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webkit / WebKit / b0d7f9b249dd6483d6c7bc4f13c440c0842b7127 / . / Source / JavaScriptCore / runtime / JSBigInt.cpp
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/*
* Copyright (C) 2017 Caio Lima <ticaiolima@gmail.com>
* Copyright (C) 2017-2018 Apple Inc. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. 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.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``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 APPLE INC. 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.
*
* Parts of the implementation below:
*
* Copyright 2017 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.
*
*
* Copyright (c) 2014 the Dart project authors. Please see the AUTHORS file [1]
* for details. All rights reserved. Use of this source code is governed by a
* BSD-style license that can be found in the LICENSE file [2].
*
* [1] https://github.com/dart-lang/sdk/blob/master/AUTHORS
* [2] https://github.com/dart-lang/sdk/blob/master/LICENSE
*
* Copyright 2009 The Go Authors. All rights reserved.
* Use of this source code is governed by a BSD-style
* license that can be found in the LICENSE file [3].
*
* [3] https://golang.org/LICENSE
*/
#include "config.h"
#include "JSBigInt.h"
#include "BigIntObject.h"
#include "CatchScope.h"
#include "JSCInlines.h"
#include "MathCommon.h"
#include "ParseInt.h"
#include <algorithm>
#include <wtf/MathExtras.h>
#define STATIC_ASSERT(cond) static_assert(cond, "JSBigInt assumes " #cond)
namespace JSC {
const ClassInfo JSBigInt::s_info =
{ "JSBigInt", nullptr, nullptr, nullptr, CREATE_METHOD_TABLE(JSBigInt) };
JSBigInt::JSBigInt(VM& vm, Structure* structure, unsigned length)
: Base(vm, structure)
, m_length(length)
{ }
void JSBigInt::initialize(InitializationType initType)
{
if (initType == InitializationType::WithZero)
memset(dataStorage(), 0, length() * sizeof(Digit));
}
Structure* JSBigInt::createStructure(VM& vm, JSGlobalObject* globalObject, JSValue prototype)
{
return Structure::create(vm, globalObject, prototype, TypeInfo(BigIntType, StructureFlags), info());
}
JSBigInt* JSBigInt::createZero(VM& vm)
{
JSBigInt* zeroBigInt = createWithLengthUnchecked(vm, 0);
return zeroBigInt;
}
inline size_t JSBigInt::allocationSize(unsigned length)
{
size_t sizeWithPadding = WTF::roundUpToMultipleOf<sizeof(size_t)>(sizeof(JSBigInt));
return sizeWithPadding + length * sizeof(Digit);
}
JSBigInt* JSBigInt::tryCreateWithLength(ExecState* exec, unsigned length)
{
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (UNLIKELY(length > maxLength)) {
throwOutOfMemoryError(exec, scope);
return nullptr;
}
scope.release();
return createWithLengthUnchecked(vm, length);
}
JSBigInt* JSBigInt::createWithLengthUnchecked(VM& vm, unsigned length)
{
ASSERT(length <= maxLength);
JSBigInt* bigInt = new (NotNull, allocateCell<JSBigInt>(vm.heap, allocationSize(length))) JSBigInt(vm, vm.bigIntStructure.get(), length);
bigInt->finishCreation(vm);
return bigInt;
}
JSBigInt* JSBigInt::createFrom(VM& vm, int32_t value)
{
if (!value)
return createZero(vm);
JSBigInt* bigInt = createWithLengthUnchecked(vm, 1);
if (value < 0) {
bigInt->setDigit(0, static_cast<Digit>(-1 * static_cast<int64_t>(value)));
bigInt->setSign(true);
} else
bigInt->setDigit(0, static_cast<Digit>(value));
return bigInt;
}
JSBigInt* JSBigInt::createFrom(VM& vm, uint32_t value)
{
if (!value)
return createZero(vm);
JSBigInt* bigInt = createWithLengthUnchecked(vm, 1);
bigInt->setDigit(0, static_cast<Digit>(value));
return bigInt;
}
JSBigInt* JSBigInt::createFrom(VM& vm, int64_t value)
{
if (!value)
return createZero(vm);
if (sizeof(Digit) == 8) {
JSBigInt* bigInt = createWithLengthUnchecked(vm, 1);
if (value < 0) {
bigInt->setDigit(0, static_cast<Digit>(static_cast<uint64_t>(-(value + 1)) + 1));
bigInt->setSign(true);
} else
bigInt->setDigit(0, static_cast<Digit>(value));
return bigInt;
}
JSBigInt* bigInt = createWithLengthUnchecked(vm, 2);
uint64_t tempValue;
bool sign = false;
if (value < 0) {
tempValue = static_cast<uint64_t>(-(value + 1)) + 1;
sign = true;
} else
tempValue = value;
Digit lowBits = static_cast<Digit>(tempValue & 0xffffffff);
Digit highBits = static_cast<Digit>((tempValue >> 32) & 0xffffffff);
bigInt->setDigit(0, lowBits);
bigInt->setDigit(1, highBits);
bigInt->setSign(sign);
return bigInt;
}
JSBigInt* JSBigInt::createFrom(VM& vm, bool value)
{
if (!value)
return createZero(vm);
JSBigInt* bigInt = createWithLengthUnchecked(vm, 1);
bigInt->setDigit(0, static_cast<Digit>(value));
return bigInt;
}
JSValue JSBigInt::toPrimitive(ExecState*, PreferredPrimitiveType) const
{
return const_cast<JSBigInt*>(this);
}
Optional<uint8_t> JSBigInt::singleDigitValueForString()
{
if (isZero())
return 0;
if (length() == 1 && !sign()) {
Digit rDigit = digit(0);
if (rDigit <= 9)
return static_cast<uint8_t>(rDigit);
}
return { };
}
JSBigInt* JSBigInt::parseInt(ExecState* exec, StringView s, ErrorParseMode parserMode)
{
if (s.is8Bit())
return parseInt(exec, s.characters8(), s.length(), parserMode);
return parseInt(exec, s.characters16(), s.length(), parserMode);
}
JSBigInt* JSBigInt::parseInt(ExecState* exec, VM& vm, StringView s, uint8_t radix, ErrorParseMode parserMode, ParseIntSign sign)
{
if (s.is8Bit())
return parseInt(exec, vm, s.characters8(), s.length(), 0, radix, parserMode, sign, ParseIntMode::DisallowEmptyString);
return parseInt(exec, vm, s.characters16(), s.length(), 0, radix, parserMode, sign, ParseIntMode::DisallowEmptyString);
}
JSBigInt* JSBigInt::stringToBigInt(ExecState* exec, StringView s)
{
return parseInt(exec, s, ErrorParseMode::IgnoreExceptions);
}
String JSBigInt::toString(ExecState* exec, unsigned radix)
{
if (this->isZero())
return exec->vm().smallStrings.singleCharacterStringRep('0');
if (hasOneBitSet(radix))
return toStringBasePowerOfTwo(exec, this, radix);
return toStringGeneric(exec, this, radix);
}
// Multiplies {this} with {factor} and adds {summand} to the result.
void JSBigInt::inplaceMultiplyAdd(Digit factor, Digit summand)
{
internalMultiplyAdd(this, factor, summand, length(), this);
}
JSBigInt* JSBigInt::multiply(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (x->isZero())
return x;
if (y->isZero())
return y;
unsigned resultLength = x->length() + y->length();
JSBigInt* result = JSBigInt::tryCreateWithLength(exec, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
result->initialize(InitializationType::WithZero);
for (unsigned i = 0; i < x->length(); i++)
multiplyAccumulate(y, x->digit(i), result, i);
result->setSign(x->sign() != y->sign());
return result->rightTrim(vm);
}
JSBigInt* JSBigInt::divide(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
// 1. If y is 0n, throw a RangeError exception.
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (y->isZero()) {
throwRangeError(exec, scope, "0 is an invalid divisor value."_s);
return nullptr;
}
// 2. Let quotient be the mathematical value of x divided by y.
