1 | // Copyright 2011 the V8 project authors. All rights reserved. |
2 | // Use of this source code is governed by a BSD-style license that can be |
3 | // found in the LICENSE file. |
4 | |
5 | #include "src/bignum.h" |
6 | #include "src/utils.h" |
7 | |
8 | namespace v8 { |
9 | namespace internal { |
10 | |
11 | Bignum::Bignum() |
12 | : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { |
13 | for (int i = 0; i < kBigitCapacity; ++i) { |
14 | bigits_[i] = 0; |
15 | } |
16 | } |
17 | |
18 | |
19 | template<typename S> |
20 | static int BitSize(S value) { |
21 | return 8 * sizeof(value); |
22 | } |
23 | |
24 | |
25 | // Guaranteed to lie in one Bigit. |
26 | void Bignum::AssignUInt16(uint16_t value) { |
27 | DCHECK_GE(kBigitSize, BitSize(value)); |
28 | Zero(); |
29 | if (value == 0) return; |
30 | |
31 | EnsureCapacity(1); |
32 | bigits_[0] = value; |
33 | used_digits_ = 1; |
34 | } |
35 | |
36 | |
37 | void Bignum::AssignUInt64(uint64_t value) { |
38 | const int kUInt64Size = 64; |
39 | |
40 | Zero(); |
41 | if (value == 0) return; |
42 | |
43 | int needed_bigits = kUInt64Size / kBigitSize + 1; |
44 | EnsureCapacity(needed_bigits); |
45 | for (int i = 0; i < needed_bigits; ++i) { |
46 | bigits_[i] = static_cast<Chunk>(value & kBigitMask); |
47 | value = value >> kBigitSize; |
48 | } |
49 | used_digits_ = needed_bigits; |
50 | Clamp(); |
51 | } |
52 | |
53 | |
54 | void Bignum::AssignBignum(const Bignum& other) { |
55 | exponent_ = other.exponent_; |
56 | for (int i = 0; i < other.used_digits_; ++i) { |
57 | bigits_[i] = other.bigits_[i]; |
58 | } |
59 | // Clear the excess digits (if there were any). |
60 | for (int i = other.used_digits_; i < used_digits_; ++i) { |
61 | bigits_[i] = 0; |
62 | } |
63 | used_digits_ = other.used_digits_; |
64 | } |
65 | |
66 | |
67 | static uint64_t ReadUInt64(Vector<const char> buffer, |
68 | int from, |
69 | int digits_to_read) { |
70 | uint64_t result = 0; |
71 | int to = from + digits_to_read; |
72 | |
73 | for (int i = from; i < to; ++i) { |
74 | int digit = buffer[i] - '0'; |
75 | DCHECK(0 <= digit && digit <= 9); |
76 | result = result * 10 + digit; |
77 | } |
78 | return result; |
79 | } |
80 | |
81 | |
82 | void Bignum::AssignDecimalString(Vector<const char> value) { |
83 | // 2^64 = 18446744073709551616 > 10^19 |
84 | const int kMaxUint64DecimalDigits = 19; |
85 | Zero(); |
86 | int length = value.length(); |
87 | int pos = 0; |
88 | // Let's just say that each digit needs 4 bits. |
89 | while (length >= kMaxUint64DecimalDigits) { |
90 | uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); |
91 | pos += kMaxUint64DecimalDigits; |
92 | length -= kMaxUint64DecimalDigits; |
93 | MultiplyByPowerOfTen(kMaxUint64DecimalDigits); |
94 | AddUInt64(digits); |
95 | } |
96 | uint64_t digits = ReadUInt64(value, pos, length); |
97 | MultiplyByPowerOfTen(length); |
98 | AddUInt64(digits); |
99 | Clamp(); |
100 | } |
101 | |
102 | |
103 | static int HexCharValue(char c) { |
104 | if ('0' <= c && c <= '9') return c - '0'; |
105 | if ('a' <= c && c <= 'f') return 10 + c - 'a'; |
106 | if ('A' <= c && c <= 'F') return 10 + c - 'A'; |
107 | UNREACHABLE(); |
108 | } |
109 | |
110 | |
111 | void Bignum::AssignHexString(Vector<const char> value) { |
112 | Zero(); |
113 | int length = value.length(); |
114 | |
115 | int needed_bigits = length * 4 / kBigitSize + 1; |
116 | EnsureCapacity(needed_bigits); |
117 | int string_index = length - 1; |
118 | for (int i = 0; i < needed_bigits - 1; ++i) { |
119 | // These bigits are guaranteed to be "full". |
120 | Chunk current_bigit = 0; |
