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 6891448 : Bignum::Bignum()
12 896011810 : : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
13 904813752 : for (int i = 0; i < kBigitCapacity; ++i) {
14 897922304 : bigits_[i] = 0;
15 : }
16 6891448 : }
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 1396994 : void Bignum::AssignUInt16(uint16_t value) {
27 : DCHECK(kBigitSize >= BitSize(value));
28 : Zero();
29 2793988 : if (value == 0) return;
30 :
31 : EnsureCapacity(1);
32 1415853 : bigits_[0] = value;
33 1415853 : used_digits_ = 1;
34 : }
35 :
36 :
37 2764926 : void Bignum::AssignUInt64(uint64_t value) {
38 : const int kUInt64Size = 64;
39 :
40 : Zero();
41 5529852 : if (value == 0) return;
42 :
43 : int needed_bigits = kUInt64Size / kBigitSize + 1;
44 : EnsureCapacity(needed_bigits);
45 8294757 : for (int i = 0; i < needed_bigits; ++i) {
46 16589514 : bigits_[i] = static_cast<Chunk>(value & kBigitMask);
47 8294757 : value = value >> kBigitSize;
48 : }
49 2764919 : used_digits_ = needed_bigits;
50 2764919 : Clamp();
51 : }
52 :
53 :
54 2045483 : void Bignum::AssignBignum(const Bignum& other) {
55 2045483 : exponent_ = other.exponent_;
56 14599879 : for (int i = 0; i < other.used_digits_; ++i) {
57 37663587 : bigits_[i] = other.bigits_[i];
58 : }
59 : // Clear the excess digits (if there were any).
60 399 : for (int i = other.used_digits_; i < used_digits_; ++i) {
61 399 : bigits_[i] = 0;
62 : }
63 2045483 : used_digits_ = other.used_digits_;
64 2045483 : }
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 123817 : int to = from + digits_to_read;
72 :
73 2288671 : for (int i = from; i < to; ++i) {
74 2288671 : int digit = buffer[i] - '0';
75 : DCHECK(0 <= digit && digit <= 9);
76 2288671 : result = result * 10 + digit;
77 : }
78 : return result;
79 : }
80 :
81 :
82 6326 : void Bignum::AssignDecimalString(Vector<const char> value) {
83 : // 2^64 = 18446744073709551616 > 10^19
84 : const int kMaxUint64DecimalDigits = 19;
85 : Zero();
86 6326 : int length = value.length();
87 : int pos = 0;
88 : // Let's just say that each digit needs 4 bits.
89 130143 : while (length >= kMaxUint64DecimalDigits) {
90 : uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
91 : pos += kMaxUint64DecimalDigits;
92 117491 : length -= kMaxUint64DecimalDigits;
93 117491 : MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
94 117491 : AddUInt64(digits);
95 : }
96 : uint64_t digits = ReadUInt64(value, pos, length);
97 6326 : MultiplyByPowerOfTen(length);
98 6326 : AddUInt64(digits);
99 6326 : Clamp();
100 6326 : }
101 :
102 :
103 21266 : static int HexCharValue(char c) {
104 21266 : if ('0' <= c && c <= '9') return c - '0';
105 7196 : if ('a' <= c && c <= 'f') return 10 + c - 'a';
106 7196 : if ('A' <= c && c <= 'F') return 10 + c - 'A';
107 0 : UNREACHABLE();
108 : return 0; // To make compiler happy.
109 : }
110 :
111 :
112 1253 : void Bignum::AssignHexString(Vector<const char> value) {
113 : Zero();
114 1253 : int length = value.length();
115 :
116 1253 : int needed_bigits = length * 4 / kBigitSize + 1;
117 : EnsureCapacity(needed_bigits);
118 1253 : int string_index = length - 1;
119 3948 : for (int i = 0; i < needed_bigits - 1; ++i) {
120 : // These bigits are guaranteed to be "full".
