/src/icu/icu4c/source/i18n/double-conversion-bignum.cpp
Line | Count | Source (jump to first uncovered line) |
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 | 16.6M | Bignum::Chunk& Bignum::RawBigit(const int index) { |
51 | 16.6M | DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity); |
52 | 16.6M | return bigits_buffer_[index]; |
53 | 16.6M | } |
54 | | |
55 | | |
56 | 4.52M | const Bignum::Chunk& Bignum::RawBigit(const int index) const { |
57 | 4.52M | DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity); |
58 | 4.52M | return bigits_buffer_[index]; |
59 | 4.52M | } |
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 | 26.4k | void Bignum::AssignUInt16(const uint16_t value) { |
70 | 26.4k | DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value)); |
71 | 26.4k | Zero(); |
72 | 26.4k | if (value > 0) { |
73 | 26.4k | RawBigit(0) = value; |
74 | 26.4k | used_bigits_ = 1; |
75 | 26.4k | } |
76 | 26.4k | } |
77 | | |
78 | | |
79 | 101k | void Bignum::AssignUInt64(uint64_t value) { |
80 | 101k | Zero(); |
81 | 306k | for(int i = 0; value > 0; ++i) { |
82 | 204k | RawBigit(i) = value & kBigitMask; |
83 | 204k | value >>= kBigitSize; |
84 | 204k | ++used_bigits_; |
85 | 204k | } |
86 | 101k | } |
87 | | |
88 | | |
89 | 15.1k | void Bignum::AssignBignum(const Bignum& other) { |
90 | 15.1k | exponent_ = other.exponent_; |
91 | 78.0k | for (int i = 0; i < other.used_bigits_; ++i) { |
92 | 62.8k | RawBigit(i) = other.RawBigit(i); |
93 | 62.8k | } |
94 | 15.1k | used_bigits_ = other.used_bigits_; |
95 | 15.1k | } |
96 | | |
97 | | |
98 | | static uint64_t ReadUInt64(const Vector<const char> buffer, |
99 | | const int from, |
100 | 50.8k | const int digits_to_read) { |
101 | 50.8k | uint64_t result = 0; |
102 | 634k | for (int i = from; i < from + digits_to_read; ++i) { |
103 | 583k | const int digit = buffer[i] - '0'; |
104 | 583k | DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9); |
105 | 583k | result = result * 10 + digit; |
106 | 583k | } |
107 | 50.8k | return result; |
108 | 50.8k | } |
109 | | |
110 | | |
111 | 27.5k | void Bignum::AssignDecimalString(const Vector<const char> value) { |
112 | | // 2^64 = 18446744073709551616 > 10^19 |
113 | 27.5k | static const int kMaxUint64DecimalDigits = 19; |
114 | 27.5k | Zero(); |
115 | 27.5k | int length = value.length(); |
116 | 27.5k | unsigned pos = 0; |
117 | | // Let's just say that each digit needs 4 bits. |
118 | 50.8k | while (length >= kMaxUint64DecimalDigits) { |
119 | 23.3k | const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); |
120 | 23.3k | pos += kMaxUint64DecimalDigits; |
121 | 23.3k | length -= kMaxUint64DecimalDigits; |
122 | 23.3k | MultiplyByPowerOfTen(kMaxUint64DecimalDigits); |
123 | 23.3k | AddUInt64(digits); |
124 | 23.3k | } |
125 | 27.5k | const uint64_t digits = ReadUInt64(value, pos, length); |
126 | 27.5k | MultiplyByPowerOfTen(length); |
127 | 27.5k | AddUInt64(digits); |
128 | 27.5k | Clamp(); |
129 | 27.5k | } |
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; |
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 | DOUBLE_CONVERSION_ASSERT(tmp <= kBigitMask); |
164 | 0 | RawBigit(used_bigits_++) = static_cast<Bignum::Chunk>(tmp & kBigitMask); |
165 | 0 | } |
166 | 0 | Clamp(); |
167 | 0 | } |
168 | | |
169 | | |
170 | 50.8k | void Bignum::AddUInt64(const uint64_t operand) { |
171 | 50.8k | if (operand == 0) { |
172 | 917 | return; |
173 | 917 | } |
174 | 49.9k | Bignum other; |
175 | 49.9k | other.AssignUInt64(operand); |
176 | 49.9k | AddBignum(other); |
177 | 49.9k | } |
178 | | |
179 | | |
180 | 49.9k | void Bignum::AddBignum(const Bignum& other) { |
181 | 49.9k | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
182 | 49.9k | DOUBLE_CONVERSION_ASSERT(other.IsClamped()); |
