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1 // Copyright 2010 the V8 project authors. All rights reserved. | |
2 // Redistribution and use in source and binary forms, with or without | |
3 // modification, are permitted provided that the following conditions are | |
4 // met: | |
5 // | |
6 // * Redistributions of source code must retain the above copyright | |
7 // notice, this list of conditions and the following disclaimer. | |
8 // * Redistributions in binary form must reproduce the above | |
9 // copyright notice, this list of conditions and the following | |
10 // disclaimer in the documentation and/or other materials provided | |
11 // with the distribution. | |
12 // * Neither the name of Google Inc. nor the names of its | |
13 // contributors may be used to endorse or promote products derived | |
14 // from this software without specific prior written permission. | |
15 // | |
16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | |
20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | |
22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | |
23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | |
24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | |
25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | |
26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
27 | |
28 #include "bignum.h" | |
29 | |
30 #include "utils.h" | |
31 | |
32 namespace WTF { | |
33 | |
34 namespace double_conversion { | |
35 | |
36 Bignum::Bignum() | |
37 : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { | |
38 for (int i = 0; i < kBigitCapacity; ++i) { | |
39 bigits_[i] = 0; | |
40 } | |
41 } | |
42 | |
43 | |
44 template<typename S> | |
45 static int BitSize(S value) { | |
46 return 8 * sizeof(value); | |
47 } | |
48 | |
49 // Guaranteed to lie in one Bigit. | |
50 void Bignum::AssignUInt16(uint16_t value) { | |
51 ASSERT(kBigitSize >= BitSize(value)); | |
52 Zero(); | |
53 if (value == 0) return; | |
54 | |
55 EnsureCapacity(1); | |
56 bigits_[0] = value; | |
57 used_digits_ = 1; | |
58 } | |
59 | |
60 | |
61 void Bignum::AssignUInt64(uint64_t value) { | |
62 const int kUInt64Size = 64; | |
63 | |
64 Zero(); | |
65 if (value == 0) return; | |
66 | |
67 int needed_bigits = kUInt64Size / kBigitSize + 1; | |
68 EnsureCapacity(needed_bigits); | |
69 for (int i = 0; i < needed_bigits; ++i) { | |
70 bigits_[i] = (uint32_t)value & kBigitMask; | |
71 value = value >> kBigitSize; | |
72 } | |
73 used_digits_ = needed_bigits; | |
74 Clamp(); | |
75 } | |
76 | |
77 | |
78 void Bignum::AssignBignum(const Bignum& other) { | |
79 exponent_ = other.exponent_; | |
80 for (int i = 0; i < other.used_digits_; ++i) { | |
81 bigits_[i] = other.bigits_[i]; | |
82 } | |
83 // Clear the excess digits (if there were any). | |
84 for (int i = other.used_digits_; i < used_digits_; ++i) { | |
85 bigits_[i] = 0; | |
86 } | |
87 used_digits_ = other.used_digits_; | |
88 } | |
89 | |
90 | |
91 static uint64_t ReadUInt64(Vector<const char> buffer, | |
92 int from, | |
93 int digits_to_read) { | |
94 uint64_t result = 0; | |
95 for (int i = from; i < from + digits_to_read; ++i) { | |
96 int digit = buffer[i] - '0'; | |
97 ASSERT(0 <= digit && digit <= 9); | |
98 result = result * 10 + digit; | |
99 } | |
100 return result; | |
101 } | |
102 | |
103 | |
104 void Bignum::AssignDecimalString(Vector<const char> value) { | |
105 // 2^64 = 18446744073709551616 > 10^19 | |
106 const int kMaxUint64DecimalDigits = 19; | |
107 Zero(); | |
108 int length = value.length(); | |
109 int pos = 0; | |
110 // Let's just say that each digit needs 4 bits. | |
111 while (length >= kMaxUint64DecimalDigits) { | |
112 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); | |
113 pos += kMaxUint64DecimalDigits; | |
114 length -= kMaxUint64DecimalDigits; | |