121 : Chunk current_bigit = 0;
122 18865 : for (int j = 0; j < kBigitSize / 4; j++) {
123 37730 : current_bigit += HexCharValue(value[string_index--]) << (j * 4);
124 : }
125 6335 : bigits_[i] = current_bigit;
126 : }
127 1253 : used_digits_ = needed_bigits - 1;
128 :
129 : Chunk most_significant_bigit = 0; // Could be = 0;
130 3654 : for (int j = 0; j <= string_index; ++j) {
131 2401 : most_significant_bigit <<= 4;
132 2401 : most_significant_bigit += HexCharValue(value[j]);
133 : }
134 1253 : if (most_significant_bigit != 0) {
135 945 : bigits_[used_digits_] = most_significant_bigit;
136 945 : used_digits_++;
137 : }
138 1253 : Clamp();
139 1253 : }
140 :
141 :
142 123943 : void Bignum::AddUInt64(uint64_t operand) {
143 124316 : if (operand == 0) return;
144 : Bignum other;
145 123570 : other.AssignUInt64(operand);
146 123570 : AddBignum(other);
147 : }
148 :
149 :
150 371067 : void Bignum::AddBignum(const Bignum& other) {
151 : DCHECK(IsClamped());
152 : DCHECK(other.IsClamped());
153 :
154 : // If this has a greater exponent than other append zero-bigits to this.
155 : // After this call exponent_ <= other.exponent_.
156 123689 : Align(other);
157 :
158 : // There are two possibilities:
159 : // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
160 : // bbbbb 00000000
161 : // ----------------
162 : // ccccccccccc 0000
163 : // or
164 : // aaaaaaaaaa 0000
165 : // bbbbbbbbb 0000000
166 : // -----------------
167 : // cccccccccccc 0000
168 : // In both cases we might need a carry bigit.
169 :
170 123689 : EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
171 : Chunk carry = 0;
172 123689 : int bigit_pos = other.exponent_ - exponent_;
173 : DCHECK(bigit_pos >= 0);
174 485211 : for (int i = 0; i < other.used_digits_; ++i) {
175 1085411 : Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
176 361522 : bigits_[bigit_pos] = sum & kBigitMask;
177 361522 : carry = sum >> kBigitSize;
178 361522 : bigit_pos++;
179 : }
180 :
181 124534 : while (carry != 0) {
182 845 : Chunk sum = bigits_[bigit_pos] + carry;
183 845 : bigits_[bigit_pos] = sum & kBigitMask;
184 845 : carry = sum >> kBigitSize;
185 845 : bigit_pos++;
186 : }
187 247378 : used_digits_ = Max(bigit_pos, used_digits_);
188 : DCHECK(IsClamped());
189 123689 : }
190 :
191 :
192 15199102 : void Bignum::SubtractBignum(const Bignum& other) {
193 : DCHECK(IsClamped());
194 : DCHECK(other.IsClamped());
195 : // We require this to be bigger than other.
196 : DCHECK(LessEqual(other, *this));
197 :
198 15199102 : Align(other);
199 :
200 15199102 : int offset = other.exponent_ - exponent_;
201 : Chunk borrow = 0;
202 : int i;
203 109920106 : for (i = 0; i < other.used_digits_; ++i) {
204 : DCHECK((borrow == 0) || (borrow == 1));
205 288337339 : Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
206 94721004 : bigits_[i + offset] = difference & kBigitMask;
207 94721004 : borrow = difference >> (kChunkSize - 1);
208 : }
209 19373429 : while (borrow != 0) {
210 8348654 : Chunk difference = bigits_[i + offset] - borrow;
211 4174327 : bigits_[i + offset] = difference & kBigitMask;
212 4174327 : borrow = difference >> (kChunkSize - 1);
213 4174327 : ++i;
214 : }
215 15199102 : Clamp();
216 15199102 : }
217 :
218 :
219 5347297 : void Bignum::ShiftLeft(int shift_amount) {
220 10694594 : if (used_digits_ == 0) return;
221 5347289 : exponent_ += shift_amount / kBigitSize;
222 5347289 : int local_shift = shift_amount % kBigitSize;
223 : EnsureCapacity(used_digits_ + 1);
224 5347289 : BigitsShiftLeft(local_shift);
225 : }
226 :
227 :
228 37360315 : void Bignum::MultiplyByUInt32(uint32_t factor) {
229 37360315 : if (factor == 1) return;
230 37360315 : if (factor == 0) {
231 : Zero();
232 : return;
233 : }
234 37360315 : if (used_digits_ == 0) return;
235 :
236 : // The product of a bigit with the factor is of size kBigitSize + 32.
