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darling-JavaScriptCore/runtime/JSBigInt.cpp

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/*
* Copyright (C) 2017 Caio Lima <ticaiolima@gmail.com>
* Copyright (C) 2017-2020 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 "JSCJSValueInlines.h"
#include "JSObjectInlines.h"
#include "MathCommon.h"
#include "ParseInt.h"
#include "StructureInlines.h"
#include <algorithm>
#include <wtf/Hasher.h>
#include <wtf/MathExtras.h>
namespace JSC {
const ClassInfo JSBigInt::s_info = { "BigInt", nullptr, nullptr, nullptr, CREATE_METHOD_TABLE(JSBigInt) };
JSBigInt::JSBigInt(VM& vm, Structure* structure, Digit* data, unsigned length)
: Base(vm, structure)
, m_length(length)
, m_data(vm, this, data, length)
{ }
void JSBigInt::visitChildren(JSCell* cell, SlotVisitor& visitor)
{
auto* thisObject = jsCast<JSBigInt*>(cell);
ASSERT_GC_OBJECT_INHERITS(thisObject, info());
Base::visitChildren(thisObject, visitor);
if (auto* data = thisObject->m_data.getUnsafe())
visitor.markAuxiliary(data);
}
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(HeapBigIntType, StructureFlags), info());
}
inline JSBigInt* JSBigInt::createZero(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm)
{
return createWithLength(nullOrGlobalObjectForOOM, vm, 0);
}
JSBigInt* JSBigInt::createZero(JSGlobalObject* globalObject)
{
return createZero(globalObject, globalObject->vm());
}
JSBigInt* JSBigInt::tryCreateZero(VM& vm)
{
return createZero(nullptr, vm);
}
inline JSBigInt* JSBigInt::createWithLength(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm, unsigned length)
{
if (UNLIKELY(length > maxLength)) {
if (nullOrGlobalObjectForOOM) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(nullOrGlobalObjectForOOM, scope, "BigInt generated from this operation is too big"_s);
}
return nullptr;
}
ASSERT(length <= maxLength);
void* data = vm.primitiveGigacageAuxiliarySpace.allocateNonVirtual(vm, length * sizeof(Digit), nullptr, AllocationFailureMode::ReturnNull);
if (UNLIKELY(!data)) {
if (nullOrGlobalObjectForOOM) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(nullOrGlobalObjectForOOM, scope);
}
return nullptr;
}
JSBigInt* bigInt = new (NotNull, allocateCell<JSBigInt>(vm.heap)) JSBigInt(vm, vm.bigIntStructure.get(), reinterpret_cast<Digit*>(data), length);
bigInt->finishCreation(vm);
return bigInt;
}
JSBigInt* JSBigInt::tryCreateWithLength(VM& vm, unsigned length)
{
return createWithLength(nullptr, vm, length);
}
JSBigInt* JSBigInt::createWithLength(JSGlobalObject* globalObject, unsigned length)
{
return createWithLength(globalObject, globalObject->vm(), length);
}
inline JSBigInt* JSBigInt::createFrom(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm, int32_t value)
{
if (!value)
return createZero(nullOrGlobalObjectForOOM, vm);
JSBigInt* bigInt = createWithLength(nullOrGlobalObjectForOOM, vm, 1);
if (UNLIKELY(!bigInt))
return nullptr;
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(JSGlobalObject* globalObject, int32_t value)
{
return createFrom(globalObject, globalObject->vm(), value);
}
JSBigInt* JSBigInt::tryCreateFrom(VM& vm, int32_t value)
{
return createFrom(nullptr, vm, value);
}
JSBigInt* JSBigInt::createFrom(JSGlobalObject* globalObject, uint32_t value)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!value)
RELEASE_AND_RETURN(scope, createZero(globalObject));
JSBigInt* bigInt = createWithLength(globalObject, 1);
RETURN_IF_EXCEPTION(scope, nullptr);
bigInt->setDigit(0, static_cast<Digit>(value));
return bigInt;
}
inline JSBigInt* JSBigInt::createFromImpl(JSGlobalObject* globalObject, uint64_t value, bool sign)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!value)
RELEASE_AND_RETURN(scope, createZero(globalObject));
// This path is not just an optimization: because we do not call rightTrim at the end of this function,
// it would be a bug to create a BigInt with length=2 in this case.
if (sizeof(Digit) == 8 || value <= UINT32_MAX) {
JSBigInt* bigInt = createWithLength(globalObject, 1);
RETURN_IF_EXCEPTION(scope, nullptr);
bigInt->setDigit(0, static_cast<Digit>(value));
bigInt->setSign(sign);
return bigInt;
}
ASSERT(sizeof(Digit) == 4);
JSBigInt* bigInt = createWithLength(globalObject, 2);
RETURN_IF_EXCEPTION(scope, nullptr);
Digit lowBits = static_cast<Digit>(value & 0xffffffff);
Digit highBits = static_cast<Digit>((value >> 32) & 0xffffffff);
ASSERT(highBits);
bigInt->setDigit(0, lowBits);
bigInt->setDigit(1, highBits);
bigInt->setSign(sign);
return bigInt;
}
JSBigInt* JSBigInt::createFrom(JSGlobalObject* globalObject, uint64_t value)
{
return createFromImpl(globalObject, value, false);
}
JSBigInt* JSBigInt::createFrom(JSGlobalObject* globalObject, int64_t value)
{
uint64_t unsignedValue;
bool sign = false;
if (value < 0) {
unsignedValue = static_cast<uint64_t>(-(value + 1)) + 1;
sign = true;
} else
unsignedValue = value;
return createFromImpl(globalObject, unsignedValue, sign);
}
JSBigInt* JSBigInt::createFrom(JSGlobalObject* globalObject, bool value)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!value)
RELEASE_AND_RETURN(scope, createZero(globalObject));
JSBigInt* bigInt = createWithLength(globalObject, 1);
RETURN_IF_EXCEPTION(scope, nullptr);
bigInt->setDigit(0, static_cast<Digit>(value));
return bigInt;
}
JSBigInt* JSBigInt::createFrom(JSGlobalObject* globalObject, double value)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
ASSERT(isInteger(value));
if (!value)
RELEASE_AND_RETURN(scope, createZero(globalObject));
bool sign = value < 0; // -0 was already handled above.
uint64_t doubleBits = bitwise_cast<uint64_t>(value);
int32_t rawExponent = static_cast<int32_t>(doubleBits >> doublePhysicalMantissaSize) & 0x7ff;
ASSERT(rawExponent != 0x7ff); // Since value is integer, exponent should not be 0x7ff (full bits, used for infinity etc.).
ASSERT(rawExponent >= 0x3ff); // Since value is integer, exponent should be >= 0 + bias (0x3ff).
int32_t exponent = rawExponent - 0x3ff;
int32_t digits = exponent / digitBits + 1;
JSBigInt* result = createWithLength(globalObject, digits);
RETURN_IF_EXCEPTION(scope, nullptr);
ASSERT(result);
result->initialize(InitializationType::WithZero);
result->setSign(sign);
// We construct a BigInt from the double value by shifting its mantissa
// according to its exponent and mapping the bit pattern onto digits.
//
// <----------- bitlength = exponent + 1 ----------->
// <----- 52 ------> <------ trailing zeroes ------>
// mantissa: 1yyyyyyyyyyyyyyyyy 0000000000000000000000000000000
// digits: 0001xxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx
// <--> <------>
// msdTopBit digitBits
//
uint64_t mantissa = (doubleBits & doublePhysicalMantissaMask) | doubleMantissaHiddenBit;
int32_t mantissaTopBit = doubleMantissaSize - 1; // 0-indexed.
// 0-indexed position of most significant bit in the most significant digit.
int32_t msdTopBit = exponent % digitBits;
// Number of unused bits in mantissa. We'll keep them shifted to the
// left (i.e. most significant part) of the underlying uint64_t.
int32_t remainingMantissaBits = 0;
// Next digit under construction.
