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27
28#include <double-conversion/bignum.h>
29#include <double-conversion/utils.h>
30
31namespace double_conversion {
32
33Bignum::Bignum()
34 : bigits_buffer_(), bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
35 for (int i = 0; i < kBigitCapacity; ++i) {
36 bigits_[i] = 0;
37 }
38}
39
40
41template<typename S>
42static int BitSize(S value) {
43 (void) value; // Mark variable as used.
44 return 8 * sizeof(value);
45}
46
47// Guaranteed to lie in one Bigit.
48void Bignum::AssignUInt16(uint16_t value) {
49 ASSERT(kBigitSize >= BitSize(value));
50 Zero();
51 if (value == 0) return;
52
53 EnsureCapacity(1);
54 bigits_[0] = value;
55 used_digits_ = 1;
56}
57
58
59void Bignum::AssignUInt64(uint64_t value) {
60 const int kUInt64Size = 64;
61
62 Zero();
63 if (value == 0) return;
64
65 int needed_bigits = kUInt64Size / kBigitSize + 1;
66 EnsureCapacity(needed_bigits);
67 for (int i = 0; i < needed_bigits; ++i) {
68 bigits_[i] = value & kBigitMask;
69 value = value >> kBigitSize;
70 }
71 used_digits_ = needed_bigits;
72 Clamp();
73}
74
75
76void Bignum::AssignBignum(const Bignum& other) {
77 exponent_ = other.exponent_;
78 for (int i = 0; i < other.used_digits_; ++i) {
79 bigits_[i] = other.bigits_[i];
80 }
81 // Clear the excess digits (if there were any).
82 for (int i = other.used_digits_; i < used_digits_; ++i) {
83 bigits_[i] = 0;
84 }
85 used_digits_ = other.used_digits_;
86}
87
88
89static uint64_t ReadUInt64(Vector<const char> buffer,
90 int from,
91 int digits_to_read) {
92 uint64_t result = 0;
93 for (int i = from; i < from + digits_to_read; ++i) {
94 int digit = buffer[i] - '0';
95 ASSERT(0 <= digit && digit <= 9);
96 result = result * 10 + digit;
97 }
98 return result;
99}
100
101
102void Bignum::AssignDecimalString(Vector<const char> value) {
103 // 2^64 = 18446744073709551616 > 10^19
104 const int kMaxUint64DecimalDigits = 19;
105 Zero();
106 int length = value.length();
107 unsigned int pos = 0;
108 // Let's just say that each digit needs 4 bits.
109 while (length >= kMaxUint64DecimalDigits) {
110 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
111 pos += kMaxUint64DecimalDigits;
112 length -= kMaxUint64DecimalDigits;
113 MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
114 AddUInt64(digits);
115 }
116 uint64_t digits = ReadUInt64(value, pos, length);
117 MultiplyByPowerOfTen(length);
118 AddUInt64(digits);
119 Clamp();
120}
121
122
123static int HexCharValue(char c) {
124 if ('0' <= c && c <= '9') return c - '0';
125 if ('a' <= c && c <= 'f') return 10 + c - 'a';
126 ASSERT('A' <= c && c <= 'F');
127 return 10 + c - 'A';
128}
129
130
131void Bignum::AssignHexString(Vector<const char> value) {
132 Zero();
133 int length = value.length();
134
135 int needed_bigits = length * 4 / kBigitSize + 1;
136 EnsureCapacity(needed_bigits);
137 int string_index = length - 1;
138 for (int i = 0; i < needed_bigits - 1; ++i) {
139 // These bigits are guaranteed to be "full".