121 | for (int j = 0; j < kBigitSize / 4; j++) { |
122 | current_bigit += HexCharValue(value[string_index--]) << (j * 4); |
123 | } |
124 | bigits_[i] = current_bigit; |
125 | } |
126 | used_digits_ = needed_bigits - 1; |
127 | |
128 | Chunk most_significant_bigit = 0; // Could be = 0; |
129 | for (int j = 0; j <= string_index; ++j) { |
130 | most_significant_bigit <<= 4; |
131 | most_significant_bigit += HexCharValue(value[j]); |
132 | } |
133 | if (most_significant_bigit != 0) { |
134 | bigits_[used_digits_] = most_significant_bigit; |
135 | used_digits_++; |
136 | } |
137 | Clamp(); |
138 | } |
139 | |
140 | |
141 | void Bignum::AddUInt64(uint64_t operand) { |
142 | if (operand == 0) return; |
143 | Bignum other; |
144 | other.AssignUInt64(operand); |
145 | AddBignum(other); |
146 | } |
147 | |
148 | |
149 | void Bignum::AddBignum(const Bignum& other) { |
150 | DCHECK(IsClamped()); |
151 | DCHECK(other.IsClamped()); |
152 | |
153 | // If this has a greater exponent than other append zero-bigits to this. |
154 | // After this call exponent_ <= other.exponent_. |
155 | Align(other); |
156 | |
157 | // There are two possibilities: |
158 | // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) |
159 | // bbbbb 00000000 |
160 | // ---------------- |
161 | // ccccccccccc 0000 |
162 | // or |
163 | // aaaaaaaaaa 0000 |
164 | // bbbbbbbbb 0000000 |
165 | // ----------------- |
166 | // cccccccccccc 0000 |
167 | // In both cases we might need a carry bigit. |
168 | |
169 | EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); |
170 | Chunk carry = 0; |
171 | int bigit_pos = other.exponent_ - exponent_; |
172 | DCHECK_GE(bigit_pos, 0); |
173 | for (int i = 0; i < other.used_digits_; ++i) { |
174 | Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; |
175 | bigits_[bigit_pos] = sum & kBigitMask; |
176 | carry = sum >> kBigitSize; |
177 | bigit_pos++; |
178 | } |
179 | |
180 | while (carry != 0) { |
181 | Chunk sum = bigits_[bigit_pos] + carry; |
182 | bigits_[bigit_pos] = sum & kBigitMask; |
183 | carry = sum >> kBigitSize; |
184 | bigit_pos++; |
185 | } |
186 | used_digits_ = Max(bigit_pos, used_digits_); |
187 | DCHECK(IsClamped()); |
188 | } |
189 | |
190 | |
191 | void Bignum::SubtractBignum(const Bignum& other) { |
192 | DCHECK(IsClamped()); |
193 | DCHECK(other.IsClamped()); |
194 | // We require this to be bigger than other. |
195 | DCHECK(LessEqual(other, *this)); |
196 | |
197 | Align(other); |
198 | |
199 | int offset = other.exponent_ - exponent_; |
200 | Chunk borrow = 0; |
201 | int i; |
202 | for (i = 0; i < other.used_digits_; ++i) { |
203 | DCHECK((borrow == 0) || (borrow == 1)); |
204 | Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; |
205 | bigits_[i + offset] = difference & kBigitMask; |
206 | borrow = difference >> (kChunkSize - 1); |
207 | } |
208 | while (borrow != 0) { |
209 | Chunk difference = bigits_[i + offset] - borrow; |
210 | bigits_[i + offset] = difference & kBigitMask; |
211 | borrow = difference >> (kChunkSize - 1); |
212 | ++i; |
213 | } |
214 | Clamp(); |
215 | } |
216 | |
217 | |
218 | void Bignum::ShiftLeft(int shift_amount) { |
219 | if (used_digits_ == 0) return; |
220 | exponent_ += shift_amount / kBigitSize; |
221 | int local_shift = shift_amount % kBigitSize; |
222 | EnsureCapacity(used_digits_ + 1); |
223 | BigitsShiftLeft(local_shift); |
224 | } |
225 | |
226 | |
227 | void Bignum::MultiplyByUInt32(uint32_t factor) { |
228 | if (factor == 1) return; |
229 | if (factor == 0) { |
230 | Zero(); |
231 | return; |
232 | } |
233 | if (used_digits_ == 0) return; |
234 | |
235 | // The product of a bigit with the factor is of size kBigitSize + 32. |