Digit digit = 0;
// First, build the MSD by shifting the mantissa appropriately.
if (msdTopBit < mantissaTopBit) {
remainingMantissaBits = mantissaTopBit - msdTopBit;
digit = static_cast<Digit>(mantissa >> remainingMantissaBits);
mantissa = mantissa << (64 - remainingMantissaBits);
} else {
ASSERT(msdTopBit >= mantissaTopBit);
digit = static_cast<Digit>(mantissa << (msdTopBit - mantissaTopBit));
mantissa = 0;
}
result->setDigit(digits - 1, digit);
// Then fill in the rest of the digits.
for (int32_t digitIndex = digits - 2; digitIndex >= 0; digitIndex--) {
if (remainingMantissaBits > 0) {
remainingMantissaBits -= digitBits;
if constexpr (sizeof(Digit) == 4) {
digit = mantissa >> 32;
mantissa = mantissa << 32;
} else {
ASSERT(sizeof(Digit) == 8);
digit = mantissa;
mantissa = 0;
}
} else
digit = 0;
result->setDigit(digitIndex, digit);
}
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
JSValue JSBigInt::toPrimitive(JSGlobalObject*, PreferredPrimitiveType) const
{
return const_cast<JSBigInt*>(this);
}
JSValue JSBigInt::parseInt(JSGlobalObject* globalObject, StringView s, ErrorParseMode parserMode)
{
if (s.is8Bit())
return parseInt(globalObject, s.characters8(), s.length(), parserMode);
return parseInt(globalObject, s.characters16(), s.length(), parserMode);
}
JSValue JSBigInt::parseInt(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm, StringView s, uint8_t radix, ErrorParseMode parserMode, ParseIntSign sign)
{
if (s.is8Bit())
return parseInt(nullOrGlobalObjectForOOM, vm, s.characters8(), s.length(), 0, radix, parserMode, sign, ParseIntMode::DisallowEmptyString);
return parseInt(nullOrGlobalObjectForOOM, vm, s.characters16(), s.length(), 0, radix, parserMode, sign, ParseIntMode::DisallowEmptyString);
}
JSValue JSBigInt::stringToBigInt(JSGlobalObject* globalObject, StringView s)
{
return parseInt(globalObject, s, ErrorParseMode::IgnoreExceptions);
}
String JSBigInt::toString(JSGlobalObject* globalObject, unsigned radix)
{
if (this->isZero())
return globalObject->vm().smallStrings.singleCharacterStringRep('0');
if (hasOneBitSet(radix))
return toStringBasePowerOfTwo(globalObject->vm(), globalObject, this, radix);
return toStringGeneric(globalObject->vm(), globalObject, this, radix);
}
String JSBigInt::tryGetString(VM& vm, JSBigInt* bigInt, unsigned radix)
{
if (bigInt->isZero())
return vm.smallStrings.singleCharacterStringRep('0');
if (hasOneBitSet(radix))
return toStringBasePowerOfTwo(vm, nullptr, bigInt, radix);
return toStringGeneric(vm, nullptr, bigInt, radix);
}
class HeapBigIntImpl {
public:
explicit HeapBigIntImpl(JSBigInt* bigInt)
: m_bigInt(bigInt)
{ }
ALWAYS_INLINE bool isZero() { return m_bigInt->isZero(); }
ALWAYS_INLINE bool sign() { return m_bigInt->sign(); }
ALWAYS_INLINE unsigned length() { return m_bigInt->length(); }
ALWAYS_INLINE JSBigInt::Digit digit(unsigned i) { return m_bigInt->digit(i); }
ALWAYS_INLINE JSBigInt* toHeapBigInt(JSGlobalObject*, VM&) { return m_bigInt; }
ALWAYS_INLINE JSBigInt* toHeapBigInt(JSGlobalObject*) { return m_bigInt; }
private:
friend struct JSBigInt::ImplResult;
JSBigInt* m_bigInt;
};
class Int32BigIntImpl {
public:
explicit Int32BigIntImpl(int32_t value)
: m_value(value)
{ }
ALWAYS_INLINE bool isZero() { return !m_value; }
ALWAYS_INLINE bool sign() { return m_value < 0; }
ALWAYS_INLINE unsigned length() { return isZero() ? 0 : 1; }
ALWAYS_INLINE JSBigInt::Digit digit(unsigned i)
{
ASSERT(length());
ASSERT_UNUSED(i, i == 0);
if (sign())
return static_cast<JSBigInt::Digit>(-static_cast<int64_t>(m_value));
return m_value;
}
ALWAYS_INLINE JSBigInt* toHeapBigInt(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm)
{
return JSBigInt::createFrom(nullOrGlobalObjectForOOM, vm, m_value);
}
ALWAYS_INLINE JSBigInt* toHeapBigInt(JSGlobalObject* globalObject)
{
return JSBigInt::createFrom(globalObject, m_value);
}
private:
friend struct JSBigInt::ImplResult;
int32_t m_value;
};
ALWAYS_INLINE JSBigInt::ImplResult::ImplResult(HeapBigIntImpl& heapImpl)
: payload(heapImpl.m_bigInt)
{ }
ALWAYS_INLINE JSBigInt::ImplResult::ImplResult(JSBigInt* heapBigInt)
: payload(heapBigInt)
{ }
#if USE(BIGINT32)
ALWAYS_INLINE JSBigInt::ImplResult::ImplResult(Int32BigIntImpl& int32Impl)
: payload(jsBigInt32(int32Impl.m_value))
{ }
#endif
ALWAYS_INLINE JSBigInt::ImplResult::ImplResult(JSValue value)
: payload(value)
{ }
static ALWAYS_INLINE JSValue tryConvertToBigInt32(JSBigInt::ImplResult implResult)
{
if (!implResult.payload)
return JSValue();
if (implResult.payload.isBigInt32())
return implResult.payload;
return tryConvertToBigInt32(implResult.payload.asHeapBigInt());
}
static ALWAYS_INLINE JSBigInt::ImplResult zeroImpl(JSGlobalObject* globalObject)
{
#if USE(BIGINT32)
UNUSED_PARAM(globalObject);
return jsBigInt32(0);
#else
return JSBigInt::createZero(globalObject);
#endif
}
// Multiplies {this} with {factor} and adds {summand} to the result.
void JSBigInt::inplaceMultiplyAdd(Digit factor, Digit summand)
{
internalMultiplyAdd(HeapBigIntImpl { this }, factor, summand, length(), this);
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::exponentiateImpl(JSGlobalObject* globalObject, BigIntImpl1 base, BigIntImpl2 exponent)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (exponent.sign()) {
throwRangeError(globalObject, scope, "Negative exponent is not allowed"_s);
return nullptr;
}
// 2. If base is 0n and exponent is 0n, return 1n.
if (exponent.isZero())
RELEASE_AND_RETURN(scope, JSBigInt::createFrom(globalObject, 1));
// 3. Return a BigInt representing the mathematical value of base raised
// to the power exponent.
if (base.isZero())
return base;
if (base.length() == 1 && base.digit(0) == 1) {
// (-1) ** even_number == 1.
if (base.sign() && !(exponent.digit(0) & 1))
RELEASE_AND_RETURN(scope, JSBigInt::unaryMinusImpl(globalObject, base));
// (-1) ** odd_number == -1; 1 ** anything == 1.
return base;
}
// For all bases >= 2, very large exponents would lead to unrepresentable
// results.
static_assert(maxLengthBits < std::numeric_limits<Digit>::max(), "maxLengthBits needs to be less than digit::max()");
if (exponent.length() > 1) {
throwOutOfMemoryError(globalObject, scope, "BigInt generated from this operation is too big"_s);
return nullptr;
}
Digit expValue = exponent.digit(0);
if (expValue == 1)
return base;
if (expValue >= maxLengthBits) {
throwOutOfMemoryError(globalObject, scope, "BigInt generated from this operation is too big"_s);
return nullptr;
}
static_assert(maxLengthBits <= maxInt, "maxLengthBits needs to be <= maxInt");
int n = static_cast<int>(expValue);
if (base.length() == 1 && base.digit(0) == 2) {
// Fast path for 2^n.
int neededDigits = 1 + (n / digitBits);
JSBigInt* result = JSBigInt::createWithLength(globalObject, neededDigits);
RETURN_IF_EXCEPTION(scope, nullptr);
result->initialize(InitializationType::WithZero);
// All bits are zero. Now set the n-th bit.
