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
8namespace v8 {
9namespace internal {
10
11Bignum::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
19template<typename S>
20static int BitSize(S value) {
21 return 8 * sizeof(value);
22}
23
24
25// Guaranteed to lie in one Bigit.
26void 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
37void 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
54void 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
67static 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
82void 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
103static 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
111void 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
141void Bignum::AddUInt64(uint64_t operand) {
142 if (operand == 0) return;
143 Bignum other;
144 other.AssignUInt64(operand);
145 AddBignum(other);
146}
147
148
149void 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
191void 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
218void 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
227void 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
253void 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
280void 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
320void 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
392void 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.
466uint16_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
529template<typename S>
530static 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
541bool 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
581Bignum::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
588int 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
606int 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
643void 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
654bool Bignum::IsClamped() const {
655 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
656}
657
658
659void 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
668void 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
692void 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
708void 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