michael@0: // Copyright 2010 the V8 project authors. All rights reserved.
michael@0: // Redistribution and use in source and binary forms, with or without
michael@0: // modification, are permitted provided that the following conditions are
michael@0: // met:
michael@0: //
michael@0: //     * Redistributions of source code must retain the above copyright
michael@0: //       notice, this list of conditions and the following disclaimer.
michael@0: //     * Redistributions in binary form must reproduce the above
michael@0: //       copyright notice, this list of conditions and the following
michael@0: //       disclaimer in the documentation and/or other materials provided
michael@0: //       with the distribution.
michael@0: //     * Neither the name of Google Inc. nor the names of its
michael@0: //       contributors may be used to endorse or promote products derived
michael@0: //       from this software without specific prior written permission.
michael@0: //
michael@0: // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
michael@0: // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
michael@0: // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
michael@0: // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
michael@0: // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
michael@0: // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
michael@0: // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
michael@0: // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
michael@0: // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
michael@0: // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
michael@0: // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
michael@0: 
michael@0: #include "bignum.h"
michael@0: #include "utils.h"
michael@0: 
michael@0: namespace double_conversion {
michael@0: 
michael@0: Bignum::Bignum()
michael@0:     : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
michael@0:   for (int i = 0; i < kBigitCapacity; ++i) {
michael@0:     bigits_[i] = 0;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: template<typename S>
michael@0: static int BitSize(S value) {
michael@0:   return 8 * sizeof(value);
michael@0: }
michael@0: 
michael@0: // Guaranteed to lie in one Bigit.
michael@0: void Bignum::AssignUInt16(uint16_t value) {
michael@0:   ASSERT(kBigitSize >= BitSize(value));
michael@0:   Zero();
michael@0:   if (value == 0) return;
michael@0: 
michael@0:   EnsureCapacity(1);
michael@0:   bigits_[0] = value;
michael@0:   used_digits_ = 1;
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::AssignUInt64(uint64_t value) {
michael@0:   const int kUInt64Size = 64;
michael@0: 
michael@0:   Zero();
michael@0:   if (value == 0) return;
michael@0: 
michael@0:   int needed_bigits = kUInt64Size / kBigitSize + 1;
michael@0:   EnsureCapacity(needed_bigits);
michael@0:   for (int i = 0; i < needed_bigits; ++i) {
michael@0:     bigits_[i] = value & kBigitMask;
michael@0:     value = value >> kBigitSize;
michael@0:   }
michael@0:   used_digits_ = needed_bigits;
michael@0:   Clamp();
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::AssignBignum(const Bignum& other) {
michael@0:   exponent_ = other.exponent_;
michael@0:   for (int i = 0; i < other.used_digits_; ++i) {
michael@0:     bigits_[i] = other.bigits_[i];
michael@0:   }
michael@0:   // Clear the excess digits (if there were any).
michael@0:   for (int i = other.used_digits_; i < used_digits_; ++i) {
michael@0:     bigits_[i] = 0;
michael@0:   }
michael@0:   used_digits_ = other.used_digits_;
michael@0: }
michael@0: 
michael@0: 
michael@0: static uint64_t ReadUInt64(Vector<const char> buffer,
michael@0:                            int from,
michael@0:                            int digits_to_read) {
michael@0:   uint64_t result = 0;
michael@0:   for (int i = from; i < from + digits_to_read; ++i) {
michael@0:     int digit = buffer[i] - '0';
michael@0:     ASSERT(0 <= digit && digit <= 9);
michael@0:     result = result * 10 + digit;
michael@0:   }
michael@0:   return result;
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::AssignDecimalString(Vector<const char> value) {
michael@0:   // 2^64 = 18446744073709551616 > 10^19
michael@0:   const int kMaxUint64DecimalDigits = 19;
michael@0:   Zero();
michael@0:   int length = value.length();
michael@0:   int pos = 0;
michael@0:   // Let's just say that each digit needs 4 bits.
