From: floitschV8@gmail.com Date: Mon, 8 Nov 2010 11:49:47 +0000 (+0000) Subject: Bignum implementation of Strtod. X-Git-Tag: upstream/4.7.83~20987 X-Git-Url: http://review.tizen.org/git/?a=commitdiff_plain;h=808d00f8efb46dd14d57085b19e56c1ee1d0c14d;p=platform%2Fupstream%2Fv8.git Bignum implementation of Strtod. This removes the dependency on Gay's strtod. Review URL: http://codereview.chromium.org/4060001 git-svn-id: http://v8.googlecode.com/svn/branches/bleeding_edge@5778 ce2b1a6d-e550-0410-aec6-3dcde31c8c00 --- diff --git a/src/SConscript b/src/SConscript index 596caf7..030c643 100755 --- a/src/SConscript +++ b/src/SConscript @@ -40,6 +40,7 @@ SOURCES = { api.cc assembler.cc ast.cc + bignum.cc bootstrapper.cc builtins.cc cached-powers.cc diff --git a/src/bignum.cc b/src/bignum.cc new file mode 100644 index 0000000..dd1537a --- /dev/null +++ b/src/bignum.cc @@ -0,0 +1,767 @@ +// Copyright 2010 the V8 project authors. All rights reserved. +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above +// copyright notice, this list of conditions and the following +// disclaimer in the documentation and/or other materials provided +// with the distribution. +// * Neither the name of Google Inc. nor the names of its +// contributors may be used to endorse or promote products derived +// from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +#include "v8.h" + +#include "bignum.h" +#include "utils.h" + +namespace v8 { +namespace internal { + +Bignum::Bignum() + : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { + for (int i = 0; i < kBigitCapacity; ++i) { + bigits_[i] = 0; + } +} + + +template +static int BitSize(S value) { + return 8 * sizeof(value); +} + +// Guaranteed to lie in one Bigit. +void Bignum::AssignUInt16(uint16_t value) { + ASSERT(kBigitSize >= BitSize(value)); + Zero(); + if (value == 0) return; + + EnsureCapacity(1); + bigits_[0] = value; + used_digits_ = 1; +} + + +void Bignum::AssignUInt64(uint64_t value) { + const int kUInt64Size = 64; + + Zero(); + if (value == 0) return; + + int needed_bigits = kUInt64Size / kBigitSize + 1; + EnsureCapacity(needed_bigits); + for (int i = 0; i < needed_bigits; ++i) { + bigits_[i] = value & kBigitMask; + value = value >> kBigitSize; + } + used_digits_ = needed_bigits; + Clamp(); +} + + +void Bignum::AssignBignum(const Bignum& other) { + exponent_ = other.exponent_; + for (int i = 0; i < other.used_digits_; ++i) { + bigits_[i] = other.bigits_[i]; + } + // Clear the excess digits (if there were any). + for (int i = other.used_digits_; i < used_digits_; ++i) { + bigits_[i] = 0; + } + used_digits_ = other.used_digits_; +} + + +static uint64_t ReadUInt64(Vector buffer, + int from, + int digits_to_read) { + uint64_t result = 0; + for (int i = from; i < from + digits_to_read; ++i) { + int digit = buffer[i] - '0'; + ASSERT(0 <= digit && digit <= 9); + result = result * 10 + digit; + } + return result; +} + + +void Bignum::AssignDecimalString(Vector value) { + // 2^64 = 18446744073709551616 > 10^19 + const int kMaxUint64DecimalDigits = 19; + Zero(); + int length = value.length(); + int pos = 0; + // Let's just say that each digit needs 4 bits. + while (length >= kMaxUint64DecimalDigits) { + uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); + pos += kMaxUint64DecimalDigits; + length -= kMaxUint64DecimalDigits; + MultiplyByPowerOfTen(kMaxUint64DecimalDigits); + AddUInt64(digits); + } + uint64_t digits = ReadUInt64(value, pos, length); + MultiplyByPowerOfTen(length); + AddUInt64(digits); + Clamp(); +} + + +static int HexCharValue(char c) { + if ('0' <= c && c <= '9') return c - '0'; + if ('a' <= c && c <= 'f') return 10 + c - 'a'; + if ('A' <= c && c <= 'F') return 10 + c - 'A'; + UNREACHABLE(); + return 0; // To make compiler happy. +} + + +void Bignum::AssignHexString(Vector value) { + Zero(); + int length = value.length(); + + int needed_bigits = length * 4 / kBigitSize + 1; + EnsureCapacity(needed_bigits); + int string_index = length - 1; + for (int i = 0; i < needed_bigits - 1; ++i) { + // These bigits are guaranteed to be "full". + Chunk current_bigit = 0; + for (int j = 0; j < kBigitSize / 4; j++) { + current_bigit += HexCharValue(value[string_index--]) << (j * 4); + } + bigits_[i] = current_bigit; + } + used_digits_ = needed_bigits - 1; + + Chunk most_significant_bigit = 0; // Could be = 0; + for (int j = 0; j <= string_index; ++j) { + most_significant_bigit <<= 4; + most_significant_bigit += HexCharValue(value[j]); + } + if (most_significant_bigit != 0) { + bigits_[used_digits_] = most_significant_bigit; + used_digits_++; + } + Clamp(); +} + + +void Bignum::AddUInt64(uint64_t operand) { + if (operand == 0) return; + Bignum other; + other.AssignUInt64(operand); + AddBignum(other); +} + + +void Bignum::AddBignum(const Bignum& other) { + ASSERT(IsClamped()); + ASSERT(other.IsClamped()); + + // If this has a greater exponent than other append zero-bigits to this. + // After this call exponent_ <= other.exponent_. + Align(other); + + // There are two possibilities: + // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) + // bbbbb 00000000 + // ---------------- + // ccccccccccc 0000 + // or + // aaaaaaaaaa 0000 + // bbbbbbbbb 0000000 + // ----------------- + // cccccccccccc 0000 + // In both cases we might need a carry bigit. + + EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); + Chunk carry = 0; + int bigit_pos = other.exponent_ - exponent_; + ASSERT(bigit_pos >= 0); + for (int i = 0; i < other.used_digits_; ++i) { + Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; + bigits_[bigit_pos] = sum & kBigitMask; + carry = sum >> kBigitSize; + bigit_pos++; + } + + while (carry != 0) { + Chunk sum = bigits_[bigit_pos] + carry; + bigits_[bigit_pos] = sum & kBigitMask; + carry = sum >> kBigitSize; + bigit_pos++; + } + used_digits_ = Max(bigit_pos, used_digits_); + ASSERT(IsClamped()); +} + + +void Bignum::SubtractBignum(const Bignum& other) { + ASSERT(IsClamped()); + ASSERT(other.IsClamped()); + // We require this to be bigger than other. + ASSERT(LessEqual(other, *this)); + + Align(other); + + int offset = other.exponent_ - exponent_; + Chunk borrow = 0; + int i; + for (i = 0; i < other.used_digits_; ++i) { + ASSERT((borrow == 0) || (borrow == 1)); + Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; + bigits_[i + offset] = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + } + while (borrow != 0) { + Chunk difference = bigits_[i + offset] - borrow; + bigits_[i + offset] = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + ++i; + } + Clamp(); +} + + +void Bignum::ShiftLeft(int shift_amount) { + if (used_digits_ == 0) return; + exponent_ += shift_amount / kBigitSize; + int local_shift = shift_amount % kBigitSize; + EnsureCapacity(used_digits_ + 1); + BigitsShiftLeft(local_shift); +} + + +void Bignum::MultiplyByUInt32(uint32_t factor) { + if (factor == 1) return; + if (factor == 0) { + Zero(); + return; + } + if (used_digits_ == 0) return; + + // The product of a bigit with the factor is of size kBigitSize + 32. + // Assert that this number + 1 (for the carry) fits into double chunk. + ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); + DoubleChunk carry = 0; + for (int i = 0; i < used_digits_; ++i) { + DoubleChunk product = static_cast(factor) * bigits_[i] + carry; + bigits_[i] = static_cast(product & kBigitMask); + carry = (product >> kBigitSize); + } + while (carry != 0) { + EnsureCapacity(used_digits_ + 1); + bigits_[used_digits_] = carry & kBigitMask; + used_digits_++; + carry >>= kBigitSize; + } +} + + +void Bignum::MultiplyByUInt64(uint64_t factor) { + if (factor == 1) return; + if (factor == 0) { + Zero(); + return; + } + ASSERT(kBigitSize < 32); + uint64_t carry = 0; + uint64_t low = factor & 0xFFFFFFFF; + uint64_t high = factor >> 32; + for (int i = 0; i < used_digits_; ++i) { + uint64_t product_low = low * bigits_[i]; + uint64_t product_high = high * bigits_[i]; + uint64_t tmp = (carry & kBigitMask) + product_low; + bigits_[i] = tmp & kBigitMask; + carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + + (product_high << (32 - kBigitSize)); + } + while (carry != 0) { + EnsureCapacity(used_digits_ + 1); + bigits_[used_digits_] = carry & kBigitMask; + used_digits_++; + carry >>= kBigitSize; + } +} + + +void Bignum::MultiplyByPowerOfTen(int exponent) { + const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765c793, fa10079d); + const uint16_t kFive1 = 5; + const uint16_t kFive2 = kFive1 * 5; + const uint16_t kFive3 = kFive2 * 5; + const uint16_t kFive4 = kFive3 * 5; + const uint16_t kFive5 = kFive4 * 5; + const uint16_t kFive6 = kFive5 * 5; + const uint32_t kFive7 = kFive6 * 5; + const uint32_t kFive8 = kFive7 * 5; + const uint32_t kFive9 = kFive8 * 5; + const uint32_t kFive10 = kFive9 * 5; + const uint32_t kFive11 = kFive10 * 5; + const uint32_t kFive12 = kFive11 * 5; + const uint32_t kFive13 = kFive12 * 5; + const uint32_t kFive1_to_12[] = + { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, + kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; + + ASSERT(exponent >= 0); + if (exponent == 0) return; + if (used_digits_ == 0) return; + + // We shift by exponent at the end just before returning. + int remaining_exponent = exponent; + while (remaining_exponent >= 27) { + MultiplyByUInt64(kFive27); + remaining_exponent -= 27; + } + while (remaining_exponent >= 13) { + MultiplyByUInt32(kFive13); + remaining_exponent -= 13; + } + if (remaining_exponent > 0) { + MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); + } + ShiftLeft(exponent); +} + + +void Bignum::Square() { + ASSERT(IsClamped()); + int product_length = 2 * used_digits_; + EnsureCapacity(product_length); + + // Comba multiplication: compute each column separately. + // Example: r = a2a1a0 * b2b1b0. + // r = 1 * a0b0 + + // 10 * (a1b0 + a0b1) + + // 100 * (a2b0 + a1b1 + a0b2) + + // 1000 * (a2b1 + a1b2) + + // 10000 * a2b2 + // + // In the worst case we have to accumulate nb-digits products of digit*digit. + // + // Assert that the additional number of bits in a DoubleChunk are enough to + // sum up used_digits of Bigit*Bigit. + if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { + UNIMPLEMENTED(); + } + DoubleChunk accumulator = 0; + // First shift the digits so we don't overwrite them. + int copy_offset = used_digits_; + for (int i = 0; i < used_digits_; ++i) { + bigits_[copy_offset + i] = bigits_[i]; + } + // We