237 : // Assert that this number + 1 (for the carry) fits into double chunk.
238 : DCHECK(kDoubleChunkSize >= kBigitSize + 32 + 1);
239 : DoubleChunk carry = 0;
240 373737292 : for (int i = 0; i < used_digits_; ++i) {
241 753357261 : DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
242 373737292 : bigits_[i] = static_cast<Chunk>(product & kBigitMask);
243 373737292 : carry = (product >> kBigitSize);
244 : }
245 41313427 : while (carry != 0) {
246 5882677 : EnsureCapacity(used_digits_ + 1);
247 5882677 : bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
248 5882677 : used_digits_++;
249 5882677 : carry >>= kBigitSize;
250 : }
251 : }
252 :
253 :
254 955943 : void Bignum::MultiplyByUInt64(uint64_t factor) {
255 955943 : if (factor == 1) return;
256 955931 : if (factor == 0) {
257 : Zero();
258 : return;
259 : }
260 : DCHECK(kBigitSize < 32);
261 : uint64_t carry = 0;
262 955931 : uint64_t low = factor & 0xFFFFFFFF;
263 955931 : uint64_t high = factor >> 32;
264 14451903 : for (int i = 0; i < used_digits_; ++i) {
265 28846333 : uint64_t product_low = low * bigits_[i];
266 13495972 : uint64_t product_high = high * bigits_[i];
267 13495972 : uint64_t tmp = (carry & kBigitMask) + product_low;
268 13495972 : bigits_[i] = static_cast<Chunk>(tmp & kBigitMask);
269 13495972 : carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
270 13495972 : (product_high << (32 - kBigitSize));
271 : }
272 2810320 : while (carry != 0) {
273 1854389 : EnsureCapacity(used_digits_ + 1);
274 1854389 : bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
275 1854389 : used_digits_++;
276 1854389 : carry >>= kBigitSize;
277 : }
278 : }
279 :
280 :
281 135861 : void Bignum::MultiplyByPowerOfTen(int exponent) {
282 : const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765c793, fa10079d);
283 : const uint16_t kFive1 = 5;
284 : const uint16_t kFive2 = kFive1 * 5;
285 : const uint16_t kFive3 = kFive2 * 5;
286 : const uint16_t kFive4 = kFive3 * 5;
287 : const uint16_t kFive5 = kFive4 * 5;
288 : const uint16_t kFive6 = kFive5 * 5;
289 : const uint32_t kFive7 = kFive6 * 5;
290 : const uint32_t kFive8 = kFive7 * 5;
291 : const uint32_t kFive9 = kFive8 * 5;
292 : const uint32_t kFive10 = kFive9 * 5;
293 : const uint32_t kFive11 = kFive10 * 5;
294 : const uint32_t kFive12 = kFive11 * 5;
295 : const uint32_t kFive13 = kFive12 * 5;
296 : const uint32_t kFive1_to_12[] =
297 : { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
298 135861 : kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
299 :
300 : DCHECK(exponent >= 0);
301 142576 : if (exponent == 0) return;
302 135473 : if (used_digits_ == 0) return;
303 :
304 : // We shift by exponent at the end just before returning.
305 : int remaining_exponent = exponent;
306 302198 : while (remaining_exponent >= 27) {
307 173052 : MultiplyByUInt64(kFive27);
308 173052 : remaining_exponent -= 27;
309 : }
310 249273 : while (remaining_exponent >= 13) {
311 120127 : MultiplyByUInt32(kFive13);
312 120127 : remaining_exponent -= 13;
313 : }
314 129146 : if (remaining_exponent > 0) {
315 127500 : MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
316 : }
317 129146 : ShiftLeft(exponent);
318 : }
319 :
320 :
321 3384925 : void Bignum::Square() {
322 : DCHECK(IsClamped());
323 3384925 : int product_length = 2 * used_digits_;
324 : EnsureCapacity(product_length);
325 :
326 : // Comba multiplication: compute each column separately.
327 : // Example: r = a2a1a0 * b2b1b0.
