Ben Murdoch | 3fb3ca8 | 2011-12-02 17:19:32 +0000 | [diff] [blame] | 1 | // Copyright 2011 the V8 project authors. All rights reserved. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 2 | // Use of this source code is governed by a BSD-style license that can be |
| 3 | // found in the LICENSE file. |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 4 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 5 | #include "src/bignum.h" |
| 6 | #include "src/utils.h" |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 7 | |
| 8 | namespace v8 { |
| 9 | namespace internal { |
| 10 | |
| 11 | Bignum::Bignum() |
| 12 | : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { |
| 13 | for (int i = 0; i < kBigitCapacity; ++i) { |
| 14 | bigits_[i] = 0; |
| 15 | } |
| 16 | } |
| 17 | |
| 18 | |
| 19 | template<typename S> |
| 20 | static int BitSize(S value) { |
| 21 | return 8 * sizeof(value); |
| 22 | } |
| 23 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 24 | |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 25 | // Guaranteed to lie in one Bigit. |
| 26 | void Bignum::AssignUInt16(uint16_t value) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 27 | DCHECK(kBigitSize >= BitSize(value)); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 28 | Zero(); |
| 29 | if (value == 0) return; |
| 30 | |
| 31 | EnsureCapacity(1); |
| 32 | bigits_[0] = value; |
| 33 | used_digits_ = 1; |
| 34 | } |
| 35 | |
| 36 | |
| 37 | void Bignum::AssignUInt64(uint64_t value) { |
| 38 | const int kUInt64Size = 64; |
| 39 | |
| 40 | Zero(); |
| 41 | if (value == 0) return; |
| 42 | |
| 43 | int needed_bigits = kUInt64Size / kBigitSize + 1; |
| 44 | EnsureCapacity(needed_bigits); |
| 45 | for (int i = 0; i < needed_bigits; ++i) { |
Steve Block | 1e0659c | 2011-05-24 12:43:12 +0100 | [diff] [blame] | 46 | bigits_[i] = static_cast<Chunk>(value & kBigitMask); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 47 | value = value >> kBigitSize; |
| 48 | } |
| 49 | used_digits_ = needed_bigits; |
| 50 | Clamp(); |
| 51 | } |
| 52 | |
| 53 | |
| 54 | void Bignum::AssignBignum(const Bignum& other) { |
| 55 | exponent_ = other.exponent_; |
| 56 | for (int i = 0; i < other.used_digits_; ++i) { |
| 57 | bigits_[i] = other.bigits_[i]; |
| 58 | } |
| 59 | // Clear the excess digits (if there were any). |
| 60 | for (int i = other.used_digits_; i < used_digits_; ++i) { |
| 61 | bigits_[i] = 0; |
| 62 | } |
| 63 | used_digits_ = other.used_digits_; |
| 64 | } |
| 65 | |
| 66 | |
| 67 | static uint64_t ReadUInt64(Vector<const char> buffer, |
| 68 | int from, |
| 69 | int digits_to_read) { |
| 70 | uint64_t result = 0; |
Ben Murdoch | 4a90d5f | 2016-03-22 12:00:34 +0000 | [diff] [blame] | 71 | int to = from + digits_to_read; |
| 72 | |
| 73 | for (int i = from; i < to; ++i) { |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 74 | int digit = buffer[i] - '0'; |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 75 | DCHECK(0 <= digit && digit <= 9); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 76 | result = result * 10 + digit; |
| 77 | } |
| 78 | return result; |
| 79 | } |
| 80 | |
| 81 | |
| 82 | void Bignum::AssignDecimalString(Vector<const char> value) { |
| 83 | // 2^64 = 18446744073709551616 > 10^19 |
| 84 | const int kMaxUint64DecimalDigits = 19; |
| 85 | Zero(); |
| 86 | int length = value.length(); |
| 87 | int pos = 0; |
| 88 | // Let's just say that each digit needs 4 bits. |
| 89 | while (length >= kMaxUint64DecimalDigits) { |
| 90 | uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); |
| 91 | pos += kMaxUint64DecimalDigits; |
| 92 | length -= kMaxUint64DecimalDigits; |
| 93 | MultiplyByPowerOfTen(kMaxUint64DecimalDigits); |
| 94 | AddUInt64(digits); |
| 95 | } |