140 Chunk current_bigit = 0;
141 for (int j = 0; j < kBigitSize / 4; j++) {
142 current_bigit += HexCharValue(value[string_index--]) << (j * 4);
143 }
144 bigits_[i] = current_bigit;
145 }
146 used_digits_ = needed_bigits - 1;
147
148 Chunk most_significant_bigit = 0; // Could be = 0;
149 for (int j = 0; j <= string_index; ++j) {
150 most_significant_bigit <<= 4;
151 most_significant_bigit += HexCharValue(value[j]);
152 }
153 if (most_significant_bigit != 0) {
154 bigits_[used_digits_] = most_significant_bigit;
155 used_digits_++;
156 }
157 Clamp();
158}
159
160
161void Bignum::AddUInt64(uint64_t operand) {
162 if (operand == 0) return;
163 Bignum other;
164 other.AssignUInt64(operand);
165 AddBignum(other);
166}
167
168
169void Bignum::AddBignum(const Bignum& other) {
170 ASSERT(IsClamped());
171 ASSERT(other.IsClamped());
172
173 // If this has a greater exponent than other append zero-bigits to this.
174 // After this call exponent_ <= other.exponent_.
175 Align(other);
176
177 // There are two possibilities:
178 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
179 // bbbbb 00000000
180 // ----------------
181 // ccccccccccc 0000
182 // or
183 // aaaaaaaaaa 0000
184 // bbbbbbbbb 0000000
185 // -----------------
186 // cccccccccccc 0000
187 // In both cases we might need a carry bigit.
188
189 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
190 Chunk carry = 0;
191 int bigit_pos = other.exponent_ - exponent_;
192 ASSERT(bigit_pos >= 0);
193 for (int i = 0; i < other.used_digits_; ++i) {
194 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
195 bigits_[bigit_pos] = sum & kBigitMask;
196 carry = sum >> kBigitSize;
197 bigit_pos++;
198 }
199
200 while (carry != 0) {
201 Chunk sum = bigits_[bigit_pos] + carry;
202 bigits_[bigit_pos] = sum & kBigitMask;
203 carry = sum >> kBigitSize;
204 bigit_pos++;
205 }
206 used_digits_ = Max(bigit_pos, used_digits_);
207 ASSERT(IsClamped());
208}
209
210
211void Bignum::SubtractBignum(const Bignum& other) {
212 ASSERT(IsClamped());
213 ASSERT(other.IsClamped());
214 // We require this to be bigger than other.
215 ASSERT(LessEqual(other, *this));
216
217 Align(other);
218
219 int offset = other.exponent_ - exponent_;
220 Chunk borrow = 0;
221 int i;
222 for (i = 0; i < other.used_digits_; ++i) {
223 ASSERT((borrow == 0) || (borrow == 1));
224 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
225 bigits_[i + offset] = difference & kBigitMask;
226 borrow = difference >> (kChunkSize - 1);
227 }
228 while (borrow != 0) {
229 Chunk difference = bigits_[i + offset] - borrow;
230 bigits_[i + offset] = difference & kBigitMask;
231 borrow = difference >> (kChunkSize - 1);
232 ++i;
233 }
234 Clamp();
235}
236
237
238void Bignum::ShiftLeft(int shift_amount) {
239 if (used_digits_ == 0) return;
240 exponent_ += shift_amount / kBigitSize;
241 int local_shift = shift_amount % kBigitSize;
242 EnsureCapacity(used_digits_ + 1);
243 BigitsShiftLeft(local_shift);
244}
245
246
247void Bignum::MultiplyByUInt32(uint32_t factor) {
248 if (factor == 1) return;
249 if (factor == 0) {
250 Zero();
251 return;
252 }
253 if (used_digits_ == 0) return;
254
255 // The product of a bigit with the factor is of size kBigitSize + 32.
256 // Assert that this number + 1 (for the carry) fits into double chunk.