michael@0:   while (length >= kMaxUint64DecimalDigits) {
michael@0:     uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
michael@0:     pos += kMaxUint64DecimalDigits;
michael@0:     length -= kMaxUint64DecimalDigits;
michael@0:     MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
michael@0:     AddUInt64(digits);
michael@0:   }
michael@0:   uint64_t digits = ReadUInt64(value, pos, length);
michael@0:   MultiplyByPowerOfTen(length);
michael@0:   AddUInt64(digits);
michael@0:   Clamp();
michael@0: }
michael@0: 
michael@0: 
michael@0: static int HexCharValue(char c) {
michael@0:   if ('0' <= c && c <= '9') return c - '0';
michael@0:   if ('a' <= c && c <= 'f') return 10 + c - 'a';
michael@0:   if ('A' <= c && c <= 'F') return 10 + c - 'A';
michael@0:   UNREACHABLE();
michael@0:   return 0;  // To make compiler happy.
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::AssignHexString(Vector<const char> value) {
michael@0:   Zero();
michael@0:   int length = value.length();
michael@0: 
michael@0:   int needed_bigits = length * 4 / kBigitSize + 1;
michael@0:   EnsureCapacity(needed_bigits);
michael@0:   int string_index = length - 1;
michael@0:   for (int i = 0; i < needed_bigits - 1; ++i) {
michael@0:     // These bigits are guaranteed to be "full".
michael@0:     Chunk current_bigit = 0;
michael@0:     for (int j = 0; j < kBigitSize / 4; j++) {
michael@0:       current_bigit += HexCharValue(value[string_index--]) << (j * 4);
michael@0:     }
michael@0:     bigits_[i] = current_bigit;
michael@0:   }
michael@0:   used_digits_ = needed_bigits - 1;
michael@0: 
michael@0:   Chunk most_significant_bigit = 0;  // Could be = 0;
michael@0:   for (int j = 0; j <= string_index; ++j) {
michael@0:     most_significant_bigit <<= 4;
michael@0:     most_significant_bigit += HexCharValue(value[j]);
michael@0:   }
michael@0:   if (most_significant_bigit != 0) {
michael@0:     bigits_[used_digits_] = most_significant_bigit;
michael@0:     used_digits_++;
michael@0:   }
michael@0:   Clamp();
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::AddUInt64(uint64_t operand) {
michael@0:   if (operand == 0) return;
michael@0:   Bignum other;
michael@0:   other.AssignUInt64(operand);
michael@0:   AddBignum(other);
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::AddBignum(const Bignum& other) {
michael@0:   ASSERT(IsClamped());
michael@0:   ASSERT(other.IsClamped());
michael@0: 
michael@0:   // If this has a greater exponent than other append zero-bigits to this.
michael@0:   // After this call exponent_ <= other.exponent_.
michael@0:   Align(other);
michael@0: 
michael@0:   // There are two possibilities:
michael@0:   //   aaaaaaaaaaa 0000  (where the 0s represent a's exponent)
michael@0:   //     bbbbb 00000000
michael@0:   //   ----------------
michael@0:   //   ccccccccccc 0000
michael@0:   // or
michael@0:   //    aaaaaaaaaa 0000
michael@0:   //  bbbbbbbbb 0000000
michael@0:   //  -----------------
michael@0:   //  cccccccccccc 0000
michael@0:   // In both cases we might need a carry bigit.
michael@0: 
michael@0:   EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
michael@0:   Chunk carry = 0;
michael@0:   int bigit_pos = other.exponent_ - exponent_;
michael@0:   ASSERT(bigit_pos >= 0);
michael@0:   for (int i = 0; i < other.used_digits_; ++i) {
michael@0:     Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
michael@0:     bigits_[bigit_pos] = sum & kBigitMask;
michael@0:     carry = sum >> kBigitSize;
michael@0:     bigit_pos++;
michael@0:   }
michael@0: 
michael@0:   while (carry != 0) {
michael@0:     Chunk sum = bigits_[bigit_pos] + carry;
michael@0:     bigits_[bigit_pos] = sum & kBigitMask;
michael@0:     carry = sum >> kBigitSize;
michael@0:     bigit_pos++;
michael@0:   }
michael@0:   used_digits_ = Max(bigit_pos, used_digits_);
michael@0:   ASSERT(IsClamped());
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::SubtractBignum(const Bignum& other) {
michael@0:   ASSERT(IsClamped());
michael@0:   ASSERT(other.IsClamped());
michael@0:   // We require this to be bigger than other.
