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 "config.h" 29 30 #include "bignum.h" 31 #include "utils.h" 32 33 namespace WTF { 34 35 namespace double_conversion { 36 37 Bignum::Bignum() 38 : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { 39 for (int i = 0; i < kBigitCapacity; ++i) { 40 bigits_[i] = 0; 41 } 42 } 43 44 45 template<typename S> 46 static int BitSize(S value) { 47 return 8 * sizeof(value); 48 } 49 50 // Guaranteed to lie in one Bigit. 51 void Bignum::AssignUInt16(uint16_t value) { 52 ASSERT(kBigitSize >= BitSize(value)); 53 Zero(); 54 if (value == 0) return; 55 56 EnsureCapacity(1); 57 bigits_[0] = value; 58 used_digits_ = 1; 59 } 60 61 62 void Bignum::AssignUInt64(uint64_t value) { 63 const int kUInt64Size = 64; 64 65 Zero(); 66 if (value == 0) return; 67 68 int needed_bigits = kUInt64Size / kBigitSize + 1; 69 EnsureCapacity(needed_bigits); 70 for (int i = 0; i < needed_bigits; ++i) { 71 bigits_[i] = (uint32_t)value & kBigitMask; 72 value = value >> kBigitSize; 73 } 74 used_digits_ = needed_bigits; 75 Clamp(); 76 } 77 78 79 void Bignum::AssignBignum(const Bignum& other) { 80 exponent_ = other.exponent_; 81 for (int i = 0; i < other.used_digits_; ++i) { 82 bigits_[i] = other.bigits_[i]; 83 } 84 // Clear the excess digits (if there were any). 85 for (int i = other.used_digits_; i < used_digits_; ++i) { 86 bigits_[i] = 0; 87 } 88 used_digits_ = other.used_digits_; 89 } 90 91 92 static uint64_t ReadUInt64(Vector<const char> buffer, 93 int from, 94 int digits_to_read) { 95 uint64_t result = 0; 96 for (int i = from; i < from + digits_to_read; ++i) { 97 int digit = buffer[i] - '0'; 98 ASSERT(0 <= digit && digit <= 9); 99 result = result * 10 + digit; 100 } 101 return result; 102 } 103 104 105 void Bignum::AssignDecimalString(Vector<const char> value) { 106 // 2^64 = 18446744073709551616 > 10^19 107 const int kMaxUint64DecimalDigits = 19; 108 Zero(); 109 int length = value.length(); 110 int pos = 0; 111 // Let's just say that each digit needs 4 bits. 112 while (length >= kMaxUint64DecimalDigits) { 113 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); 114 pos += kMaxUint64DecimalDigits; 115 length -= kMaxUint64DecimalDigits; 116 MultiplyByPowerOfTen(kMaxUint64DecimalDigits); 117 AddUInt64(digits); 118 } 119 uint64_t digits = ReadUInt64(value, pos, length); 120 MultiplyByPowerOfTen(length); 121 AddUInt64(digits); 122 Clamp(); 123 } 124 125 126 static int HexCharValue(char c) { 127 if ('0' <= c && c <= '9') return c - '0'; 128 if ('a' <= c && c <= 'f') return 10 + c - 'a'; 129 if ('A' <= c && c <= 'F') return 10 + c - 'A'; 130 UNREACHABLE(); 131 return 0; // To make compiler happy. 132 } 133 134 135 void Bignum::AssignHexString(Vector<const char> value) { 136 Zero(); 137 int length = value.length(); 138 139 int needed_bigits = length * 4 / kBigitSize + 1; 140 EnsureCapacity(needed_bigits); 141 int string_index = length - 1; 142 for (int i = 0; i < needed_bigits - 1; ++i) { 143 // These bigits are guaranteed to be "full". 144 Chunk current_bigit = 0; 145 for (int j = 0; j < kBigitSize / 4; j++) { 146 current_bigit += HexCharValue(value[string_index--]) << (j * 4); 147 } 148 bigits_[i] = current_bigit; 149 } 150 used_digits_ = needed_bigits - 1; 151 152 Chunk most_significant_bigit = 0; // Could be = 0; 153 for (int j = 0; j <= string_index; ++j) { 154 most_significant_bigit <<= 4; 155 most_significant_bigit += HexCharValue(value[j]); 156 } 157 if (most_significant_bigit != 0) { 158 bigits_[used_digits_] = most_significant_bigit; 159 used_digits_++; 160 } 161 Clamp(); 162 } 163 164 165 void Bignum::AddUInt64(uint64_t operand) { 166 if (operand == 0) return; 167 Bignum other; 168 other.AssignUInt64(operand); 169 AddBignum(other); 170 } 171 172 173 void Bignum::AddBignum(const Bignum& other) { 174 ASSERT(IsClamped()); 175 ASSERT(other.IsClamped()); 176 177 // If this has a greater exponent than other append zero-bigits to this. 178 // After this call exponent_ <= other.exponent_. 