183 | | |
184 | | // If this has a greater exponent than other append zero-bigits to this. |
185 | | // After this call exponent_ <= other.exponent_. |
186 | 49.9k | Align(other); |
187 | | |
188 | | // There are two possibilities: |
189 | | // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) |
190 | | // bbbbb 00000000 |
191 | | // ---------------- |
192 | | // ccccccccccc 0000 |
193 | | // or |
194 | | // aaaaaaaaaa 0000 |
195 | | // bbbbbbbbb 0000000 |
196 | | // ----------------- |
197 | | // cccccccccccc 0000 |
198 | | // In both cases we might need a carry bigit. |
199 | | |
200 | 49.9k | EnsureCapacity(1 + (std::max)(BigitLength(), other.BigitLength()) - exponent_); |
201 | 49.9k | Chunk carry = 0; |
202 | 49.9k | int bigit_pos = other.exponent_ - exponent_; |
203 | 49.9k | DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0); |
204 | 49.9k | for (int i = used_bigits_; i < bigit_pos; ++i) { |
205 | 0 | RawBigit(i) = 0; |
206 | 0 | } |
207 | 152k | for (int i = 0; i < other.used_bigits_; ++i) { |
208 | 102k | const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0; |
209 | 102k | const Chunk sum = my + other.RawBigit(i) + carry; |
210 | 102k | RawBigit(bigit_pos) = sum & kBigitMask; |
211 | 102k | carry = sum >> kBigitSize; |
212 | 102k | ++bigit_pos; |
213 | 102k | } |
214 | 50.3k | while (carry != 0) { |
215 | 337 | const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0; |
216 | 337 | const Chunk sum = my + carry; |
217 | 337 | RawBigit(bigit_pos) = sum & kBigitMask; |
218 | 337 | carry = sum >> kBigitSize; |
219 | 337 | ++bigit_pos; |
220 | 337 | } |
221 | 49.9k | used_bigits_ = static_cast<int16_t>(std::max(bigit_pos, static_cast<int>(used_bigits_))); |
222 | 49.9k | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
223 | 49.9k | } |
224 | | |
225 | | |
226 | 197k | void Bignum::SubtractBignum(const Bignum& other) { |
227 | 197k | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
228 | 197k | DOUBLE_CONVERSION_ASSERT(other.IsClamped()); |
229 | | // We require this to be bigger than other. |
230 | 197k | DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this)); |
231 | | |
232 | 197k | Align(other); |
233 | | |
234 | 197k | const int offset = other.exponent_ - exponent_; |
235 | 197k | Chunk borrow = 0; |
236 | 197k | int i; |
237 | 1.79M | for (i = 0; i < other.used_bigits_; ++i) { |
238 | 1.59M | DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1)); |
239 | 1.59M | const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow; |
240 | 1.59M | RawBigit(i + offset) = difference & kBigitMask; |
241 | 1.59M | borrow = difference >> (kChunkSize - 1); |
242 | 1.59M | } |
243 | 227k | while (borrow != 0) { |
244 | 30.3k | const Chunk difference = RawBigit(i + offset) - borrow; |
245 | 30.3k | RawBigit(i + offset) = difference & kBigitMask; |
246 | 30.3k | borrow = difference >> (kChunkSize - 1); |
247 | 30.3k | ++i; |
248 | 30.3k | } |
249 | 197k | Clamp(); |
250 | 197k | } |
251 | | |
252 | | |
253 | 148k | void Bignum::ShiftLeft(const int shift_amount) { |
254 | 148k | if (used_bigits_ == 0) { |
255 | 0 | return; |
256 | 0 | } |
257 | 148k | exponent_ += static_cast<int16_t>(shift_amount / kBigitSize); |
258 | 148k | const int local_shift = shift_amount % kBigitSize; |
259 | 148k | EnsureCapacity(used_bigits_ + 1); |
260 | 148k | BigitsShiftLeft(local_shift); |
261 | 148k | } |
262 | | |
263 | | |
264 | 518k | void Bignum::MultiplyByUInt32(const uint32_t factor) { |
265 | 518k | if (factor == 1) { |
266 | 0 | return; |
267 | 0 | } |
268 | 518k | if (factor == 0) { |
269 | 0 | Zero(); |
270 | 0 | return; |
271 | 0 | } |
272 | 518k | if (used_bigits_ == 0) { |
273 | 0 | return; |
274 | 0 | } |
275 | | // The product of a bigit with the factor is of size kBigitSize + 32. |