michael@0:   ASSERT(LessEqual(other, *this));
michael@0: 
michael@0:   Align(other);
michael@0: 
michael@0:   int offset = other.exponent_ - exponent_;
michael@0:   Chunk borrow = 0;
michael@0:   int i;
michael@0:   for (i = 0; i < other.used_digits_; ++i) {
michael@0:     ASSERT((borrow == 0) || (borrow == 1));
michael@0:     Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
michael@0:     bigits_[i + offset] = difference & kBigitMask;
michael@0:     borrow = difference >> (kChunkSize - 1);
michael@0:   }
michael@0:   while (borrow != 0) {
michael@0:     Chunk difference = bigits_[i + offset] - borrow;
michael@0:     bigits_[i + offset] = difference & kBigitMask;
michael@0:     borrow = difference >> (kChunkSize - 1);
michael@0:     ++i;
michael@0:   }
michael@0:   Clamp();
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::ShiftLeft(int shift_amount) {
michael@0:   if (used_digits_ == 0) return;
michael@0:   exponent_ += shift_amount / kBigitSize;
michael@0:   int local_shift = shift_amount % kBigitSize;
michael@0:   EnsureCapacity(used_digits_ + 1);
michael@0:   BigitsShiftLeft(local_shift);
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::MultiplyByUInt32(uint32_t factor) {
michael@0:   if (factor == 1) return;
michael@0:   if (factor == 0) {
michael@0:     Zero();
michael@0:     return;
michael@0:   }
michael@0:   if (used_digits_ == 0) return;
michael@0: 
michael@0:   // The product of a bigit with the factor is of size kBigitSize + 32.
michael@0:   // Assert that this number + 1 (for the carry) fits into double chunk.
michael@0:   ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
michael@0:   DoubleChunk carry = 0;
michael@0:   for (int i = 0; i < used_digits_; ++i) {
michael@0:     DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
michael@0:     bigits_[i] = static_cast<Chunk>(product & kBigitMask);
michael@0:     carry = (product >> kBigitSize);
michael@0:   }
michael@0:   while (carry != 0) {
michael@0:     EnsureCapacity(used_digits_ + 1);
michael@0:     bigits_[used_digits_] = carry & kBigitMask;
michael@0:     used_digits_++;
michael@0:     carry >>= kBigitSize;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::MultiplyByUInt64(uint64_t factor) {
michael@0:   if (factor == 1) return;
michael@0:   if (factor == 0) {
michael@0:     Zero();
michael@0:     return;
michael@0:   }
michael@0:   ASSERT(kBigitSize < 32);
michael@0:   uint64_t carry = 0;
michael@0:   uint64_t low = factor & 0xFFFFFFFF;
michael@0:   uint64_t high = factor >> 32;
michael@0:   for (int i = 0; i < used_digits_; ++i) {
michael@0:     uint64_t product_low = low * bigits_[i];
michael@0:     uint64_t product_high = high * bigits_[i];
michael@0:     uint64_t tmp = (carry & kBigitMask) + product_low;
michael@0:     bigits_[i] = tmp & kBigitMask;
michael@0:     carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
michael@0:         (product_high << (32 - kBigitSize));
michael@0:   }
michael@0:   while (carry != 0) {
michael@0:     EnsureCapacity(used_digits_ + 1);
michael@0:     bigits_[used_digits_] = carry & kBigitMask;
michael@0:     used_digits_++;
michael@0:     carry >>= kBigitSize;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::MultiplyByPowerOfTen(int exponent) {
michael@0:   const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
michael@0:   const uint16_t kFive1 = 5;
michael@0:   const uint16_t kFive2 = kFive1 * 5;
michael@0:   const uint16_t kFive3 = kFive2 * 5;
michael@0:   const uint16_t kFive4 = kFive3 * 5;
michael@0:   const uint16_t kFive5 = kFive4 * 5;
