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 "v8.h" 29 30 #include "bignum.h" 31 #include "utils.h" 32 33 namespace v8 { 34 namespace internal { 35 36 Bignum::Bignum() 37 : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { 38 for (int i = 0; i < kBigitCapacity; ++i) { 39 bigits_[i] = 0; 40 } 41 } 42 43 44 template<typename S> 45 static int BitSize(S value) { 46 return 8 * sizeof(value); 47 } 48 49 // Guaranteed to lie in one Bigit. 50 void Bignum::AssignUInt16(uint16_t value) { 51 ASSERT(kBigitSize >= BitSize(value)); 52 Zero(); 53 if (value == 0) return; 54 55 EnsureCapacity(1); 56 bigits_[0] = value; 57 used_digits_ = 1; 58 } 59 60 61 void Bignum::AssignUInt64(uint64_t value) { 62 const int kUInt64Size = 64; 63 64 Zero(); 65 if (value == 0) return; 66 67 int needed_bigits = kUInt64Size / kBigitSize + 1; 68 EnsureCapacity(needed_bigits); 69 for (int i = 0; i < needed_bigits; ++i) { 70 bigits_[i] = static_cast<Chunk>(value & kBigitMask); 71 value = value >> kBigitSize; 72 } 73 used_digits_ = needed_bigits; 74 Clamp(); 75 } 76 77 78 void Bignum::AssignBignum(const Bignum& other) { 79 exponent_ = other.exponent_; 80 for (int i = 0; i < other.used_digits_; ++i) { 81 bigits_[i] = other.bigits_[i]; 82 } 83 // Clear the excess digits (if there were any). 84 for (int i = other.used_digits_; i < used_digits_; ++i) { 85 bigits_[i] = 0; 86 } 87 used_digits_ = other.used_digits_; 88 } 89 90 91 static uint64_t ReadUInt64(Vector<const char> buffer, 92 int from, 93 int digits_to_read) { 94 uint64_t result = 0; 95 for (int i = from; i < from + digits_to_read; ++i) { 96 int digit = buffer[i] - '0'; 97 ASSERT(0 <= digit && digit <= 9); 98 result = result * 10 + digit; 99 } 100 return result; 101 } 102 103 104 void Bignum::AssignDecimalString(Vector<const char> value) { 105 // 2^64 = 18446744073709551616 > 10^19 106 const int kMaxUint64DecimalDigits = 19; 107 Zero(); 108 int length = value.length(); 109 int pos = 0; 110 // Let's just say that each digit needs 4 bits. 111 while (length >= kMaxUint64DecimalDigits) { 112 uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); 113 pos += kMaxUint64DecimalDigits; 114 length -= kMaxUint64DecimalDigits; 115 MultiplyByPowerOfTen(kMaxUint64DecimalDigits); 116 AddUInt64(digits); 117 } 118 uint64_t digits = ReadUInt64(value, pos, length); 119 MultiplyByPowerOfTen(length); 120 AddUInt64(digits); 121 Clamp(); 122 } 123 124 125 static int HexCharValue(char c) { 126 if ('0' <= c && c <= '9') return c - '0'; 127 if ('a' <= c && c <= 'f') return 10 + c - 'a'; 128 if ('A' <= c && c <= 'F') return 10 + c - 'A'; 129 UNREACHABLE(); 130 return 0; // To make compiler happy. 131 } 132 133 134 void Bignum::AssignHexString(Vector<const char> value) { 135 Zero(); 136 int length = value.length(); 137 138 int needed_bigits = length * 4 / kBigitSize + 1; 139 EnsureCapacity(needed_bigits); 140 int string_index = length - 1; 141 for (int i = 0; i < needed_bigits - 1; ++i) { 142 // These bigits are guaranteed to be "full". 143 Chunk current_bigit = 0; 144 for (int j = 0; j < kBigitSize / 4; j++) { 145 current_bigit += HexCharValue(value[string_index--]) << (j * 4); 146 } 147 bigits_[i] = current_bigit; 148 } 149 used_digits_ = needed_bigits - 1; 150 151 Chunk most_significant_bigit = 0; // Could be = 0; 152 for (int j = 0; j <= string_index; ++j) { 153 most_significant_bigit <<= 4; 154 most_significant_bigit += HexCharValue(value[j]); 155 } 156 if (most_significant_bigit != 0) { 157 bigits_[used_digits_] = most_significant_bigit; 158 used_digits_++; 159 } 160 Clamp(); 161 } 162 163 164 void Bignum::AddUInt64(uint64_t operand) { 165 if (operand == 0) return; 166 Bignum other; 167 other.AssignUInt64(operand); 168 AddBignum(other); 169 } 170 171 172 void Bignum::AddBignum(const Bignum& other) { 173 ASSERT(IsClamped()); 174 ASSERT(other.IsClamped()); 175 176 // If this has a greater exponent than other append zero-bigits to this. 177 // After this call exponent_ <= other.exponent_. 