179 Align(other); 180 181 // There are two possibilities: 182 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) 183 // bbbbb 00000000 184 // ---------------- 185 // ccccccccccc 0000 186 // or 187 // aaaaaaaaaa 0000 188 // bbbbbbbbb 0000000 189 // ----------------- 190 // cccccccccccc 0000 191 // In both cases we might need a carry bigit. 192 193 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); 194 Chunk carry = 0; 195 int bigit_pos = other.exponent_ - exponent_; 196 ASSERT(bigit_pos >= 0); 197 for (int i = 0; i < other.used_digits_; ++i) { 198 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; 199 bigits_[bigit_pos] = sum & kBigitMask; 200 carry = sum >> kBigitSize; 201 bigit_pos++; 202 } 203 204 while (carry != 0) { 205 Chunk sum = bigits_[bigit_pos] + carry; 206 bigits_[bigit_pos] = sum & kBigitMask; 207 carry = sum >> kBigitSize; 208 bigit_pos++; 209 } 210 used_digits_ = Max(bigit_pos, used_digits_); 211 ASSERT(IsClamped()); 212 } 213 214 215 void Bignum::SubtractBignum(const Bignum& other) { 216 ASSERT(IsClamped()); 217 ASSERT(other.IsClamped()); 218 // We require this to be bigger than other. 219 ASSERT(LessEqual(other, *this)); 220 221 Align(other); 222 223 int offset = other.exponent_ - exponent_; 224 Chunk borrow = 0; 225 int i; 226 for (i = 0; i < other.used_digits_; ++i) { 227 ASSERT((borrow == 0) || (borrow == 1)); 228 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; 229 bigits_[i + offset] = difference & kBigitMask; 230 borrow = difference >> (kChunkSize - 1); 231 } 232 while (borrow != 0) { 233 Chunk difference = bigits_[i + offset] - borrow; 234 bigits_[i + offset] = difference & kBigitMask; 235 borrow = difference >> (kChunkSize - 1); 236 ++i; 237 } 238 Clamp(); 239 } 240 241 242 void Bignum::ShiftLeft(int shift_amount) { 243 if (used_digits_ == 0) return; 244 exponent_ += shift_amount / kBigitSize; 245 int local_shift = shift_amount % kBigitSize; 246 EnsureCapacity(used_digits_ + 1); 247 BigitsShiftLeft(local_shift); 248 } 249 250 251 void Bignum::MultiplyByUInt32(uint32_t factor) { 252 if (factor == 1) return; 253 if (factor == 0) { 254 Zero(); 255 return; 256 } 257 if (used_digits_ == 0) return; 258 259 // The product of a bigit with the factor is of size kBigitSize + 32. 260 // Assert that this number + 1 (for the carry) fits into double chunk. 261 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); 262 DoubleChunk carry = 0; 263 for (int i = 0; i < used_digits_; ++i) { 264 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; 265 bigits_[i] = static_cast<Chunk>(product & kBigitMask); 266 carry = (product >> kBigitSize); 267 } 268 while (carry != 0) { 269 EnsureCapacity(used_digits_ + 1); 270 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; 271 used_digits_++; 272 carry >>= kBigitSize; 273 } 274 } 275 276 277 void Bignum::MultiplyByUInt64(uint64_t factor) { 278 if (factor == 1) return; 279 if (factor == 0) { 280 Zero(); 281 return; 282 } 283 ASSERT(kBigitSize < 32); 284 uint64_t carry = 0; 285 uint64_t low = factor & 0xFFFFFFFF; 286 uint64_t high = factor >> 32; 287 for (int i = 0; i < used_digits_; ++i) { 288 uint64_t product_low = low * bigits_[i]; 289 uint64_t product_high = high * bigits_[i]; 290 uint64_t tmp = (carry & kBigitMask) + product_low; 291 bigits_[i] = (uint32_t)tmp & kBigitMask; 292 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + 293 (product_high << (32 - kBigitSize)); 294 } 295 while (carry != 0) { 296 EnsureCapacity(used_digits_ + 1); 297 bigits_[used_digits_] = (uint32_t)carry & kBigitMask; 298 used_digits_++; 299 carry >>= kBigitSize; 300 } 301 } 302 303 304 void Bignum::MultiplyByPowerOfTen(int exponent) { 305 const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d); 306 const uint16_t kFive1 = 5; 307 const uint16_t kFive2 = kFive1 * 5; 308 const uint16_t kFive3 = kFive2 * 5; 309 const uint16_t kFive4 = kFive3 * 5; 310 const uint16_t kFive5 = kFive4 * 5; 311 const uint16_t kFive6 = kFive5 * 5; 312 const uint32_t kFive7 = kFive6 * 5; 313 const uint32_t kFive8 = kFive7 * 5; 314 const uint32_t kFive9 = kFive8 * 5; 315 const uint32_t kFive10 = kFive9 * 5; 316 const uint32_t kFive11 = kFive10 * 5; 317 const uint32_t kFive12 = kFive11 * 5; 318 const uint32_t kFive13 = kFive12 * 5; 319 const uint32_t kFive1_to_12[] = 320 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, 321 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; 322 323 ASSERT(exponent >= 0); 324 if (exponent == 0) return; 325 if (used_digits_ == 0) return; 326 327 // We shift by exponent at the end just before returning. 328 int remaining_exponent = exponent; 329 while (remaining_exponent >= 27) { 330 MultiplyByUInt64(kFive27); 331 remaining_exponent -= 27; 332 } 333 while (remaining_exponent >= 13) { 334 MultiplyByUInt32(kFive13); 335 remaining_exponent -= 13; 336 } 337 if (remaining_exponent > 0) { 338 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); 339 } 340 ShiftLeft(exponent); 341 } 342 343 344 void Bignum::Square() { 345 ASSERT(IsClamped()); 346 int product_length = 2 * used_digits_; 347 EnsureCapacity(product_length); 348 349 // Comba multiplication: compute each column separately. 350 // Example: r = a2a1a0 * b2b1b0. 351 // r = 1 * a0b0 + 352 // 10 * (a1b0 + a0b1) + 353 // 100 * (a2b0 + a1b1 + a0b2) + 354 // 1000 * (a2b1 + a1b2) + 355 // 10000 * a2b2 356 // 357 // In the worst case we have to accumulate nb-digits products of digit*digit. 358 // 359 // Assert that the additional number of bits in a DoubleChunk are enough to 360 // sum up used_digits of Bigit*Bigit. 361 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { 362 UNIMPLEMENTED(); 363 } 364 DoubleChunk accumulator = 0; 365 // First shift the digits so we don't overwrite them. 366 int copy_offset = used_digits_; 367 for (int i = 0; i < used_digits_; ++i) { 368 bigits_[copy_offset + i] = bigits_[i]; 369 } 370 // We have two loops to avoid some 'if's in the loop. 371 for (int i = 0; i < used_digits_; ++i) { 372 // Process temporary digit i with power i. 373 // The sum of the two indices must be equal to i. 374 int bigit_index1 = i; 375 int bigit_index2 = 0; 376 // Sum all of the sub-products. 377 while (bigit_index1 >= 0) { 378 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 379 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 380 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 381 bigit_index1--; 382 bigit_index2++; 383 } 384 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 385 accumulator >>= kBigitSize; 386 } 387 for (int i = used_digits_; i < product_length; ++i) { 388 int bigit_index1 = used_digits_ - 1; 389 int bigit_index2 = i - bigit_index1; 390 // Invariant: sum of both indices is again equal to i. 391 // Inner loop runs 0 times on last iteration, emptying accumulator. 392 while (bigit_index2 < used_digits_) { 393 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 394 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 395 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 396 bigit_index1--; 397 bigit_index2++; 398 } 399 // The overwritten bigits_[i] will never be read in further loop iterations, 400 // because bigit_index1 and bigit_index2 are always greater 401 // than i - used_digits_. 