michael@0:   const uint16_t kFive6 = kFive5 * 5;
michael@0:   const uint32_t kFive7 = kFive6 * 5;
michael@0:   const uint32_t kFive8 = kFive7 * 5;
michael@0:   const uint32_t kFive9 = kFive8 * 5;
michael@0:   const uint32_t kFive10 = kFive9 * 5;
michael@0:   const uint32_t kFive11 = kFive10 * 5;
michael@0:   const uint32_t kFive12 = kFive11 * 5;
michael@0:   const uint32_t kFive13 = kFive12 * 5;
michael@0:   const uint32_t kFive1_to_12[] =
michael@0:       { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
michael@0:         kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
michael@0: 
michael@0:   ASSERT(exponent >= 0);
michael@0:   if (exponent == 0) return;
michael@0:   if (used_digits_ == 0) return;
michael@0: 
michael@0:   // We shift by exponent at the end just before returning.
michael@0:   int remaining_exponent = exponent;
michael@0:   while (remaining_exponent >= 27) {
michael@0:     MultiplyByUInt64(kFive27);
michael@0:     remaining_exponent -= 27;
michael@0:   }
michael@0:   while (remaining_exponent >= 13) {
michael@0:     MultiplyByUInt32(kFive13);
michael@0:     remaining_exponent -= 13;
michael@0:   }
michael@0:   if (remaining_exponent > 0) {
michael@0:     MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
michael@0:   }
michael@0:   ShiftLeft(exponent);
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::Square() {
michael@0:   ASSERT(IsClamped());
michael@0:   int product_length = 2 * used_digits_;
michael@0:   EnsureCapacity(product_length);
michael@0: 
michael@0:   // Comba multiplication: compute each column separately.
michael@0:   // Example: r = a2a1a0 * b2b1b0.
michael@0:   //    r =  1    * a0b0 +
michael@0:   //        10    * (a1b0 + a0b1) +
michael@0:   //        100   * (a2b0 + a1b1 + a0b2) +
michael@0:   //        1000  * (a2b1 + a1b2) +
michael@0:   //        10000 * a2b2
michael@0:   //
michael@0:   // In the worst case we have to accumulate nb-digits products of digit*digit.
michael@0:   //
michael@0:   // Assert that the additional number of bits in a DoubleChunk are enough to
michael@0:   // sum up used_digits of Bigit*Bigit.
michael@0:   if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
michael@0:     UNIMPLEMENTED();
michael@0:   }
michael@0:   DoubleChunk accumulator = 0;
michael@0:   // First shift the digits so we don't overwrite them.
michael@0:   int copy_offset = used_digits_;
michael@0:   for (int i = 0; i < used_digits_; ++i) {
michael@0:     bigits_[copy_offset + i] = bigits_[i];
michael@0:   }
michael@0:   // We have two loops to avoid some 'if's in the loop.
michael@0:   for (int i = 0; i < used_digits_; ++i) {
michael@0:     // Process temporary digit i with power i.
michael@0:     // The sum of the two indices must be equal to i.
michael@0:     int bigit_index1 = i;
michael@0:     int bigit_index2 = 0;
michael@0:     // Sum all of the sub-products.
michael@0:     while (bigit_index1 >= 0) {
michael@0:       Chunk chunk1 = bigits_[copy_offset + bigit_index1];
michael@0:       Chunk chunk2 = bigits_[copy_offset + bigit_index2];
michael@0:       accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
michael@0:       bigit_index1--;
michael@0:       bigit_index2++;
michael@0:     }
michael@0:     bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
michael@0:     accumulator >>= kBigitSize;
michael@0:   }
michael@0:   for (int i = used_digits_; i < product_length; ++i) {
michael@0:     int bigit_index1 = used_digits_ - 1;
michael@0:     int bigit_index2 = i - bigit_index1;
michael@0:     // Invariant: sum of both indices is again equal to i.
