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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,
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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 0 : Bignum::Bignum()
34 0 : : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
35 0 : for (int i = 0; i < kBigitCapacity; ++i) {
36 0 : bigits_[i] = 0;
37 : }
38 0 : }
39 :
40 :
41 : template<typename S>
42 0 : static int BitSize(S value) {
43 : (void) value; // Mark variable as used.
44 0 : return 8 * sizeof(value);
45 : }
46 :
47 : // Guaranteed to lie in one Bigit.
48 0 : void Bignum::AssignUInt16(uint16_t value) {
49 0 : ASSERT(kBigitSize >= BitSize(value));
50 0 : Zero();
51 0 : if (value == 0) return;
52 :
53 0 : EnsureCapacity(1);
54 0 : bigits_[0] = value;
55 0 : used_digits_ = 1;
56 : }
57 :
58 :
59 0 : void Bignum::AssignUInt64(uint64_t value) {
60 0 : const int kUInt64Size = 64;
61 :
62 0 : Zero();
63 0 : if (value == 0) return;
64 :
65 0 : int needed_bigits = kUInt64Size / kBigitSize + 1;
66 0 : EnsureCapacity(needed_bigits);
67 0 : for (int i = 0; i < needed_bigits; ++i) {
68 0 : bigits_[i] = value & kBigitMask;
69 0 : value = value >> kBigitSize;
70 : }
71 0 : used_digits_ = needed_bigits;
72 0 : Clamp();
73 : }
74 :
75 :
76 0 : void Bignum::AssignBignum(const Bignum& other) {
77 0 : exponent_ = other.exponent_;
78 0 : for (int i = 0; i < other.used_digits_; ++i) {
79 0 : bigits_[i] = other.bigits_[i];
80 : }
81 : // Clear the excess digits (if there were any).
82 0 : for (int i = other.used_digits_; i < used_digits_; ++i) {
83 0 : bigits_[i] = 0;
84 : }
85 0 : used_digits_ = other.used_digits_;
86 0 : }
87 :
88 :
89 0 : static uint64_t ReadUInt64(Vector<const char> buffer,
90 : int from,
91 : int digits_to_read) {
92 0 : uint64_t result = 0;
93 0 : for (int i = from; i < from + digits_to_read; ++i) {
94 0 : int digit = buffer[i] - '0';
95 0 : ASSERT(0 <= digit && digit <= 9);
96 0 : result = result * 10 + digit;
97 : }
98 0 : return result;
99 : }
100 :
101 :
102 0 : void Bignum::AssignDecimalString(Vector<const char> value) {
103 : // 2^64 = 18446744073709551616 > 10^19
104 0 : const int kMaxUint64DecimalDigits = 19;
105 0 : Zero();
106 0 : int length = value.length();
107 0 : unsigned int pos = 0;
108 : // Let's just say that each digit needs 4 bits.
109 0 : while (length >= kMaxUint64DecimalDigits) {
110 0 : uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
111 0 : pos += kMaxUint64DecimalDigits;
112 0 : length -= kMaxUint64DecimalDigits;
113 0 : MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
114 0 : AddUInt64(digits);
115 : }
116 0 : uint64_t digits = ReadUInt64(value, pos, length);
117 0 : MultiplyByPowerOfTen(length);
118 0 : AddUInt64(digits);
119 0 : Clamp();
120 0 : }
121 :
122 :
123 0 : static int HexCharValue(char c) {
124 0 : if ('0' <= c && c <= '9') return c - '0';
125 0 : if ('a' <= c && c <= 'f') return 10 + c - 'a';
126 0 : ASSERT('A' <= c && c <= 'F');
127 0 : return 10 + c - 'A';
128 : }
129 :
130 :
131 0 : void Bignum::AssignHexString(Vector<const char> value) {
132 0 : Zero();
133 0 : int length = value.length();
134 :
135 0 : int needed_bigits = length * 4 / kBigitSize + 1;
136 0 : EnsureCapacity(needed_bigits);
137 0 : int string_index = length - 1;
138 0 : for (int i = 0; i < needed_bigits - 1; ++i) {
139 : // These bigits are guaranteed to be "full".