402 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 403 accumulator >>= kBigitSize; 404 } 405 // Since the result was guaranteed to lie inside the number the 406 // accumulator must be 0 now. 407 ASSERT(accumulator == 0); 408 409 // Don't forget to update the used_digits and the exponent. 410 used_digits_ = product_length; 411 exponent_ *= 2; 412 Clamp(); 413 } 414 415 416 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { 417 ASSERT(base != 0); 418 ASSERT(power_exponent >= 0); 419 if (power_exponent == 0) { 420 AssignUInt16(1); 421 return; 422 } 423 Zero(); 424 int shifts = 0; 425 // We expect base to be in range 2-32, and most often to be 10. 426 // It does not make much sense to implement different algorithms for counting 427 // the bits. 428 while ((base & 1) == 0) { 429 base >>= 1; 430 shifts++; 431 } 432 int bit_size = 0; 433 int tmp_base = base; 434 while (tmp_base != 0) { 435 tmp_base >>= 1; 436 bit_size++; 437 } 438 int final_size = bit_size * power_exponent; 439 // 1 extra bigit for the shifting, and one for rounded final_size. 440 EnsureCapacity(final_size / kBigitSize + 2); 441 442 // Left to Right exponentiation. 443 int mask = 1; 444 while (power_exponent >= mask) mask <<= 1; 445 446 // The mask is now pointing to the bit above the most significant 1-bit of 447 // power_exponent. 448 // Get rid of first 1-bit; 449 mask >>= 2; 450 uint64_t this_value = base; 451 452 bool delayed_multipliciation = false; 453 const uint64_t max_32bits = 0xFFFFFFFF; 454 while (mask != 0 && this_value <= max_32bits) { 455 this_value = this_value * this_value; 456 // Verify that there is enough space in this_value to perform the 457 // multiplication. The first bit_size bits must be 0. 458 if ((power_exponent & mask) != 0) { 459 uint64_t base_bits_mask = 460 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); 461 bool high_bits_zero = (this_value & base_bits_mask) == 0; 462 if (high_bits_zero) { 463 this_value *= base; 464 } else { 465 delayed_multipliciation = true; 466 } 467 } 468 mask >>= 1; 469 } 470 AssignUInt64(this_value); 471 if (delayed_multipliciation) { 472 MultiplyByUInt32(base); 473 } 474 475 // Now do the same thing as a bignum. 476 while (mask != 0) { 477 Square(); 478 if ((power_exponent & mask) != 0) { 479 MultiplyByUInt32(base); 480 } 481 mask >>= 1; 482 } 483 484 // And finally add the saved shifts. 485 ShiftLeft(shifts * power_exponent); 486 } 487 488 489 // Precondition: this/other < 16bit. 490 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { 491 ASSERT(IsClamped()); 492 ASSERT(other.IsClamped()); 493 ASSERT(other.used_digits_ > 0); 494 495 // Easy case: if we have less digits than the divisor than the result is 0. 496 // Note: this handles the case where this == 0, too. 497 if (BigitLength() < other.BigitLength()) { 498 return 0; 499 } 500 501 Align(other); 502 503 uint16_t result = 0; 504 505 // Start by removing multiples of 'other' until both numbers have the same 506 // number of digits. 507 while (BigitLength() > other.BigitLength()) { 508 // This naive approach is extremely inefficient if the this divided other 509 // might be big. This function is implemented for doubleToString where 510 // the result should be small (less than 10). 511 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); 512 // Remove the multiples of the first digit. 513 // Example this = 23 and other equals 9. -> Remove 2 multiples. 