178 Align(other); 179 180 // There are two possibilities: 181 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) 182 // bbbbb 00000000 183 // ---------------- 184 // ccccccccccc 0000 185 // or 186 // aaaaaaaaaa 0000 187 // bbbbbbbbb 0000000 188 // ----------------- 189 // cccccccccccc 0000 190 // In both cases we might need a carry bigit. 191 192 EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); 193 Chunk carry = 0; 194 int bigit_pos = other.exponent_ - exponent_; 195 ASSERT(bigit_pos >= 0); 196 for (int i = 0; i < other.used_digits_; ++i) { 197 Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; 198 bigits_[bigit_pos] = sum & kBigitMask; 199 carry = sum >> kBigitSize; 200 bigit_pos++; 201 } 202 203 while (carry != 0) { 204 Chunk sum = bigits_[bigit_pos] + carry; 205 bigits_[bigit_pos] = sum & kBigitMask; 206 carry = sum >> kBigitSize; 207 bigit_pos++; 208 } 209 used_digits_ = Max(bigit_pos, used_digits_); 210 ASSERT(IsClamped()); 211 } 212 213 214 void Bignum::SubtractBignum(const Bignum& other) { 215 ASSERT(IsClamped()); 216 ASSERT(other.IsClamped()); 217 // We require this to be bigger than other. 218 ASSERT(LessEqual(other, *this)); 219 220 Align(other); 221 222 int offset = other.exponent_ - exponent_; 223 Chunk borrow = 0; 224 int i; 225 for (i = 0; i < other.used_digits_; ++i) { 226 ASSERT((borrow == 0) || (borrow == 1)); 227 Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; 228 bigits_[i + offset] = difference & kBigitMask; 229 borrow = difference >> (kChunkSize - 1); 230 } 231 while (borrow != 0) { 232 Chunk difference = bigits_[i + offset] - borrow; 233 bigits_[i + offset] = difference & kBigitMask; 234 borrow = difference >> (kChunkSize - 1); 235 ++i; 236 } 237 Clamp(); 238 } 239 240 241 void Bignum::ShiftLeft(int shift_amount) { 242 if (used_digits_ == 0) return; 243 exponent_ += shift_amount / kBigitSize; 244 int local_shift = shift_amount % kBigitSize; 245 EnsureCapacity(used_digits_ + 1); 246 BigitsShiftLeft(local_shift); 247 } 248 249 250 void Bignum::MultiplyByUInt32(uint32_t factor) { 251 if (factor == 1) return; 252 if (factor == 0) { 253 Zero(); 254 return; 255 } 256 if (used_digits_ == 0) return; 257 258 // The product of a bigit with the factor is of size kBigitSize + 32. 259 // Assert that this number + 1 (for the carry) fits into double chunk. 260 ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); 261 DoubleChunk carry = 0; 262 for (int i = 0; i < used_digits_; ++i) { 263 DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; 264 bigits_[i] = static_cast<Chunk>(product & kBigitMask); 265 carry = (product >> kBigitSize); 266 } 267 while (carry != 0) { 268 EnsureCapacity(used_digits_ + 1); 269 bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); 270 used_digits_++; 271 carry >>= kBigitSize; 272 } 273 } 274 275 276 void Bignum::MultiplyByUInt64(uint64_t factor) { 277 if (factor == 1) return; 278 if (factor == 0) { 279 Zero(); 280 return; 281 } 282 ASSERT(kBigitSize < 32); 283 uint64_t carry = 0; 284 uint64_t low = factor & 0xFFFFFFFF; 285 uint64_t high = factor >> 32; 286 for (int i = 0; i < used_digits_; ++i) { 287 uint64_t product_low = low * bigits_[i]; 288 uint64_t product_high = high * bigits_[i]; 289 uint64_t tmp = (carry & kBigitMask) + product_low; 