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.
7 // Redistribution and use in source and binary forms, with or without
8 // modification, are permitted provided that the following conditions are
9 // met:
10 //
11 // * Redistributions of source code must retain the above copyright
12 // notice, this list of conditions and the following disclaimer.
13 // * Redistributions in binary form must reproduce the above
14 // copyright notice, this list of conditions and the following
15 // disclaimer in the documentation and/or other materials provided
16 // with the distribution.
17 // * Neither the name of Google Inc. nor the names of its
18 // contributors may be used to endorse or promote products derived
19 // from this software without specific prior written permission.
20 //
21 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
22 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
23 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
24 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
25 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
26 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
27 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
28 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
29 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
30 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
31 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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
45 U_NAMESPACE_BEGIN
46
47 namespace double_conversion {
48
49 // We assume that doubles and uint64_t have the same endianness.
double_to_uint64(double d)50 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
uint64_to_double(uint64_t d64)51 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
float_to_uint32(float f)52 static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
uint32_to_float(uint32_t d32)53 static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }
54
55 // Helper functions for doubles.
56 class Double {
57 public:
58 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000);
59 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000);
60 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
61 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000);
62 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
63 static const int kSignificandSize = 53;
64
Double()65 Double() : d64_(0) {}
Double(double d)66 explicit Double(double d) : d64_(double_to_uint64(d)) {}
Double(uint64_t d64)67 explicit Double(uint64_t d64) : d64_(d64) {}
Double(DiyFp diy_fp)68 explicit Double(DiyFp diy_fp)
69 : d64_(DiyFpToUint64(diy_fp)) {}
70
71 // The value encoded by this Double must be greater or equal to +0.0.
72 // It must not be special (infinity, or NaN).
AsDiyFp()73 DiyFp AsDiyFp() const {
74 ASSERT(Sign() > 0);
75 ASSERT(!IsSpecial());
76 return DiyFp(Significand(), Exponent());
77 }
78
79 // The value encoded by this Double must be strictly greater than 0.
AsNormalizedDiyFp()80 DiyFp AsNormalizedDiyFp() const {
81 ASSERT(value() > 0.0);
82 uint64_t f = Significand();
83 int e = Exponent();
84
85 // The current double could be a denormal.
86 while ((f & kHiddenBit) == 0) {
87 f <<= 1;
88 e--;
89 }
90 // Do the final shifts in one go.
91 f <<= DiyFp::kSignificandSize - kSignificandSize;
92 e -= DiyFp::kSignificandSize - kSignificandSize;
93 return DiyFp(f, e);
94 }
95
96 // Returns the double's bit as uint64.
AsUint64()97 uint64_t AsUint64() const {
98 return d64_;
99 }
100
101 // Returns the next greater double. Returns +infinity on input +infinity.
NextDouble()102 double NextDouble() const {
103 if (d64_ == kInfinity) return Double(kInfinity).value();
104 if (Sign() < 0 && Significand() == 0) {
105 // -0.0
106 return 0.0;
107 }
108 if (Sign() < 0) {
109 return Double(d64_ - 1).value();
110 } else {
111 return Double(d64_ + 1).value();
112 }
113 }
114
PreviousDouble()115 double PreviousDouble() const {
116 if (d64_ == (kInfinity | kSignMask)) return -Infinity();
117 if (Sign() < 0) {
118 return Double(d64_ + 1).value();
119 } else {
120 if (Significand() == 0) return -0.0;
121 return Double(d64_ - 1).value();
122 }
123 }
124
Exponent()125 int Exponent() const {
126 if (IsDenormal()) return kDenormalExponent;
127
128 uint64_t d64 = AsUint64();
129 int biased_e =
130 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
131 return biased_e - kExponentBias;
132 }
133
Significand()134 uint64_t Significand() const {
135 uint64_t d64 = AsUint64();
136 uint64_t significand = d64 & kSignificandMask;
137 if (!IsDenormal()) {
138 return significand + kHiddenBit;
139 } else {
140 return significand;
141 }
142 }
143
144 // Returns true if the double is a denormal.
IsDenormal()145 bool IsDenormal() const {
146 uint64_t d64 = AsUint64();
147 return (d64 & kExponentMask) == 0;
148 }
149
150 // We consider denormals not to be special.
151 // Hence only Infinity and NaN are special.
IsSpecial()152 bool IsSpecial() const {
153 uint64_t d64 = AsUint64();
154 return (d64 & kExponentMask) == kExponentMask;
155 }
156
IsNan()157 bool IsNan() const {
158 uint64_t d64 = AsUint64();
159 return ((d64 & kExponentMask) == kExponentMask) &&
160 ((d64 & kSignificandMask) != 0);
161 }
162
IsInfinite()163 bool IsInfinite() const {
164 uint64_t d64 = AsUint64();
165 return ((d64 & kExponentMask) == kExponentMask) &&
166 ((d64 & kSignificandMask) == 0);
167 }
168
Sign()169 int Sign() const {
170 uint64_t d64 = AsUint64();
171 return (d64 & kSignMask) == 0? 1: -1;
172 }
173
174 // Precondition: the value encoded by this Double must be greater or equal
175 // than +0.0.