328 : // r = 1 * a0b0 +
329 : // 10 * (a1b0 + a0b1) +
330 : // 100 * (a2b0 + a1b1 + a0b2) +
331 : // 1000 * (a2b1 + a1b2) +
332 : // 10000 * a2b2
333 : //
334 : // In the worst case we have to accumulate nb-digits products of digit*digit.
335 : //
336 : // Assert that the additional number of bits in a DoubleChunk are enough to
337 : // sum up used_digits of Bigit*Bigit.
338 3384925 : if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
339 0 : UNIMPLEMENTED();
340 : }
341 : DoubleChunk accumulator = 0;
342 : // First shift the digits so we don't overwrite them.
343 : int copy_offset = used_digits_;
344 15933615 : for (int i = 0; i < used_digits_; ++i) {
345 169810627 : bigits_[copy_offset + i] = bigits_[i];
346 : }
347 : // We have two loops to avoid some 'if's in the loop.
348 15933615 : for (int i = 0; i < used_digits_; ++i) {
349 : // Process temporary digit i with power i.
350 : // The sum of the two indices must be equal to i.
351 : int bigit_index1 = i;
352 : int bigit_index2 = 0;
353 : // Sum all of the sub-products.
354 76938506 : while (bigit_index1 >= 0) {
355 122009782 : Chunk chunk1 = bigits_[copy_offset + bigit_index1];
356 122009782 : Chunk chunk2 = bigits_[copy_offset + bigit_index2];
357 61004891 : accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
358 61004891 : bigit_index1--;
359 61004891 : bigit_index2++;
360 : }
361 15933615 : bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
362 15933615 : accumulator >>= kBigitSize;
363 : }
364 15933615 : for (int i = used_digits_; i < product_length; ++i) {
365 15933615 : int bigit_index1 = used_digits_ - 1;
366 15933615 : int bigit_index2 = i - bigit_index1;
367 : // Invariant: sum of both indices is again equal to i.
368 : // Inner loop runs 0 times on last iteration, emptying accumulator.
369 76938506 : while (bigit_index2 < used_digits_) {
370 90142552 : Chunk chunk1 = bigits_[copy_offset + bigit_index1];
371 90142552 : Chunk chunk2 = bigits_[copy_offset + bigit_index2];
372 45071276 : accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
373 45071276 : bigit_index1--;
374 45071276 : bigit_index2++;
375 : }
376 : // The overwritten bigits_[i] will never be read in further loop iterations,
377 : // because bigit_index1 and bigit_index2 are always greater
378 : // than i - used_digits_.
379 15933615 : bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
380 15933615 : accumulator >>= kBigitSize;
381 : }
382 : // Since the result was guaranteed to lie inside the number the
383 : // accumulator must be 0 now.
384 : DCHECK(accumulator == 0);
385 :
386 : // Don't forget to update the used_digits and the exponent.
387 3384925 : used_digits_ = product_length;
388 3384925 : exponent_ *= 2;
389 3384925 : Clamp();
390 3384925 : }
391 :
392 :
393 1715706 : void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
394 : DCHECK(base != 0);
395 : DCHECK(power_exponent >= 0);
396 1715706 : if (power_exponent == 0) {
397 : AssignUInt16(1);
398 1715706 : return;
399 : }
400 : Zero();
401 : int shifts = 0;
402 : // We expect base to be in range 2-32, and most often to be 10.
403 : // It does not make much sense to implement different algorithms for counting
404 : // the bits.
405 5090534 : while ((base & 1) == 0) {
406 1696910 : base >>= 1;
407 1696910 : shifts++;
408 : }
409 : int bit_size = 0;
410 1696812 : int tmp_base = base;
411 8484011 : while (tmp_base != 0) {
412 5090387 : tmp_base >>= 1;
413 5090387 : bit_size++;
414 : }
415 1696812 : int final_size = bit_size * power_exponent;
416 : // 1 extra bigit for the shifting, and one for rounded final_size.
417 : EnsureCapacity(final_size / kBigitSize + 2);
418 :
419 : // Left to Right exponentiation.
420 : int mask = 1;
421 10919316 : while (power_exponent >= mask) mask <<= 1;
422 :
423 : // The mask is now pointing to the bit above the most significant 1-bit of
424 : // power_exponent.
