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Issue 2764243002: Move files in wtf/ to platform/wtf/ (Part 9). (Closed)
Patch Set: Rebase. Created 3 years, 9 months ago
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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
30 #include "utils.h"
31
32 namespace WTF {
33
34 namespace double_conversion {
35
36 Bignum::Bignum()
37 : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
38 for (int i = 0; i < kBigitCapacity; ++i) {
39 bigits_[i] = 0;
40 }
41 }
42
43
44 template<typename S>
45 static int BitSize(S value) {
46 return 8 * sizeof(value);
47 }
48
49 // Guaranteed to lie in one Bigit.
50 void Bignum::AssignUInt16(uint16_t value) {
51 ASSERT(kBigitSize >= BitSize(value));
52 Zero();
53 if (value == 0) return;
54
55 EnsureCapacity(1);
56 bigits_[0] = value;
57 used_digits_ = 1;
58 }
59
60
61 void Bignum::AssignUInt64(uint64_t value) {
62 const int kUInt64Size = 64;
63
64 Zero();
65 if (value == 0) return;
66
67 int needed_bigits = kUInt64Size / kBigitSize + 1;
68 EnsureCapacity(needed_bigits);
69 for (int i = 0; i < needed_bigits; ++i) {
70 bigits_[i] = (uint32_t)value & kBigitMask;
71 value = value >> kBigitSize;
72 }
73 used_digits_ = needed_bigits;
74 Clamp();
75 }
76
77
78 void Bignum::AssignBignum(const Bignum& other) {
79 exponent_ = other.exponent_;
80 for (int i = 0; i < other.used_digits_; ++i) {
81 bigits_[i] = other.bigits_[i];
82 }
83 // Clear the excess digits (if there were any).
84 for (int i = other.used_digits_; i < used_digits_; ++i) {
85 bigits_[i] = 0;
86 }
87 used_digits_ = other.used_digits_;
88 }
89
90
91 static uint64_t ReadUInt64(Vector<const char> buffer,
92 int from,
93 int digits_to_read) {
94 uint64_t result = 0;
95 for (int i = from; i < from + digits_to_read; ++i) {
96 int digit = buffer[i] - '0';
97 ASSERT(0 <= digit && digit <= 9);
98 result = result * 10 + digit;
99 }
100 return result;
101 }
102
103
104 void Bignum::AssignDecimalString(Vector<const char> value) {
105 // 2^64 = 18446744073709551616 > 10^19
106 const int kMaxUint64DecimalDigits = 19;
107 Zero();
108 int length = value.length();
109 int pos = 0;
110 // Let's just say that each digit needs 4 bits.
111 while (length >= kMaxUint64DecimalDigits) {
112 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
113 pos += kMaxUint64DecimalDigits;
114 length -= kMaxUint64DecimalDigits;
115 MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
116 AddUInt64(digits);
117 }
118 uint64_t digits = ReadUInt64(value, pos, length);
119 MultiplyByPowerOfTen(length);
120 AddUInt64(digits);
121 Clamp();
122 }
123
124
125 static int HexCharValue(char c) {
126 if ('0' <= c && c <= '9') return c - '0';
127 if ('a' <= c && c <= 'f') return 10 + c - 'a';
128 if ('A' <= c && c <= 'F') return 10 + c - 'A';
129 UNREACHABLE();
130 return 0; // To make compiler happy.
131 }
132
133
134 void Bignum::AssignHexString(Vector<const char> value) {
135 Zero();
136 int length = value.length();
137
138 int needed_bigits = length * 4 / kBigitSize + 1;
139 EnsureCapacity(needed_bigits);
140 int string_index = length - 1;
141 for (int i = 0; i < needed_bigits - 1; ++i) {
142 // These bigits are guaranteed to be "full".