Digit msd = static_cast<Digit>(1) << (n % digitBits);
result->setDigit(neededDigits - 1, msd);
// Result is negative for odd powers of -2n.
if (base.sign())
result->setSign(static_cast<bool>(n & 1));
return result;
}
JSBigInt* result = nullptr;
JSBigInt* runningSquare = base.toHeapBigInt(globalObject);
RETURN_IF_EXCEPTION(scope, nullptr);
// This implicitly sets the result's sign correctly.
if (n & 1) {
result = base.toHeapBigInt(globalObject);
RETURN_IF_EXCEPTION(scope, nullptr);
}
n >>= 1;
for (; n; n >>= 1) {
ImplResult temp = JSBigInt::multiplyImpl(globalObject, HeapBigIntImpl { runningSquare }, HeapBigIntImpl { runningSquare });
RETURN_IF_EXCEPTION(scope, nullptr);
ASSERT(temp.payload);
ASSERT(temp.payload.isHeapBigInt());
JSBigInt* maybeResult = temp.payload.asHeapBigInt();
runningSquare = maybeResult;
if (n & 1) {
if (!result)
result = runningSquare;
else {
temp = JSBigInt::multiplyImpl(globalObject, HeapBigIntImpl { result }, HeapBigIntImpl { runningSquare });
RETURN_IF_EXCEPTION(scope, nullptr);
ASSERT(temp.payload);
ASSERT(temp.payload.isHeapBigInt());
maybeResult = temp.payload.asHeapBigInt();
result = maybeResult;
}
}
}
return result;
}
JSValue JSBigInt::exponentiate(JSGlobalObject* globalObject, JSBigInt* base, JSBigInt* exponent)
{
return tryConvertToBigInt32(exponentiateImpl(globalObject, HeapBigIntImpl { base }, HeapBigIntImpl { exponent }));
}
#if USE(BIGINT32)
JSValue JSBigInt::exponentiate(JSGlobalObject* globalObject, JSBigInt* base, int32_t exponent)
{
return tryConvertToBigInt32(exponentiateImpl(globalObject, HeapBigIntImpl { base }, Int32BigIntImpl { exponent }));
}
JSValue JSBigInt::exponentiate(JSGlobalObject* globalObject, int32_t base, JSBigInt* exponent)
{
return tryConvertToBigInt32(exponentiateImpl(globalObject, Int32BigIntImpl { base }, HeapBigIntImpl { exponent }));
}
JSValue JSBigInt::exponentiate(JSGlobalObject* globalObject, int32_t base, int32_t exponent)
{
return tryConvertToBigInt32(exponentiateImpl(globalObject, Int32BigIntImpl { base }, Int32BigIntImpl { exponent }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::multiplyImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
VM& vm = globalObject->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::createWithLength(globalObject, 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());
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
JSValue JSBigInt::multiply(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(multiplyImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::multiply(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(multiplyImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
JSValue JSBigInt::multiply(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(multiplyImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::divideImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
// 1. If y is 0n, throw a RangeError exception.
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (y.isZero()) {
throwRangeError(globalObject, 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)
RELEASE_AND_RETURN(scope, zeroImpl(globalObject));
JSBigInt* quotient = nullptr;
bool resultSign = x.sign() != y.sign();
if (y.length() == 1) {
Digit divisor = y.digit(0);
if (divisor == 1) {
if (resultSign == x.sign())
return JSBigInt::ImplResult { x };
RELEASE_AND_RETURN(scope, JSBigInt::unaryMinusImpl(globalObject, x));
}
Digit remainder;
absoluteDivWithDigitDivisor(globalObject, vm, x, divisor, &quotient, remainder);
RETURN_IF_EXCEPTION(scope, nullptr);
} else {
JSBigInt* yBigInt = y.toHeapBigInt(globalObject);
RETURN_IF_EXCEPTION(scope, nullptr);
absoluteDivWithBigIntDivisor(globalObject, x, yBigInt, &quotient, nullptr);
RETURN_IF_EXCEPTION(scope, nullptr);
}
quotient->setSign(resultSign);
RELEASE_AND_RETURN(scope, quotient->rightTrim(globalObject));
}
JSValue JSBigInt::divide(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(divideImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::divide(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(divideImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::divide(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(divideImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl>
JSBigInt* JSBigInt::copy(JSGlobalObject* globalObject, BigIntImpl x)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
ASSERT(!x.isZero());
JSBigInt* result = createWithLength(globalObject, x.length());
RETURN_IF_EXCEPTION(scope, nullptr);
for (unsigned i = 0; i < result->length(); ++i)
result->setDigit(i, x.digit(i));
result->setSign(x.sign());
return result;
}
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::unaryMinusImpl(JSGlobalObject* globalObject, BigIntImpl x)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (x.isZero())
RELEASE_AND_RETURN(scope, zeroImpl(globalObject));
JSBigInt* result = copy(globalObject, x);
RETURN_IF_EXCEPTION(scope, nullptr);
result->setSign(!x.sign());
return result;
}
JSValue JSBigInt::unaryMinus(JSGlobalObject* globalObject, JSBigInt* x)
{
return tryConvertToBigInt32(unaryMinusImpl(globalObject, HeapBigIntImpl { x }));
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::remainderImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
// 1. If y is 0n, throw a RangeError exception.
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (y.isZero()) {
throwRangeError(globalObject, 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)
RELEASE_AND_RETURN(scope, zeroImpl(globalObject));
Digit remainderDigit;
absoluteDivWithDigitDivisor(globalObject, vm, x, divisor, nullptr, remainderDigit);
RETURN_IF_EXCEPTION(scope, nullptr);
if (!remainderDigit)
RELEASE_AND_RETURN(scope, zeroImpl(globalObject));
remainder = createWithLength(globalObject, 1);
RETURN_IF_EXCEPTION(scope, nullptr);
remainder->setDigit(0, remainderDigit);
} else {
JSBigInt* yBigInt = y.toHeapBigInt(globalObject);
RETURN_IF_EXCEPTION(scope, nullptr);
absoluteDivWithBigIntDivisor(globalObject, x, yBigInt, nullptr, &remainder);
RETURN_IF_EXCEPTION(scope, nullptr);
}
remainder->setSign(x.sign());
RELEASE_AND_RETURN(scope, remainder->rightTrim(globalObject));
}
JSValue JSBigInt::remainder(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(remainderImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::remainder(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(remainderImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::remainder(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(remainderImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::incImpl(JSGlobalObject* globalObject, BigIntImpl x)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!x.sign())
RELEASE_AND_RETURN(scope, absoluteAddOne(globalObject, x, SignOption::Unsigned));
JSBigInt* result = absoluteSubOne(globalObject, x, x.length());
RETURN_IF_EXCEPTION(scope, nullptr);
if (result->isZero())
return result;
result->setSign(true);
return result;
}
JSValue JSBigInt::inc(JSGlobalObject* globalObject, JSBigInt* x)
{
return tryConvertToBigInt32(incImpl(globalObject, HeapBigIntImpl { x }));
}
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::decImpl(JSGlobalObject* globalObject, BigIntImpl x)
{
if (x.isZero()) {
#if USE(BIGINT32)
return jsBigInt32(-1);
#else
return createFrom(globalObject, -1);
#endif
}
if (!x.sign())
return absoluteSubOne(globalObject, x, x.length());
return absoluteAddOne(globalObject, x, SignOption::Signed);
}
JSValue JSBigInt::dec(JSGlobalObject* globalObject, JSBigInt* x)
{
return tryConvertToBigInt32(decImpl(globalObject, HeapBigIntImpl { x }));
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::addImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
bool xSign = x.sign();
// x + y == x + y
// -x + -y == -(x + y)
if (xSign == y.sign())
return absoluteAdd(globalObject, 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(globalObject, x, y, xSign);
return absoluteSub(globalObject, y, x, !xSign);
}
JSValue JSBigInt::add(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(addImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::add(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(addImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::add(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(addImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::subImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
bool xSign = x.sign();
if (xSign != y.sign()) {
// x - (-y) == x + y
// (-x) - y == -(x + y)
return absoluteAdd(globalObject, 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(globalObject, x, y, xSign);
return absoluteSub(globalObject, y, x, !xSign);
}
JSValue JSBigInt::sub(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(subImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::sub(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(subImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::sub(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(subImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::bitwiseAndImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!x.sign() && !y.sign())