| 96 | uint64_t digits = ReadUInt64(value, pos, length); |
| 97 | MultiplyByPowerOfTen(length); |
| 98 | AddUInt64(digits); |
| 99 | Clamp(); |
| 100 | } |
| 101 | |
| 102 | |
| 103 | static int HexCharValue(char c) { |
| 104 | if ('0' <= c && c <= '9') return c - '0'; |
| 105 | if ('a' <= c && c <= 'f') return 10 + c - 'a'; |
| 106 | if ('A' <= c && c <= 'F') return 10 + c - 'A'; |
| 107 | UNREACHABLE(); |
| 108 | return 0; // To make compiler happy. |
| 109 | } |
| 110 | |
| 111 | |
| 112 | void Bignum::AssignHexString(Vector<const char> value) { |
| 113 | Zero(); |
| 114 | int length = value.length(); |
| 115 | |
| 116 | int needed_bigits = length * 4 / kBigitSize + 1; |
| 117 | EnsureCapacity(needed_bigits); |
| 118 | int string_index = length - 1; |
| 119 | for (int i = 0; i < needed_bigits - 1; ++i) { |
| 120 | // These bigits are guaranteed to be "full". |
| 121 | Chunk current_bigit = 0; |
| 122 | for (int j = 0; j < kBigitSize / 4; j++) { |
| 123 | current_bigit += HexCharValue(value[string_index--]) << (j * 4); |
| 124 | } |
| 125 | bigits_[i] = current_bigit; |
| 126 | } |
| 127 | used_digits_ = needed_bigits - 1; |
| 128 | |
| 129 | Chunk most_significant_bigit = 0; // Could be = 0; |
| 130 | for (int j = 0; j <= string_index; ++j) { |
| 131 | most_significant_bigit <<= 4; |
| 132 | most_significant_bigit += HexCharValue(value[j]); |
| 133 | } |
| 134 | if (most_significant_bigit != 0) { |
| 135 | bigits_[used_digits_] = most_significant_bigit; |
| 136 | used_digits_++; |
| 137 | } |
| 138 | Clamp(); |
| 139 | } |
| 140 | |
| 141 | |
| 142 | void Bignum::AddUInt64(uint64_t operand) { |
| 143 | if (operand == 0) return; |
| 144 | Bignum other; |
| 145 | other.AssignUInt64(operand); |
| 146 | AddBignum(other); |
| 147 | } |
| 148 | |
| 149 | |
| 150 | void Bignum::AddBignum(const Bignum& other) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 151 | DCHECK(IsClamped()); |
| 152 | DCHECK(other.IsClamped()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 153 | |
| 154 | // If this has a greater exponent than other append zero-bigits to this. |
| 155 | // After this call exponent_ <= other.exponent_. |
| 156 | Align(other); |
| 157 | |
| 158 | // There are two possibilities: |
| 159 | // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) |
| 160 | // bbbbb 00000000 |
| 161 | // ---------------- |
| 162 | // ccccccccccc 0000 |
| 163 | // or |
| 164 | // aaaaaaaaaa 0000 |
| 165 | // bbbbbbbbb 0000000 |
| 166 | // ----------------- |
| 167 | // cccccccccccc 0000 |
| 168 | // In both cases we might need a carry bigit. |
| 169 | |
| 170 | EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); |
| 171 | Chunk carry = 0; |
| 172 | int bigit_pos = other.exponent_ - exponent_; |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 173 | DCHECK(bigit_pos >= 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 174 | for (int i = 0; i < other.used_digits_; ++i) { |
| 175 | Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; |
| 176 | bigits_[bigit_pos] = sum & kBigitMask; |
| 177 | carry = sum >> kBigitSize; |
| 178 | bigit_pos++; |
| 179 | } |
| 180 | |
| 181 | while (carry != 0) { |
| 182 | Chunk sum = bigits_[bigit_pos] + carry; |
| 183 | bigits_[bigit_pos] = sum & kBigitMask; |
| 184 | carry = sum >> kBigitSize; |
| 185 | bigit_pos++; |
| 186 | } |
| 187 | used_digits_ = Max(bigit_pos, used_digits_); |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 188 | DCHECK(IsClamped()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 189 | } |
| 190 | |
| 191 | |
| 192 | void Bignum::SubtractBignum(const Bignum& other) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 193 | DCHECK(IsClamped()); |
