/src/icu/source/i18n/double-conversion-bignum.cpp
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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 2010 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 | | #include <algorithm> |
38 | | #include <cstring> |
39 | | |
40 | | // ICU PATCH: Customize header file paths for ICU. |
41 | | |
42 | | #include "double-conversion-bignum.h" |
43 | | #include "double-conversion-utils.h" |
44 | | |
45 | | // ICU PATCH: Wrap in ICU namespace |
46 | | U_NAMESPACE_BEGIN |
47 | | |
48 | | namespace double_conversion { |
49 | | |
50 | 0 | Bignum::Chunk& Bignum::RawBigit(const int index) { |
51 | 0 | DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity); |
52 | 0 | return bigits_buffer_[index]; |
53 | 0 | } |
54 | | |
55 | | |
56 | 0 | const Bignum::Chunk& Bignum::RawBigit(const int index) const { |
57 | 0 | DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity); |
58 | 0 | return bigits_buffer_[index]; |
59 | 0 | } |
60 | | |
61 | | |
62 | | template<typename S> |
63 | | static int BitSize(const S value) { |
64 | | (void) value; // Mark variable as used. |
65 | | return 8 * sizeof(value); |
66 | | } |
67 | | |
68 | | // Guaranteed to lie in one Bigit. |
69 | 0 | void Bignum::AssignUInt16(const uint16_t value) { |
70 | 0 | DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value)); |
71 | 0 | Zero(); |
72 | 0 | if (value > 0) { |
73 | 0 | RawBigit(0) = value; |
74 | 0 | used_bigits_ = 1; |
75 | 0 | } |
76 | 0 | } |
77 | | |
78 | | |
79 | 0 | void Bignum::AssignUInt64(uint64_t value) { |
80 | 0 | Zero(); |
81 | 0 | for(int i = 0; value > 0; ++i) { |
82 | 0 | RawBigit(i) = value & kBigitMask; |
83 | 0 | value >>= kBigitSize; |
84 | 0 | ++used_bigits_; |
85 | 0 | } |
86 | 0 | } |
87 | | |
88 | | |
89 | 0 | void Bignum::AssignBignum(const Bignum& other) { |
90 | 0 | exponent_ = other.exponent_; |
91 | 0 | for (int i = 0; i < other.used_bigits_; ++i) { |
92 | 0 | RawBigit(i) = other.RawBigit(i); |
93 | 0 | } |
94 | 0 | used_bigits_ = other.used_bigits_; |
95 | 0 | } |
96 | | |
97 | | |
98 | | static uint64_t ReadUInt64(const Vector<const char> buffer, |
99 | | const int from, |
100 | 0 | const int digits_to_read) { |
101 | 0 | uint64_t result = 0; |
102 | 0 | for (int i = from; i < from + digits_to_read; ++i) { |
103 | 0 | const int digit = buffer[i] - '0'; |
104 | 0 | DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9); |
105 | 0 | result = result * 10 + digit; |
106 | 0 | } |
107 | 0 | return result; |
108 | 0 | } |
109 | | |
110 | | |
111 | 0 | void Bignum::AssignDecimalString(const Vector<const char> value) { |
112 | | // 2^64 = 18446744073709551616 > 10^19 |
113 | 0 | static const int kMaxUint64DecimalDigits = 19; |
114 | 0 | Zero(); |
115 | 0 | int length = value.length(); |
116 | 0 | unsigned pos = 0; |
117 | | // Let's just say that each digit needs 4 bits. |
118 | 0 | while (length >= kMaxUint64DecimalDigits) { |
119 | 0 | const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); |
120 | 0 | pos += kMaxUint64DecimalDigits; |
121 | 0 | length -= kMaxUint64DecimalDigits; |
122 | 0 | MultiplyByPowerOfTen(kMaxUint64DecimalDigits); |
123 | 0 | AddUInt64(digits); |
124 | 0 | } |
125 | 0 | const uint64_t digits = ReadUInt64(value, pos, length); |
126 | 0 | MultiplyByPowerOfTen(length); |
127 | 0 | AddUInt64(digits); |
128 | 0 | Clamp(); |
129 | 0 | } |
130 | | |
131 | | |
132 | 0 | static uint64_t HexCharValue(const int c) { |
133 | 0 | if ('0' <= c && c <= '9') { |
134 | 0 | return c - '0'; |
135 | 0 | } |
136 | 0 | if ('a' <= c && c <= 'f') { |
137 | 0 | return 10 + c - 'a'; |
138 | 0 | } |
139 | 0 | DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F'); |
140 | 0 | return 10 + c - 'A'; |
141 | 0 | } |
142 | | |
143 | | |