140 0 : Chunk current_bigit = 0;
141 0 : for (int j = 0; j < kBigitSize / 4; j++) {
142 0 : current_bigit += HexCharValue(value[string_index--]) << (j * 4);
143 : }
144 0 : bigits_[i] = current_bigit;
145 : }
146 0 : used_digits_ = needed_bigits - 1;
147 :
148 0 : Chunk most_significant_bigit = 0; // Could be = 0;
149 0 : for (int j = 0; j <= string_index; ++j) {
150 0 : most_significant_bigit <<= 4;
151 0 : most_significant_bigit += HexCharValue(value[j]);
152 : }
153 0 : if (most_significant_bigit != 0) {
154 0 : bigits_[used_digits_] = most_significant_bigit;
155 0 : used_digits_++;
156 : }
157 0 : Clamp();
158 0 : }
159 :
160 :
161 0 : void Bignum::AddUInt64(uint64_t operand) {
162 0 : if (operand == 0) return;
163 0 : Bignum other;
164 0 : other.AssignUInt64(operand);
165 0 : AddBignum(other);
166 : }
167 :
168 :
169 0 : void Bignum::AddBignum(const Bignum& other) {
170 0 : ASSERT(IsClamped());
171 0 : 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 0 : 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 0 : EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
190 0 : Chunk carry = 0;
191 0 : int bigit_pos = other.exponent_ - exponent_;
192 0 : ASSERT(bigit_pos >= 0);
193 0 : for (int i = 0; i < other.used_digits_; ++i) {
194 0 : Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
195 0 : bigits_[bigit_pos] = sum & kBigitMask;
196 0 : carry = sum >> kBigitSize;
197 0 : bigit_pos++;
198 : }
199 :
200 0 : while (carry != 0) {
201 0 : Chunk sum = bigits_[bigit_pos] + carry;
202 0 : bigits_[bigit_pos] = sum & kBigitMask;
203 0 : carry = sum >> kBigitSize;
204 0 : bigit_pos++;
205 : }
206 0 : used_digits_ = Max(bigit_pos, used_digits_);
207 0 : ASSERT(IsClamped());
208 0 : }
209 :
210 :
211 0 : void Bignum::SubtractBignum(const Bignum& other) {
212 0 : ASSERT(IsClamped());
213 0 : ASSERT(other.IsClamped());
214 : // We require this to be bigger than other.
215 0 : ASSERT(LessEqual(other, *this));
216 :
217 0 : Align(other);
218 :
219 0 : int offset = other.exponent_ - exponent_;
220 0 : Chunk borrow = 0;
221 : int i;
222 0 : for (i = 0; i < other.used_digits_; ++i) {
223 0 : ASSERT((borrow == 0) || (borrow == 1));
224 0 : Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
225 0 : bigits_[i + offset] = difference & kBigitMask;
226 0 : borrow = difference >> (kChunkSize - 1);
227 : }
228 0 : while (borrow != 0) {
229 0 : Chunk difference = bigits_[i + offset] - borrow;
230 0 : bigits_[i + offset] = difference & kBigitMask;
231 0 : borrow = difference >> (kChunkSize - 1);
232 0 : ++i;
233 : }
234 0 : Clamp();
235 0 : }
236 :
237 :
238 0 : void Bignum::ShiftLeft(int shift_amount) {
239 0 : if (used_digits_ == 0) return;
240 0 : exponent_ += shift_amount / kBigitSize;
241 0 : int local_shift = shift_amount % kBigitSize;
242 0 : EnsureCapacity(used_digits_ + 1);
243 0 : BigitsShiftLeft(local_shift);
244 : }
245 :
246 :
247 0 : void Bignum::MultiplyByUInt32(uint32_t factor) {
248 0 : if (factor == 1) return;
249 0 : if (factor == 0) {
250 0 : Zero();
251 0 : return;
252 : }
253 0 : 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 0 : DoubleChunk carry = 0;
259 0 : for (int i = 0; i < used_digits_; ++i) {
260 0 : DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
261 0 : bigits_[i] = static_cast<Chunk>(product & kBigitMask);
262 0 : carry = (product >> kBigitSize);
263 : }
264 0 : while (carry != 0) {
265 0 : EnsureCapacity(used_digits_ + 1);
266 0 : bigits_[used_digits_] = carry & kBigitMask;
267 0 : used_digits_++;
268 0 : carry >>= kBigitSize;
269 : }
270 : }
271 :
272 :
273 0 : void Bignum::MultiplyByUInt64(uint64_t factor) {
274 0 : if (factor == 1) return;
275 0 : if (factor == 0) {
276 0 : Zero();
277 0 : return;
278 : }
279 : ASSERT(kBigitSize < 32);
280 0 : uint64_t carry = 0;
281 0 : uint64_t low = factor & 0xFFFFFFFF;
282 0 : uint64_t high = factor >> 32;
