uint32_t significand = d32 & kSignificandMask;
301 if (!IsDenormal()) {
302 return significand + kHiddenBit;
303 } else {
304 return significand;
305 }
306 }
307
308 // Returns true if the single is a denormal.
309 bool IsDenormal() const {
310 uint32_t d32 = AsUint32();
311 return (d32 & kExponentMask) == 0;
312 }
313
314 // We consider denormals not to be special.
315 // Hence only Infinity and NaN are special.
316 bool IsSpecial() const {
317 uint32_t d32 = AsUint32();
318 return (d32 & kExponentMask) == kExponentMask;
319 }
320
321 bool IsNan() const {
322 uint32_t d32 = AsUint32();
323 return ((d32 & kExponentMask) == kExponentMask) &&
324 ((d32 & kSignificandMask) != 0);
325 }
326
327 bool IsInfinite() const {
328 uint32_t d32 = AsUint32();
329 return ((d32 & kExponentMask) == kExponentMask) &&
330 ((d32 & kSignificandMask) == 0);
331 }
332
333 int Sign() const {
334 uint32_t d32 = AsUint32();
335 return (d32 & kSignMask) == 0? 1: -1;
336 }
337
338 // Computes the two boundaries of this.
339 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
340 // exponent as m_plus.
341 // Precondition: the value encoded by this Single must be greater than 0.
342 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
343 ASSERT(value() > 0.0);
344 DiyFp v = this->AsDiyFp();
345 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
346 DiyFp m_minus;
347 if (LowerBoundaryIsCloser()) {
348 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
349 } else {
350 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
351 }
352 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
353 m_minus.set_e(m_plus.e());
354 *out_m_plus = m_plus;
355 *out_m_minus = m_minus;
356 }
357
358 // Precondition: the value encoded by this Single must be greater or equal
359 // than +0.0.
360 DiyFp UpperBoundary() const {
361 ASSERT(Sign() > 0);
362 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
363 }
364
365 bool LowerBoundaryIsCloser() const {
366 // The boundary is closer if the significand is of the form f == 2^p-1 then
367 // the lower boundary is closer.
368 // Think of v = 1000e10 and v- = 9999e9.
369 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
370 // at a distance of 1e8.
371 // The only exception is for the smallest normal: the largest denormal is
372 // at the same distance as its successor.
373 // Note: denormals have the same exponent as the smallest normals.
374 bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0);
375 return physical_significand_is_zero && (Exponent() != kDenormalExponent);
376 }
377
378 float value() const { return uint32_to_float(d32_); }
379
380 static float Infinity() {
381 return Single(kInfinity).value();
382 }
383
384 static float NaN() {
385 return Single(kNaN).value();
386 }
387
388 private:
389 static const int kExponentBias = 0x7F + kPhysicalSignificandSize;
390 static const int kDenormalExponent = -kExponentBias + 1;
391 static const int kMaxExponent = 0xFF - kExponentBias;
392 static const uint32_t kInfinity = 0x7F800000;
393 static const uint32_t kNaN = 0x7FC00000;
394
395 const uint32_t d32_;
396
397 DC_DISALLOW_COPY_AND_ASSIGN(Single);
398};
399
400} // namespace double_conversion
401
402#endif // DOUBLE_CONVERSION_DOUBLE_H_
403