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27
28#include <algorithm>
29#include <cstring>
30
31#include "bignum.h"
32#include "utils.h"
33
34namespace double_conversion {
35
36Bignum::Chunk& Bignum::RawBigit(const int index) {
37 DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
38 return bigits_buffer_[index];
39}
40
41
42const Bignum::Chunk& Bignum::RawBigit(const int index) const {
43 DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
44 return bigits_buffer_[index];
45}
46
47
48template<typename S>
49static int BitSize(const S value) {
50 (void) value; // Mark variable as used.
51 return 8 * sizeof(value);
52}
53
54// Guaranteed to lie in one Bigit.
55void Bignum::AssignUInt16(const uint16_t value) {
56 DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value));
57 Zero();
58 if (value > 0) {
59 RawBigit(0) = value;
60 used_bigits_ = 1;
61 }
62}
63
64
65void Bignum::AssignUInt64(uint64_t value) {
66 Zero();
67 for(int i = 0; value > 0; ++i) {
68 RawBigit(i) = value & kBigitMask;
69 value >>= kBigitSize;
70 ++used_bigits_;
71 }
72}
73
74
75void Bignum::AssignBignum(const Bignum& other) {
76 exponent_ = other.exponent_;
77 for (int i = 0; i < other.used_bigits_; ++i) {
78 RawBigit(i) = other.RawBigit(i);
79 }
80 used_bigits_ = other.used_bigits_;
81}
82
83
84static uint64_t ReadUInt64(const Vector<const char> buffer,
85 const int from,
86 const int digits_to_read) {
87 uint64_t result = 0;
88 for (int i = from; i < from + digits_to_read; ++i) {
89 const int digit = buffer[i] - '0';
90 DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);
91 result = result * 10 + digit;
92 }
93 return result;
94}
95
96
97void Bignum::AssignDecimalString(const Vector<const char> value) {
98 // 2^64 = 18446744073709551616 > 10^19
99 static const int kMaxUint64DecimalDigits = 19;
100 Zero();
101 int length = value.length();
102 unsigned pos = 0;
103 // Let's just say that each digit needs 4 bits.
104 while (length >= kMaxUint64DecimalDigits) {
105 const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
106 pos += kMaxUint64DecimalDigits;
107 length -= kMaxUint64DecimalDigits;
108 MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
109 AddUInt64(digits);
110 }
111 const uint64_t digits = ReadUInt64(value, pos, length);
112 MultiplyByPowerOfTen(length);
113 AddUInt64(digits);
114 Clamp();
115}
116
117
118static uint64_t HexCharValue(const int c) {
119 if ('0' <= c && c <= '9') {
120 return c - '0';
121 }
122 if ('a' <= c && c <= 'f') {
123 return 10 + c - 'a';
124 }
125 DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F');
126 return 10 + c - 'A';
127}
128
129
130// Unlike AssignDecimalString(), this function is "only" used
131// for unit-tests and therefore not performance critical.
132void Bignum::AssignHexString(Vector<const char> value) {
133 Zero();
134 // Required capacity could be reduced by ignoring leading zeros.
135 EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize);
136 DOUBLE_CONVERSION_ASSERT(sizeof(uint64_t) * 8 >= kBigitSize + 4); // TODO: static_assert
137 // Accumulates converted hex digits until at least kBigitSize bits.
138 // Works with non-factor-of-four kBigitSizes.
139 uint64_t tmp = 0; // Accumulates converted hex digits until at least
140 for (int cnt = 0; !value.is_empty(); value.pop_back()) {
141 tmp |= (HexCharValue(value.last()) << cnt);
142 if ((cnt += 4) >= kBigitSize) {
143 RawBigit(used_bigits_++) = (tmp & kBigitMask);
144 cnt -= kBigitSize;
145 tmp >>= kBigitSize;
146 }
147 }
148 if (tmp > 0) {
149 RawBigit(used_bigits_++) = tmp;
150 }
151 Clamp();
152}
153
154
155void Bignum::AddUInt64(const uint64_t operand) {
156 if (operand == 0) {
157 return;
158 }
159 Bignum other;
160 other.AssignUInt64(operand);
161 AddBignum(other);
162}
163
164
165void Bignum::AddBignum(const Bignum& other) {
166 DOUBLE_CONVERSION_ASSERT(IsClamped());
167 DOUBLE_CONVERSION_ASSERT(other.IsClamped());
168
169 // If this has a greater exponent than other append zero-bigits to this.