283 0 : for (int i = 0; i < used_digits_; ++i) {
284 0 : uint64_t product_low = low * bigits_[i];
285 0 : uint64_t product_high = high * bigits_[i];
286 0 : uint64_t tmp = (carry & kBigitMask) + product_low;
287 0 : bigits_[i] = tmp & kBigitMask;
288 0 : carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
289 0 : (product_high << (32 - kBigitSize));
290 : }
291 0 : while (carry != 0) {
292 0 : EnsureCapacity(used_digits_ + 1);
293 0 : bigits_[used_digits_] = carry & kBigitMask;
294 0 : used_digits_++;
295 0 : carry >>= kBigitSize;
296 : }
297 : }
298 :
299 :
300 0 : void Bignum::MultiplyByPowerOfTen(int exponent) {
301 0 : const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
302 0 : const uint16_t kFive1 = 5;
303 0 : const uint16_t kFive2 = kFive1 * 5;
304 0 : const uint16_t kFive3 = kFive2 * 5;
305 0 : const uint16_t kFive4 = kFive3 * 5;
306 0 : const uint16_t kFive5 = kFive4 * 5;
307 0 : const uint16_t kFive6 = kFive5 * 5;
308 0 : const uint32_t kFive7 = kFive6 * 5;
309 0 : const uint32_t kFive8 = kFive7 * 5;
310 0 : const uint32_t kFive9 = kFive8 * 5;
311 0 : const uint32_t kFive10 = kFive9 * 5;
312 0 : const uint32_t kFive11 = kFive10 * 5;
313 0 : const uint32_t kFive12 = kFive11 * 5;
314 0 : const uint32_t kFive13 = kFive12 * 5;
315 : const uint32_t kFive1_to_12[] =
316 : { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
317 0 : kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
318 :
319 0 : ASSERT(exponent >= 0);
320 0 : if (exponent == 0) return;
321 0 : if (used_digits_ == 0) return;
322 :
323 : // We shift by exponent at the end just before returning.
324 0 : int remaining_exponent = exponent;
325 0 : while (remaining_exponent >= 27) {
326 0 : MultiplyByUInt64(kFive27);
327 0 : remaining_exponent -= 27;
328 : }
329 0 : while (remaining_exponent >= 13) {
330 0 : MultiplyByUInt32(kFive13);
331 0 : remaining_exponent -= 13;
332 : }
333 0 : if (remaining_exponent > 0) {
334 0 : MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
335 : }
336 0 : ShiftLeft(exponent);
337 : }
338 :
339 :
340 0 : void Bignum::Square() {
341 0 : ASSERT(IsClamped());
342 0 : int product_length = 2 * used_digits_;
343 0 : 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 0 : if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
358 0 : UNIMPLEMENTED();
359 : }
360 0 : DoubleChunk accumulator = 0;
361 : // First shift the digits so we don't overwrite them.
362 0 : int copy_offset = used_digits_;
363 0 : for (int i = 0; i < used_digits_; ++i) {
364 0 : bigits_[copy_offset + i] = bigits_[i];
365 : }
366 : // We have two loops to avoid some 'if's in the loop.
367 0 : 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 0 : int bigit_index1 = i;
371 0 : int bigit_index2 = 0;
372 : // Sum all of the sub-products.
373 0 : while (bigit_index1 >= 0) {
374 0 : Chunk chunk1 = bigits_[copy_offset + bigit_index1];
375 0 : Chunk chunk2 = bigits_[copy_offset + bigit_index2];
376 0 : accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
377 0 : bigit_index1--;
378 0 : bigit_index2++;
379 : }
380 0 : bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
381 0 : accumulator >>= kBigitSize;
382 : }
383 0 : for (int i = used_digits_; i < product_length; ++i) {
384 0 : int bigit_index1 = used_digits_ - 1;
385 0 : 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 0 : while (bigit_index2 < used_digits_) {
389 0 : Chunk chunk1 = bigits_[copy_offset + bigit_index1];
390 0 : Chunk chunk2 = bigits_[copy_offset + bigit_index2];
391 0 : accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
392 0 : bigit_index1--;
393 0 : 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 0 : bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
399 0 : accumulator >>= kBigitSize;
400 : }
401 : // Since the result was guaranteed to lie inside the number the
402 : // accumulator must be 0 now.