276 | | // Assert that this number + 1 (for the carry) fits into double chunk. |
277 | 518k | DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); |
278 | 518k | DoubleChunk carry = 0; |
279 | 3.31M | for (int i = 0; i < used_bigits_; ++i) { |
280 | 2.79M | const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry; |
281 | 2.79M | RawBigit(i) = static_cast<Chunk>(product & kBigitMask); |
282 | 2.79M | carry = (product >> kBigitSize); |
283 | 2.79M | } |
284 | 642k | while (carry != 0) { |
285 | 123k | EnsureCapacity(used_bigits_ + 1); |
286 | 123k | RawBigit(used_bigits_) = carry & kBigitMask; |
287 | 123k | used_bigits_++; |
288 | 123k | carry >>= kBigitSize; |
289 | 123k | } |
290 | 518k | } |
291 | | |
292 | | |
293 | 22.9k | void Bignum::MultiplyByUInt64(const uint64_t factor) { |
294 | 22.9k | if (factor == 1) { |
295 | 0 | return; |
296 | 0 | } |
297 | 22.9k | if (factor == 0) { |
298 | 0 | Zero(); |
299 | 0 | return; |
300 | 0 | } |
301 | 22.9k | if (used_bigits_ == 0) { |
302 | 0 | return; |
303 | 0 | } |
304 | 22.9k | DOUBLE_CONVERSION_ASSERT(kBigitSize < 32); |
305 | 22.9k | uint64_t carry = 0; |
306 | 22.9k | const uint64_t low = factor & 0xFFFFFFFF; |
307 | 22.9k | const uint64_t high = factor >> 32; |
308 | 258k | for (int i = 0; i < used_bigits_; ++i) { |
309 | 235k | const uint64_t product_low = low * RawBigit(i); |
310 | 235k | const uint64_t product_high = high * RawBigit(i); |
311 | 235k | const uint64_t tmp = (carry & kBigitMask) + product_low; |
312 | 235k | RawBigit(i) = tmp & kBigitMask; |
313 | 235k | carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + |
314 | 235k | (product_high << (32 - kBigitSize)); |
315 | 235k | } |
316 | 75.0k | while (carry != 0) { |
317 | 52.0k | EnsureCapacity(used_bigits_ + 1); |
318 | 52.0k | RawBigit(used_bigits_) = carry & kBigitMask; |
319 | 52.0k | used_bigits_++; |
320 | 52.0k | carry >>= kBigitSize; |
321 | 52.0k | } |
322 | 22.9k | } |
323 | | |
324 | | |
325 | 78.3k | void Bignum::MultiplyByPowerOfTen(const int exponent) { |
326 | 78.3k | static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d); |
327 | 78.3k | static const uint16_t kFive1 = 5; |
328 | 78.3k | static const uint16_t kFive2 = kFive1 * 5; |
329 | 78.3k | static const uint16_t kFive3 = kFive2 * 5; |
330 | 78.3k | static const uint16_t kFive4 = kFive3 * 5; |
331 | 78.3k | static const uint16_t kFive5 = kFive4 * 5; |
332 | 78.3k | static const uint16_t kFive6 = kFive5 * 5; |
333 | 78.3k | static const uint32_t kFive7 = kFive6 * 5; |
334 | 78.3k | static const uint32_t kFive8 = kFive7 * 5; |
335 | 78.3k | static const uint32_t kFive9 = kFive8 * 5; |
336 | 78.3k | static const uint32_t kFive10 = kFive9 * 5; |
337 | 78.3k | static const uint32_t kFive11 = kFive10 * 5; |
338 | 78.3k | static const uint32_t kFive12 = kFive11 * 5; |
339 | 78.3k | static const uint32_t kFive13 = kFive12 * 5; |
340 | 78.3k | static const uint32_t kFive1_to_12[] = |
341 | 78.3k | { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, |
342 | 78.3k | kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; |
343 | | |
344 | 78.3k | DOUBLE_CONVERSION_ASSERT(exponent >= 0); |
345 | | |
346 | 78.3k | if (exponent == 0) { |
347 | 2.90k | return; |
348 | 2.90k | } |
349 | 75.4k | if (used_bigits_ == 0) { |
350 | 27.5k | return; |
351 | 27.5k | } |
352 | | // We shift by exponent at the end just before returning. |
353 | 47.9k | int remaining_exponent = exponent; |
354 | 69.0k | while (remaining_exponent >= 27) { |
355 | 21.1k | MultiplyByUInt64(kFive27); |
356 | 21.1k | remaining_exponent -= 27; |
357 | 21.1k | } |
358 | 53.4k | while (remaining_exponent >= 13) { |
359 | 5.47k | MultiplyByUInt32(kFive13); |
360 | 5.47k | remaining_exponent -= 13; |
361 | 5.47k | } |