425 : // Get rid of first 1-bit;
426 1696812 : mask >>= 2;
427 1696812 : uint64_t this_value = base;
428 :
429 : bool delayed_multipliciation = false;
430 : const uint64_t max_32bits = 0xFFFFFFFF;
431 9231238 : while (mask != 0 && this_value <= max_32bits) {
432 5837614 : this_value = this_value * this_value;
433 : // Verify that there is enough space in this_value to perform the
434 : // multiplication. The first bit_size bits must be 0.
435 5837614 : if ((power_exponent & mask) != 0) {
436 : uint64_t base_bits_mask =
437 2557102 : ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
438 2557102 : bool high_bits_zero = (this_value & base_bits_mask) == 0;
439 2557102 : if (high_bits_zero) {
440 2557102 : this_value *= base;
441 : } else {
442 : delayed_multipliciation = true;
443 : }
444 : }
445 5837614 : mask >>= 1;
446 : }
447 1696812 : AssignUInt64(this_value);
448 1696812 : if (delayed_multipliciation) {
449 0 : MultiplyByUInt32(base);
450 : }
451 :
452 : // Now do the same thing as a bignum.
453 5081702 : while (mask != 0) {
454 3384890 : Square();
455 3384890 : if ((power_exponent & mask) != 0) {
456 1672520 : MultiplyByUInt32(base);
457 : }
458 3384890 : mask >>= 1;
459 : }
460 :
461 : // And finally add the saved shifts.
462 1696812 : ShiftLeft(shifts * power_exponent);
463 : }
464 :
465 :
466 : // Precondition: this/other < 16bit.
467 112961220 : uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
468 : DCHECK(IsClamped());
469 : DCHECK(other.IsClamped());
470 : DCHECK(other.used_digits_ > 0);
471 :
472 : // Easy case: if we have less digits than the divisor than the result is 0.
473 : // Note: this handles the case where this == 0, too.
474 24868793 : if (BigitLength() < other.BigitLength()) {
475 : return 0;
476 : }
477 :
478 23734227 : Align(other);
479 :
480 : uint16_t result = 0;
481 :
482 : // Start by removing multiples of 'other' until both numbers have the same
483 : // number of digits.
484 55346044 : while (BigitLength() > other.BigitLength()) {
485 : // This naive approach is extremely inefficient if the this divided other
486 : // might be big. This function is implemented for doubleToString where
487 : // the result should be small (less than 10).
488 : DCHECK(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
489 : // Remove the multiples of the first digit.
490 : // Example this = 23 and other equals 9. -> Remove 2 multiples.
491 39489407 : result += bigits_[used_digits_ - 1];
492 7877590 : SubtractTimes(other, bigits_[used_digits_ - 1]);
493 : }
494 :
495 : DCHECK(BigitLength() == other.BigitLength());
496 :
497 : // Both bignums are at the same length now.
498 : // Since other has more than 0 digits we know that the access to
499 : // bigits_[used_digits_ - 1] is safe.
500 47468454 : Chunk this_bigit = bigits_[used_digits_ - 1];
501 47468454 : Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
502 :
503 23734227 : if (other.used_digits_ == 1) {
504 : // Shortcut for easy (and common) case.
505 11477972 : int quotient = this_bigit / other_bigit;
506 11477972 : bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
507 11477972 : result += quotient;
508 11477972 : Clamp();
509 11477972 : return result;
510 : }
511 :
512 12256255 : int division_estimate = this_bigit / (other_bigit + 1);
513 12256255 : result += division_estimate;
514 12256255 : SubtractTimes(other, division_estimate);
515 :
516 12256255 : if (other_bigit * (division_estimate + 1) > this_bigit) {
517 : // No need to even try to subtract. Even if other's remaining digits were 0
518 : // another subtraction would be too much.
519 : return result;
520 : }
521 :
522 3322424 : while (LessEqual(other, *this)) {
523 1735224 : SubtractBignum(other);
524 1735224 : result++;
525 : }
526 : return result;
527 : }
528 :
529 :
530 : template<typename S>
531 : static int SizeInHexChars(S number) {
532 : DCHECK(number > 0);
533 : int result = 0;
534 5341 : while (number != 0) {
535 4074 : number >>= 4;
536 4074 : result++;
537 : }
538 : return result;
539 : }
540 :
541 :
542 2590 : bool Bignum::ToHexString(char* buffer, int buffer_size) const {
543 : DCHECK(IsClamped());
544 : // Each bigit must be printable as separate hex-character.