170 // After this call exponent_ <= other.exponent_.
171 Align(other);
172
173 // There are two possibilities:
174 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
175 // bbbbb 00000000
176 // ----------------
177 // ccccccccccc 0000
178 // or
179 // aaaaaaaaaa 0000
180 // bbbbbbbbb 0000000
181 // -----------------
182 // cccccccccccc 0000
183 // In both cases we might need a carry bigit.
184
185 EnsureCapacity(1 + (std::max)(BigitLength(), other.BigitLength()) - exponent_);
186 Chunk carry = 0;
187 int bigit_pos = other.exponent_ - exponent_;
188 DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0);
189 for (int i = used_bigits_; i < bigit_pos; ++i) {
190 RawBigit(i) = 0;
191 }
192 for (int i = 0; i < other.used_bigits_; ++i) {
193 const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
194 const Chunk sum = my + other.RawBigit(i) + carry;
195 RawBigit(bigit_pos) = sum & kBigitMask;
196 carry = sum >> kBigitSize;
197 ++bigit_pos;
198 }
199 while (carry != 0) {
200 const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
201 const Chunk sum = my + carry;
202 RawBigit(bigit_pos) = sum & kBigitMask;
203 carry = sum >> kBigitSize;
204 ++bigit_pos;
205 }
206 used_bigits_ = (std::max)(bigit_pos, static_cast<int>(used_bigits_));
207 DOUBLE_CONVERSION_ASSERT(IsClamped());
208}
209
210
211void Bignum::SubtractBignum(const Bignum& other) {
212 DOUBLE_CONVERSION_ASSERT(IsClamped());
213 DOUBLE_CONVERSION_ASSERT(other.IsClamped());
214 // We require this to be bigger than other.
215 DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this));
216
217 Align(other);
218
219 const int offset = other.exponent_ - exponent_;
220 Chunk borrow = 0;
221 int i;
222 for (i = 0; i < other.used_bigits_; ++i) {
223 DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1));
224 const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow;
225 RawBigit(i + offset) = difference & kBigitMask;
226 borrow = difference >> (kChunkSize - 1);
227 }
228 while (borrow != 0) {
229 const Chunk difference = RawBigit(i + offset) - borrow;
230 RawBigit(i + offset) = difference & kBigitMask;
231 borrow = difference >> (kChunkSize - 1);
232 ++i;
233 }
234 Clamp();
235}
236
237
238void Bignum::ShiftLeft(const int shift_amount) {
239 if (used_bigits_ == 0) {
240 return;
241 }
242 exponent_ += (shift_amount / kBigitSize);
243 const int local_shift = shift_amount % kBigitSize;
244 EnsureCapacity(used_bigits_ + 1);
245 BigitsShiftLeft(local_shift);
246}
247
248
249void Bignum::MultiplyByUInt32(const uint32_t factor) {
250 if (factor == 1) {
251 return;
252 }
253 if (factor == 0) {
254 Zero();
255 return;
256 }
257 if (used_bigits_ == 0) {
258 return;
259 }
260 // The product of a bigit with the factor is of size kBigitSize + 32.
261 // Assert that this number + 1 (for the carry) fits into double chunk.
