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bigint.cc
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bigint.cc
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// 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.
// Parts of the implementation below:
// 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 "src/objects/bigint.h"
#include "src/execution/isolate-inl.h"
#include "src/heap/factory.h"
#include "src/heap/heap-write-barrier-inl.h"
#include "src/numbers/conversions.h"
#include "src/numbers/double.h"
#include "src/objects/heap-number-inl.h"
#include "src/objects/instance-type-inl.h"
#include "src/objects/objects-inl.h"
#include "src/objects/smi.h"
namespace v8 {
namespace internal {
// The MutableBigInt class is an implementation detail designed to prevent
// accidental mutation of a BigInt after its construction. Step-by-step
// construction of a BigInt must happen in terms of MutableBigInt, the
// final result is then passed through MutableBigInt::MakeImmutable and not
// modified further afterwards.
// Many of the functions in this class use arguments of type {BigIntBase},
// indicating that they will be used in a read-only capacity, and both
// {BigInt} and {MutableBigInt} objects can be passed in.
class MutableBigInt : public FreshlyAllocatedBigInt {
public:
// Bottleneck for converting MutableBigInts to BigInts.
static MaybeHandle<BigInt> MakeImmutable(MaybeHandle<MutableBigInt> maybe);
template <typename Isolate = v8::internal::Isolate>
static Handle<BigInt> MakeImmutable(Handle<MutableBigInt> result);
static void Canonicalize(MutableBigInt result);
// Allocation helpers.
template <typename LocalIsolate>
static MaybeHandle<MutableBigInt> New(
LocalIsolate* isolate, int length,
AllocationType allocation = AllocationType::kYoung);
static Handle<BigInt> NewFromInt(Isolate* isolate, int value);
static Handle<BigInt> NewFromDouble(Isolate* isolate, double value);
void InitializeDigits(int length, byte value = 0);
static Handle<MutableBigInt> Copy(Isolate* isolate,
Handle<BigIntBase> source);
template <typename LocalIsolate>
static Handle<BigInt> Zero(
LocalIsolate* isolate,
AllocationType allocation = AllocationType::kYoung) {
// TODO(jkummerow): Consider caching a canonical zero-BigInt.
return MakeImmutable<LocalIsolate>(
New(isolate, 0, allocation).ToHandleChecked());
}
static Handle<MutableBigInt> Cast(Handle<FreshlyAllocatedBigInt> bigint) {
SLOW_DCHECK(bigint->IsBigInt());
return Handle<MutableBigInt>::cast(bigint);
}
static MutableBigInt cast(Object o) {
SLOW_DCHECK(o.IsBigInt());
return MutableBigInt(o.ptr());
}
static MutableBigInt unchecked_cast(Object o) {
return MutableBigInt(o.ptr());
}
// Internal helpers.
static MaybeHandle<MutableBigInt> BitwiseAnd(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y);
static MaybeHandle<MutableBigInt> BitwiseXor(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y);
static MaybeHandle<MutableBigInt> BitwiseOr(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y);
static Handle<BigInt> TruncateToNBits(Isolate* isolate, int n,
Handle<BigInt> x);
static Handle<BigInt> TruncateAndSubFromPowerOfTwo(Isolate* isolate, int n,
Handle<BigInt> x,
bool result_sign);
static MaybeHandle<BigInt> AbsoluteAdd(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y, bool result_sign);
static void AbsoluteAdd(MutableBigInt result, BigInt x, BigInt y);
static Handle<BigInt> AbsoluteSub(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y, bool result_sign);
static void AbsoluteSub(MutableBigInt result, BigInt x, BigInt y);
static MaybeHandle<MutableBigInt> AbsoluteAddOne(
Isolate* isolate, Handle<BigIntBase> x, bool sign,
MutableBigInt result_storage = MutableBigInt());
static Handle<MutableBigInt> AbsoluteSubOne(Isolate* isolate,
Handle<BigIntBase> x);
static MaybeHandle<MutableBigInt> AbsoluteSubOne(Isolate* isolate,
Handle<BigIntBase> x,
int result_length);
enum ExtraDigitsHandling { kCopy, kSkip };
enum SymmetricOp { kSymmetric, kNotSymmetric };
static inline Handle<MutableBigInt> AbsoluteBitwiseOp(
Isolate* isolate, Handle<BigIntBase> x, Handle<BigIntBase> y,
MutableBigInt result_storage, ExtraDigitsHandling extra_digits,
SymmetricOp symmetric,
const std::function<digit_t(digit_t, digit_t)>& op);
static Handle<MutableBigInt> AbsoluteAnd(
Isolate* isolate, Handle<BigIntBase> x, Handle<BigIntBase> y,
MutableBigInt result_storage = MutableBigInt());
static Handle<MutableBigInt> AbsoluteAndNot(
Isolate* isolate, Handle<BigIntBase> x, Handle<BigIntBase> y,
MutableBigInt result_storage = MutableBigInt());
static Handle<MutableBigInt> AbsoluteOr(
Isolate* isolate, Handle<BigIntBase> x, Handle<BigIntBase> y,
MutableBigInt result_storage = MutableBigInt());
static Handle<MutableBigInt> AbsoluteXor(
Isolate* isolate, Handle<BigIntBase> x, Handle<BigIntBase> y,
MutableBigInt result_storage = MutableBigInt());
static int AbsoluteCompare(Handle<BigIntBase> x, Handle<BigIntBase> y);
static int AbsoluteCompare(BigIntBase x, BigIntBase y);
static void MultiplyAccumulate(Handle<BigIntBase> multiplicand,
digit_t multiplier,
Handle<MutableBigInt> accumulator,
int accumulator_index);
static void InternalMultiplyAdd(BigIntBase source, digit_t factor,
digit_t summand, int n, MutableBigInt result);
void InplaceMultiplyAdd(uintptr_t factor, uintptr_t summand);
// Specialized helpers for Divide/Remainder.
