summaryrefslogtreecommitdiffstats
path: root/src/3rdparty/double-conversion/double-conversion/ieee.h
blob: 3c2a5979ffee017419d751f3dbb7950c3077e682 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
// Copyright 2012 the V8 project authors. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
//     * Redistributions of source code must retain the above copyright
//       notice, this list of conditions and the following disclaimer.
//     * Redistributions in binary form must reproduce the above
//       copyright notice, this list of conditions and the following
//       disclaimer in the documentation and/or other materials provided
//       with the distribution.
//     * Neither the name of Google Inc. nor the names of its
//       contributors may be used to endorse or promote products derived
//       from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

#ifndef DOUBLE_CONVERSION_DOUBLE_H_
#define DOUBLE_CONVERSION_DOUBLE_H_

#include "diy-fp.h"

namespace double_conversion {

// We assume that doubles and uint64_t have the same endianness.
static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }

// Helper functions for doubles.
class Double {
 public:
  static const uint64_t kSignMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000);
  static const uint64_t kExponentMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
  static const uint64_t kSignificandMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
  static const uint64_t kHiddenBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00100000, 00000000);
  static const uint64_t kQuietNanBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00080000, 00000000);
  static const int kPhysicalSignificandSize = 52;  // Excludes the hidden bit.
  static const int kSignificandSize = 53;
  static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
  static const int kMaxExponent = 0x7FF - kExponentBias;

  Double() : d64_(0) {}
  explicit Double(double d) : d64_(double_to_uint64(d)) {}
  explicit Double(uint64_t d64) : d64_(d64) {}
  explicit Double(DiyFp diy_fp)
    : d64_(DiyFpToUint64(diy_fp)) {}

  // The value encoded by this Double must be greater or equal to +0.0.
  // It must not be special (infinity, or NaN).
  DiyFp AsDiyFp() const {
    DOUBLE_CONVERSION_ASSERT(Sign() > 0);
    DOUBLE_CONVERSION_ASSERT(!IsSpecial());
    return DiyFp(Significand(), Exponent());
  }

  // The value encoded by this Double must be strictly greater than 0.
  DiyFp AsNormalizedDiyFp() const {
    DOUBLE_CONVERSION_ASSERT(value() > 0.0);
    uint64_t f = Significand();
    int e = Exponent();

    // The current double could be a denormal.
    while ((f & kHiddenBit) == 0) {
      f <<= 1;
      e--;
    }
    // Do the final shifts in one go.
    f <<= DiyFp::kSignificandSize - kSignificandSize;
    e -= DiyFp::kSignificandSize - kSignificandSize;
    return DiyFp(f, e);
  }

  // Returns the double's bit as uint64.
  uint64_t AsUint64() const {
    return d64_;
  }

  // Returns the next greater double. Returns +infinity on input +infinity.
  double NextDouble() const {
    if (d64_ == kInfinity) return Double(kInfinity).value();
    if (Sign() < 0 && Significand() == 0) {
      // -0.0
      return 0.0;
    }
    if (Sign() < 0) {
      return Double(d64_ - 1).value();
    } else {
      return Double(d64_ + 1).value();
    }
  }

  double PreviousDouble() const {
    if (d64_ == (kInfinity | kSignMask)) return -Infinity();
    if (Sign() < 0) {
      return Double(d64_ + 1).value();
    } else {
      if (Significand() == 0) return -0.0;
      return Double(d64_ - 1).value();
    }
  }

  int Exponent() const {
    if (IsDenormal()) return kDenormalExponent;

    uint64_t d64 = AsUint64();
    int biased_e =
        static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
    return biased_e - kExponentBias;
  }

  uint64_t Significand() const {
    uint64_t d64 = AsUint64();
    uint64_t significand = d64 & kSignificandMask;
    if (!IsDenormal()) {
      return significand + kHiddenBit;
    } else {
      return significand;
    }
  }

  // Returns true if the double is a denormal.
  bool IsDenormal() const {
    uint64_t d64 = AsUint64();
    return (d64 & kExponentMask) == 0;
  }