michael@0:     // Inner loop runs 0 times on last iteration, emptying accumulator.
michael@0:     while (bigit_index2 < used_digits_) {
michael@0:       Chunk chunk1 = bigits_[copy_offset + bigit_index1];
michael@0:       Chunk chunk2 = bigits_[copy_offset + bigit_index2];
michael@0:       accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
michael@0:       bigit_index1--;
michael@0:       bigit_index2++;
michael@0:     }
michael@0:     // The overwritten bigits_[i] will never be read in further loop iterations,
michael@0:     // because bigit_index1 and bigit_index2 are always greater
michael@0:     // than i - used_digits_.
michael@0:     bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
michael@0:     accumulator >>= kBigitSize;
michael@0:   }
michael@0:   // Since the result was guaranteed to lie inside the number the
michael@0:   // accumulator must be 0 now.
michael@0:   ASSERT(accumulator == 0);
michael@0: 
michael@0:   // Don't forget to update the used_digits and the exponent.
michael@0:   used_digits_ = product_length;
michael@0:   exponent_ *= 2;
michael@0:   Clamp();
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
michael@0:   ASSERT(base != 0);
michael@0:   ASSERT(power_exponent >= 0);
michael@0:   if (power_exponent == 0) {
michael@0:     AssignUInt16(1);
michael@0:     return;
michael@0:   }
michael@0:   Zero();
michael@0:   int shifts = 0;
michael@0:   // We expect base to be in range 2-32, and most often to be 10.
michael@0:   // It does not make much sense to implement different algorithms for counting
michael@0:   // the bits.
michael@0:   while ((base & 1) == 0) {
michael@0:     base >>= 1;
michael@0:     shifts++;
michael@0:   }
michael@0:   int bit_size = 0;
michael@0:   int tmp_base = base;
michael@0:   while (tmp_base != 0) {
michael@0:     tmp_base >>= 1;
michael@0:     bit_size++;
michael@0:   }
michael@0:   int final_size = bit_size * power_exponent;
michael@0:   // 1 extra bigit for the shifting, and one for rounded final_size.
michael@0:   EnsureCapacity(final_size / kBigitSize + 2);
michael@0: 
michael@0:   // Left to Right exponentiation.
michael@0:   int mask = 1;
michael@0:   while (power_exponent >= mask) mask <<= 1;
michael@0: 
michael@0:   // The mask is now pointing to the bit above the most significant 1-bit of
michael@0:   // power_exponent.
michael@0:   // Get rid of first 1-bit;
michael@0:   mask >>= 2;
michael@0:   uint64_t this_value = base;
michael@0: 
michael@0:   bool delayed_multipliciation = false;
michael@0:   const uint64_t max_32bits = 0xFFFFFFFF;
michael@0:   while (mask != 0 && this_value <= max_32bits) {
michael@0:     this_value = this_value * this_value;
michael@0:     // Verify that there is enough space in this_value to perform the
michael@0:     // multiplication.  The first bit_size bits must be 0.
michael@0:     if ((power_exponent & mask) != 0) {
michael@0:       uint64_t base_bits_mask =
michael@0:           ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
michael@0:       bool high_bits_zero = (this_value & base_bits_mask) == 0;
michael@0:       if (high_bits_zero) {
michael@0:         this_value *= base;
michael@0:       } else {
michael@0:         delayed_multipliciation = true;
michael@0:       }
michael@0:     }
michael@0:     mask >>= 1;
michael@0:   }
michael@0:   AssignUInt64(this_value);
michael@0:   if (delayed_multipliciation) {
michael@0:     MultiplyByUInt32(base);
michael@0:   }
michael@0: 
michael@0:   // Now do the same thing as a bignum.
