1// © 2018 and later: Unicode, Inc. and others.
2// License & terms of use: http://www.unicode.org/copyright.html
3//
4// From the double-conversion library. Original license:
5//
6// Copyright 2012 the V8 project authors. All rights reserved.
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8// modification, are permitted provided that the following conditions are
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32
33// ICU PATCH: ifdef around UCONFIG_NO_FORMATTING
34#include "unicode/utypes.h"
35#if !UCONFIG_NO_FORMATTING
36
37#ifndef DOUBLE_CONVERSION_DOUBLE_H_
38#define DOUBLE_CONVERSION_DOUBLE_H_
39
40// ICU PATCH: Customize header file paths for ICU.
41
42#include "double-conversion-diy-fp.h"
43
44// ICU PATCH: Wrap in ICU namespace
45U_NAMESPACE_BEGIN
46
47namespace double_conversion {
48
49// We assume that doubles and uint64_t have the same endianness.
50static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
51static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
52static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
53static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }
54
55// Helper functions for doubles.
56class Double {
57 public:
58 static const uint64_t kSignMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000);
59 static const uint64_t kExponentMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
60 static const uint64_t kSignificandMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
61 static const uint64_t kHiddenBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00100000, 00000000);
62 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
63 static const int kSignificandSize = 53;
64 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
65 static const int kMaxExponent = 0x7FF - kExponentBias;
66
67 Double() : d64_(0) {}
68 explicit Double(double d) : d64_(double_to_uint64(d)) {}
69 explicit Double(uint64_t d64) : d64_(d64) {}
70 explicit Double(DiyFp diy_fp)
71 : d64_(DiyFpToUint64(diy_fp)) {}
72
73 // The value encoded by this Double must be greater or equal to +0.0.
74 // It must not be special (infinity, or NaN).
75 DiyFp AsDiyFp() const {
76 DOUBLE_CONVERSION_ASSERT(Sign() > 0);
77 DOUBLE_CONVERSION_ASSERT(!IsSpecial());
78 return DiyFp(Significand(), Exponent());
79 }
80
81 // The value encoded by this Double must be strictly greater than 0.
82 DiyFp AsNormalizedDiyFp() const {
83 DOUBLE_CONVERSION_ASSERT(value() > 0.0);
84 uint64_t f = Significand();
85 int e = Exponent();
86
87 // The current double could be a denormal.
88 while ((f & kHiddenBit) == 0) {
89 f <<= 1;
90 e--;
91 }
92 // Do the final shifts in one go.
93 f <<= DiyFp::kSignificandSize - kSignificandSize;
94 e -= DiyFp::kSignificandSize - kSignificandSize;
95 return DiyFp(f, e);
96 }
97
98 // Returns the double's bit as uint64.
99 uint64_t AsUint64() const {
100 return d64_;
101 }
102
103 // Returns the next greater double. Returns +infinity on input +infinity.
104 double NextDouble() const {
105 if (d64_ == kInfinity) return Double(kInfinity).value();
106 if (Sign() < 0 && Significand() == 0) {
107 // -0.0
108 return 0.0;
109 }
110 if (Sign() < 0) {
111 return Double(d64_ - 1).value();
112 } else {
113 return Double(d64_ + 1).value();
114 }
115 }
116
117 double PreviousDouble() const {
118 if (d64_ == (kInfinity | kSignMask)) return -Infinity();
119 if (Sign() < 0) {
120 return Double(d64_ + 1).value();
121 } else {
122 if (Significand() == 0) return -0.0;
123 return Double(d64_ - 1).value();
124 }
125 }
126
127 int Exponent() const {
128 if (IsDenormal()) return kDenormalExponent;
129
130 uint64_t d64 = AsUint64();
131 int biased_e =
132 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
133 return biased_e - kExponentBias;
134 }
135
136 uint64_t Significand() const {
137 uint64_t d64 = AsUint64();
138 uint64_t significand = d64 & kSignificandMask;
139 if (!IsDenormal()) {
140 return significand + kHiddenBit;
141 } else {
142 return significand;
143 }
144 }
145
146 // Returns true if the double is a denormal.
147 bool IsDenormal() const {
148 uint64_t d64 = AsUint64();
149 return (d64 & kExponentMask) == 0;
150 }
151
152 // We consider denormals not to be special.
153 // Hence only Infinity and NaN are special.