RELEASE_AND_RETURN(scope, absoluteAnd(globalObject, 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(globalObject, x, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
JSBigInt* y1 = absoluteSubOne(globalObject, y, y.length());
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteOr(globalObject, HeapBigIntImpl { result }, HeapBigIntImpl { y1 });
RETURN_IF_EXCEPTION(scope, nullptr);
RELEASE_AND_RETURN(scope, absoluteAddOne(globalObject, HeapBigIntImpl { result }, SignOption::Signed));
}
ASSERT(x.sign() != y.sign());
// x & (-y) == x & ~(y-1)
auto computeResult = [&] (auto x, auto y) -> JSBigInt* {
ASSERT(!x.sign());
ASSERT(y.sign());
JSBigInt* y1 = absoluteSubOne(globalObject, y, y.length());
RETURN_IF_EXCEPTION(scope, nullptr);
RELEASE_AND_RETURN(scope, absoluteAndNot(globalObject, x, HeapBigIntImpl { y1 }));
};
if (x.sign())
return computeResult(y, x);
return computeResult(x, y);
}
JSValue JSBigInt::bitwiseAnd(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(bitwiseAndImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::bitwiseAnd(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(bitwiseAndImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::bitwiseAnd(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(bitwiseAndImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::bitwiseOrImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
unsigned resultLength = std::max(x.length(), y.length());
if (!x.sign() && !y.sign())
RELEASE_AND_RETURN(scope, absoluteOr(globalObject, 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(globalObject, x, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
JSBigInt* y1 = absoluteSubOne(globalObject, y, y.length());
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteAnd(globalObject, HeapBigIntImpl { result }, HeapBigIntImpl { y1 });
RETURN_IF_EXCEPTION(scope, nullptr);
RELEASE_AND_RETURN(scope, absoluteAddOne(globalObject, HeapBigIntImpl { result }, SignOption::Signed));
}
ASSERT(x.sign() != y.sign());
// x | (-y) == x | ~(y-1) == ~((y-1) &~ x) == -(((y-1) &~ x) + 1)
auto computeResult = [&] (auto x, auto y) -> JSBigInt* {
ASSERT(!x.sign());
ASSERT(y.sign());
JSBigInt* result = absoluteSubOne(globalObject, y, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteAndNot(globalObject, HeapBigIntImpl { result }, x);
RETURN_IF_EXCEPTION(scope, nullptr);
RELEASE_AND_RETURN(scope, absoluteAddOne(globalObject, HeapBigIntImpl { result }, SignOption::Signed));
};
if (x.sign())
return computeResult(y, x);
return computeResult(x, y);
}
JSValue JSBigInt::bitwiseOr(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(bitwiseOrImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::bitwiseOr(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(bitwiseOrImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::bitwiseOr(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(bitwiseOrImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::bitwiseXorImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (!x.sign() && !y.sign())
RELEASE_AND_RETURN(scope, absoluteXor(globalObject, 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(globalObject, x, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
JSBigInt* y1 = absoluteSubOne(globalObject, y, y.length());
RETURN_IF_EXCEPTION(scope, nullptr);
RELEASE_AND_RETURN(scope, absoluteXor(globalObject, HeapBigIntImpl { result }, HeapBigIntImpl { y1 }));
}
ASSERT(x.sign() != y.sign());
int resultLength = std::max(x.length(), y.length()) + 1;
// x ^ (-y) == x ^ ~(y-1) == ~(x ^ (y-1)) == -((x ^ (y-1)) + 1)
auto computeResult = [&] (auto x, auto y) -> JSBigInt* {
ASSERT(!x.sign());
ASSERT(y.sign());
JSBigInt* result = absoluteSubOne(globalObject, y, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
result = absoluteXor(globalObject, HeapBigIntImpl { result }, x);
RETURN_IF_EXCEPTION(scope, nullptr);
RELEASE_AND_RETURN(scope, absoluteAddOne(globalObject, HeapBigIntImpl { result }, SignOption::Signed));
};
// Assume that x is the positive BigInt.
if (x.sign())
return computeResult(y, x);
return computeResult(x, y);
}
JSValue JSBigInt::bitwiseXor(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(bitwiseXorImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::bitwiseXor(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(bitwiseXorImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::bitwiseXor(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(bitwiseXorImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::leftShiftImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
if (x.isZero() || y.isZero())
return x;
if (y.sign())
return rightShiftByAbsolute(globalObject, x, y);
return leftShiftByAbsolute(globalObject, x, y);
}
JSValue JSBigInt::leftShift(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(leftShiftImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::leftShift(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(leftShiftImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::leftShift(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(leftShiftImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
JSValue JSBigInt::leftShiftSlow(JSGlobalObject* globalObject, int32_t x, int32_t y)
{
return tryConvertToBigInt32(leftShiftImpl(globalObject, Int32BigIntImpl { x }, Int32BigIntImpl { y }));
}
#endif
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::signedRightShiftImpl(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
if (x.isZero() || y.isZero())
return x;
if (y.sign())
return leftShiftByAbsolute(globalObject, x, y);
return rightShiftByAbsolute(globalObject, x, y);
}
JSValue JSBigInt::signedRightShift(JSGlobalObject* globalObject, JSBigInt* x, JSBigInt* y)
{
return tryConvertToBigInt32(signedRightShiftImpl(globalObject, HeapBigIntImpl { x }, HeapBigIntImpl { y }));
}
#if USE(BIGINT32)
JSValue JSBigInt::signedRightShift(JSGlobalObject* globalObject, JSBigInt* x, int32_t y)
{
return tryConvertToBigInt32(signedRightShiftImpl(globalObject, HeapBigIntImpl { x }, Int32BigIntImpl { y }));
}
JSValue JSBigInt::signedRightShift(JSGlobalObject* globalObject, int32_t x, JSBigInt* y)
{
return tryConvertToBigInt32(signedRightShiftImpl(globalObject, Int32BigIntImpl { x }, HeapBigIntImpl { y }));
}
#endif
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::bitwiseNotImpl(JSGlobalObject* globalObject, BigIntImpl x)
{
if (x.sign()) {
// ~(-x) == ~(~(x-1)) == x-1
return absoluteSubOne(globalObject, x, x.length());
}
// ~x == -x-1 == -(x+1)
return absoluteAddOne(globalObject, x, SignOption::Signed);
}
JSValue JSBigInt::bitwiseNot(JSGlobalObject* globalObject, JSBigInt* x)
{
return tryConvertToBigInt32(bitwiseNotImpl(globalObject, HeapBigIntImpl { x }));
}
#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.
template <typename BigIntImpl>
void JSBigInt::internalMultiplyAdd(BigIntImpl 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.
template <typename BigIntImpl>
void JSBigInt::multiplyAccumulate(BigIntImpl 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;
}
template <typename BigIntImpl1, typename BigIntImpl2>
inline JSBigInt::ComparisonResult JSBigInt::absoluteCompare(BigIntImpl1 x, BigIntImpl2 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;
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ComparisonResult JSBigInt::compareImpl(BigIntImpl1 x, BigIntImpl2 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;
}
JSBigInt::ComparisonResult JSBigInt::compare(JSBigInt* x, JSBigInt* y)
{
return compareImpl(HeapBigIntImpl { x }, HeapBigIntImpl { y });
}
JSBigInt::ComparisonResult JSBigInt::compare(int32_t x, JSBigInt* y)
{
return compareImpl(Int32BigIntImpl { x }, HeapBigIntImpl { y });
}
JSBigInt::ComparisonResult JSBigInt::compare(JSBigInt* x, int32_t y)
{
return compareImpl(HeapBigIntImpl { x }, Int32BigIntImpl { y });
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::absoluteAdd(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y, bool resultSign)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (x.length() < y.length())
RELEASE_AND_RETURN(scope, absoluteAdd(globalObject, y, x, resultSign));
if (x.isZero()) {
ASSERT(y.isZero());
return x;
}
if (y.isZero()) {
if (resultSign == x.sign())
return x;
RELEASE_AND_RETURN(scope, unaryMinusImpl(globalObject, x));
}
JSBigInt* result = createWithLength(globalObject, x.length() + 1);
RETURN_IF_EXCEPTION(scope, nullptr);
ASSERT(result);
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);
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::absoluteSub(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y, bool resultSign)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
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()) {
if (resultSign == x.sign())
return ImplResult { x };
RELEASE_AND_RETURN(scope, JSBigInt::unaryMinusImpl(globalObject, x));
}
if (comparisonResult == ComparisonResult::Equal)
RELEASE_AND_RETURN(scope, zeroImpl(globalObject));
JSBigInt* result = createWithLength(globalObject, x.length());
RETURN_IF_EXCEPTION(scope, nullptr);
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);
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
// 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.