michael@0:   while (mask != 0) {
michael@0:     Square();
michael@0:     if ((power_exponent & mask) != 0) {
michael@0:       MultiplyByUInt32(base);
michael@0:     }
michael@0:     mask >>= 1;
michael@0:   }
michael@0: 
michael@0:   // And finally add the saved shifts.
michael@0:   ShiftLeft(shifts * power_exponent);
michael@0: }
michael@0: 
michael@0: 
michael@0: // Precondition: this/other < 16bit.
michael@0: uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
michael@0:   ASSERT(IsClamped());
michael@0:   ASSERT(other.IsClamped());
michael@0:   ASSERT(other.used_digits_ > 0);
michael@0: 
michael@0:   // Easy case: if we have less digits than the divisor than the result is 0.
michael@0:   // Note: this handles the case where this == 0, too.
michael@0:   if (BigitLength() < other.BigitLength()) {
michael@0:     return 0;
michael@0:   }
michael@0: 
michael@0:   Align(other);
michael@0: 
michael@0:   uint16_t result = 0;
michael@0: 
michael@0:   // Start by removing multiples of 'other' until both numbers have the same
michael@0:   // number of digits.
michael@0:   while (BigitLength() > other.BigitLength()) {
michael@0:     // This naive approach is extremely inefficient if `this` divided by other
michael@0:     // is big. This function is implemented for doubleToString where
michael@0:     // the result should be small (less than 10).
michael@0:     ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
michael@0:     // Remove the multiples of the first digit.
michael@0:     // Example this = 23 and other equals 9. -> Remove 2 multiples.
michael@0:     result += bigits_[used_digits_ - 1];
michael@0:     SubtractTimes(other, bigits_[used_digits_ - 1]);
michael@0:   }
michael@0: 
michael@0:   ASSERT(BigitLength() == other.BigitLength());
michael@0: 
michael@0:   // Both bignums are at the same length now.
michael@0:   // Since other has more than 0 digits we know that the access to
michael@0:   // bigits_[used_digits_ - 1] is safe.
michael@0:   Chunk this_bigit = bigits_[used_digits_ - 1];
michael@0:   Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
michael@0: 
michael@0:   if (other.used_digits_ == 1) {
michael@0:     // Shortcut for easy (and common) case.
michael@0:     int quotient = this_bigit / other_bigit;
michael@0:     bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
michael@0:     result += quotient;
michael@0:     Clamp();
michael@0:     return result;
michael@0:   }
michael@0: 
michael@0:   int division_estimate = this_bigit / (other_bigit + 1);
michael@0:   result += division_estimate;
michael@0:   SubtractTimes(other, division_estimate);
michael@0: 
michael@0:   if (other_bigit * (division_estimate + 1) > this_bigit) {
michael@0:     // No need to even try to subtract. Even if other's remaining digits were 0
michael@0:     // another subtraction would be too much.
michael@0:     return result;
michael@0:   }
michael@0: 
michael@0:   while (LessEqual(other, *this)) {
michael@0:     SubtractBignum(other);
michael@0:     result++;
michael@0:   }
michael@0:   return result;
michael@0: }
michael@0: 
michael@0: 
michael@0: template<typename S>
michael@0: static int SizeInHexChars(S number) {
michael@0:   ASSERT(number > 0);
michael@0:   int result = 0;
michael@0:   while (number != 0) {
michael@0:     number >>= 4;
michael@0:     result++;
michael@0:   }
michael@0:   return result;
michael@0: }
michael@0: 
michael@0: 
michael@0: static char HexCharOfValue(int value) {
michael@0:   ASSERT(0 <= value && value <= 16);
michael@0:   if (value < 10) return value + '0';
michael@0:   return value - 10 + 'A';
michael@0: }
michael@0: 
michael@0: 
michael@0: bool Bignum::ToHexString(char* buffer, int buffer_size) const {
michael@0:   ASSERT(IsClamped());
michael@0:   // Each bigit must be printable as separate hex-character.