// 3. Return a BigInt representing quotient rounded towards 0 to the next
// integral value.
if (absoluteCompare(x, y) == ComparisonResult::LessThan)
return createZero(vm);
JSBigInt* quotient = nullptr;
bool resultSign = x->sign() != y->sign();
if (y->length() == 1) {
Digit divisor = y->digit(0);
if (divisor == 1)
return resultSign == x->sign() ? x : unaryMinus(vm, x);
Digit remainder;
absoluteDivWithDigitDivisor(vm, x, divisor, &quotient, remainder);
} else {
absoluteDivWithBigIntDivisor(exec, x, y, &quotient, nullptr);
RETURN_IF_EXCEPTION(scope, nullptr);
}
quotient->setSign(resultSign);
return quotient->rightTrim(vm);
}
JSBigInt* JSBigInt::copy(VM& vm, JSBigInt* x)
{
ASSERT(!x->isZero());
JSBigInt* result = JSBigInt::createWithLengthUnchecked(vm, x->length());
std::copy(x->dataStorage(), x->dataStorage() + x->length(), result->dataStorage());
result->setSign(x->sign());
return result;
}
JSBigInt* JSBigInt::unaryMinus(VM& vm, JSBigInt* x)
{
if (x->isZero())
return x;
JSBigInt* result = copy(vm, x);
result->setSign(!x->sign());
return result;
}
JSBigInt* JSBigInt::remainder(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
// 1. If y is 0n, throw a RangeError exception.
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (y->isZero()) {
throwRangeError(exec, scope, "0 is an invalid divisor value."_s);
return nullptr;
}
// 2. Return the JSBigInt representing x modulo y.
// See https://github.com/tc39/proposal-bigint/issues/84 though.
if (absoluteCompare(x, y) == ComparisonResult::LessThan)
return x;
JSBigInt* remainder;
if (y->length() == 1) {
Digit divisor = y->digit(0);
if (divisor == 1)
return createZero(vm);
Digit remainderDigit;
absoluteDivWithDigitDivisor(vm, x, divisor, nullptr, remainderDigit);
if (!remainderDigit)
return createZero(vm);
remainder = createWithLengthUnchecked(vm, 1);
remainder->setDigit(0, remainderDigit);
} else {
absoluteDivWithBigIntDivisor(exec, x, y, nullptr, &remainder);
RETURN_IF_EXCEPTION(scope, nullptr);
}
remainder->setSign(x->sign());
return remainder->rightTrim(vm);
}
JSBigInt* JSBigInt::add(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
bool xSign = x->sign();
// x + y == x + y
// -x + -y == -(x + y)
if (xSign == y->sign())
return absoluteAdd(exec, x, y, xSign);
// x + -y == x - y == -(y - x)
// -x + y == y - x == -(x - y)
ComparisonResult comparisonResult = absoluteCompare(x, y);
if (comparisonResult == ComparisonResult::GreaterThan || comparisonResult == ComparisonResult::Equal)
return absoluteSub(vm, x, y, xSign);
return absoluteSub(vm, y, x, !xSign);
}
JSBigInt* JSBigInt::sub(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
bool xSign = x->sign();
if (xSign != y->sign()) {
// x - (-y) == x + y
// (-x) - y == -(x + y)
return absoluteAdd(exec, x, y, xSign);
}
// x - y == -(y - x)
// (-x) - (-y) == y - x == -(x - y)
ComparisonResult comparisonResult = absoluteCompare(x, y);
if (comparisonResult == ComparisonResult::GreaterThan || comparisonResult == ComparisonResult::Equal)
return absoluteSub(vm, x, y, xSign);
return absoluteSub(vm, y, x, !xSign);
}
JSBigInt* JSBigInt::bitwiseAnd(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!x->sign() && !y->sign()) {
scope.release();
return absoluteAnd(vm, x, y);
}
if (x->sign() && y->sign()) {
int resultLength = std::max(x->length(), y->length()) + 1;
// (-x) & (-y) == ~(x-1) & ~(y-1) == ~((x-1) | (y-1))
// == -(((x-1) | (y-1)) + 1)
JSBigInt* result = absoluteSubOne(exec, x, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
JSBigInt* y1 = absoluteSubOne(exec, y, y->length());
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteOr(vm, result, y1);
scope.release();
return absoluteAddOne(exec, result, SignOption::Signed);
}
ASSERT(x->sign() != y->sign());
// Assume that x is the positive BigInt.
if (x->sign())
std::swap(x, y);
// x & (-y) == x & ~(y-1) == x & ~(y-1)
JSBigInt* y1 = absoluteSubOne(exec, y, y->length());
RETURN_IF_EXCEPTION(scope, nullptr);
return absoluteAndNot(vm, x, y1);
}
JSBigInt* JSBigInt::bitwiseOr(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
unsigned resultLength = std::max(x->length(), y->length());
if (!x->sign() && !y->sign()) {
scope.release();
return absoluteOr(vm, x, y);
}
if (x->sign() && y->sign()) {
// (-x) | (-y) == ~(x-1) | ~(y-1) == ~((x-1) & (y-1))
// == -(((x-1) & (y-1)) + 1)
JSBigInt* result = absoluteSubOne(exec, x, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
JSBigInt* y1 = absoluteSubOne(exec, y, y->length());
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteAnd(vm, result, y1);
RETURN_IF_EXCEPTION(scope, nullptr);
scope.release();
return absoluteAddOne(exec, result, SignOption::Signed);
}
ASSERT(x->sign() != y->sign());
// Assume that x is the positive BigInt.
if (x->sign())
std::swap(x, y);
// x | (-y) == x | ~(y-1) == ~((y-1) &~ x) == -(((y-1) &~ x) + 1)
JSBigInt* result = absoluteSubOne(exec, y, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteAndNot(vm, result, x);
scope.release();
return absoluteAddOne(exec, result, SignOption::Signed);
}
JSBigInt* JSBigInt::bitwiseXor(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!x->sign() && !y->sign()) {
scope.release();
return absoluteXor(vm, x, y);
}
if (x->sign() && y->sign()) {
int resultLength = std::max(x->length(), y->length());
// (-x) ^ (-y) == ~(x-1) ^ ~(y-1) == (x-1) ^ (y-1)
JSBigInt* result = absoluteSubOne(exec, x, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
JSBigInt* y1 = absoluteSubOne(exec, y, y->length());
RETURN_IF_EXCEPTION(scope, nullptr);
scope.release();
return absoluteXor(vm, result, y1);
}
ASSERT(x->sign() != y->sign());
int resultLength = std::max(x->length(), y->length()) + 1;
// Assume that x is the positive BigInt.
if (x->sign())
std::swap(x, y);
// x ^ (-y) == x ^ ~(y-1) == ~(x ^ (y-1)) == -((x ^ (y-1)) + 1)
JSBigInt* result = absoluteSubOne(exec, y, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteXor(vm, result, x);
scope.release();
return absoluteAddOne(exec, result, SignOption::Signed);
}
JSBigInt* JSBigInt::leftShift(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
if (y->isZero() || x->isZero())
return x;
if (y->sign())
return rightShiftByAbsolute(exec, x, y);
return leftShiftByAbsolute(exec, x, y);
}
JSBigInt* JSBigInt::signedRightShift(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
if (y->isZero() || x->isZero())
return x;
if (y->sign())
return leftShiftByAbsolute(exec, x, y);
return rightShiftByAbsolute(exec, x, y);
}
JSBigInt* JSBigInt::bitwiseNot(ExecState* exec, JSBigInt* x)
{
if (x->sign()) {
// ~(-x) == ~(~(x-1)) == x-1
return absoluteSubOne(exec, x, x->length());
}
// ~x == -x-1 == -(x+1)
return absoluteAddOne(exec, x, SignOption::Signed);
}
#if USE(JSVALUE32_64)
#define HAVE_TWO_DIGIT 1
typedef uint64_t TwoDigit;
#elif HAVE(INT128_T)
#define HAVE_TWO_DIGIT 1
typedef __uint128_t TwoDigit;
#else
#define HAVE_TWO_DIGIT 0
#endif
// {carry} must point to an initialized Digit and will either be incremented
// by one or left alone.
inline JSBigInt::Digit JSBigInt::digitAdd(Digit a, Digit b, Digit& carry)
{
Digit result = a + b;
carry += static_cast<bool>(result < a);
return result;
}
// {borrow} must point to an initialized Digit and will either be incremented
// by one or left alone.
inline JSBigInt::Digit JSBigInt::digitSub(Digit a, Digit b, Digit& borrow)
{
Digit result = a - b;
borrow += static_cast<bool>(result > a);
return result;
}
// Returns the low half of the result. High half is in {high}.
inline JSBigInt::Digit JSBigInt::digitMul(Digit a, Digit b, Digit& high)
{
#if HAVE(TWO_DIGIT)
TwoDigit result = static_cast<TwoDigit>(a) * static_cast<TwoDigit>(b);
high = result >> digitBits;
return static_cast<Digit>(result);
#else
// Multiply in half-pointer-sized chunks.