545 : DCHECK(kBigitSize % 4 == 0);
546 : const int kHexCharsPerBigit = kBigitSize / 4;
547 :
548 1323 : if (used_digits_ == 0) {
549 56 : if (buffer_size < 2) return false;
550 56 : buffer[0] = '0';
551 56 : buffer[1] = '\0';
552 56 : return true;
553 : }
554 : // We add 1 for the terminating '\0' character.
555 2534 : int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
556 12670 : SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
557 1267 : if (needed_chars > buffer_size) return false;
558 : int string_index = needed_chars - 1;
559 1267 : buffer[string_index--] = '\0';
560 2303 : for (int i = 0; i < exponent_; ++i) {
561 7252 : for (int j = 0; j < kHexCharsPerBigit; ++j) {
562 7252 : buffer[string_index--] = '0';
563 : }
564 : }
565 7602 : for (int i = 0; i < used_digits_ - 1; ++i) {
566 7602 : Chunk current_bigit = bigits_[i];
567 60816 : for (int j = 0; j < kHexCharsPerBigit; ++j) {
568 106428 : buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
569 53214 : current_bigit >>= 4;
570 : }
571 : }
572 : // And finally the last bigit.
573 1267 : Chunk most_significant_bigit = bigits_[used_digits_ - 1];
574 6608 : while (most_significant_bigit != 0) {
575 8148 : buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
576 4074 : most_significant_bigit >>= 4;
577 : }
578 : return true;
579 : }
580 :
581 :
582 0 : Bignum::Chunk Bignum::BigitAt(int index) const {
583 70831957 : if (index >= BigitLength()) return 0;
584 60622320 : if (index < exponent_) return 0;
585 120736568 : return bigits_[index - exponent_];
586 : }
587 :
588 :
589 30724218 : int Bignum::Compare(const Bignum& a, const Bignum& b) {
590 : DCHECK(a.IsClamped());
591 : DCHECK(b.IsClamped());
592 : int bigit_length_a = a.BigitLength();
593 : int bigit_length_b = b.BigitLength();
594 15362109 : if (bigit_length_a < bigit_length_b) return -1;
595 15324385 : if (bigit_length_a > bigit_length_b) return +1;
596 33637604 : for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
597 : Chunk bigit_a = a.BigitAt(i);
598 : Chunk bigit_b = b.BigitAt(i);
599 14663018 : if (bigit_a < bigit_b) return -1;
600 12627816 : if (bigit_a > bigit_b) return +1;
601 : // Otherwise they are equal up to this digit. Try the next digit.
602 : }
603 : return 0;
604 : }
605 :
606 :
607 39283725 : int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
608 : DCHECK(a.IsClamped());
609 : DCHECK(b.IsClamped());
610 : DCHECK(c.IsClamped());
611 13119685 : if (a.BigitLength() < b.BigitLength()) {
612 : return PlusCompare(b, a, c);
613 : }
614 26164040 : if (a.BigitLength() + 1 < c.BigitLength()) return -1;
615 12965433 : if (a.BigitLength() > c.BigitLength()) return +1;
616 : // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
617 : // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
618 : // of 'a'.
619 12955871 : if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
620 : return -1;
621 : }
622 :
623 : Chunk borrow = 0;
624 : // Starting at min_exponent all digits are == 0. So no need to compare them.
625 : int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
626 13841144 : for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
627 : Chunk chunk_a = a.BigitAt(i);
628 : Chunk chunk_b = b.BigitAt(i);
629 : Chunk chunk_c = c.BigitAt(i);
630 13835307 : Chunk sum = chunk_a + chunk_b;
631 13835307 : if (sum > chunk_c + borrow) {
632 : return +1;
633 : } else {
634 12492885 : borrow = chunk_c + borrow - sum;
635 12492885 : if (borrow > 1) return -1;
636 935995 : borrow <<= kBigitSize;
637 : }
638 : }
639 5837 : if (borrow == 0) return 0;
640 21 : return -1;
641 : }
642 :
643 :
644 40990471 : void Bignum::Clamp() {
645 141369103 : while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
646 9257772 : used_digits_--;
647 : }
648 40990471 : if (used_digits_ == 0) {
649 : // Zero.