362 | 47.9k | if (remaining_exponent > 0) { |
363 | 45.6k | MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); |
364 | 45.6k | } |
365 | 47.9k | ShiftLeft(exponent); |
366 | 47.9k | } |
367 | | |
368 | | |
369 | 15.9k | void Bignum::Square() { |
370 | 15.9k | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
371 | 15.9k | const int product_length = 2 * used_bigits_; |
372 | 15.9k | EnsureCapacity(product_length); |
373 | | |
374 | | // Comba multiplication: compute each column separately. |
375 | | // Example: r = a2a1a0 * b2b1b0. |
376 | | // r = 1 * a0b0 + |
377 | | // 10 * (a1b0 + a0b1) + |
378 | | // 100 * (a2b0 + a1b1 + a0b2) + |
379 | | // 1000 * (a2b1 + a1b2) + |
380 | | // 10000 * a2b2 |
381 | | // |
382 | | // In the worst case we have to accumulate nb-digits products of digit*digit. |
383 | | // |
384 | | // Assert that the additional number of bits in a DoubleChunk are enough to |
385 | | // sum up used_digits of Bigit*Bigit. |
386 | 15.9k | if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) { |
387 | 0 | DOUBLE_CONVERSION_UNIMPLEMENTED(); |
388 | 0 | } |
389 | 15.9k | DoubleChunk accumulator = 0; |
390 | | // First shift the digits so we don't overwrite them. |
391 | 15.9k | const int copy_offset = used_bigits_; |
392 | 105k | for (int i = 0; i < used_bigits_; ++i) { |
393 | 89.1k | RawBigit(copy_offset + i) = RawBigit(i); |
394 | 89.1k | } |
395 | | // We have two loops to avoid some 'if's in the loop. |
396 | 105k | for (int i = 0; i < used_bigits_; ++i) { |
397 | | // Process temporary digit i with power i. |
398 | | // The sum of the two indices must be equal to i. |
399 | 89.1k | int bigit_index1 = i; |
400 | 89.1k | int bigit_index2 = 0; |
401 | | // Sum all of the sub-products. |
402 | 492k | while (bigit_index1 >= 0) { |
403 | 403k | const Chunk chunk1 = RawBigit(copy_offset + bigit_index1); |
404 | 403k | const Chunk chunk2 = RawBigit(copy_offset + bigit_index2); |
405 | 403k | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
406 | 403k | bigit_index1--; |
407 | 403k | bigit_index2++; |
408 | 403k | } |
409 | 89.1k | RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask; |
410 | 89.1k | accumulator >>= kBigitSize; |
411 | 89.1k | } |
412 | 105k | for (int i = used_bigits_; i < product_length; ++i) { |
413 | 89.1k | int bigit_index1 = used_bigits_ - 1; |
414 | 89.1k | int bigit_index2 = i - bigit_index1; |
415 | | // Invariant: sum of both indices is again equal to i. |
416 | | // Inner loop runs 0 times on last iteration, emptying accumulator. |
417 | 403k | while (bigit_index2 < used_bigits_) { |
418 | 313k | const Chunk chunk1 = RawBigit(copy_offset + bigit_index1); |
419 | 313k | const Chunk chunk2 = RawBigit(copy_offset + bigit_index2); |
420 | 313k | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
421 | 313k | bigit_index1--; |
422 | 313k | bigit_index2++; |
423 | 313k | } |
424 | | // The overwritten RawBigit(i) will never be read in further loop iterations, |
425 | | // because bigit_index1 and bigit_index2 are always greater |
426 | | // than i - used_bigits_. |
427 | 89.1k | RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask; |
428 | 89.1k | accumulator >>= kBigitSize; |
429 | 89.1k | } |
430 | | // Since the result was guaranteed to lie inside the number the |
431 | | // accumulator must be 0 now. |
432 | 15.9k | DOUBLE_CONVERSION_ASSERT(accumulator == 0); |
433 | | |
434 | | // Don't forget to update the used_digits and the exponent. |
435 | 15.9k | used_bigits_ = static_cast<int16_t>(product_length); |
436 | 15.9k | exponent_ *= 2; |
437 | 15.9k | Clamp(); |
438 | 15.9k | } |
439 | | |
440 | | |
441 | 13.6k | void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) { |
442 | 13.6k | DOUBLE_CONVERSION_ASSERT(base != 0); |