  // We consider denormals not to be special.
  // Hence only Infinity and NaN are special.
  bool IsSpecial() const {
    uint64_t d64 = AsUint64();
    return (d64 & kExponentMask) == kExponentMask;
  }

  bool IsNan() const {
    uint64_t d64 = AsUint64();
    return ((d64 & kExponentMask) == kExponentMask) &&
        ((d64 & kSignificandMask) != 0);
  }

  bool IsQuietNan() const {
    return IsNan() && ((AsUint64() & kQuietNanBit) != 0);
  }

  bool IsSignalingNan() const {
    return IsNan() && ((AsUint64() & kQuietNanBit) == 0);
  }


  bool IsInfinite() const {
    uint64_t d64 = AsUint64();
    return ((d64 & kExponentMask) == kExponentMask) &&
        ((d64 & kSignificandMask) == 0);
  }

  int Sign() const {
    uint64_t d64 = AsUint64();
    return (d64 & kSignMask) == 0? 1: -1;
  }

  // Precondition: the value encoded by this Double must be greater or equal
  // than +0.0.
  DiyFp UpperBoundary() const {
    DOUBLE_CONVERSION_ASSERT(Sign() > 0);
    return DiyFp(Significand() * 2 + 1, Exponent() - 1);
  }

  // Computes the two boundaries of this.
  // The bigger boundary (m_plus) is normalized. The lower boundary has the same
  // exponent as m_plus.
  // Precondition: the value encoded by this Double must be greater than 0.
  void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
    DOUBLE_CONVERSION_ASSERT(value() > 0.0);
    DiyFp v = this->AsDiyFp();
    DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
    DiyFp m_minus;
    if (LowerBoundaryIsCloser()) {
      m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
    } else {
      m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
    }
    m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
    m_minus.set_e(m_plus.e());
    *out_m_plus = m_plus;
    *out_m_minus = m_minus;
  }

  bool LowerBoundaryIsCloser() const {
    // The boundary is closer if the significand is of the form f == 2^p-1 then
    // the lower boundary is closer.
    // Think of v = 1000e10 and v- = 9999e9.
    // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
    // at a distance of 1e8.
    // The only exception is for the smallest normal: the largest denormal is
    // at the same distance as its successor.
    // Note: denormals have the same exponent as the smallest normals.
    bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
    return physical_significand_is_zero && (Exponent() != kDenormalExponent);
  }

  double value() const { return uint64_to_double(d64_); }

  // Returns the significand size for a given order of magnitude.
  // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
  // This function returns the number of significant binary digits v will have
  // once it's encoded into a double. In almost all cases this is equal to
  // kSignificandSize. The only exceptions are denormals. They start with
  // leading zeroes and their effective significand-size is hence smaller.
  static int SignificandSizeForOrderOfMagnitude(int order) {
    if (order >= (kDenormalExponent + kSignificandSize)) {
      return kSignificandSize;
    }
    if (order <= kDenormalExponent) return 0;
    return order - kDenormalExponent;
  }

  static double Infinity() {
    return Double(kInfinity).value();
  }

  static double NaN() {
    return Double(kNaN).value();
  }

 private:
  static const int kDenormalExponent = -kExponentBias + 1;
  static const uint64_t kInfinity = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
  static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF80000, 00000000);

  const uint64_t d64_;

  static uint64_t DiyFpToUint64(DiyFp diy_fp) {
    uint64_t significand = diy_fp.f();
    int exponent = diy_fp.e();
    while (significand > kHiddenBit + kSignificandMask) {
      significand >>= 1;
      exponent++;
    }
    if (exponent >= kMaxExponent) {
      return kInfinity;
    }
    if (exponent < kDenormalExponent) {
      return 0;
    }
    while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
      significand <<= 1;
      exponent--;
    }
    uint64_t biased_exponent;
    if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
      biased_exponent = 0;
    } else {
      biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
    }
    return (significand & kSignificandMask) |
        (biased_exponent << kPhysicalSignificandSize);
  }

  DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Double);
};

class Single {
 public:
  static const uint32_t kSignMask = 0x80000000;
  static const uint32_t kExponentMask = 0x7F800000;
  static const uint32_t kSignificandMask = 0x007FFFFF;
  static const uint32_t kHiddenBit = 0x00800000;
  static const uint32_t kQuietNanBit = 0x00400000;
  static const int kPhysicalSignificandSize = 23;  // Excludes the hidden bit.
  static const int kSignificandSize = 24;