// For inputs [AH AL]*[BH BL], the result is:
//
// [AL*BL] // rLow
// + [AL*BH] // rMid1
// + [AH*BL] // rMid2
// + [AH*BH] // rHigh
// = [R4 R3 R2 R1] // high = [R4 R3], low = [R2 R1]
//
// Where of course we must be careful with carries between the columns.
Digit aLow = a & halfDigitMask;
Digit aHigh = a >> halfDigitBits;
Digit bLow = b & halfDigitMask;
Digit bHigh = b >> halfDigitBits;
Digit rLow = aLow * bLow;
Digit rMid1 = aLow * bHigh;
Digit rMid2 = aHigh * bLow;
Digit rHigh = aHigh * bHigh;
Digit carry = 0;
Digit low = digitAdd(rLow, rMid1 << halfDigitBits, carry);
low = digitAdd(low, rMid2 << halfDigitBits, carry);
high = (rMid1 >> halfDigitBits) + (rMid2 >> halfDigitBits) + rHigh + carry;
return low;
#endif
}
// Raises {base} to the power of {exponent}. Does not check for overflow.
inline JSBigInt::Digit JSBigInt::digitPow(Digit base, Digit exponent)
{
Digit result = 1ull;
while (exponent > 0) {
if (exponent & 1)
result *= base;
exponent >>= 1;
base *= base;
}
return result;
}
// Returns the quotient.
// quotient = (high << digitBits + low - remainder) / divisor
inline JSBigInt::Digit JSBigInt::digitDiv(Digit high, Digit low, Digit divisor, Digit& remainder)
{
ASSERT(high < divisor);
#if CPU(X86_64) && COMPILER(GCC_COMPATIBLE)
Digit quotient;
Digit rem;
__asm__("divq %[divisor]"
// Outputs: {quotient} will be in rax, {rem} in rdx.
: "=a"(quotient), "=d"(rem)
// Inputs: put {high} into rdx, {low} into rax, and {divisor} into
// any register or stack slot.
: "d"(high), "a"(low), [divisor] "rm"(divisor));
remainder = rem;
return quotient;
#elif CPU(X86) && COMPILER(GCC_COMPATIBLE)
Digit quotient;
Digit rem;
__asm__("divl %[divisor]"
// Outputs: {quotient} will be in eax, {rem} in edx.
: "=a"(quotient), "=d"(rem)
// Inputs: put {high} into edx, {low} into eax, and {divisor} into
// any register or stack slot.
: "d"(high), "a"(low), [divisor] "rm"(divisor));
remainder = rem;
return quotient;
#else
static constexpr Digit halfDigitBase = 1ull << halfDigitBits;
// Adapted from Warren, Hacker's Delight, p. 152.
unsigned s = clz(divisor);
// If {s} is digitBits here, it causes an undefined behavior.
// But {s} is never digitBits since {divisor} is never zero here.
ASSERT(s != digitBits);
divisor <<= s;
Digit vn1 = divisor >> halfDigitBits;
Digit vn0 = divisor & halfDigitMask;
// {sZeroMask} which is 0 if s == 0 and all 1-bits otherwise.
// {s} can be 0. If {s} is 0, performing "low >> (digitBits - s)" must not be done since it causes an undefined behavior
// since `>> digitBits` is undefied in C++. Quoted from C++ spec, "The type of the result is that of the promoted left operand.
// The behavior is undefined if the right operand is negative, or greater than or equal to the length in bits of the promoted
// left operand". We mask the right operand of the shift by {shiftMask} (`digitBits - 1`), which makes `digitBits - 0` zero.
// This shifting produces a value which covers 0 < {s} <= (digitBits - 1) cases. {s} == digitBits never happen as we asserted.
// Since {sZeroMask} clears the value in the case of {s} == 0, {s} == 0 case is also covered.
STATIC_ASSERT(sizeof(CPURegister) == sizeof(Digit));
Digit sZeroMask = static_cast<Digit>((-static_cast<CPURegister>(s)) >> (digitBits - 1));
static constexpr unsigned shiftMask = digitBits - 1;
Digit un32 = (high << s) | ((low >> ((digitBits - s) & shiftMask)) & sZeroMask);
Digit un10 = low << s;
Digit un1 = un10 >> halfDigitBits;
Digit un0 = un10 & halfDigitMask;
Digit q1 = un32 / vn1;
Digit rhat = un32 - q1 * vn1;
while (q1 >= halfDigitBase || q1 * vn0 > rhat * halfDigitBase + un1) {
q1--;
rhat += vn1;
if (rhat >= halfDigitBase)
break;
}
Digit un21 = un32 * halfDigitBase + un1 - q1 * divisor;
Digit q0 = un21 / vn1;
rhat = un21 - q0 * vn1;
while (q0 >= halfDigitBase || q0 * vn0 > rhat * halfDigitBase + un0) {
q0--;
rhat += vn1;
if (rhat >= halfDigitBase)
break;
}
remainder = (un21 * halfDigitBase + un0 - q0 * divisor) >> s;
return q1 * halfDigitBase + q0;
#endif
}
// Multiplies {source} with {factor} and adds {summand} to the result.
// {result} and {source} may be the same BigInt for inplace modification.
void JSBigInt::internalMultiplyAdd(JSBigInt* source, Digit factor, Digit summand, unsigned n, JSBigInt* result)
{
ASSERT(source->length() >= n);
ASSERT(result->length() >= n);
Digit carry = summand;
Digit high = 0;
for (unsigned i = 0; i < n; i++) {
Digit current = source->digit(i);
Digit newCarry = 0;
// Compute this round's multiplication.
Digit newHigh = 0;
current = digitMul(current, factor, newHigh);
// Add last round's carryovers.
current = digitAdd(current, high, newCarry);
current = digitAdd(current, carry, newCarry);
// Store result and prepare for next round.
result->setDigit(i, current);
carry = newCarry;
high = newHigh;
}
if (result->length() > n) {
result->setDigit(n++, carry + high);
// Current callers don't pass in such large results, but let's be robust.
while (n < result->length())
result->setDigit(n++, 0);
} else
ASSERT(!(carry + high));
}
// Multiplies {multiplicand} with {multiplier} and adds the result to
// {accumulator}, starting at {accumulatorIndex} for the least-significant
// digit.
// Callers must ensure that {accumulator} is big enough to hold the result.
void JSBigInt::multiplyAccumulate(JSBigInt* multiplicand, Digit multiplier, JSBigInt* accumulator, unsigned accumulatorIndex)
{
ASSERT(accumulator->length() > multiplicand->length() + accumulatorIndex);
if (!multiplier)
return;
Digit carry = 0;
Digit high = 0;
for (unsigned i = 0; i < multiplicand->length(); i++, accumulatorIndex++) {
Digit acc = accumulator->digit(accumulatorIndex);
Digit newCarry = 0;
// Add last round's carryovers.
acc = digitAdd(acc, high, newCarry);
acc = digitAdd(acc, carry, newCarry);
// Compute this round's multiplication.