have two loops to avoid some 'if's in the loop. + for (int i = 0; i < used_digits_; ++i) { + // Process temporary digit i with power i. + // The sum of the two indices must be equal to i. + int bigit_index1 = i; + int bigit_index2 = 0; + // Sum all of the sub-products. + while (bigit_index1 >= 0) { + Chunk chunk1 = bigits_[copy_offset + bigit_index1]; + Chunk chunk2 = bigits_[copy_offset + bigit_index2]; + accumulator += static_cast(chunk1) * chunk2; + bigit_index1--; + bigit_index2++; + } + bigits_[i] = static_cast(accumulator) & kBigitMask; + accumulator >>= kBigitSize; + } + for (int i = used_digits_; i < product_length; ++i) { + int bigit_index1 = used_digits_ - 1; + int bigit_index2 = i - bigit_index1; + // Invariant: sum of both indices is again equal to i. + // Inner loop runs 0 times on last iteration, emptying accumulator. + while (bigit_index2 < used_digits_) { + Chunk chunk1 = bigits_[copy_offset + bigit_index1]; + Chunk chunk2 = bigits_[copy_offset + bigit_index2]; + accumulator += static_cast(chunk1) * chunk2; + bigit_index1--; + bigit_index2++; + } + // The overwritten bigits_[i] will never be read in further loop iterations, + // because bigit_index1 and bigit_index2 are always greater + // than i - used_digits_. + bigits_[i] = static_cast(accumulator) & kBigitMask; + accumulator >>= kBigitSize; + } + // Since the result was guaranteed to lie inside the number the + // accumulator must be 0 now. + ASSERT(accumulator == 0); + + // Don't forget to update the used_digits and the exponent. + used_digits_ = product_length; + exponent_ *= 2; + Clamp(); +} + + +void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { + ASSERT(base != 0); + ASSERT(power_exponent >= 0); + if (power_exponent == 0) { + AssignUInt16(1); + return; + } + Zero(); + int shifts = 0; + // We expect base to be in range 2-32, and most often to be 10. + // It does not make much sense to implement different algorithms for counting + // the bits. + while ((base & 1) == 0) { + base >>= 1; + shifts++; + } + int bit_size = 0; + int tmp_base = base; + while (tmp_base != 0) { + tmp_base >>= 1; + bit_size++; + } + int final_size = bit_size * power_exponent; + // 1 extra bigit for the shifting, and one for rounded final_size. + EnsureCapacity(final_size / kBigitSize + 2); + + // Left to Right exponentiation. + int mask = 1; + while (power_exponent >= mask) mask <<= 1; + + // The mask is now pointing to the bit above the most significant 1-bit of + // power_exponent. + // Get rid of first 1-bit; + mask >>= 2; + uint64_t this_value = base; + + bool delayed_multipliciation = false; + const uint64_t max_32bits = 0xFFFFFFFF; + while (mask != 0 && this_value <= max_32bits) { + this_value = this_value * this_value; + // Verify that there is enough space in this_value to perform the + // multiplication. The first bit_size bits must be 0. + if ((power_exponent & mask) != 0) { + uint64_t base_bits_mask = + ~((static_cast(1) << (64 - bit_size)) - 1); + bool high_bits_zero = (this_value & base_bits_mask) == 0; + if (high_bits_zero) { + this_value *= base; + } else { + delayed_multipliciation = true; + } + } + mask >>= 1; + } + AssignUInt64(this_value); + if (delayed_multipliciation) { + MultiplyByUInt32(base); + } + + // Now do the same thing as a bignum. + while (mask != 0) { + Square(); + if ((power_exponent & mask) != 0) { + MultiplyByUInt32(base); + } + mask >>= 1; + } + + // And finally add the saved shifts. + ShiftLeft(shifts * power_exponent); +} + + +// Precondition: this/other < 16bit. +uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { + ASSERT(IsClamped()); + ASSERT(other.IsClamped()); + ASSERT(other.used_digits_ > 0); + + // Easy case: if we have less digits than the divisor than the result is 0. + // Note: this handles the case where this == 0, too. + if (BigitLength() < other.BigitLength()) { + return 0; + } + + Align(other); + + uint16_t result = 0; + + // Start by removing multiples of 'other' until both numbers have the same + // number of digits. + while (BigitLength() > other.BigitLength()) { + // This naive approach is extremely inefficient if the this divided other + // might be big. This function is implemented for doubleToString where + // the result should be small (less than 10). + ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); + // Remove the multiples of the first digit. + // Example this = 23 and other equals 9. -> Remove 2 multiples. + result += bigits_[used_digits_ - 1]; + SubtractTimes(other, bigits_[used_digits_ - 1]); + } + + ASSERT(BigitLength() == other.BigitLength()); + + // Both bignums are at the same length now. + // Since other has more than 0 digits we know that the access to + // bigits_[used_digits_ - 1] is safe. + Chunk this_bigit = bigits_[used_digits_ - 1]; + Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; + + if (other.used_digits_ == 1) { + // Shortcut for easy (and common) case. + int quotient = this_bigit / other_bigit; + bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; + result += quotient; + Clamp(); + return result; + } + + int division_estimate = this_bigit / (other_bigit + 1); + result += division_estimate; + SubtractTimes(other, division_estimate); + + if (other_bigit * (division_estimate + 1) > this_bigit) { + // No need to even try to subtract. Even if other's remaining digits were 0 + // another subtraction would be too much. + return result; + } + + while (LessEqual(other, *this)) { + SubtractBignum(other); + result++; + } + return result; +} + + +template +static int SizeInHexChars(S number) { + ASSERT(number > 0); + int result = 0; + while (number != 0) { + number >>= 4; + result++; + } + return result; +} + + +static char HexCharOfValue(int value) { + ASSERT(0 <= value && value <= 16); + if (value < 10) return value + '0'; + return value - 10 + 'A'; +} + + +bool Bignum::ToHexString(char* buffer, int buffer_size) const { + ASSERT(IsClamped()); + // Each bigit must be printable as separate hex-character. + ASSERT(kBigitSize % 4 == 0); + const int kHexCharsPerBigit = kBigitSize / 4; + + if (used_digits_ == 0) { + if (buffer_size < 2) return false; + buffer[0] = '0'; + buffer[1] = '\0'; + return true; + } + // We add 1 for the terminating '\0' character. + int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + + SizeInHexChars(bigits_[used_digits_ - 1]) + 1; + if (needed_chars > buffer_size) return false; + int string_index = needed_chars - 1; + buffer[string_index--] = '\0'; + for (int i = 0; i < exponent_; ++i) { + for (int j = 0; j < kHexCharsPerBigit; ++j) { + buffer[string_index--] = '0'; + } + } + for (int i = 0; i < used_digits_ - 1; ++i) { + Chunk current_bigit = bigits_[i]; + for (int j = 0; j < kHexCharsPerBigit; ++j) { + buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); + current_bigit >>= 4; + } + } + // And finally the last bigit. + Chunk most_significant_bigit = bigits_[used_digits_ - 1]; + while (most_significant_bigit != 0) { + buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); + most_significant_bigit >>= 4; + } + return true; +} + + +Bignum::Chunk Bignum::BigitAt(int index) const { + if (index >= BigitLength()) return 0; + if (index < exponent_) return 0; + return bigits_[index - exponent_]; +} + + +int Bignum::Compare(const Bignum& a, const Bignum& b) { + ASSERT(a.IsClamped()); + ASSERT(b.IsClamped()); + int bigit_length_a = a.BigitLength(); + int bigit_length_b = b.BigitLength(); + if (bigit_length_a < bigit_length_b) return -1; + if (bigit_length_a > bigit_length_b) return +1; + for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { + Chunk bigit_a = a.BigitAt(i); + Chunk bigit_b = b.BigitAt(i); + if (bigit_a < bigit_b) return -1; + if (bigit_a > bigit_b) return +1; + // Otherwise they are equal up to this digit. Try the next digit. + } + return 0; +} + + +int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { + ASSERT(a.IsClamped()); + ASSERT(b.IsClamped()); + ASSERT(c.IsClamped()); + if (a.BigitLength() < b.BigitLength()) { + return PlusCompare(b, a, c); + } + if (a.BigitLength() + 1 < c.BigitLength()) return -1; + if (a.BigitLength() > c.BigitLength()) return +1; + // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than + // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one + // of 'a'. + if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { + return -1; + } + + Chunk borrow = 0; + // Starting at min_exponent all digits are == 0. So no need to compare them. + int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); + for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { + Chunk chunk_a = a.BigitAt(i); + Chunk chunk_b = b.BigitAt(i); + Chunk chunk_c = c.BigitAt(i); + Chunk sum = chunk_a + chunk_b; + if (sum > chunk_c + borrow) { + return +1; + } else { + borrow = chunk_c + borrow - sum; + if (borrow > 1) return -1; + borrow <<= kBigitSize; + } + } + if (borrow == 0) return 0; + return -1; +} + + +void Bignum::Clamp() { + while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { + used_digits_--; + } + if (used_digits_ == 0) { + // Zero. + exponent_ = 0; + } +} + + +bool Bignum::IsClamped() const { + return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; +} + + +void Bignum::Zero() { + for (int i = 0; i < used_digits_; ++i) { + bigits_[i] = 0; + } + used_digits_ = 0; + exponent_ = 0; +} + + +void Bignum::Align(const Bignum& other) { + if (exponent_ > other.exponent_) { + // If "X" represents a "hidden" digit (by the exponent) then we are in the + // following case (a == this, b == other): + // a: aaaaaaXXXX or a: aaaaaXXX + // b: bbbbbbX b: bbbbbbbbXX + // We replace some of the hidden digits (X) of a with 0 digits. + // a: aaaaaa000X or a: aaaaa0XX + int zero_digits = exponent_ - other.exponent_; + EnsureCapacity(used_digits_ + zero_digits); + for (int i = used_digits_ - 1; i >= 0; --i) { + bigits_[i + zero_digits] = bigits_[i]; + } + for (int i = 0; i < zero_digits; ++i) { + bigits_[i] = 0; + } + used_digits_ += zero_digits; + exponent_ -= zero_digits; + ASSERT(used_digits_ >= 0); + ASSERT(exponent_ >= 0); + } +} + + +void Bignum::BigitsShiftLeft(int shift_amount) { + ASSERT(shift_amount < kBigitSize); + ASSERT(shift_amount >= 0); + Chunk carry = 0; + for (int i = 0; i < used_digits_; ++i) { + Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); + bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; + carry = new_carry; + } + if (carry != 0) { + bigits_[used_digits_] = carry; + used_digits_++; + } +} + + +void Bignum::SubtractTimes(const Bignum& other, int factor) { + ASSERT(exponent_ <= other.exponent_); + if (factor < 3) { + for (int i = 0; i < factor; ++i) { + SubtractBignum(other); + } + return; + } + Chunk borrow = 0; + int exponent_diff = other.exponent_ - exponent_; + for (int i = 0; i < other.used_digits_; ++i) { + DoubleChunk product = static_cast(factor) * other.bigits_[i]; + DoubleChunk remove = borrow + product; + Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask); + bigits_[i + exponent_diff] = difference & kBigitMask; + borrow = static_cast((difference >> (kChunkSize - 1)) + + (remove >> kBigitSize)); + } + for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { + if (borrow == 0) return; + Chunk difference = bigits_[i] - borrow; + bigits_[i] = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + ++i; + } + Clamp(); +} + + +} } // namespace v8::internal diff --git a/src/bignum.h b/src/bignum.h new file mode 100644 index 0000000..1d2bff6 --- /dev/null +++ b/src/bignum.h @@ -0,0 +1,140 @@ +// Copyright 2010 the V8 project authors. All rights reserved. +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above +// copyright notice, this list of conditions and the following +// disclaimer in the documentation and/or other materials provided +// with the distribution. +// * Neither the name of Google Inc. nor the names of its +// contributors may be used to endorse or promote products derived +// from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +#ifndef V8_BIGNUM_H_ +#define V8_BIGNUM_H_ + +namespace v8 { +namespace internal { + +class Bignum { + public: + // 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately. + // This bignum can encode much bigger numbers, since it contains an + // exponent. + static const int kMaxSignificantBits = 3584; + + Bignum(); + void AssignUInt16(uint16_t value); + void AssignUInt64(uint64_t value); + void AssignBignum(const Bignum& other); + + void AssignDecimalString(Vector value); + void AssignHexString(Vector value); + + void AssignPowerUInt16(uint16_t base, int exponent); + + void AddUInt16(uint16_t operand); + void AddUInt64(uint64_t operand); + void AddBignum(const Bignum& other); + // Precondition: this >= other. + void SubtractBignum(const Bignum& other); + + void Square(); + void ShiftLeft(int shift_amount); + void MultiplyByUInt32(uint32_t factor); + void MultiplyByUInt64(uint64_t factor); + void MultiplyByPowerOfTen(int exponent); + void Times10() { return MultiplyByUInt32(10); } + // Pseudocode: + // int result = this / other; + // this = this % other; + // In the worst case this function is in O(this/other). + uint16_t DivideModuloIntBignum(const Bignum& other); + + bool ToHexString(char* buffer, int buffer_size) const; + + static int Compare(const Bignum& a, const Bignum& b); + static bool Equal(const Bignum& a, const Bignum& b) { + return Compare(a, b) == 0; + } + static bool LessEqual(const Bignum& a, const Bignum& b) { + return Compare(a, b) <= 0; + } + static bool Less(const Bignum& a, const Bignum& b) { + return Compare(a, b) < 0; + } + // Returns Compare(a + b, c); + static int PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c); + // Returns a + b == c + static bool PlusEqual(const Bignum& a, const Bignum& b, const Bignum& c) { + return PlusCompare(a, b, c) == 0; + } + // Returns a + b <= c + static bool PlusLessEqual(const Bignum& a, const Bignum& b, const Bignum& c) { + return PlusCompare(a, b, c) <= 0; + } + // Returns a + b < c + static bool PlusLess(const Bignum& a, const Bignum& b, const Bignum& c) { + return PlusCompare(a, b, c) < 0; + } + private: + typedef uint32_t Chunk; + typedef uint64_t DoubleChunk; + + static const int kChunkSize = sizeof(Chunk) * 8; + static const int kDoubleChunkSize = sizeof(DoubleChunk) * 8; + // With bigit size of 28 we loose some bits, but a double still fits easily + // into two chunks, and more importantly we can use the Comba multiplication. + static const int kBigitSize = 28; + static const Chunk kBigitMask = (1 << kBigitSize) - 1; + // Every instance allocates kBigitLength chunks on the stack. Bignums cannot + // grow. There are no checks if the stack-allocated space is sufficient. + static const int kBigitCapacity = kMaxSignificantBits / kBigitSize; + + void EnsureCapacity(int size) { + if (size > kBigitCapacity) { + UNREACHABLE(); + } + } + void Align(const Bignum& other); + void Clamp(); + bool IsClamped() const; + void Zero(); + // Requires this to have enough capacity (no tests done). + // Updates used_digits_ if necessary. + // by must be < kBigitSize. + void BigitsShiftLeft(int shift_amount); + // BigitLength includes the "hidden" digits encoded in the exponent. + int BigitLength() const { return used_digits_ + exponent_; } + Chunk BigitAt(int index) const; + void SubtractTimes(const Bignum& other, int factor); + + Chunk bigits_buffer_[kBigitCapacity]; + // A vector backed by bigits_buffer_. This way accesses to the array are + // checked for out-of-bounds errors. + Vector bigits_; + int used_digits_; + // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize). + int exponent_; + + DISALLOW_COPY_AND_ASSIGN(Bignum); +}; + +} } // namespace v8::internal + +#endif // V8_BIGNUM_H_ diff --git a/src/double.h b/src/double.h index e805173..9db8ea7 100644 --- a/src/double.h +++ b/src/double.h @@ -82,6 +82,11 @@ class Double { return d64_; } + double NextDouble() const { + if (d64_ == kInfinity) return kInfinity; + return Double(d64_ + 1).value(); + } + int Exponent() const { if (IsDenormal()) return kDenormalExponent; @@ -120,19 +125,20 @@ class Double { ((d64 & kSignificandMask) != 0); } - bool IsInfinite() const { uint64_t d64 = AsUint64(); return ((d64 & kExponentMask) == kExponentMask) && ((d64 & kSignificandMask) == 0); } - int Sign() const { uint64_t d64 = AsUint64(); return (d64 & kSignMask) == 0? 1: -1; } + DiyFp UpperBoundary() const { + return DiyFp(Significand() * 2 + 1, Exponent() - 1); + } // Returns the two boundaries of this. // The bigger boundary (m_plus) is normalized. The lower boundary has the same diff --git a/src/strtod.cc b/src/strtod.cc index 0ed1b0d..0523d88 100644 --- a/src/strtod.cc +++ b/src/strtod.cc @@ -31,6 +31,7 @@ #include "v8.h" #include "strtod.h" +#include "bignum.h" #include "cached-powers.h" #include "double.h" @@ -83,44 +84,12 @@ static const double exact_powers_of_ten[] = { // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22 10000000000000000000000.0 }; - static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten); - -extern "C" double gay_strtod(const char* s00, const char** se); - -static double old_strtod(Vector buffer, int exponent) { - // gay_strtod is broken on Linux,x86. For numbers with few decimal digits - // the computation is done using floating-point operations which (on Linux) - // are prone to double-rounding errors. - // By adding several zeroes to the buffer gay_strtod falls back to a slower - // (but correct) algorithm. - const int kInsertedZeroesCount = 20; - char gay_buffer[1024]; - Vector gay_buffer_vector(gay_buffer, sizeof(gay_buffer)); - int pos = 0; - for (int i = 0; i < buffer.length(); ++i) { - gay_buffer_vector[pos++] = buffer[i]; - } - for (int i = 0; i < kInsertedZeroesCount; ++i) { - gay_buffer_vector[pos++] = '0'; - } - exponent -= kInsertedZeroesCount; - gay_buffer_vector[pos++] = 'e'; - if (exponent < 0) { - gay_buffer_vector[pos++] = '-'; - exponent = -exponent; - } - const int kNumberOfExponentDigits = 5; - for (int i = kNumberOfExponentDigits - 1; i >= 0; i--) { - gay_buffer_vector[pos + i] = exponent % 10 + '0'; - exponent /= 10; - } - pos += kNumberOfExponentDigits; - gay_buffer_vector[pos] = '\0'; - return gay_strtod(gay_buffer, NULL); -} - +// Maximum number of significant digits in the decimal representation. +// In fact the value is 772 (see conversions.cc), but to give us some margin +// we round up to 780. +static const int kMaxSignificantDecimalDigits = 780; static Vector TrimLeadingZeros(Vector buffer) { for (int i = 0; i < buffer.length(); i++) { @@ -142,6 +111,23 @@ static Vector TrimTrailingZeros(Vector buffer) { } +static void TrimToMaxSignificantDigits(Vector buffer, + int exponent, + char* significant_buffer, + int* significant_exponent) { + for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { + significant_buffer[i] = buffer[i]; + } + // The input buffer has been trimmed. Therefore the last digit must be + // different from '0'. + ASSERT(buffer[buffer.length() - 1] != '0'); + // Set the last digit to be non-zero. This is sufficient to guarantee + // correct rounding. + significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; + *significant_exponent = + exponent + (buffer.length() - kMaxSignificantDecimalDigits); +} + // Reads digits from the buffer and converts them to a uint64. // Reads in as many digits as fit into a uint64. // When the string starts with "1844674407370955161" no further digit is read. @@ -374,20 +360,81 @@ static bool DiyFpStrtod(Vector buffer, } +// Returns the correct double for the buffer*10^exponent. +// The variable guess should be a close guess that is either the correct double +// or its lower neighbor (the nearest double less than the correct one). +// Preconditions: +// buffer.length() + exponent <= kMaxDecimalPower + 1 +// buffer.length() + exponent > kMinDecimalPower +// buffer.length() <= kMaxDecimalSignificantDigits +static double BignumStrtod(Vector buffer, + int exponent, + double guess) { + if (guess == V8_INFINITY) { + return guess; + } + + DiyFp upper_boundary = Double(guess).UpperBoundary(); + + ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1); + ASSERT(buffer.length() + exponent > kMinDecimalPower); + ASSERT(buffer.length() <= kMaxSignificantDecimalDigits); + // Make sure that the Bignum will be able to hold all our numbers. + // Our Bignum implementation has a separate field for exponents. Shifts will + // consume at most one bigit (< 64 bits). + // ln(10) == 3.3219... + ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits); + Bignum input; + Bignum boundary; + input.AssignDecimalString(buffer); + boundary.AssignUInt64(upper_boundary.f()); + if (exponent >= 0) { + input.MultiplyByPowerOfTen(exponent); + } else { + boundary.MultiplyByPowerOfTen(-exponent); + } + if (upper_boundary.e() > 