static void AbsoluteDivSmall(Isolate* isolate, Handle<BigIntBase> x,
digit_t divisor, Handle<MutableBigInt>* quotient,
digit_t* remainder);
static bool AbsoluteDivLarge(Isolate* isolate, Handle<BigIntBase> dividend,
Handle<BigIntBase> divisor,
Handle<MutableBigInt>* quotient,
Handle<MutableBigInt>* remainder);
static bool ProductGreaterThan(digit_t factor1, digit_t factor2, digit_t high,
digit_t low);
digit_t InplaceAdd(Handle<BigIntBase> summand, int start_index);
digit_t InplaceSub(Handle<BigIntBase> subtrahend, int start_index);
void InplaceRightShift(int shift);
enum SpecialLeftShiftMode {
kSameSizeResult,
kAlwaysAddOneDigit,
};
static MaybeHandle<MutableBigInt> SpecialLeftShift(Isolate* isolate,
Handle<BigIntBase> x,
int shift,
SpecialLeftShiftMode mode);
// Specialized helpers for shift operations.
static MaybeHandle<BigInt> LeftShiftByAbsolute(Isolate* isolate,
Handle<BigIntBase> x,
Handle<BigIntBase> y);
static Handle<BigInt> RightShiftByAbsolute(Isolate* isolate,
Handle<BigIntBase> x,
Handle<BigIntBase> y);
static Handle<BigInt> RightShiftByMaximum(Isolate* isolate, bool sign);
static Maybe<digit_t> ToShiftAmount(Handle<BigIntBase> x);
static MaybeHandle<String> ToStringBasePowerOfTwo(Isolate* isolate,
Handle<BigIntBase> x,
int radix,
ShouldThrow should_throw);
static MaybeHandle<String> ToStringGeneric(Isolate* isolate,
Handle<BigIntBase> x, int radix,
ShouldThrow should_throw);
static double ToDouble(Handle<BigIntBase> x);
enum Rounding { kRoundDown, kTie, kRoundUp };
static Rounding DecideRounding(Handle<BigIntBase> x, int mantissa_bits_unset,
int digit_index, uint64_t current_digit);
// Returns the least significant 64 bits, simulating two's complement
// representation.
static uint64_t GetRawBits(BigIntBase x, bool* lossless);
// Digit arithmetic helpers.
static inline digit_t digit_add(digit_t a, digit_t b, digit_t* carry);
static inline digit_t digit_sub(digit_t a, digit_t b, digit_t* borrow);
static inline digit_t digit_mul(digit_t a, digit_t b, digit_t* high);
static inline digit_t digit_div(digit_t high, digit_t low, digit_t divisor,
digit_t* remainder);
static digit_t digit_pow(digit_t base, digit_t exponent);
static inline bool digit_ismax(digit_t x) {
return static_cast<digit_t>(~x) == 0;
}
// Internal field setters. Non-mutable BigInts don't have these.
#include "src/objects/object-macros.h"
inline void set_sign(bool new_sign) {
int32_t bitfield = RELAXED_READ_INT32_FIELD(*this, kBitfieldOffset);
bitfield = SignBits::update(bitfield, new_sign);
RELAXED_WRITE_INT32_FIELD(*this, kBitfieldOffset, bitfield);
}
inline void synchronized_set_length(int new_length) {
int32_t bitfield = RELAXED_READ_INT32_FIELD(*this, kBitfieldOffset);
bitfield = LengthBits::update(bitfield, new_length);
RELEASE_WRITE_INT32_FIELD(*this, kBitfieldOffset, bitfield);
}
inline void initialize_bitfield(bool sign, int length) {
int32_t bitfield = LengthBits::encode(length) | SignBits::encode(sign);
WriteField<int32_t>(kBitfieldOffset, bitfield);
}
inline void set_digit(int n, digit_t value) {
SLOW_DCHECK(0 <= n && n < length());
WriteField<digit_t>(kDigitsOffset + n * kDigitSize, value);
}
void set_64_bits(uint64_t bits);
bool IsMutableBigInt() const { return IsBigInt(); }
NEVER_READ_ONLY_SPACE
OBJECT_CONSTRUCTORS(MutableBigInt, FreshlyAllocatedBigInt);
};
OBJECT_CONSTRUCTORS_IMPL(MutableBigInt, FreshlyAllocatedBigInt)
NEVER_READ_ONLY_SPACE_IMPL(MutableBigInt)
#include "src/base/platform/wrappers.h"
#include "src/objects/object-macros-undef.h"
template <typename T, typename Isolate>
MaybeHandle<T> ThrowBigIntTooBig(Isolate* isolate) {
// If the result of a BigInt computation is truncated to 64 bit, Turbofan
// can sometimes truncate intermediate results already, which can prevent
// those from exceeding the maximum length, effectively preventing a
// RangeError from being thrown. As this is a performance optimization, this
// behavior is accepted. To prevent the correctness fuzzer from detecting this
// difference, we crash the program.