115 MultiplyByPowerOfTen(kMaxUint64DecimalDigits); | |
116 AddUInt64(digits); | |
117 } | |
118 uint64_t digits = ReadUInt64(value, pos, length); | |
119 MultiplyByPowerOfTen(length); | |
120 AddUInt64(digits); | |
121 Clamp(); | |
122 } | |
123 | |
124 | |
125 static int HexCharValue(char c) { | |
126 if ('0' <= c && c <= '9') return c - '0'; | |
127 if ('a' <= c && c <= 'f') return 10 + c - 'a'; | |
128 if ('A' <= c && c <= 'F') return 10 + c - 'A'; | |
129 UNREACHABLE(); | |
130 return 0; // To make compiler happy. | |
131 } | |
132 | |
133 | |
134 void Bignum::AssignHexString(Vector<const char> value) { | |
135 Zero(); | |
136 int length = value.length(); | |
137 | |
138 int needed_bigits = length * 4 / kBigitSize + 1; | |
139 EnsureCapacity(needed_bigits); | |
140 int string_index = length - 1; | |
141 for (int i = 0; i < needed_bigits - 1; ++i) { | |
142 // These bigits are guaranteed to be "full". | |
143 Chunk current_bigit = 0; | |
144 for (int j = 0; j < kBigitSize / 4; j++) { | |
145 current_bigit += HexCharValue(value[string_index--]) << (j * 4); | |
146 } | |
147 bigits_[i] = current_bigit; | |
148 } | |
149 used_digits_ = needed_bigits - 1; | |
150 | |
151 Chunk most_significant_bigit = 0; // Could be = 0; | |
152 for (int j = 0; j <= string_index; ++j) { | |
153 most_significant_bigit <<= 4; | |
154 most_significant_bigit += HexCharValue(value[j]); | |
155 } | |
156 if (most_significant_bigit != 0) { | |
157 bigits_[used_digits_] = most_significant_bigit; | |
158 used_digits_++; | |
159 } | |
160 Clamp(); | |
161 } | |
162 | |
163 | |
164 void Bignum::AddUInt64(uint64_t operand) { | |
165 if (operand == 0) return; | |
166 Bignum other; | |
167 other.AssignUInt64(operand); | |
168 AddBignum(other); | |
169 } | |
170 | |
171 | |
172 void Bignum::AddBignum(const Bignum& other) { | |
173 ASSERT(IsClamped()); | |
174 ASSERT(other.IsClamped()); | |
175 | |
176 // If this has a greater exponent than other append zero-bigits to this. | |
177 // After this call exponent_ <= other.exponent_. | |
178 Align(other); | |
179 | |
180 // There are two possibilities: | |
181 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) | |
182 // bbbbb 00000000 | |
183 // ---------------- | |
184 // ccccccccccc 0000 | |
185 // or | |
186 // aaaaaaaaaa 0000 | |
187 // bbbbbbbbb 0000000 | |
188 // ----------------- | |
189 // cccccccccccc 0000 | |
190 // In both cases we might need a carry bigit. | |
191 | |
192 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); | |
193 Chunk carry = 0; | |
194 int bigit_pos = other.exponent_ - exponent_; | |
195 ASSERT(bigit_pos >= 0); | |
196 for (int i = 0; i < other.used_digits_; ++i) { | |
197 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; | |
198 bigits_[bigit_pos] = sum & kBigitMask; | |
199 carry = sum >> kBigitSize; | |
200 bigit_pos++; | |
201 } | |
202 | |
203 while (carry != 0) { | |
204 Chunk sum = bigits_[bigit_pos] + carry; | |
205 bigits_[bigit_pos] = sum & kBigitMask; | |
206 carry = sum >> kBigitSize; | |
207 bigit_pos++; | |
208 } | |
209 used_digits_ = Max(bigit_pos, used_digits_); | |
210 ASSERT(IsClamped()); | |
211 } | |
212 | |
213 | |
214 void Bignum::SubtractBignum(const Bignum& other) { | |
215 ASSERT(IsClamped()); | |
216 ASSERT(other.IsClamped()); | |
217 // We require this to be bigger than other. | |
218 ASSERT(LessEqual(other, *this)); | |
219 | |
220 Align(other); | |
221 | |
222 int offset = other.exponent_ - exponent_; | |
223 Chunk borrow = 0; | |
224 int i; | |
225 for (i = 0; i < other.used_digits_; ++i) { | |
226 ASSERT((borrow == 0) || (borrow == 1)); | |
227 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; | |
228 bigits_[i + offset] = difference & kBigitMask; | |
229 borrow = difference >> (kChunkSize - 1); | |