Digit multiplicandDigit = multiplicand->digit(i);
Digit low = digitMul(multiplier, multiplicandDigit, high);
acc = digitAdd(acc, low, newCarry);
// Store result and prepare for next round.
accumulator->setDigit(accumulatorIndex, acc);
carry = newCarry;
}
while (carry || high) {
ASSERT(accumulatorIndex < accumulator->length());
Digit acc = accumulator->digit(accumulatorIndex);
Digit newCarry = 0;
acc = digitAdd(acc, high, newCarry);
high = 0;
acc = digitAdd(acc, carry, newCarry);
accumulator->setDigit(accumulatorIndex, acc);
carry = newCarry;
accumulatorIndex++;
}
}
bool JSBigInt::equals(JSBigInt* x, JSBigInt* y)
{
if (x->sign() != y->sign())
return false;
if (x->length() != y->length())
return false;
for (unsigned i = 0; i < x->length(); i++) {
if (x->digit(i) != y->digit(i))
return false;
}
return true;
}
JSBigInt::ComparisonResult JSBigInt::compare(JSBigInt* x, JSBigInt* y)
{
bool xSign = x->sign();
if (xSign != y->sign())
return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
ComparisonResult result = absoluteCompare(x, y);
if (result == ComparisonResult::GreaterThan)
return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
if (result == ComparisonResult::LessThan)
return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan;
return ComparisonResult::Equal;
}
inline JSBigInt::ComparisonResult JSBigInt::absoluteCompare(JSBigInt* x, JSBigInt* y)
{
ASSERT(!x->length() || x->digit(x->length() - 1));
ASSERT(!y->length() || y->digit(y->length() - 1));
int diff = x->length() - y->length();
if (diff)
return diff < 0 ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
int i = x->length() - 1;
while (i >= 0 && x->digit(i) == y->digit(i))
i--;
if (i < 0)
return ComparisonResult::Equal;
return x->digit(i) > y->digit(i) ? ComparisonResult::GreaterThan : ComparisonResult::LessThan;
}
JSBigInt* JSBigInt::absoluteAdd(ExecState* exec, JSBigInt* x, JSBigInt* y, bool resultSign)
{
VM& vm = exec->vm();
if (x->length() < y->length())
return absoluteAdd(exec, y, x, resultSign);
if (x->isZero()) {
ASSERT(y->isZero());
return x;
}
if (y->isZero())
return resultSign == x->sign() ? x : unaryMinus(vm, x);
JSBigInt* result = JSBigInt::tryCreateWithLength(exec, x->length() + 1);
if (!result)
return nullptr;
Digit carry = 0;
unsigned i = 0;
for (; i < y->length(); i++) {
Digit newCarry = 0;
Digit sum = digitAdd(x->digit(i), y->digit(i), newCarry);
sum = digitAdd(sum, carry, newCarry);
result->setDigit(i, sum);
carry = newCarry;
}
for (; i < x->length(); i++) {
Digit newCarry = 0;
Digit sum = digitAdd(x->digit(i), carry, newCarry);
result->setDigit(i, sum);
carry = newCarry;
}
result->setDigit(i, carry);
result->setSign(resultSign);
return result->rightTrim(vm);
}
JSBigInt* JSBigInt::absoluteSub(VM& vm, JSBigInt* x, JSBigInt* y, bool resultSign)
{
ComparisonResult comparisonResult = absoluteCompare(x, y);
ASSERT(x->length() >= y->length());
ASSERT(comparisonResult == ComparisonResult::GreaterThan || comparisonResult == ComparisonResult::Equal);
if (x->isZero()) {
ASSERT(y->isZero());
return x;
}
if (y->isZero())
return resultSign == x->sign() ? x : unaryMinus(vm, x);
if (comparisonResult == ComparisonResult::Equal)
return JSBigInt::createZero(vm);
JSBigInt* result = JSBigInt::createWithLengthUnchecked(vm, x->length());
Digit borrow = 0;
unsigned i = 0;
for (; i < y->length(); i++) {
Digit newBorrow = 0;
Digit difference = digitSub(x->digit(i), y->digit(i), newBorrow);
difference = digitSub(difference, borrow, newBorrow);
result->setDigit(i, difference);
borrow = newBorrow;
}
for (; i < x->length(); i++) {
Digit newBorrow = 0;
Digit difference = digitSub(x->digit(i), borrow, newBorrow);
result->setDigit(i, difference);
borrow = newBorrow;
}
ASSERT(!borrow);
result->setSign(resultSign);
return result->rightTrim(vm);
}
// Divides {x} by {divisor}, returning the result in {quotient} and {remainder}.
// Mathematically, the contract is:
// quotient = (x - remainder) / divisor, with 0 <= remainder < divisor.
// If {quotient} is an empty handle, an appropriately sized BigInt will be
// allocated for it; otherwise the caller must ensure that it is big enough.
// {quotient} can be the same as {x} for an in-place division. {quotient} can
// also be nullptr if the caller is only interested in the remainder.
void JSBigInt::absoluteDivWithDigitDivisor(VM& vm, JSBigInt* x, Digit divisor, JSBigInt** quotient, Digit& remainder)
{
ASSERT(divisor);
ASSERT(!x->isZero());
remainder = 0;
if (divisor == 1) {
if (quotient != nullptr)
*quotient = x;
return;
}
unsigned length = x->length();
if (quotient != nullptr) {
if (*quotient == nullptr)
*quotient = JSBigInt::createWithLengthUnchecked(vm, length);
for (int i = length - 1; i >= 0; i--) {
Digit q = digitDiv(remainder, x->digit(i), divisor, remainder);
(*quotient)->setDigit(i, q);
}
} else {
for (int i = length - 1; i >= 0; i--)
digitDiv(remainder, x->digit(i), divisor, remainder);
}
}
// Divides {dividend} by {divisor}, returning the result in {quotient} and
// {remainder}. Mathematically, the contract is:
// quotient = (dividend - remainder) / divisor, with 0 <= remainder < divisor.
// Both {quotient} and {remainder} are optional, for callers that are only
// interested in one of them.
// See Knuth, Volume 2, section 4.3.1, Algorithm D.
void JSBigInt::absoluteDivWithBigIntDivisor(ExecState* exec, JSBigInt* dividend, JSBigInt* divisor, JSBigInt** quotient, JSBigInt** remainder)
{
ASSERT(divisor->length() >= 2);
ASSERT(dividend->length() >= divisor->length());
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
// The unusual variable names inside this function are consistent with
// Knuth's book, as well as with Go's implementation of this algorithm.
// Maintaining this consistency is probably more useful than trying to
// come up with more descriptive names for them.
unsigned n = divisor->length();
unsigned m = dividend->length() - n;
// The quotient to be computed.
JSBigInt* q = nullptr;
if (quotient != nullptr)
q = createWithLengthUnchecked(exec->vm(), m + 1);
// In each iteration, {qhatv} holds {divisor} * {current quotient digit}.
// "v" is the book's name for {divisor}, "qhat" the current quotient digit.
JSBigInt* qhatv = tryCreateWithLength(exec, n + 1);
RETURN_IF_EXCEPTION(scope, void());
// D1.
// Left-shift inputs so that the divisor's MSB is set. This is necessary
// to prevent the digit-wise divisions (see digit_div call below) from
// overflowing (they take a two digits wide input, and return a one digit
// result).
Digit lastDigit = divisor->digit(n - 1);
unsigned shift = clz(lastDigit);
if (shift > 0) {
divisor = absoluteLeftShiftAlwaysCopy(exec, divisor, shift, LeftShiftMode::SameSizeResult);
RETURN_IF_EXCEPTION(scope, void());
}
// Holds the (continuously updated) remaining part of the dividend, which
// eventually becomes the remainder.
JSBigInt* u = absoluteLeftShiftAlwaysCopy(exec, dividend, shift, LeftShiftMode::AlwaysAddOneDigit);
RETURN_IF_EXCEPTION(scope, void());
// D2.
// Iterate over the dividend's digit (like the "grad school" algorithm).
// {vn1} is the divisor's most significant digit.
Digit vn1 = divisor->digit(n - 1);
for (int j = m; j >= 0; j--) {
// D3.
// Estimate the current iteration's quotient digit (see Knuth for details).
// {qhat} is the current quotient digit.
Digit qhat = std::numeric_limits<Digit>::max();
// {ujn} is the dividend's most significant remaining digit.
Digit ujn = u->digit(j + n);
if (ujn != vn1) {
// {rhat} is the current iteration's remainder.