443 | 13.6k | DOUBLE_CONVERSION_ASSERT(power_exponent >= 0); |
444 | 13.6k | if (power_exponent == 0) { |
445 | 955 | AssignUInt16(1); |
446 | 955 | return; |
447 | 955 | } |
448 | 12.6k | Zero(); |
449 | 12.6k | int shifts = 0; |
450 | | // We expect base to be in range 2-32, and most often to be 10. |
451 | | // It does not make much sense to implement different algorithms for counting |
452 | | // the bits. |
453 | 25.3k | while ((base & 1) == 0) { |
454 | 12.6k | base >>= 1; |
455 | 12.6k | shifts++; |
456 | 12.6k | } |
457 | 12.6k | int bit_size = 0; |
458 | 12.6k | int tmp_base = base; |
459 | 50.7k | while (tmp_base != 0) { |
460 | 38.0k | tmp_base >>= 1; |
461 | 38.0k | bit_size++; |
462 | 38.0k | } |
463 | 12.6k | const int final_size = bit_size * power_exponent; |
464 | | // 1 extra bigit for the shifting, and one for rounded final_size. |
465 | 12.6k | EnsureCapacity(final_size / kBigitSize + 2); |
466 | | |
467 | | // Left to Right exponentiation. |
468 | 12.6k | int mask = 1; |
469 | 84.2k | while (power_exponent >= mask) mask <<= 1; |
470 | | |
471 | | // The mask is now pointing to the bit above the most significant 1-bit of |
472 | | // power_exponent. |
473 | | // Get rid of first 1-bit; |
474 | 12.6k | mask >>= 2; |
475 | 12.6k | uint64_t this_value = base; |
476 | | |
477 | 12.6k | bool delayed_multiplication = false; |
478 | 12.6k | const uint64_t max_32bits = 0xFFFFFFFF; |
479 | 55.5k | while (mask != 0 && this_value <= max_32bits) { |
480 | 42.9k | this_value = this_value * this_value; |
481 | | // Verify that there is enough space in this_value to perform the |
482 | | // multiplication. The first bit_size bits must be 0. |
483 | 42.9k | if ((power_exponent & mask) != 0) { |
484 | 16.6k | DOUBLE_CONVERSION_ASSERT(bit_size > 0); |
485 | 16.6k | const uint64_t base_bits_mask = |
486 | 16.6k | ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); |
487 | 16.6k | const bool high_bits_zero = (this_value & base_bits_mask) == 0; |
488 | 16.6k | if (high_bits_zero) { |
489 | 16.6k | this_value *= base; |
490 | 16.6k | } else { |
491 | 0 | delayed_multiplication = true; |
492 | 0 | } |
493 | 16.6k | } |
494 | 42.9k | mask >>= 1; |
495 | 42.9k | } |
496 | 12.6k | AssignUInt64(this_value); |
497 | 12.6k | if (delayed_multiplication) { |
498 | 0 | MultiplyByUInt32(base); |
499 | 0 | } |
500 | | |
501 | | // Now do the same thing as a bignum. |
502 | 28.6k | while (mask != 0) { |
503 | 15.9k | Square(); |
504 | 15.9k | if ((power_exponent & mask) != 0) { |
505 | 8.40k | MultiplyByUInt32(base); |
506 | 8.40k | } |
507 | 15.9k | mask >>= 1; |
508 | 15.9k | } |
509 | | |
510 | | // And finally add the saved shifts. |
511 | 12.6k | ShiftLeft(shifts * power_exponent); |
512 | 12.6k | } |
513 | | |
514 | | |
515 | | // Precondition: this/other < 16bit. |
516 | 224k | uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { |
517 | 224k | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
518 | 224k | DOUBLE_CONVERSION_ASSERT(other.IsClamped()); |
519 | 224k | DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 0); |
520 | | |
521 | | // Easy case: if we have less digits than the divisor than the result is 0. |
522 | | // Note: this handles the case where this == 0, too. |
523 | 224k | if (BigitLength() < other.BigitLength()) { |
524 | 10.7k | return 0; |
525 | 10.7k | } |
526 | | |
527 | 214k | Align(other); |
528 | | |
529 | 214k | uint16_t result = 0; |
530 | | |
531 | | // Start by removing multiples of 'other' until both numbers have the same |
532 | | // number of digits. |
533 | 270k | while (BigitLength() > other.BigitLength()) { |
534 | | // This naive approach is extremely inefficient if `this` divided by other |
535 | | // is big. This function is implemented for doubleToString where |