257 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
258 DoubleChunk carry = 0;
259 for (int i = 0; i < used_digits_; ++i) {
260 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
261 bigits_[i] = static_cast<Chunk>(product & kBigitMask);
262 carry = (product >> kBigitSize);
263 }
264 while (carry != 0) {
265 EnsureCapacity(used_digits_ + 1);
266 bigits_[used_digits_] = carry & kBigitMask;
267 used_digits_++;
268 carry >>= kBigitSize;
269 }
270}
271
272
273void Bignum::MultiplyByUInt64(uint64_t factor) {
274 if (factor == 1) return;
275 if (factor == 0) {
276 Zero();
277 return;
278 }
279 ASSERT(kBigitSize < 32);
280 uint64_t carry = 0;
281 uint64_t low = factor & 0xFFFFFFFF;
282 uint64_t high = factor >> 32;
283 for (int i = 0; i < used_digits_; ++i) {
284 uint64_t product_low = low * bigits_[i];
285 uint64_t product_high = high * bigits_[i];
286 uint64_t tmp = (carry & kBigitMask) + product_low;
287 bigits_[i] = tmp & kBigitMask;
288 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
289 (product_high << (32 - kBigitSize));
290 }
291 while (carry != 0) {
292 EnsureCapacity(used_digits_ + 1);
293 bigits_[used_digits_] = carry & kBigitMask;
294 used_digits_++;
295 carry >>= kBigitSize;
296 }
297}
298
299
300void Bignum::MultiplyByPowerOfTen(int exponent) {
301 const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
302 const uint16_t kFive1 = 5;
303 const uint16_t kFive2 = kFive1 * 5;
304 const uint16_t kFive3 = kFive2 * 5;
305 const uint16_t kFive4 = kFive3 * 5;
306 const uint16_t kFive5 = kFive4 * 5;
307 const uint16_t kFive6 = kFive5 * 5;
308 const uint32_t kFive7 = kFive6 * 5;
309 const uint32_t kFive8 = kFive7 * 5;
310 const uint32_t kFive9 = kFive8 * 5;
311 const uint32_t kFive10 = kFive9 * 5;
312 const uint32_t kFive11 = kFive10 * 5;
313 const uint32_t kFive12 = kFive11 * 5;
314 const uint32_t kFive13 = kFive12 * 5;
315 const uint32_t kFive1_to_12[] =
316 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
317 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
318
319 ASSERT(exponent >= 0);
320 if (exponent == 0) return;
321 if (used_digits_ == 0) return;
322
323 // We shift by exponent at the end just before returning.
324 int remaining_exponent = exponent;
325 while (remaining_exponent >= 27) {
326 MultiplyByUInt64(kFive27);
327 remaining_exponent -= 27;
328 }
329 while (remaining_exponent >= 13) {
330 MultiplyByUInt32(kFive13);
331 remaining_exponent -= 13;
332 }
333 if (remaining_exponent > 0) {
334 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
335 }
336 ShiftLeft(exponent);
337}
338
339
340void Bignum::Square() {
341 ASSERT(IsClamped());
342 int product_length = 2 * used_digits_;
343 EnsureCapacity(product_length);
344
345 // Comba multiplication: compute each column separately.
346 // Example: r = a2a1a0 * b2b1b0.
347 // r = 1 * a0b0 +
348 // 10 * (a1b0 + a0b1) +
349 // 100 * (a2b0 + a1b1 + a0b2) +
350 // 1000 * (a2b1 + a1b2) +
351 // 10000 * a2b2
352 //
353 // In the worst case we have to accumulate nb-digits products of digit*digit.
354 //
355 // Assert that the additional number of bits in a DoubleChunk are enough to
356 // sum up used_digits of Bigit*Bigit.
357 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
358 UNIMPLEMENTED();
359 }
360 DoubleChunk accumulator = 0;
361 // First shift the digits so we don't overwrite them.
362 int copy_offset = used_digits_;
363 for (int i = 0; i < used_digits_; ++i) {
364 bigits_[copy_offset + i] = bigits_[i];
365 }
366 // We have two loops to avoid some 'if's in the loop.
367 for (int i = 0; i < used_digits_; ++i) {
368 // Process temporary digit i with power i.
369 // The sum of the two indices must be equal to i.
370 int bigit_index1 = i;
371 int bigit_index2 = 0;
372 // Sum all of the sub-products.
373 while (bigit_index1 >= 0) {
374 Chunk chunk1 = bigits_[copy_offset + bigit_index1];
375 Chunk chunk2 = bigits_[copy_offset + bigit_index2];
376 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
377 bigit_index1--;
378 bigit_index2++;
379 }
380 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
381 accumulator >>= kBigitSize;
382 }
383 for (int i = used_digits_; i < product_length; ++i) {
384 int bigit_index1 = used_digits_ - 1;
385 int bigit_index2 = i - bigit_index1;
386 // Invariant: sum of both indices is again equal to i.