144 | | // Unlike AssignDecimalString(), this function is "only" used |
145 | | // for unit-tests and therefore not performance critical. |
146 | 0 | void Bignum::AssignHexString(Vector<const char> value) { |
147 | 0 | Zero(); |
148 | | // Required capacity could be reduced by ignoring leading zeros. |
149 | 0 | EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize); |
150 | 0 | DOUBLE_CONVERSION_ASSERT(sizeof(uint64_t) * 8 >= kBigitSize + 4); // TODO: static_assert |
151 | | // Accumulates converted hex digits until at least kBigitSize bits. |
152 | | // Works with non-factor-of-four kBigitSizes. |
153 | 0 | uint64_t tmp = 0; // Accumulates converted hex digits until at least |
154 | 0 | for (int cnt = 0; !value.is_empty(); value.pop_back()) { |
155 | 0 | tmp |= (HexCharValue(value.last()) << cnt); |
156 | 0 | if ((cnt += 4) >= kBigitSize) { |
157 | 0 | RawBigit(used_bigits_++) = (tmp & kBigitMask); |
158 | 0 | cnt -= kBigitSize; |
159 | 0 | tmp >>= kBigitSize; |
160 | 0 | } |
161 | 0 | } |
162 | 0 | if (tmp > 0) { |
163 | 0 | RawBigit(used_bigits_++) = tmp; |
164 | 0 | } |
165 | 0 | Clamp(); |
166 | 0 | } |
167 | | |
168 | | |
169 | 0 | void Bignum::AddUInt64(const uint64_t operand) { |
170 | 0 | if (operand == 0) { |
171 | 0 | return; |
172 | 0 | } |
173 | 0 | Bignum other; |
174 | 0 | other.AssignUInt64(operand); |
175 | 0 | AddBignum(other); |
176 | 0 | } |
177 | | |
178 | | |
179 | 0 | void Bignum::AddBignum(const Bignum& other) { |
180 | 0 | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
181 | 0 | DOUBLE_CONVERSION_ASSERT(other.IsClamped()); |
182 | | |
183 | | // If this has a greater exponent than other append zero-bigits to this. |
184 | | // After this call exponent_ <= other.exponent_. |
185 | 0 | Align(other); |
186 | | |
187 | | // There are two possibilities: |
188 | | // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) |
189 | | // bbbbb 00000000 |
190 | | // ---------------- |
191 | | // ccccccccccc 0000 |
192 | | // or |
193 | | // aaaaaaaaaa 0000 |
194 | | // bbbbbbbbb 0000000 |
195 | | // ----------------- |
196 | | // cccccccccccc 0000 |
197 | | // In both cases we might need a carry bigit. |
198 | |
|
199 | 0 | EnsureCapacity(1 + (std::max)(BigitLength(), other.BigitLength()) - exponent_); |
200 | 0 | Chunk carry = 0; |
201 | 0 | int bigit_pos = other.exponent_ - exponent_; |
202 | 0 | DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0); |
203 | 0 | for (int i = used_bigits_; i < bigit_pos; ++i) { |
204 | 0 | RawBigit(i) = 0; |
205 | 0 | } |
206 | 0 | for (int i = 0; i < other.used_bigits_; ++i) { |
207 | 0 | const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0; |
208 | 0 | const Chunk sum = my + other.RawBigit(i) + carry; |
209 | 0 | RawBigit(bigit_pos) = sum & kBigitMask; |
210 | 0 | carry = sum >> kBigitSize; |
211 | 0 | ++bigit_pos; |
212 | 0 | } |
213 | 0 | while (carry != 0) { |
214 | 0 | const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0; |
215 | 0 | const Chunk sum = my + carry; |
216 | 0 | RawBigit(bigit_pos) = sum & kBigitMask; |
217 | 0 | carry = sum >> kBigitSize; |
218 | 0 | ++bigit_pos; |
219 | 0 | } |
220 | 0 | used_bigits_ = (std::max)(bigit_pos, static_cast<int>(used_bigits_)); |
221 | 0 | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
222 | 0 | } |
223 | | |
224 | | |
225 | 0 | void Bignum::SubtractBignum(const Bignum& other) { |
226 | 0 | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
227 | 0 | DOUBLE_CONVERSION_ASSERT(other.IsClamped()); |
228 | | // We require this to be bigger than other. |
229 | 0 | DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this)); |
230 | |
|
231 | 0 | Align(other); |
232 | |
|
233 | 0 | const int offset = other.exponent_ - exponent_; |
234 | 0 | Chunk borrow = 0; |
235 | 0 | int i; |