536 | | // the result should be small (less than 10). |
537 | 56.4k | DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16)); |
538 | 56.4k | DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000); |
539 | | // Remove the multiples of the first digit. |
540 | | // Example this = 23 and other equals 9. -> Remove 2 multiples. |
541 | 56.4k | result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1)); |
542 | 56.4k | SubtractTimes(other, RawBigit(used_bigits_ - 1)); |
543 | 56.4k | } |
544 | | |
545 | 214k | DOUBLE_CONVERSION_ASSERT(BigitLength() == other.BigitLength()); |
546 | | |
547 | | // Both bignums are at the same length now. |
548 | | // Since other has more than 0 digits we know that the access to |
549 | | // RawBigit(used_bigits_ - 1) is safe. |
550 | 214k | const Chunk this_bigit = RawBigit(used_bigits_ - 1); |
551 | 214k | const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1); |
552 | | |
553 | 214k | if (other.used_bigits_ == 1) { |
554 | | // Shortcut for easy (and common) case. |
555 | 35.9k | int quotient = this_bigit / other_bigit; |
556 | 35.9k | RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient; |
557 | 35.9k | DOUBLE_CONVERSION_ASSERT(quotient < 0x10000); |
558 | 35.9k | result += static_cast<uint16_t>(quotient); |
559 | 35.9k | Clamp(); |
560 | 35.9k | return result; |
561 | 35.9k | } |
562 | | |
563 | 178k | const int division_estimate = this_bigit / (other_bigit + 1); |
564 | 178k | DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000); |
565 | 178k | result += static_cast<uint16_t>(division_estimate); |
566 | 178k | SubtractTimes(other, division_estimate); |
567 | | |
568 | 178k | if (other_bigit * (division_estimate + 1) > this_bigit) { |
569 | | // No need to even try to subtract. Even if other's remaining digits were 0 |
570 | | // another subtraction would be too much. |
571 | 87.6k | return result; |
572 | 87.6k | } |
573 | | |
574 | 178k | while (LessEqual(other, *this)) { |
575 | 88.3k | SubtractBignum(other); |
576 | 88.3k | result++; |
577 | 88.3k | } |
578 | 90.6k | return result; |
579 | 178k | } |
580 | | |
581 | | |
582 | | template<typename S> |
583 | 0 | static int SizeInHexChars(S number) { |
584 | 0 | DOUBLE_CONVERSION_ASSERT(number > 0); |
585 | 0 | int result = 0; |
586 | 0 | while (number != 0) { |
587 | 0 | number >>= 4; |
588 | 0 | result++; |
589 | 0 | } |
590 | 0 | return result; |
591 | 0 | } |
592 | | |
593 | | |
594 | 0 | static char HexCharOfValue(const int value) { |
595 | 0 | DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16); |
596 | 0 | if (value < 10) { |
597 | 0 | return static_cast<char>(value + '0'); |
598 | 0 | } |
599 | 0 | return static_cast<char>(value - 10 + 'A'); |
600 | 0 | } |
601 | | |
602 | | |
603 | 0 | bool Bignum::ToHexString(char* buffer, const int buffer_size) const { |
604 | 0 | DOUBLE_CONVERSION_ASSERT(IsClamped()); |
605 | | // Each bigit must be printable as separate hex-character. |
606 | 0 | DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0); |
607 | 0 | static const int kHexCharsPerBigit = kBigitSize / 4; |
608 | |
|
609 | 0 | if (used_bigits_ == 0) { |
610 | 0 | if (buffer_size < 2) { |
611 | 0 | return false; |
612 | 0 | } |
613 | 0 | buffer[0] = '0'; |
614 | 0 | buffer[1] = '\0'; |
615 | 0 | return true; |
616 | 0 | } |
617 | | // We add 1 for the terminating '\0' character. |
618 | 0 | const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + |
619 | 0 | SizeInHexChars(RawBigit(used_bigits_ - 1)) + 1; |
620 | 0 | if (needed_chars > buffer_size) { |
621 | 0 | return false; |
622 | 0 | } |
623 | 0 | int string_index = needed_chars - 1; |
624 | 0 | buffer[string_index--] = '\0'; |
625 | 0 | for (int i = 0; i < exponent_; ++i) { |