if (FLAG_correctness_fuzzer_suppressions) {
FATAL("Aborting on invalid BigInt length");
}
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig), T);
}
template <typename LocalIsolate>
MaybeHandle<MutableBigInt> MutableBigInt::New(LocalIsolate* isolate, int length,
AllocationType allocation) {
if (length > BigInt::kMaxLength) {
return ThrowBigIntTooBig<MutableBigInt>(isolate);
}
Handle<MutableBigInt> result =
Cast(isolate->factory()->NewBigInt(length, allocation));
result->initialize_bitfield(false, length);
#if DEBUG
result->InitializeDigits(length, 0xBF);
#endif
return result;
}
Handle<BigInt> MutableBigInt::NewFromInt(Isolate* isolate, int value) {
if (value == 0) return Zero(isolate);
Handle<MutableBigInt> result = Cast(isolate->factory()->NewBigInt(1));
bool sign = value < 0;
result->initialize_bitfield(sign, 1);
if (!sign) {
result->set_digit(0, value);
} else {
if (value == kMinInt) {
STATIC_ASSERT(kMinInt == -kMaxInt - 1);
result->set_digit(0, static_cast<BigInt::digit_t>(kMaxInt) + 1);
} else {
result->set_digit(0, -value);
}
}
return MakeImmutable(result);
}
Handle<BigInt> MutableBigInt::NewFromDouble(Isolate* isolate, double value) {
DCHECK_EQ(value, std::floor(value));
if (value == 0) return Zero(isolate);
bool sign = value < 0; // -0 was already handled above.
uint64_t double_bits = bit_cast<uint64_t>(value);
int raw_exponent =
static_cast<int>(double_bits >> Double::kPhysicalSignificandSize) & 0x7FF;
DCHECK_NE(raw_exponent, 0x7FF);
DCHECK_GE(raw_exponent, 0x3FF);
int exponent = raw_exponent - 0x3FF;
int digits = exponent / kDigitBits + 1;
Handle<MutableBigInt> result = Cast(isolate->factory()->NewBigInt(digits));
result->initialize_bitfield(sign, digits);
// 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
// <--> <------>
// msd_topbit kDigitBits
//
uint64_t mantissa =
(double_bits & Double::kSignificandMask) | Double::kHiddenBit;
const int kMantissaTopBit = Double::kSignificandSize - 1; // 0-indexed.
// 0-indexed position of most significant bit in the most significant digit.
int msd_topbit = exponent % kDigitBits;
// Number of unused bits in {mantissa}. We'll keep them shifted to the
// left (i.e. most significant part) of the underlying uint64_t.
int remaining_mantissa_bits = 0;
// Next digit under construction.
digit_t digit;
// First, build the MSD by shifting the mantissa appropriately.
if (msd_topbit < kMantissaTopBit) {
remaining_mantissa_bits = kMantissaTopBit - msd_topbit;
digit = mantissa >> remaining_mantissa_bits;
mantissa = mantissa << (64 - remaining_mantissa_bits);
} else {
DCHECK_GE(msd_topbit, kMantissaTopBit);
digit = mantissa << (msd_topbit - kMantissaTopBit);
mantissa = 0;
}
result->set_digit(digits - 1, digit);
// Then fill in the rest of the digits.
for (int digit_index = digits - 2; digit_index >= 0; digit_index--) {
if (remaining_mantissa_bits > 0) {
remaining_mantissa_bits -= kDigitBits;
if (sizeof(digit) == 4) {
digit = mantissa >> 32;
mantissa = mantissa << 32;
} else {
DCHECK_EQ(sizeof(digit), 8);
digit = mantissa;
mantissa = 0;
}
} else {
digit = 0;
}
result->set_digit(digit_index, digit);
}
return MakeImmutable(result);
}
Handle<MutableBigInt> MutableBigInt::Copy(Isolate* isolate,
Handle<BigIntBase> source) {
int length = source->length();
// Allocating a BigInt of the same length as an existing BigInt cannot throw.