230 } | |
231 while (borrow != 0) { | |
232 Chunk difference = bigits_[i + offset] - borrow; | |
233 bigits_[i + offset] = difference & kBigitMask; | |
234 borrow = difference >> (kChunkSize - 1); | |
235 ++i; | |
236 } | |
237 Clamp(); | |
238 } | |
239 | |
240 | |
241 void Bignum::ShiftLeft(int shift_amount) { | |
242 if (used_digits_ == 0) return; | |
243 exponent_ += shift_amount / kBigitSize; | |
244 int local_shift = shift_amount % kBigitSize; | |
245 EnsureCapacity(used_digits_ + 1); | |
246 BigitsShiftLeft(local_shift); | |
247 } | |
248 | |
249 | |
250 void Bignum::MultiplyByUInt32(uint32_t factor) { | |
251 if (factor == 1) return; | |
252 if (factor == 0) { | |
253 Zero(); | |
254 return; | |
255 } | |
256 if (used_digits_ == 0) return; | |
257 | |
258 // The product of a bigit with the factor is of size kBigitSize + 32. | |
259 // Assert that this number + 1 (for the carry) fits into double chunk. | |
260 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); | |
261 DoubleChunk carry = 0; | |
262 for (int i = 0; i < used_digits_; ++i) { | |
263 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i]
+ carry; | |
264 bigits_[i] = static_cast<Chunk>(product & kBigitMask); | |
265 carry = (product >> kBigitSize); | |
266 } | |
267 while (carry != 0) { | |
268 EnsureCapacity(used_digits_ + 1); | |
269 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; | |
270 used_digits_++; | |
271 carry >>= kBigitSize; | |
272 } | |
273 } | |
274 | |
275 | |
276 void Bignum::MultiplyByUInt64(uint64_t factor) { | |
277 if (factor == 1) return; | |
278 if (factor == 0) { | |
279 Zero(); | |
280 return; | |
281 } | |
282 ASSERT(kBigitSize < 32); | |
283 uint64_t carry = 0; | |
284 uint64_t low = factor & 0xFFFFFFFF; | |
285 uint64_t high = factor >> 32; | |
286 for (int i = 0; i < used_digits_; ++i) { | |
287 uint64_t product_low = low * bigits_[i]; | |
288 uint64_t product_high = high * bigits_[i]; | |
289 uint64_t tmp = (carry & kBigitMask) + product_low; | |
290 bigits_[i] = (uint32_t)tmp & kBigitMask; | |
291 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + | |
292 (product_high << (32 - kBigitSize)); | |
293 } | |
294 while (carry != 0) { | |
295 EnsureCapacity(used_digits_ + 1); | |
296 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; | |
297 used_digits_++; | |
298 carry >>= kBigitSize; | |
299 } | |
300 } | |
301 | |
302 | |
303 void Bignum::MultiplyByPowerOfTen(int exponent) { | |
304 const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d); | |
305 const uint16_t kFive1 = 5; | |
306 const uint16_t kFive2 = kFive1 * 5; | |
307 const uint16_t kFive3 = kFive2 * 5; | |
308 const uint16_t kFive4 = kFive3 * 5; | |
309 const uint16_t kFive5 = kFive4 * 5; | |
310 const uint16_t kFive6 = kFive5 * 5; | |
311 const uint32_t kFive7 = kFive6 * 5; | |
312 const uint32_t kFive8 = kFive7 * 5; | |
313 const uint32_t kFive9 = kFive8 * 5; | |
314 const uint32_t kFive10 = kFive9 * 5; | |
315 const uint32_t kFive11 = kFive10 * 5; | |
316 const uint32_t kFive12 = kFive11 * 5; | |
317 const uint32_t kFive13 = kFive12 * 5; | |
318 const uint32_t kFive1_to_12[] = | |
319 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, | |
320 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; | |
321 | |
322 ASSERT(exponent >= 0); | |
323 if (exponent == 0) return; | |
324 if (used_digits_ == 0) return; | |
325 | |
326 // We shift by exponent at the end just before returning. | |
327 int remaining_exponent = exponent; | |
328 while (remaining_exponent >= 27) { | |
329 MultiplyByUInt64(kFive27); | |
330 remaining_exponent -= 27; | |
331 } | |
332 while (remaining_exponent >= 13) { | |
333 MultiplyByUInt32(kFive13); | |
334 remaining_exponent -= 13; | |
335 } | |
336 if (remaining_exponent > 0) { | |