650 117854 : exponent_ = 0;
651 : }
652 40990471 : }
653 :
654 :
655 0 : bool Bignum::IsClamped() const {
656 0 : return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
657 : }
658 :
659 :
660 0 : void Bignum::Zero() {
661 5446 : for (int i = 0; i < used_digits_; ++i) {
662 10892 : bigits_[i] = 0;
663 : }
664 5885205 : used_digits_ = 0;
665 5885205 : exponent_ = 0;
666 0 : }
667 :
668 :
669 39057018 : void Bignum::Align(const Bignum& other) {
670 39057018 : if (exponent_ > other.exponent_) {
671 : // If "X" represents a "hidden" digit (by the exponent) then we are in the
672 : // following case (a == this, b == other):
673 : // a: aaaaaaXXXX or a: aaaaaXXX
674 : // b: bbbbbbX b: bbbbbbbbXX
675 : // We replace some of the hidden digits (X) of a with 0 digits.
676 : // a: aaaaaa000X or a: aaaaa0XX
677 580052 : int zero_digits = exponent_ - other.exponent_;
678 580052 : EnsureCapacity(used_digits_ + zero_digits);
679 2302605 : for (int i = used_digits_ - 1; i >= 0; --i) {
680 10454565 : bigits_[i + zero_digits] = bigits_[i];
681 : }
682 7009459 : for (int i = 0; i < zero_digits; ++i) {
683 7009459 : bigits_[i] = 0;
684 : }
685 580052 : used_digits_ += zero_digits;
686 580052 : exponent_ -= zero_digits;
687 : DCHECK(used_digits_ >= 0);
688 : DCHECK(exponent_ >= 0);
689 : }
690 39057018 : }
691 :
692 :
693 5347289 : void Bignum::BigitsShiftLeft(int shift_amount) {
694 : DCHECK(shift_amount < kBigitSize);
695 : DCHECK(shift_amount >= 0);
696 : Chunk carry = 0;
697 40923737 : for (int i = 0; i < used_digits_; ++i) {
698 72642604 : Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
699 35576448 : bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
700 : carry = new_carry;
701 : }
702 5347289 : if (carry != 0) {
703 1489708 : bigits_[used_digits_] = carry;
704 1489708 : used_digits_++;
705 : }
706 5347289 : }
707 :
708 :
709 20133845 : void Bignum::SubtractTimes(const Bignum& other, int factor) {
710 : #ifdef DEBUG
711 : Bignum a, b;
712 : a.AssignBignum(*this);
713 : b.AssignBignum(other);
714 : b.MultiplyByUInt32(factor);
715 : a.SubtractBignum(b);
716 : #endif
717 : DCHECK(exponent_ <= other.exponent_);
718 20133845 : if (factor < 3) {
719 13463773 : for (int i = 0; i < factor; ++i) {
720 13463773 : SubtractBignum(other);
721 : }
722 : return;
723 : }
724 : Chunk borrow = 0;
725 8155974 : int exponent_diff = other.exponent_ - exponent_;
726 95266988 : for (int i = 0; i < other.used_digits_; ++i) {
727 174222028 : DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
728 87111014 : DoubleChunk remove = borrow + product;
729 : Chunk difference =
730 174999642 : bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask);
731 87111014 : bigits_[i + exponent_diff] = difference & kBigitMask;
732 87111014 : borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
733 87111014 : (remove >> kBigitSize));
734 : }
735 8933588 : for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
736 777614 : if (borrow == 0) return;
737 777614 : Chunk difference = bigits_[i] - borrow;
738 777614 : bigits_[i] = difference & kBigitMask;
739 777614 : borrow = difference >> (kChunkSize - 1);
740 : }
741 8155974 : Clamp();
742 : DCHECK(Bignum::Equal(a, *this));
743 : }
744 :
745 :
746 : } // namespace internal
747 : } // namespace v8
|
