Home | History | Annotate | Download | only in src
      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