154 bool IsSpecial() const {
155 uint64_t d64 = AsUint64();
156 return (d64 & kExponentMask) == kExponentMask;
157 }
158
159 bool IsNan() const {
160 uint64_t d64 = AsUint64();
161 return ((d64 & kExponentMask) == kExponentMask) &&
162 ((d64 & kSignificandMask) != 0);
163 }
164
165 bool IsInfinite() const {
166 uint64_t d64 = AsUint64();
167 return ((d64 & kExponentMask) == kExponentMask) &&
168 ((d64 & kSignificandMask) == 0);
169 }
170
171 int Sign() const {
172 uint64_t d64 = AsUint64();
173 return (d64 & kSignMask) == 0? 1: -1;
174 }
175
176 // Precondition: the value encoded by this Double must be greater or equal
177 // than +0.0.
178 DiyFp UpperBoundary() const {
179 DOUBLE_CONVERSION_ASSERT(Sign() > 0);
180 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
181 }
182
183 // Computes the two boundaries of this.
184 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
185 // exponent as m_plus.
186 // Precondition: the value encoded by this Double must be greater than 0.
187 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
188 DOUBLE_CONVERSION_ASSERT(value() > 0.0);
189 DiyFp v = this->AsDiyFp();
190 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
191 DiyFp m_minus;
192 if (LowerBoundaryIsCloser()) {
193 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
194 } else {
195 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
196 }
197 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
198 m_minus.set_e(m_plus.e());
199 *out_m_plus = m_plus;
200 *out_m_minus = m_minus;
201 }
202
203 bool LowerBoundaryIsCloser() const {
204 // The boundary is closer if the significand is of the form f == 2^p-1 then
205 // the lower boundary is closer.
206 // Think of v = 1000e10 and v- = 9999e9.
207 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
208 // at a distance of 1e8.
209 // The only exception is for the smallest normal: the largest denormal is
210 // at the same distance as its successor.
211 // Note: denormals have the same exponent as the smallest normals.
212 bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
213 return physical_significand_is_zero && (Exponent() != kDenormalExponent);
214 }
215
216 double value() const { return uint64_to_double(d64_); }
217
218 // Returns the significand size for a given order of magnitude.
219 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
220 // This function returns the number of significant binary digits v will have
221 // once it's encoded into a double. In almost all cases this is equal to
222 // kSignificandSize. The only exceptions are denormals. They start with
223 // leading zeroes and their effective significand-size is hence smaller.
224 static int SignificandSizeForOrderOfMagnitude(int order) {
225 if (order >= (kDenormalExponent + kSignificandSize)) {
226 return kSignificandSize;
227 }
228 if (order <= kDenormalExponent) return 0;
229 return order - kDenormalExponent;
230 }
231
232 static double Infinity() {
233 return Double(kInfinity).value();
234 }
235
236 static double NaN() {
237 return Double(kNaN).value();
238 }
239
240 private:
241 static const int kDenormalExponent = -kExponentBias + 1;
242 static const uint64_t kInfinity = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
243 static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF80000, 00000000);
244
245 const uint64_t d64_;
246
247 static uint64_t DiyFpToUint64(DiyFp diy_fp) {
248 uint64_t significand = diy_fp.f();
249 int exponent = diy_fp.e();
250 while (significand > kHiddenBit + kSignificandMask) {
251 significand >>= 1;
252 exponent++;
253 }
254 if (exponent >= kMaxExponent) {
255 return kInfinity;
256 }
257 if (exponent < kDenormalExponent) {
258 return 0;
259 }
260 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
261 significand <<= 1;
262 exponent--;
263 }
264 uint64_t biased_exponent;
265 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
266 biased_exponent = 0;
267 } else {
268 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
269 }
270 return (significand & kSignificandMask) |
271 (biased_exponent << kPhysicalSignificandSize);
272 }
273
274 DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Double);
275};
276
277class Single {
278 public:
279 static const uint32_t kSignMask = 0x80000000;
280 static const uint32_t kExponentMask = 0x7F800000;
281 static const uint32_t kSignificandMask = 0x007FFFFF;
282 static const uint32_t kHiddenBit = 0x00800000;
283 static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit.