template <typename BigIntImpl>
bool JSBigInt::absoluteDivWithDigitDivisor(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm, BigIntImpl x, Digit divisor, JSBigInt** quotient, Digit& remainder)
{
ASSERT(divisor);
ASSERT(!x.isZero());
remainder = 0;
if (divisor == 1) {
if (quotient) {
JSBigInt* result = x.toHeapBigInt(nullOrGlobalObjectForOOM, vm);
if (UNLIKELY(!result))
return false;
*quotient = result;
}
return true;
}
unsigned length = x.length();
if (quotient) {
if (*quotient == nullptr) {
JSBigInt* result = createWithLength(nullOrGlobalObjectForOOM, vm, length);
if (UNLIKELY(!result))
return false;
*quotient = result;
}
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);
}
return true;
}
// 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.
template <typename BigIntImpl1>
void JSBigInt::absoluteDivWithBigIntDivisor(JSGlobalObject* globalObject, BigIntImpl1 dividend, JSBigInt* divisor, JSBigInt** quotient, JSBigInt** remainder)
{
ASSERT(divisor->length() >= 2);
ASSERT(dividend.length() >= divisor->length());
VM& vm = globalObject->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 = createWithLength(globalObject, m + 1);
RETURN_IF_EXCEPTION(scope, void());
}
// In each iteration, {qhatv} holds {divisor} * {current quotient digit}.
// "v" is the book's name for {divisor}, "qhat" the current quotient digit.
JSBigInt* qhatv = createWithLength(globalObject, 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(globalObject, HeapBigIntImpl { 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(globalObject, 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(HeapBigIntImpl { 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 << digitBits) + 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.
template <typename BigIntImpl>
JSBigInt* JSBigInt::absoluteLeftShiftAlwaysCopy(JSGlobalObject* globalObject, BigIntImpl x, unsigned shift, LeftShiftMode mode)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
ASSERT(shift < digitBits);
ASSERT(!x.isZero());
unsigned n = x.length();
unsigned resultLength = mode == LeftShiftMode::AlwaysAddOneDigit ? n + 1 : n;
JSBigInt* result = createWithLength(globalObject, resultLength);
RETURN_IF_EXCEPTION(scope, { });
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 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 BigIntImpl1, typename BigIntImpl2, typename BitwiseOp>
inline JSBigInt* JSBigInt::absoluteBitwiseOp(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y, ExtraDigitsHandling extraDigits, BitwiseOp&& op)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
unsigned xLength = x.length();
unsigned yLength = y.length();
unsigned numPairs = yLength;
unsigned maxLength = xLength;
if (xLength < yLength) {
numPairs = xLength;
maxLength = yLength;
}
ASSERT(numPairs == std::min(xLength, yLength));
ASSERT(maxLength == std::max(xLength, yLength));
unsigned resultLength = extraDigits == ExtraDigitsHandling::Copy ? maxLength : numPairs;
JSBigInt* result = createWithLength(globalObject, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
unsigned i = 0;
for (; i < numPairs; i++)
result->setDigit(i, op(x.digit(i), y.digit(i)));
if (extraDigits == ExtraDigitsHandling::Copy) {
if (xLength > yLength) {
for (; i < xLength; i++)
result->setDigit(i, x.digit(i));
} else {
for (; i < yLength; i++)
result->setDigit(i, y.digit(i));
}
}
for (; i < resultLength; i++)
result->setDigit(i, 0);
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt* JSBigInt::absoluteAnd(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
auto digitOperation = [](Digit a, Digit b) {
return a & b;
};
return absoluteBitwiseOp(globalObject, x, y, ExtraDigitsHandling::Skip, digitOperation);
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt* JSBigInt::absoluteOr(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
auto digitOperation = [](Digit a, Digit b) {
return a | b;
};
return absoluteBitwiseOp(globalObject, x, y, ExtraDigitsHandling::Copy, digitOperation);
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt* JSBigInt::absoluteAndNot(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
// x & ~y
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
unsigned xLength = x.length();
unsigned yLength = y.length();
unsigned resultLength = xLength;
JSBigInt* result = createWithLength(globalObject, resultLength);
RETURN_IF_EXCEPTION(scope, nullptr);
unsigned i = 0;
for (; i < std::min(xLength, yLength); i++)
result->setDigit(i, x.digit(i) & ~y.digit(i));
for (; i < resultLength; ++i)
result->setDigit(i, x.digit(i));
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt* JSBigInt::absoluteXor(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
auto digitOperation = [](Digit a, Digit b) {
return a ^ b;
};
return absoluteBitwiseOp(globalObject, x, y, ExtraDigitsHandling::Copy, digitOperation);
}
template <typename BigIntImpl>
JSBigInt* JSBigInt::absoluteAddOne(JSGlobalObject* globalObject, BigIntImpl x, SignOption signOption)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
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 = createWithLength(globalObject, resultLength);
RETURN_IF_EXCEPTION(scope, 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);
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
template <typename BigIntImpl>
JSBigInt* JSBigInt::absoluteSubOne(JSGlobalObject* globalObject, BigIntImpl x, unsigned resultLength)
{
ASSERT(!x.isZero());
ASSERT(resultLength >= x.length());
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
JSBigInt* result = createWithLength(globalObject, 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);
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::leftShiftByAbsolute(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
auto optionalShift = toShiftAmount(y);
if (!optionalShift) {
throwOutOfMemoryError(globalObject, 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) {
throwOutOfMemoryError(globalObject, scope, "BigInt generated from this operation is too big"_s);
return nullptr;
}
JSBigInt* result = createWithLength(globalObject, 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());
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
template <typename BigIntImpl1, typename BigIntImpl2>
JSBigInt::ImplResult JSBigInt::rightShiftByAbsolute(JSGlobalObject* globalObject, BigIntImpl1 x, BigIntImpl2 y)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
unsigned length = x.length();
bool sign = x.sign();
auto optionalShift = toShiftAmount(y);
if (!optionalShift)
RELEASE_AND_RETURN(scope, rightShiftByMaximum(globalObject, 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)
RELEASE_AND_RETURN(scope, rightShiftByMaximum(globalObject, 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 = createWithLength(globalObject, static_cast<unsigned>(resultLength));
RETURN_IF_EXCEPTION(scope, nullptr);
if (!bitsShift) {
result->setDigit(resultLength - 1, 0);
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(globalObject);
RETURN_IF_EXCEPTION(scope, nullptr);
RELEASE_AND_RETURN(scope, absoluteAddOne(globalObject, HeapBigIntImpl { result }, SignOption::Signed));
}
}
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
JSBigInt::ImplResult JSBigInt::rightShiftByMaximum(JSGlobalObject* globalObject, bool sign)
{
if (sign)
return createFrom(globalObject, -1);
return createZero(globalObject);
}
// 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(VM& vm, JSGlobalObject* nullOrGlobalObjectForOOM, JSBigInt* x, unsigned radix)
{
ASSERT(hasOneBitSet(radix));
ASSERT(radix >= 2 && radix <= 32);
ASSERT(!x->isZero());
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) {
if (nullOrGlobalObjectForOOM) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(nullOrGlobalObjectForOOM, 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(VM& vm, JSGlobalObject* nullOrGlobalObjectForOOM, JSBigInt* x, unsigned radix)
{
// FIXME: [JSC] Revisit usage of Vector into JSBigInt::toString
// https://bugs.webkit.org/show_bug.cgi?id=180671
Vector<LChar> resultString;
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) {
if (nullOrGlobalObjectForOOM) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(nullOrGlobalObjectForOOM, 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;
bool success = absoluteDivWithDigitDivisor(nullOrGlobalObjectForOOM, vm, HeapBigIntImpl { *dividend }, chunkDivisor, &rest, chunk);
if (!success)
return String();