Handle<MutableBigInt> result = New(isolate, length).ToHandleChecked();
base::Memcpy(
reinterpret_cast<void*>(result->address() + BigIntBase::kHeaderSize),
reinterpret_cast<void*>(source->address() + BigIntBase::kHeaderSize),
BigInt::SizeFor(length) - BigIntBase::kHeaderSize);
return result;
}
void MutableBigInt::InitializeDigits(int length, byte value) {
memset(reinterpret_cast<void*>(ptr() + kDigitsOffset - kHeapObjectTag), value,
length * kDigitSize);
}
MaybeHandle<BigInt> MutableBigInt::MakeImmutable(
MaybeHandle<MutableBigInt> maybe) {
Handle<MutableBigInt> result;
if (!maybe.ToHandle(&result)) return MaybeHandle<BigInt>();
return MakeImmutable(result);
}
template <typename LocalIsolate>
Handle<BigInt> MutableBigInt::MakeImmutable(Handle<MutableBigInt> result) {
MutableBigInt::Canonicalize(*result);
return Handle<BigInt>::cast(result);
}
void MutableBigInt::Canonicalize(MutableBigInt result) {
// Check if we need to right-trim any leading zero-digits.
int old_length = result.length();
int new_length = old_length;
while (new_length > 0 && result.digit(new_length - 1) == 0) new_length--;
int to_trim = old_length - new_length;
if (to_trim != 0) {
int size_delta = to_trim * MutableBigInt::kDigitSize;
Address new_end = result.address() + BigInt::SizeFor(new_length);
Heap* heap = result.GetHeap();
if (!heap->IsLargeObject(result)) {
// We do not create a filler for objects in large object space.
// TODO(hpayer): We should shrink the large object page if the size
// of the object changed significantly.
heap->CreateFillerObjectAt(new_end, size_delta, ClearRecordedSlots::kNo);
}
result.synchronized_set_length(new_length);
// Canonicalize -0n.
if (new_length == 0) {
result.set_sign(false);
// TODO(jkummerow): If we cache a canonical 0n, return that here.
}
}
DCHECK_IMPLIES(result.length() > 0,
result.digit(result.length() - 1) != 0); // MSD is non-zero.
}
template <typename LocalIsolate>
Handle<BigInt> BigInt::Zero(LocalIsolate* isolate, AllocationType allocation) {
return MutableBigInt::Zero(isolate, allocation);
}
template Handle<BigInt> BigInt::Zero(Isolate* isolate,
AllocationType allocation);
template Handle<BigInt> BigInt::Zero(LocalIsolate* isolate,
AllocationType allocation);
Handle<BigInt> BigInt::UnaryMinus(Isolate* isolate, Handle<BigInt> x) {
// Special case: There is no -0n.
if (x->is_zero()) {
return x;
}
Handle<MutableBigInt> result = MutableBigInt::Copy(isolate, x);
result->set_sign(!x->sign());
return MutableBigInt::MakeImmutable(result);
}
MaybeHandle<BigInt> BigInt::BitwiseNot(Isolate* isolate, Handle<BigInt> x) {
MaybeHandle<MutableBigInt> result;
if (x->sign()) {
// ~(-x) == ~(~(x-1)) == x-1
result = MutableBigInt::AbsoluteSubOne(isolate, x, x->length());
} else {
// ~x == -x-1 == -(x+1)
result = MutableBigInt::AbsoluteAddOne(isolate, x, true);
}
return MutableBigInt::MakeImmutable(result);
}
MaybeHandle<BigInt> BigInt::Exponentiate(Isolate* isolate, Handle<BigInt> base,
Handle<BigInt> exponent) {
// 1. If exponent is < 0, throw a RangeError exception.
if (exponent->sign()) {
THROW_NEW_ERROR(isolate,
NewRangeError(MessageTemplate::kBigIntNegativeExponent),
BigInt);
}
// 2. If base is 0n and exponent is 0n, return 1n.
if (exponent->is_zero()) {
return MutableBigInt::NewFromInt(isolate, 1);
}
// 3. Return a BigInt representing the mathematical value of base raised
// to the power exponent.
if (base->is_zero()) return base;
if (base->length() == 1 && base->digit(0) == 1) {
// (-1) ** even_number == 1.
if (base->sign() && (exponent->digit(0) & 1) == 0) {
return UnaryMinus(isolate, base);
}
// (-1) ** odd_number == -1; 1 ** anything == 1.
return base;
}
// For all bases >= 2, very large exponents would lead to unrepresentable
// results.