626 | 0 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
627 | 0 | buffer[string_index--] = '0'; |
628 | 0 | } |
629 | 0 | } |
630 | 0 | for (int i = 0; i < used_bigits_ - 1; ++i) { |
631 | 0 | Chunk current_bigit = RawBigit(i); |
632 | 0 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
633 | 0 | buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); |
634 | 0 | current_bigit >>= 4; |
635 | 0 | } |
636 | 0 | } |
637 | | // And finally the last bigit. |
638 | 0 | Chunk most_significant_bigit = RawBigit(used_bigits_ - 1); |
639 | 0 | while (most_significant_bigit != 0) { |
640 | 0 | buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); |
641 | 0 | most_significant_bigit >>= 4; |
642 | 0 | } |
643 | 0 | return true; |
644 | 0 | } |
645 | | |
646 | | |
647 | 1.86M | Bignum::Chunk Bignum::BigitOrZero(const int index) const { |
648 | 1.86M | if (index >= BigitLength()) { |
649 | 292k | return 0; |
650 | 292k | } |
651 | 1.57M | if (index < exponent_) { |
652 | 18.2k | return 0; |
653 | 18.2k | } |
654 | 1.55M | return RawBigit(index - exponent_); |
655 | 1.57M | } |
656 | | |
657 | | |
658 | 457k | int Bignum::Compare(const Bignum& a, const Bignum& b) { |
659 | 457k | DOUBLE_CONVERSION_ASSERT(a.IsClamped()); |
660 | 457k | DOUBLE_CONVERSION_ASSERT(b.IsClamped()); |
661 | 457k | const int bigit_length_a = a.BigitLength(); |
662 | 457k | const int bigit_length_b = b.BigitLength(); |
663 | 457k | if (bigit_length_a < bigit_length_b) { |
664 | 5.37k | return -1; |
665 | 5.37k | } |
666 | 451k | if (bigit_length_a > bigit_length_b) { |
667 | 188k | return +1; |
668 | 188k | } |
669 | 441k | for (int i = bigit_length_a - 1; i >= (std::min)(a.exponent_, b.exponent_); --i) { |
670 | 410k | const Chunk bigit_a = a.BigitOrZero(i); |
671 | 410k | const Chunk bigit_b = b.BigitOrZero(i); |
672 | 410k | if (bigit_a < bigit_b) { |
673 | 94.9k | return -1; |
674 | 94.9k | } |
675 | 316k | if (bigit_a > bigit_b) { |
676 | 137k | return +1; |
677 | 137k | } |
678 | | // Otherwise they are equal up to this digit. Try the next digit. |
679 | 316k | } |
680 | 30.7k | return 0; |
681 | 263k | } |
682 | | |
683 | | |
684 | 252k | int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { |
685 | 252k | DOUBLE_CONVERSION_ASSERT(a.IsClamped()); |
686 | 252k | DOUBLE_CONVERSION_ASSERT(b.IsClamped()); |
687 | 252k | DOUBLE_CONVERSION_ASSERT(c.IsClamped()); |
688 | 252k | if (a.BigitLength() < b.BigitLength()) { |
689 | 5.07k | return PlusCompare(b, a, c); |
690 | 5.07k | } |
691 | 247k | if (a.BigitLength() + 1 < c.BigitLength()) { |
692 | 3.72k | return -1; |
693 | 3.72k | } |
694 | 243k | if (a.BigitLength() > c.BigitLength()) { |
695 | 1.27k | return +1; |
696 | 1.27k | } |
697 | | // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than |
698 | | // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one |
699 | | // of 'a'. |
700 | 242k | if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { |
701 | 0 | return -1; |
702 | 0 | } |
703 | | |
704 | 242k | Chunk borrow = 0; |
705 | | // Starting at min_exponent all digits are == 0. So no need to compare them. |
706 | 242k | const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_); |
707 | 354k | for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { |
708 | 348k | const Chunk chunk_a = a.BigitOrZero(i); |
709 | 348k | const Chunk chunk_b = b.BigitOrZero(i); |
710 | 348k | const Chunk chunk_c = c.BigitOrZero(i); |
711 | 348k | const Chunk sum = chunk_a + chunk_b; |
712 | 348k | if (sum > chunk_c + borrow) { |
713 | 12.9k | return +1; |
714 | 335k | } else { |
715 | 335k | borrow = chunk_c + borrow - sum; |
716 | 335k | if (borrow > 1) { |
717 | 223k | return -1; |
718 | 223k | } |
719 | 111k | borrow <<= kBigitSize; |
720 | 111k | } |
721 | 348k | } |