0) { + boundary.ShiftLeft(upper_boundary.e()); + } else { + input.ShiftLeft(-upper_boundary.e()); + } + int comparison = Bignum::Compare(input, boundary); + if (comparison < 0) { + return guess; + } else if (comparison > 0) { + return Double(guess).NextDouble(); + } else if ((Double(guess).Significand() & 1) == 0) { + // Round towards even. + return guess; + } else { + return Double(guess).NextDouble(); + } +} + + double Strtod(Vector buffer, int exponent) { Vector left_trimmed = TrimLeadingZeros(buffer); Vector trimmed = TrimTrailingZeros(left_trimmed); exponent += left_trimmed.length() - trimmed.length(); if (trimmed.length() == 0) return 0.0; + if (trimmed.length() > kMaxSignificantDecimalDigits) { + char significant_buffer[kMaxSignificantDecimalDigits]; + int significant_exponent; + TrimToMaxSignificantDigits(trimmed, exponent, + significant_buffer, &significant_exponent); + trimmed = + Vector(significant_buffer, kMaxSignificantDecimalDigits); + exponent = significant_exponent; + } if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY; if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0; - double result; - if (DoubleStrtod(trimmed, exponent, &result) || - DiyFpStrtod(trimmed, exponent, &result)) { - return result; + double guess; + if (DoubleStrtod(trimmed, exponent, &guess) || + DiyFpStrtod(trimmed, exponent, &guess)) { + return guess; } - return old_strtod(trimmed, exponent); + return BignumStrtod(trimmed, exponent, guess); } } } // namespace v8::internal diff --git a/test/cctest/SConscript b/test/cctest/SConscript index 006653c..620cd82 100644 --- a/test/cctest/SConscript +++ b/test/cctest/SConscript @@ -41,6 +41,7 @@ SOURCES = { 'test-alloc.cc', 'test-api.cc', 'test-ast.cc', + 'test-bignum.cc', 'test-circular-queue.cc', 'test-compiler.cc', 'test-conversions.cc', diff --git a/test/cctest/test-bignum.cc b/test/cctest/test-bignum.cc new file mode 100644 index 0000000..9aa5ef3 --- /dev/null +++ b/test/cctest/test-bignum.cc @@ -0,0 +1,1502 @@ +// Copyright 2010 the V8 project authors. All rights reserved. +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above +// copyright notice, this list of conditions and the following +// disclaimer in the documentation and/or other materials provided +// with the distribution. +// * Neither the name of Google Inc. nor the names of its +// contributors may be used to endorse or promote products derived +// from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +#include + +#include "v8.h" + +#include "platform.h" +#include "cctest.h" +#include "bignum.h" + +using namespace v8::internal; + + +static const int kBufferSize = 1024; + +static void AssignHexString(Bignum* bignum, const char* str) { + bignum->AssignHexString(Vector(str, StrLength(str))); +} + + +static void AssignDecimalString(Bignum* bignum, const char* str) { + bignum->AssignDecimalString(Vector(str, StrLength(str))); +} + + +TEST(Assign) { + char buffer[kBufferSize]; + Bignum bignum; + Bignum bignum2; + bignum.AssignUInt16(0); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + bignum.AssignUInt16(0xA); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A", buffer); + bignum.AssignUInt16(0x20); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("20", buffer); + + + bignum.AssignUInt64(0); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + bignum.AssignUInt64(0xA); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A", buffer); + bignum.AssignUInt64(0x20); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("20", buffer); + bignum.AssignUInt64(0x100); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100", buffer); + + // The first real test, since this will not fit into one bigit. + bignum.AssignUInt64(0x12345678); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("12345678", buffer); + + uint64_t big = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF); + bignum.AssignUInt64(big); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFFFF", buffer); + + big = V8_2PART_UINT64_C(0x12345678, 9ABCDEF0); + bignum.AssignUInt64(big); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("123456789ABCDEF0", buffer); + + bignum2.AssignBignum(bignum); + CHECK(bignum2.ToHexString(buffer, kBufferSize)); + CHECK_EQ("123456789ABCDEF0", buffer); + + AssignDecimalString(&bignum, "0"); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + + AssignDecimalString(&bignum, "1"); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + AssignDecimalString(&bignum, "1234567890"); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("499602D2", buffer); + + AssignHexString(&bignum, "0"); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + + AssignHexString(&bignum, "123456789ABCDEF0"); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("123456789ABCDEF0", buffer); +} + + +TEST(ShiftLeft) { + char buffer[kBufferSize]; + Bignum bignum; + AssignHexString(&bignum, "0"); + bignum.ShiftLeft(100); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + + AssignHexString(&bignum, "1"); + bignum.ShiftLeft(1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2", buffer); + + AssignHexString(&bignum, "1"); + bignum.ShiftLeft(4); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10", buffer); + + AssignHexString(&bignum, "1"); + bignum.ShiftLeft(32); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100000000", buffer); + + AssignHexString(&bignum, "1"); + bignum.ShiftLeft(64); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000", buffer); + + AssignHexString(&bignum, "123456789ABCDEF"); + bignum.ShiftLeft(64); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("123456789ABCDEF0000000000000000", buffer); + bignum.ShiftLeft(1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2468ACF13579BDE0000000000000000", buffer); +} + + +TEST(AddUInt64) { + char buffer[kBufferSize]; + Bignum bignum; + AssignHexString(&bignum, "0"); + bignum.AddUInt64(0xA); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A", buffer); + + AssignHexString(&bignum, "1"); + bignum.AddUInt64(0xA); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("B", buffer); + + AssignHexString(&bignum, "1"); + bignum.AddUInt64(0x100); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("101", buffer); + + AssignHexString(&bignum, "1"); + bignum.AddUInt64(0xFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000", buffer); + + AssignHexString(&bignum, "FFFFFFF"); + bignum.AddUInt64(0x1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000000000000000000"); + bignum.AddUInt64(0xFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1000000000000000000000000000000000000000FFFF", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + bignum.AddUInt64(0x1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100000000000000000000000000000000000000000000", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + bignum.AddUInt64(1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000001", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + bignum.AddUInt64(0xFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1000000000000000000000FFFF", buffer); + + AssignHexString(&bignum, "0"); + bignum.AddUInt64(V8_2PART_UINT64_C(0xA, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A00000000", buffer); + + AssignHexString(&bignum, "1"); + bignum.AddUInt64(V8_2PART_UINT64_C(0xA, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A00000001", buffer); + + AssignHexString(&bignum, "1"); + bignum.AddUInt64(V8_2PART_UINT64_C(0x100, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000001", buffer); + + AssignHexString(&bignum, "1"); + bignum.AddUInt64(V8_2PART_UINT64_C(0xFFFF, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFF00000001", buffer); + + AssignHexString(&bignum, "FFFFFFF"); + bignum.AddUInt64(V8_2PART_UINT64_C(0x1, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10FFFFFFF", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000000000000000000"); + bignum.AddUInt64(V8_2PART_UINT64_C(0xFFFF, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000000000000FFFF00000000", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + bignum.AddUInt64(V8_2PART_UINT64_C(0x1, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1000000000000000000000000000000000000FFFFFFFF", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + bignum.AddUInt64(V8_2PART_UINT64_C(0x1, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000100000000", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + bignum.AddUInt64(V8_2PART_UINT64_C(0xFFFF, 00000000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000FFFF00000000", buffer); +} + + +TEST(AddBignum) { + char buffer[kBufferSize]; + Bignum bignum; + Bignum other; + + AssignHexString(&other, "1"); + AssignHexString(&bignum, "0"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + AssignHexString(&bignum, "1"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2", buffer); + + AssignHexString(&bignum, "FFFFFFF"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFF"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100000000000000", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000000000000000000"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000000000000000000000001", buffer); + + AssignHexString(&other, "1000000000000"); + + AssignHexString(&bignum, "1"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1000000000001", buffer); + + AssignHexString(&bignum, "FFFFFFF"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100000FFFFFFF", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000000000000000000"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000000000001000000000000", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1000000000000000000000000000000FFFFFFFFFFFF", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000001000000000000", buffer); + + other.ShiftLeft(64); + // other == "10000000000000000000000000000" + + bignum.AssignUInt16(0x1); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000000001", buffer); + + AssignHexString(&bignum, "FFFFFFF"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1000000000000000000000FFFFFFF", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000000000000000000"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000010000000000000000000000000000", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100000000000000FFFFFFFFFFFFFFFFFFFFFFFFFFFF", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + bignum.AddBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10010000000000000000000000000", buffer); +} + + +TEST(SubtractBignum) { + char buffer[kBufferSize]; + Bignum bignum; + Bignum other; + + AssignHexString(&bignum, "1"); + AssignHexString(&other, "0"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + AssignHexString(&bignum, "2"); + AssignHexString(&other, "0"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2", buffer); + + AssignHexString(&bignum, "10000000"); + AssignHexString(&other, "1"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFF", buffer); + + AssignHexString(&bignum, "100000000000000"); + AssignHexString(&other, "1"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFF", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000000000000000001"); + AssignHexString(&other, "1"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000000000000000000000000", buffer); + + AssignHexString(&bignum, "1000000000001"); + AssignHexString(&other, "1000000000000"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + AssignHexString(&bignum, "100000FFFFFFF"); + AssignHexString(&other, "1000000000000"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFF", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000001000000000000"); + AssignHexString(&other, "1000000000000"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000000000000000000000000", buffer); + + AssignHexString(&bignum, "1000000000000000000000000000000FFFFFFFFFFFF"); + AssignHexString(&other, "1000000000000"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + // "10 0000 0000 0000 0000 0000 0000" + AssignHexString(&other, "1000000000000"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFF000000000000", buffer); + + AssignHexString(&other, "1000000000000"); + other.ShiftLeft(48); + // other == "1000000000000000000000000" + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + // bignum == "10000000000000000000000000" + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("F000000000000000000000000", buffer); + + other.AssignUInt16(0x1); + other.ShiftLeft(35); + // other == "800000000" + AssignHexString(&bignum, "FFFFFFF"); + bignum.ShiftLeft(60); + // bignum = FFFFFFF000000000000000 + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFEFFFFFF800000000", buffer); + + AssignHexString(&bignum, "10000000000000000000000000000000000000000000"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF800000000", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"); + bignum.SubtractBignum(other); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFF", buffer); +} + + +TEST(MultiplyUInt32) { + char buffer[kBufferSize]; + Bignum bignum; + + AssignHexString(&bignum, "0"); + bignum.MultiplyByUInt32(0x25); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + + AssignHexString(&bignum, "2"); + bignum.MultiplyByUInt32(0x5); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A", buffer); + + AssignHexString(&bignum, "10000000"); + bignum.MultiplyByUInt32(0x9); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("90000000", buffer); + + AssignHexString(&bignum, "100000000000000"); + bignum.MultiplyByUInt32(0xFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFF00000000000000", buffer); + + AssignHexString(&bignum, "100000000000000"); + bignum.MultiplyByUInt32(0xFFFFFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFF00000000000000", buffer); + + AssignHexString(&bignum, "1234567ABCD"); + bignum.MultiplyByUInt32(0xFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("12333335552433", buffer); + + AssignHexString(&bignum, "1234567ABCD"); + bignum.MultiplyByUInt32(0xFFFFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("12345679998A985433", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt32(0x2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1FFFFFFFFFFFFFFFE", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt32(0x4); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("3FFFFFFFFFFFFFFFC", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt32(0xF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("EFFFFFFFFFFFFFFF1", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt32(0xFFFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFEFFFFFFFFFF000001", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + // "10 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt32(2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("20000000000000000000000000", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + // "10 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt32(0xF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("F0000000000000000000000000", buffer); + + bignum.AssignUInt16(0xFFFF); + bignum.ShiftLeft(100); + // "FFFF0 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt32(0xFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFE00010000000000000000000000000", buffer); + + bignum.AssignUInt16(0xFFFF); + bignum.ShiftLeft(100); + // "FFFF0 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt32(0xFFFFFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFEFFFF00010000000000000000000000000", buffer); + + bignum.AssignUInt16(0xFFFF); + bignum.ShiftLeft(100); + // "FFFF0 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt32(0xFFFFFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFEFFFF00010000000000000000000000000", buffer); + + AssignDecimalString(&bignum, "15611230384529777"); + bignum.MultiplyByUInt32(10000000); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("210EDD6D4CDD2580EE80", buffer); +} + + +TEST(MultiplyUInt64) { + char buffer[kBufferSize]; + Bignum bignum; + + AssignHexString(&bignum, "0"); + bignum.MultiplyByUInt64(0x25); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + + AssignHexString(&bignum, "2"); + bignum.MultiplyByUInt64(0x5); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A", buffer); + + AssignHexString(&bignum, "10000000"); + bignum.MultiplyByUInt64(0x9); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("90000000", buffer); + + AssignHexString(&bignum, "100000000000000"); + bignum.MultiplyByUInt64(0xFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFF00000000000000", buffer); + + AssignHexString(&bignum, "100000000000000"); + bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFFFF00000000000000", buffer); + + AssignHexString(&bignum, "1234567ABCD"); + bignum.MultiplyByUInt64(0xFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("12333335552433", buffer); + + AssignHexString(&bignum, "1234567ABCD"); + bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFF, FFFFFFFF)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1234567ABCBDCBA985433", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt64(0x2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1FFFFFFFFFFFFFFFE", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt64(0x4); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("3FFFFFFFFFFFFFFFC", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt64(0xF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("EFFFFFFFFFFFFFFF1", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFFFF"); + bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFFFE0000000000000001", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + // "10 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt64(2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("20000000000000000000000000", buffer); + + bignum.AssignUInt16(0x1); + bignum.ShiftLeft(100); + // "10 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt64(0xF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("F0000000000000000000000000", buffer); + + bignum.AssignUInt16(0xFFFF); + bignum.ShiftLeft(100); + // "FFFF0 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt64(0xFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFE00010000000000000000000000000", buffer); + + bignum.AssignUInt16(0xFFFF); + bignum.ShiftLeft(100); + // "FFFF0 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt64(0xFFFFFFFF); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFEFFFF00010000000000000000000000000", buffer); + + bignum.AssignUInt16(0xFFFF); + bignum.ShiftLeft(100); + // "FFFF0 0000 0000 0000 0000 0000 0000" + bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFEFFFFFFFFFFFF00010000000000000000000000000", buffer); + + AssignDecimalString(&bignum, "15611230384529777"); + bignum.MultiplyByUInt64(V8_2PART_UINT64_C(0x8ac72304, 89e80000)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1E10EE4B11D15A7F3DE7F3C7680000", buffer); +} + + +TEST(MultiplyPowerOfTen) { + char buffer[kBufferSize]; + Bignum bignum; + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("3034", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1E208", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(3); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("12D450", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(4); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("BC4B20", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(5); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("75AEF40", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(6); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("498D5880", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(7); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2DF857500", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(8); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1CBB369200", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(9); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("11F5021B400", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(10); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("B3921510800", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(11); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("703B4D2A5000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(12); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("4625103A72000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(13); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2BD72A24874000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(14); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1B667A56D488000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(15); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("11200C7644D50000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(16); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