STATIC_ASSERT(kMaxLengthBits < std::numeric_limits<digit_t>::max());
if (exponent->length() > 1) {
return ThrowBigIntTooBig<BigInt>(isolate);
}
digit_t exp_value = exponent->digit(0);
if (exp_value == 1) return base;
if (exp_value >= kMaxLengthBits) {
return ThrowBigIntTooBig<BigInt>(isolate);
}
STATIC_ASSERT(kMaxLengthBits <= kMaxInt);
int n = static_cast<int>(exp_value);
if (base->length() == 1 && base->digit(0) == 2) {
// Fast path for 2^n.
int needed_digits = 1 + (n / kDigitBits);
Handle<MutableBigInt> result;
if (!MutableBigInt::New(isolate, needed_digits).ToHandle(&result)) {
return MaybeHandle<BigInt>();
}
result->InitializeDigits(needed_digits);
// All bits are zero. Now set the n-th bit.
digit_t msd = static_cast<digit_t>(1) << (n % kDigitBits);
result->set_digit(needed_digits - 1, msd);
// Result is negative for odd powers of -2n.
if (base->sign()) result->set_sign((n & 1) != 0);
return MutableBigInt::MakeImmutable(result);
}
Handle<BigInt> result;
Handle<BigInt> running_square = base;
// This implicitly sets the result's sign correctly.
if (n & 1) result = base;
n >>= 1;
for (; n != 0; n >>= 1) {
MaybeHandle<BigInt> maybe_result =
Multiply(isolate, running_square, running_square);
if (!maybe_result.ToHandle(&running_square)) return maybe_result;
if (n & 1) {
if (result.is_null()) {
result = running_square;
} else {
maybe_result = Multiply(isolate, result, running_square);
if (!maybe_result.ToHandle(&result)) return maybe_result;
}
}
}
return result;
}
MaybeHandle<BigInt> BigInt::Multiply(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
if (x->is_zero()) return x;
if (y->is_zero()) return y;
int result_length = x->length() + y->length();
Handle<MutableBigInt> result;
if (!MutableBigInt::New(isolate, result_length).ToHandle(&result)) {
return MaybeHandle<BigInt>();
}
result->InitializeDigits(result_length);
uintptr_t work_estimate = 0;
for (int i = 0; i < x->length(); i++) {
MutableBigInt::MultiplyAccumulate(y, x->digit(i), result, i);
// Multiplication can take a long time. Check for interrupt requests
// every now and then (roughly every 10-20 of milliseconds -- rarely
// enough not to create noticeable overhead, frequently enough not to
// appear frozen).
work_estimate += y->length();
if (work_estimate > 5000000) {
work_estimate = 0;
StackLimitCheck interrupt_check(isolate);
if (interrupt_check.InterruptRequested() &&
isolate->stack_guard()->HandleInterrupts().IsException(isolate)) {
return MaybeHandle<BigInt>();
}
}
}
result->set_sign(x->sign() != y->sign());
return MutableBigInt::MakeImmutable(result);
}
MaybeHandle<BigInt> BigInt::Divide(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
// 1. If y is 0n, throw a RangeError exception.
if (y->is_zero()) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntDivZero),
BigInt);
}
// 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 (MutableBigInt::AbsoluteCompare(x, y) < 0) {
return Zero(isolate);
}
Handle<MutableBigInt> quotient;
bool result_sign = x->sign() != y->sign();
if (y->length() == 1) {
digit_t divisor = y->digit(0);
if (divisor == 1) {
return result_sign == x->sign() ? x : UnaryMinus(isolate, x);
}
digit_t remainder;
MutableBigInt::AbsoluteDivSmall(isolate, x, divisor, "ient, &remainder);
} else {
if (!MutableBigInt::AbsoluteDivLarge(isolate, x, y, "ient, nullptr)) {
return MaybeHandle<BigInt>();
}
}
quotient->set_sign(x->sign() != y->sign());
return MutableBigInt::MakeImmutable(quotient);
}
MaybeHandle<BigInt> BigInt::Remainder(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
// 1. If y is 0n, throw a RangeError exception.
if (y->is_zero()) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntDivZero),
BigInt);
}
// 2. Return the BigInt representing x modulo y.
// See https://github.com/tc39/proposal-bigint/issues/84 though.