290 bigits_[i] = static_cast<Chunk>(tmp & kBigitMask); 291 carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + 292 (product_high << (32 - kBigitSize)); 293 } 294 while (carry != 0) { 295 EnsureCapacity(used_digits_ + 1); 296 bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); 297 used_digits_++; 298 carry >>= kBigitSize; 299 } 300 } 301 302 303 void Bignum::MultiplyByPowerOfTen(int exponent) { 304 const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765c793, fa10079d); 305 const uint16_t kFive1 = 5; 306 const uint16_t kFive2 = kFive1 * 5; 307 const uint16_t kFive3 = kFive2 * 5; 308 const uint16_t kFive4 = kFive3 * 5; 309 const uint16_t kFive5 = kFive4 * 5; 310 const uint16_t kFive6 = kFive5 * 5; 311 const uint32_t kFive7 = kFive6 * 5; 312 const uint32_t kFive8 = kFive7 * 5; 313 const uint32_t kFive9 = kFive8 * 5; 314 const uint32_t kFive10 = kFive9 * 5; 315 const uint32_t kFive11 = kFive10 * 5; 316 const uint32_t kFive12 = kFive11 * 5; 317 const uint32_t kFive13 = kFive12 * 5; 318 const uint32_t kFive1_to_12[] = 319 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, 320 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; 321 322 ASSERT(exponent >= 0); 323 if (exponent == 0) return; 324 if (used_digits_ == 0) return; 325 326 // We shift by exponent at the end just before returning. 327 int remaining_exponent = exponent; 328 while (remaining_exponent >= 27) { 329 MultiplyByUInt64(kFive27); 330 remaining_exponent -= 27; 331 } 332 while (remaining_exponent >= 13) { 333 MultiplyByUInt32(kFive13); 334 remaining_exponent -= 13; 335 } 336 if (remaining_exponent > 0) { 337 MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); 338 } 339 ShiftLeft(exponent); 340 } 341 342 343 void Bignum::Square() { 344 ASSERT(IsClamped()); 345 int product_length = 2 * used_digits_; 346 EnsureCapacity(product_length); 347 348 // Comba multiplication: compute each column separately. 349 // Example: r = a2a1a0 * b2b1b0. 350 // r = 1 * a0b0 + 351 // 10 * (a1b0 + a0b1) + 352 // 100 * (a2b0 + a1b1 + a0b2) + 353 // 1000 * (a2b1 + a1b2) + 354 // 10000 * a2b2 355 // 356 // In the worst case we have to accumulate nb-digits products of digit*digit. 357 // 358 // Assert that the additional number of bits in a DoubleChunk are enough to 359 // sum up used_digits of Bigit*Bigit. 360 if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { 361 UNIMPLEMENTED(); 362 } 363 DoubleChunk accumulator = 0; 364 // First shift the digits so we don't overwrite them. 365 int copy_offset = used_digits_; 366 for (int i = 0; i < used_digits_; ++i) { 367 bigits_[copy_offset + i] = bigits_[i]; 368 } 369 // We have two loops to avoid some 'if's in the loop. 370 for (int i = 0; i < used_digits_; ++i) { 371 // Process temporary digit i with power i. 372 // The sum of the two indices must be equal to i. 373 int bigit_index1 = i; 374 int bigit_index2 = 0; 375 // Sum all of the sub-products. 376 while (bigit_index1 >= 0) { 377 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 378 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 379 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 380 bigit_index1--; 381 bigit_index2++; 382 } 383 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 384 accumulator >>= kBigitSize; 385 } 386 for (int i = used_digits_; i < product_length; ++i) { 387 int bigit_index1 = used_digits_ - 1; 388 int bigit_index2 = i - bigit_index1; 389 // Invariant: sum of both indices is again equal to i. 390 // Inner loop runs 0 times on last iteration, emptying accumulator. 