michael@0:   ASSERT(kBigitSize % 4 == 0);
michael@0:   const int kHexCharsPerBigit = kBigitSize / 4;
michael@0: 
michael@0:   if (used_digits_ == 0) {
michael@0:     if (buffer_size < 2) return false;
michael@0:     buffer[0] = '0';
michael@0:     buffer[1] = '\0';
michael@0:     return true;
michael@0:   }
michael@0:   // We add 1 for the terminating '\0' character.
michael@0:   int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
michael@0:       SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
michael@0:   if (needed_chars > buffer_size) return false;
michael@0:   int string_index = needed_chars - 1;
michael@0:   buffer[string_index--] = '\0';
michael@0:   for (int i = 0; i < exponent_; ++i) {
michael@0:     for (int j = 0; j < kHexCharsPerBigit; ++j) {
michael@0:       buffer[string_index--] = '0';
michael@0:     }
michael@0:   }
michael@0:   for (int i = 0; i < used_digits_ - 1; ++i) {
michael@0:     Chunk current_bigit = bigits_[i];
michael@0:     for (int j = 0; j < kHexCharsPerBigit; ++j) {
michael@0:       buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
michael@0:       current_bigit >>= 4;
michael@0:     }
michael@0:   }
michael@0:   // And finally the last bigit.
michael@0:   Chunk most_significant_bigit = bigits_[used_digits_ - 1];
michael@0:   while (most_significant_bigit != 0) {
michael@0:     buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
michael@0:     most_significant_bigit >>= 4;
michael@0:   }
michael@0:   return true;
michael@0: }
michael@0: 
michael@0: 
michael@0: Bignum::Chunk Bignum::BigitAt(int index) const {
michael@0:   if (index >= BigitLength()) return 0;
michael@0:   if (index < exponent_) return 0;
michael@0:   return bigits_[index - exponent_];
michael@0: }
michael@0: 
michael@0: 
michael@0: int Bignum::Compare(const Bignum& a, const Bignum& b) {
michael@0:   ASSERT(a.IsClamped());
michael@0:   ASSERT(b.IsClamped());
michael@0:   int bigit_length_a = a.BigitLength();
michael@0:   int bigit_length_b = b.BigitLength();
michael@0:   if (bigit_length_a < bigit_length_b) return -1;
michael@0:   if (bigit_length_a > bigit_length_b) return +1;
michael@0:   for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
michael@0:     Chunk bigit_a = a.BigitAt(i);
michael@0:     Chunk bigit_b = b.BigitAt(i);
michael@0:     if (bigit_a < bigit_b) return -1;
michael@0:     if (bigit_a > bigit_b) return +1;
michael@0:     // Otherwise they are equal up to this digit. Try the next digit.
michael@0:   }
michael@0:   return 0;
michael@0: }
michael@0: 
michael@0: 
michael@0: int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
michael@0:   ASSERT(a.IsClamped());
michael@0:   ASSERT(b.IsClamped());
michael@0:   ASSERT(c.IsClamped());
michael@0:   if (a.BigitLength() < b.BigitLength()) {
michael@0:     return PlusCompare(b, a, c);
michael@0:   }
michael@0:   if (a.BigitLength() + 1 < c.BigitLength()) return -1;
michael@0:   if (a.BigitLength() > c.BigitLength()) return +1;
michael@0:   // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
michael@0:   // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
michael@0:   // of 'a'.
michael@0:   if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
michael@0:     return -1;
michael@0:   }
michael@0: 
michael@0:   Chunk borrow = 0;
michael@0:   // Starting at min_exponent all digits are == 0. So no need to compare them.