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(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm)
{
if (isZero()) {
ASSERT(!sign());
return this;
}
int nonZeroIndex = m_length - 1;
while (nonZeroIndex >= 0 && !digit(nonZeroIndex))
nonZeroIndex--;
if (nonZeroIndex < 0)
return createZero(nullOrGlobalObjectForOOM, vm);
if (nonZeroIndex == static_cast<int>(m_length - 1))
return this;
unsigned newLength = nonZeroIndex + 1;
JSBigInt* trimmedBigInt = createWithLength(nullOrGlobalObjectForOOM, vm, newLength);
if (UNLIKELY(!trimmedBigInt))
return nullptr;
std::copy(dataStorage(), dataStorage() + newLength, trimmedBigInt->dataStorage());
trimmedBigInt->setSign(this->sign());
ensureStillAliveHere(this);
return trimmedBigInt;
}
JSBigInt* JSBigInt::rightTrim(JSGlobalObject* globalObject)
{
return rightTrim(globalObject, globalObject->vm());
}
JSBigInt* JSBigInt::tryRightTrim(VM& vm)
{
return rightTrim(nullptr, vm);
}
JSBigInt* JSBigInt::allocateFor(JSGlobalObject* nullOrGlobalObjectForOOM, 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)
return createWithLength(nullOrGlobalObjectForOOM, vm, length);
}
}
if (nullOrGlobalObjectForOOM) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwOutOfMemoryError(nullOrGlobalObjectForOOM, scope, "BigInt generated from this operation is too big"_s);
}
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(JSGlobalObject* globalObject) const
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
throwTypeError(globalObject, scope, "Conversion from 'BigInt' to 'number' is not allowed."_s);
return 0.0;
}
template <typename CharType>
JSValue JSBigInt::parseInt(JSGlobalObject* globalObject, CharType* data, unsigned length, ErrorParseMode errorParseMode)
{
VM& vm = globalObject->vm();
unsigned p = 0;
while (p < length && isStrWhiteSpace(data[p]))
++p;
// Check Radix from first characters
if (static_cast<unsigned>(p) + 1 < static_cast<unsigned>(length) && data[p] == '0') {
if (isASCIIAlphaCaselessEqual(data[p + 1], 'b'))
return parseInt(globalObject, vm, data, length, p + 2, 2, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString);
if (isASCIIAlphaCaselessEqual(data[p + 1], 'x'))
return parseInt(globalObject, vm, data, length, p + 2, 16, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString);
if (isASCIIAlphaCaselessEqual(data[p + 1], 'o'))
return parseInt(globalObject, vm, data, length, p + 2, 8, errorParseMode, ParseIntSign::Unsigned, ParseIntMode::DisallowEmptyString);
}
ParseIntSign sign = ParseIntSign::Unsigned;
if (p < length) {
if (data[p] == '-') {
sign = ParseIntSign::Signed;
++p;
} else if (data[p] == '+')
++p;
}
return parseInt(globalObject, vm, data, length, p, 10, errorParseMode, sign);
}
template <typename CharType>
JSValue JSBigInt::parseInt(JSGlobalObject* nullOrGlobalObjectForOOM, VM& vm, CharType* data, unsigned length, unsigned startIndex, unsigned radix, ErrorParseMode errorParseMode, ParseIntSign sign, ParseIntMode parseMode)
{
unsigned p = startIndex;
if (parseMode != ParseIntMode::AllowEmptyString && startIndex == length) {
ASSERT(nullOrGlobalObjectForOOM);
if (errorParseMode == ErrorParseMode::ThrowExceptions) {
auto scope = DECLARE_THROW_SCOPE(vm);
throwVMError(nullOrGlobalObjectForOOM, scope, createSyntaxError(nullOrGlobalObjectForOOM, "Failed to parse String to BigInt"));
}
return JSValue();
}
// 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) {
#if USE(BIGINT32)
return jsBigInt32(0);
#else
return createZero(nullOrGlobalObjectForOOM, vm);
#endif
}
unsigned lengthLimitForBigInt32;
#if USE(BIGINT32)
static_assert(sizeof(Digit) >= sizeof(uint64_t));
// The idea is to pick the limit such that:
// radix ** lengthLimitForBigInt32 >= INT32_MAX
// radix ** (lengthLimitForBigInt32 - 1) <= INT32_MAX
#if ASSERT_ENABLED
auto limitWorks = [&] {
double lengthLimit = lengthLimitForBigInt32;
double lowerLimit = pow(static_cast<double>(radix), lengthLimit - 1);
double upperLimit = pow(static_cast<double>(radix), lengthLimit);
double target = std::numeric_limits<int32_t>::max();
return lowerLimit <= target && target <= upperLimit && upperLimit <= std::numeric_limits<int64_t>::max();
};
#endif
switch (radix) {
case 2:
lengthLimitForBigInt32 = 31;
ASSERT(limitWorks());
break;
case 8:
lengthLimitForBigInt32 = 11;
ASSERT(limitWorks());
break;
case 10:
lengthLimitForBigInt32 = 10;
ASSERT(limitWorks());
break;
case 16:
lengthLimitForBigInt32 = 8;
ASSERT(limitWorks());
break;
default:
lengthLimitForBigInt32 = 1;
break;
}
#else
// The idea is to pick the largest limit such that:
// radix ** lengthLimitForBigInt32 <= INT32_MAX
#if ASSERT_ENABLED
auto limitWorks = [&] {
double lengthLimit = lengthLimitForBigInt32;
double valueLimit = pow(static_cast<double>(radix), lengthLimit);
double overValueLimit = pow(static_cast<double>(radix), lengthLimit + 1);
double target = std::numeric_limits<int32_t>::max();
return valueLimit <= target && target < overValueLimit;
};
#endif
switch (radix) {
case 2:
lengthLimitForBigInt32 = 30;
ASSERT(limitWorks());
break;
case 8:
lengthLimitForBigInt32 = 10;
ASSERT(limitWorks());
break;
case 10:
lengthLimitForBigInt32 = 9;
ASSERT(limitWorks());
break;
case 16:
lengthLimitForBigInt32 = 7;
ASSERT(limitWorks());
break;
default:
lengthLimitForBigInt32 = 1;
break;
}
#endif // USE(BIGINT32)
JSBigInt* heapResult = nullptr;
unsigned limit0 = '0' + (radix < 10 ? radix : 10);
unsigned limita = 'a' + (static_cast<int32_t>(radix) - 10);
unsigned limitA = 'A' + (static_cast<int32_t>(radix) - 10);
unsigned initialLength = length - p;
while (p < length) {
Checked<uint64_t, CrashOnOverflow> digit = 0;
Checked<uint64_t, CrashOnOverflow> multiplier = 1;
for (unsigned i = 0; i < lengthLimitForBigInt32 && p < length; ++i, ++p) {
digit *= radix;
multiplier *= radix;
if (data[p] >= '0' && data[p] < limit0)
digit += static_cast<uint64_t>(data[p] - '0');
else if (data[p] >= 'a' && data[p] < limita)
digit += static_cast<uint64_t>(data[p] - 'a' + 10);
else if (data[p] >= 'A' && data[p] < limitA)
digit += static_cast<uint64_t>(data[p] - 'A' + 10);
else {
if (errorParseMode == ErrorParseMode::ThrowExceptions) {
auto scope = DECLARE_THROW_SCOPE(vm);
ASSERT(nullOrGlobalObjectForOOM);
throwVMError(nullOrGlobalObjectForOOM, scope, createSyntaxError(nullOrGlobalObjectForOOM, "Failed to parse String to BigInt"));
}
return JSValue();
}
}
if (!heapResult) {
if (p == length) {
ASSERT(digit.unsafeGet() <= std::numeric_limits<int64_t>::max());
int64_t maybeResult = digit.unsafeGet();
ASSERT(maybeResult >= 0);
if (sign == ParseIntSign::Signed)
maybeResult *= -1;
if (static_cast<int64_t>(static_cast<int32_t>(maybeResult)) == maybeResult) {
#if USE(BIGINT32)
return jsBigInt32(static_cast<int32_t>(maybeResult));
#else
return JSBigInt::createFrom(nullOrGlobalObjectForOOM, vm, static_cast<int32_t>(maybeResult));
#endif
}
}
heapResult = allocateFor(nullOrGlobalObjectForOOM, vm, radix, initialLength);
if (UNLIKELY(!heapResult))
return JSValue();
heapResult->initialize(InitializationType::WithZero);
}
ASSERT(static_cast<uint64_t>(static_cast<Digit>(multiplier.unsafeGet())) == multiplier.unsafeGet());
ASSERT(static_cast<uint64_t>(static_cast<Digit>(digit.unsafeGet())) == digit.unsafeGet());
heapResult->inplaceMultiplyAdd(static_cast<Digit>(multiplier.unsafeGet()), static_cast<Digit>(digit.unsafeGet()));
}
heapResult->setSign(sign == ParseIntSign::Signed);
return heapResult->rightTrim(nullOrGlobalObjectForOOM, vm);
}
JSObject* JSBigInt::toObject(JSGlobalObject* globalObject) const
{
return BigIntObject::create(globalObject->vm(), globalObject, const_cast<JSBigInt*>(this));
}
bool JSBigInt::equalsToNumber(JSValue numValue)
{
ASSERT(numValue.isNumber());
if (numValue.isInt32())
return equalsToInt32(numValue.asInt32());
double value = numValue.asDouble();
return compareToDouble(this, value) == ComparisonResult::Equal;
}
bool JSBigInt::equalsToInt32(int32_t value)
{
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))));
}
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;
}
template <typename BigIntImpl>
Optional<JSBigInt::Digit> JSBigInt::toShiftAmount(BigIntImpl 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;
}
JSBigInt::RoundingResult JSBigInt::decideRounding(JSBigInt* bigInt, int32_t mantissaBitsUnset, int32_t digitIndex, uint64_t currentDigit)
{
if (mantissaBitsUnset > 0)
return RoundingResult::RoundDown;
int32_t topUnconsumedBit = 0;
if (mantissaBitsUnset < 0) {
// There are unconsumed bits in currentDigit.