236 | // Assert that this number + 1 (for the carry) fits into double chunk. |
237 | DCHECK_GE(kDoubleChunkSize, kBigitSize + 32 + 1); |
238 | DoubleChunk carry = 0; |
239 | for (int i = 0; i < used_digits_; ++i) { |
240 | DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; |
241 | bigits_[i] = static_cast<Chunk>(product & kBigitMask); |
242 | carry = (product >> kBigitSize); |
243 | } |
244 | while (carry != 0) { |
245 | EnsureCapacity(used_digits_ + 1); |
246 | bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); |
247 | used_digits_++; |
248 | carry >>= kBigitSize; |
249 | } |
250 | } |
251 | |
252 | |
253 | void Bignum::MultiplyByUInt64(uint64_t factor) { |
254 | if (factor == 1) return; |
255 | if (factor == 0) { |
256 | Zero(); |
257 | return; |
258 | } |
259 | DCHECK_LT(kBigitSize, 32); |
260 | uint64_t carry = 0; |
261 | uint64_t low = factor & 0xFFFFFFFF; |
262 | uint64_t high = factor >> 32; |
263 | for (int i = 0; i < used_digits_; ++i) { |
264 | uint64_t product_low = low * bigits_[i]; |
265 | uint64_t product_high = high * bigits_[i]; |
266 | uint64_t tmp = (carry & kBigitMask) + product_low; |
267 | bigits_[i] = static_cast<Chunk>(tmp & kBigitMask); |
268 | carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + |
269 | (product_high << (32 - kBigitSize)); |
270 | } |
271 | while (carry != 0) { |
272 | EnsureCapacity(used_digits_ + 1); |
273 | bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); |
274 | used_digits_++; |
275 | carry >>= kBigitSize; |
276 | } |
277 | } |
278 | |
279 | |
280 | void Bignum::MultiplyByPowerOfTen(int exponent) { |
281 | const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765C793, fa10079d); |
282 | const uint16_t kFive1 = 5; |
283 | const uint16_t kFive2 = kFive1 * 5; |
284 | const uint16_t kFive3 = kFive2 * 5; |
285 | const uint16_t kFive4 = kFive3 * 5; |
286 | const uint16_t kFive5 = kFive4 * 5; |
287 | const uint16_t kFive6 = kFive5 * 5; |
288 | const uint32_t kFive7 = kFive6 * 5; |
289 | const uint32_t kFive8 = kFive7 * 5; |
290 | const uint32_t kFive9 = kFive8 * 5; |
291 | const uint32_t kFive10 = kFive9 * 5; |
292 | const uint32_t kFive11 = kFive10 * 5; |
293 | const uint32_t kFive12 = kFive11 * 5; |
294 | const uint32_t kFive13 = kFive12 * 5; |
295 | const uint32_t kFive1_to_12[] = |
296 | { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, |
297 | kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; |
298 | |
299 | DCHECK_GE(exponent, 0); |
300 | if (exponent == 0) return; |
301 | if (used_digits_ == 0) return; |
302 | |
303 | // We shift by exponent at the end just before returning. |
304 | int remaining_exponent = exponent; |
305 | while (remaining_exponent >= 27) { |
306 | MultiplyByUInt64(kFive27); |
307 | remaining_exponent -= 27; |
308 | } |
309 | while (remaining_exponent >= 13) { |
310 | MultiplyByUInt32(kFive13); |
311 | remaining_exponent -= 13; |
312 | } |
313 | if (remaining_exponent > 0) { |
314 | MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); |
315 | } |
316 | ShiftLeft(exponent); |
317 | } |
318 | |
319 | |
320 | void Bignum::Square() { |
321 | DCHECK(IsClamped()); |
322 | int product_length = 2 * used_digits_; |
323 | EnsureCapacity(product_length); |
324 | |
325 | // Comba multiplication: compute each column separately. |
326 | // Example: r = a2a1a0 * b2b1b0. |
327 | // r = 1 * a0b0 + |
328 | // 10 * (a1b0 + a0b1) + |
329 | // 100 * (a2b0 + a1b1 + a0b2) + |
330 | // 1000 * (a2b1 + a1b2) + |
331 | // 10000 * a2b2 |
332 | // |
333 | // In the worst case we have to accumulate nb-digits products of digit*digit. |