michael@0:   int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
michael@0:   for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
michael@0:     Chunk chunk_a = a.BigitAt(i);
michael@0:     Chunk chunk_b = b.BigitAt(i);
michael@0:     Chunk chunk_c = c.BigitAt(i);
michael@0:     Chunk sum = chunk_a + chunk_b;
michael@0:     if (sum > chunk_c + borrow) {
michael@0:       return +1;
michael@0:     } else {
michael@0:       borrow = chunk_c + borrow - sum;
michael@0:       if (borrow > 1) return -1;
michael@0:       borrow <<= kBigitSize;
michael@0:     }
michael@0:   }
michael@0:   if (borrow == 0) return 0;
michael@0:   return -1;
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::Clamp() {
michael@0:   while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
michael@0:     used_digits_--;
michael@0:   }
michael@0:   if (used_digits_ == 0) {
michael@0:     // Zero.
michael@0:     exponent_ = 0;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: bool Bignum::IsClamped() const {
michael@0:   return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::Zero() {
michael@0:   for (int i = 0; i < used_digits_; ++i) {
michael@0:     bigits_[i] = 0;
michael@0:   }
michael@0:   used_digits_ = 0;
michael@0:   exponent_ = 0;
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::Align(const Bignum& other) {
michael@0:   if (exponent_ > other.exponent_) {
michael@0:     // If "X" represents a "hidden" digit (by the exponent) then we are in the
michael@0:     // following case (a == this, b == other):
michael@0:     // a:  aaaaaaXXXX   or a:   aaaaaXXX
michael@0:     // b:     bbbbbbX      b: bbbbbbbbXX
michael@0:     // We replace some of the hidden digits (X) of a with 0 digits.
michael@0:     // a:  aaaaaa000X   or a:   aaaaa0XX
michael@0:     int zero_digits = exponent_ - other.exponent_;
michael@0:     EnsureCapacity(used_digits_ + zero_digits);
michael@0:     for (int i = used_digits_ - 1; i >= 0; --i) {
michael@0:       bigits_[i + zero_digits] = bigits_[i];
michael@0:     }
michael@0:     for (int i = 0; i < zero_digits; ++i) {
michael@0:       bigits_[i] = 0;
michael@0:     }
michael@0:     used_digits_ += zero_digits;
michael@0:     exponent_ -= zero_digits;
michael@0:     ASSERT(used_digits_ >= 0);
michael@0:     ASSERT(exponent_ >= 0);
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::BigitsShiftLeft(int shift_amount) {
michael@0:   ASSERT(shift_amount < kBigitSize);
michael@0:   ASSERT(shift_amount >= 0);
michael@0:   Chunk carry = 0;
michael@0:   for (int i = 0; i < used_digits_; ++i) {
michael@0:     Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
michael@0:     bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
michael@0:     carry = new_carry;
michael@0:   }
michael@0:   if (carry != 0) {
michael@0:     bigits_[used_digits_] = carry;
michael@0:     used_digits_++;
michael@0:   }
michael@0: }
michael@0: 
michael@0: 
michael@0: void Bignum::SubtractTimes(const Bignum& other, int factor) {
michael@0:   ASSERT(exponent_ <= other.exponent_);
michael@0:   if (factor < 3) {
michael@0:     for (int i = 0; i < factor; ++i) {
michael@0:       SubtractBignum(other);
michael@0:     }
michael@0:     return;
michael@0:   }
michael@0:   Chunk borrow = 0;
michael@0:   int exponent_diff = other.exponent_ - exponent_;
michael@0:   for (int i = 0; i < other.used_digits_; ++i) {
michael@0:     DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
michael@0:     DoubleChunk remove = borrow + product;
michael@0:     Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
michael@0:     bigits_[i + exponent_diff] = difference & kBigitMask;
michael@0:     borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
michael@0:                                 (remove >> kBigitSize));
michael@0:   }
michael@0:   for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
michael@0:     if (borrow == 0) return;
michael@0:     Chunk difference = bigits_[i] - borrow;
michael@0:     bigits_[i] = difference & kBigitMask;
michael@0:     borrow = difference >> (kChunkSize - 1);
michael@0:   }
michael@0:   Clamp();
michael@0: }
michael@0: 
michael@0: 
michael@0: }  // namespace double_conversion