if (MutableBigInt::AbsoluteCompare(x, y) < 0) return x;
Handle<MutableBigInt> remainder;
if (y->length() == 1) {
digit_t divisor = y->digit(0);
if (divisor == 1) return Zero(isolate);
digit_t remainder_digit;
MutableBigInt::AbsoluteDivSmall(isolate, x, divisor, nullptr,
&remainder_digit);
if (remainder_digit == 0) {
return Zero(isolate);
}
remainder = MutableBigInt::New(isolate, 1).ToHandleChecked();
remainder->set_digit(0, remainder_digit);
} else {
if (!MutableBigInt::AbsoluteDivLarge(isolate, x, y, nullptr, &remainder)) {
return MaybeHandle<BigInt>();
}
}
remainder->set_sign(x->sign());
return MutableBigInt::MakeImmutable(remainder);
}
MaybeHandle<BigInt> BigInt::Add(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
bool xsign = x->sign();
if (xsign == y->sign()) {
// x + y == x + y
// -x + -y == -(x + y)
return MutableBigInt::AbsoluteAdd(isolate, x, y, xsign);
}
// x + -y == x - y == -(y - x)
// -x + y == y - x == -(x - y)
if (MutableBigInt::AbsoluteCompare(x, y) >= 0) {
return MutableBigInt::AbsoluteSub(isolate, x, y, xsign);
}
return MutableBigInt::AbsoluteSub(isolate, y, x, !xsign);
}
MaybeHandle<BigInt> BigInt::Subtract(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
bool xsign = x->sign();
if (xsign != y->sign()) {
// x - (-y) == x + y
// (-x) - y == -(x + y)
return MutableBigInt::AbsoluteAdd(isolate, x, y, xsign);
}
// x - y == -(y - x)
// (-x) - (-y) == y - x == -(x - y)
if (MutableBigInt::AbsoluteCompare(x, y) >= 0) {
return MutableBigInt::AbsoluteSub(isolate, x, y, xsign);
}
return MutableBigInt::AbsoluteSub(isolate, y, x, !xsign);
}
MaybeHandle<BigInt> BigInt::LeftShift(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
if (y->is_zero() || x->is_zero()) return x;
if (y->sign()) return MutableBigInt::RightShiftByAbsolute(isolate, x, y);
return MutableBigInt::LeftShiftByAbsolute(isolate, x, y);
}
MaybeHandle<BigInt> BigInt::SignedRightShift(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
if (y->is_zero() || x->is_zero()) return x;
if (y->sign()) return MutableBigInt::LeftShiftByAbsolute(isolate, x, y);
return MutableBigInt::RightShiftByAbsolute(isolate, x, y);
}
MaybeHandle<BigInt> BigInt::UnsignedRightShift(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y) {
THROW_NEW_ERROR(isolate, NewTypeError(MessageTemplate::kBigIntShr), BigInt);
}
namespace {
// Produces comparison result for {left_negative} == sign(x) != sign(y).
ComparisonResult UnequalSign(bool left_negative) {
return left_negative ? ComparisonResult::kLessThan
: ComparisonResult::kGreaterThan;
}
// Produces result for |x| > |y|, with {both_negative} == sign(x) == sign(y);
ComparisonResult AbsoluteGreater(bool both_negative) {
return both_negative ? ComparisonResult::kLessThan
: ComparisonResult::kGreaterThan;
}
// Produces result for |x| < |y|, with {both_negative} == sign(x) == sign(y).
ComparisonResult AbsoluteLess(bool both_negative) {
return both_negative ? ComparisonResult::kGreaterThan
: ComparisonResult::kLessThan;
}
} // namespace
// (Never returns kUndefined.)
ComparisonResult BigInt::CompareToBigInt(Handle<BigInt> x, Handle<BigInt> y) {
bool x_sign = x->sign();
if (x_sign != y->sign()) return UnequalSign(x_sign);
int result = MutableBigInt::AbsoluteCompare(x, y);
if (result > 0) return AbsoluteGreater(x_sign);
if (result < 0) return AbsoluteLess(x_sign);
return ComparisonResult::kEqual;
}
bool BigInt::EqualToBigInt(BigInt x, BigInt y) {
if (x.sign() != y.sign()) return false;
if (x.length() != y.length()) return false;
for (int i = 0; i < x.length(); i++) {
if (x.digit(i) != y.digit(i)) return false;
}
return true;
}
MaybeHandle<BigInt> BigInt::BitwiseAnd(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
return MutableBigInt::MakeImmutable(MutableBigInt::BitwiseAnd(isolate, x, y));
}
MaybeHandle<MutableBigInt> MutableBigInt::BitwiseAnd(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y) {
if (!x->sign() && !y->sign()) {
return AbsoluteAnd(isolate, x, y);
} else if (x->sign() && y->sign()) {
int result_length = std::max(x->length(), y->length()) + 1;
// (-x) & (-y) == ~(x-1) & ~(y-1) == ~((x-1) | (y-1))
// == -(((x-1) | (y-1)) + 1)
Handle<MutableBigInt> result;
if (!AbsoluteSubOne(isolate, x, result_length).ToHandle(&result)) {
return MaybeHandle<MutableBigInt>();
}
Handle<MutableBigInt> y_1 = AbsoluteSubOne(isolate, y);
result = AbsoluteOr(isolate, result, y_1, *result);
return AbsoluteAddOne(isolate, result, true, *result);
} else {
DCHECK(x->sign() != y->sign());
// Assume that x is the positive BigInt.
if (x->sign()) std::swap(x, y);
// x & (-y) == x & ~(y-1) == x &~ (y-1)
Handle<MutableBigInt> y_1 = AbsoluteSubOne(isolate, y);
return AbsoluteAndNot(isolate, x, y_1);
}
}
MaybeHandle<BigInt> BigInt::BitwiseXor(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
return MutableBigInt::MakeImmutable(MutableBigInt::BitwiseXor(isolate, x, y));
}
MaybeHandle<MutableBigInt> MutableBigInt::BitwiseXor(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y) {
if (!x->sign() && !y->sign()) {
return AbsoluteXor(isolate, x, y);
} else if (x->sign() && y->sign()) {
int result_length = std::max(x->length(), y->length());
// (-x) ^ (-y) == ~(x-1) ^ ~(y-1) == (x-1) ^ (y-1)
Handle<MutableBigInt> result =
AbsoluteSubOne(isolate, x, result_length).ToHandleChecked();
Handle<MutableBigInt> y_1 = AbsoluteSubOne(isolate, y);
return AbsoluteXor(isolate, result, y_1, *result);
} else {
DCHECK(x->sign() != y->sign());
int result_length = std::max(x->length(), y->length()) + 1;
// Assume that x is the positive BigInt.