387 // Inner loop runs 0 times on last iteration, emptying accumulator.
388 while (bigit_index2 < used_digits_) {
389 Chunk chunk1 = bigits_[copy_offset + bigit_index1];
390 Chunk chunk2 = bigits_[copy_offset + bigit_index2];
391 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
392 bigit_index1--;
393 bigit_index2++;
394 }
395 // The overwritten bigits_[i] will never be read in further loop iterations,
396 // because bigit_index1 and bigit_index2 are always greater
397 // than i - used_digits_.
398 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
399 accumulator >>= kBigitSize;
400 }
401 // Since the result was guaranteed to lie inside the number the
402 // accumulator must be 0 now.
403 ASSERT(accumulator == 0);
404
405 // Don't forget to update the used_digits and the exponent.
406 used_digits_ = product_length;
407 exponent_ *= 2;
408 Clamp();
409}
410
411
412void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
413 ASSERT(base != 0);
414 ASSERT(power_exponent >= 0);
415 if (power_exponent == 0) {
416 AssignUInt16(1);
417 return;
418 }
419 Zero();
420 int shifts = 0;
421 // We expect base to be in range 2-32, and most often to be 10.
422 // It does not make much sense to implement different algorithms for counting
423 // the bits.
424 while ((base & 1) == 0) {
425 base >>= 1;
426 shifts++;
427 }
428 int bit_size = 0;
429 int tmp_base = base;
430 while (tmp_base != 0) {
431 tmp_base >>= 1;
432 bit_size++;
433 }
434 int final_size = bit_size * power_exponent;
435 // 1 extra bigit for the shifting, and one for rounded final_size.
436 EnsureCapacity(final_size / kBigitSize + 2);
437
438 // Left to Right exponentiation.
439 int mask = 1;
440 while (power_exponent >= mask) mask <<= 1;
441
442 // The mask is now pointing to the bit above the most significant 1-bit of
443 // power_exponent.
444 // Get rid of first 1-bit;
445 mask >>= 2;
446 uint64_t this_value = base;
447
448 bool delayed_multiplication = false;
449 const uint64_t max_32bits = 0xFFFFFFFF;
450 while (mask != 0 && this_value <= max_32bits) {
451 this_value = this_value * this_value;
452 // Verify that there is enough space in this_value to perform the
453 // multiplication. The first bit_size bits must be 0.
454 if ((power_exponent & mask) != 0) {
455 ASSERT(bit_size > 0);
456 uint64_t base_bits_mask =
457 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
458 bool high_bits_zero = (this_value & base_bits_mask) == 0;
459 if (high_bits_zero) {
460 this_value *= base;
461 } else {
462 delayed_multiplication = true;
463 }
464 }
465 mask >>= 1;
466 }
467 AssignUInt64(this_value);
468 if (delayed_multiplication) {
469 MultiplyByUInt32(base);
470 }
471
472 // Now do the same thing as a bignum.
473 while (mask != 0) {
474 Square();
475 if ((power_exponent & mask) != 0) {
476 MultiplyByUInt32(base);
477 }
478 mask >>= 1;
479 }
480
481 // And finally add the saved shifts.
482 ShiftLeft(shifts * power_exponent);
483}
484
485
486// Precondition: this/other < 16bit.
487uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
488 ASSERT(IsClamped());
489 ASSERT(other.IsClamped());
490 ASSERT(other.used_digits_ > 0);
491
492 // Easy case: if we have less digits than the divisor than the result is 0.
493 // Note: this handles the case where this == 0, too.
494 if (BigitLength() < other.BigitLength()) {
495 return 0;
496 }
497
498 Align(other);
499
500 uint16_t result = 0;
501
502 // Start by removing multiples of 'other' until both numbers have the same
503 // number of digits.
504 while (BigitLength() > other.BigitLength()) {
505 // This naive approach is extremely inefficient if `this` divided by other
506 // is big. This function is implemented for doubleToString where
507 // the result should be small (less than 10).
508 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
509 ASSERT(bigits_[used_digits_ - 1] < 0x10000);
510 // Remove the multiples of the first digit.