514 result += bigits_[used_digits_ - 1]; 515 SubtractTimes(other, bigits_[used_digits_ - 1]); 516 } 517 518 ASSERT(BigitLength() == other.BigitLength()); 519 520 // Both bignums are at the same length now. 521 // Since other has more than 0 digits we know that the access to 522 // bigits_[used_digits_ - 1] is safe. 523 Chunk this_bigit = bigits_[used_digits_ - 1]; 524 Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; 525 526 if (other.used_digits_ == 1) { 527 // Shortcut for easy (and common) case. 528 int quotient = this_bigit / other_bigit; 529 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; 530 result += quotient; 531 Clamp(); 532 return result; 533 } 534 535 int division_estimate = this_bigit / (other_bigit + 1); 536 result += division_estimate; 537 SubtractTimes(other, division_estimate); 538 539 if (other_bigit * (division_estimate + 1) > this_bigit) { 540 // No need to even try to subtract. Even if other's remaining digits were 0 541 // another subtraction would be too much. 542 return result; 543 } 544 545 while (LessEqual(other, *this)) { 546 SubtractBignum(other); 547 result++; 548 } 549 return result; 550 } 551 552 553 template<typename S> 554 static int SizeInHexChars(S number) { 555 ASSERT(number > 0); 556 int result = 0; 557 while (number != 0) { 558 number >>= 4; 559 result++; 560 } 561 return result; 562 } 563 564 565 static char HexCharOfValue(int value) { 566 ASSERT(0 <= value && value <= 16); 567 if (value < 10) return value + '0'; 568 return value - 10 + 'A'; 569 } 570 571 572 bool Bignum::ToHexString(char* buffer, int buffer_size) const { 573 ASSERT(IsClamped()); 574 // Each bigit must be printable as separate hex-character. 575 ASSERT(kBigitSize % 4 == 0); 576 const int kHexCharsPerBigit = kBigitSize / 4; 577 578 if (used_digits_ == 0) { 579 if (buffer_size < 2) return false; 580 buffer[0] = '0'; 581 buffer[1] = '\0'; 582 return true; 583 } 584 // We add 1 for the terminating '\0' character. 585 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + 586 SizeInHexChars(bigits_[used_digits_ - 1]) + 1; 587 if (needed_chars > buffer_size) return false; 588 int string_index = needed_chars - 1; 589 buffer[string_index--] = '\0'; 590 for (int i = 0; i < exponent_; ++i) { 591 for (int j = 0; j < kHexCharsPerBigit; ++j) { 592 buffer[string_index--] = '0'; 593 } 594 } 595 for (int i = 0; i < used_digits_ - 1; ++i) { 596 Chunk current_bigit = bigits_[i]; 597 for (int j = 0; j < kHexCharsPerBigit; ++j) { 598 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); 599 current_bigit >>= 4; 600 } 601 } 602 // And finally the last bigit. 603 Chunk most_significant_bigit = bigits_[used_digits_ - 1]; 604 while (most_significant_bigit != 0) { 605 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); 606 most_significant_bigit >>= 4; 607 } 608 return true; 609 } 610 611 612 Bignum::Chunk Bignum::BigitAt(int index) const { 613 if (index >= BigitLength()) return 0; 614 if (index < exponent_) return 0; 615 return bigits_[index - exponent_]; 616 } 617 618 619 int Bignum::Compare(const Bignum& a, const Bignum& b) { 620 ASSERT(a.IsClamped()); 621 ASSERT(b.IsClamped()); 622 int bigit_length_a = a.BigitLength(); 623 int bigit_length_b = b.BigitLength(); 624 if (bigit_length_a < bigit_length_b) return -1; 625 if (bigit_length_a > bigit_length_b) return +1; 626 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { 627 Chunk bigit_a = a.BigitAt(i); 628 Chunk bigit_b = b.BigitAt(i); 629 if (bigit_a < bigit_b) return -1; 630 if (bigit_a > bigit_b) return +1; 631 // Otherwise they are equal up to this digit. Try the next digit. 