391 while (bigit_index2 < used_digits_) { 392 Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 393 Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 394 accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 395 bigit_index1--; 396 bigit_index2++; 397 } 398 // The overwritten bigits_[i] will never be read in further loop iterations, 399 // because bigit_index1 and bigit_index2 are always greater 400 // than i - used_digits_. 401 bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 402 accumulator >>= kBigitSize; 403 } 404 // Since the result was guaranteed to lie inside the number the 405 // accumulator must be 0 now. 406 ASSERT(accumulator == 0); 407 408 // Don't forget to update the used_digits and the exponent. 409 used_digits_ = product_length; 410 exponent_ *= 2; 411 Clamp(); 412 } 413 414 415 void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { 416 ASSERT(base != 0); 417 ASSERT(power_exponent >= 0); 418 if (power_exponent == 0) { 419 AssignUInt16(1); 420 return; 421 } 422 Zero(); 423 int shifts = 0; 424 // We expect base to be in range 2-32, and most often to be 10. 425 // It does not make much sense to implement different algorithms for counting 426 // the bits. 427 while ((base & 1) == 0) { 428 base >>= 1; 429 shifts++; 430 } 431 int bit_size = 0; 432 int tmp_base = base; 433 while (tmp_base != 0) { 434 tmp_base >>= 1; 435 bit_size++; 436 } 437 int final_size = bit_size * power_exponent; 438 // 1 extra bigit for the shifting, and one for rounded final_size. 439 EnsureCapacity(final_size / kBigitSize + 2); 440 441 // Left to Right exponentiation. 442 int mask = 1; 443 while (power_exponent >= mask) mask <<= 1; 444 445 // The mask is now pointing to the bit above the most significant 1-bit of 446 // power_exponent. 447 // Get rid of first 1-bit; 448 mask >>= 2; 449 uint64_t this_value = base; 450 451 bool delayed_multipliciation = false; 452 const uint64_t max_32bits = 0xFFFFFFFF; 453 while (mask != 0 && this_value <= max_32bits) { 454 this_value = this_value * this_value; 455 // Verify that there is enough space in this_value to perform the 456 // multiplication. The first bit_size bits must be 0. 457 if ((power_exponent & mask) != 0) { 458 uint64_t base_bits_mask = 459 ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); 460 bool high_bits_zero = (this_value & base_bits_mask) == 0; 461 if (high_bits_zero) { 462 this_value *= base; 463 } else { 464 delayed_multipliciation = true; 465 } 466 } 467 mask >>= 1; 468 } 469 AssignUInt64(this_value); 470 if (delayed_multipliciation) { 471 MultiplyByUInt32(base); 472 } 473 474 // Now do the same thing as a bignum. 475 while (mask != 0) { 476 Square(); 477 if ((power_exponent & mask) != 0) { 478 MultiplyByUInt32(base); 479 } 480 mask >>= 1; 481 } 482 483 // And finally add the saved shifts. 484 ShiftLeft(shifts * power_exponent); 485 } 486 487 488 // Precondition: this/other < 16bit. 489 uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { 490 ASSERT(IsClamped()); 491 ASSERT(other.IsClamped()); 492 ASSERT(other.used_digits_ > 0); 493 494 // Easy case: if we have less digits than the divisor than the result is 0. 495 // Note: this handles the case where this == 0, too. 496 if (BigitLength() < other.BigitLength()) { 497 return 0; 498 } 499 500 Align(other); 501 502 uint16_t result = 0; 503 504 // Start by removing multiples of 'other' until both numbers have the same 505 // number of digits. 506 while (BigitLength() > other.BigitLength()) { 507 // This naive approach is extremely inefficient if the this divided other 508 // might be big. This function is implemented for doubleToString where 509 // the result should be small (less than 10). 