UpperBoundary()176 DiyFp UpperBoundary() const {
177 ASSERT(Sign() > 0);
178 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
179 }
180
181 // Computes the two boundaries of this.
182 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
183 // exponent as m_plus.
184 // Precondition: the value encoded by this Double must be greater than 0.
NormalizedBoundaries(DiyFp * out_m_minus,DiyFp * out_m_plus)185 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
186 ASSERT(value() > 0.0);
187 DiyFp v = this->AsDiyFp();
188 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
189 DiyFp m_minus;
190 if (LowerBoundaryIsCloser()) {
191 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
192 } else {
193 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
194 }
195 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
196 m_minus.set_e(m_plus.e());
197 *out_m_plus = m_plus;
198 *out_m_minus = m_minus;
199 }
200
LowerBoundaryIsCloser()201 bool LowerBoundaryIsCloser() const {
202 // The boundary is closer if the significand is of the form f == 2^p-1 then
203 // the lower boundary is closer.
204 // Think of v = 1000e10 and v- = 9999e9.
205 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
206 // at a distance of 1e8.
207 // The only exception is for the smallest normal: the largest denormal is
208 // at the same distance as its successor.
209 // Note: denormals have the same exponent as the smallest normals.
210 bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
211 return physical_significand_is_zero && (Exponent() != kDenormalExponent);
212 }
213
value()214 double value() const { return uint64_to_double(d64_); }
215
216 // Returns the significand size for a given order of magnitude.
217 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
218 // This function returns the number of significant binary digits v will have
219 // once it's encoded into a double. In almost all cases this is equal to
220 // kSignificandSize. The only exceptions are denormals. They start with
221 // leading zeroes and their effective significand-size is hence smaller.
SignificandSizeForOrderOfMagnitude(int order)222 static int SignificandSizeForOrderOfMagnitude(int order) {
223 if (order >= (kDenormalExponent + kSignificandSize)) {
224 return kSignificandSize;
225 }
226 if (order <= kDenormalExponent) return 0;
227 return order - kDenormalExponent;
228 }
229
Infinity()230 static double Infinity() {
231 return Double(kInfinity).value();
232 }
233
NaN()234 static double NaN() {
235 return Double(kNaN).value();
236 }
237
238 private:
239 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
240 static const int kDenormalExponent = -kExponentBias + 1;
241 static const int kMaxExponent = 0x7FF - kExponentBias;
242 static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000);
243 static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000);
244
245 const uint64_t d64_;
246
DiyFpToUint64(DiyFp diy_fp)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 DISALLOW_COPY_AND_ASSIGN(Double);
275 };
276
277 class 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
Single()286 Single() : d32_(0) {}
Single(float f)287 explicit Single(float f) : d32_(float_to_uint32(f)) {}
Single(uint32_t d32)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).
AsDiyFp()292 DiyFp AsDiyFp() const {
293 ASSERT(Sign() > 0);
294 ASSERT(!IsSpecial());
295 return DiyFp(Significand(), Exponent());
296 }
297
298 // Returns the single's bit as uint64.
AsUint32()299 uint32_t AsUint32() const {
300 return d32_;
301 }
302
Exponent()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
Significand()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.
IsDenormal()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.
IsSpecial()330 bool IsSpecial() const {
331 uint32_t d32 = AsUint32();
332 return (d32 & kExponentMask) == kExponentMask;
333 }
334
IsNan()335 bool IsNan() const {
336 uint32_t d32 = AsUint32();
337 return ((d32 & kExponentMask) == kExponentMask) &&
338 ((d32 & kSignificandMask) != 0);
339 }
340
IsInfinite()341 bool IsInfinite() const {
342 uint32_t d32 = AsUint32();
343 return ((d32 & kExponentMask) == kExponentMask) &&
344 ((d32 & kSignificandMask) == 0);
345 }
346
Sign()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.
NormalizedBoundaries(DiyFp * out_m_minus,DiyFp * out_m_plus)356 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
357 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.
UpperBoundary()374 DiyFp UpperBoundary() const {
375 ASSERT(Sign() > 0);
376 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
377 }
378
LowerBoundaryIsCloser()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
value()392 float value() const { return uint32_to_float(d32_); }
393
Infinity()394 static float Infinity() {
395 return Single(kInfinity).value();
396 }
397
NaN()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 DISALLOW_COPY_AND_ASSIGN(Single);
412 };
413
414 } // namespace double_conversion
415
416 // ICU PATCH: Close ICU namespace
417 U_NAMESPACE_END
418
419 #endif // DOUBLE_CONVERSION_DOUBLE_H_
420 #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING
421