403 0 : ASSERT(accumulator == 0);
404 :
405 : // Don't forget to update the used_digits and the exponent.
406 0 : used_digits_ = product_length;
407 0 : exponent_ *= 2;
408 0 : Clamp();
409 0 : }
410 :
411 :
412 0 : void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
413 0 : ASSERT(base != 0);
414 0 : ASSERT(power_exponent >= 0);
415 0 : if (power_exponent == 0) {
416 0 : AssignUInt16(1);
417 0 : return;
418 : }
419 0 : Zero();
420 0 : 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 0 : while ((base & 1) == 0) {
425 0 : base >>= 1;
426 0 : shifts++;
427 : }
428 0 : int bit_size = 0;
429 0 : int tmp_base = base;
430 0 : while (tmp_base != 0) {
431 0 : tmp_base >>= 1;
432 0 : bit_size++;
433 : }
434 0 : int final_size = bit_size * power_exponent;
435 : // 1 extra bigit for the shifting, and one for rounded final_size.
436 0 : EnsureCapacity(final_size / kBigitSize + 2);
437 :
438 : // Left to Right exponentiation.
439 0 : int mask = 1;
440 0 : 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 0 : mask >>= 2;
446 0 : uint64_t this_value = base;
447 :
448 0 : bool delayed_multipliciation = false;
449 0 : const uint64_t max_32bits = 0xFFFFFFFF;
450 0 : while (mask != 0 && this_value <= max_32bits) {
451 0 : 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 0 : if ((power_exponent & mask) != 0) {
455 : uint64_t base_bits_mask =
456 0 : ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
457 0 : bool high_bits_zero = (this_value & base_bits_mask) == 0;
458 0 : if (high_bits_zero) {
459 0 : this_value *= base;
460 : } else {
461 0 : delayed_multipliciation = true;
462 : }
463 : }
464 0 : mask >>= 1;
465 : }
466 0 : AssignUInt64(this_value);
467 0 : if (delayed_multipliciation) {
468 0 : MultiplyByUInt32(base);
469 : }
470 :
471 : // Now do the same thing as a bignum.
472 0 : while (mask != 0) {
473 0 : Square();
474 0 : if ((power_exponent & mask) != 0) {
475 0 : MultiplyByUInt32(base);
476 : }
477 0 : mask >>= 1;
478 : }
479 :
480 : // And finally add the saved shifts.
481 0 : ShiftLeft(shifts * power_exponent);
482 : }
483 :
484 :
485 : // Precondition: this/other < 16bit.
486 0 : uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
487 0 : ASSERT(IsClamped());
488 0 : ASSERT(other.IsClamped());
489 0 : 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 0 : if (BigitLength() < other.BigitLength()) {
494 0 : return 0;
495 : }
496 :
497 0 : Align(other);
498 :
499 0 : uint16_t result = 0;
500 :
501 : // Start by removing multiples of 'other' until both numbers have the same
502 : // number of digits.
503 0 : 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 0 : ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
508 0 : ASSERT(bigits_[used_digits_ - 1] < 0x10000);
509 : // Remove the multiples of the first digit.
510 : // Example this = 23 and other equals 9. -> Remove 2 multiples.
511 0 : result += static_cast<uint16_t>(bigits_[used_digits_ - 1]);
512 0 : SubtractTimes(other, bigits_[used_digits_ - 1]);
513 : }
514 :
515 0 : ASSERT(BigitLength() == other.BigitLength());
516 :
517 : // Both bignums are at the same length now.
518 : // Since other has more than 0 digits we know that the access to
519 : // bigits_[used_digits_ - 1] is safe.
520 0 : Chunk this_bigit = bigits_[used_digits_ - 1];
521 0 : Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
522 :
523 0 : if (other.used_digits_ == 1) {
524 : // Shortcut for easy (and common) case.