Digit rhat = 0;
// Estimate the current quotient digit by dividing the most significant
// digits of dividend and divisor. The result will not be too small,
// but could be a bit too large.
qhat = digitDiv(ujn, u->digit(j + n - 1), vn1, rhat);
// Decrement the quotient estimate as needed by looking at the next
// digit, i.e. by testing whether
// qhat * v_{n-2} > (rhat << digitBits) + u_{j+n-2}.
Digit vn2 = divisor->digit(n - 2);
Digit ujn2 = u->digit(j + n - 2);
while (productGreaterThan(qhat, vn2, rhat, ujn2)) {
qhat--;
Digit prevRhat = rhat;
rhat += vn1;
// v[n-1] >= 0, so this tests for overflow.
if (rhat < prevRhat)
break;
}
}
// D4.
// Multiply the divisor with the current quotient digit, and subtract
// it from the dividend. If there was "borrow", then the quotient digit
// was one too high, so we must correct it and undo one subtraction of
// the (shifted) divisor.
internalMultiplyAdd(divisor, qhat, 0, n, qhatv);
Digit c = u->absoluteInplaceSub(qhatv, j);
if (c) {
c = u->absoluteInplaceAdd(divisor, j);
u->setDigit(j + n, u->digit(j + n) + c);
qhat--;
}
if (quotient != nullptr)
q->setDigit(j, qhat);
}
if (quotient != nullptr) {
// Caller will right-trim.
*quotient = q;
}
if (remainder != nullptr) {
u->inplaceRightShift(shift);
*remainder = u;
}
}
// Returns whether (factor1 * factor2) > (high << kDigitBits) + low.
inline bool JSBigInt::productGreaterThan(Digit factor1, Digit factor2, Digit high, Digit low)
{
Digit resultHigh;
Digit resultLow = digitMul(factor1, factor2, resultHigh);
return resultHigh > high || (resultHigh == high && resultLow > low);
}
// Adds {summand} onto {this}, starting with {summand}'s 0th digit
// at {this}'s {startIndex}'th digit. Returns the "carry" (0 or 1).
JSBigInt::Digit JSBigInt::absoluteInplaceAdd(JSBigInt* summand, unsigned startIndex)
{
Digit carry = 0;
unsigned n = summand->length();
ASSERT(length() >= startIndex + n);
for (unsigned i = 0; i < n; i++) {
Digit newCarry = 0;
Digit sum = digitAdd(digit(startIndex + i), summand->digit(i), newCarry);
sum = digitAdd(sum, carry, newCarry);
setDigit(startIndex + i, sum);
carry = newCarry;
}
return carry;
}
// Subtracts {subtrahend} from {this}, starting with {subtrahend}'s 0th digit
// at {this}'s {startIndex}-th digit. Returns the "borrow" (0 or 1).
JSBigInt::Digit JSBigInt::absoluteInplaceSub(JSBigInt* subtrahend, unsigned startIndex)
{
Digit borrow = 0;
unsigned n = subtrahend->length();
ASSERT(length() >= startIndex + n);
for (unsigned i = 0; i < n; i++) {
Digit newBorrow = 0;
Digit difference = digitSub(digit(startIndex + i), subtrahend->digit(i), newBorrow);
difference = digitSub(difference, borrow, newBorrow);
setDigit(startIndex + i, difference);
borrow = newBorrow;
}
return borrow;
}
void JSBigInt::inplaceRightShift(unsigned shift)
{
ASSERT(shift < digitBits);
ASSERT(!(digit(0) & ((static_cast<Digit>(1) << shift) - 1)));
if (!shift)
return;
Digit carry = digit(0) >> shift;
unsigned last = length() - 1;
for (unsigned i = 0; i < last; i++) {
Digit d = digit(i + 1);
setDigit(i, (d << (digitBits - shift)) | carry);
carry = d >> shift;
}
setDigit(last, carry);
}
// Always copies the input, even when {shift} == 0.
JSBigInt* JSBigInt::absoluteLeftShiftAlwaysCopy(ExecState* exec, JSBigInt* x, unsigned shift, LeftShiftMode mode)
{
ASSERT(shift < digitBits);
ASSERT(!x->isZero());
unsigned n = x->length();
unsigned resultLength = mode == LeftShiftMode::AlwaysAddOneDigit ? n + 1 : n;
JSBigInt* result = tryCreateWithLength(exec, resultLength);
if (!result)
return nullptr;
if (!shift) {
for (unsigned i = 0; i < n; i++)
result->setDigit(i, x->digit(i));
if (mode == LeftShiftMode::AlwaysAddOneDigit)
result->setDigit(n, 0);
return result;
}
Digit carry = 0;
for (unsigned i = 0; i < n; i++) {
Digit d = x->digit(i);
result->setDigit(i, (d << shift) | carry);
carry = d >> (digitBits - shift);
}
if (mode == LeftShiftMode::AlwaysAddOneDigit)
result->setDigit(n, carry);
else {
ASSERT(mode == LeftShiftMode::SameSizeResult);
ASSERT(!carry);
}
return result;
}
// Helper for Absolute{And,AndNot,Or,Xor}.
// Performs the given binary {op} on digit pairs of {x} and {y}; when the
// end of the shorter of the two is reached, {extraDigits} configures how
// remaining digits in the longer input (if {symmetric} == Symmetric, in
// {x} otherwise) are handled: copied to the result or ignored.
// Example:
// y: [ y2 ][ y1 ][ y0 ]
// x: [ x3 ][ x2 ][ x1 ][ x0 ]
// | | | |
// (Copy) (op) (op) (op)
// | | | |
// v v v v
// result: [ 0 ][ x3 ][ r2 ][ r1 ][ r0 ]
template<typename BitwiseOp>
inline JSBigInt* JSBigInt::absoluteBitwiseOp(VM& vm, JSBigInt* x, JSBigInt* y, ExtraDigitsHandling extraDigits, SymmetricOp symmetric, BitwiseOp&& op)
{
unsigned xLength = x->length();
unsigned yLength = y->length();
unsigned numPairs = yLength;
if (xLength < yLength) {
numPairs = xLength;
if (symmetric == SymmetricOp::Symmetric) {
std::swap(x, y);
std::swap(xLength, yLength);
}
}
ASSERT(numPairs == std::min(xLength, yLength));
unsigned resultLength = extraDigits == ExtraDigitsHandling::Copy ? xLength : numPairs;
JSBigInt* result = createWithLengthUnchecked(vm, resultLength);
unsigned i = 0;
for (; i < numPairs; i++)
result->setDigit(i, op(x->digit(i), y->digit(i)));
if (extraDigits == ExtraDigitsHandling::Copy) {
for (; i < xLength; i++)
result->setDigit(i, x->digit(i));
}
for (; i < resultLength; i++)
result->setDigit(i, 0);
return result->rightTrim(vm);
}
JSBigInt* JSBigInt::absoluteAnd(VM& vm, JSBigInt* x, JSBigInt* y)
{
auto digitOperation = [](Digit a, Digit b) {
return a & b;
};
return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Skip, SymmetricOp::Symmetric, digitOperation);
}
JSBigInt* JSBigInt::absoluteOr(VM& vm, JSBigInt* x, JSBigInt* y)
{
auto digitOperation = [](Digit a, Digit b) {
return a | b;
};
return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Copy, SymmetricOp::Symmetric, digitOperation);
}
JSBigInt* JSBigInt::absoluteAndNot(VM& vm, JSBigInt* x, JSBigInt* y)
{
auto digitOperation = [](Digit a, Digit b) {
return a & ~b;
};
return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Copy, SymmetricOp::NotSymmetric, digitOperation);
}
JSBigInt* JSBigInt::absoluteXor(VM& vm, JSBigInt* x, JSBigInt* y)
{
auto digitOperation = [](Digit a, Digit b) {
return a ^ b;
};
return absoluteBitwiseOp(vm, x, y, ExtraDigitsHandling::Copy, SymmetricOp::Symmetric, digitOperation);
}
JSBigInt* JSBigInt::absoluteAddOne(ExecState* exec, JSBigInt* x, SignOption signOption)
{
unsigned inputLength = x->length();
// The addition will overflow into a new digit if all existing digits are
// at maximum.
bool willOverflow = true;
for (unsigned i = 0; i < inputLength; i++) {
if (std::numeric_limits<Digit>::max() != x->digit(i)) {
willOverflow = false;
break;
}
}
unsigned resultLength = inputLength + willOverflow;
JSBigInt* result = tryCreateWithLength(exec, resultLength);
if (!result)
return nullptr;
Digit carry = 1;
for (unsigned i = 0; i < inputLength; i++) {
Digit newCarry = 0;
result->setDigit(i, digitAdd(x->digit(i), carry, newCarry));
carry = newCarry;
}
if (resultLength > inputLength)
result->setDigit(inputLength, carry);
else
ASSERT(!carry);
result->setSign(signOption == SignOption::Signed);
return result->rightTrim(exec->vm());
}
JSBigInt* JSBigInt::absoluteSubOne(ExecState* exec, JSBigInt* x, unsigned resultLength)
{
ASSERT(!x->isZero());
ASSERT(resultLength >= x->length());
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
JSBigInt* result = tryCreateWithLength(exec, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
unsigned length = x->length();
Digit borrow = 1;
for (unsigned i = 0; i < length; i++) {
Digit newBorrow = 0;
result->setDigit(i, digitSub(x->digit(i), borrow, newBorrow));
borrow = newBorrow;
}
ASSERT(!borrow);
for (unsigned i = length; i < resultLength; i++)
result->setDigit(i, borrow);
return result->rightTrim(vm);
}
JSBigInt* JSBigInt::leftShiftByAbsolute(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
auto optionalShift = toShiftAmount(y);
if (!optionalShift) {
throwRangeError(exec, scope, "BigInt generated from this operation is too big"_s);
return nullptr;
}
Digit shift = *optionalShift;
unsigned digitShift = static_cast<unsigned>(shift / digitBits);
unsigned bitsShift = static_cast<unsigned>(shift % digitBits);
unsigned length = x->length();
bool grow = bitsShift && (x->digit(length - 1) >> (digitBits - bitsShift));
int resultLength = length + digitShift + grow;
if (static_cast<unsigned>(resultLength) > maxLength) {
throwRangeError(exec, scope, "BigInt generated from this operation is too big"_s);
return nullptr;
}
JSBigInt* result = tryCreateWithLength(exec, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
if (!bitsShift) {
unsigned i = 0;
for (; i < digitShift; i++)
result->setDigit(i, 0ul);
for (; i < static_cast<unsigned>(resultLength); i++)
result->setDigit(i, x->digit(i - digitShift));
} else {
Digit carry = 0;
for (unsigned i = 0; i < digitShift; i++)
result->setDigit(i, 0ul);
for (unsigned i = 0; i < length; i++) {
Digit d = x->digit(i);
result->setDigit(i + digitShift, (d << bitsShift) | carry);
carry = d >> (digitBits - bitsShift);
}
if (grow)
result->setDigit(length + digitShift, carry);
else
ASSERT(!carry);
}
result->setSign(x->sign());
return result->rightTrim(vm);
}
JSBigInt* JSBigInt::rightShiftByAbsolute(ExecState* exec, JSBigInt* x, JSBigInt* y)
{
VM& vm = exec->vm();
unsigned length = x->length();
bool sign = x->sign();
auto optionalShift = toShiftAmount(y);
if (!optionalShift)
return rightShiftByMaximum(vm, sign);
Digit shift = *optionalShift;
unsigned digitalShift = static_cast<unsigned>(shift / digitBits);
unsigned bitsShift = static_cast<unsigned>(shift % digitBits);
int resultLength = length - digitalShift;
if (resultLength <= 0)
return rightShiftByMaximum(vm, sign);
// For negative numbers, round down if any bit was shifted out (so that e.g.
// -5n >> 1n == -3n and not -2n). Check now whether this will happen and
// whether it can cause overflow into a new digit. If we allocate the result
// large enough up front, it avoids having to do a second allocation later.
bool mustRoundDown = false;
if (sign) {
const Digit mask = (static_cast<Digit>(1) << bitsShift) - 1;
if (x->digit(digitalShift) & mask)
mustRoundDown = true;
else {
for (unsigned i = 0; i < digitalShift; i++) {
if (x->digit(i)) {
mustRoundDown = true;
break;
}
}
}
}
// If bitsShift is non-zero, it frees up bits, preventing overflow.
if (mustRoundDown && !bitsShift) {
// Overflow cannot happen if the most significant digit has unset bits.
Digit msd = x->digit(length - 1);
bool roundingCanOverflow = !static_cast<Digit>(~msd);
if (roundingCanOverflow)
resultLength++;
}
ASSERT(static_cast<unsigned>(resultLength) <= length);
JSBigInt* result = createWithLengthUnchecked(vm, static_cast<unsigned>(resultLength));
if (!bitsShift) {
for (unsigned i = digitalShift; i < length; i++)
result->setDigit(i - digitalShift, x->digit(i));
} else {
Digit carry = x->digit(digitalShift) >> bitsShift;
unsigned last = length - digitalShift - 1;
for (unsigned i = 0; i < last; i++) {
Digit d = x->digit(i + digitalShift + 1);
result->setDigit(i, (d << (digitBits - bitsShift)) | carry);
carry = d >> bitsShift;
}
result->setDigit(last, carry);
}
if (sign) {
result->setSign(true);
if (mustRoundDown) {
// Since the result is negative, rounding down means adding one to
// its absolute value. This cannot overflow.
result = result->rightTrim(vm);
return absoluteAddOne(exec, result, SignOption::Signed);
}
}
return result->rightTrim(vm);
}
JSBigInt* JSBigInt::rightShiftByMaximum(VM& vm, bool sign)
{
if (sign)
return createFrom(vm, -1);
return createZero(vm);
}
// Lookup table for the maximum number of bits required per character of a
// base-N string representation of a number. To increase accuracy, the array
// value is the actual value multiplied by 32. To generate this table:
// for (var i = 0; i <= 36; i++) { print(Math.ceil(Math.log2(i) * 32) + ","); }
constexpr uint8_t maxBitsPerCharTable[] = {
0, 0, 32, 51, 64, 75, 83, 90, 96, // 0..8
102, 107, 111, 115, 119, 122, 126, 128, // 9..16
131, 134, 136, 139, 141, 143, 145, 147, // 17..24
149, 151, 153, 154, 156, 158, 159, 160, // 25..32
162, 163, 165, 166, // 33..36
};
static constexpr unsigned bitsPerCharTableShift = 5;
static constexpr size_t bitsPerCharTableMultiplier = 1u << bitsPerCharTableShift;
// Compute (an overapproximation of) the length of the resulting string:
// Divide bit length of the BigInt by bits representable per character.
uint64_t JSBigInt::calculateMaximumCharactersRequired(unsigned length, unsigned radix, Digit lastDigit, bool sign)
{
unsigned leadingZeros = clz(lastDigit);
size_t bitLength = length * digitBits - leadingZeros;
// Maximum number of bits we can represent with one character. We'll use this
// to find an appropriate chunk size below.
uint8_t maxBitsPerChar = maxBitsPerCharTable[radix];
// For estimating result length, we have to be pessimistic and work with
// the minimum number of bits one character can represent.
uint8_t minBitsPerChar = maxBitsPerChar - 1;
// Perform the following computation with uint64_t to avoid overflows.
uint64_t maximumCharactersRequired = bitLength;
maximumCharactersRequired *= bitsPerCharTableMultiplier;
// Round up.
maximumCharactersRequired += minBitsPerChar - 1;
maximumCharactersRequired /= minBitsPerChar;
maximumCharactersRequired += sign;
return maximumCharactersRequired;
}
String JSBigInt::toStringBasePowerOfTwo(ExecState* exec, JSBigInt* x, unsigned radix)
{
ASSERT(hasOneBitSet(radix));
ASSERT(radix >= 2 && radix <= 32);
ASSERT(!x->isZero());
VM& vm = exec->vm();
const unsigned length = x->length();
const bool sign = x->sign();
const unsigned bitsPerChar = ctz(radix);
const unsigned charMask = radix - 1;
// Compute the length of the resulting string: divide the bit length of the
// BigInt by the number of bits representable per character (rounding up).
const Digit msd = x->digit(length - 1);
const unsigned msdLeadingZeros = clz(msd);
const size_t bitLength = length * digitBits - msdLeadingZeros;
const size_t charsRequired = (bitLength + bitsPerChar - 1) / bitsPerChar + sign;
if (charsRequired > JSString::MaxLength) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(exec, scope);
return String();
}
Vector<LChar> resultString(charsRequired);
Digit digit = 0;
// Keeps track of how many unprocessed bits there are in {digit}.
unsigned availableBits = 0;
int pos = static_cast<int>(charsRequired - 1);
for (unsigned i = 0; i < length - 1; i++) {
Digit newDigit = x->digit(i);
// Take any leftover bits from the last iteration into account.
int current = (digit | (newDigit << availableBits)) & charMask;
resultString[pos--] = radixDigits[current];
int consumedBits = bitsPerChar - availableBits;
digit = newDigit >> consumedBits;
availableBits = digitBits - consumedBits;
while (availableBits >= bitsPerChar) {
resultString[pos--] = radixDigits[digit & charMask];
digit >>= bitsPerChar;
availableBits -= bitsPerChar;
}
}
// Take any leftover bits from the last iteration into account.
int current = (digit | (msd << availableBits)) & charMask;
resultString[pos--] = radixDigits[current];
digit = msd >> (bitsPerChar - availableBits);
while (digit) {
resultString[pos--] = radixDigits[digit & charMask];
digit >>= bitsPerChar;
}
if (sign)
resultString[pos--] = '-';
ASSERT(pos == -1);
return StringImpl::adopt(WTFMove(resultString));
}
String JSBigInt::toStringGeneric(ExecState* exec, JSBigInt* x, unsigned radix)
{
// FIXME: [JSC] Revisit usage of Vector into JSBigInt::toString
// https://bugs.webkit.org/show_bug.cgi?id=18067
Vector<LChar> resultString;
VM& vm = exec->vm();
ASSERT(radix >= 2 && radix <= 36);
ASSERT(!x->isZero());
unsigned length = x->length();
bool sign = x->sign();
uint8_t maxBitsPerChar = maxBitsPerCharTable[radix];
uint64_t maximumCharactersRequired = calculateMaximumCharactersRequired(length, radix, x->digit(length - 1), sign);
if (maximumCharactersRequired > JSString::MaxLength) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(exec, scope);
return String();
}
Digit lastDigit;
if (length == 1)
lastDigit = x->digit(0);
else {
unsigned chunkChars = digitBits * bitsPerCharTableMultiplier / maxBitsPerChar;
Digit chunkDivisor = digitPow(radix, chunkChars);
// By construction of chunkChars, there can't have been overflow.
ASSERT(chunkDivisor);
unsigned nonZeroDigit = length - 1;
ASSERT(x->digit(nonZeroDigit));
// {rest} holds the part of the BigInt that we haven't looked at yet.
// Not to be confused with "remainder"!
JSBigInt* rest = nullptr;
// In the first round, divide the input, allocating a new BigInt for
// the result == rest; from then on divide the rest in-place.
JSBigInt** dividend = &x;
do {
Digit chunk;
absoluteDivWithDigitDivisor(vm, *dividend, chunkDivisor, &rest, chunk);
dividend = &rest;
for (unsigned i = 0; i < chunkChars; i++) {
resultString.append(radixDigits[chunk % radix]);
chunk /= radix;
}
ASSERT(!chunk);
if (!rest->digit(nonZeroDigit))
nonZeroDigit--;
// We can never clear more than one digit per iteration, because
// chunkDivisor is smaller than max digit value.
ASSERT(rest->digit(nonZeroDigit));
} while (nonZeroDigit > 0);
lastDigit = rest->digit(0);
}
do {
resultString.append(radixDigits[lastDigit % radix]);
lastDigit /= radix;
} while (lastDigit > 0);
ASSERT(resultString.size());
ASSERT(resultString.size() <= static_cast<size_t>(maximumCharactersRequired));
// Remove leading zeroes.
unsigned newSizeNoLeadingZeroes = resultString.size();
while (newSizeNoLeadingZeroes > 1 && resultString[newSizeNoLeadingZeroes - 1] == '0')
newSizeNoLeadingZeroes--;
resultString.shrink(newSizeNoLeadingZeroes);
if (sign)
resultString.append('-');
std::reverse(resultString.begin(), resultString.end());
return StringImpl::adopt(WTFMove(resultString));
}
JSBigInt* JSBigInt::rightTrim(VM& vm)
{
if (isZero()) {
ASSERT(!sign());
return this;
}
int nonZeroIndex = m_length - 1;
while (nonZeroIndex >= 0 && !digit(nonZeroIndex))
nonZeroIndex--;
if (nonZeroIndex < 0)
return createZero(vm);
if (nonZeroIndex == static_cast<int>(m_length - 1))
return this;
unsigned newLength = nonZeroIndex + 1;
JSBigInt* trimmedBigInt = createWithLengthUnchecked(vm, newLength);
std::copy(dataStorage(), dataStorage() + newLength, trimmedBigInt->dataStorage());
trimmedBigInt->setSign(this->sign());
return trimmedBigInt;
}
JSBigInt* JSBigInt::allocateFor(ExecState* exec, VM& vm, unsigned radix, unsigned charcount)
{
ASSERT(2 <= radix && radix <= 36);
size_t bitsPerChar = maxBitsPerCharTable[radix];
size_t chars = charcount;
const unsigned roundup = bitsPerCharTableMultiplier - 1;
if (chars <= (std::numeric_limits<size_t>::max() - roundup) / bitsPerChar) {
size_t bitsMin = bitsPerChar * chars;
// Divide by 32 (see table), rounding up.
bitsMin = (bitsMin + roundup) >> bitsPerCharTableShift;
if (bitsMin <= static_cast<size_t>(maxInt)) {
// Divide by kDigitsBits, rounding up.