337 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); | |
338 } | |
339 ShiftLeft(exponent); | |
340 } | |
341 | |
342 | |
343 void Bignum::Square() { | |
344 ASSERT(IsClamped()); | |
345 int product_length = 2 * used_digits_; | |
346 EnsureCapacity(product_length); | |
347 | |
348 // Comba multiplication: compute each column separately. | |
349 // Example: r = a2a1a0 * b2b1b0. | |
350 // r = 1 * a0b0 + | |
351 // 10 * (a1b0 + a0b1) + | |
352 // 100 * (a2b0 + a1b1 + a0b2) + | |
353 // 1000 * (a2b1 + a1b2) + | |
354 // 10000 * a2b2 | |
355 // | |
356 // In the worst case we have to accumulate nb-digits products of digit*d
igit. | |
357 // | |
358 // Assert that the additional number of bits in a DoubleChunk are enough
to | |
359 // sum up used_digits of Bigit*Bigit. | |
360 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { | |
361 UNIMPLEMENTED(); | |
362 } | |
363 DoubleChunk accumulator = 0; | |
364 // First shift the digits so we don't overwrite them. | |
365 int copy_offset = used_digits_; | |
366 for (int i = 0; i < used_digits_; ++i) { | |
367 bigits_[copy_offset + i] = bigits_[i]; | |
368 } | |
369 // We have two loops to avoid some 'if's in the loop. | |
370 for (int i = 0; i < used_digits_; ++i) { | |
371 // Process temporary digit i with power i. | |
372 // The sum of the two indices must be equal to i. | |
373 int bigit_index1 = i; | |
374 int bigit_index2 = 0; | |
375 // Sum all of the sub-products. | |
376 while (bigit_index1 >= 0) { | |
377 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; | |
378 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; | |
379 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; | |
380 bigit_index1--; | |
381 bigit_index2++; | |
382 } | |
383 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; | |
384 accumulator >>= kBigitSize; | |
385 } | |
386 for (int i = used_digits_; i < product_length; ++i) { | |
387 int bigit_index1 = used_digits_ - 1; | |
388 int bigit_index2 = i - bigit_index1; | |
389 // Invariant: sum of both indices is again equal to i. | |
390 // Inner loop runs 0 times on last iteration, emptying accumulator. | |
391 while (bigit_index2 < used_digits_) { | |
392 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; | |
393 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; | |
394 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; | |
395 bigit_index1--; | |
396 bigit_index2++; | |
397 } | |
398 // The overwritten bigits_[i] will never be read in further loop ite
rations, | |
399 // because bigit_index1 and bigit_index2 are always greater | |
400 // than i - used_digits_. | |
401 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; | |
402 accumulator >>= kBigitSize; | |
403 } | |
404 // Since the result was guaranteed to lie inside the number the | |
405 // accumulator must be 0 now. | |
406 ASSERT(accumulator == 0); | |
407 | |
408 // Don't forget to update the used_digits and the exponent. | |
409 used_digits_ = product_length; | |
410 exponent_ *= 2; | |
411 Clamp(); | |
412 } | |
413 | |
414 | |
415 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { | |
416 ASSERT(base != 0); | |
417 ASSERT(power_exponent >= 0); | |
418 if (power_exponent == 0) { | |
419 AssignUInt16(1); | |
420 return; | |
421 } | |
422 Zero(); | |
423 int shifts = 0; | |
424 // We expect base to be in range 2-32, and most often to be 10. | |
425 // It does not make much sense to implement different algorithms for cou
nting | |
426 // the bits. | |
427 while ((base & 1) == 0) { | |
428 base >>= 1; | |
429 shifts++; | |
430 } | |
431 int bit_size = 0; | |
432 int tmp_base = base; | |
433 while (tmp_base != 0) { | |
434 tmp_base >>= 1; | |
435 bit_size++; | |
436 } | |
437 int final_size = bit_size * power_exponent; | |
438 // 1 extra bigit for the shifting, and one for rounded final_size. | |
