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27
28#ifndef DOUBLE_CONVERSION_DOUBLE_H_
29#define DOUBLE_CONVERSION_DOUBLE_H_
30
31#include "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
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 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 DISALLOW_COPY_AND_ASSIGN(Single);
398};
399
400} // namespace double_conversion
401
402#endif // DOUBLE_CONVERSION_DOUBLE_H_
403