143 Chunk current_bigit = 0;
144 for (int j = 0; j < kBigitSize / 4; j++) {
145 current_bigit += HexCharValue(value[string_index--]) << (j * 4);
146 }
147 bigits_[i] = current_bigit;
148 }
149 used_digits_ = needed_bigits - 1;
150
151 Chunk most_significant_bigit = 0; // Could be = 0;
152 for (int j = 0; j <= string_index; ++j) {
153 most_significant_bigit <<= 4;
154 most_significant_bigit += HexCharValue(value[j]);
155 }
156 if (most_significant_bigit != 0) {
157 bigits_[used_digits_] = most_significant_bigit;
158 used_digits_++;
159 }
160 Clamp();
161 }
162
163
164 void Bignum::AddUInt64(uint64_t operand) {
165 if (operand == 0) return;
166 Bignum other;
167 other.AssignUInt64(operand);
168 AddBignum(other);
169 }
170
171
172 void Bignum::AddBignum(const Bignum& other) {
173 ASSERT(IsClamped());
174 ASSERT(other.IsClamped());
175
176 // If this has a greater exponent than other append zero-bigits to this.
177 // After this call exponent_ <= other.exponent_.
178 Align(other);
179
180 // There are two possibilities:
181 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
182 // bbbbb 00000000
183 // ----------------
184 // ccccccccccc 0000
185 // or
186 // aaaaaaaaaa 0000
187 // bbbbbbbbb 0000000
188 // -----------------
189 // cccccccccccc 0000
190 // In both cases we might need a carry bigit.
191
192 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
193 Chunk carry = 0;
194 int bigit_pos = other.exponent_ - exponent_;
195 ASSERT(bigit_pos >= 0);
196 for (int i = 0; i < other.used_digits_; ++i) {
197 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
198 bigits_[bigit_pos] = sum & kBigitMask;
199 carry = sum >> kBigitSize;
200 bigit_pos++;
201 }
202
203 while (carry != 0) {
204 Chunk sum = bigits_[bigit_pos] + carry;
205 bigits_[bigit_pos] = sum & kBigitMask;
206 carry = sum >> kBigitSize;
207 bigit_pos++;
208 }
209 used_digits_ = Max(bigit_pos, used_digits_);
210 ASSERT(IsClamped());
211 }
212
213
214 void Bignum::SubtractBignum(const Bignum& other) {
215 ASSERT(IsClamped());
216 ASSERT(other.IsClamped());
217 // We require this to be bigger than other.
218 ASSERT(LessEqual(other, *this));
219
220 Align(other);
221
222 int offset = other.exponent_ - exponent_;
223 Chunk borrow = 0;
224 int i;
225 for (i = 0; i < other.used_digits_; ++i) {
226 ASSERT((borrow == 0) || (borrow == 1));
227 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
228 bigits_[i + offset] = difference & kBigitMask;
229 borrow = difference >> (kChunkSize - 1);
230 }
231 while (borrow != 0) {
232 Chunk difference = bigits_[i + offset] - borrow;
233 bigits_[i + offset] = difference & kBigitMask;
234 borrow = difference >> (kChunkSize - 1);
235 ++i;
236 }
237 Clamp();
238 }
239
240
241 void Bignum::ShiftLeft(int shift_amount) {
242 if (used_digits_ == 0) return;
243 exponent_ += shift_amount / kBigitSize;
244 int local_shift = shift_amount % kBigitSize;
245 EnsureCapacity(used_digits_ + 1);
246 BigitsShiftLeft(local_shift);
247 }
248
249
250 void Bignum::MultiplyByUInt32(uint32_t factor) {
251 if (factor == 1) return;
252 if (factor == 0) {
253 Zero();
254 return;
255 }
256 if (used_digits_ == 0) return;
257
258 // The product of a bigit with the factor is of size kBigitSize + 32.
259 // Assert that this number + 1 (for the carry) fits into double chunk.
260 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
261 DoubleChunk carry = 0;
262 for (int i = 0; i < used_digits_; ++i) {
263 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
264 bigits_[i] = static_cast<Chunk>(product & kBigitMask);
265 carry = (product >> kBigitSize);
266 }
267 while (carry != 0) {
268 EnsureCapacity(used_digits_ + 1);
269 bigits_[used_digits_] = (uint32_t)carry & kBigitMask;
270 used_digits_++;
271 carry >>= kBigitSize;
272 }
273 }
274
275
276 void Bignum::MultiplyByUInt64(uint64_t factor) {
277 if (factor == 1) return;
278 if (factor == 0) {
279 Zero();
280 return;
281 }
282 ASSERT(kBigitSize < 32);
283 uint64_t carry = 0;
284 uint64_t low = factor & 0xFFFFFFFF;
285 uint64_t high = factor >> 32;
286 for (int i = 0; i < used_digits_; ++i) {
287 uint64_t product_low = low * bigits_[i];
288 uint64_t product_high = high * bigits_[i];
289 uint64_t tmp = (carry & kBigitMask) + product_low;
290 bigits_[i] = (uint32_t)tmp & kBigitMask;
291 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
292 (product_high << (32 - kBigitSize));
293 }
294 while (carry != 0) {
295 EnsureCapacity(used_digits_ + 1);
296 bigits_[used_digits_] = (uint32_t)carry & kBigitMask;
297 used_digits_++;
298 carry >>= kBigitSize;
299 }
300 }
301
302
303 void Bignum::MultiplyByPowerOfTen(int exponent) {
304 const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
305 const uint16_t kFive1 = 5;
306 const uint16_t kFive2 = kFive1 * 5;
307 const uint16_t kFive3 = kFive2 * 5;
308 const uint16_t kFive4 = kFive3 * 5;
309 const uint16_t kFive5 = kFive4 * 5;
310 const uint16_t kFive6 = kFive5 * 5;
311 const uint32_t kFive7 = kFive6 * 5;
312 const uint32_t kFive8 = kFive7 * 5;
313 const uint32_t kFive9 = kFive8 * 5;
314 const uint32_t kFive10 = kFive9 * 5;
315 const uint32_t kFive11 = kFive10 * 5;
316 const uint32_t kFive12 = kFive11 * 5;
317 const uint32_t kFive13 = kFive12 * 5;
318 const uint32_t kFive1_to_12[] =
319 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
320 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
321
322 ASSERT(exponent >= 0);
323 if (exponent == 0) return;
324 if (used_digits_ == 0) return;
325
326 // We shift by exponent at the end just before returning.
327 int remaining_exponent = exponent;
328 while (remaining_exponent >= 27) {
329 MultiplyByUInt64(kFive27);
330 remaining_exponent -= 27;
331 }
332 while (remaining_exponent >= 13) {
333 MultiplyByUInt32(kFive13);
334 remaining_exponent -= 13;
335 }
336 if (remaining_exponent > 0) {
337 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
338 }
339 ShiftLeft(exponent);
340 }
341
342
343 void Bignum::Square() {
344 ASSERT(IsClamped());
345 int product_length = 2 * used_digits_;
346 EnsureCapacity(product_length);
347
348 // Comba multiplication: compute each column separately.
349 // Example: r = a2a1a0 * b2b1b0.
350 // r = 1 * a0b0 +
351 // 10 * (a1b0 + a0b1) +
352 // 100 * (a2b0 + a1b1 + a0b2) +
353 // 1000 * (a2b1 + a1b2) +
354 // 10000 * a2b2
355 //
356 // In the worst case we have to accumulate nb-digits products of digit*d igit.
357 //
358 // Assert that the additional number of bits in a DoubleChunk are enough to
359 // sum up used_digits of Bigit*Bigit.
360 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
361 UNIMPLEMENTED();
362 }
363 DoubleChunk accumulator = 0;
364 // First shift the digits so we don't overwrite them.
365 int copy_offset = used_digits_;
366 for (int i = 0; i < used_digits_; ++i) {
367 bigits_[copy_offset + i] = bigits_[i];
368 }
369 // We have two loops to avoid some 'if's in the loop.
370 for (int i = 0; i < used_digits_; ++i) {
371 // Process temporary digit i with power i.
372 // The sum of the two indices must be equal to i.
373 int bigit_index1 = i;
374 int bigit_index2 = 0;
375 // Sum all of the sub-products.
376 while (bigit_index1 >= 0) {
377 Chunk chunk1 = bigits_[copy_offset + bigit_index1];
378 Chunk chunk2 = bigits_[copy_offset + bigit_index2];
379 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
380 bigit_index1--;
381 bigit_index2++;
382 }
383 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
384 accumulator >>= kBigitSize;
385 }
386 for (int i = used_digits_; i < product_length; ++i) {
387 int bigit_index1 = used_digits_ - 1;
388 int bigit_index2 = i - bigit_index1;
389 // Invariant: sum of both indices is again equal to i.
390 // Inner loop runs 0 times on last iteration, emptying accumulator.
391 while (bigit_index2 < used_digits_) {
392 Chunk chunk1 = bigits_[copy_offset + bigit_index1];
393 Chunk chunk2 = bigits_[copy_offset + bigit_index2];
394 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
395 bigit_index1--;
396 bigit_index2++;
397 }
398 // The overwritten bigits_[i] will never be read in further loop ite rations,
399 // because bigit_index1 and bigit_index2 are always greater
400 // than i - used_digits_.
401 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
402 accumulator >>= kBigitSize;
403 }
404 // Since the result was guaranteed to lie inside the number the
405 // accumulator must be 0 now.
406 ASSERT(accumulator == 0);
407
408 // Don't forget to update the used_digits and the exponent.
409 used_digits_ = product_length;
410 exponent_ *= 2;
411 Clamp();
412 }
413
414
415 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
416 ASSERT(base != 0);
417 ASSERT(power_exponent >= 0);
418 if (power_exponent == 0) {
419 AssignUInt16(1);
420 return;
421 }
422 Zero();
423 int shifts = 0;
424 // We expect base to be in range 2-32, and most often to be 10.
425 // It does not make much sense to implement different algorithms for cou nting
426 // the bits.
427 while ((base & 1) == 0) {
428 base >>= 1;
429 shifts++;
430 }
431 int bit_size = 0;
432 int tmp_base = base;
433 while (tmp_base != 0) {
434 tmp_base >>= 1;
435 bit_size++;
436 }
437 int final_size = bit_size * power_exponent;
438 // 1 extra bigit for the shifting, and one for rounded final_size.
439 EnsureCapacity(final_size / kBigitSize + 2);
440
441 // Left to Right exponentiation.
442 int mask = 1;
443 while (power_exponent >= mask) mask <<= 1;
444
445 // The mask is now pointing to the bit above the most significant 1-bit of
446 // power_exponent.
447 // Get rid of first 1-bit;
448 mask >>= 2;
449 uint64_t this_value = base;
450
451 bool delayed_multipliciation = false;
452 const uint64_t max_32bits = 0xFFFFFFFF;
453 while (mask != 0 && this_value <= max_32bits) {
454 this_value = this_value * this_value;
455 // Verify that there is enough space in this_value to perform the
456 // multiplication. The first bit_size bits must be 0.
457 if ((power_exponent & mask) != 0) {
458 uint64_t base_bits_mask =
459 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
460 bool high_bits_zero = (this_value & base_bits_mask) == 0;
461 if (high_bits_zero) {
462 this_value *= base;
463 } else {
464 delayed_multipliciation = true;
465 }
466 }
467 mask >>= 1;
468 }
469 AssignUInt64(this_value);
470 if (delayed_multipliciation) {
471 MultiplyByUInt32(base);
472 }
473
474 // Now do the same thing as a bignum.
475 while (mask != 0) {
476 Square();
477 if ((power_exponent & mask) != 0) {
478 MultiplyByUInt32(base);
479 }
480 mask >>= 1;
481 }
482
483 // And finally add the saved shifts.
484 ShiftLeft(shifts * power_exponent);
485 }
486
487
488 // Precondition: this/other < 16bit.
489 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
490 ASSERT(IsClamped());
491 ASSERT(other.IsClamped());
492 ASSERT(other.used_digits_ > 0);
493
494 // Easy case: if we have less digits than the divisor than the result is 0.
495 // Note: this handles the case where this == 0, too.
496 if (BigitLength() < other.BigitLength()) {
497 return 0;
498 }
499
500 Align(other);
501
502 uint16_t result = 0;
503
504 // Start by removing multiples of 'other' until both numbers have the sa me
505 // number of digits.
506 while (BigitLength() > other.BigitLength()) {
507 // This naive approach is extremely inefficient if the this divided other
508 // might be big. This function is implemented for doubleToString whe re
509 // the result should be small (less than 10).
510 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
511 // Remove the multiples of the first digit.
512 // Example this = 23 and other equals 9. -> Remove 2 multiples.
513 result += static_cast<uint16_t>(bigits_[used_digits_ - 1]);
514 SubtractTimes(other, bigits_[used_digits_ - 1]);
515 }
516
517 ASSERT(BigitLength() == other.BigitLength());
518
519 // Both bignums are at the same length now.
520 // Since other has more than 0 digits we know that the access to
521 // bigits_[used_digits_ - 1] is safe.
522 Chunk this_bigit = bigits_[used_digits_ - 1];
523 Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
524
525 if (other.used_digits_ == 1) {
526 // Shortcut for easy (and common) case.
527 uint16_t quotient = static_cast<uint16_t>(this_bigit / other_bigit);
528 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
529 result += quotient;
530 Clamp();
531 return result;
532 }
533
534 uint16_t division_estimate = static_cast<uint16_t>(this_bigit / (other_b igit + 1));
535 result += division_estimate;
536 SubtractTimes(other, division_estimate);
537
538 if (other_bigit * (division_estimate + 1) > this_bigit) {
539 // No need to even try to subtract. Even if other's remaining digits were 0
540 // another subtraction would be too much.
541 return result;
542 }
543
544 while (LessEqual(other, *this)) {
545 SubtractBignum(other);
546 result++;
547 }
548 return result;
549 }
550
551
552 template<typename S>
553 static int SizeInHexChars(S number) {
554 ASSERT(number > 0);
555 int result = 0;
556 while (number != 0) {
557 number >>= 4;
558 result++;
559 }
560 return result;
561 }
562
563
564 static char HexCharOfValue(uint8_t value) {
565 ASSERT(0 <= value && value <= 16);
566 if (value < 10) return value + '0';
567 return value - 10 + 'A';
568 }
569
570
571 bool Bignum::ToHexString(char* buffer, int buffer_size) const {
572 ASSERT(IsClamped());
573 // Each bigit must be printable as separate hex-character.
574 ASSERT(kBigitSize % 4 == 0);
575 const int kHexCharsPerBigit = kBigitSize / 4;
576
577 if (used_digits_ == 0) {
578 if (buffer_size < 2) return false;
579 buffer[0] = '0';
580 buffer[1] = '\0';
581 return true;
582 }
583 // We add 1 for the terminating '\0' character.
584 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
585 SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
586 if (needed_chars > buffer_size) return false;
587 int string_index = needed_chars - 1;
588 buffer[string_index--] = '\0';
589 for (int i = 0; i < exponent_; ++i) {
590 for (int j = 0; j < kHexCharsPerBigit; ++j) {
591 buffer[string_index--] = '0';
592 }
593 }
594 for (int i = 0; i < used_digits_ - 1; ++i) {
595 Chunk current_bigit = bigits_[i];
596 for (int j = 0; j < kHexCharsPerBigit; ++j) {
597 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
598 current_bigit >>= 4;
599 }
600 }
601 // And finally the last bigit.
602 Chunk most_significant_bigit = bigits_[used_digits_ - 1];
603 while (most_significant_bigit != 0) {
604 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF );
605 most_significant_bigit >>= 4;
606 }
607 return true;
608 }
609
610
611 Bignum::Chunk Bignum::BigitAt(int index) const {
612 if (index >= BigitLength()) return 0;
613 if (index < exponent_) return 0;
614 return bigits_[index - exponent_];
615 }
616
617
618 int Bignum::Compare(const Bignum& a, const Bignum& b) {
619 ASSERT(a.IsClamped());
620 ASSERT(b.IsClamped());
621 int bigit_length_a = a.BigitLength();
622 int bigit_length_b = b.BigitLength();
623 if (bigit_length_a < bigit_length_b) return -1;
624 if (bigit_length_a > bigit_length_b) return +1;
625 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i ) {
626 Chunk bigit_a = a.BigitAt(i);
627 Chunk bigit_b = b.BigitAt(i);
628 if (bigit_a < bigit_b) return -1;
629 if (bigit_a > bigit_b) return +1;
630 // Otherwise they are equal up to this digit. Try the next digit.