if (x->sign()) std::swap(x, y);
// x ^ (-y) == x ^ ~(y-1) == ~(x ^ (y-1)) == -((x ^ (y-1)) + 1)
Handle<MutableBigInt> result;
if (!AbsoluteSubOne(isolate, y, result_length).ToHandle(&result)) {
return MaybeHandle<MutableBigInt>();
}
result = AbsoluteXor(isolate, result, x, *result);
return AbsoluteAddOne(isolate, result, true, *result);
}
}
MaybeHandle<BigInt> BigInt::BitwiseOr(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y) {
return MutableBigInt::MakeImmutable(MutableBigInt::BitwiseOr(isolate, x, y));
}
MaybeHandle<MutableBigInt> MutableBigInt::BitwiseOr(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y) {
int result_length = std::max(x->length(), y->length());
if (!x->sign() && !y->sign()) {
return AbsoluteOr(isolate, x, y);
} else if (x->sign() && y->sign()) {
// (-x) | (-y) == ~(x-1) | ~(y-1) == ~((x-1) & (y-1))
// == -(((x-1) & (y-1)) + 1)
Handle<MutableBigInt> result =
AbsoluteSubOne(isolate, x, result_length).ToHandleChecked();
Handle<MutableBigInt> y_1 = AbsoluteSubOne(isolate, y);
result = AbsoluteAnd(isolate, result, y_1, *result);
return AbsoluteAddOne(isolate, result, true, *result);
} else {
DCHECK(x->sign() != y->sign());
// Assume that x is the positive BigInt.
if (x->sign()) std::swap(x, y);
// x | (-y) == x | ~(y-1) == ~((y-1) &~ x) == -(((y-1) &~ x) + 1)
Handle<MutableBigInt> result =
AbsoluteSubOne(isolate, y, result_length).ToHandleChecked();
result = AbsoluteAndNot(isolate, result, x, *result);
return AbsoluteAddOne(isolate, result, true, *result);
}
}
MaybeHandle<BigInt> BigInt::Increment(Isolate* isolate, Handle<BigInt> x) {
if (x->sign()) {
Handle<MutableBigInt> result = MutableBigInt::AbsoluteSubOne(isolate, x);
result->set_sign(true);
return MutableBigInt::MakeImmutable(result);
} else {
return MutableBigInt::MakeImmutable(
MutableBigInt::AbsoluteAddOne(isolate, x, false));
}
}
MaybeHandle<BigInt> BigInt::Decrement(Isolate* isolate, Handle<BigInt> x) {
MaybeHandle<MutableBigInt> result;
if (x->sign()) {
result = MutableBigInt::AbsoluteAddOne(isolate, x, true);
} else if (x->is_zero()) {
// TODO(jkummerow): Consider caching a canonical -1n BigInt.
return MutableBigInt::NewFromInt(isolate, -1);
} else {
result = MutableBigInt::AbsoluteSubOne(isolate, x);
}
return MutableBigInt::MakeImmutable(result);
}
Maybe<ComparisonResult> BigInt::CompareToString(Isolate* isolate,
Handle<BigInt> x,
Handle<String> y) {
// a. Let ny be StringToBigInt(y);
MaybeHandle<BigInt> maybe_ny = StringToBigInt(isolate, y);
// b. If ny is NaN, return undefined.
Handle<BigInt> ny;
if (!maybe_ny.ToHandle(&ny)) {
if (isolate->has_pending_exception()) {
return Nothing<ComparisonResult>();
} else {
return Just(ComparisonResult::kUndefined);
}
}
// c. Return BigInt::lessThan(x, ny).
return Just(CompareToBigInt(x, ny));
}
Maybe<bool> BigInt::EqualToString(Isolate* isolate, Handle<BigInt> x,
Handle<String> y) {
// a. Let n be StringToBigInt(y).
MaybeHandle<BigInt> maybe_n = StringToBigInt(isolate, y);
// b. If n is NaN, return false.
Handle<BigInt> n;
if (!maybe_n.ToHandle(&n)) {
if (isolate->has_pending_exception()) {
return Nothing<bool>();
} else {
return Just(false);
}
}
// c. Return the result of x == n.
return Just(EqualToBigInt(*x, *n));
}
bool BigInt::EqualToNumber(Handle<BigInt> x, Handle<Object> y) {
DCHECK(y->IsNumber());
// a. If x or y are any of NaN, +∞, or -∞, return false.
// b. If the mathematical value of x is equal to the mathematical value of y,
// return true, otherwise return false.
if (y->IsSmi()) {
int value = Smi::ToInt(*y);
if (value == 0) return x->is_zero();
// Any multi-digit BigInt is bigger than a Smi.