334 | // |
335 | // Assert that the additional number of bits in a DoubleChunk are enough to |
336 | // sum up used_digits of Bigit*Bigit. |
337 | if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { |
338 | UNIMPLEMENTED(); |
339 | } |
340 | DoubleChunk accumulator = 0; |
341 | // First shift the digits so we don't overwrite them. |
342 | int copy_offset = used_digits_; |
343 | for (int i = 0; i < used_digits_; ++i) { |
344 | bigits_[copy_offset + i] = bigits_[i]; |
345 | } |
346 | // We have two loops to avoid some 'if's in the loop. |
347 | for (int i = 0; i < used_digits_; ++i) { |
348 | // Process temporary digit i with power i. |
349 | // The sum of the two indices must be equal to i. |
350 | int bigit_index1 = i; |
351 | int bigit_index2 = 0; |
352 | // Sum all of the sub-products. |
353 | while (bigit_index1 >= 0) { |
354 | Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
355 | Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
356 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
357 | bigit_index1--; |
358 | bigit_index2++; |
359 | } |
360 | bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
361 | accumulator >>= kBigitSize; |
362 | } |
363 | for (int i = used_digits_; i < product_length; ++i) { |
364 | int bigit_index1 = used_digits_ - 1; |
365 | int bigit_index2 = i - bigit_index1; |
366 | // Invariant: sum of both indices is again equal to i. |
367 | // Inner loop runs 0 times on last iteration, emptying accumulator. |
368 | while (bigit_index2 < used_digits_) { |
369 | Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
370 | Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
371 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
372 | bigit_index1--; |
373 | bigit_index2++; |
374 | } |
375 | // The overwritten bigits_[i] will never be read in further loop iterations, |
376 | // because bigit_index1 and bigit_index2 are always greater |
377 | // than i - used_digits_. |
378 | bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
379 | accumulator >>= kBigitSize; |
380 | } |
381 | // Since the result was guaranteed to lie inside the number the |
382 | // accumulator must be 0 now. |
383 | DCHECK_EQ(accumulator, 0); |
384 | |
385 | // Don't forget to update the used_digits and the exponent. |
386 | used_digits_ = product_length; |
387 | exponent_ *= 2; |
388 | Clamp(); |
389 | } |
390 | |
391 | |
392 | void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { |
393 | DCHECK_NE(base, 0); |
394 | DCHECK_GE(power_exponent, 0); |
395 | if (power_exponent == 0) { |
396 | AssignUInt16(1); |
397 | return; |
398 | } |
399 | Zero(); |
400 | int shifts = 0; |
401 | // We expect base to be in range 2-32, and most often to be 10. |
402 | // It does not make much sense to implement different algorithms for counting |
403 | // the bits. |
404 | while ((base & 1) == 0) { |
405 | base >>= 1; |
406 | shifts++; |
407 | } |
408 | int bit_size = 0; |
409 | int tmp_base = base; |
410 | while (tmp_base != 0) { |
411 | tmp_base >>= 1; |
412 | bit_size++; |
413 | } |
414 | int final_size = bit_size * power_exponent; |
415 | // 1 extra bigit for the shifting, and one for rounded final_size. |
416 | EnsureCapacity(final_size / kBigitSize + 2); |
417 | |
418 | // Left to Right exponentiation. |
419 | int mask = 1; |
420 | while (power_exponent >= mask) mask <<= 1; |
421 | |
422 | // The mask is now pointing to the bit above the most significant 1-bit of |
423 | // power_exponent. |
424 | // Get rid of first 1-bit; |
425 | mask >>= 2; |
426 | uint64_t this_value = base; |
427 | |
428 | bool delayed_multipliciation = false; |