511 // Example this = 23 and other equals 9. -> Remove 2 multiples.
512 result += static_cast<uint16_t>(bigits_[used_digits_ - 1]);
513 SubtractTimes(other, bigits_[used_digits_ - 1]);
514 }
515
516 ASSERT(BigitLength() == other.BigitLength());
517
518 // Both bignums are at the same length now.
519 // Since other has more than 0 digits we know that the access to
520 // bigits_[used_digits_ - 1] is safe.
521 Chunk this_bigit = bigits_[used_digits_ - 1];
522 Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
523
524 if (other.used_digits_ == 1) {
525 // Shortcut for easy (and common) case.
526 int quotient = this_bigit / other_bigit;
527 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
528 ASSERT(quotient < 0x10000);
529 result += static_cast<uint16_t>(quotient);
530 Clamp();
531 return result;
532 }
533
534 int division_estimate = this_bigit / (other_bigit + 1);
535 ASSERT(division_estimate < 0x10000);
536 result += static_cast<uint16_t>(division_estimate);
537 SubtractTimes(other, division_estimate);
538
539 if (other_bigit * (division_estimate + 1) > this_bigit) {
540 // No need to even try to subtract. Even if other's remaining digits were 0
541 // another subtraction would be too much.
542 return result;
543 }
544
545 while (LessEqual(other, *this)) {
546 SubtractBignum(other);
547 result++;
548 }
549 return result;
550}
551
552
553template<typename S>
554static int SizeInHexChars(S number) {
555 ASSERT(number > 0);
556 int result = 0;
557 while (number != 0) {
558 number >>= 4;
559 result++;
560 }
561 return result;
562}
563
564
565static char HexCharOfValue(int value) {
566 ASSERT(0 <= value && value <= 16);
567 if (value < 10) return static_cast<char>(value + '0');
568 return static_cast<char>(value - 10 + 'A');
569}
570
571
572bool Bignum::ToHexString(char* buffer, int buffer_size) const {
573 ASSERT(IsClamped());
574 // Each bigit must be printable as separate hex-character.
575 ASSERT(kBigitSize % 4 == 0);
576 const int kHexCharsPerBigit = kBigitSize / 4;
577
578 if (used_digits_ == 0) {
579 if (buffer_size < 2) return false;
580 buffer[0] = '0';
581 buffer[1] = '\0';
582 return true;
583 }
584 // We add 1 for the terminating '\0' character.
585 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
586 SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
587 if (needed_chars > buffer_size) return false;
588 int string_index = needed_chars - 1;
589 buffer[string_index--] = '\0';
590 for (int i = 0; i < exponent_; ++i) {
591 for (int j = 0; j < kHexCharsPerBigit; ++j) {
592 buffer[string_index--] = '0';
593 }
594 }
595 for (int i = 0; i < used_digits_ - 1; ++i) {
596 Chunk current_bigit = bigits_[i];
597 for (int j = 0; j < kHexCharsPerBigit; ++j) {
598 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
599 current_bigit >>= 4;
600 }
601 }
602 // And finally the last bigit.
603 Chunk most_significant_bigit = bigits_[used_digits_ - 1];
604 while (most_significant_bigit != 0) {
605 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
606 most_significant_bigit >>= 4;
607 }
608 return true;
609}
610
611
612Bignum::Chunk Bignum::BigitAt(int index) const {
613 if (index >= BigitLength()) return 0;
614 if (index < exponent_) return 0;
615 return bigits_[index - exponent_];
616}
617
618
619int Bignum::Compare(const Bignum& a, const Bignum& b) {
620 ASSERT(a.IsClamped());
621 ASSERT(b.IsClamped());
622 int bigit_length_a = a.BigitLength();
623 int bigit_length_b = b.BigitLength();
624 if (bigit_length_a < bigit_length_b) return -1;
625 if (bigit_length_a > bigit_length_b) return +1;
626 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
627 Chunk bigit_a = a.BigitAt(i);
628 Chunk bigit_b = b.BigitAt(i);
629 if (bigit_a < bigit_b) return -1;
630 if (bigit_a > bigit_b) return +1;
631 // Otherwise they are equal up to this digit. Try the next digit.
632 }
633 return 0;
634}
635
636
637int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
638 ASSERT(a.IsClamped());
639 ASSERT(b.IsClamped());
640 ASSERT(c.IsClamped());
641 if (a.BigitLength() < b.BigitLength()) {
642 return PlusCompare(b, a, c);
643 }
644 if (a.BigitLength() + 1 < c.BigitLength()) return -1;
645 if (a.BigitLength() > c.BigitLength()) return +1;
646 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
647 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
648 // of 'a'.
649 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
650 return -1;
651 }
652
653 Chunk borrow = 0;
654 // Starting at min_exponent all digits are == 0. So no need to compare them.
655 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
656 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
657 Chunk chunk_a = a.BigitAt(i);
658 Chunk chunk_b = b.BigitAt(i);
659 Chunk chunk_c = c.BigitAt(i);
660 Chunk sum = chunk_a + chunk_b;
661 if (sum > chunk_c + borrow) {
662 return +1;
663 } else {
664 borrow = chunk_c + borrow - sum;
665 if (borrow > 1) return -1;
666 borrow <<= kBigitSize;
667 }
668 }
669 if (borrow == 0) return 0;
670 return -1;
671}
672
673
674void Bignum::Clamp() {
675 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
676 used_digits_--;
677 }
678 if (used_digits_ == 0) {
679 // Zero.
680 exponent_ = 0;
681 }
682}
683
684
685bool Bignum::IsClamped() const {
686 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
687}
688
689
690void Bignum::Zero() {
691 for (int i = 0; i < used_digits_; ++i) {
692 bigits_[i] = 0;
693 }
694 used_digits_ = 0;
695 exponent_ = 0;
696}
697
698
699void Bignum::Align(const Bignum& other) {
700 if (exponent_ > other.exponent_) {
701 // If "X" represents a "hidden" digit (by the exponent) then we are in the
702 // following case (a == this, b == other):
703 // a: aaaaaaXXXX or a: aaaaaXXX
704 // b: bbbbbbX b: bbbbbbbbXX
705 // We replace some of the hidden digits (X) of a with 0 digits.
706 // a: aaaaaa000X or a: aaaaa0XX
707 int zero_digits = exponent_ - other.exponent_;
708 EnsureCapacity(used_digits_ + zero_digits);
709 for (int i = used_digits_ - 1; i >= 0; --i) {
710 bigits_[i + zero_digits] = bigits_[i];
711 }
712 for (int i = 0; i < zero_digits; ++i) {
713 bigits_[i] = 0;
714 }
715 used_digits_ += zero_digits;
716 exponent_ -= zero_digits;
717 ASSERT(used_digits_ >= 0);
718 ASSERT(exponent_ >= 0);
719 }
720}
721
722
723void Bignum::BigitsShiftLeft(int shift_amount) {
724 ASSERT(shift_amount < kBigitSize);
725 ASSERT(shift_amount >= 0);
726 Chunk carry = 0;
727 for (int i = 0; i < used_digits_; ++i) {
728 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
729 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
730 carry = new_carry;
731 }
732 if (carry != 0) {
733 bigits_[used_digits_] = carry;
734 used_digits_++;
735 }
736}
737
738
739void Bignum::SubtractTimes(const Bignum& other, int factor) {
740 ASSERT(exponent_ <= other.exponent_);
741 if (factor < 3) {
742 for (int i = 0; i < factor; ++i) {
743 SubtractBignum(other);
744 }
745 return;
746 }
747 Chunk borrow = 0;
748 int exponent_diff = other.exponent_ - exponent_;
749 for (int i = 0; i < other.used_digits_; ++i) {
750 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
751 DoubleChunk remove = borrow + product;
752 Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
753 bigits_[i + exponent_diff] = difference & kBigitMask;
754 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
755 (remove >> kBigitSize));
756 }
757 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
758 if (borrow == 0) return;
759 Chunk difference = bigits_[i] - borrow;
760 bigits_[i] = difference & kBigitMask;
761 borrow = difference >> (kChunkSize - 1);
762 }
763 Clamp();
764}
765
766
767} // namespace double_conversion
768