STATIC_ASSERT(sizeof(digit_t) >= sizeof(value));
return (x->length() == 1) && (x->sign() == (value < 0)) &&
(x->digit(0) ==
static_cast<digit_t>(std::abs(static_cast<int64_t>(value))));
}
DCHECK(y->IsHeapNumber());
double value = Handle<HeapNumber>::cast(y)->value();
return CompareToDouble(x, value) == ComparisonResult::kEqual;
}
ComparisonResult BigInt::CompareToNumber(Handle<BigInt> x, Handle<Object> y) {
DCHECK(y->IsNumber());
if (y->IsSmi()) {
bool x_sign = x->sign();
int y_value = Smi::ToInt(*y);
bool y_sign = (y_value < 0);
if (x_sign != y_sign) return UnequalSign(x_sign);
if (x->is_zero()) {
DCHECK(!y_sign);
return y_value == 0 ? ComparisonResult::kEqual
: ComparisonResult::kLessThan;
}
// Any multi-digit BigInt is bigger than a Smi.
STATIC_ASSERT(sizeof(digit_t) >= sizeof(y_value));
if (x->length() > 1) return AbsoluteGreater(x_sign);
digit_t abs_value = std::abs(static_cast<int64_t>(y_value));
digit_t x_digit = x->digit(0);
if (x_digit > abs_value) return AbsoluteGreater(x_sign);
if (x_digit < abs_value) return AbsoluteLess(x_sign);
return ComparisonResult::kEqual;
}
DCHECK(y->IsHeapNumber());
double value = Handle<HeapNumber>::cast(y)->value();
return CompareToDouble(x, value);
}
ComparisonResult BigInt::CompareToDouble(Handle<BigInt> x, double y) {
if (std::isnan(y)) return ComparisonResult::kUndefined;
if (y == V8_INFINITY) return ComparisonResult::kLessThan;
if (y == -V8_INFINITY) return ComparisonResult::kGreaterThan;
bool x_sign = 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 y_sign = (y < 0);
if (x_sign != y_sign) return UnequalSign(x_sign);
if (y == 0) {
DCHECK(!x_sign);
return x->is_zero() ? ComparisonResult::kEqual
: ComparisonResult::kGreaterThan;
}
if (x->is_zero()) {
DCHECK(!y_sign);
return ComparisonResult::kLessThan;
}
uint64_t double_bits = bit_cast<uint64_t>(y);
int raw_exponent =
static_cast<int>(double_bits >> Double::kPhysicalSignificandSize) & 0x7FF;
uint64_t mantissa = double_bits & Double::kSignificandMask;
// Non-finite doubles are handled above.
DCHECK_NE(raw_exponent, 0x7FF);
int exponent = raw_exponent - 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.
DCHECK(!x->is_zero());
return AbsoluteGreater(x_sign);
}
int x_length = x->length();
digit_t x_msd = x->digit(x_length - 1);
int msd_leading_zeros = base::bits::CountLeadingZeros(x_msd);
int x_bitlength = x_length * kDigitBits - msd_leading_zeros;
int y_bitlength = exponent + 1;
if (x_bitlength < y_bitlength) return AbsoluteLess(x_sign);
if (x_bitlength > y_bitlength) return AbsoluteGreater(x_sign);
// 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 ...
// <--> <------>
// msd_topbit kDigitBits
//
mantissa |= Double::kHiddenBit;
const int kMantissaTopBit = 52; // 0-indexed.
// 0-indexed position of {x}'s most significant bit within the {msd}.
int msd_topbit = kDigitBits - 1 - msd_leading_zeros;
DCHECK_EQ(msd_topbit, (x_bitlength - 1) % kDigitBits);
// Shifted chunk of {mantissa} for comparing with {digit}.
digit_t compare_mantissa;
// 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 remaining_mantissa_bits = 0;
// First, compare the most significant digit against the beginning of
// the mantissa.
if (msd_topbit < kMantissaTopBit) {
remaining_mantissa_bits = (kMantissaTopBit - msd_topbit);
compare_mantissa = mantissa >> remaining_mantissa_bits;
mantissa = mantissa << (64 - remaining_mantissa_bits);
} else {
DCHECK_GE(msd_topbit, kMantissaTopBit);
compare_mantissa = mantissa << (msd_topbit - kMantissaTopBit);
mantissa = 0;
}
if (x_msd > compare_mantissa) return AbsoluteGreater(x_sign);
if (x_msd < compare_mantissa) return AbsoluteLess(x_sign);
// Then, compare additional digits against any remaining mantissa bits.
for (int digit_index = x_length - 2; digit_index >= 0; digit_index--) {
if (remaining_mantissa_bits > 0) {
remaining_mantissa_bits -= kDigitBits;
if (sizeof(mantissa) != sizeof(x_msd)) {
compare_mantissa = mantissa >> (64 - kDigitBits);
// "& 63" to appease compilers. kDigitBits is 32 here anyway.
mantissa = mantissa << (kDigitBits & 63);
} else {
compare_mantissa = mantissa;
mantissa = 0;
}
} else {
compare_mantissa = 0;
}