topUnconsumedBit = -mantissaBitsUnset - 1;
} else {
ASSERT(mantissaBitsUnset == 0);
// currentDigit fit the mantissa exactly; look at the next digit.
if (digitIndex == 0)
return RoundingResult::RoundDown;
digitIndex--;
currentDigit = static_cast<uint64_t>(bigInt->digit(digitIndex));
topUnconsumedBit = digitBits - 1;
}
// If the most significant remaining bit is 0, round down.
uint64_t bitmask = static_cast<uint64_t>(1) << topUnconsumedBit;
if ((currentDigit & bitmask) == 0)
return RoundingResult::RoundDown;
// If any other remaining bit is set, round up.
bitmask -= 1;
if ((currentDigit & bitmask) != 0)
return RoundingResult::RoundUp;
while (digitIndex > 0) {
digitIndex--;
if (bigInt->digit(digitIndex) != 0)
return RoundingResult::RoundUp;
}
return RoundingResult::Tie;
}
JSValue JSBigInt::toNumberHeap(JSBigInt* bigInt)
{
if (bigInt->isZero())
return jsNumber(0);
ASSERT(bigInt->length());
// Conversion mechanism is the following.
//
// 1. Get exponent bits.
// 2. Collect mantissa 52 bits.
// 3. Add rounding result of unused bits to mantissa and adjust mantissa & exponent bits.
// 4. Generate double by combining (1) and (3).
const unsigned length = bigInt->length();
const bool sign = bigInt->sign();
const Digit msd = bigInt->digit(length - 1);
const unsigned msdLeadingZeros = clz(msd);
const size_t bitLength = length * digitBits - msdLeadingZeros;
// Double's exponent bits overflow.
if (bitLength > 1024)
return jsDoubleNumber(sign ? -std::numeric_limits<double>::infinity() : std::numeric_limits<double>::infinity());
uint64_t exponent = bitLength - 1;
uint64_t currentDigit = msd;
int32_t digitIndex = length - 1;
int32_t shiftAmount = msdLeadingZeros + 1 + (64 - digitBits);
ASSERT(1 <= shiftAmount);
ASSERT(shiftAmount <= 64);
uint64_t mantissa = (shiftAmount == 64) ? 0 : currentDigit << shiftAmount;
// unsetBits = 64 - setBits - 12 // 12 for non-mantissa bits
// setBits = 64 - (msdLeadingZeros + 1 + bitsNotAvailableDueToDigitSize); // 1 for hidden mantissa bit.
// = 64 - (msdLeadingZeros + 1 + (64 - digitBits))
// = 64 - shiftAmount
// Hence, unsetBits = 64 - (64 - shiftAmount) - 12 = shiftAmount - 12
mantissa >>= 12; // (12 = 64 - 52), we shift 12 bits to put 12 zeros in uint64_t mantissa.
int32_t mantissaBitsUnset = shiftAmount - 12;
// If not all mantissa bits are defined yet, get more digits as needed.
// Collect mantissa 52bits from several digits.
if constexpr (digitBits < 64) {
if (mantissaBitsUnset >= static_cast<int32_t>(digitBits) && digitIndex > 0) {
digitIndex--;
currentDigit = static_cast<uint64_t>(bigInt->digit(digitIndex));
mantissa |= (currentDigit << (mantissaBitsUnset - digitBits));
mantissaBitsUnset -= digitBits;
}
}
if (mantissaBitsUnset > 0 && digitIndex > 0) {
ASSERT(mantissaBitsUnset < static_cast<int32_t>(digitBits));
digitIndex--;
currentDigit = static_cast<uint64_t>(bigInt->digit(digitIndex));
mantissa |= (currentDigit >> (digitBits - mantissaBitsUnset));
mantissaBitsUnset -= digitBits;
}
// If there are unconsumed digits left, we may have to round.
RoundingResult rounding = decideRounding(bigInt, mantissaBitsUnset, digitIndex, currentDigit);
if (rounding == RoundingResult::RoundUp || (rounding == RoundingResult::Tie && (mantissa & 1) == 1)) {
++mantissa;
// Incrementing the mantissa can overflow the mantissa bits. In that case the new mantissa will be all zero (plus hidden bit).
if ((mantissa >> doublePhysicalMantissaSize) != 0) {
mantissa = 0;
exponent++;
// Incrementing the exponent can overflow too.
if (exponent > 1023)
return jsDoubleNumber(sign ? -std::numeric_limits<double>::infinity() : std::numeric_limits<double>::infinity());
}
}
uint64_t signBit = sign ? (static_cast<uint64_t>(1) << 63) : 0;
exponent = (exponent + 0x3ff) << doublePhysicalMantissaSize; // 0x3ff is double exponent bias.
uint64_t doubleBits = signBit | exponent | mantissa;
ASSERT((doubleBits & (static_cast<uint64_t>(1) << 63)) == signBit);
ASSERT((doubleBits & (static_cast<uint64_t>(0x7ff) << 52)) == exponent);
ASSERT((doubleBits & ((static_cast<uint64_t>(1) << 52) - 1)) == mantissa);
return jsNumber(bitwise_cast<double>(doubleBits));
}
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::asIntNImpl(JSGlobalObject* globalObject, uint64_t n, BigIntImpl bigInt)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (bigInt.isZero())
return bigInt;
if (n == 0)
RELEASE_AND_RETURN(scope, zeroImpl(globalObject));
uint64_t neededLength = (n + digitBits - 1) / digitBits;
uint64_t length = static_cast<uint64_t>(bigInt.length());
// If bigInt has less than n bits, return it directly.
if (length < neededLength)
return bigInt;
ASSERT(neededLength <= INT32_MAX);
Digit topDigit = bigInt.digit(static_cast<int32_t>(neededLength) - 1);
Digit compareDigit = static_cast<Digit>(1) << ((n - 1) % digitBits);
if (length == neededLength && topDigit < compareDigit)
return bigInt;
// Otherwise we have to truncate (which is a no-op in the special case
// of bigInt == -2^(n-1)), and determine the right sign. We also might have
// to subtract from 2^n to simulate having two's complement representation.
// In most cases, the result's sign is bigInt.sign() xor "(n-1)th bit present".