429 | const uint64_t max_32bits = 0xFFFFFFFF; |
430 | while (mask != 0 && this_value <= max_32bits) { |
431 | this_value = this_value * this_value; |
432 | // Verify that there is enough space in this_value to perform the |
433 | // multiplication. The first bit_size bits must be 0. |
434 | if ((power_exponent & mask) != 0) { |
435 | uint64_t base_bits_mask = |
436 | ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); |
437 | bool high_bits_zero = (this_value & base_bits_mask) == 0; |
438 | if (high_bits_zero) { |
439 | this_value *= base; |
440 | } else { |
441 | delayed_multipliciation = true; |
442 | } |
443 | } |
444 | mask >>= 1; |
445 | } |
446 | AssignUInt64(this_value); |
447 | if (delayed_multipliciation) { |
448 | MultiplyByUInt32(base); |
449 | } |
450 | |
451 | // Now do the same thing as a bignum. |
452 | while (mask != 0) { |
453 | Square(); |
454 | if ((power_exponent & mask) != 0) { |
455 | MultiplyByUInt32(base); |
456 | } |
457 | mask >>= 1; |
458 | } |
459 | |
460 | // And finally add the saved shifts. |
461 | ShiftLeft(shifts * power_exponent); |
462 | } |
463 | |
464 | |
465 | // Precondition: this/other < 16bit. |
466 | uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { |
467 | DCHECK(IsClamped()); |
468 | DCHECK(other.IsClamped()); |
469 | DCHECK_GT(other.used_digits_, 0); |
470 | |
471 | // Easy case: if we have less digits than the divisor than the result is 0. |
472 | // Note: this handles the case where this == 0, too. |
473 | if (BigitLength() < other.BigitLength()) { |
474 | return 0; |
475 | } |
476 | |
477 | Align(other); |
478 | |
479 | uint16_t result = 0; |
480 | |
481 | // Start by removing multiples of 'other' until both numbers have the same |
482 | // number of digits. |
483 | while (BigitLength() > other.BigitLength()) { |
484 | // This naive approach is extremely inefficient if the this divided other |
485 | // might be big. This function is implemented for doubleToString where |
486 | // the result should be small (less than 10). |
487 | DCHECK(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); |
488 | // Remove the multiples of the first digit. |
489 | // Example this = 23 and other equals 9. -> Remove 2 multiples. |
490 | result += bigits_[used_digits_ - 1]; |
491 | SubtractTimes(other, bigits_[used_digits_ - 1]); |
492 | } |
493 | |
494 | DCHECK(BigitLength() == other.BigitLength()); |
495 | |
496 | // Both bignums are at the same length now. |
497 | // Since other has more than 0 digits we know that the access to |
498 | // bigits_[used_digits_ - 1] is safe. |
499 | Chunk this_bigit = bigits_[used_digits_ - 1]; |
500 | Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; |
501 | |
502 | if (other.used_digits_ == 1) { |
503 | // Shortcut for easy (and common) case. |
504 | int quotient = this_bigit / other_bigit; |
505 | bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; |
506 | result += quotient; |
507 | Clamp(); |
508 | return result; |
509 | } |
510 | |
511 | int division_estimate = this_bigit / (other_bigit + 1); |
512 | result += division_estimate; |
513 | SubtractTimes(other, division_estimate); |
514 | |
515 | if (other_bigit * (division_estimate + 1) > this_bigit) { |
516 | // No need to even try to subtract. Even if other's remaining digits were 0 |
517 | // another subtraction would be too much. |
518 | return result; |
519 | } |
520 | |
521 | while (LessEqual(other, *this)) { |
522 | SubtractBignum(other); |
523 | result++; |
524 | } |
525 | return result; |
526 | } |
527 | |
528 | |
529 | template<typename S> |
530 | static int SizeInHexChars(S number) { |