| 194 | DCHECK(other.IsClamped()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 195 | // We require this to be bigger than other. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 196 | DCHECK(LessEqual(other, *this)); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 197 | |
| 198 | Align(other); |
| 199 | |
| 200 | int offset = other.exponent_ - exponent_; |
| 201 | Chunk borrow = 0; |
| 202 | int i; |
| 203 | for (i = 0; i < other.used_digits_; ++i) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 204 | DCHECK((borrow == 0) || (borrow == 1)); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 205 | Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; |
| 206 | bigits_[i + offset] = difference & kBigitMask; |
| 207 | borrow = difference >> (kChunkSize - 1); |
| 208 | } |
| 209 | while (borrow != 0) { |
| 210 | Chunk difference = bigits_[i + offset] - borrow; |
| 211 | bigits_[i + offset] = difference & kBigitMask; |
| 212 | borrow = difference >> (kChunkSize - 1); |
| 213 | ++i; |
| 214 | } |
| 215 | Clamp(); |
| 216 | } |
| 217 | |
| 218 | |
| 219 | void Bignum::ShiftLeft(int shift_amount) { |
| 220 | if (used_digits_ == 0) return; |
| 221 | exponent_ += shift_amount / kBigitSize; |
| 222 | int local_shift = shift_amount % kBigitSize; |
| 223 | EnsureCapacity(used_digits_ + 1); |
| 224 | BigitsShiftLeft(local_shift); |
| 225 | } |
| 226 | |
| 227 | |
| 228 | void Bignum::MultiplyByUInt32(uint32_t factor) { |
| 229 | if (factor == 1) return; |
| 230 | if (factor == 0) { |
| 231 | Zero(); |
| 232 | return; |
| 233 | } |
| 234 | if (used_digits_ == 0) return; |
| 235 | |
| 236 | // The product of a bigit with the factor is of size kBigitSize + 32. |
| 237 | // Assert that this number + 1 (for the carry) fits into double chunk. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 238 | DCHECK(kDoubleChunkSize >= kBigitSize + 32 + 1); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 239 | DoubleChunk carry = 0; |
| 240 | for (int i = 0; i < used_digits_; ++i) { |
| 241 | DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; |
| 242 | bigits_[i] = static_cast<Chunk>(product & kBigitMask); |
| 243 | carry = (product >> kBigitSize); |
| 244 | } |
| 245 | while (carry != 0) { |
| 246 | EnsureCapacity(used_digits_ + 1); |
Steve Block | 1e0659c | 2011-05-24 12:43:12 +0100 | [diff] [blame] | 247 | bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 248 | used_digits_++; |
| 249 | carry >>= kBigitSize; |
| 250 | } |
| 251 | } |
| 252 | |
| 253 | |
| 254 | void Bignum::MultiplyByUInt64(uint64_t factor) { |
| 255 | if (factor == 1) return; |
| 256 | if (factor == 0) { |
| 257 | Zero(); |
| 258 | return; |
| 259 | } |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 260 | DCHECK(kBigitSize < 32); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 261 | uint64_t carry = 0; |
| 262 | uint64_t low = factor & 0xFFFFFFFF; |
| 263 | uint64_t high = factor >> 32; |
| 264 | for (int i = 0; i < used_digits_; ++i) { |
| 265 | uint64_t product_low = low * bigits_[i]; |
| 266 | uint64_t product_high = high * bigits_[i]; |
| 267 | uint64_t tmp = (carry & kBigitMask) + product_low; |
Steve Block | 1e0659c | 2011-05-24 12:43:12 +0100 | [diff] [blame] | 268 | bigits_[i] = static_cast<Chunk>(tmp & kBigitMask); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 269 | carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + |
| 270 | (product_high << (32 - kBigitSize)); |
| 271 | } |
| 272 | while (carry != 0) { |
| 273 | EnsureCapacity(used_digits_ + 1); |
Steve Block | 1e0659c | 2011-05-24 12:43:12 +0100 | [diff] [blame] | 274 | bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 275 | used_digits_++; |
| 276 | carry >>= kBigitSize; |
| 277 | } |
| 278 | } |
| 279 | |
| 280 | |
| 281 | void Bignum::MultiplyByPowerOfTen(int exponent) { |