722 | 5.75k | if (borrow == 0) { |
723 | 5.75k | return 0; |
724 | 5.75k | } |
725 | 0 | return -1; |
726 | 5.75k | } |
727 | | |
728 | | |
729 | 399k | void Bignum::Clamp() { |
730 | 482k | while (used_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) { |
731 | 83.3k | used_bigits_--; |
732 | 83.3k | } |
733 | 399k | if (used_bigits_ == 0) { |
734 | | // Zero. |
735 | 2.38k | exponent_ = 0; |
736 | 2.38k | } |
737 | 399k | } |
738 | | |
739 | | |
740 | 461k | void Bignum::Align(const Bignum& other) { |
741 | 461k | if (exponent_ > other.exponent_) { |
742 | | // If "X" represents a "hidden" bigit (by the exponent) then we are in the |
743 | | // following case (a == this, b == other): |
744 | | // a: aaaaaaXXXX or a: aaaaaXXX |
745 | | // b: bbbbbbX b: bbbbbbbbXX |
746 | | // We replace some of the hidden digits (X) of a with 0 digits. |
747 | | // a: aaaaaa000X or a: aaaaa0XX |
748 | 4.62k | const int zero_bigits = exponent_ - other.exponent_; |
749 | 4.62k | EnsureCapacity(used_bigits_ + zero_bigits); |
750 | 18.7k | for (int i = used_bigits_ - 1; i >= 0; --i) { |
751 | 14.1k | RawBigit(i + zero_bigits) = RawBigit(i); |
752 | 14.1k | } |
753 | 69.6k | for (int i = 0; i < zero_bigits; ++i) { |
754 | 65.0k | RawBigit(i) = 0; |
755 | 65.0k | } |
756 | 4.62k | used_bigits_ += static_cast<int16_t>(zero_bigits); |
757 | 4.62k | exponent_ -= static_cast<int16_t>(zero_bigits); |
758 | | |
759 | 4.62k | DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0); |
760 | 4.62k | DOUBLE_CONVERSION_ASSERT(exponent_ >= 0); |
761 | 4.62k | } |
762 | 461k | } |
763 | | |
764 | | |
765 | 148k | void Bignum::BigitsShiftLeft(const int shift_amount) { |
766 | 148k | DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize); |
767 | 148k | DOUBLE_CONVERSION_ASSERT(shift_amount >= 0); |
768 | 148k | Chunk carry = 0; |
769 | 729k | for (int i = 0; i < used_bigits_; ++i) { |
770 | 580k | const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount); |
771 | 580k | RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask; |
772 | 580k | carry = new_carry; |
773 | 580k | } |
774 | 148k | if (carry != 0) { |
775 | 22.2k | RawBigit(used_bigits_) = carry; |
776 | 22.2k | used_bigits_++; |
777 | 22.2k | } |
778 | 148k | } |
779 | | |
780 | | |
781 | 234k | void Bignum::SubtractTimes(const Bignum& other, const int factor) { |
782 | 234k | DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_); |
783 | 234k | if (factor < 3) { |
784 | 221k | for (int i = 0; i < factor; ++i) { |
785 | 109k | SubtractBignum(other); |
786 | 109k | } |
787 | 112k | return; |
788 | 112k | } |
789 | 122k | Chunk borrow = 0; |
790 | 122k | const int exponent_diff = other.exponent_ - exponent_; |
791 | 1.11M | for (int i = 0; i < other.used_bigits_; ++i) { |
792 | 993k | const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i); |
793 | 993k | const DoubleChunk remove = borrow + product; |
794 | 993k | const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask); |
795 | 993k | RawBigit(i + exponent_diff) = difference & kBigitMask; |
796 | 993k | borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + |
797 | 993k | (remove >> kBigitSize)); |
798 | 993k | } |
799 | 135k | for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) { |
800 | 13.5k | if (borrow == 0) { |
801 | 0 | return; |
802 | 0 | } |
803 | 13.5k | const Chunk difference = RawBigit(i) - borrow; |
804 | 13.5k | RawBigit(i) = difference & kBigitMask; |
805 | 13.5k | borrow = difference >> (kChunkSize - 1); |
806 | 13.5k | } |
807 | 122k | Clamp(); |
808 | 122k | } |
809 | | |
810 | | |
811 | | } // namespace double_conversion |
812 | | |
813 | | // ICU PATCH: Close ICU namespace |
814 | | U_NAMESPACE_END |
815 | | #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING |