// Copyright 2011 the V8 project authors. All rights reserved.

// Use of this source code is governed by a BSD-style license that can be

// found in the LICENSE file.

#include "src/v8.h"

#include "src/bignum.h"

#include "src/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<typename S>

static int BitSize(S value) {

return 8 * sizeof(value);

}

// Guaranteed to lie in one Bigit.

void Bignum::AssignUInt16(uint16_t value) {

DCHECK(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] = static_cast<Chunk>(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<const char> 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';

DCHECK(0 <= digit && digit <= 9);

result = result * 10 + digit;

}

return result;

}

void Bignum::AssignDecimalString(Vector<const char> 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<const char> 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) {

DCHECK(IsClamped());

DCHECK(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_;

DCHECK(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_);

DCHECK(IsClamped());

}

void Bignum::SubtractBignum(const Bignum& other) {

DCHECK(IsClamped());

DCHECK(other.IsClamped());

// We require this to be bigger than other.

DCHECK(LessEqual(other, *this));

Align(other);

int offset = other.exponent_ - exponent_;

Chunk borrow = 0;

int i;

for (i = 0; i < other.used_digits_; ++i) {

DCHECK((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.

DCHECK(kDoubleChunkSize >= kBigitSize + 32 + 1);

DoubleChunk carry = 0;

for (int i = 0; i < used_digits_; ++i) {

DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;

bigits_[i] = static_cast<Chunk>(product & kBigitMask);

carry = (product >> kBigitSize);

}

while (carry != 0) {

EnsureCapacity(used_digits_ + 1);

bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);

used_digits_++;

carry >>= kBigitSize;

}

}

void Bignum::MultiplyByUInt64(uint64_t factor) {

if (factor == 1) return;

if (factor == 0) {

Zero();

return;

}

DCHECK(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] = static_cast<Chunk>(tmp & kBigitMask);

carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +

(product_high << (32 - kBigitSize));

}

while (carry != 0) {

EnsureCapacity(used_digits_ + 1);

bigits_[used_digits_] = static_cast<Chunk>(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 };

DCHECK(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() {

DCHECK(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<DoubleChunk>(chunk1) * chunk2;

bigit_index1--;

bigit_index2++;

}

bigits_[i] = static_cast<Chunk>(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<DoubleChunk>(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<Chunk>(accumulator) & kBigitMask;

accumulator >>= kBigitSize;

}

// Since the result was guaranteed to lie inside the number the

// accumulator must be 0 now.

DCHECK(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) {

DCHECK(base != 0);

DCHECK(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<uint64_t>(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) {

DCHECK(IsClamped());

DCHECK(other.IsClamped());

DCHECK(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).

DCHECK(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]);

}

DCHECK(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<typename S>

static int SizeInHexChars(S number) {

DCHECK(number > 0);

int result = 0;

while (number != 0) {

number >>= 4;

result++;

}

return result;

}

static char HexCharOfValue(int value) {

DCHECK(0 <= value && value <= 16);

if (value < 10) return value + '0';

return value - 10 + 'A';

}

bool Bignum::ToHexString(char* buffer, int buffer_size) const {

DCHECK(IsClamped());

// Each bigit must be printable as separate hex-character.

DCHECK(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) {

DCHECK(a.IsClamped());

DCHECK(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) {

DCHECK(a.IsClamped());

DCHECK(b.IsClamped());

DCHECK(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;

DCHECK(used_digits_ >= 0);

DCHECK(exponent_ >= 0);

}

}

void Bignum::BigitsShiftLeft(int shift_amount) {

DCHECK(shift_amount < kBigitSize);

DCHECK(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) {

#ifdef DEBUG

Bignum a, b;

a.AssignBignum(*this);

b.AssignBignum(other);

b.MultiplyByUInt32(factor);

a.SubtractBignum(b);

#endif

DCHECK(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<DoubleChunk>(factor) * other.bigits_[i];

DoubleChunk remove = borrow + product;

Chunk difference =

bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask);

bigits_[i + exponent_diff] = difference & kBigitMask;

borrow = static_cast<Chunk>((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);

}

Clamp();

DCHECK(Bignum::Equal(a, *this));

}

} } // namespace v8::internal