525 0 : int quotient = this_bigit / other_bigit;
526 0 : bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
527 0 : ASSERT(quotient < 0x10000);
528 0 : result += static_cast<uint16_t>(quotient);
529 0 : Clamp();
530 0 : return result;
531 : }
532 :
533 0 : int division_estimate = this_bigit / (other_bigit + 1);
534 0 : ASSERT(division_estimate < 0x10000);
535 0 : result += static_cast<uint16_t>(division_estimate);
536 0 : SubtractTimes(other, division_estimate);
537 :
538 0 : 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 0 : return result;
542 : }
543 :
544 0 : while (LessEqual(other, *this)) {
545 0 : SubtractBignum(other);
546 0 : result++;
547 : }
548 0 : return result;
549 : }
550 :
551 :
552 : template<typename S>
553 0 : static int SizeInHexChars(S number) {
554 0 : ASSERT(number > 0);
555 0 : int result = 0;
556 0 : while (number != 0) {
557 0 : number >>= 4;
558 0 : result++;
559 : }
560 0 : return result;
561 : }
562 :
563 :
564 0 : static char HexCharOfValue(int value) {
565 0 : ASSERT(0 <= value && value <= 16);
566 0 : if (value < 10) return static_cast<char>(value + '0');
567 0 : return static_cast<char>(value - 10 + 'A');
568 : }
569 :
570 :
571 0 : bool Bignum::ToHexString(char* buffer, int buffer_size) const {
572 0 : ASSERT(IsClamped());
573 : // Each bigit must be printable as separate hex-character.
574 : ASSERT(kBigitSize % 4 == 0);
575 0 : const int kHexCharsPerBigit = kBigitSize / 4;
576 :
577 0 : if (used_digits_ == 0) {
578 0 : if (buffer_size < 2) return false;
579 0 : buffer[0] = '0';
580 0 : buffer[1] = '\0';
581 0 : return true;
582 : }
583 : // We add 1 for the terminating '\0' character.
584 0 : int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
585 0 : SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
586 0 : if (needed_chars > buffer_size) return false;
587 0 : int string_index = needed_chars - 1;
588 0 : buffer[string_index--] = '\0';
589 0 : for (int i = 0; i < exponent_; ++i) {
590 0 : for (int j = 0; j < kHexCharsPerBigit; ++j) {
591 0 : buffer[string_index--] = '0';
592 : }
593 : }
594 0 : for (int i = 0; i < used_digits_ - 1; ++i) {
595 0 : Chunk current_bigit = bigits_[i];
596 0 : for (int j = 0; j < kHexCharsPerBigit; ++j) {
597 0 : buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
598 0 : current_bigit >>= 4;
599 : }
600 : }
601 : // And finally the last bigit.
602 0 : Chunk most_significant_bigit = bigits_[used_digits_ - 1];
603 0 : while (most_significant_bigit != 0) {
604 0 : buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
605 0 : most_significant_bigit >>= 4;
606 : }
607 0 : return true;
608 : }
609 :
610 :
611 0 : Bignum::Chunk Bignum::BigitAt(int index) const {
612 0 : if (index >= BigitLength()) return 0;
613 0 : if (index < exponent_) return 0;
614 0 : return bigits_[index - exponent_];
615 : }
616 :
617 :
618 0 : int Bignum::Compare(const Bignum& a, const Bignum& b) {
619 0 : ASSERT(a.IsClamped());
620 0 : ASSERT(b.IsClamped());
621 0 : int bigit_length_a = a.BigitLength();
622 0 : int bigit_length_b = b.BigitLength();
623 0 : if (bigit_length_a < bigit_length_b) return -1;
624 0 : if (bigit_length_a > bigit_length_b) return +1;
625 0 : for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
626 0 : Chunk bigit_a = a.BigitAt(i);
627 0 : Chunk bigit_b = b.BigitAt(i);
628 0 : if (bigit_a < bigit_b) return -1;
629 0 : if (bigit_a > bigit_b) return +1;
630 : // Otherwise they are equal up to this digit. Try the next digit.