284 static const int kSignificandSize = 24;
285
286 Single() : d32_(0) {}
287 explicit Single(float f) : d32_(float_to_uint32(f)) {}
288 explicit Single(uint32_t d32) : d32_(d32) {}
289
290 // The value encoded by this Single must be greater or equal to +0.0.
291 // It must not be special (infinity, or NaN).
292 DiyFp AsDiyFp() const {
293 DOUBLE_CONVERSION_ASSERT(Sign() > 0);
294 DOUBLE_CONVERSION_ASSERT(!IsSpecial());
295 return DiyFp(Significand(), Exponent());
296 }
297
298 // Returns the single's bit as uint64.
299 uint32_t AsUint32() const {
300 return d32_;
301 }
302
303 int Exponent() const {
304 if (IsDenormal()) return kDenormalExponent;
305
306 uint32_t d32 = AsUint32();
307 int biased_e =
308 static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize);
309 return biased_e - kExponentBias;
310 }
311
312 uint32_t Significand() const {
313 uint32_t d32 = AsUint32();
314 uint32_t significand = d32 & kSignificandMask;
315 if (!IsDenormal()) {
316 return significand + kHiddenBit;
317 } else {
318 return significand;
319 }
320 }
321
322 // Returns true if the single is a denormal.
323 bool IsDenormal() const {
324 uint32_t d32 = AsUint32();
325 return (d32 & kExponentMask) == 0;
326 }
327
328 // We consider denormals not to be special.
329 // Hence only Infinity and NaN are special.
330 bool IsSpecial() const {
331 uint32_t d32 = AsUint32();
332 return (d32 & kExponentMask) == kExponentMask;
333 }
334
335 bool IsNan() const {
336 uint32_t d32 = AsUint32();
337 return ((d32 & kExponentMask) == kExponentMask) &&
338 ((d32 & kSignificandMask) != 0);
339 }
340
341 bool IsInfinite() const {
342 uint32_t d32 = AsUint32();
343 return ((d32 & kExponentMask) == kExponentMask) &&
344 ((d32 & kSignificandMask) == 0);
345 }
346
347 int Sign() const {
348 uint32_t d32 = AsUint32();
349 return (d32 & kSignMask) == 0? 1: -1;
350 }
351
352 // Computes the two boundaries of this.
353 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
354 // exponent as m_plus.
355 // Precondition: the value encoded by this Single must be greater than 0.
356 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
357 DOUBLE_CONVERSION_ASSERT(value() > 0.0);
358 DiyFp v = this->AsDiyFp();
359 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
360 DiyFp m_minus;
361 if (LowerBoundaryIsCloser()) {
362 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
363 } else {
364 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
365 }
366 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
367 m_minus.set_e(m_plus.e());
368 *out_m_plus = m_plus;
369 *out_m_minus = m_minus;
370 }
371
372 // Precondition: the value encoded by this Single must be greater or equal
373 // than +0.0.
374 DiyFp UpperBoundary() const {
375 DOUBLE_CONVERSION_ASSERT(Sign() > 0);
376 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
377 }
378
379 bool LowerBoundaryIsCloser() const {
380 // The boundary is closer if the significand is of the form f == 2^p-1 then
381 // the lower boundary is closer.
382 // Think of v = 1000e10 and v- = 9999e9.
383 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
384 // at a distance of 1e8.
385 // The only exception is for the smallest normal: the largest denormal is
386 // at the same distance as its successor.
387 // Note: denormals have the same exponent as the smallest normals.
388 bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0);
389 return physical_significand_is_zero && (Exponent() != kDenormalExponent);
390 }
391
392 float value() const { return uint32_to_float(d32_); }
393
394 static float Infinity() {
395 return Single(kInfinity).value();
396 }
397
398 static float NaN() {
399 return Single(kNaN).value();
400 }
401
402 private:
403 static const int kExponentBias = 0x7F + kPhysicalSignificandSize;
404 static const int kDenormalExponent = -kExponentBias + 1;
405 static const int kMaxExponent = 0xFF - kExponentBias;
406 static const uint32_t kInfinity = 0x7F800000;
407 static const uint32_t kNaN = 0x7FC00000;
408
409 const uint32_t d32_;
410
411 DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Single);
412};
413
414} // namespace double_conversion
415
416// ICU PATCH: Close ICU namespace
417U_NAMESPACE_END
418
419#endif // DOUBLE_CONVERSION_DOUBLE_H_
420#endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING
421