439 EnsureCapacity(final_size / kBigitSize + 2); | |
440 | |
441 // Left to Right exponentiation. | |
442 int mask = 1; | |
443 while (power_exponent >= mask) mask <<= 1; | |
444 | |
445 // The mask is now pointing to the bit above the most significant 1-bit
of | |
446 // power_exponent. | |
447 // Get rid of first 1-bit; | |
448 mask >>= 2; | |
449 uint64_t this_value = base; | |
450 | |
451 bool delayed_multipliciation = false; | |
452 const uint64_t max_32bits = 0xFFFFFFFF; | |
453 while (mask != 0 && this_value <= max_32bits) { | |
454 this_value = this_value * this_value; | |
455 // Verify that there is enough space in this_value to perform the | |
456 // multiplication. The first bit_size bits must be 0. | |
457 if ((power_exponent & mask) != 0) { | |
458 uint64_t base_bits_mask = | |
459 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); | |
460 bool high_bits_zero = (this_value & base_bits_mask) == 0; | |
461 if (high_bits_zero) { | |
462 this_value *= base; | |
463 } else { | |
464 delayed_multipliciation = true; | |
465 } | |
466 } | |
467 mask >>= 1; | |
468 } | |
469 AssignUInt64(this_value); | |
470 if (delayed_multipliciation) { | |
471 MultiplyByUInt32(base); | |
472 } | |
473 | |
474 // Now do the same thing as a bignum. | |
475 while (mask != 0) { | |
476 Square(); | |
477 if ((power_exponent & mask) != 0) { | |
478 MultiplyByUInt32(base); | |
479 } | |
480 mask >>= 1; | |
481 } | |
482 | |
483 // And finally add the saved shifts. | |
484 ShiftLeft(shifts * power_exponent); | |
485 } | |
486 | |
487 | |
488 // Precondition: this/other < 16bit. | |
489 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { | |
490 ASSERT(IsClamped()); | |
491 ASSERT(other.IsClamped()); | |
492 ASSERT(other.used_digits_ > 0); | |
493 | |
494 // Easy case: if we have less digits than the divisor than the result is
0. | |
495 // Note: this handles the case where this == 0, too. | |
496 if (BigitLength() < other.BigitLength()) { | |
497 return 0; | |
498 } | |
499 | |
500 Align(other); | |
501 | |
502 uint16_t result = 0; | |
503 | |
504 // Start by removing multiples of 'other' until both numbers have the sa
me | |
505 // number of digits. | |
506 while (BigitLength() > other.BigitLength()) { | |
507 // This naive approach is extremely inefficient if the this divided
other | |
508 // might be big. This function is implemented for doubleToString whe
re | |
509 // the result should be small (less than 10). | |
510 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) /
16)); | |
511 // Remove the multiples of the first digit. | |
512 // Example this = 23 and other equals 9. -> Remove 2 multiples. | |
513 result += static_cast<uint16_t>(bigits_[used_digits_ - 1]); | |
514 SubtractTimes(other, bigits_[used_digits_ - 1]); | |
515 } | |
516 | |
517 ASSERT(BigitLength() == other.BigitLength()); | |
518 | |
519 // Both bignums are at the same length now. | |
520 // Since other has more than 0 digits we know that the access to | |
521 // bigits_[used_digits_ - 1] is safe. | |
522 Chunk this_bigit = bigits_[used_digits_ - 1]; | |
523 Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; | |
524 | |
525 if (other.used_digits_ == 1) { | |
526 // Shortcut for easy (and common) case. | |
527 uint16_t quotient = static_cast<uint16_t>(this_bigit / other_bigit); | |
528 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; | |
529 result += quotient; | |
530 Clamp(); | |
531 return result; | |
532 } | |
533 | |
534 uint16_t division_estimate = static_cast<uint16_t>(this_bigit / (other_b
igit + 1)); | |
535 result += division_estimate; | |
536 SubtractTimes(other, division_estimate); | |
537 | |
538 if (other_bigit * (division_estimate + 1) > this_bigit) { | |