236 | 0 | for (i = 0; i < other.used_bigits_; ++i) { |
237 | 0 | DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1)); |
238 | 0 | const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow; |
239 | 0 | RawBigit(i + offset) = difference & kBigitMask; |
240 | 0 | borrow = difference >> (kChunkSize - 1); |
241 | 0 | } |
242 | 0 | while (borrow != 0) { |
243 | 0 | const Chunk difference = RawBigit(i + offset) - borrow; |
244 | 0 | RawBigit(i + offset) = difference & kBigitMask; |
245 | 0 | borrow = difference >> (kChunkSize - 1); |
246 | 0 | ++i; |
247 | 0 | } |
248 | 0 | Clamp(); |
249 | 0 | } |
250 | | |
251 | | |
252 | 0 | void Bignum::ShiftLeft(const int shift_amount) { |
253 | 0 | if (used_bigits_ == 0) { |
254 | 0 | return; |
255 | 0 | } |
256 | 0 | exponent_ += (shift_amount / kBigitSize); |
257 | 0 | const int local_shift = shift_amount % kBigitSize; |
258 | 0 | EnsureCapacity(used_bigits_ + 1); |
259 | 0 | BigitsShiftLeft(local_shift); |
260 | 0 | } |
261 | | |
262 | | |
263 | 0 | void Bignum::MultiplyByUInt32(const uint32_t factor) { |
264 | 0 | if (factor == 1) { |
265 | 0 | return; |
266 | 0 | } |
267 | 0 | if (factor == 0) { |
268 | 0 | Zero(); |
269 | 0 | return; |
270 | 0 | } |
271 | 0 | if (used_bigits_ == 0) { |
272 | 0 | return; |
273 | 0 | } |
274 | | // The product of a bigit with the factor is of size kBigitSize + 32. |
275 | | // Assert that this number + 1 (for the carry) fits into double chunk. |
276 | 0 | DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); |
277 | 0 | DoubleChunk carry = 0; |
278 | 0 | for (int i = 0; i < used_bigits_; ++i) { |
279 | 0 | const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry; |
280 | 0 | RawBigit(i) = static_cast<Chunk>(product & kBigitMask); |
281 | 0 | carry = (product >> kBigitSize); |
282 | 0 | } |
283 | 0 | while (carry != 0) { |
284 | 0 | EnsureCapacity(used_bigits_ + 1); |
285 | 0 | RawBigit(used_bigits_) = carry & kBigitMask; |
286 | 0 | used_bigits_++; |
287 | 0 | carry >>= kBigitSize; |
288 | 0 | } |
289 | 0 | } |
290 | | |
291 | | |
292 | 0 | void Bignum::MultiplyByUInt64(const uint64_t factor) { |
293 | 0 | if (factor == 1) { |
294 | 0 | return; |
295 | 0 | } |
296 | 0 | if (factor == 0) { |
297 | 0 | Zero(); |
298 | 0 | return; |
299 | 0 | } |
300 | 0 | if (used_bigits_ == 0) { |
301 | 0 | return; |
302 | 0 | } |
303 | 0 | DOUBLE_CONVERSION_ASSERT(kBigitSize < 32); |
304 | 0 | uint64_t carry = 0; |
305 | 0 | const uint64_t low = factor & 0xFFFFFFFF; |
306 | 0 | const uint64_t high = factor >> 32; |
307 | 0 | for (int i = 0; i < used_bigits_; ++i) { |
308 | 0 | const uint64_t product_low = low * RawBigit(i); |
309 | 0 | const uint64_t product_high = high * RawBigit(i); |
310 | 0 | const uint64_t tmp = (carry & kBigitMask) + product_low; |
311 | 0 | RawBigit(i) = tmp & kBigitMask; |
312 | 0 | carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + |
313 | 0 | (product_high << (32 - kBigitSize)); |
314 | 0 | } |
315 | 0 | while (carry != 0) { |
316 | 0 | EnsureCapacity(used_bigits_ + 1); |
317 | 0 | RawBigit(used_bigits_) = carry & kBigitMask; |
318 | 0 | used_bigits_++; |
319 | 0 | carry >>= kBigitSize; |
320 | 0 | } |
321 | 0 | } |
322 | | |
323 | | |
324 | 0 | void Bignum::MultiplyByPowerOfTen(const int exponent) { |
325 | 0 | static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d); |
326 | 0 | static const uint16_t kFive1 = 5; |
327 | 0 | static const uint16_t kFive2 = kFive1 * 5; |
328 | 0 | static const uint16_t kFive3 = kFive2 * 5; |
329 | 0 | static const uint16_t kFive4 = kFive3 * 5; |
330 | 0 | static const uint16_t kFive5 = kFive4 * 5; |
331 | 0 | static const uint16_t kFive6 = kFive5 * 5; |
332 | 0 | static const uint32_t kFive7 = kFive6 * 5; |
333 | 0 | static const uint32_t kFive8 = kFive7 * 5; |
334 | 0 | static const uint32_t kFive9 = kFive8 * 5; |
335 | 0 | static const uint32_t kFive10 = kFive9 * 5; |
336 | 0 | static const uint32_t kFive11 = kFive10 * 5; |
337 | 0 | static const uint32_t kFive12 = kFive11 * 5; |
338 | 0 | static const uint32_t kFive13 = kFive12 * 5; |
339 | 0 | static const uint32_t kFive1_to_12[] = |
340 | 0 | { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, |
341 | 0 | kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; |
342 | |
|
343 | 0 | DOUBLE_CONVERSION_ASSERT(exponent >= 0); |
344 | |
|
345 | 0 | if (exponent == 0) { |
346 | 0 | return; |
347 | 0 | } |
348 | 0 | if (used_bigits_ == 0) { |
349 | 0 | return; |
350 | 0 | } |
351 | | // We shift by exponent at the end just before returning. |
352 | 0 | int remaining_exponent = exponent; |
353 | 0 | while (remaining_exponent >= 27) { |
354 | 0 | MultiplyByUInt64(kFive27); |
355 | 0 | remaining_exponent -= 27; |
356 | 0 | } |
357 | 0 | while (remaining_exponent >= 13) { |
358 | 0 | MultiplyByUInt32(kFive13); |
359 | 0 | remaining_exponent -= 13; |
360 | 0 | } |
361 | 0 | if (remaining_exponent > 0) { |
362 | 0 | MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); |
363 | 0 | } |
364 | 0 | ShiftLeft(exponent); |
365 | 0 | } |
366 | | |
367 | | |
368 | 0 | void Bignum::Square() { |
369 | 0 | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
370 | 0 | const int product_length = 2 * used_bigits_; |
371 | 0 | EnsureCapacity(product_length); |
372 | | |
373 | | // Comba multiplication: compute each column separately. |
374 | | // Example: r = a2a1a0 * b2b1b0. |
375 | | // r = 1 * a0b0 + |
376 | | // 10 * (a1b0 + a0b1) + |
377 | | // 100 * (a2b0 + a1b1 + a0b2) + |
378 | | // 1000 * (a2b1 + a1b2) + |
379 | | // 10000 * a2b2 |
380 | | // |
381 | | // In the worst case we have to accumulate nb-digits products of digit*digit. |
382 | | // |
383 | | // Assert that the additional number of bits in a DoubleChunk are enough to |
384 | | // sum up used_digits of Bigit*Bigit. |
385 | 0 | if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) { |
386 | 0 | DOUBLE_CONVERSION_UNIMPLEMENTED(); |
387 | 0 | } |
388 | 0 | DoubleChunk accumulator = 0; |
389 | | // First shift the digits so we don't overwrite them. |
390 | 0 | const int copy_offset = used_bigits_; |
391 | 0 | for (int i = 0; i < used_bigits_; ++i) { |
392 | 0 | RawBigit(copy_offset + i) = RawBigit(i); |
393 | 0 | } |
394 | | // We have two loops to avoid some 'if's in the loop. |
395 | 0 | for (int i = 0; i < used_bigits_; ++i) { |
396 | | // Process temporary digit i with power i. |
397 | | // The sum of the two indices must be equal to i. |
398 | 0 | int bigit_index1 = i; |
399 | 0 | int bigit_index2 = 0; |
400 | | // Sum all of the sub-products. |
401 | 0 | while (bigit_index1 >= 0) { |
402 | 0 | const Chunk chunk1 = RawBigit(copy_offset + bigit_index1); |
403 | 0 | const Chunk chunk2 = RawBigit(copy_offset + bigit_index2); |
404 | 0 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
405 | 0 | bigit_index1--; |
406 | 0 | bigit_index2++; |
407 | 0 | } |
408 | 0 | RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask; |
409 | 0 | accumulator >>= kBigitSize; |
410 | 0 | } |
411 | 0 | for (int i = used_bigits_; i < product_length; ++i) { |
412 | 0 | int bigit_index1 = used_bigits_ - 1; |
413 | 0 | int bigit_index2 = i - bigit_index1; |
414 | | // Invariant: sum of both indices is again equal to i. |
415 | | // Inner loop runs 0 times on last iteration, emptying accumulator. |
416 | 0 | while (bigit_index2 < used_bigits_) { |
417 | 0 | const Chunk chunk1 = RawBigit(copy_offset + bigit_index1); |
418 | 0 | const Chunk chunk2 = RawBigit(copy_offset + bigit_index2); |
419 | 0 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
420 | 0 | bigit_index1--; |
421 | 0 | bigit_index2++; |
422 | 0 | } |
423 | | // The overwritten RawBigit(i) will never be read in further loop iterations, |
424 | | // because bigit_index1 and bigit_index2 are always greater |
425 | | // than i - used_bigits_. |
426 | 0 | RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask; |
427 | 0 | accumulator >>= kBigitSize; |
428 | 0 | } |
429 | | // Since the result was guaranteed to lie inside the number the |
430 | | // accumulator must be 0 now. |
431 | 0 | DOUBLE_CONVERSION_ASSERT(accumulator == 0); |
432 | | |
433 | | // Don't forget to update the used_digits and the exponent. |
434 | 0 | used_bigits_ = product_length; |
435 | 0 | exponent_ *= 2; |
436 | 0 | Clamp(); |
437 | 0 | } |
438 | | |
439 | | |
440 | 0 | void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) { |
441 | 0 | DOUBLE_CONVERSION_ASSERT(base != 0); |
442 | 0 | DOUBLE_CONVERSION_ASSERT(power_exponent >= 0); |
443 | 0 | if (power_exponent == 0) { |
444 | 0 | AssignUInt16(1); |
445 | 0 | return; |
446 | 0 | } |
447 | 0 | Zero(); |
448 | 0 | int shifts = 0; |
449 | | // We expect base to be in range 2-32, and most often to be 10. |
450 | | // It does not make much sense to implement different algorithms for counting |
451 | | // the bits. |
452 | 0 | while ((base & 1) == 0) { |
453 | 0 | base >>= 1; |
454 | 0 | shifts++; |
455 | 0 | } |
456 | 0 | int bit_size = 0; |
457 | 0 | int tmp_base = base; |
458 | 0 | while (tmp_base != 0) { |
459 | 0 | tmp_base >>= 1; |
460 | 0 | bit_size++; |
461 | 0 | } |
462 | 0 | const int final_size = bit_size * power_exponent; |
463 | | // 1 extra bigit for the shifting, and one for rounded final_size. |
464 | 0 | EnsureCapacity(final_size / kBigitSize + 2); |
465 | | |
466 | | // Left to Right exponentiation. |
467 | 0 | int mask = 1; |
468 | 0 | while (power_exponent >= mask) mask <<= 1; |
469 | | |
470 | | // The mask is now pointing to the bit above the most significant 1-bit of |
471 | | // power_exponent. |
472 | | // Get rid of first 1-bit; |
473 | 0 | mask >>= 2; |
474 | 0 | uint64_t this_value = base; |
475 | |
|
476 | 0 | bool delayed_multiplication = false; |
477 | 0 | const uint64_t max_32bits = 0xFFFFFFFF; |
478 | 0 | while (mask != 0 && this_value <= max_32bits) { |
479 | 0 | this_value = this_value * this_value; |
480 | | // Verify that there is enough space in this_value to perform the |
481 | | // multiplication. The first bit_size bits must be 0. |
482 | 0 | if ((power_exponent & mask) != 0) { |
483 | 0 | DOUBLE_CONVERSION_ASSERT(bit_size > 0); |
484 | 0 | const uint64_t base_bits_mask = |
485 | 0 | ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); |
486 | 0 | const bool high_bits_zero = (this_value & base_bits_mask) == 0; |
487 | 0 | if (high_bits_zero) { |
488 | 0 | this_value *= base; |
489 | 0 | } else { |
490 | 0 | delayed_multiplication = true; |
491 | 0 | } |
492 | 0 | } |
493 | 0 | mask >>= 1; |
494 | 0 | } |
495 | 0 | AssignUInt64(this_value); |
496 | 0 | if (delayed_multiplication) { |
497 | 0 | MultiplyByUInt32(base); |
498 | 0 | } |
499 | | |
500 | | // Now do the same thing as a bignum. |
501 | 0 | while (mask != 0) { |
502 | 0 | Square(); |
503 | 0 | if ((power_exponent & mask) != 0) { |
504 | 0 | MultiplyByUInt32(base); |
505 | 0 | } |
506 | 0 | mask >>= 1; |
507 | 0 | } |
508 | | |
509 | | // And finally add the saved shifts. |
510 | 0 | ShiftLeft(shifts * power_exponent); |
511 | 0 | } |
512 | | |
513 | | |
514 | | // Precondition: this/other < 16bit. |
515 | 0 | uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { |
516 | 0 | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
517 | 0 | DOUBLE_CONVERSION_ASSERT(other.IsClamped()); |
518 | 0 | DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 0); |
519 | | |
520 | | // Easy case: if we have less digits than the divisor than the result is 0. |
521 | | // Note: this handles the case where this == 0, too. |
522 | 0 | if (BigitLength() < other.BigitLength()) { |
523 | 0 | return 0; |
524 | 0 | } |
525 | | |
526 | 0 | Align(other); |
527 | |
|
528 | 0 | uint16_t result = 0; |
529 | | |
530 | | // Start by removing multiples of 'other' until both numbers have the same |
531 | | // number of digits. |
532 | 0 | while (BigitLength() > other.BigitLength()) { |
533 | | // This naive approach is extremely inefficient if `this` divided by other |
534 | | // is big. This function is implemented for doubleToString where |
535 | | // the result should be small (less than 10). |
536 | 0 | DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16)); |
537 | 0 | DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000); |
538 | | // Remove the multiples of the first digit. |
539 | | // Example this = 23 and other equals 9. -> Remove 2 multiples. |
540 | 0 | result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1)); |
541 | 0 | SubtractTimes(other, RawBigit(used_bigits_ - 1)); |
542 | 0 | } |
543 | |
|
544 | 0 | DOUBLE_CONVERSION_ASSERT(BigitLength() == other.BigitLength()); |
545 | | |
546 | | // Both bignums are at the same length now. |
547 | | // Since other has more than 0 digits we know that the access to |
548 | | // RawBigit(used_bigits_ - 1) is safe. |
549 | 0 | const Chunk this_bigit = RawBigit(used_bigits_ - 1); |
550 | 0 | const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1); |
551 | |
|
552 | 0 | if (other.used_bigits_ == 1) { |
553 | | // Shortcut for easy (and common) case. |
554 | 0 | int quotient = this_bigit / other_bigit; |
555 | 0 | RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient; |
556 | 0 | DOUBLE_CONVERSION_ASSERT(quotient < 0x10000); |
557 | 0 | result += static_cast<uint16_t>(quotient); |
558 | 0 | Clamp(); |
559 | 0 | return result; |
560 | 0 | } |
561 | | |
562 | 0 | const int division_estimate = this_bigit / (other_bigit + 1); |
563 | 0 | DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000); |
564 | 0 | result += static_cast<uint16_t>(division_estimate); |
565 | 0 | SubtractTimes(other, division_estimate); |
566 | |
|
567 | 0 | if (other_bigit * (division_estimate + 1) > this_bigit) { |
568 | | // No need to even try to subtract. Even if other's remaining digits were 0 |
569 | | // another subtraction would be too much. |
570 | 0 | return result; |
571 | 0 | } |
572 | | |
573 | 0 | while (LessEqual(other, *this)) { |
574 | 0 | SubtractBignum(other); |
575 | 0 | result++; |
576 | 0 | } |
577 | 0 | return result; |
578 | 0 | } |
579 | | |
580 | | |
581 | | template<typename S> |
582 | 0 | static int SizeInHexChars(S number) { |
583 | 0 | DOUBLE_CONVERSION_ASSERT(number > 0); |
584 | 0 | int result = 0; |
585 | 0 | while (number != 0) { |
586 | 0 | number >>= 4; |
587 | 0 | result++; |
588 | 0 | } |
589 | 0 | return result; |
590 | 0 | } |
591 | | |
592 | | |
593 | 0 | static char HexCharOfValue(const int value) { |
594 | 0 | DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16); |
595 | 0 | if (value < 10) { |
596 | 0 | return static_cast<char>(value + '0'); |
597 | 0 | } |
598 | 0 | return static_cast<char>(value - 10 + 'A'); |
599 | 0 | } |
600 | | |
601 | | |
602 | 0 | bool Bignum::ToHexString(char* buffer, const int buffer_size) const { |
603 | 0 | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
604 | | // Each bigit must be printable as separate hex-character. |
605 | 0 | DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0); |
606 | 0 | static const int kHexCharsPerBigit = kBigitSize / 4; |
607 | |
|
608 | 0 | if (used_bigits_ == 0) { |
609 | 0 | if (buffer_size < 2) { |
610 | 0 | return false; |
611 | 0 | } |
612 | 0 | buffer[0] = '0'; |
613 | 0 | buffer[1] = '\0'; |
614 | 0 | return true; |
615 | 0 | } |
616 | | // We add 1 for the terminating '\0' character. |
617 | 0 | const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + |
618 | 0 | SizeInHexChars(RawBigit(used_bigits_ - 1)) + 1; |
619 | 0 | if (needed_chars > buffer_size) { |
620 | 0 | return false; |
621 | 0 | } |
622 | 0 | int string_index = needed_chars - 1; |
623 | 0 | buffer[string_index--] = '\0'; |
624 | 0 | for (int i = 0; i < exponent_; ++i) { |
625 | 0 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
626 | 0 | buffer[string_index--] = '0'; |
627 | 0 | } |
628 | 0 | } |
629 | 0 | for (int i = 0; i < used_bigits_ - 1; ++i) { |
630 | 0 | Chunk current_bigit = RawBigit(i); |
631 | 0 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
632 | 0 | buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); |
633 | 0 | current_bigit >>= 4; |
634 | 0 | } |
635 | 0 | } |
636 | | // And finally the last bigit. |
637 | 0 | Chunk most_significant_bigit = RawBigit(used_bigits_ - 1); |
638 | 0 | while (most_significant_bigit != 0) { |
639 | 0 | buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); |
640 | 0 | most_significant_bigit >>= 4; |
641 | 0 | } |
642 | 0 | return true; |
643 | 0 | } |
644 | | |
645 | | |
646 | 0 | Bignum::Chunk Bignum::BigitOrZero(const int index) const { |
647 | 0 | if (index >= BigitLength()) { |
648 | 0 | return 0; |
649 | 0 | } |
650 | 0 | if (index < exponent_) { |
651 | 0 | return 0; |
652 | 0 | } |
653 | 0 | return RawBigit(index - exponent_); |
654 | 0 | } |
655 | | |
656 | | |
657 | 0 | int Bignum::Compare(const Bignum& a, const Bignum& b) { |
658 | 0 | DOUBLE_CONVERSION_ASSERT(a.IsClamped()); |
659 | 0 | DOUBLE_CONVERSION_ASSERT(b.IsClamped()); |
660 | 0 | const int bigit_length_a = a.BigitLength(); |
661 | 0 | const int bigit_length_b = b.BigitLength(); |
662 | 0 | if (bigit_length_a < bigit_length_b) { |
663 | 0 | return -1; |
664 | 0 | } |
665 | 0 | if (bigit_length_a > bigit_length_b) { |
666 | 0 | return +1; |
667 | 0 | } |
668 | 0 | for (int i = bigit_length_a - 1; i >= (std::min)(a.exponent_, b.exponent_); --i) { |
669 | 0 | const Chunk bigit_a = a.BigitOrZero(i); |
670 | 0 | const Chunk bigit_b = b.BigitOrZero(i); |
671 | 0 | if (bigit_a < bigit_b) { |
672 | 0 | return -1; |
673 | 0 | } |
674 | 0 | if (bigit_a > bigit_b) { |
675 | 0 | return +1; |
676 | 0 | } |
677 | | // Otherwise they are equal up to this digit. Try the next digit. |
678 | 0 | } |
679 | 0 | return 0; |
680 | 0 | } |
681 | | |
682 | | |
683 | 0 | int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { |
684 | 0 | DOUBLE_CONVERSION_ASSERT(a.IsClamped()); |
685 | 0 | DOUBLE_CONVERSION_ASSERT(b.IsClamped()); |
686 | 0 | DOUBLE_CONVERSION_ASSERT(c.IsClamped()); |
687 | 0 | if (a.BigitLength() < b.BigitLength()) { |
688 | 0 | return PlusCompare(b, a, c); |
689 | 0 | } |
690 | 0 | if (a.BigitLength() + 1 < c.BigitLength()) { |
691 | 0 | return -1; |
692 | 0 | } |
693 | 0 | if (a.BigitLength() > c.BigitLength()) { |
694 | 0 | return +1; |
695 | 0 | } |
696 | | // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than |
697 | | // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one |
698 | | // of 'a'. |
699 | 0 | if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { |
700 | 0 | return -1; |
701 | 0 | } |
702 | | |
703 | 0 | Chunk borrow = 0; |
704 | | // Starting at min_exponent all digits are == 0. So no need to compare them. |
705 | 0 | const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_); |
706 | 0 | for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { |
707 | 0 | const Chunk chunk_a = a.BigitOrZero(i); |
708 | 0 | const Chunk chunk_b = b.BigitOrZero(i); |
709 | 0 | const Chunk chunk_c = c.BigitOrZero(i); |
710 | 0 | const Chunk sum = chunk_a + chunk_b; |
711 | 0 | if (sum > chunk_c + borrow) { |
712 | 0 | return +1; |
713 | 0 | } else { |
714 | 0 | borrow = chunk_c + borrow - sum; |
715 | 0 | if (borrow > 1) { |
716 | 0 | return -1; |
717 | 0 | } |
718 | 0 | borrow <<= kBigitSize; |
719 | 0 | } |
720 | 0 | } |
721 | 0 | if (borrow == 0) { |
722 | 0 | return 0; |
723 | 0 | } |
724 | 0 | return -1; |
725 | 0 | } |
726 | | |
727 | | |
728 | 0 | void Bignum::Clamp() { |
729 | 0 | while (used_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) { |
730 | 0 | used_bigits_--; |
731 | 0 | } |
732 | 0 | if (used_bigits_ == 0) { |
733 | | // Zero. |
734 | 0 | exponent_ = 0; |
735 | 0 | } |
736 | 0 | } |
737 | | |
738 | | |
739 | 0 | void Bignum::Align(const Bignum& other) { |
740 | 0 | if (exponent_ > other.exponent_) { |
741 | | // If "X" represents a "hidden" bigit (by the exponent) then we are in the |
742 | | // following case (a == this, b == other): |
743 | | // a: aaaaaaXXXX or a: aaaaaXXX |
744 | | // b: bbbbbbX b: bbbbbbbbXX |
745 | | // We replace some of the hidden digits (X) of a with 0 digits. |
746 | | // a: aaaaaa000X or a: aaaaa0XX |
747 | 0 | const int zero_bigits = exponent_ - other.exponent_; |
748 | 0 | EnsureCapacity(used_bigits_ + zero_bigits); |
749 | 0 | for (int i = used_bigits_ - 1; i >= 0; --i) { |
750 | 0 | RawBigit(i + zero_bigits) = RawBigit(i); |
751 | 0 | } |
752 | 0 | for (int i = 0; i < zero_bigits; ++i) { |
753 | 0 | RawBigit(i) = 0; |
754 | 0 | } |
755 | 0 | used_bigits_ += zero_bigits; |
756 | 0 | exponent_ -= zero_bigits; |
757 | |
|
758 | 0 | DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0); |
759 | 0 | DOUBLE_CONVERSION_ASSERT(exponent_ >= 0); |
760 | 0 | } |
761 | 0 | } |
762 | | |
763 | | |
764 | 0 | void Bignum::BigitsShiftLeft(const int shift_amount) { |
765 | 0 | DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize); |
766 | 0 | DOUBLE_CONVERSION_ASSERT(shift_amount >= 0); |
767 | 0 | Chunk carry = 0; |
768 | 0 | for (int i = 0; i < used_bigits_; ++i) { |
769 | 0 | const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount); |
770 | 0 | RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask; |
771 | 0 | carry = new_carry; |
772 | 0 | } |
773 | 0 | if (carry != 0) { |
774 | 0 | RawBigit(used_bigits_) = carry; |
775 | 0 | used_bigits_++; |
776 | 0 | } |
777 | 0 | } |
778 | | |
779 | | |
780 | 0 | void Bignum::SubtractTimes(const Bignum& other, const int factor) { |
781 | 0 | DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_); |
782 | 0 | if (factor < 3) { |
783 | 0 | for (int i = 0; i < factor; ++i) { |
784 | 0 | SubtractBignum(other); |
785 | 0 | } |
786 | 0 | return; |
787 | 0 | } |
788 | 0 | Chunk borrow = 0; |
789 | 0 | const int exponent_diff = other.exponent_ - exponent_; |
790 | 0 | for (int i = 0; i < other.used_bigits_; ++i) { |
791 | 0 | const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i); |
792 | 0 | const DoubleChunk remove = borrow + product; |
793 | 0 | const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask); |
794 | 0 | RawBigit(i + exponent_diff) = difference & kBigitMask; |
795 | 0 | borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + |
796 | 0 | (remove >> kBigitSize)); |
797 | 0 | } |
798 | 0 | for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) { |
799 | 0 | if (borrow == 0) { |
800 | 0 | return; |
801 | 0 | } |
802 | 0 | const Chunk difference = RawBigit(i) - borrow; |
803 | 0 | RawBigit(i) = difference & kBigitMask; |
804 | 0 | borrow = difference >> (kChunkSize - 1); |
805 | 0 | } |
806 | 0 | Clamp(); |
807 | 0 | } |
808 | | |
809 | | |
810 | | } // namespace double_conversion |
811 | | |
812 | | // ICU PATCH: Close ICU namespace |
813 | | U_NAMESPACE_END |
814 | | #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING |