Line data Source code
1 : // Copyright 2011 the V8 project authors. All rights reserved.
2 : // Use of this source code is governed by a BSD-style license that can be
3 : // found in the LICENSE file.
4 :
5 : #include "src/bignum.h"
6 : #include "src/utils.h"
7 :
8 : namespace v8 {
9 : namespace internal {
10 :
11 5736728 : Bignum::Bignum()
12 11561791 : : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
13 1497041191 : for (int i = 0; i < kBigitCapacity; ++i) {
14 1491216128 : bigits_[i] = 0;
15 : }
16 5736728 : }
17 :
18 :
19 : template<typename S>
20 : static int BitSize(S value) {
21 : return 8 * sizeof(value);
22 : }
23 :
24 :
25 : // Guaranteed to lie in one Bigit.
26 1162954 : void Bignum::AssignUInt16(uint16_t value) {
27 : DCHECK_GE(kBigitSize, BitSize(value));
28 : Zero();
29 1162954 : if (value == 0) return;
30 :
31 : EnsureCapacity(1);
32 1178680 : bigits_[0] = value;
33 1178680 : used_digits_ = 1;
34 : }
35 :
36 :
37 2287004 : void Bignum::AssignUInt64(uint64_t value) {
38 : const int kUInt64Size = 64;
39 :
40 : Zero();
41 2287004 : if (value == 0) return;
42 :
43 : int needed_bigits = kUInt64Size / kBigitSize + 1;
44 : EnsureCapacity(needed_bigits);
45 16008993 : for (int i = 0; i < needed_bigits; ++i) {
46 13721994 : bigits_[i] = static_cast<Chunk>(value & kBigitMask);
47 6860997 : value = value >> kBigitSize;
48 : }
49 2286999 : used_digits_ = needed_bigits;
50 : Clamp();
51 : }
52 :
53 :
54 1702106 : void Bignum::AssignBignum(const Bignum& other) {
55 1702106 : exponent_ = other.exponent_;
56 22487014 : for (int i = 0; i < other.used_digits_; ++i) {
57 20784908 : bigits_[i] = other.bigits_[i];
58 : }
59 : // Clear the excess digits (if there were any).
60 1702676 : for (int i = other.used_digits_; i < used_digits_; ++i) {
61 570 : bigits_[i] = 0;
62 : }
63 1702106 : used_digits_ = other.used_digits_;
64 1702106 : }
65 :
66 :
67 : static uint64_t ReadUInt64(Vector<const char> buffer,
68 : int from,
69 : int digits_to_read) {
70 : uint64_t result = 0;
71 88501 : int to = from + digits_to_read;
72 :
73 3360367 : for (int i = from; i < to; ++i) {
74 3271866 : int digit = buffer[i] - '0';
75 : DCHECK(0 <= digit && digit <= 9);
76 1635933 : result = result * 10 + digit;
77 : }
78 : return result;
79 : }
80 :
81 :
82 4514 : void Bignum::AssignDecimalString(Vector<const char> value) {
83 : // 2^64 = 18446744073709551616 > 10^19
84 : const int kMaxUint64DecimalDigits = 19;
85 : Zero();
86 : int length = value.length();
87 : int pos = 0;
88 : // Let's just say that each digit needs 4 bits.
89 172488 : while (length >= kMaxUint64DecimalDigits) {
90 : uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
91 : pos += kMaxUint64DecimalDigits;
92 83987 : length -= kMaxUint64DecimalDigits;
93 83987 : MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
94 83987 : AddUInt64(digits);
95 : }
96 : uint64_t digits = ReadUInt64(value, pos, length);
97 4514 : MultiplyByPowerOfTen(length);
98 4514 : AddUInt64(digits);
99 : Clamp();
100 4514 : }
101 :
102 :
103 15190 : static int HexCharValue(char c) {
104 15190 : if ('0' <= c && c <= '9') return c - '0';
105 5140 : if ('a' <= c && c <= 'f') return 10 + c - 'a';
106 5140 : if ('A' <= c && c <= 'F') return 10 + c - 'A';
107 0 : UNREACHABLE();
108 : }
109 :
110 :
111 895 : void Bignum::AssignHexString(Vector<const char> value) {
112 : Zero();
113 : int length = value.length();
114 :
115 895 : int needed_bigits = length * 4 / kBigitSize + 1;
116 : EnsureCapacity(needed_bigits);
117 895 : int string_index = length - 1;
118 4745 : for (int i = 0; i < needed_bigits - 1; ++i) {
119 : // These bigits are guaranteed to be "full".
120 : Chunk current_bigit = 0;
121 28875 : for (int j = 0; j < kBigitSize / 4; j++) {
122 26950 : current_bigit += HexCharValue(value[string_index--]) << (j * 4);
123 : }
124 3850 : bigits_[i] = current_bigit;
125 : }
126 895 : used_digits_ = needed_bigits - 1;
127 :
128 : Chunk most_significant_bigit = 0; // Could be = 0;
129 4325 : for (int j = 0; j <= string_index; ++j) {
130 1715 : most_significant_bigit <<= 4;
131 3430 : most_significant_bigit += HexCharValue(value[j]);
132 : }
133 895 : if (most_significant_bigit != 0) {
134 1350 : bigits_[used_digits_] = most_significant_bigit;
135 675 : used_digits_++;
136 : }
137 : Clamp();
138 895 : }
139 :
140 :
141 88591 : void Bignum::AddUInt64(uint64_t operand) {
142 88847 : if (operand == 0) return;
143 : Bignum other;
144 88335 : other.AssignUInt64(operand);
145 88335 : AddBignum(other);
146 : }
147 :
148 :
149 88420 : void Bignum::AddBignum(const Bignum& other) {
150 : DCHECK(IsClamped());
151 : DCHECK(other.IsClamped());
152 :
153 : // If this has a greater exponent than other append zero-bigits to this.
154 : // After this call exponent_ <= other.exponent_.
155 88420 : Align(other);
156 :
157 : // There are two possibilities:
158 : // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
159 : // bbbbb 00000000
160 : // ----------------
161 : // ccccccccccc 0000
162 : // or
163 : // aaaaaaaaaa 0000
164 : // bbbbbbbbb 0000000
165 : // -----------------
166 : // cccccccccccc 0000
167 : // In both cases we might need a carry bigit.
168 :
169 88420 : EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
170 : Chunk carry = 0;
171 88420 : int bigit_pos = other.exponent_ - exponent_;
172 : DCHECK_GE(bigit_pos, 0);
173 605244 : for (int i = 0; i < other.used_digits_; ++i) {
174 775236 : Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
175 258412 : bigits_[bigit_pos] = sum & kBigitMask;
176 258412 : carry = sum >> kBigitSize;
177 258412 : bigit_pos++;
178 : }
179 :
180 89606 : while (carry != 0) {
181 1186 : Chunk sum = bigits_[bigit_pos] + carry;
182 593 : bigits_[bigit_pos] = sum & kBigitMask;
183 593 : carry = sum >> kBigitSize;
184 593 : bigit_pos++;
185 : }
186 176840 : used_digits_ = Max(bigit_pos, used_digits_);
187 : DCHECK(IsClamped());
188 88420 : }
189 :
190 :
191 12657455 : void Bignum::SubtractBignum(const Bignum& other) {
192 : DCHECK(IsClamped());
193 : DCHECK(other.IsClamped());
194 : // We require this to be bigger than other.
195 : DCHECK(LessEqual(other, *this));
196 :
197 12657455 : Align(other);
198 :
199 12657455 : int offset = other.exponent_ - exponent_;
200 : Chunk borrow = 0;
201 : int i;
202 170494479 : for (i = 0; i < other.used_digits_; ++i) {
203 : DCHECK((borrow == 0) || (borrow == 1));
204 236755536 : Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
205 78918512 : bigits_[i + offset] = difference & kBigitMask;
206 78918512 : borrow = difference >> (kChunkSize - 1);
207 : }
208 19607327 : while (borrow != 0) {
209 6949872 : Chunk difference = bigits_[i + offset] - borrow;
210 3474936 : bigits_[i + offset] = difference & kBigitMask;
211 3474936 : borrow = difference >> (kChunkSize - 1);
212 3474936 : ++i;
213 : }
214 : Clamp();
215 12657455 : }
216 :
217 :
218 4435680 : void Bignum::ShiftLeft(int shift_amount) {
219 4435680 : if (used_digits_ == 0) return;
220 4435674 : exponent_ += shift_amount / kBigitSize;
221 4435674 : int local_shift = shift_amount % kBigitSize;
222 : EnsureCapacity(used_digits_ + 1);
223 4435674 : BigitsShiftLeft(local_shift);
224 : }
225 :
226 :
227 31082287 : void Bignum::MultiplyByUInt32(uint32_t factor) {
228 31082287 : if (factor == 1) return;
229 31082287 : if (factor == 0) {
230 : Zero();
231 : return;
232 : }
233 31082287 : if (used_digits_ == 0) return;
234 :
235 : // The product of a bigit with the factor is of size kBigitSize + 32.
236 : // Assert that this number + 1 (for the carry) fits into double chunk.
237 : DCHECK_GE(kDoubleChunkSize, kBigitSize + 32 + 1);
238 : DoubleChunk carry = 0;
239 650097285 : for (int i = 0; i < used_digits_; ++i) {
240 620625406 : DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
241 310312703 : bigits_[i] = static_cast<Chunk>(product & kBigitMask);
242 310312703 : carry = (product >> kBigitSize);
243 : }
244 39220019 : while (carry != 0) {
245 4874070 : EnsureCapacity(used_digits_ + 1);
246 9748140 : bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
247 4874070 : used_digits_++;
248 4874070 : carry >>= kBigitSize;
249 : }
250 : }
251 :
252 :
253 775729 : void Bignum::MultiplyByUInt64(uint64_t factor) {
254 775729 : if (factor == 1) return;
255 775719 : if (factor == 0) {
256 : Zero();
257 : return;
258 : }
259 : DCHECK_LT(kBigitSize, 32);
260 : uint64_t carry = 0;
261 775719 : uint64_t low = factor & 0xFFFFFFFF;
262 775719 : uint64_t high = factor >> 32;
263 22196857 : for (int i = 0; i < used_digits_; ++i) {
264 21421138 : uint64_t product_low = low * bigits_[i];
265 10710569 : uint64_t product_high = high * bigits_[i];
266 10710569 : uint64_t tmp = (carry & kBigitMask) + product_low;
267 10710569 : bigits_[i] = static_cast<Chunk>(tmp & kBigitMask);
268 10710569 : carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
269 10710569 : (product_high << (32 - kBigitSize));
270 : }
271 3773807 : while (carry != 0) {
272 1499044 : EnsureCapacity(used_digits_ + 1);
273 2998088 : bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
274 1499044 : used_digits_++;
275 1499044 : carry >>= kBigitSize;
276 : }
277 : }
278 :
279 :
280 97099 : void Bignum::MultiplyByPowerOfTen(int exponent) {
281 : const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765C793, fa10079d);
282 : const uint16_t kFive1 = 5;
283 : const uint16_t kFive2 = kFive1 * 5;
284 : const uint16_t kFive3 = kFive2 * 5;
285 : const uint16_t kFive4 = kFive3 * 5;
286 : const uint16_t kFive5 = kFive4 * 5;
287 : const uint16_t kFive6 = kFive5 * 5;
288 : const uint32_t kFive7 = kFive6 * 5;
289 : const uint32_t kFive8 = kFive7 * 5;
290 : const uint32_t kFive9 = kFive8 * 5;
291 : const uint32_t kFive10 = kFive9 * 5;
292 : const uint32_t kFive11 = kFive10 * 5;
293 : const uint32_t kFive12 = kFive11 * 5;
294 : const uint32_t kFive13 = kFive12 * 5;
295 : const uint32_t kFive1_to_12[] =
296 : { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
297 97099 : kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
298 :
299 : DCHECK_GE(exponent, 0);
300 101893 : if (exponent == 0) return;
301 96820 : if (used_digits_ == 0) return;
302 :
303 : // We shift by exponent at the end just before returning.
304 : int remaining_exponent = exponent;
305 339565 : while (remaining_exponent >= 27) {
306 123630 : MultiplyByUInt64(kFive27);
307 123630 : remaining_exponent -= 27;
308 : }
309 264039 : while (remaining_exponent >= 13) {
310 85867 : MultiplyByUInt32(kFive13);
311 85867 : remaining_exponent -= 13;
312 : }
313 92305 : if (remaining_exponent > 0) {
314 91131 : MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
315 : }
316 92305 : ShiftLeft(exponent);
317 : }
318 :
319 :
320 2820235 : void Bignum::Square() {
321 : DCHECK(IsClamped());
322 2820235 : int product_length = 2 * used_digits_;
323 : EnsureCapacity(product_length);
324 :
325 : // Comba multiplication: compute each column separately.
326 : // Example: r = a2a1a0 * b2b1b0.
327 : // r = 1 * a0b0 +
328 : // 10 * (a1b0 + a0b1) +
329 : // 100 * (a2b0 + a1b1 + a0b2) +
330 : // 1000 * (a2b1 + a1b2) +
331 : // 10000 * a2b2
332 : //
333 : // In the worst case we have to accumulate nb-digits products of digit*digit.
334 : //
335 : // Assert that the additional number of bits in a DoubleChunk are enough to
336 : // sum up used_digits of Bigit*Bigit.
337 2820235 : if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
338 0 : UNIMPLEMENTED();
339 : }
340 : DoubleChunk accumulator = 0;
341 : // First shift the digits so we don't overwrite them.
342 : int copy_offset = used_digits_;
343 29371697 : for (int i = 0; i < used_digits_; ++i) {
344 39827193 : bigits_[copy_offset + i] = bigits_[i];
345 : }
346 : // We have two loops to avoid some 'if's in the loop.
347 29371697 : for (int i = 0; i < used_digits_; ++i) {
348 : // Process temporary digit i with power i.
349 : // The sum of the two indices must be equal to i.
350 : int bigit_index1 = i;
351 : int bigit_index2 = 0;
352 : // Sum all of the sub-products.
353 114934689 : while (bigit_index1 >= 0) {
354 101658958 : Chunk chunk1 = bigits_[copy_offset + bigit_index1];
355 101658958 : Chunk chunk2 = bigits_[copy_offset + bigit_index2];
356 50829479 : accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
357 50829479 : bigit_index1--;
358 50829479 : bigit_index2++;
359 : }
360 26551462 : bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
361 13275731 : accumulator >>= kBigitSize;
362 : }
363 29371697 : for (int i = used_digits_; i < product_length; ++i) {
364 13275731 : int bigit_index1 = used_digits_ - 1;
365 13275731 : int bigit_index2 = i - bigit_index1;
366 : // Invariant: sum of both indices is again equal to i.
367 : // Inner loop runs 0 times on last iteration, emptying accumulator.
368 88383227 : while (bigit_index2 < used_digits_) {
369 75107496 : Chunk chunk1 = bigits_[copy_offset + bigit_index1];
370 75107496 : Chunk chunk2 = bigits_[copy_offset + bigit_index2];
371 37553748 : accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
372 37553748 : bigit_index1--;
373 37553748 : bigit_index2++;
374 : }
375 : // The overwritten bigits_[i] will never be read in further loop iterations,
376 : // because bigit_index1 and bigit_index2 are always greater
377 : // than i - used_digits_.
378 26551462 : bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
379 13275731 : accumulator >>= kBigitSize;
380 : }
381 : // Since the result was guaranteed to lie inside the number the
382 : // accumulator must be 0 now.
383 : DCHECK_EQ(accumulator, 0);
384 :
385 : // Don't forget to update the used_digits and the exponent.
386 2820235 : used_digits_ = product_length;
387 2820235 : exponent_ *= 2;
388 : Clamp();
389 2820235 : }
390 :
391 :
392 1429073 : void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
393 : DCHECK_NE(base, 0);
394 : DCHECK_GE(power_exponent, 0);
395 1429073 : if (power_exponent == 0) {
396 : AssignUInt16(1);
397 : return;
398 : }
399 : Zero();
400 : int shifts = 0;
401 : // We expect base to be in range 2-32, and most often to be 10.
402 : // It does not make much sense to implement different algorithms for counting
403 : // the bits.
404 4240106 : while ((base & 1) == 0) {
405 1413392 : base >>= 1;
406 1413392 : shifts++;
407 : }
408 : int bit_size = 0;
409 1413322 : int tmp_base = base;
410 9893184 : while (tmp_base != 0) {
411 4239931 : tmp_base >>= 1;
412 4239931 : bit_size++;
413 : }
414 1413322 : int final_size = bit_size * power_exponent;
415 : // 1 extra bigit for the shifting, and one for rounded final_size.
416 : EnsureCapacity(final_size / kBigitSize + 2);
417 :
418 : // Left to Right exponentiation.
419 : int mask = 1;
420 10509690 : while (power_exponent >= mask) mask <<= 1;
421 :
422 : // The mask is now pointing to the bit above the most significant 1-bit of
423 : // power_exponent.
424 : // Get rid of first 1-bit;
425 1413322 : mask >>= 2;
426 1413322 : uint64_t this_value = base;
427 :
428 : bool delayed_multipliciation = false;
429 : const uint64_t max_32bits = 0xFFFFFFFF;
430 11138994 : while (mask != 0 && this_value <= max_32bits) {
431 4862836 : this_value = this_value * this_value;
432 : // Verify that there is enough space in this_value to perform the
433 : // multiplication. The first bit_size bits must be 0.
434 4862836 : if ((power_exponent & mask) != 0) {
435 : uint64_t base_bits_mask =
436 2129960 : ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
437 2129960 : bool high_bits_zero = (this_value & base_bits_mask) == 0;
438 2129960 : if (high_bits_zero) {
439 2129960 : this_value *= base;
440 : } else {
441 : delayed_multipliciation = true;
442 : }
443 : }
444 4862836 : mask >>= 1;
445 : }
446 1413322 : AssignUInt64(this_value);
447 1413322 : if (delayed_multipliciation) {
448 0 : MultiplyByUInt32(base);
449 : }
450 :
451 : // Now do the same thing as a bignum.
452 7053742 : while (mask != 0) {
453 2820210 : Square();
454 2820210 : if ((power_exponent & mask) != 0) {
455 1393570 : MultiplyByUInt32(base);
456 : }
457 2820210 : mask >>= 1;
458 : }
459 :
460 : // And finally add the saved shifts.
461 1413322 : ShiftLeft(shifts * power_exponent);
462 : }
463 :
464 :
465 : // Precondition: this/other < 16bit.
466 20716567 : uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
467 : DCHECK(IsClamped());
468 : DCHECK(other.IsClamped());
469 : DCHECK_GT(other.used_digits_, 0);
470 :
471 : // Easy case: if we have less digits than the divisor than the result is 0.
472 : // Note: this handles the case where this == 0, too.
473 20716567 : if (BigitLength() < other.BigitLength()) {
474 : return 0;
475 : }
476 :
477 19768498 : Align(other);
478 :
479 : uint16_t result = 0;
480 :
481 : // Start by removing multiples of 'other' until both numbers have the same
482 : // number of digits.
483 32884148 : while (BigitLength() > other.BigitLength()) {
484 : // This naive approach is extremely inefficient if the this divided other
485 : // might be big. This function is implemented for doubleToString where
486 : // the result should be small (less than 10).
487 : DCHECK(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
488 : // Remove the multiples of the first digit.
489 : // Example this = 23 and other equals 9. -> Remove 2 multiples.
490 13115650 : result += bigits_[used_digits_ - 1];
491 6557825 : SubtractTimes(other, bigits_[used_digits_ - 1]);
492 : }
493 :
494 : DCHECK(BigitLength() == other.BigitLength());
495 :
496 : // Both bignums are at the same length now.
497 : // Since other has more than 0 digits we know that the access to
498 : // bigits_[used_digits_ - 1] is safe.
499 39536996 : Chunk this_bigit = bigits_[used_digits_ - 1];
500 39536996 : Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
501 :
502 19768498 : if (other.used_digits_ == 1) {
503 : // Shortcut for easy (and common) case.
504 9557788 : int quotient = this_bigit / other_bigit;
505 9557788 : bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
506 9557788 : result += quotient;
507 : Clamp();
508 : return result;
509 : }
510 :
511 10210710 : int division_estimate = this_bigit / (other_bigit + 1);
512 10210710 : result += division_estimate;
513 10210710 : SubtractTimes(other, division_estimate);
514 :
515 10210710 : if (other_bigit * (division_estimate + 1) > this_bigit) {
516 : // No need to even try to subtract. Even if other's remaining digits were 0
517 : // another subtraction would be too much.