632 } 633 return 0; 634 } 635 636 637 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { 638 ASSERT(a.IsClamped()); 639 ASSERT(b.IsClamped()); 640 ASSERT(c.IsClamped()); 641 if (a.BigitLength() < b.BigitLength()) { 642 return PlusCompare(b, a, c); 643 } 644 if (a.BigitLength() + 1 < c.BigitLength()) return -1; 645 if (a.BigitLength() > c.BigitLength()) return +1; 646 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than 647 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one 648 // of 'a'. 649 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { 650 return -1; 651 } 652 653 Chunk borrow = 0; 654 // Starting at min_exponent all digits are == 0. So no need to compare them. 655 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); 656 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { 657 Chunk chunk_a = a.BigitAt(i); 658 Chunk chunk_b = b.BigitAt(i); 659 Chunk chunk_c = c.BigitAt(i); 660 Chunk sum = chunk_a + chunk_b; 661 if (sum > chunk_c + borrow) { 662 return +1; 663 } else { 664 borrow = chunk_c + borrow - sum; 665 if (borrow > 1) return -1; 666 borrow <<= kBigitSize; 667 } 668 } 669 if (borrow == 0) return 0; 670 return -1; 671 } 672 673 674 void Bignum::Clamp() { 675 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { 676 used_digits_--; 677 } 678 if (used_digits_ == 0) { 679 // Zero. 680 exponent_ = 0; 681 } 682 } 683 684 685 bool Bignum::IsClamped() const { 686 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; 687 } 688 689 690 void Bignum::Zero() { 691 for (int i = 0; i < used_digits_; ++i) { 692 bigits_[i] = 0; 693 } 694 used_digits_ = 0; 695 exponent_ = 0; 696 } 697 698 699 void Bignum::Align(const Bignum& other) { 700 if (exponent_ > other.exponent_) { 701 // If "X" represents a "hidden" digit (by the exponent) then we are in the 702 // following case (a == this, b == other): 703 // a: aaaaaaXXXX or a: aaaaaXXX 704 // b: bbbbbbX b: bbbbbbbbXX 705 // We replace some of the hidden digits (X) of a with 0 digits. 706 // a: aaaaaa000X or a: aaaaa0XX 707 int zero_digits = exponent_ - other.exponent_; 708 EnsureCapacity(used_digits_ + zero_digits); 709 for (int i = used_digits_ - 1; i >= 0; --i) { 710 bigits_[i + zero_digits] = bigits_[i]; 711 } 712 for (int i = 0; i < zero_digits; ++i) { 713 bigits_[i] = 0; 714 } 715 used_digits_ += zero_digits; 716 exponent_ -= zero_digits; 717 ASSERT(used_digits_ >= 0); 718 ASSERT(exponent_ >= 0); 719 } 720 } 721 722 723 void Bignum::BigitsShiftLeft(int shift_amount) { 724 ASSERT(shift_amount < kBigitSize); 725 ASSERT(shift_amount >= 0); 726 Chunk carry = 0; 727 for (int i = 0; i < used_digits_; ++i) { 728 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); 729 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; 730 carry = new_carry; 731 } 732 if (carry != 0) { 733 bigits_[used_digits_] = carry; 734 used_digits_++; 735 } 736 } 737 738 739 void Bignum::SubtractTimes(const Bignum& other, int factor) { 740 ASSERT(exponent_ <= other.exponent_); 741 if (factor < 3) { 742 for (int i = 0; i < factor; ++i) { 743 SubtractBignum(other); 744 } 745 return; 746 } 747 Chunk borrow = 0; 748 int exponent_diff = other.exponent_ - exponent_; 749 for (int i = 0; i < other.used_digits_; ++i) { 750 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; 751 DoubleChunk remove = borrow + product; 752 Chunk difference = bigits_[i + exponent_diff] - ((uint32_t)remove & kBigitMask); 753 bigits_[i + exponent_diff] = difference & kBigitMask; 754 borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + 755 (remove >> kBigitSize)); 756 } 757 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { 758 if (borrow == 0) return; 759 Chunk difference = bigits_[i] - borrow; 760 bigits_[i] = difference & kBigitMask; 761 borrow = difference >> (kChunkSize - 1); 762 ++i; 763 } 764 Clamp(); 765 } 766 767 768 } // namespace double_conversion 769 770 } // namespace WTF 771