531 | DCHECK_GT(number, 0); |
532 | int result = 0; |
533 | while (number != 0) { |
534 | number >>= 4; |
535 | result++; |
536 | } |
537 | return result; |
538 | } |
539 | |
540 | |
541 | bool Bignum::ToHexString(char* buffer, int buffer_size) const { |
542 | DCHECK(IsClamped()); |
543 | // Each bigit must be printable as separate hex-character. |
544 | DCHECK_EQ(kBigitSize % 4, 0); |
545 | const int kHexCharsPerBigit = kBigitSize / 4; |
546 | |
547 | if (used_digits_ == 0) { |
548 | if (buffer_size < 2) return false; |
549 | buffer[0] = '0'; |
550 | buffer[1] = '\0'; |
551 | return true; |
552 | } |
553 | // We add 1 for the terminating '\0' character. |
554 | int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + |
555 | SizeInHexChars(bigits_[used_digits_ - 1]) + 1; |
556 | if (needed_chars > buffer_size) return false; |
557 | int string_index = needed_chars - 1; |
558 | buffer[string_index--] = '\0'; |
559 | for (int i = 0; i < exponent_; ++i) { |
560 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
561 | buffer[string_index--] = '0'; |
562 | } |
563 | } |
564 | for (int i = 0; i < used_digits_ - 1; ++i) { |
565 | Chunk current_bigit = bigits_[i]; |
566 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
567 | buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); |
568 | current_bigit >>= 4; |
569 | } |
570 | } |
571 | // And finally the last bigit. |
572 | Chunk most_significant_bigit = bigits_[used_digits_ - 1]; |
573 | while (most_significant_bigit != 0) { |
574 | buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); |
575 | most_significant_bigit >>= 4; |
576 | } |
577 | return true; |
578 | } |
579 | |
580 | |
581 | Bignum::Chunk Bignum::BigitAt(int index) const { |
582 | if (index >= BigitLength()) return 0; |
583 | if (index < exponent_) return 0; |
584 | return bigits_[index - exponent_]; |
585 | } |
586 | |
587 | |
588 | int Bignum::Compare(const Bignum& a, const Bignum& b) { |
589 | DCHECK(a.IsClamped()); |
590 | DCHECK(b.IsClamped()); |
591 | int bigit_length_a = a.BigitLength(); |
592 | int bigit_length_b = b.BigitLength(); |
593 | if (bigit_length_a < bigit_length_b) return -1; |
594 | if (bigit_length_a > bigit_length_b) return +1; |
595 | for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { |
596 | Chunk bigit_a = a.BigitAt(i); |
597 | Chunk bigit_b = b.BigitAt(i); |
598 | if (bigit_a < bigit_b) return -1; |
599 | if (bigit_a > bigit_b) return +1; |
600 | // Otherwise they are equal up to this digit. Try the next digit. |
601 | } |
602 | return 0; |
603 | } |
604 | |
605 | |
606 | int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { |
607 | DCHECK(a.IsClamped()); |
608 | DCHECK(b.IsClamped()); |
609 | DCHECK(c.IsClamped()); |
610 | if (a.BigitLength() < b.BigitLength()) { |
611 | return PlusCompare(b, a, c); |
612 | } |
613 | if (a.BigitLength() + 1 < c.BigitLength()) return -1; |
614 | if (a.BigitLength() > c.BigitLength()) return +1; |
615 | // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than |
616 | // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one |
617 | // of 'a'. |
618 | if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { |
619 | return -1; |
620 | } |
621 | |
622 | Chunk borrow = 0; |
623 | // Starting at min_exponent all digits are == 0. So no need to compare them. |
624 | int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); |
625 | for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { |
626 | Chunk chunk_a = a.BigitAt(i); |
627 | Chunk chunk_b = b.BigitAt(i); |
628 | Chunk chunk_c = c.BigitAt(i); |
629 | Chunk sum = chunk_a + chunk_b; |