("AB407C9EB0520000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(17); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("6B084DE32E3340000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(18); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("42E530ADFCE0080000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(19); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("29CF3E6CBE0C0500000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(20); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1A218703F6C783200000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(21); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1054F4627A3CB1F400000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(22); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A3518BD8C65EF38800000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(23); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("6612F7677BFB5835000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(24); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("3FCBDAA0AD7D17212000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(25); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("27DF68A46C6E2E74B4000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(26); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("18EBA166C3C4DD08F08000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(27); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("F9344E03A5B0A259650000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(28); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("9BC0B0C2478E6577DF20000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(29); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("61586E796CB8FF6AEB740000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(30); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("3CD7450BE3F39FA2D32880000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(31); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("26068B276E7843C5C3F9500000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(50); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("149D1B4CFED03B23AB5F4E1196EF45C08000000000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(100); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("5827249F27165024FBC47DFCA9359BF316332D1B91ACEECF471FBAB06D9B2" + "0000000000000000000000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(200); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("64C1F5C06C3816AFBF8DAFD5A3D756365BB0FD020E6F084E759C1F7C99E4F" + "55B9ACC667CEC477EB958C2AEEB3C6C19BA35A1AD30B35C51EB72040920000" + "0000000000000000000000000000000000000000000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(500); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("96741A625EB5D7C91039FEB5C5ACD6D9831EDA5B083D800E6019442C8C8223" + "3EAFB3501FE2058062221E15121334928880827DEE1EC337A8B26489F3A40A" + "CB440A2423734472D10BFCE886F41B3AF9F9503013D86D088929CA86EEB4D8" + "B9C831D0BD53327B994A0326227CFD0ECBF2EB48B02387AAE2D4CCCDF1F1A1" + "B8CC4F1FA2C56AD40D0E4DAA9C28CDBF0A549098EA13200000000000000000" + "00000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000", buffer); + + AssignDecimalString(&bignum, "1234"); + bignum.MultiplyByPowerOfTen(1000); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1258040F99B1CD1CC9819C676D413EA50E4A6A8F114BB0C65418C62D399B81" + "6361466CA8E095193E1EE97173553597C96673AF67FAFE27A66E7EF2E5EF2E" + "E3F5F5070CC17FE83BA53D40A66A666A02F9E00B0E11328D2224B8694C7372" + "F3D536A0AD1985911BD361496F268E8B23112500EAF9B88A9BC67B2AB04D38" + "7FEFACD00F5AF4F764F9ABC3ABCDE54612DE38CD90CB6647CA389EA0E86B16" + "BF7A1F34086E05ADBE00BD1673BE00FAC4B34AF1091E8AD50BA675E0381440" + "EA8E9D93E75D816BAB37C9844B1441C38FC65CF30ABB71B36433AF26DD97BD" + "ABBA96C03B4919B8F3515B92826B85462833380DC193D79F69D20DD6038C99" + "6114EF6C446F0BA28CC772ACBA58B81C04F8FFDE7B18C4E5A3ABC51E637FDF" + "6E37FDFF04C940919390F4FF92000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000", buffer); + + Bignum bignum2; + AssignHexString(&bignum2, "3DA774C07FB5DF54284D09C675A492165B830D5DAAEB2A7501" + "DA17CF9DFA1CA2282269F92A25A97314296B717E3DCBB9FE17" + "41A842FE2913F540F40796F2381155763502C58B15AF7A7F88" + "6F744C9164FF409A28F7FA0C41F89ED79C1BE9F322C8578B97" + "841F1CBAA17D901BE1230E3C00E1C643AF32638B5674E01FEA" + "96FC90864E621B856A9E1CE56E6EB545B9C2F8F0CC10DDA88D" + "CC6D282605F8DB67044F2DFD3695E7BA63877AE16701536AE6" + "567C794D0BFE338DFBB42D92D4215AF3BB22BF0A8B283FDDC2" + "C667A10958EA6D2"); + CHECK(bignum2.ToHexString(buffer, kBufferSize)); + CHECK_EQ("3DA774C07FB5DF54284D09C675A492165B830D5DAAEB2A7501" + "DA17CF9DFA1CA2282269F92A25A97314296B717E3DCBB9FE17" + "41A842FE2913F540F40796F2381155763502C58B15AF7A7F88" + "6F744C9164FF409A28F7FA0C41F89ED79C1BE9F322C8578B97" + "841F1CBAA17D901BE1230E3C00E1C643AF32638B5674E01FEA" + "96FC90864E621B856A9E1CE56E6EB545B9C2F8F0CC10DDA88D" + "CC6D282605F8DB67044F2DFD3695E7BA63877AE16701536AE6" + "567C794D0BFE338DFBB42D92D4215AF3BB22BF0A8B283FDDC2" + "C667A10958EA6D2", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2688A8F84FD1AB949930261C0986DB4DF931E85A8AD2FA8921284EE1C2BC51" + "E55915823BBA5789E7EC99E326EEE69F543ECE890929DED9AC79489884BE57" + "630AD569E121BB76ED8DAC8FB545A8AFDADF1F8860599AFC47A93B6346C191" + "7237F5BD36B73EB29371F4A4EE7A116CB5E8E5808D1BEA4D7F7E3716090C13" + "F29E5DDA53F0FD513362A2D20F6505314B9419DB967F8A8A89589FC43917C3" + "BB892062B17CBE421DB0D47E34ACCCE060D422CFF60DCBD0277EE038BD509C" + "7BC494D8D854F5B76696F927EA99BC00C4A5D7928434", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1815699B31E30B3CDFBE17D185F44910BBBF313896C3DC95B4B9314D19B5B32" + "F57AD71655476B630F3E02DF855502394A74115A5BA2B480BCBCD5F52F6F69D" + "E6C5622CB5152A54788BD9D14B896DE8CB73B53C3800DDACC9C51E0C38FAE76" + "2F9964232872F9C2738E7150C4AE3F1B18F70583172706FAEE26DC5A78C77A2" + "FAA874769E52C01DA5C3499F233ECF3C90293E0FB69695D763DAA3AEDA5535B" + "43DAEEDF6E9528E84CEE0EC000C3C8495C1F9C89F6218AF4C23765261CD5ADD" + "0787351992A01E5BB8F2A015807AE7A6BB92A08", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(5); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("5E13A4863ADEE3E5C9FE8D0A73423D695D62D8450CED15A8C9F368952C6DC3" + "F0EE7D82F3D1EFB7AF38A3B3920D410AFCAD563C8F5F39116E141A3C5C14B3" + "58CD73077EA35AAD59F6E24AD98F10D5555ABBFBF33AC361EAF429FD5FBE94" + "17DA9EF2F2956011F9F93646AA38048A681D984ED88127073443247CCC167C" + "B354A32206EF5A733E73CF82D795A1AD598493211A6D613C39515E0E0F6304" + "DCD9C810F3518C7F6A7CB6C81E99E02FCC65E8FDB7B7AE97306CC16A8631CE" + "0A2AEF6568276BE4C176964A73C153FDE018E34CB4C2F40", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(10); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("8F8CB8EB51945A7E815809F6121EF2F4E61EF3405CD9432CAD2709749EEAFD" + "1B81E843F14A3667A7BDCCC9E0BB795F63CDFDB62844AC7438976C885A0116" + "29607DA54F9C023CC366570B7637ED0F855D931752038A614922D0923E382C" + "B8E5F6C975672DB76E0DE471937BB9EDB11E28874F1C122D5E1EF38CECE9D0" + "0723056BCBD4F964192B76830634B1D322B7EB0062F3267E84F5C824343A77" + "4B7DCEE6DD464F01EBDC8C671BB18BB4EF4300A42474A6C77243F2A12B03BF" + "0443C38A1C0D2701EDB393135AE0DEC94211F9D4EB51F990800", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(50); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("107A8BE345E24407372FC1DE442CBA696BC23C4FFD5B4BDFD9E5C39559815" + "86628CF8472D2D589F2FC2BAD6E0816EC72CBF85CCA663D8A1EC6C51076D8" + "2D247E6C26811B7EC4D4300FB1F91028DCB7B2C4E7A60C151161AA7E65E79" + "B40917B12B2B5FBE7745984D4E8EFA31F9AE6062427B068B144A9CB155873" + "E7C0C9F0115E5AC72DC5A73C4796DB970BF9205AB8C77A6996EB1B417F9D1" + "6232431E6313C392203601B9C22CC10DDA88DCC6D282605F8DB67044F2DFD" + "3695E7BA63877AE16701536AE6567C794D0BFE338DFBB42D924CF964BD2C0" + "F586E03A2FCD35A408000000000000", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(100); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("46784A90ACD0ED3E7759CC585FB32D36EB6034A6F78D92604E3BAA5ED3D8B" + "6E60E854439BE448897FB4B7EA5A3D873AA0FCB3CFFD80D0530880E45F511" + "722A50CE7E058B5A6F5464DB7500E34984EE3202A9441F44FA1554C0CEA96" + "B438A36F25E7C9D56D71AE2CD313EC37534DA299AC0854FC48591A7CF3171" + "31265AA4AE62DE32344CE7BEEEF894AE686A2DAAFE5D6D9A10971FFD9C064" + "5079B209E1048F58B5192D41D84336AC4C8C489EEF00939CFC9D55C122036" + "01B9C22CC10DDA88DCC6D282605F8DB67044F2DFD3695E7BA3F67B96D3A32" + "E11FB5561B68744C4035B0800DC166D49D98E3FD1D5BB2000000000000000" + "0000000000", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(200); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("508BD351221DF139D72D88CDC0416845A53EE2D0E6B98352509A9AC312F8C" + "6CB1A144889416201E0B6CE66EA3EBE259B5FD79ECFC1FD77963CE516CC7E" + "2FE73D4B5B710C19F6BCB092C7A2FD76286543B8DBD2C596DFF2C896720BA" + "DFF7BC9C366ACEA3A880AEC287C5E6207DF2739B5326FC19D773BD830B109" + "ED36C7086544BF8FDB9D4B73719C2B5BC2F571A5937EC46876CD428281F6B" + "F287E1E07F25C1B1D46BC37324FF657A8B2E0071DB83B86123CA34004F406" + "001082D7945E90C6E8C9A9FEC2B44BE0DDA46E9F52B152E4D1336D2FCFBC9" + "96E30CA0082256737365158FE36482AA7EB9DAF2AB128F10E7551A3CD5BE6" + "0A922F3A7D5EED38B634A7EC95BCF7021BA6820A292000000000000000000" + "00000000000000000000000000000000", buffer); + + bignum.AssignBignum(bignum2); + bignum.MultiplyByPowerOfTen(500); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("7845F900E475B5086885BAAAE67C8E85185ACFE4633727F82A4B06B5582AC" + "BE933C53357DA0C98C20C5AC900C4D76A97247DF52B79F48F9E35840FB715" + "D392CE303E22622B0CF82D9471B398457DD3196F639CEE8BBD2C146873841" + "F0699E6C41F04FC7A54B48CEB995BEB6F50FE81DE9D87A8D7F849CC523553" + "7B7BBBC1C7CAAFF6E9650BE03B308C6D31012AEF9580F70D3EE2083ADE126" + "8940FA7D6308E239775DFD2F8C97FF7EBD525DAFA6512216F7047A62A93DC" + "38A0165BDC67E250DCC96A0181DE935A70B38704DC71819F02FC5261FF7E1" + "E5F11907678B0A3E519FF4C10A867B0C26CE02BE6960BA8621A87303C101C" + "3F88798BB9F7739655946F8B5744E6B1EAF10B0C5621330F0079209033C69" + "20DE2E2C8D324F0624463735D482BF291926C22A910F5B80FA25170B6B57D" + "8D5928C7BCA3FE87461275F69BD5A1B83181DAAF43E05FC3C72C4E93111B6" + "6205EBF49B28FEDFB7E7526CBDA658A332000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000", buffer); +} + + +TEST(DivideModuloIntBignum) { + char buffer[kBufferSize]; + Bignum bignum; + Bignum other; + Bignum