518 : return result;
519 : }
520 :
521 4210449 : while (LessEqual(other, *this)) {
522 1444600 : SubtractBignum(other);
523 1444600 : result++;
524 : }
525 : return result;
526 : }
527 :
528 :
529 : template<typename S>
530 : static int SizeInHexChars(S number) {
531 : DCHECK_GT(number, 0);
532 : int result = 0;
533 3815 : while (number != 0) {
534 2910 : number >>= 4;
535 2910 : result++;
536 : }
537 : return result;
538 : }
539 :
540 :
541 945 : bool Bignum::ToHexString(char* buffer, int buffer_size) const {
542 : DCHECK(IsClamped());
543 : // Each bigit must be printable as separate hex-character.
544 : DCHECK_EQ(kBigitSize % 4, 0);
545 : const int kHexCharsPerBigit = kBigitSize / 4;
546 :
547 945 : if (used_digits_ == 0) {
548 40 : if (buffer_size < 2) return false;
549 40 : buffer[0] = '0';
550 40 : buffer[1] = '\0';
551 40 : return true;
552 : }
553 : // We add 1 for the terminating '\0' character.
554 1810 : int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
555 2715 : SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
556 905 : if (needed_chars > buffer_size) return false;
557 : int string_index = needed_chars - 1;
558 905 : buffer[string_index--] = '\0';
559 2385 : for (int i = 0; i < exponent_; ++i) {
560 11100 : for (int j = 0; j < kHexCharsPerBigit; ++j) {
561 5180 : buffer[string_index--] = '0';
562 : }
563 : }
564 11765 : for (int i = 0; i < used_digits_ - 1; ++i) {
565 10860 : Chunk current_bigit = bigits_[i];
566 81450 : for (int j = 0; j < kHexCharsPerBigit; ++j) {
567 76020 : buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
568 38010 : current_bigit >>= 4;
569 : }
570 : }
571 : // And finally the last bigit.
572 1810 : Chunk most_significant_bigit = bigits_[used_digits_ - 1];
573 6725 : while (most_significant_bigit != 0) {
574 5820 : buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
575 2910 : most_significant_bigit >>= 4;
576 : }
577 : return true;
578 : }
579 :
580 :
581 0 : Bignum::Chunk Bignum::BigitAt(int index) const {
582 58957147 : if (index >= BigitLength()) return 0;
583 50459479 : if (index < exponent_) return 0;
584 100496618 : return bigits_[index - exponent_];
585 : }
586 :
587 :
588 12784430 : int Bignum::Compare(const Bignum& a, const Bignum& b) {
589 : DCHECK(a.IsClamped());
590 : DCHECK(b.IsClamped());
591 : int bigit_length_a = a.BigitLength();
592 : int bigit_length_b = b.BigitLength();
593 12784430 : if (bigit_length_a < bigit_length_b) return -1;
594 12753176 : if (bigit_length_a > bigit_length_b) return +1;
595 28002542 : for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
596 : Chunk bigit_a = a.BigitAt(i);
597 : Chunk bigit_b = b.BigitAt(i);
598 12205931 : if (bigit_a < bigit_b) return -1;
599 10512750 : if (bigit_a > bigit_b) return +1;
600 : // Otherwise they are equal up to this digit. Try the next digit.
601 : }
602 : return 0;
603 : }
604 :
605 :
606 10888949 : int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
607 : DCHECK(a.IsClamped());
608 : DCHECK(b.IsClamped());
609 : DCHECK(c.IsClamped());
610 10920164 : if (a.BigitLength() < b.BigitLength()) {
611 : return PlusCompare(b, a, c);
612 : }
613 21777898 : if (a.BigitLength() + 1 < c.BigitLength()) return -1;
614 10791803 : if (a.BigitLength() > c.BigitLength()) return +1;
615 : // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
616 : // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
617 : // of 'a'.
618 10783934 : if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
619 : return -1;
620 : }
621 :
622 : Chunk borrow = 0;
623 : // Starting at min_exponent all digits are == 0. So no need to compare them.
624 : int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
625 11519863 : for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
626 : Chunk chunk_a = a.BigitAt(i);
627 : Chunk chunk_b = b.BigitAt(i);
628 : Chunk chunk_c = c.BigitAt(i);
629 11515095 : Chunk sum = chunk_a + chunk_b;
630 11515095 : if (sum > chunk_c + borrow) {
631 : return +1;
632 : } else {
633 10397090 : borrow = chunk_c + borrow - sum;
634 10397090 : if (borrow > 1) return -1;
635 778194 : borrow <<= kBigitSize;
636 : }
637 : }
638 4768 : if (borrow == 0) return 0;
639 15 : return -1;
640 : }
641 :
642 :
643 0 : void Bignum::Clamp() {
644 83559662 : while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
645 7708283 : used_digits_--;
646 : }
647 34120644 : if (used_digits_ == 0) {
648 : // Zero.
649 98192 : exponent_ = 0;
650 : }
651 0 : }
652 :
653 :
654 0 : bool Bignum::IsClamped() const {
655 0 : return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
656 : }
657 :
658 :
659 0 : void Bignum::Zero() {
660 4892220 : for (int i = 0; i < used_digits_; ++i) {
661 7780 : bigits_[i] = 0;
662 : }
663 4884440 : used_digits_ = 0;
664 4884440 : exponent_ = 0;
665 0 : }
666 :
667 :
668 32514373 : void Bignum::Align(const Bignum& other) {
669 32514373 : if (exponent_ > other.exponent_) {
670 : // If "X" represents a "hidden" digit (by the exponent) then we are in the
671 : // following case (a == this, b == other):
672 : // a: aaaaaaXXXX or a: aaaaaXXX
673 : // b: bbbbbbX b: bbbbbbbbXX
674 : // We replace some of the hidden digits (X) of a with 0 digits.
675 : // a: aaaaaa000X or a: aaaaa0XX
676 483287 : int zero_digits = exponent_ - other.exponent_;
677 483287 : EnsureCapacity(used_digits_ + zero_digits);
678 1918491 : for (int i = used_digits_ - 1; i >= 0; --i) {
679 4305612 : bigits_[i + zero_digits] = bigits_[i];
680 : }
681 12164697 : for (int i = 0; i < zero_digits; ++i) {
682 11681410 : bigits_[i] = 0;
683 : }
684 483287 : used_digits_ += zero_digits;
685 483287 : exponent_ -= zero_digits;
686 : DCHECK_GE(used_digits_, 0);
687 : DCHECK_GE(exponent_, 0);
688 : }
689 32514373 : }
690 :
691 :
692 4435674 : void Bignum::BigitsShiftLeft(int shift_amount) {
693 : DCHECK_LT(shift_amount, kBigitSize);
694 : DCHECK_GE(shift_amount, 0);
695 : Chunk carry = 0;
696 62537030 : for (int i = 0; i < used_digits_; ++i) {
697 58101356 : Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
698 29050678 : bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
699 : carry = new_carry;
700 : }
701 4435674 : if (carry != 0) {
702 2460678 : bigits_[used_digits_] = carry;
703 1230339 : used_digits_++;
704 : }
705 4435674 : }
706 :
707 :
708 16768535 : void Bignum::SubtractTimes(const Bignum& other, int factor) {
709 : #ifdef DEBUG
710 : Bignum a, b;
711 : a.AssignBignum(*this);
712 : b.AssignBignum(other);
713 : b.MultiplyByUInt32(factor);
714 : a.SubtractBignum(b);
715 : #endif
716 : DCHECK(exponent_ <= other.exponent_);
717 16768535 : if (factor < 3) {
718 32401337 : for (int i = 0; i < factor; ++i) {
719 11212780 : SubtractBignum(other);
720 : }
721 : return;
722 : }
723 : Chunk borrow = 0;
724 6792758 : int exponent_diff = other.exponent_ - exponent_;
725 151951216 : for (int i = 0; i < other.used_digits_; ++i) {
726 145158458 : DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
727 72579229 : DoubleChunk remove = borrow + product;
728 : Chunk difference =
729 145158458 : bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask);
730 72579229 : bigits_[i + exponent_diff] = difference & kBigitMask;
731 72579229 : borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
732 72579229 : (remove >> kBigitSize));
733 : }
734 7438826 : for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
735 646068 : if (borrow == 0) return;
736 1292136 : Chunk difference = bigits_[i] - borrow;
737 646068 : bigits_[i] = difference & kBigitMask;
738 646068 : borrow = difference >> (kChunkSize - 1);
739 : }
740 : Clamp();
741 : DCHECK(Bignum::Equal(a, *this));
742 : }
743 :
744 :
745 : } // namespace internal
746 121996 : } // namespace v8
|