630 | if (sum > chunk_c + borrow) { |
631 | return +1; |
632 | } else { |
633 | borrow = chunk_c + borrow - sum; |
634 | if (borrow > 1) return -1; |
635 | borrow <<= kBigitSize; |
636 | } |
637 | } |
638 | if (borrow == 0) return 0; |
639 | return -1; |
640 | } |
641 | |
642 | |
643 | void Bignum::Clamp() { |
644 | while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { |
645 | used_digits_--; |
646 | } |
647 | if (used_digits_ == 0) { |
648 | // Zero. |
649 | exponent_ = 0; |
650 | } |
651 | } |
652 | |
653 | |
654 | bool Bignum::IsClamped() const { |
655 | return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; |
656 | } |
657 | |
658 | |
659 | void Bignum::Zero() { |
660 | for (int i = 0; i < used_digits_; ++i) { |
661 | bigits_[i] = 0; |
662 | } |
663 | used_digits_ = 0; |
664 | exponent_ = 0; |
665 | } |
666 | |
667 | |
668 | void Bignum::Align(const Bignum& other) { |
669 | if (exponent_ > other.exponent_) { |
670 | // If "X" represents a "hidden" digit (by the exponent) then we are in the |
671 | // following case (a == this, b == other): |
672 | // a: aaaaaaXXXX or a: aaaaaXXX |
673 | // b: bbbbbbX b: bbbbbbbbXX |
674 | // We replace some of the hidden digits (X) of a with 0 digits. |
675 | // a: aaaaaa000X or a: aaaaa0XX |
676 | int zero_digits = exponent_ - other.exponent_; |
677 | EnsureCapacity(used_digits_ + zero_digits); |
678 | for (int i = used_digits_ - 1; i >= 0; --i) { |
679 | bigits_[i + zero_digits] = bigits_[i]; |
680 | } |
681 | for (int i = 0; i < zero_digits; ++i) { |
682 | bigits_[i] = 0; |
683 | } |
684 | used_digits_ += zero_digits; |
685 | exponent_ -= zero_digits; |
686 | DCHECK_GE(used_digits_, 0); |
687 | DCHECK_GE(exponent_, 0); |
688 | } |
689 | } |
690 | |
691 | |
692 | void Bignum::BigitsShiftLeft(int shift_amount) { |
693 | DCHECK_LT(shift_amount, kBigitSize); |
694 | DCHECK_GE(shift_amount, 0); |
695 | Chunk carry = 0; |
696 | for (int i = 0; i < used_digits_; ++i) { |
697 | Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); |
698 | bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; |
699 | carry = new_carry; |
700 | } |
701 | if (carry != 0) { |
702 | bigits_[used_digits_] = carry; |
703 | used_digits_++; |
704 | } |
705 | } |
706 | |
707 | |
708 | void Bignum::SubtractTimes(const Bignum& other, int factor) { |
709 | #ifdef DEBUG |
710 | Bignum a, b; |
711 | a.AssignBignum(*this); |
712 | b.AssignBignum(other); |
713 | b.MultiplyByUInt32(factor); |
714 | a.SubtractBignum(b); |
715 | #endif |
716 | DCHECK(exponent_ <= other.exponent_); |
717 | if (factor < 3) { |
718 | for (int i = 0; i < factor; ++i) { |
719 | SubtractBignum(other); |
720 | } |
721 | return; |
722 | } |
723 | Chunk borrow = 0; |
724 | int exponent_diff = other.exponent_ - exponent_; |
725 | for (int i = 0; i < other.used_digits_; ++i) { |
726 | DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; |
727 | DoubleChunk remove = borrow + product; |
728 | Chunk difference = |
729 | bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask); |
730 | bigits_[i + exponent_diff] = difference & kBigitMask; |
731 | borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + |
732 | (remove >> kBigitSize)); |
733 | } |
734 | for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { |
735 | if (borrow == 0) return; |
736 | Chunk difference = bigits_[i] - borrow; |
737 | bigits_[i] = difference & kBigitMask; |
738 | borrow = difference >> (kChunkSize - 1); |
739 | } |
740 | Clamp(); |
741 | DCHECK(Bignum::Equal(a, *this)); |
742 | } |
743 | |
744 | |
745 | } // namespace internal |
746 | } // namespace v8 |
747 | |