  Single() : d32_(0) {}
  explicit Single(float f) : d32_(float_to_uint32(f)) {}
  explicit Single(uint32_t d32) : d32_(d32) {}

  // The value encoded by this Single must be greater or equal to +0.0.
  // It must not be special (infinity, or NaN).
  DiyFp AsDiyFp() const {
    DOUBLE_CONVERSION_ASSERT(Sign() > 0);
    DOUBLE_CONVERSION_ASSERT(!IsSpecial());
    return DiyFp(Significand(), Exponent());
  }

  // Returns the single's bit as uint64.
  uint32_t AsUint32() const {
    return d32_;
  }

  int Exponent() const {
    if (IsDenormal()) return kDenormalExponent;

    uint32_t d32 = AsUint32();
    int biased_e =
        static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize);
    return biased_e - kExponentBias;
  }

  uint32_t Significand() const {
    uint32_t d32 = AsUint32();
    uint32_t significand = d32 & kSignificandMask;
    if (!IsDenormal()) {
      return significand + kHiddenBit;
    } else {
      return significand;
    }
  }

  // Returns true if the single is a denormal.
  bool IsDenormal() const {
    uint32_t d32 = AsUint32();
    return (d32 & kExponentMask) == 0;
  }

  // We consider denormals not to be special.
  // Hence only Infinity and NaN are special.
  bool IsSpecial() const {
    uint32_t d32 = AsUint32();
    return (d32 & kExponentMask) == kExponentMask;
  }

  bool IsNan() const {
    uint32_t d32 = AsUint32();
    return ((d32 & kExponentMask) == kExponentMask) &&
        ((d32 & kSignificandMask) != 0);
  }

  bool IsQuietNan() const {
    return IsNan() && ((AsUint32() & kQuietNanBit) != 0);
  }

  bool IsSignalingNan() const {
    return IsNan() && ((AsUint32() & kQuietNanBit) == 0);
  }


  bool IsInfinite() const {
    uint32_t d32 = AsUint32();
    return ((d32 & kExponentMask) == kExponentMask) &&
        ((d32 & kSignificandMask) == 0);
  }

  int Sign() const {
    uint32_t d32 = AsUint32();
    return (d32 & kSignMask) == 0? 1: -1;
  }

  // Computes the two boundaries of this.
  // The bigger boundary (m_plus) is normalized. The lower boundary has the same
  // exponent as m_plus.
  // Precondition: the value encoded by this Single must be greater than 0.
  void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
    DOUBLE_CONVERSION_ASSERT(value() > 0.0);
    DiyFp v = this->AsDiyFp();
    DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
    DiyFp m_minus;
    if (LowerBoundaryIsCloser()) {
      m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
    } else {
      m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
    }
    m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
    m_minus.set_e(m_plus.e());
    *out_m_plus = m_plus;
    *out_m_minus = m_minus;
  }

  // Precondition: the value encoded by this Single must be greater or equal
  // than +0.0.
  DiyFp UpperBoundary() const {
    DOUBLE_CONVERSION_ASSERT(Sign() > 0);
    return DiyFp(Significand() * 2 + 1, Exponent() - 1);
  }

  bool LowerBoundaryIsCloser() const {
    // The boundary is closer if the significand is of the form f == 2^p-1 then
    // the lower boundary is closer.
    // Think of v = 1000e10 and v- = 9999e9.
    // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
    // at a distance of 1e8.
    // The only exception is for the smallest normal: the largest denormal is
    // at the same distance as its successor.
    // Note: denormals have the same exponent as the smallest normals.
    bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0);
    return physical_significand_is_zero && (Exponent() != kDenormalExponent);
  }

  float value() const { return uint32_to_float(d32_); }

  static float Infinity() {
    return Single(kInfinity).value();
  }

  static float NaN() {
    return Single(kNaN).value();
  }

 private:
  static const int kExponentBias = 0x7F + kPhysicalSignificandSize;
  static const int kDenormalExponent = -kExponentBias + 1;
  static const int kMaxExponent = 0xFF - kExponentBias;
  static const uint32_t kInfinity = 0x7F800000;
  static const uint32_t kNaN = 0x7FC00000;

  const uint32_t d32_;

  DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Single);
};

}  // namespace double_conversion

#endif  // DOUBLE_CONVERSION_DOUBLE_H_