| 282 | const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765c793, fa10079d); |
| 283 | const uint16_t kFive1 = 5; |
| 284 | const uint16_t kFive2 = kFive1 * 5; |
| 285 | const uint16_t kFive3 = kFive2 * 5; |
| 286 | const uint16_t kFive4 = kFive3 * 5; |
| 287 | const uint16_t kFive5 = kFive4 * 5; |
| 288 | const uint16_t kFive6 = kFive5 * 5; |
| 289 | const uint32_t kFive7 = kFive6 * 5; |
| 290 | const uint32_t kFive8 = kFive7 * 5; |
| 291 | const uint32_t kFive9 = kFive8 * 5; |
| 292 | const uint32_t kFive10 = kFive9 * 5; |
| 293 | const uint32_t kFive11 = kFive10 * 5; |
| 294 | const uint32_t kFive12 = kFive11 * 5; |
| 295 | const uint32_t kFive13 = kFive12 * 5; |
| 296 | const uint32_t kFive1_to_12[] = |
| 297 | { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, |
| 298 | kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; |
| 299 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 300 | DCHECK(exponent >= 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 301 | if (exponent == 0) return; |
| 302 | if (used_digits_ == 0) return; |
| 303 | |
| 304 | // We shift by exponent at the end just before returning. |
| 305 | int remaining_exponent = exponent; |
| 306 | while (remaining_exponent >= 27) { |
| 307 | MultiplyByUInt64(kFive27); |
| 308 | remaining_exponent -= 27; |
| 309 | } |
| 310 | while (remaining_exponent >= 13) { |
| 311 | MultiplyByUInt32(kFive13); |
| 312 | remaining_exponent -= 13; |
| 313 | } |
| 314 | if (remaining_exponent > 0) { |
| 315 | MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); |
| 316 | } |
| 317 | ShiftLeft(exponent); |
| 318 | } |
| 319 | |
| 320 | |
| 321 | void Bignum::Square() { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 322 | DCHECK(IsClamped()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 323 | int product_length = 2 * used_digits_; |
| 324 | EnsureCapacity(product_length); |
| 325 | |
| 326 | // Comba multiplication: compute each column separately. |
| 327 | // Example: r = a2a1a0 * b2b1b0. |
| 328 | // r = 1 * a0b0 + |
| 329 | // 10 * (a1b0 + a0b1) + |
| 330 | // 100 * (a2b0 + a1b1 + a0b2) + |
| 331 | // 1000 * (a2b1 + a1b2) + |
| 332 | // 10000 * a2b2 |
| 333 | // |
| 334 | // In the worst case we have to accumulate nb-digits products of digit*digit. |
| 335 | // |
| 336 | // Assert that the additional number of bits in a DoubleChunk are enough to |
| 337 | // sum up used_digits of Bigit*Bigit. |
| 338 | if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { |
| 339 | UNIMPLEMENTED(); |
| 340 | } |
| 341 | DoubleChunk accumulator = 0; |
| 342 | // First shift the digits so we don't overwrite them. |
| 343 | int copy_offset = used_digits_; |
| 344 | for (int i = 0; i < used_digits_; ++i) { |
| 345 | bigits_[copy_offset + i] = bigits_[i]; |
| 346 | } |
| 347 | // We have two loops to avoid some 'if's in the loop. |
| 348 | for (int i = 0; i < used_digits_; ++i) { |
| 349 | // Process temporary digit i with power i. |
| 350 | // The sum of the two indices must be equal to i. |
| 351 | int bigit_index1 = i; |
| 352 | int bigit_index2 = 0; |
| 353 | // Sum all of the sub-products. |
| 354 | while (bigit_index1 >= 0) { |
| 355 | Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
| 356 | Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
| 357 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
| 358 | bigit_index1--; |
| 359 | bigit_index2++; |
| 360 | } |
| 361 | bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
| 362 | accumulator >>= kBigitSize; |
| 363 | } |
| 364 | for (int i = used_digits_; i < product_length; ++i) { |
| 365 | int bigit_index1 = used_digits_ - 1; |
| 366 | int bigit_index2 = i - bigit_index1; |
| 367 | // Invariant: sum of both indices is again equal to i. |
| 368 | // Inner loop runs 0 times on last iteration, emptying accumulator. |