unsigned length = (bitsMin + digitBits - 1) / digitBits;
if (length <= maxLength) {
JSBigInt* result = JSBigInt::createWithLengthUnchecked(vm, length);
return result;
}
}
}
if (exec) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(exec, scope);
}
return nullptr;
}
size_t JSBigInt::estimatedSize(JSCell* cell, VM& vm)
{
return Base::estimatedSize(cell, vm) + jsCast<JSBigInt*>(cell)->m_length * sizeof(Digit);
}
double JSBigInt::toNumber(ExecState* exec) const
{
VM& vm = exec->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
throwTypeError(exec, scope, "Conversion from 'BigInt' to 'number' is not allowed."_s);
return 0.0;
}
bool JSBigInt::getPrimitiveNumber(ExecState* exec, double& number, JSValue& result) const
{
result = this;
number = toNumber(exec);
return true;
}
template <typename CharType>
JSBigInt* JSBigInt::parseInt(ExecState* exec, CharType* data, unsigned length, ErrorParseMode errorParseMode)
{
VM& vm = exec->vm();
unsigned p = 0;
while (p < length && isStrWhiteSpace(data[p]))
++p;
// Check Radix from frist characters
if (static_cast<unsigned>(p) + 1 < static_cast<unsigned>(length) && data[p] == '0') {
if (isASCIIAlphaCaselessEqual(data[p + 1], 'b'))
return parseInt(exec, vm, data, length, p + 2, 2, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString);
if (isASCIIAlphaCaselessEqual(data[p + 1], 'x'))
return parseInt(exec, vm, data, length, p + 2, 16, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString);
if (isASCIIAlphaCaselessEqual(data[p + 1], 'o'))
return parseInt(exec, vm, data, length, p + 2, 8, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString);
}
ParseIntSign sign = ParseIntSign::Unsigned;
if (p < length) {
if (data[p] == '+')
++p;
else if (data[p] == '-') {
sign = ParseIntSign::Signed;
++p;
}
}
JSBigInt* result = parseInt(exec, vm, data, length, p, 10, errorParseMode, sign);
if (result && !result->isZero())
result->setSign(sign == ParseIntSign::Signed);
return result;
}
template <typename CharType>
JSBigInt* JSBigInt::parseInt(ExecState* exec, VM& vm, CharType* data, unsigned length, unsigned startIndex, unsigned radix, ErrorParseMode errorParseMode, ParseIntSign sign, ParseIntMode parseMode)
{
ASSERT(length >= 0);
unsigned p = startIndex;
auto scope = DECLARE_THROW_SCOPE(vm);
if (parseMode != ParseIntMode::AllowEmptyString && startIndex == length) {
ASSERT(exec);
if (errorParseMode == ErrorParseMode::ThrowExceptions)
throwVMError(exec, scope, createSyntaxError(exec, "Failed to parse String to BigInt"));
return nullptr;
}
// Skipping leading zeros
while (p < length && data[p] == '0')
++p;
int endIndex = length - 1;
// Removing trailing spaces
while (endIndex >= static_cast<int>(p) && isStrWhiteSpace(data[endIndex]))
--endIndex;
length = endIndex + 1;
if (p == length)
return createZero(vm);
unsigned limit0 = '0' + (radix < 10 ? radix : 10);
unsigned limita = 'a' + (radix - 10);
unsigned limitA = 'A' + (radix - 10);
JSBigInt* result = allocateFor(exec, vm, radix, length - p);
RETURN_IF_EXCEPTION(scope, nullptr);
result->initialize(InitializationType::WithZero);
for (unsigned i = p; i < length; i++, p++) {
uint32_t digit;
if (data[i] >= '0' && data[i] < limit0)
digit = data[i] - '0';
else if (data[i] >= 'a' && data[i] < limita)
digit = data[i] - 'a' + 10;
else if (data[i] >= 'A' && data[i] < limitA)
digit = data[i] - 'A' + 10;
else
break;
result->inplaceMultiplyAdd(static_cast<Digit>(radix), static_cast<Digit>(digit));
}
result->setSign(sign == ParseIntSign::Signed ? true : false);
if (p == length)
return result->rightTrim(vm);
ASSERT(exec);
if (errorParseMode == ErrorParseMode::ThrowExceptions)
throwVMError(exec, scope, createSyntaxError(exec, "Failed to parse String to BigInt"));
return nullptr;
}
inline JSBigInt::Digit JSBigInt::digit(unsigned n)
{
ASSERT(n < length());
return dataStorage()[n];
}
inline void JSBigInt::setDigit(unsigned n, Digit value)
{
ASSERT(n < length());
dataStorage()[n] = value;
}
JSObject* JSBigInt::toObject(ExecState* exec, JSGlobalObject* globalObject) const
{
return BigIntObject::create(exec->vm(), globalObject, const_cast<JSBigInt*>(this));
}
bool JSBigInt::equalsToNumber(JSValue numValue)
{
ASSERT(numValue.isNumber());
if (numValue.isInt32()) {
int value = numValue.asInt32();
if (!value)
return this->isZero();
return (this->length() == 1) && (this->sign() == (value < 0)) && (this->digit(0) == static_cast<Digit>(std::abs(static_cast<int64_t>(value))));
}
double value = numValue.asDouble();
return compareToDouble(this, value) == ComparisonResult::Equal;
}
JSBigInt::ComparisonResult JSBigInt::compareToDouble(JSBigInt* x, double y)
{
// This algorithm expect that the double format is IEEE 754
uint64_t doubleBits = bitwise_cast<uint64_t>(y);
int rawExponent = static_cast<int>(doubleBits >> 52) & 0x7FF;
if (rawExponent == 0x7FF) {
if (std::isnan(y))
return ComparisonResult::Undefined;
return (y == std::numeric_limits<double>::infinity()) ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
}
bool xSign = x->sign();
// Note that this is different from the double's sign bit for -0. That's
// intentional because -0 must be treated like 0.
bool ySign = y < 0;
if (xSign != ySign)
return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
if (!y) {
ASSERT(!xSign);
return x->isZero() ? ComparisonResult::Equal : ComparisonResult::GreaterThan;
}
if (x->isZero())
return ComparisonResult::LessThan;
uint64_t mantissa = doubleBits & 0x000FFFFFFFFFFFFF;
// Non-finite doubles are handled above.
ASSERT(rawExponent != 0x7FF);
int exponent = rawExponent - 0x3FF;
if (exponent < 0) {
// The absolute value of the double is less than 1. Only 0n has an
// absolute value smaller than that, but we've already covered that case.
return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
}
int xLength = x->length();
Digit xMSD = x->digit(xLength - 1);
int msdLeadingZeros = clz(xMSD);
int xBitLength = xLength * digitBits - msdLeadingZeros;
int yBitLength = exponent + 1;
if (xBitLength < yBitLength)
return xSign? ComparisonResult::GreaterThan : ComparisonResult::LessThan;
if (xBitLength > yBitLength)
return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
// At this point, we know that signs and bit lengths (i.e. position of
// the most significant bit in exponent-free representation) are identical.
// {x} is not zero, {y} is finite and not denormal.
// Now we virtually convert the double to an integer by shifting its
// mantissa according to its exponent, so it will align with the BigInt {x},
// and then we compare them bit for bit until we find a difference or the
// least significant bit.
// <----- 52 ------> <-- virtual trailing zeroes -->
// y / mantissa: 1yyyyyyyyyyyyyyyyy 0000000000000000000000000000000
// x / digits: 0001xxxx xxxxxxxx xxxxxxxx ...
// <--> <------>
// msdTopBit digitBits
//
mantissa |= 0x0010000000000000;
const int mantissaTopBit = 52; // 0-indexed.
// 0-indexed position of {x}'s most significant bit within the {msd}.
int msdTopBit = digitBits - 1 - msdLeadingZeros;
ASSERT(msdTopBit == static_cast<int>((xBitLength - 1) % digitBits));
// Shifted chunk of {mantissa} for comparing with {digit}.
Digit compareMantissa;
// Number of unprocessed bits in {mantissa}. We'll keep them shifted to
// the left (i.e. most significant part) of the underlying uint64_t.
int remainingMantissaBits = 0;
// First, compare the most significant digit against the beginning of
// the mantissa and then we align them.
if (msdTopBit < mantissaTopBit) {
remainingMantissaBits = (mantissaTopBit - msdTopBit);
compareMantissa = static_cast<Digit>(mantissa >> remainingMantissaBits);
mantissa = mantissa << (64 - remainingMantissaBits);
} else {
compareMantissa = static_cast<Digit>(mantissa << (msdTopBit - mantissaTopBit));
mantissa = 0;
}
if (xMSD > compareMantissa)
return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
if (xMSD < compareMantissa)
return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan;
// Then, compare additional digits against any remaining mantissa bits.
for (int digitIndex = xLength - 2; digitIndex >= 0; digitIndex--) {
if (remainingMantissaBits > 0) {
remainingMantissaBits -= digitBits;
if (sizeof(mantissa) != sizeof(xMSD)) {
compareMantissa = static_cast<Digit>(mantissa >> (64 - digitBits));
// "& 63" to appease compilers. digitBits is 32 here anyway.
mantissa = mantissa << (digitBits & 63);
} else {
compareMantissa = static_cast<Digit>(mantissa);
mantissa = 0;
}
} else
compareMantissa = 0;
Digit digit = x->digit(digitIndex);
if (digit > compareMantissa)
return xSign ? ComparisonResult::LessThan : ComparisonResult::GreaterThan;
if (digit < compareMantissa)
return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan;
}
// Integer parts are equal; check whether {y} has a fractional part.
if (mantissa) {
ASSERT(remainingMantissaBits > 0);
return xSign ? ComparisonResult::GreaterThan : ComparisonResult::LessThan;
}
return ComparisonResult::Equal;
}
Optional<JSBigInt::Digit> JSBigInt::toShiftAmount(JSBigInt* x)
{
if (x->length() > 1)
return WTF::nullopt;
Digit value = x->digit(0);
static_assert(maxLengthBits < std::numeric_limits<Digit>::max(), "maxLengthBits needs to be less than digit");
if (value > maxLengthBits)
return WTF::nullopt;
return value;
}
} // namespace JSC