510 ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); 511 // Remove the multiples of the first digit. 512 // Example this = 23 and other equals 9. -> Remove 2 multiples. 513 result += bigits_[used_digits_ - 1]; 514 SubtractTimes(other, bigits_[used_digits_ - 1]); 515 } 516 517 ASSERT(BigitLength() == other.BigitLength()); 518 519 // Both bignums are at the same length now. 520 // Since other has more than 0 digits we know that the access to 521 // bigits_[used_digits_ - 1] is safe. 522 Chunk this_bigit = bigits_[used_digits_ - 1]; 523 Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; 524 525 if (other.used_digits_ == 1) { 526 // Shortcut for easy (and common) case. 527 int quotient = this_bigit / other_bigit; 528 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; 529 result += quotient; 530 Clamp(); 531 return result; 532 } 533 534 int division_estimate = this_bigit / (other_bigit + 1); 535 result += division_estimate; 536 SubtractTimes(other, division_estimate); 537 538 if (other_bigit * (division_estimate + 1) > this_bigit) { 539 // No need to even try to subtract. Even if other's remaining digits were 0 540 // another subtraction would be too much. 541 return result; 542 } 543 544 while (LessEqual(other, *this)) { 545 SubtractBignum(other); 546 result++; 547 } 548 return result; 549 } 550 551 552 template<typename S> 553 static int SizeInHexChars(S number) { 554 ASSERT(number > 0); 555 int result = 0; 556 while (number != 0) { 557 number >>= 4; 558 result++; 559 } 560 return result; 561 } 562 563 564 static char HexCharOfValue(int value) { 565 ASSERT(0 <= value && value <= 16); 566 if (value < 10) return value + '0'; 567 return value - 10 + 'A'; 568 } 569 570 571 bool Bignum::ToHexString(char* buffer, int buffer_size) const { 572 ASSERT(IsClamped()); 573 // Each bigit must be printable as separate hex-character. 574 ASSERT(kBigitSize % 4 == 0); 575 const int kHexCharsPerBigit = kBigitSize / 4; 576 577 if (used_digits_ == 0) { 578 if (buffer_size < 2) return false; 579 buffer[0] = '0'; 580 buffer[1] = '\0'; 581 return true; 582 } 583 // We add 1 for the terminating '\0' character. 584 int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + 585 SizeInHexChars(bigits_[used_digits_ - 1]) + 1; 586 if (needed_chars > buffer_size) return false; 587 int string_index = needed_chars - 1; 588 buffer[string_index--] = '\0'; 589 for (int i = 0; i < exponent_; ++i) { 590 for (int j = 0; j < kHexCharsPerBigit; ++j) { 591 buffer[string_index--] = '0'; 592 } 593 } 594 for (int i = 0; i < used_digits_ - 1; ++i) { 595 Chunk current_bigit = bigits_[i]; 596 for (int j = 0; j < kHexCharsPerBigit; ++j) { 597 buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); 598 current_bigit >>= 4; 599 } 600 } 601 // And finally the last bigit. 602 Chunk most_significant_bigit = bigits_[used_digits_ - 1]; 603 while (most_significant_bigit != 0) { 604 buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); 605 most_significant_bigit >>= 4; 606 } 607 return true; 608 } 609 610 611 Bignum::Chunk Bignum::BigitAt(int index) const { 612 if (index >= BigitLength()) return 0; 613 if (index < exponent_) return 0; 614 return bigits_[index - exponent_]; 615 } 616 617 618 int Bignum::Compare(const Bignum& a, const Bignum& b) { 619 ASSERT(a.IsClamped()); 620 ASSERT(b.IsClamped()); 621 int bigit_length_a = a.BigitLength(); 622 int bigit_length_b = b.BigitLength(); 623 if (bigit_length_a < bigit_length_b) return -1; 624 if (bigit_length_a > bigit_length_b) return +1; 625 for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { 626 Chunk bigit_a = a.BigitAt(i); 627 Chunk bigit_b = b.BigitAt(i); 628 if (bigit_a < bigit_b) return -1; 629 if (bigit_a > bigit_b) return +1; 630 // Otherwise they are equal up to this digit. Try the next digit. 