539 // No need to even try to subtract. Even if other's remaining digits
were 0 | |
540 // another subtraction would be too much. | |
541 return result; | |
542 } | |
543 | |
544 while (LessEqual(other, *this)) { | |
545 SubtractBignum(other); | |
546 result++; | |
547 } | |
548 return result; | |
549 } | |
550 | |
551 | |
552 template<typename S> | |
553 static int SizeInHexChars(S number) { | |
554 ASSERT(number > 0); | |
555 int result = 0; | |
556 while (number != 0) { | |
557 number >>= 4; | |
558 result++; | |
559 } | |
560 return result; | |
561 } | |
562 | |
563 | |
564 static char HexCharOfValue(uint8_t value) { | |
565 ASSERT(0 <= value && value <= 16); | |
566 if (value < 10) return value + '0'; | |
567 return value - 10 + 'A'; | |
568 } | |
569 | |
570 | |
571 bool Bignum::ToHexString(char* buffer, int buffer_size) const { | |
572 ASSERT(IsClamped()); | |
573 // Each bigit must be printable as separate hex-character. | |
574 ASSERT(kBigitSize % 4 == 0); | |
575 const int kHexCharsPerBigit = kBigitSize / 4; | |
576 | |
577 if (used_digits_ == 0) { | |
578 if (buffer_size < 2) return false; | |
579 buffer[0] = '0'; | |
580 buffer[1] = '\0'; | |
581 return true; | |
582 } | |
583 // We add 1 for the terminating '\0' character. | |
584 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + | |
585 SizeInHexChars(bigits_[used_digits_ - 1]) + 1; | |
586 if (needed_chars > buffer_size) return false; | |
587 int string_index = needed_chars - 1; | |
588 buffer[string_index--] = '\0'; | |
589 for (int i = 0; i < exponent_; ++i) { | |
590 for (int j = 0; j < kHexCharsPerBigit; ++j) { | |
591 buffer[string_index--] = '0'; | |
592 } | |
593 } | |
594 for (int i = 0; i < used_digits_ - 1; ++i) { | |
595 Chunk current_bigit = bigits_[i]; | |
596 for (int j = 0; j < kHexCharsPerBigit; ++j) { | |
597 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); | |
598 current_bigit >>= 4; | |
599 } | |
600 } | |
601 // And finally the last bigit. | |
602 Chunk most_significant_bigit = bigits_[used_digits_ - 1]; | |
603 while (most_significant_bigit != 0) { | |
604 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF
); | |
605 most_significant_bigit >>= 4; | |
606 } | |
607 return true; | |
608 } | |
609 | |
610 | |
611 Bignum::Chunk Bignum::BigitAt(int index) const { | |
612 if (index >= BigitLength()) return 0; | |
613 if (index < exponent_) return 0; | |
614 return bigits_[index - exponent_]; | |
615 } | |
616 | |
617 | |
618 int Bignum::Compare(const Bignum& a, const Bignum& b) { | |
619 ASSERT(a.IsClamped()); | |
620 ASSERT(b.IsClamped()); | |
621 int bigit_length_a = a.BigitLength(); | |
622 int bigit_length_b = b.BigitLength(); | |
623 if (bigit_length_a < bigit_length_b) return -1; | |
624 if (bigit_length_a > bigit_length_b) return +1; | |
625 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i
) { | |
626 Chunk bigit_a = a.BigitAt(i); | |
627 Chunk bigit_b = b.BigitAt(i); | |
628 if (bigit_a < bigit_b) return -1; | |
629 if (bigit_a > bigit_b) return +1; | |
630 // Otherwise they are equal up to this digit. Try the next digit. | |
631 } | |
632 return 0; | |
633 } | |
634 | |
635 | |
636 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { | |
637 ASSERT(a.IsClamped()); | |
638 ASSERT(b.IsClamped()); | |
639 ASSERT(c.IsClamped()); | |
640 if (a.BigitLength() < b.BigitLength()) { | |
641 return PlusCompare(b, a, c); | |
642 } | |
643 if (a.BigitLength() + 1 < c.BigitLength()) return -1; | |
644 if (a.BigitLength() > c.BigitLength()) return +1; | |
645 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' t
han | |
646 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the
one | |
647 // of 'a'. | |
648 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength())
{ | |
649 return -1; | |
650 } | |
651 | |
652 Chunk borrow = 0; | |