631 }
632 return 0;
633 }
634
635
636 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
637 ASSERT(a.IsClamped());
638 ASSERT(b.IsClamped());
639 ASSERT(c.IsClamped());
640 if (a.BigitLength() < b.BigitLength()) {
641 return PlusCompare(b, a, c);
642 }
643 if (a.BigitLength() + 1 < c.BigitLength()) return -1;
644 if (a.BigitLength() > c.BigitLength()) return +1;
645 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' t han
646 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
647 // of 'a'.
648 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
649 return -1;
650 }
651
652 Chunk borrow = 0;
653 // Starting at min_exponent all digits are == 0. So no need to compare t hem.
654 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
655 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
656 Chunk chunk_a = a.BigitAt(i);
657 Chunk chunk_b = b.BigitAt(i);
658 Chunk chunk_c = c.BigitAt(i);
659 Chunk sum = chunk_a + chunk_b;
660 if (sum > chunk_c + borrow) {
661 return +1;
662 } else {
663 borrow = chunk_c + borrow - sum;
664 if (borrow > 1) return -1;
665 borrow <<= kBigitSize;
666 }
667 }
668 if (borrow == 0) return 0;
669 return -1;
670 }
671
672
673 void Bignum::Clamp() {
674 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
675 used_digits_--;
676 }
677 if (used_digits_ == 0) {
678 // Zero.
679 exponent_ = 0;
680 }
681 }
682
683
684 bool Bignum::IsClamped() const {
685 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
686 }
687
688
689 void Bignum::Zero() {
690 for (int i = 0; i < used_digits_; ++i) {
691 bigits_[i] = 0;
692 }
693 used_digits_ = 0;
694 exponent_ = 0;
695 }
696
697
698 void Bignum::Align(const Bignum& other) {
699 if (exponent_ > other.exponent_) {
700 // If "X" represents a "hidden" digit (by the exponent) then we are in the
701 // following case (a == this, b == other):
702 // a: aaaaaaXXXX or a: aaaaaXXX
703 // b: bbbbbbX b: bbbbbbbbXX
704 // We replace some of the hidden digits (X) of a with 0 digits.
705 // a: aaaaaa000X or a: aaaaa0XX
706 int zero_digits = exponent_ - other.exponent_;
707 EnsureCapacity(used_digits_ + zero_digits);
708 for (int i = used_digits_ - 1; i >= 0; --i) {
709 bigits_[i + zero_digits] = bigits_[i];
710 }
711 for (int i = 0; i < zero_digits; ++i) {
712 bigits_[i] = 0;
713 }
714 used_digits_ += zero_digits;
715 exponent_ -= zero_digits;
716 ASSERT(used_digits_ >= 0);
717 ASSERT(exponent_ >= 0);
718 }
719 }
720
721
722 void Bignum::BigitsShiftLeft(int shift_amount) {
723 ASSERT(shift_amount < kBigitSize);
724 ASSERT(shift_amount >= 0);
725 Chunk carry = 0;
726 for (int i = 0; i < used_digits_; ++i) {
727 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
728 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
729 carry = new_carry;
730 }
731 if (carry != 0) {
732 bigits_[used_digits_] = carry;
733 used_digits_++;
734 }
735 }
736
737
738 void Bignum::SubtractTimes(const Bignum& other, int factor) {
739 ASSERT(exponent_ <= other.exponent_);
740 if (factor < 3) {
741 for (int i = 0; i < factor; ++i) {
742 SubtractBignum(other);
743 }
744 return;
745 }
746 Chunk borrow = 0;
747 int exponent_diff = other.exponent_ - exponent_;
748 for (int i = 0; i < other.used_digits_; ++i) {
749 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigit s_[i];
750 DoubleChunk remove = borrow + product;
751 Chunk difference = bigits_[i + exponent_diff] - ((uint32_t)remove & kBigitMask);
752 bigits_[i + exponent_diff] = difference & kBigitMask;
753 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
754 (remove >> kBigitSize));
755 }
756 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
757 if (borrow == 0) return;
758 Chunk difference = bigits_[i] - borrow;
759 bigits_[i] = difference & kBigitMask;
760 borrow = difference >> (kChunkSize - 1);
761 }
762 Clamp();
763 }
764
765
766 } // namespace double_conversion
767
768 } // namespace WTF
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