third; + + bignum.AssignUInt16(10); + other.AssignUInt16(2); + CHECK_EQ(5, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("0", buffer); + + bignum.AssignUInt16(10); + bignum.ShiftLeft(500); + other.AssignUInt16(2); + other.ShiftLeft(500); + CHECK_EQ(5, bignum.DivideModuloIntBignum(other)); + CHECK_EQ("0", buffer); + + bignum.AssignUInt16(11); + other.AssignUInt16(2); + CHECK_EQ(5, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignUInt16(10); + bignum.ShiftLeft(500); + other.AssignUInt16(1); + bignum.AddBignum(other); + other.AssignUInt16(2); + other.ShiftLeft(500); + CHECK_EQ(5, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignUInt16(10); + bignum.ShiftLeft(500); + other.AssignBignum(bignum); + bignum.MultiplyByUInt32(0x1234); + third.AssignUInt16(0xFFF); + bignum.AddBignum(third); + CHECK_EQ(0x1234, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFF", buffer); + + bignum.AssignUInt16(10); + AssignHexString(&other, "1234567890"); + CHECK_EQ(0, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A", buffer); + + AssignHexString(&bignum, "12345678"); + AssignHexString(&other, "3789012"); + CHECK_EQ(5, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("D9861E", buffer); + + AssignHexString(&bignum, "70000001"); + AssignHexString(&other, "1FFFFFFF"); + CHECK_EQ(3, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000004", buffer); + + AssignHexString(&bignum, "28000000"); + AssignHexString(&other, "12A05F20"); + CHECK_EQ(2, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2BF41C0", buffer); + + bignum.AssignUInt16(10); + bignum.ShiftLeft(500); + other.AssignBignum(bignum); + bignum.MultiplyByUInt32(0x1234); + third.AssignUInt16(0xFFF); + other.SubtractBignum(third); + CHECK_EQ(0x1234, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1232DCC", buffer); + CHECK_EQ(0, bignum.DivideModuloIntBignum(other)); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1232DCC", buffer); +} + + +TEST(Compare) { + Bignum bignum1; + Bignum bignum2; + bignum1.AssignUInt16(1); + bignum2.AssignUInt16(1); + CHECK_EQ(0, Bignum::Compare(bignum1, bignum2)); + CHECK(Bignum::Equal(bignum1, bignum2)); + CHECK(Bignum::LessEqual(bignum1, bignum2)); + CHECK(!Bignum::Less(bignum1, bignum2)); + + bignum1.AssignUInt16(0); + bignum2.AssignUInt16(1); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + CHECK(!Bignum::Equal(bignum1, bignum2)); + CHECK(!Bignum::Equal(bignum2, bignum1)); + CHECK(Bignum::LessEqual(bignum1, bignum2)); + CHECK(!Bignum::LessEqual(bignum2, bignum1)); + CHECK(Bignum::Less(bignum1, bignum2)); + CHECK(!Bignum::Less(bignum2, bignum1)); + + AssignHexString(&bignum1, "1234567890ABCDEF12345"); + AssignHexString(&bignum2, "1234567890ABCDEF12345"); + CHECK_EQ(0, Bignum::Compare(bignum1, bignum2)); + + AssignHexString(&bignum1, "1234567890ABCDEF12345"); + AssignHexString(&bignum2, "1234567890ABCDEF12346"); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "1234567890ABCDEF12345"); + bignum1.ShiftLeft(500); + AssignHexString(&bignum2, "1234567890ABCDEF12345"); + bignum2.ShiftLeft(500); + CHECK_EQ(0, Bignum::Compare(bignum1, bignum2)); + + AssignHexString(&bignum1, "1234567890ABCDEF12345"); + bignum1.ShiftLeft(500); + AssignHexString(&bignum2, "1234567890ABCDEF12346"); + bignum2.ShiftLeft(500); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + + bignum1.AssignUInt16(1); + bignum1.ShiftLeft(64); + AssignHexString(&bignum2, "10000000000000000"); + CHECK_EQ(0, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(0, Bignum::Compare(bignum2, bignum1)); + + bignum1.AssignUInt16(1); + bignum1.ShiftLeft(64); + AssignHexString(&bignum2, "10000000000000001"); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + + bignum1.AssignUInt16(1); + bignum1.ShiftLeft(96); + AssignHexString(&bignum2, "10000000000000001"); + bignum2.ShiftLeft(32); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF"); + bignum2.AssignUInt16(1); + bignum2.ShiftLeft(64); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF"); + bignum1.ShiftLeft(32); + bignum2.AssignUInt16(1); + bignum2.ShiftLeft(96); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF"); + bignum1.ShiftLeft(32); + bignum2.AssignUInt16(1); + bignum2.ShiftLeft(95); + CHECK_EQ(+1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(-1, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "FFFFFFFFFFFFFFFF"); + bignum1.ShiftLeft(32); + bignum2.AssignUInt16(1); + bignum2.ShiftLeft(100); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "100000000000000"); + bignum2.AssignUInt16(1); + bignum2.ShiftLeft(14*4); + CHECK_EQ(0, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(0, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "100000000000001"); + bignum2.AssignUInt16(1); + bignum2.ShiftLeft(14*4); + CHECK_EQ(+1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(-1, Bignum::Compare(bignum2, bignum1)); + + AssignHexString(&bignum1, "200000000000000"); + bignum2.AssignUInt16(3); + bignum2.ShiftLeft(14*4); + CHECK_EQ(-1, Bignum::Compare(bignum1, bignum2)); + CHECK_EQ(+1, Bignum::Compare(bignum2, bignum1)); +} + + +TEST(PlusCompare) { + Bignum a; + Bignum b; + Bignum c; + a.AssignUInt16(1); + b.AssignUInt16(0); + c.AssignUInt16(1); + CHECK_EQ(0, Bignum::PlusCompare(a, b, c)); + CHECK(Bignum::PlusEqual(a, b, c)); + CHECK(Bignum::PlusLessEqual(a, b, c)); + CHECK(!Bignum::PlusLess(a, b, c)); + + a.AssignUInt16(0); + b.AssignUInt16(0); + c.AssignUInt16(1); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + CHECK_EQ(+1, Bignum::PlusCompare(c, b, a)); + CHECK(!Bignum::PlusEqual(a, b, c)); + CHECK(!Bignum::PlusEqual(c, b, a)); + CHECK(Bignum::PlusLessEqual(a, b, c)); + CHECK(!Bignum::PlusLessEqual(c, b, a)); + CHECK(Bignum::PlusLess(a, b, c)); + CHECK(!Bignum::PlusLess(c, b, a)); + + AssignHexString(&a, "1234567890ABCDEF12345"); + b.AssignUInt16(1); + AssignHexString(&c, "1234567890ABCDEF12345"); + CHECK_EQ(+1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890ABCDEF12344"); + b.AssignUInt16(1); + AssignHexString(&c, "1234567890ABCDEF12345"); + CHECK_EQ(0, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4); + AssignHexString(&b, "ABCDEF12345"); + AssignHexString(&c, "1234567890ABCDEF12345"); + CHECK_EQ(0, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4); + AssignHexString(&b, "ABCDEF12344"); + AssignHexString(&c, "1234567890ABCDEF12345"); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4); + AssignHexString(&b, "ABCDEF12346"); + AssignHexString(&c, "1234567890ABCDEF12345"); + CHECK_EQ(1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567891"); + a.ShiftLeft(11*4); + AssignHexString(&b, "ABCDEF12345"); + AssignHexString(&c, "1234567890ABCDEF12345"); + CHECK_EQ(1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567889"); + a.ShiftLeft(11*4); + AssignHexString(&b, "ABCDEF12345"); + AssignHexString(&c, "1234567890ABCDEF12345"); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF12345"); + c.ShiftLeft(32); + CHECK_EQ(0, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12344"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF12345"); + c.ShiftLeft(32); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12346"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF12345"); + c.ShiftLeft(32); + CHECK_EQ(1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567891"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF12345"); + c.ShiftLeft(32); + CHECK_EQ(1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567889"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF12345"); + c.ShiftLeft(32); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF1234500000000"); + CHECK_EQ(0, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12344"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF1234500000000"); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12346"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF1234500000000"); + CHECK_EQ(1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567891"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF1234500000000"); + CHECK_EQ(1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567889"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(32); + AssignHexString(&c, "1234567890ABCDEF1234500000000"); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + AssignHexString(&c, "123456789000000000ABCDEF12345"); + CHECK_EQ(0, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12346"); + AssignHexString(&c, "123456789000000000ABCDEF12345"); + CHECK_EQ(1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12344"); + AssignHexString(&c, "123456789000000000ABCDEF12345"); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(16); + AssignHexString(&c, "12345678900000ABCDEF123450000"); + CHECK_EQ(0, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12344"); + b.ShiftLeft(16); + AssignHexString(&c, "12345678900000ABCDEF123450000"); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12345"); + b.ShiftLeft(16); + AssignHexString(&c, "12345678900000ABCDEF123450001"); + CHECK_EQ(-1, Bignum::PlusCompare(a, b, c)); + + AssignHexString(&a, "1234567890"); + a.ShiftLeft(11*4 + 32); + AssignHexString(&b, "ABCDEF12346"); + b.ShiftLeft(16); + AssignHexString(&c, "12345678900000ABCDEF123450000"); + CHECK_EQ(+1, Bignum::PlusCompare(a, b, c)); +} + + +TEST(Square) { + Bignum bignum; + char buffer[kBufferSize]; + + bignum.AssignUInt16(1); + bignum.Square(); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignUInt16(2); + bignum.Square(); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("4", buffer); + + bignum.AssignUInt16(10); + bignum.Square(); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("64", buffer); + + AssignHexString(&bignum, "FFFFFFF"); + bignum.Square(); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFE0000001", buffer); + + AssignHexString(&bignum, "FFFFFFFFFFFFFF"); + bignum.Square(); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FFFFFFFFFFFFFE00000000000001", buffer); +} + + +TEST(AssignPowerUInt16) { + Bignum bignum; + char buffer[kBufferSize]; + + bignum.AssignPowerUInt16(1, 0); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignPowerUInt16(1, 1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignPowerUInt16(1, 2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignPowerUInt16(2, 0); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignPowerUInt16(2, 1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2", buffer); + + bignum.AssignPowerUInt16(2, 2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("4", buffer); + + bignum.AssignPowerUInt16(16, 