631 } 632 return 0; 633 } 634 635 636 int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { 637 ASSERT(a.IsClamped()); 638 ASSERT(b.IsClamped()); 639 ASSERT(c.IsClamped()); 640 if (a.BigitLength() < b.BigitLength()) { 641 return PlusCompare(b, a, c); 642 } 643 if (a.BigitLength() + 1 < c.BigitLength()) return -1; 644 if (a.BigitLength() > c.BigitLength()) return +1; 645 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than 646 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one 647 // of 'a'. 648 if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { 649 return -1; 650 } 651 652 Chunk borrow = 0; 653 // Starting at min_exponent all digits are == 0. So no need to compare them. 654 int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); 655 for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { 656 Chunk chunk_a = a.BigitAt(i); 657 Chunk chunk_b = b.BigitAt(i); 658 Chunk chunk_c = c.BigitAt(i); 659 Chunk sum = chunk_a + chunk_b; 660 if (sum > chunk_c + borrow) { 661 return +1; 662 } else { 663 borrow = chunk_c + borrow - sum; 664 if (borrow > 1) return -1; 665 borrow <<= kBigitSize; 666 } 667 } 668 if (borrow == 0) return 0; 669 return -1; 670 } 671 672 673 void Bignum::Clamp() { 674 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { 675 used_digits_--; 676 } 677 if (used_digits_ == 0) { 678 // Zero. 679 exponent_ = 0; 680 } 681 } 682 683 684 bool Bignum::IsClamped() const { 685 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; 686 } 687 688 689 void Bignum::Zero() { 690 for (int i = 0; i < used_digits_; ++i) { 691 bigits_[i] = 0; 692 } 693 used_digits_ = 0; 694 exponent_ = 0; 695 } 696 697 698 void Bignum::Align(const Bignum& other) { 699 if (exponent_ > other.exponent_) { 700 // If "X" represents a "hidden" digit (by the exponent) then we are in the 701 // following case (a == this, b == other): 702 // a: aaaaaaXXXX or a: aaaaaXXX 703 // b: bbbbbbX b: bbbbbbbbXX 704 // We replace some of the hidden digits (X) of a with 0 digits. 705 // a: aaaaaa000X or a: aaaaa0XX 706 int zero_digits = exponent_ - other.exponent_; 707 EnsureCapacity(used_digits_ + zero_digits); 708 for (int i = used_digits_ - 1; i >= 0; --i) { 709 bigits_[i + zero_digits] = bigits_[i]; 710 } 711 for (int i = 0; i < zero_digits; ++i) { 712 bigits_[i] = 0; 713 } 714 used_digits_ += zero_digits; 715 exponent_ -= zero_digits; 716 ASSERT(used_digits_ >= 0); 717 ASSERT(exponent_ >= 0); 718 } 719 } 720 721 722 void Bignum::BigitsShiftLeft(int shift_amount) { 723 ASSERT(shift_amount < kBigitSize); 724 ASSERT(shift_amount >= 0); 725 Chunk carry = 0; 726 for (int i = 0; i < used_digits_; ++i) { 727 Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); 728 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; 729 carry = new_carry; 730 } 731 if (carry != 0) { 732 bigits_[used_digits_] = carry; 733 used_digits_++; 734 } 735 } 736 737 738 void Bignum::SubtractTimes(const Bignum& other, int factor) { 739 ASSERT(exponent_ <= other.exponent_); 740 if (factor < 3) { 741 for (int i = 0; i < factor; ++i) { 742 SubtractBignum(other); 743 } 744 return; 745 } 746 Chunk borrow = 0; 747 int exponent_diff = other.exponent_ - exponent_; 748 for (int i = 0; i < other.used_digits_; ++i) { 749 DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; 750 DoubleChunk remove = borrow + product; 751 Chunk difference = 752 bigits_[i + exponent_diff] - static_cast<Chunk>(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 v8::internal 769