| 369 | while (bigit_index2 < used_digits_) { |
| 370 | Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
| 371 | Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
| 372 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
| 373 | bigit_index1--; |
| 374 | bigit_index2++; |
| 375 | } |
| 376 | // The overwritten bigits_[i] will never be read in further loop iterations, |
| 377 | // because bigit_index1 and bigit_index2 are always greater |
| 378 | // than i - used_digits_. |
| 379 | bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
| 380 | accumulator >>= kBigitSize; |
| 381 | } |
| 382 | // Since the result was guaranteed to lie inside the number the |
| 383 | // accumulator must be 0 now. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 384 | DCHECK(accumulator == 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 385 | |
| 386 | // Don't forget to update the used_digits and the exponent. |
| 387 | used_digits_ = product_length; |
| 388 | exponent_ *= 2; |
| 389 | Clamp(); |
| 390 | } |
| 391 | |
| 392 | |
| 393 | void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 394 | DCHECK(base != 0); |
| 395 | DCHECK(power_exponent >= 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 396 | if (power_exponent == 0) { |
| 397 | AssignUInt16(1); |
| 398 | return; |
| 399 | } |
| 400 | Zero(); |
| 401 | int shifts = 0; |
| 402 | // We expect base to be in range 2-32, and most often to be 10. |
| 403 | // It does not make much sense to implement different algorithms for counting |
| 404 | // the bits. |
| 405 | while ((base & 1) == 0) { |
| 406 | base >>= 1; |
| 407 | shifts++; |
| 408 | } |
| 409 | int bit_size = 0; |
| 410 | int tmp_base = base; |
| 411 | while (tmp_base != 0) { |
| 412 | tmp_base >>= 1; |
| 413 | bit_size++; |
| 414 | } |
| 415 | int final_size = bit_size * power_exponent; |
| 416 | // 1 extra bigit for the shifting, and one for rounded final_size. |
| 417 | EnsureCapacity(final_size / kBigitSize + 2); |
| 418 | |
| 419 | // Left to Right exponentiation. |
| 420 | int mask = 1; |
| 421 | while (power_exponent >= mask) mask <<= 1; |
| 422 | |
| 423 | // The mask is now pointing to the bit above the most significant 1-bit of |
| 424 | // power_exponent. |
| 425 | // Get rid of first 1-bit; |
| 426 | mask >>= 2; |
| 427 | uint64_t this_value = base; |
| 428 | |
| 429 | bool delayed_multipliciation = false; |
| 430 | const uint64_t max_32bits = 0xFFFFFFFF; |
| 431 | while (mask != 0 && this_value <= max_32bits) { |
| 432 | this_value = this_value * this_value; |
| 433 | // Verify that there is enough space in this_value to perform the |
| 434 | // multiplication. The first bit_size bits must be 0. |
| 435 | if ((power_exponent & mask) != 0) { |
| 436 | uint64_t base_bits_mask = |
| 437 | ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); |
| 438 | bool high_bits_zero = (this_value & base_bits_mask) == 0; |
| 439 | if (high_bits_zero) { |
| 440 | this_value *= base; |
| 441 | } else { |
| 442 | delayed_multipliciation = true; |
| 443 | } |
| 444 | } |
| 445 | mask >>= 1; |
| 446 | } |
| 447 | AssignUInt64(this_value); |
| 448 | if (delayed_multipliciation) { |
| 449 | MultiplyByUInt32(base); |
| 450 | } |
| 451 | |
| 452 | // Now do the same thing as a bignum. |
| 453 | while (mask != 0) { |
| 454 | Square(); |
| 455 | if ((power_exponent & mask) != 0) { |
| 456 | MultiplyByUInt32(base); |
| 457 | } |
| 458 | mask >>= 1; |
| 459 | } |
| 460 | |
| 461 | // And finally add the saved shifts. |
| 462 | ShiftLeft(shifts * power_exponent); |
| 463 | } |
| 464 | |
| 465 | |
| 466 | // Precondition: this/other < 16bit. |
| 467 | uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 468 | DCHECK(IsClamped()); |
| 469 | DCHECK(other.IsClamped()); |
| 470 | DCHECK(other.used_digits_ > 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 471 | |
| 472 | // Easy case: if we have less digits than the divisor than the result is 0. |
| 473 | // Note: this handles the case where this == 0, too. |
| 474 | if (BigitLength() < other.BigitLength()) { |
| 475 | return 0; |
| 476 | } |
| 477 | |
| 478 | Align(other); |
| 479 | |
| 480 | uint16_t result = 0; |
| 481 | |
| 482 | // Start by removing multiples of 'other' until both numbers have the same |
| 483 | // number of digits. |
| 484 | while (BigitLength() > other.BigitLength()) { |
| 485 | // This naive approach is extremely inefficient if the this divided other |
| 486 | // might be big. This function is implemented for doubleToString where |
| 487 | // the result should be small (less than 10). |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 488 | DCHECK(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 489 | // Remove the multiples of the first digit. |
| 490 | // Example this = 23 and other equals 9. -> Remove 2 multiples. |
| 491 | result += bigits_[used_digits_ - 1]; |
| 492 | SubtractTimes(other, bigits_[used_digits_ - 1]); |
| 493 | } |
| 494 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 495 | DCHECK(BigitLength() == other.BigitLength()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 496 | |
| 497 | // Both bignums are at the same length now. |
| 498 | // Since other has more than 0 digits we know that the access to |
| 499 | // bigits_[used_digits_ - 1] is safe. |
| 500 | Chunk this_bigit = bigits_[used_digits_ - 1]; |
| 501 | Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; |
| 502 | |
| 503 | if (other.used_digits_ == 1) { |
| 504 | // Shortcut for easy (and common) case. |
| 505 | int quotient = this_bigit / other_bigit; |
| 506 | bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; |
| 507 | result += quotient; |
| 508 | Clamp(); |
| 509 | return result; |
| 510 | } |
| 511 | |
| 512 | int division_estimate = this_bigit / (other_bigit + 1); |
| 513 | result += division_estimate; |
| 514 | SubtractTimes(other, division_estimate); |
| 515 | |
| 516 | if (other_bigit * (division_estimate + 1) > this_bigit) { |
| 517 | // No need to even try to subtract. Even if other's remaining digits were 0 |
| 518 | // another subtraction would be too much. |
| 519 | return result; |
| 520 | } |
| 521 | |
| 522 | while (LessEqual(other, *this)) { |
| 523 | SubtractBignum(other); |
| 524 | result++; |
| 525 | } |
| 526 | return result; |
| 527 | } |
| 528 | |
| 529 | |
| 530 | template<typename S> |
| 531 | static int SizeInHexChars(S number) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 532 | DCHECK(number > 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 533 | int result = 0; |
| 534 | while (number != 0) { |
| 535 | number >>= 4; |
| 536 | result++; |
| 537 | } |
| 538 | return result; |
| 539 | } |
| 540 | |
| 541 | |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 542 | bool Bignum::ToHexString(char* buffer, int buffer_size) const { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 543 | DCHECK(IsClamped()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 544 | // Each bigit must be printable as separate hex-character. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 545 | DCHECK(kBigitSize % 4 == 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 546 | const int kHexCharsPerBigit = kBigitSize / 4; |
| 547 | |
| 548 | if (used_digits_ == 0) { |
| 549 | if (buffer_size < 2) return false; |
| 550 | buffer[0] = '0'; |
| 551 | buffer[1] = '\0'; |
| 552 | return true; |
| 553 | } |
| 554 | // We add 1 for the terminating '\0' character. |
| 555 | int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + |
| 556 | SizeInHexChars(bigits_[used_digits_ - 1]) + 1; |
| 557 | if (needed_chars > buffer_size) return false; |
| 558 | int string_index = needed_chars - 1; |
| 559 | buffer[string_index--] = '\0'; |
| 560 | for (int i = 0; i < exponent_; ++i) { |
| 561 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
| 562 | buffer[string_index--] = '0'; |
| 563 | } |
| 564 | } |
| 565 | for (int i = 0; i < used_digits_ - 1; ++i) { |
| 566 | Chunk current_bigit = bigits_[i]; |
| 567 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
| 568 | buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); |
| 569 | current_bigit >>= 4; |
| 570 | } |
| 571 | } |
| 572 | // And finally the last bigit. |
| 573 | Chunk most_significant_bigit = bigits_[used_digits_ - 1]; |
| 574 | while (most_significant_bigit != 0) { |
| 575 | buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); |
| 576 | most_significant_bigit >>= 4; |
| 577 | } |
| 578 | return true; |
| 579 | } |
| 580 | |
| 581 | |
| 582 | Bignum::Chunk Bignum::BigitAt(int index) const { |
| 583 | if (index >= BigitLength()) return 0; |
| 584 | if (index < exponent_) return 0; |
| 585 | return bigits_[index - exponent_]; |
| 586 | } |
| 587 | |
| 588 | |
| 589 | int Bignum::Compare(const Bignum& a, const Bignum& b) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 590 | DCHECK(a.IsClamped()); |
| 591 | DCHECK(b.IsClamped()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 592 | int bigit_length_a = a.BigitLength(); |
| 593 | int bigit_length_b = b.BigitLength(); |
| 594 | if (bigit_length_a < bigit_length_b) return -1; |
| 595 | if (bigit_length_a > bigit_length_b) return +1; |
| 596 | for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { |
| 597 | Chunk bigit_a = a.BigitAt(i); |
| 598 | Chunk bigit_b = b.BigitAt(i); |
| 599 | if (bigit_a < bigit_b) return -1; |
| 600 | if (bigit_a > bigit_b) return +1; |
| 601 | // Otherwise they are equal up to this digit. Try the next digit. |
| 602 | } |
| 603 | return 0; |
| 604 | } |
| 605 | |
| 606 | |
| 607 | int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 608 | DCHECK(a.IsClamped()); |
| 609 | DCHECK(b.IsClamped()); |
| 610 | DCHECK(c.IsClamped()); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 611 | if (a.BigitLength() < b.BigitLength()) { |
| 612 | return PlusCompare(b, a, c); |
| 613 | } |
| 614 | if (a.BigitLength() + 1 < c.BigitLength()) return -1; |
| 615 | if (a.BigitLength() > c.BigitLength()) return +1; |
| 616 | // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than |
| 617 | // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one |
| 618 | // of 'a'. |
| 619 | if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { |
| 620 | return -1; |
| 621 | } |
| 622 | |
| 623 | Chunk borrow = 0; |
| 624 | // Starting at min_exponent all digits are == 0. So no need to compare them. |
| 625 | int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); |
| 626 | for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { |
| 627 | Chunk chunk_a = a.BigitAt(i); |
| 628 | Chunk chunk_b = b.BigitAt(i); |
| 629 | Chunk chunk_c = c.BigitAt(i); |
| 630 | Chunk sum = chunk_a + chunk_b; |
| 631 | if (sum > chunk_c + borrow) { |
| 632 | return +1; |
| 633 | } else { |
| 634 | borrow = chunk_c + borrow - sum; |
| 635 | if (borrow > 1) return -1; |
| 636 | borrow <<= kBigitSize; |
| 637 | } |
| 638 | } |
| 639 | if (borrow == 0) return 0; |
| 640 | return -1; |
| 641 | } |
| 642 | |
| 643 | |
| 644 | void Bignum::Clamp() { |
| 645 | while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { |
| 646 | used_digits_--; |
| 647 | } |
| 648 | if (used_digits_ == 0) { |
| 649 | // Zero. |
| 650 | exponent_ = 0; |
| 651 | } |
| 652 | } |
| 653 | |
| 654 | |
| 655 | bool Bignum::IsClamped() const { |
| 656 | return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; |
| 657 | } |
| 658 | |
| 659 | |
| 660 | void Bignum::Zero() { |
| 661 | for (int i = 0; i < used_digits_; ++i) { |
| 662 | bigits_[i] = 0; |
| 663 | } |
| 664 | used_digits_ = 0; |
| 665 | exponent_ = 0; |
| 666 | } |
| 667 | |
| 668 | |
| 669 | void Bignum::Align(const Bignum& other) { |
| 670 | if (exponent_ > other.exponent_) { |
| 671 | // If "X" represents a "hidden" digit (by the exponent) then we are in the |
| 672 | // following case (a == this, b == other): |
| 673 | // a: aaaaaaXXXX or a: aaaaaXXX |
| 674 | // b: bbbbbbX b: bbbbbbbbXX |
| 675 | // We replace some of the hidden digits (X) of a with 0 digits. |
| 676 | // a: aaaaaa000X or a: aaaaa0XX |
| 677 | int zero_digits = exponent_ - other.exponent_; |
| 678 | EnsureCapacity(used_digits_ + zero_digits); |
| 679 | for (int i = used_digits_ - 1; i >= 0; --i) { |
| 680 | bigits_[i + zero_digits] = bigits_[i]; |
| 681 | } |
| 682 | for (int i = 0; i < zero_digits; ++i) { |
| 683 | bigits_[i] = 0; |
| 684 | } |
| 685 | used_digits_ += zero_digits; |
| 686 | exponent_ -= zero_digits; |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 687 | DCHECK(used_digits_ >= 0); |
| 688 | DCHECK(exponent_ >= 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 689 | } |
| 690 | } |
| 691 | |
| 692 | |
| 693 | void Bignum::BigitsShiftLeft(int shift_amount) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 694 | DCHECK(shift_amount < kBigitSize); |
| 695 | DCHECK(shift_amount >= 0); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 696 | Chunk carry = 0; |
| 697 | for (int i = 0; i < used_digits_; ++i) { |
| 698 | Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); |
| 699 | bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; |
| 700 | carry = new_carry; |
| 701 | } |
| 702 | if (carry != 0) { |
| 703 | bigits_[used_digits_] = carry; |
| 704 | used_digits_++; |
| 705 | } |
| 706 | } |
| 707 | |
| 708 | |
| 709 | void Bignum::SubtractTimes(const Bignum& other, int factor) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 710 | #ifdef DEBUG |
| 711 | Bignum a, b; |
| 712 | a.AssignBignum(*this); |
| 713 | b.AssignBignum(other); |
| 714 | b.MultiplyByUInt32(factor); |
| 715 | a.SubtractBignum(b); |
| 716 | #endif |
| 717 | DCHECK(exponent_ <= other.exponent_); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 718 | if (factor < 3) { |
| 719 | for (int i = 0; i < factor; ++i) { |
| 720 | SubtractBignum(other); |
| 721 | } |
| 722 | return; |
| 723 | } |
| 724 | Chunk borrow = 0; |
| 725 | int exponent_diff = other.exponent_ - exponent_; |
| 726 | for (int i = 0; i < other.used_digits_; ++i) { |
| 727 | DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; |
| 728 | DoubleChunk remove = borrow + product; |
Steve Block | 1e0659c | 2011-05-24 12:43:12 +0100 | [diff] [blame] | 729 | Chunk difference = |
| 730 | bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 731 | bigits_[i + exponent_diff] = difference & kBigitMask; |
| 732 | borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + |
| 733 | (remove >> kBigitSize)); |
| 734 | } |
| 735 | for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { |
| 736 | if (borrow == 0) return; |
| 737 | Chunk difference = bigits_[i] - borrow; |
| 738 | bigits_[i] = difference & kBigitMask; |
| 739 | borrow = difference >> (kChunkSize - 1); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 740 | } |
| 741 | Clamp(); |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 742 | DCHECK(Bignum::Equal(a, *this)); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 743 | } |
| 744 | |
| 745 | |
Ben Murdoch | 4a90d5f | 2016-03-22 12:00:34 +0000 | [diff] [blame] | 746 | } // namespace internal |
| 747 | } // namespace v8 |