1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10", buffer); + + bignum.AssignPowerUInt16(16, 2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100", buffer); + + bignum.AssignPowerUInt16(16, 5); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100000", buffer); + + bignum.AssignPowerUInt16(16, 8); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("100000000", buffer); + + bignum.AssignPowerUInt16(16, 16); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000", buffer); + + bignum.AssignPowerUInt16(16, 30); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1000000000000000000000000000000", buffer); + + bignum.AssignPowerUInt16(10, 0); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignPowerUInt16(10, 1); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("A", buffer); + + bignum.AssignPowerUInt16(10, 2); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("64", buffer); + + bignum.AssignPowerUInt16(10, 5); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("186A0", buffer); + + bignum.AssignPowerUInt16(10, 8); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("5F5E100", buffer); + + bignum.AssignPowerUInt16(10, 16); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("2386F26FC10000", buffer); + + bignum.AssignPowerUInt16(10, 30); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("C9F2C9CD04674EDEA40000000", buffer); + + bignum.AssignPowerUInt16(10, 31); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("7E37BE2022C0914B2680000000", buffer); + + bignum.AssignPowerUInt16(2, 0); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignPowerUInt16(2, 100); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("10000000000000000000000000", buffer); + + bignum.AssignPowerUInt16(17, 0); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1", buffer); + + bignum.AssignPowerUInt16(17, 99); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("1942BB9853FAD924A3D4DD92B89B940E0207BEF05DB9C26BC1B757" + "80BE0C5A2C2990E02A681224F34ED68558CE4C6E33760931", + buffer); + + bignum.AssignPowerUInt16(0xFFFF, 99); + CHECK(bignum.ToHexString(buffer, kBufferSize)); + CHECK_EQ("FF9D12F09B886C54E77E7439C7D2DED2D34F669654C0C2B6B8C288250" + "5A2211D0E3DC9A61831349EAE674B11D56E3049D7BD79DAAD6C9FA2BA" + "528E3A794299F2EE9146A324DAFE3E88967A0358233B543E233E575B9" + "DD4E3AA7942146426C328FF55BFD5C45E0901B1629260AF9AE2F310C5" + "50959FAF305C30116D537D80CF6EBDBC15C5694062AF1AC3D956D0A41" + "B7E1B79FF11E21D83387A1CE1F5882B31E4B5D8DE415BDBE6854466DF" + "343362267A7E8833119D31D02E18DB5B0E8F6A64B0ED0D0062FFFF", + buffer); +} diff --git a/test/cctest/test-strtod.cc b/test/cctest/test-strtod.cc index 56b26ea..34c474f 100644 --- a/test/cctest/test-strtod.cc +++ b/test/cctest/test-strtod.cc @@ -4,7 +4,10 @@ #include "v8.h" +#include "bignum.h" #include "cctest.h" +#include "diy-fp.h" +#include "double.h" #include "strtod.h" using namespace v8::internal; @@ -202,11 +205,14 @@ TEST(Strtod) { CHECK_EQ(1.7976931348623158E+308, StrtodChar("17976931348623158", 292)); CHECK_EQ(V8_INFINITY, StrtodChar("17976931348623159", 292)); - // The following number is the result of 89255.0/1e-22. Both floating-point + // The following number is the result of 89255.0/1e22. Both floating-point // numbers can be accurately represented with doubles. However on Linux,x86 // the floating-point stack is set to 80bits and the double-rounding // introduces an error. CHECK_EQ(89255e-22, StrtodChar("89255", -22)); + + // Some random values. + CHECK_EQ(358416272e-33, StrtodChar("358416272", -33)); CHECK_EQ(104110013277974872254e-225, StrtodChar("104110013277974872254", -225)); @@ -252,4 +258,158 @@ TEST(Strtod) { StrtodChar("1234567890123456789052345", 114)); CHECK_EQ(1234567890123456789052345e115, StrtodChar("1234567890123456789052345", 115)); + + // Boundary cases. + // 0x1FFFFFFFFFFFF * 2^3 = 72057594037927928 + // next: 72057594037927936 + // boundary: 72057594037927932 + CHECK_EQ(72057594037927928.0, StrtodChar("72057594037927928", 0)); + CHECK_EQ(72057594037927936.0, StrtodChar("72057594037927936", 0)); + CHECK_EQ(72057594037927936.0, StrtodChar("72057594037927932", 0)); + CHECK_EQ(72057594037927928.0, StrtodChar("7205759403792793199999", -5)); + CHECK_EQ(72057594037927936.0, StrtodChar("7205759403792793200001", -5)); + + // 0x1FFFFFFFFFFFF * 2^10 = 9223372036854774784 + // next: 9223372036854775808 + // boundary: 9223372036854775296 + CHECK_EQ(9223372036854774784.0, StrtodChar("9223372036854774784", 0)); + CHECK_EQ(9223372036854775808.0, StrtodChar("9223372036854775808", 0)); + CHECK_EQ(9223372036854775296.0, StrtodChar("9223372036854775296", 0)); + CHECK_EQ(9223372036854774784.0, StrtodChar("922337203685477529599999", -5)); + CHECK_EQ(9223372036854775808.0, StrtodChar("922337203685477529600001", -5)); + + // 0x1FFFFFFFFFFFF * 2^50 = 10141204801825834086073718800384 + // next: 10141204801825835211973625643008 + // boundary: 10141204801825834649023672221696 + CHECK_EQ(10141204801825834086073718800384.0, + StrtodChar("10141204801825834086073718800384", 0)); + CHECK_EQ(10141204801825835211973625643008.0, + StrtodChar("10141204801825835211973625643008", 0)); + CHECK_EQ(10141204801825834649023672221696.0, + StrtodChar("10141204801825834649023672221696", 0)); + CHECK_EQ(10141204801825834086073718800384.0, + StrtodChar("1014120480182583464902367222169599999", -5)); + CHECK_EQ(10141204801825835211973625643008.0, + StrtodChar("1014120480182583464902367222169600001", -5)); + + // 0x1FFFFFFFFFFFF * 2^99 = 5708990770823838890407843763683279797179383808 + // next: 5708990770823839524233143877797980545530986496 + // boundary: 5708990770823839207320493820740630171355185152 + CHECK_EQ(5708990770823838890407843763683279797179383808.0, + StrtodChar("5708990770823838890407843763683279797179383808", 0)); + CHECK_EQ(5708990770823839524233143877797980545530986496.0, + StrtodChar("5708990770823839524233143877797980545530986496", 0)); + CHECK_EQ(5708990770823839207320493820740630171355185152.0, + StrtodChar("5708990770823839207320493820740630171355185152", 0)); + CHECK_EQ(5708990770823838890407843763683279797179383808.0, + StrtodChar("5708990770823839207320493820740630171355185151999", -3)); + CHECK_EQ(5708990770823839524233143877797980545530986496.0, + StrtodChar("5708990770823839207320493820740630171355185152001", -3)); +} + + +static int CompareBignumToDiyFp(const Bignum& bignum_digits, + int bignum_exponent, + DiyFp diy_fp) { + Bignum bignum; + bignum.AssignBignum(bignum_digits); + Bignum other; + other.AssignUInt64(diy_fp.f()); + if (bignum_exponent >= 0) { + bignum.MultiplyByPowerOfTen(bignum_exponent); + } else { + other.MultiplyByPowerOfTen(-bignum_exponent); + } + if (diy_fp.e() >= 0) { + other.ShiftLeft(diy_fp.e()); + } else { + bignum.ShiftLeft(-diy_fp.e()); + } + return Bignum::Compare(bignum, other); +} + + +static bool CheckDouble(Vector buffer, + int exponent, + double to_check) { + DiyFp lower_boundary; + DiyFp upper_boundary; + Bignum input_digits; + input_digits.AssignDecimalString(buffer); + if (to_check == 0.0) { + const double kMinDouble = 4e-324; + // Check that the buffer*10^exponent < (0 + kMinDouble)/2. + Double d(kMinDouble); + d.NormalizedBoundaries(&lower_boundary, &upper_boundary); + return CompareBignumToDiyFp(input_digits, exponent, lower_boundary) <= 0; + } + if (to_check == V8_INFINITY) { + const double kMaxDouble = 1.7976931348623157e308; + // Check that the buffer*10^exponent >= boundary between kMaxDouble and inf. + Double d(kMaxDouble); + d.NormalizedBoundaries(&lower_boundary, &upper_boundary); + return CompareBignumToDiyFp(input_digits, exponent, upper_boundary) >= 0; + } + Double d(to_check); + d.NormalizedBoundaries(&lower_boundary, &upper_boundary); + if ((d.Significand() & 1) == 0) { + return CompareBignumToDiyFp(input_digits, exponent, lower_boundary) >= 0 && + CompareBignumToDiyFp(input_digits, exponent, upper_boundary) <= 0; + } else { + return CompareBignumToDiyFp(input_digits, exponent, lower_boundary) > 0 && + CompareBignumToDiyFp(input_digits, exponent, upper_boundary) < 0; + } +} + + +// Copied from v8.cc and adapted to make the function deterministic. +static uint32_t DeterministicRandom() { + // Random number generator using George Marsaglia's MWC algorithm. + static uint32_t hi = 0; + static uint32_t lo = 0; + + // Initialization values don't have any special meaning. (They are the result + // of two calls to random().) + if (hi == 0) hi = 0xbfe166e7; + if (lo == 0) lo = 0x64d1c3c9; + + // Mix the bits. + hi = 36969 * (hi & 0xFFFF) + (hi >> 16); + lo = 18273 * (lo & 0xFFFF) + (lo >> 16); + return (hi << 16) + (lo & 0xFFFF); +} + + +static const int kBufferSize = 1024; +static const int kShortStrtodRandomCount = 2; +static const int kLargeStrtodRandomCount = 2; + +TEST(RandomStrtod) { + char buffer[kBufferSize]; + for (int length = 1; length < 15; length++) { + for (int i = 0; i < kShortStrtodRandomCount; ++i) { + int pos = 0; + for (int j = 0; j < length; ++j) { + buffer[pos++] = random() % 10 + '0'; + } + int exponent = DeterministicRandom() % (25*2 + 1) - 25 - length; + buffer[pos] = '\0'; + Vector vector(buffer, pos); + double strtod_result = Strtod(vector, exponent); + CHECK(CheckDouble(vector, exponent, strtod_result)); + } + } + for (int length = 15; length < 800; length += 2) { + for (int i = 0; i < kLargeStrtodRandomCount; ++i) { + int pos = 0; + for (int j = 0; j < length; ++j) { + buffer[pos++] = random() % 10 + '0'; + } + int exponent = DeterministicRandom() % (308*2 + 1) - 308 - length; + buffer[pos] = '\0'; + Vector vector(buffer, pos); + double strtod_result = Strtod(vector, exponent); + CHECK(CheckDouble(vector, exponent, strtod_result)); + } + } } diff --git a/tools/gyp/v8.gyp b/tools/gyp/v8.gyp index 3e40fcc..bfb8921 100644 --- a/tools/gyp/v8.gyp +++ b/tools/gyp/v8.gyp @@ -280,6 +280,10 @@ '../../src/ast.cc', '../../src/ast-inl.h', '../../src/ast.h', + '../../src/bignum.cc', + '../../src/bignum.h', + '../../src/bignum-dtoa.cc', + '../../src/bignum-dtoa.h', '../../src/bootstrapper.cc', '../../src/bootstrapper.h', '../../src/builtins.cc', diff --git a/tools/visual_studio/v8_base.vcproj b/tools/visual_studio/v8_base.vcproj index bddf38e..d1ee48d 100644 --- a/tools/visual_studio/v8_base.vcproj +++ b/tools/visual_studio/v8_base.vcproj @@ -145,6 +145,22 @@ + + + + + + + + @@ -241,6 +257,22 @@ > + + + + + + + +