653 // Starting at min_exponent all digits are == 0. So no need to compare t
hem. | |
654 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); | |
655 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { | |
656 Chunk chunk_a = a.BigitAt(i); | |
657 Chunk chunk_b = b.BigitAt(i); | |
658 Chunk chunk_c = c.BigitAt(i); | |
659 Chunk sum = chunk_a + chunk_b; | |
660 if (sum > chunk_c + borrow) { | |
661 return +1; | |
662 } else { | |
663 borrow = chunk_c + borrow - sum; | |
664 if (borrow > 1) return -1; | |
665 borrow <<= kBigitSize; | |
666 } | |
667 } | |
668 if (borrow == 0) return 0; | |
669 return -1; | |
670 } | |
671 | |
672 | |
673 void Bignum::Clamp() { | |
674 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { | |
675 used_digits_--; | |
676 } | |
677 if (used_digits_ == 0) { | |
678 // Zero. | |
679 exponent_ = 0; | |
680 } | |
681 } | |
682 | |
683 | |
684 bool Bignum::IsClamped() const { | |
685 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; | |
686 } | |
687 | |
688 | |
689 void Bignum::Zero() { | |
690 for (int i = 0; i < used_digits_; ++i) { | |
691 bigits_[i] = 0; | |
692 } | |
693 used_digits_ = 0; | |
694 exponent_ = 0; | |
695 } | |
696 | |
697 | |
698 void Bignum::Align(const Bignum& other) { | |
699 if (exponent_ > other.exponent_) { | |
700 // If "X" represents a "hidden" digit (by the exponent) then we are
in the | |
701 // following case (a == this, b == other): | |
702 // a: aaaaaaXXXX or a: aaaaaXXX | |
703 // b: bbbbbbX b: bbbbbbbbXX | |
704 // We replace some of the hidden digits (X) of a with 0 digits. | |
705 // a: aaaaaa000X or a: aaaaa0XX | |
706 int zero_digits = exponent_ - other.exponent_; | |
707 EnsureCapacity(used_digits_ + zero_digits); | |
708 for (int i = used_digits_ - 1; i >= 0; --i) { | |
709 bigits_[i + zero_digits] = bigits_[i]; | |
710 } | |
711 for (int i = 0; i < zero_digits; ++i) { | |
712 bigits_[i] = 0; | |
713 } | |
714 used_digits_ += zero_digits; | |
715 exponent_ -= zero_digits; | |
716 ASSERT(used_digits_ >= 0); | |
717 ASSERT(exponent_ >= 0); | |
718 } | |
719 } | |
720 | |
721 | |
722 void Bignum::BigitsShiftLeft(int shift_amount) { | |
723 ASSERT(shift_amount < kBigitSize); | |
724 ASSERT(shift_amount >= 0); | |
725 Chunk carry = 0; | |
726 for (int i = 0; i < used_digits_; ++i) { | |
727 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); | |
728 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; | |
729 carry = new_carry; | |
730 } | |
731 if (carry != 0) { | |
732 bigits_[used_digits_] = carry; | |
733 used_digits_++; | |
734 } | |
735 } | |
736 | |
737 | |
738 void Bignum::SubtractTimes(const Bignum& other, int factor) { | |
739 ASSERT(exponent_ <= other.exponent_); | |
740 if (factor < 3) { | |
741 for (int i = 0; i < factor; ++i) { | |
742 SubtractBignum(other); | |
743 } | |
744 return; | |
745 } | |
746 Chunk borrow = 0; | |
747 int exponent_diff = other.exponent_ - exponent_; | |
748 for (int i = 0; i < other.used_digits_; ++i) { | |
749 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigit
s_[i]; | |
750 DoubleChunk remove = borrow + product; | |
751 Chunk difference = bigits_[i + exponent_diff] - ((uint32_t)remove &
kBigitMask); | |
752 bigits_[i + exponent_diff] = difference & kBigitMask; | |
753 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + | |
754 (remove >> kBigitSize)); | |
755 } | |
756 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i)
{ | |
757 if (borrow == 0) return; | |
758 Chunk difference = bigits_[i] - borrow; | |
759 bigits_[i] = difference & kBigitMask; | |
760 borrow = difference >> (kChunkSize - 1); | |
761 } | |
762 Clamp(); | |
763 } | |
764 | |
765 | |
766 } // namespace double_conversion | |
767 | |
768 } // namespace WTF | |
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