262 DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
263 DoubleChunk carry = 0;
264 for (int i = 0; i < used_bigits_; ++i) {
265 const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry;
266 RawBigit(i) = static_cast<Chunk>(product & kBigitMask);
267 carry = (product >> kBigitSize);
268 }
269 while (carry != 0) {
270 EnsureCapacity(used_bigits_ + 1);
271 RawBigit(used_bigits_) = carry & kBigitMask;
272 used_bigits_++;
273 carry >>= kBigitSize;
274 }
275}
276
277
278void Bignum::MultiplyByUInt64(const uint64_t factor) {
279 if (factor == 1) {
280 return;
281 }
282 if (factor == 0) {
283 Zero();
284 return;
285 }
286 if (used_bigits_ == 0) {
287 return;
288 }
289 DOUBLE_CONVERSION_ASSERT(kBigitSize < 32);
290 uint64_t carry = 0;
291 const uint64_t low = factor & 0xFFFFFFFF;
292 const uint64_t high = factor >> 32;
293 for (int i = 0; i < used_bigits_; ++i) {
294 const uint64_t product_low = low * RawBigit(i);
295 const uint64_t product_high = high * RawBigit(i);
296 const uint64_t tmp = (carry & kBigitMask) + product_low;
297 RawBigit(i) = tmp & kBigitMask;
298 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
299 (product_high << (32 - kBigitSize));
300 }
301 while (carry != 0) {
302 EnsureCapacity(used_bigits_ + 1);
303 RawBigit(used_bigits_) = carry & kBigitMask;
304 used_bigits_++;
305 carry >>= kBigitSize;
306 }
307}
308
309
310void Bignum::MultiplyByPowerOfTen(const int exponent) {
311 static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d);
312 static const uint16_t kFive1 = 5;
313 static const uint16_t kFive2 = kFive1 * 5;
314 static const uint16_t kFive3 = kFive2 * 5;
315 static const uint16_t kFive4 = kFive3 * 5;
316 static const uint16_t kFive5 = kFive4 * 5;
317 static const uint16_t kFive6 = kFive5 * 5;
318 static const uint32_t kFive7 = kFive6 * 5;
319 static const uint32_t kFive8 = kFive7 * 5;
320 static const uint32_t kFive9 = kFive8 * 5;
321 static const uint32_t kFive10 = kFive9 * 5;
322 static const uint32_t kFive11 = kFive10 * 5;
323 static const uint32_t kFive12 = kFive11 * 5;
324 static const uint32_t kFive13 = kFive12 * 5;
325 static const uint32_t kFive1_to_12[] =
326 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
327 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
328
329 DOUBLE_CONVERSION_ASSERT(exponent >= 0);
330
331 if (exponent == 0) {
332 return;
333 }
334 if (used_bigits_ == 0) {
335 return;
336 }
337 // We shift by exponent at the end just before returning.
338 int remaining_exponent = exponent;
339 while (remaining_exponent >= 27) {
340 MultiplyByUInt64(kFive27);
341 remaining_exponent -= 27;
342 }
343 while (remaining_exponent >= 13) {
344 MultiplyByUInt32(kFive13);
345 remaining_exponent -= 13;
346 }
347 if (remaining_exponent > 0) {
348 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
349 }
350 ShiftLeft(exponent);
351}
352
353
354void Bignum::Square() {
355 DOUBLE_CONVERSION_ASSERT(IsClamped());
356 const int product_length = 2 * used_bigits_;
357 EnsureCapacity(product_length);
358
359 // Comba multiplication: compute each column separately.
360 // Example: r = a2a1a0 * b2b1b0.
361 // r = 1 * a0b0 +
362 // 10 * (a1b0 + a0b1) +
363 // 100 * (a2b0 + a1b1 + a0b2) +
364 // 1000 * (a2b1 + a1b2) +
365 // 10000 * a2b2
366 //
367 // In the worst case we have to accumulate nb-digits products of digit*digit.
368 //
369 // Assert that the additional number of bits in a DoubleChunk are enough to
370 // sum up used_digits of Bigit*Bigit.
371 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) {
372 DOUBLE_CONVERSION_UNIMPLEMENTED();
373 }
374 DoubleChunk accumulator = 0;
375 // First shift the digits so we don't overwrite them.
376 const int copy_offset = used_bigits_;
377 for (int i = 0; i < used_bigits_; ++i) {
378 RawBigit(copy_offset + i) = RawBigit(i);
379 }
380 // We have two loops to avoid some 'if's in the loop.
381 for (int i = 0; i < used_bigits_; ++i) {
382 // Process temporary digit i with power i.
383 // The sum of the two indices must be equal to i.
384 int bigit_index1 = i;
385 int bigit_index2 = 0;
386 // Sum all of the sub-products.
387 while (bigit_index1 >= 0) {
388 const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
389 const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
390 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
391 bigit_index1--;
392 bigit_index2++;
393 }
394 RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
395 accumulator >>= kBigitSize;
396 }
397 for (int i = used_bigits_; i < product_length; ++i) {
398 int bigit_index1 = used_bigits_ - 1;
399 int bigit_index2 = i - bigit_index1;
400 // Invariant: sum of both indices is again equal to i.
401 // Inner loop runs 0 times on last iteration, emptying accumulator.