// The only exception is when bigInt is negative, has the (n-1)th bit, and all
// its bits below (n-1) are zero. In that case, the result is the minimum
// n-bit integer (example: asIntN(3, -12n) => -4n).
bool hasBit = (topDigit & compareDigit) == compareDigit;
ASSERT(n <= INT32_MAX);
int32_t N = static_cast<int32_t>(n);
if (!hasBit)
RELEASE_AND_RETURN(scope, truncateToNBits(globalObject, N, bigInt));
if (!bigInt.sign())
RELEASE_AND_RETURN(scope, truncateAndSubFromPowerOfTwo(globalObject, N, bigInt, true));
// Negative numbers must subtract from 2^n, except for the special case
// described above.
if ((topDigit & (compareDigit - 1)) == 0) {
for (int32_t i = static_cast<int32_t>(neededLength) - 2; i >= 0; i--) {
if (bigInt.digit(i) != 0)
RELEASE_AND_RETURN(scope, truncateAndSubFromPowerOfTwo(globalObject, N, bigInt, false));
}
// Truncation is no-op if bigInt == -2^(n-1).
if (length == neededLength && topDigit == compareDigit)
return bigInt;
RELEASE_AND_RETURN(scope, truncateToNBits(globalObject, N, bigInt));
}
RELEASE_AND_RETURN(scope, truncateAndSubFromPowerOfTwo(globalObject, N, bigInt, false));
}
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::asUintNImpl(JSGlobalObject* globalObject, uint64_t n, BigIntImpl bigInt)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
if (bigInt.isZero())
return bigInt;
if (n == 0)
RELEASE_AND_RETURN(scope, zeroImpl(globalObject));
// If bigInt is negative, simulate two's complement representation.
if (bigInt.sign()) {
if (n > maxLengthBits) {
throwOutOfMemoryError(globalObject, scope, "BigInt generated from this operation is too big"_s);
return nullptr;
}
RELEASE_AND_RETURN(scope, truncateAndSubFromPowerOfTwo(globalObject, static_cast<int32_t>(n), bigInt, false));
}
// If bigInt is positive and has up to n bits, return it directly.
if (n >= maxLengthBits)
return bigInt;
static_assert(maxLengthBits < INT32_MAX - digitBits);
int32_t neededLength = static_cast<int32_t>((n + digitBits - 1) / digitBits);
if (static_cast<int32_t>(bigInt.length()) < neededLength)
return bigInt;
int32_t bitsInTopDigit = n % digitBits;
if (static_cast<int32_t>(bigInt.length()) == neededLength) {
if (bitsInTopDigit == 0)
return bigInt;
Digit topDigit = bigInt.digit(neededLength - 1);
if ((topDigit >> bitsInTopDigit) == 0)
return bigInt;
}
// Otherwise, truncate.
ASSERT(n <= INT32_MAX);
RELEASE_AND_RETURN(scope, truncateToNBits(globalObject, static_cast<int32_t>(n), bigInt));
}
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::truncateToNBits(JSGlobalObject* globalObject, int32_t n, BigIntImpl bigInt)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
ASSERT(n != 0);
ASSERT(bigInt.length() > n / digitBits);
int32_t neededDigits = (n + (digitBits - 1)) / digitBits;
ASSERT(neededDigits <= static_cast<int32_t>(bigInt.length()));
JSBigInt* result = createWithLength(globalObject, neededDigits);
RETURN_IF_EXCEPTION(scope, nullptr);
ASSERT(result);
// Copy all digits except the MSD.
int32_t last = neededDigits - 1;
for (int32_t i = 0; i < last; i++)
result->setDigit(i, bigInt.digit(i));
// The MSD might contain extra bits that we don't want.
Digit msd = bigInt.digit(last);
if (n % digitBits != 0) {
int32_t drop = digitBits - (n % digitBits);
msd = (msd << drop) >> drop;
}
result->setDigit(last, msd);
result->setSign(bigInt.sign());
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
// Subtracts the least significant n bits of abs(bigInt) from 2^n.
template <typename BigIntImpl>
JSBigInt::ImplResult JSBigInt::truncateAndSubFromPowerOfTwo(JSGlobalObject* globalObject, int32_t n, BigIntImpl bigInt, bool resultSign)
{
VM& vm = globalObject->vm();
auto scope = DECLARE_THROW_SCOPE(vm);
ASSERT(n != 0);
ASSERT(n <= static_cast<int32_t>(maxLengthBits));
int32_t neededDigits = (n + (digitBits - 1)) / digitBits;
ASSERT(neededDigits <= static_cast<int32_t>(maxLength)); // Follows from n <= maxLengthBits.
JSBigInt* result = createWithLength(globalObject, neededDigits);
RETURN_IF_EXCEPTION(scope, nullptr);
ASSERT(result);
// Process all digits except the MSD.
int32_t i = 0;
int32_t last = neededDigits - 1;
int32_t length = bigInt.length();
Digit borrow = 0;
// Take digits from bigInt unless its length is exhausted.
int32_t limit = std::min(last, length);
for (; i < limit; i++) {
Digit newBorrow = 0;
Digit difference = digitSub(0, bigInt.digit(i), newBorrow);
difference = digitSub(difference, borrow, newBorrow);
result->setDigit(i, difference);
borrow = newBorrow;
}
// Then simulate leading zeroes in {bigInt} as needed.
for (; i < last; i++) {
Digit newBorrow = 0;
Digit difference = digitSub(0, borrow, newBorrow);
result->setDigit(i, difference);
borrow = newBorrow;
}
// The MSD might contain extra bits that we don't want.
Digit msd = last < length ? bigInt.digit(last) : 0;
int32_t msdBitsConsumed = n % digitBits;
Digit resultMSD;
if (msdBitsConsumed == 0) {
Digit newBorrow = 0;
resultMSD = digitSub(0, msd, newBorrow);
resultMSD = digitSub(resultMSD, borrow, newBorrow);
} else {
int32_t drop = digitBits - msdBitsConsumed;
msd = (msd << drop) >> drop;
Digit minuendMSD = static_cast<Digit>(1) << (digitBits - drop);
Digit newBorrow = 0;
resultMSD = digitSub(minuendMSD, msd, newBorrow);
resultMSD = digitSub(resultMSD, borrow, newBorrow);
ASSERT(newBorrow == 0); // result < 2^n.
// If all subtracted bits were zero, we have to get rid of the
// materialized minuendMSD again.
resultMSD &= (minuendMSD - 1);
}
result->setDigit(last, resultMSD);
result->setSign(resultSign);
RELEASE_AND_RETURN(scope, result->rightTrim(globalObject));
}
JSValue JSBigInt::asIntN(JSGlobalObject* globalObject, uint64_t n, JSBigInt* bigInt)
{
return tryConvertToBigInt32(asIntNImpl(globalObject, n, HeapBigIntImpl { bigInt }));
}
JSValue JSBigInt::asUintN(JSGlobalObject* globalObject, uint64_t n, JSBigInt* bigInt)
{
return tryConvertToBigInt32(asUintNImpl(globalObject, n, HeapBigIntImpl { bigInt }));
}
#if USE(BIGINT32)
JSValue JSBigInt::asIntN(JSGlobalObject* globalObject, uint64_t n, int32_t bigInt)
{
return tryConvertToBigInt32(asIntNImpl(globalObject, n, Int32BigIntImpl { bigInt }));
}
JSValue JSBigInt::asUintN(JSGlobalObject* globalObject, uint64_t n, int32_t bigInt)
{
return tryConvertToBigInt32(asUintNImpl(globalObject, n, Int32BigIntImpl { bigInt }));
}
#endif
uint64_t JSBigInt::toBigUInt64Heap(JSBigInt* bigInt)
{
auto length = bigInt->length();
if (!length)
return 0;
uint64_t value = 0;
if constexpr (sizeof(Digit) == 4) {
value = static_cast<uint64_t>(bigInt->digit(0));
if (length > 1)
value |= static_cast<uint64_t>(bigInt->digit(1)) << 32;
} else {
ASSERT(sizeof(Digit) == 8);
value = bigInt->digit(0);
}
if (!bigInt->sign())
return value;
return ~(value - 1); // To avoid undefined behavior, we compute two's compliment by hand in C while this is simply `-value`.
}
static ALWAYS_INLINE unsigned computeHash(JSBigInt::Digit* digits, unsigned length, bool sign)
{
Hasher hasher;
WTF::add(hasher, sign);
for (unsigned index = 0; index < length; ++index)
WTF::add(hasher, digits[index]);
return hasher.hash();
}
Optional<unsigned> JSBigInt::concurrentHash()
{
// FIXME: Implement JSBigInt::concurrentHash by inserting right store barriers.
// https://bugs.webkit.org/show_bug.cgi?id=216801
return WTF::nullopt;
}
unsigned JSBigInt::hashSlow()
{
ASSERT(!m_hash);
m_hash = computeHash(dataStorage(), length(), m_sign);
return m_hash;
}
} // namespace JSC
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