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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, | |
| 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*d
igit. | |
| 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 ite
rations, | |
| 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 cou
nting | |
| 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 sa
me | |
| 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 whe
re | |
| 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' t
han | |
| 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 t
hem. | |
| 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.bigit
s_[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 | |
| OLD | NEW |
|---|
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Issue 14238015:
Move Source/WTF/wtf to Source/wtf (Closed)
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