402 while (bigit_index2 < used_bigits_) {
403 const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
404 const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
405 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
406 bigit_index1--;
407 bigit_index2++;
408 }
409 // The overwritten RawBigit(i) will never be read in further loop iterations,
410 // because bigit_index1 and bigit_index2 are always greater
411 // than i - used_bigits_.
412 RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
413 accumulator >>= kBigitSize;
414 }
415 // Since the result was guaranteed to lie inside the number the
416 // accumulator must be 0 now.
417 DOUBLE_CONVERSION_ASSERT(accumulator == 0);
418
419 // Don't forget to update the used_digits and the exponent.
420 used_bigits_ = product_length;
421 exponent_ *= 2;
422 Clamp();
423}
424
425
426void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) {
427 DOUBLE_CONVERSION_ASSERT(base != 0);
428 DOUBLE_CONVERSION_ASSERT(power_exponent >= 0);
429 if (power_exponent == 0) {
430 AssignUInt16(1);
431 return;
432 }
433 Zero();
434 int shifts = 0;
435 // We expect base to be in range 2-32, and most often to be 10.
436 // It does not make much sense to implement different algorithms for counting
437 // the bits.
438 while ((base & 1) == 0) {
439 base >>= 1;
440 shifts++;
441 }
442 int bit_size = 0;
443 int tmp_base = base;
444 while (tmp_base != 0) {
445 tmp_base >>= 1;
446 bit_size++;
447 }
448 const int final_size = bit_size * power_exponent;
449 // 1 extra bigit for the shifting, and one for rounded final_size.
450 EnsureCapacity(final_size / kBigitSize + 2);
451
452 // Left to Right exponentiation.
453 int mask = 1;
454 while (power_exponent >= mask) mask <<= 1;
455
456 // The mask is now pointing to the bit above the most significant 1-bit of
457 // power_exponent.
458 // Get rid of first 1-bit;
459 mask >>= 2;
460 uint64_t this_value = base;
461
462 bool delayed_multiplication = false;
463 const uint64_t max_32bits = 0xFFFFFFFF;
464 while (mask != 0 && this_value <= max_32bits) {
465 this_value = this_value * this_value;
466 // Verify that there is enough space in this_value to perform the
467 // multiplication. The first bit_size bits must be 0.
468 if ((power_exponent & mask) != 0) {
469 DOUBLE_CONVERSION_ASSERT(bit_size > 0);
470 const uint64_t base_bits_mask =
471 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
472 const bool high_bits_zero = (this_value & base_bits_mask) == 0;
473 if (high_bits_zero) {
474 this_value *= base;
475 } else {
476 delayed_multiplication = true;
477 }
478 }
479 mask >>= 1;
480 }
481 AssignUInt64(this_value);
482 if (delayed_multiplication) {
483 MultiplyByUInt32(base);
484 }
485
486 // Now do the same thing as a bignum.
487 while (mask != 0) {
488 Square();
489 if ((power_exponent & mask) != 0) {
490 MultiplyByUInt32(base);
491 }
492 mask >>= 1;
493 }
494
495 // And finally add the saved shifts.
496 ShiftLeft(shifts * power_exponent);
497}
498
499
500// Precondition: this/other < 16bit.
501uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
502 DOUBLE_CONVERSION_ASSERT(IsClamped());
503 DOUBLE_CONVERSION_ASSERT(other.IsClamped());
504 DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 0);
505
506 // Easy case: if we have less digits than the divisor than the result is 0.
507 // Note: this handles the case where this == 0, too.
508 if (BigitLength() < other.BigitLength()) {
509 return 0;
510 }
511
512 Align(other);
513
514 uint16_t result = 0;
515
516 // Start by removing multiples of 'other' until both numbers have the same
517 // number of digits.
518 while (BigitLength() > other.BigitLength()) {
519 // This naive approach is extremely inefficient if `this` divided by other
520 // is big. This function is implemented for doubleToString where
521 // the result should be small (less than 10).
522 DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16));
523 DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000);
524 // Remove the multiples of the first digit.
525 // Example this = 23 and other equals 9. -> Remove 2 multiples.
526 result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1));
527 SubtractTimes(other, RawBigit(used_bigits_ - 1));
528 }
529
530 DOUBLE_CONVERSION_ASSERT(BigitLength() == other.BigitLength());
531
532 // Both bignums are at the same length now.
