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comparison: mfbt/double-conversion/bignum.cc

mfbt/double-conversion/bignum.cc

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1 // Copyright 2010 the V8 project authors. All rights reserved.
2 // Redistribution and use in source and binary forms, with or without
3 // modification, are permitted provided that the following conditions are
4 // met:
5 //
6 // * Redistributions of source code must retain the above copyright
7 // notice, this list of conditions and the following disclaimer.
8 // * Redistributions in binary form must reproduce the above
9 // copyright notice, this list of conditions and the following
10 // disclaimer in the documentation and/or other materials provided
11 // with the distribution.
12 // * Neither the name of Google Inc. nor the names of its
13 // contributors may be used to endorse or promote products derived
14 // from this software without specific prior written permission.
15 //
16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27
28 #include "bignum.h"
29 #include "utils.h"
30
31 namespace double_conversion {
32
33 Bignum::Bignum()
34 : 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
41 template<typename S>
42 static int BitSize(S value) {
43 return 8 * sizeof(value);
44 }
45
46 // Guaranteed to lie in one Bigit.
47 void Bignum::AssignUInt16(uint16_t value) {
48 ASSERT(kBigitSize >= BitSize(value));
49 Zero();
50 if (value == 0) return;
51
52 EnsureCapacity(1);
53 bigits_[0] = value;
54 used_digits_ = 1;
55 }
56
57
58 void Bignum::AssignUInt64(uint64_t value) {
59 const int kUInt64Size = 64;
60
61 Zero();
62 if (value == 0) return;
63
64 int needed_bigits = kUInt64Size / kBigitSize + 1;
65 EnsureCapacity(needed_bigits);
66 for (int i = 0; i < needed_bigits; ++i) {
67 bigits_[i] = value & kBigitMask;
68 value = value >> kBigitSize;
69 }
70 used_digits_ = needed_bigits;
71 Clamp();
72 }
73
74
75 void Bignum::AssignBignum(const Bignum& other) {
76 exponent_ = other.exponent_;
77 for (int i = 0; i < other.used_digits_; ++i) {
78 bigits_[i] = other.bigits_[i];
79 }
80 // Clear the excess digits (if there were any).
81 for (int i = other.used_digits_; i < used_digits_; ++i) {
82 bigits_[i] = 0;
83 }
84 used_digits_ = other.used_digits_;
85 }
86
87
88 static uint64_t ReadUInt64(Vector<const char> buffer,
89 int from,
90 int digits_to_read) {
91 uint64_t result = 0;
92 for (int i = from; i < from + digits_to_read; ++i) {
93 int digit = buffer[i] - '0';
94 ASSERT(0 <= digit && digit <= 9);
95 result = result * 10 + digit;
96 }
97 return result;
98 }
99
100
101 void Bignum::AssignDecimalString(Vector<const char> value) {
102 // 2^64 = 18446744073709551616 > 10^19
103 const int kMaxUint64DecimalDigits = 19;
104 Zero();
105 int length = value.length();
106 int pos = 0;
107 // Let's just say that each digit needs 4 bits.
108 while (length >= kMaxUint64DecimalDigits) {
109 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
110 pos += kMaxUint64DecimalDigits;
111 length -= kMaxUint64DecimalDigits;
112 MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
113 AddUInt64(digits);
114 }
115 uint64_t digits = ReadUInt64(value, pos, length);
116 MultiplyByPowerOfTen(length);
117 AddUInt64(digits);
118 Clamp();
119 }
120
121
122 static int HexCharValue(char c) {
123 if ('0' <= c && c <= '9') return c - '0';
124 if ('a' <= c && c <= 'f') return 10 + c - 'a';
125 if ('A' <= c && c <= 'F') return 10 + c - 'A';
126 UNREACHABLE();
127 return 0; // To make compiler happy.
128 }
129
130
131 void 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
161 void Bignum::AddUInt64(uint64_t operand) {
162 if (operand == 0) return;
163 Bignum other;
164 other.AssignUInt64(operand);
165 AddBignum(other);
166 }
167
168
169 void 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
211 void 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
238 void 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
247 void 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
273 void 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
300 void 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
340 void 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
412 void 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_multipliciation = 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 uint64_t base_bits_mask =
456 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
457 bool high_bits_zero = (this_value & base_bits_mask) == 0;
458 if (high_bits_zero) {
459 this_value *= base;
460 } else {
461 delayed_multipliciation = true;
462 }
463 }
464 mask >>= 1;
465 }
466 AssignUInt64(this_value);
467 if (delayed_multipliciation) {
468 MultiplyByUInt32(base);
469 }
470
471 // Now do the same thing as a bignum.
472 while (mask != 0) {
473 Square();
474 if ((power_exponent & mask) != 0) {
475 MultiplyByUInt32(base);
476 }
477 mask >>= 1;
478 }
479
480 // And finally add the saved shifts.
481 ShiftLeft(shifts * power_exponent);
482 }
483
484
485 // Precondition: this/other < 16bit.
486 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
487 ASSERT(IsClamped());
488 ASSERT(other.IsClamped());
489 ASSERT(other.used_digits_ > 0);
490
491 // Easy case: if we have less digits than the divisor than the result is 0.
492 // Note: this handles the case where this == 0, too.
493 if (BigitLength() < other.BigitLength()) {
494 return 0;
495 }
496
497 Align(other);
498
499 uint16_t result = 0;
500
501 // Start by removing multiples of 'other' until both numbers have the same
502 // number of digits.
503 while (BigitLength() > other.BigitLength()) {
504 // This naive approach is extremely inefficient if `this` divided by other
505 // is big. This function is implemented for doubleToString where
506 // the result should be small (less than 10).
507 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
508 // Remove the multiples of the first digit.
509 // Example this = 23 and other equals 9. -> Remove 2 multiples.
510 result += bigits_[used_digits_ - 1];
511 SubtractTimes(other, bigits_[used_digits_ - 1]);
512 }
513
514 ASSERT(BigitLength() == other.BigitLength());
515
516 // Both bignums are at the same length now.
517 // Since other has more than 0 digits we know that the access to
518 // bigits_[used_digits_ - 1] is safe.
519 Chunk this_bigit = bigits_[used_digits_ - 1];
520 Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
521
522 if (other.used_digits_ == 1) {
523 // Shortcut for easy (and common) case.
524 int quotient = this_bigit / other_bigit;
525 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
526 result += quotient;
527 Clamp();
528 return result;
529 }
530
531 int division_estimate = this_bigit / (other_bigit + 1);
532 result += division_estimate;
533 SubtractTimes(other, division_estimate);
534
535 if (other_bigit * (division_estimate + 1) > this_bigit) {
536 // No need to even try to subtract. Even if other's remaining digits were 0
537 // another subtraction would be too much.
538 return result;
539 }
540
541 while (LessEqual(other, *this)) {
542 SubtractBignum(other);
543 result++;
544 }
545 return result;
546 }
547
548
549 template<typename S>
550 static int SizeInHexChars(S number) {
551 ASSERT(number > 0);
552 int result = 0;
553 while (number != 0) {
554 number >>= 4;
555 result++;
556 }
557 return result;
558 }
559
560
561 static char HexCharOfValue(int value) {
562 ASSERT(0 <= value && value <= 16);
563 if (value < 10) return value + '0';
564 return value - 10 + 'A';
565 }
566
567
568 bool Bignum::ToHexString(char* buffer, int buffer_size) const {
569 ASSERT(IsClamped());
570 // Each bigit must be printable as separate hex-character.
571 ASSERT(kBigitSize % 4 == 0);
572 const int kHexCharsPerBigit = kBigitSize / 4;
573
574 if (used_digits_ == 0) {
575 if (buffer_size < 2) return false;
576 buffer[0] = '0';
577 buffer[1] = '\0';
578 return true;
579 }
580 // We add 1 for the terminating '\0' character.
581 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
582 SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
583 if (needed_chars > buffer_size) return false;
584 int string_index = needed_chars - 1;
585 buffer[string_index--] = '\0';
586 for (int i = 0; i < exponent_; ++i) {
587 for (int j = 0; j < kHexCharsPerBigit; ++j) {
588 buffer[string_index--] = '0';
589 }
590 }
591 for (int i = 0; i < used_digits_ - 1; ++i) {
592 Chunk current_bigit = bigits_[i];
593 for (int j = 0; j < kHexCharsPerBigit; ++j) {
594 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
595 current_bigit >>= 4;
596 }
597 }
598 // And finally the last bigit.
599 Chunk most_significant_bigit = bigits_[used_digits_ - 1];
600 while (most_significant_bigit != 0) {
601 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
602 most_significant_bigit >>= 4;
603 }
604 return true;
605 }
606
607
608 Bignum::Chunk Bignum::BigitAt(int index) const {
609 if (index >= BigitLength()) return 0;
610 if (index < exponent_) return 0;
611 return bigits_[index - exponent_];
612 }
613
614
615 int Bignum::Compare(const Bignum& a, const Bignum& b) {
616 ASSERT(a.IsClamped());
617 ASSERT(b.IsClamped());
618 int bigit_length_a = a.BigitLength();
619 int bigit_length_b = b.BigitLength();
620 if (bigit_length_a < bigit_length_b) return -1;
621 if (bigit_length_a > bigit_length_b) return +1;
622 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
623 Chunk bigit_a = a.BigitAt(i);
624 Chunk bigit_b = b.BigitAt(i);
625 if (bigit_a < bigit_b) return -1;
626 if (bigit_a > bigit_b) return +1;
627 // Otherwise they are equal up to this digit. Try the next digit.
628 }
629 return 0;
630 }
631
632
633 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
634 ASSERT(a.IsClamped());
635 ASSERT(b.IsClamped());
636 ASSERT(c.IsClamped());
637 if (a.BigitLength() < b.BigitLength()) {
638 return PlusCompare(b, a, c);
639 }
640 if (a.BigitLength() + 1 < c.BigitLength()) return -1;
641 if (a.BigitLength() > c.BigitLength()) return +1;
642 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
643 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
644 // of 'a'.
645 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
646 return -1;
647 }
648
649 Chunk borrow = 0;
650 // Starting at min_exponent all digits are == 0. So no need to compare them.
651 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
652 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
653 Chunk chunk_a = a.BigitAt(i);
654 Chunk chunk_b = b.BigitAt(i);
655 Chunk chunk_c = c.BigitAt(i);
656 Chunk sum = chunk_a + chunk_b;
657 if (sum > chunk_c + borrow) {
658 return +1;
659 } else {
660 borrow = chunk_c + borrow - sum;
661 if (borrow > 1) return -1;
662 borrow <<= kBigitSize;
663 }
664 }
665 if (borrow == 0) return 0;
666 return -1;
667 }
668
669
670 void Bignum::Clamp() {
671 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
672 used_digits_--;
673 }
674 if (used_digits_ == 0) {
675 // Zero.
676 exponent_ = 0;
677 }
678 }
679
680
681 bool Bignum::IsClamped() const {
682 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
683 }
684
685
686 void Bignum::Zero() {
687 for (int i = 0; i < used_digits_; ++i) {
688 bigits_[i] = 0;
689 }
690 used_digits_ = 0;
691 exponent_ = 0;
692 }
693
694
695 void Bignum::Align(const Bignum& other) {
696 if (exponent_ > other.exponent_) {
697 // If "X" represents a "hidden" digit (by the exponent) then we are in the
698 // following case (a == this, b == other):
699 // a: aaaaaaXXXX or a: aaaaaXXX
700 // b: bbbbbbX b: bbbbbbbbXX
701 // We replace some of the hidden digits (X) of a with 0 digits.
702 // a: aaaaaa000X or a: aaaaa0XX
703 int zero_digits = exponent_ - other.exponent_;
704 EnsureCapacity(used_digits_ + zero_digits);
705 for (int i = used_digits_ - 1; i >= 0; --i) {
706 bigits_[i + zero_digits] = bigits_[i];
707 }
708 for (int i = 0; i < zero_digits; ++i) {
709 bigits_[i] = 0;
710 }
711 used_digits_ += zero_digits;
712 exponent_ -= zero_digits;
713 ASSERT(used_digits_ >= 0);
714 ASSERT(exponent_ >= 0);
715 }
716 }
717
718
719 void Bignum::BigitsShiftLeft(int shift_amount) {
720 ASSERT(shift_amount < kBigitSize);
721 ASSERT(shift_amount >= 0);
722 Chunk carry = 0;
723 for (int i = 0; i < used_digits_; ++i) {
724 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
725 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
726 carry = new_carry;
727 }
728 if (carry != 0) {
729 bigits_[used_digits_] = carry;
730 used_digits_++;
731 }
732 }
733
734
735 void Bignum::SubtractTimes(const Bignum& other, int factor) {
736 ASSERT(exponent_ <= other.exponent_);
737 if (factor < 3) {
738 for (int i = 0; i < factor; ++i) {
739 SubtractBignum(other);
740 }
741 return;
742 }
743 Chunk borrow = 0;
744 int exponent_diff = other.exponent_ - exponent_;
745 for (int i = 0; i < other.used_digits_; ++i) {
746 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
747 DoubleChunk remove = borrow + product;
748 Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
749 bigits_[i + exponent_diff] = difference & kBigitMask;
750 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
751 (remove >> kBigitSize));
752 }
753 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
754 if (borrow == 0) return;
755 Chunk difference = bigits_[i] - borrow;
756 bigits_[i] = difference & kBigitMask;
757 borrow = difference >> (kChunkSize - 1);
758 }
759 Clamp();
760 }
761
762
763 } // namespace double_conversion

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