631 : }
632 0 : return 0;
633 : }
634 :
635 :
636 0 : int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
637 0 : ASSERT(a.IsClamped());
638 0 : ASSERT(b.IsClamped());
639 0 : ASSERT(c.IsClamped());
640 0 : if (a.BigitLength() < b.BigitLength()) {
641 0 : return PlusCompare(b, a, c);
642 : }
643 0 : if (a.BigitLength() + 1 < c.BigitLength()) return -1;
644 0 : if (a.BigitLength() > c.BigitLength()) return +1;
645 : // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
646 : // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
647 : // of 'a'.
648 0 : if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
649 0 : return -1;
650 : }
651 :
652 0 : Chunk borrow = 0;
653 : // Starting at min_exponent all digits are == 0. So no need to compare them.
654 0 : int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
655 0 : for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
656 0 : Chunk chunk_a = a.BigitAt(i);
657 0 : Chunk chunk_b = b.BigitAt(i);
658 0 : Chunk chunk_c = c.BigitAt(i);
659 0 : Chunk sum = chunk_a + chunk_b;
660 0 : if (sum > chunk_c + borrow) {
661 0 : return +1;
662 : } else {
663 0 : borrow = chunk_c + borrow - sum;
664 0 : if (borrow > 1) return -1;
665 0 : borrow <<= kBigitSize;
666 : }
667 : }
668 0 : if (borrow == 0) return 0;
669 0 : return -1;
670 : }
671 :
672 :
673 0 : void Bignum::Clamp() {
674 0 : while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
675 0 : used_digits_--;
676 : }
677 0 : if (used_digits_ == 0) {
678 : // Zero.
679 0 : exponent_ = 0;
680 : }
681 0 : }
682 :
683 :
684 0 : bool Bignum::IsClamped() const {
685 0 : return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
686 : }
687 :
688 :
689 0 : void Bignum::Zero() {
690 0 : for (int i = 0; i < used_digits_; ++i) {
691 0 : bigits_[i] = 0;
692 : }
693 0 : used_digits_ = 0;
694 0 : exponent_ = 0;
695 0 : }
696 :
697 :
698 0 : void Bignum::Align(const Bignum& other) {
699 0 : 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 0 : int zero_digits = exponent_ - other.exponent_;
707 0 : EnsureCapacity(used_digits_ + zero_digits);
708 0 : for (int i = used_digits_ - 1; i >= 0; --i) {
709 0 : bigits_[i + zero_digits] = bigits_[i];
710 : }
711 0 : for (int i = 0; i < zero_digits; ++i) {
712 0 : bigits_[i] = 0;
713 : }
714 0 : used_digits_ += zero_digits;
715 0 : exponent_ -= zero_digits;
716 0 : ASSERT(used_digits_ >= 0);
717 0 : ASSERT(exponent_ >= 0);
718 : }
719 0 : }
720 :
721 :
722 0 : void Bignum::BigitsShiftLeft(int shift_amount) {
723 0 : ASSERT(shift_amount < kBigitSize);
724 0 : ASSERT(shift_amount >= 0);
725 0 : Chunk carry = 0;
726 0 : for (int i = 0; i < used_digits_; ++i) {
727 0 : Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
728 0 : bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
729 0 : carry = new_carry;
730 : }
731 0 : if (carry != 0) {
732 0 : bigits_[used_digits_] = carry;
733 0 : used_digits_++;
734 : }
735 0 : }
736 :
737 :
738 0 : void Bignum::SubtractTimes(const Bignum& other, int factor) {
739 0 : ASSERT(exponent_ <= other.exponent_);
740 0 : if (factor < 3) {
741 0 : for (int i = 0; i < factor; ++i) {
742 0 : SubtractBignum(other);
743 : }
744 0 : return;
745 : }
746 0 : Chunk borrow = 0;
747 0 : int exponent_diff = other.exponent_ - exponent_;
748 0 : for (int i = 0; i < other.used_digits_; ++i) {
749 0 : DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
750 0 : DoubleChunk remove = borrow + product;
751 0 : Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
752 0 : bigits_[i + exponent_diff] = difference & kBigitMask;
753 0 : borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
754 0 : (remove >> kBigitSize));
755 : }
756 0 : for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
757 0 : if (borrow == 0) return;
758 0 : Chunk difference = bigits_[i] - borrow;
759 0 : bigits_[i] = difference & kBigitMask;
760 0 : borrow = difference >> (kChunkSize - 1);
761 : }
762 0 : Clamp();
763 : }
764 :
765 :
766 : } // namespace double_conversion
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