533 // Since other has more than 0 digits we know that the access to
534 // RawBigit(used_bigits_ - 1) is safe.
535 const Chunk this_bigit = RawBigit(used_bigits_ - 1);
536 const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1);
537
538 if (other.used_bigits_ == 1) {
539 // Shortcut for easy (and common) case.
540 int quotient = this_bigit / other_bigit;
541 RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient;
542 DOUBLE_CONVERSION_ASSERT(quotient < 0x10000);
543 result += static_cast<uint16_t>(quotient);
544 Clamp();
545 return result;
546 }
547
548 const int division_estimate = this_bigit / (other_bigit + 1);
549 DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000);
550 result += static_cast<uint16_t>(division_estimate);
551 SubtractTimes(other, division_estimate);
552
553 if (other_bigit * (division_estimate + 1) > this_bigit) {
554 // No need to even try to subtract. Even if other's remaining digits were 0
555 // another subtraction would be too much.
556 return result;
557 }
558
559 while (LessEqual(other, *this)) {
560 SubtractBignum(other);
561 result++;
562 }
563 return result;
564}
565
566
567template<typename S>
568static int SizeInHexChars(S number) {
569 DOUBLE_CONVERSION_ASSERT(number > 0);
570 int result = 0;
571 while (number != 0) {
572 number >>= 4;
573 result++;
574 }
575 return result;
576}
577
578
579static char HexCharOfValue(const int value) {
580 DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16);
581 if (value < 10) {
582 return static_cast<char>(value + '0');
583 }
584 return static_cast<char>(value - 10 + 'A');
585}
586
587
588bool Bignum::ToHexString(char* buffer, const int buffer_size) const {
589 DOUBLE_CONVERSION_ASSERT(IsClamped());
590 // Each bigit must be printable as separate hex-character.
591 DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0);
592 static const int kHexCharsPerBigit = kBigitSize / 4;
593
594 if (used_bigits_ == 0) {
595 if (buffer_size < 2) {
596 return false;
597 }
598 buffer[0] = '0';
599 buffer[1] = '\0';
600 return true;
601 }
602 // We add 1 for the terminating '\0' character.
603 const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
604 SizeInHexChars(RawBigit(used_bigits_ - 1)) + 1;
605 if (needed_chars > buffer_size) {
606 return false;
607 }
608 int string_index = needed_chars - 1;
609 buffer[string_index--] = '\0';
610 for (int i = 0; i < exponent_; ++i) {
611 for (int j = 0; j < kHexCharsPerBigit; ++j) {
612 buffer[string_index--] = '0';
613 }
614 }
615 for (int i = 0; i < used_bigits_ - 1; ++i) {
616 Chunk current_bigit = RawBigit(i);
617 for (int j = 0; j < kHexCharsPerBigit; ++j) {
618 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
619 current_bigit >>= 4;
620 }
621 }
622 // And finally the last bigit.
623 Chunk most_significant_bigit = RawBigit(used_bigits_ - 1);
624 while (most_significant_bigit != 0) {
625 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
626 most_significant_bigit >>= 4;
627 }
628 return true;
629}
630
631
632Bignum::Chunk Bignum::BigitOrZero(const int index) const {
633 if (index >= BigitLength()) {
634 return 0;
635 }
636 if (index < exponent_) {
637 return 0;
638 }
639 return RawBigit(index - exponent_);
640}
641
642
643int Bignum::Compare(const Bignum& a, const Bignum& b) {
644 DOUBLE_CONVERSION_ASSERT(a.IsClamped());
645 DOUBLE_CONVERSION_ASSERT(b.IsClamped());
646 const int bigit_length_a = a.BigitLength();
647 const int bigit_length_b = b.BigitLength();
648 if (bigit_length_a < bigit_length_b) {
649 return -1;
650 }
651 if (bigit_length_a > bigit_length_b) {
652 return +1;
653 }
654 for (int i = bigit_length_a - 1; i >= (std::min)(a.exponent_, b.exponent_); --i) {
655 const Chunk bigit_a = a.BigitOrZero(i);
656 const Chunk bigit_b = b.BigitOrZero(i);
657 if (bigit_a < bigit_b) {
658 return -1;
659 }
660 if (bigit_a > bigit_b) {
661 return +1;
662 }
663 // Otherwise they are equal up to this digit. Try the next digit.
664 }
665 return 0;
666}
667
668
669int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
670 DOUBLE_CONVERSION_ASSERT(a.IsClamped());
671 DOUBLE_CONVERSION_ASSERT(b.IsClamped());
672 DOUBLE_CONVERSION_ASSERT(c.IsClamped());
673 if (a.BigitLength() < b.BigitLength()) {
674 return PlusCompare(b, a, c);
675 }
676 if (a.BigitLength() + 1 < c.BigitLength()) {
677 return -1;
678 }
679 if (a.BigitLength() > c.BigitLength()) {
680 return +1;
681 }
682 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
683 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
684 // of 'a'.
685 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
686 return -1;
687 }
688
689 Chunk borrow = 0;
690 // Starting at min_exponent all digits are == 0. So no need to compare them.
691 const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_);
692 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
693 const Chunk chunk_a = a.BigitOrZero(i);
694 const Chunk chunk_b = b.BigitOrZero(i);
695 const Chunk chunk_c = c.BigitOrZero(i);
696 const Chunk sum = chunk_a + chunk_b;
697 if (sum > chunk_c + borrow) {
698 return +1;
699 } else {
700 borrow = chunk_c + borrow - sum;
701 if (borrow > 1) {
702 return -1;
703 }
704 borrow <<= kBigitSize;
705 }
706 }
707 if (borrow == 0) {
708 return 0;
709 }
710 return -1;
711}
712
713
714void Bignum::Clamp() {
715 while (used_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) {
716 used_bigits_--;
717 }
718 if (used_bigits_ == 0) {
719 // Zero.
720 exponent_ = 0;
721 }
722}
723
724
725void Bignum::Align(const Bignum& other) {
726 if (exponent_ > other.exponent_) {
727 // If "X" represents a "hidden" bigit (by the exponent) then we are in the
728 // following case (a == this, b == other):
729 // a: aaaaaaXXXX or a: aaaaaXXX
730 // b: bbbbbbX b: bbbbbbbbXX
731 // We replace some of the hidden digits (X) of a with 0 digits.
732 // a: aaaaaa000X or a: aaaaa0XX
733 const int zero_bigits = exponent_ - other.exponent_;
734 EnsureCapacity(used_bigits_ + zero_bigits);
735 for (int i = used_bigits_ - 1; i >= 0; --i) {
736 RawBigit(i + zero_bigits) = RawBigit(i);
737 }
738 for (int i = 0; i < zero_bigits; ++i) {
739 RawBigit(i) = 0;
740 }
741 used_bigits_ += zero_bigits;
742 exponent_ -= zero_bigits;
743
744 DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0);
745 DOUBLE_CONVERSION_ASSERT(exponent_ >= 0);
746 }
747}
748
749
750void Bignum::BigitsShiftLeft(const int shift_amount) {
751 DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize);
752 DOUBLE_CONVERSION_ASSERT(shift_amount >= 0);
753 Chunk carry = 0;
754 for (int i = 0; i < used_bigits_; ++i) {
755 const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount);
756 RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask;
757 carry = new_carry;
758 }
759 if (carry != 0) {
760 RawBigit(used_bigits_) = carry;
761 used_bigits_++;
762 }
763}
764
765
766void Bignum::SubtractTimes(const Bignum& other, const int factor) {
767 DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_);
768 if (factor < 3) {
769 for (int i = 0; i < factor; ++i) {
770 SubtractBignum(other);
771 }
772 return;
773 }
774 Chunk borrow = 0;
775 const int exponent_diff = other.exponent_ - exponent_;
776 for (int i = 0; i < other.used_bigits_; ++i) {
777 const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i);
778 const DoubleChunk remove = borrow + product;
779 const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask);
780 RawBigit(i + exponent_diff) = difference & kBigitMask;
781 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
782 (remove >> kBigitSize));
783 }
784 for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) {
785 if (borrow == 0) {
786 return;
787 }
788 const Chunk difference = RawBigit(i) - borrow;
789 RawBigit(i) = difference & kBigitMask;
790 borrow = difference >> (kChunkSize - 1);
791 }
792 Clamp();
793}
794
795
796} // namespace double_conversion
797