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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/double.h"
#include "src/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);
static Handle<BigInt> MakeImmutable(Handle<MutableBigInt> result);
// Allocation helpers.
static MaybeHandle<MutableBigInt> New(Isolate* isolate, int length,
PretenureFlag pretenure = NOT_TENURED);
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);
static Handle<BigInt> Zero(Isolate* isolate) {
// TODO(jkummerow): Consider caching a canonical zero-BigInt.
return MakeImmutable(New(isolate, 0)).ToHandleChecked();
}
static Handle<MutableBigInt> Cast(Handle<FreshlyAllocatedBigInt> bigint) {
SLOW_DCHECK(bigint->IsBigInt());
return Handle<MutableBigInt>::cast(bigint);
}
static MutableBigInt unchecked_cast(ObjectPtr 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 Handle<BigInt> AbsoluteSub(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y, bool result_sign);
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 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);
WRITE_INT32_FIELD(this, kBitfieldOffset, bitfield);
}
inline void set_digit(int n, digit_t value) {
SLOW_DCHECK(0 <= n && n < length());
Address address = FIELD_ADDR(this, kDigitsOffset + n * kDigitSize);
(*reinterpret_cast<digit_t*>(address)) = 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/objects/object-macros-undef.h"
MaybeHandle<MutableBigInt> MutableBigInt::New(Isolate* isolate, int length,
PretenureFlag pretenure) {
if (length > BigInt::kMaxLength) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig),
MutableBigInt);
}
Handle<MutableBigInt> result =
Cast(isolate->factory()->NewBigInt(length, pretenure));
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();
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);
}
Handle<BigInt> MutableBigInt::MakeImmutable(Handle<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 * 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.
return Handle<BigInt>(result.location());
}
Handle<BigInt> BigInt::Zero(Isolate* isolate) {
return MutableBigInt::Zero(isolate);
}
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) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig),
BigInt);
}
digit_t exp_value = exponent->digit(0);
if (exp_value == 1) return base;
if (exp_value >= kMaxLengthBits) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig),
BigInt);
}
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);
for (int i = 0; i < x->length(); i++) {
MutableBigInt::MultiplyAccumulate(y, x->digit(i), result, i);
}
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, &quotient, &remainder);
} else {
if (!MutableBigInt::AbsoluteDivLarge(isolate, x, y, &quotient, 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 = 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)
return AbsoluteAndNot(isolate, x, AbsoluteSubOne(isolate, y));
}
}
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 = 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 = 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 = 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);
}
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)) {
DCHECK(!isolate->has_pending_exception());
return ComparisonResult::kUndefined;
}
// c. Return BigInt::lessThan(x, ny).
return CompareToBigInt(x, ny);
}
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)) {
DCHECK(!isolate->has_pending_exception());
return false;
}
// c. Return the result of x == n.
return 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;
}
digit_t digit = x->digit(digit_index);
if (digit > compare_mantissa) return AbsoluteGreater(x_sign);
if (digit < compare_mantissa) return AbsoluteLess(x_sign);
}
// Integer parts are equal; check whether {y} has a fractional part.
if (mantissa != 0) {
DCHECK_GT(remaining_mantissa_bits, 0);
return AbsoluteLess(x_sign);
}
return ComparisonResult::kEqual;
}
MaybeHandle<String> BigInt::ToString(Isolate* isolate, Handle<BigInt> bigint,
int radix, ShouldThrow should_throw) {
if (bigint->is_zero()) {
return isolate->factory()->NewStringFromStaticChars("0");
}
if (base::bits::IsPowerOfTwo(radix)) {
return MutableBigInt::ToStringBasePowerOfTwo(isolate, bigint, radix,
should_throw);
}
return MutableBigInt::ToStringGeneric(isolate, bigint, radix, should_throw);
}
MaybeHandle<BigInt> BigInt::FromNumber(Isolate* isolate,
Handle<Object> number) {
DCHECK(number->IsNumber());
if (number->IsSmi()) {
return MutableBigInt::NewFromInt(isolate, Smi::ToInt(*number));
}
double value = HeapNumber::cast(*number)->value();
if (!std::isfinite(value) || (DoubleToInteger(value) != value)) {
THROW_NEW_ERROR(isolate,
NewRangeError(MessageTemplate::kBigIntFromNumber, number),
BigInt);
}
return MutableBigInt::NewFromDouble(isolate, value);
}
MaybeHandle<BigInt> BigInt::FromObject(Isolate* isolate, Handle<Object> obj) {
if (obj->IsJSReceiver()) {
ASSIGN_RETURN_ON_EXCEPTION(
isolate, obj,
JSReceiver::ToPrimitive(Handle<JSReceiver>::cast(obj),
ToPrimitiveHint::kNumber),
BigInt);
}
if (obj->IsBoolean()) {
return MutableBigInt::NewFromInt(isolate, obj->BooleanValue(isolate));
}
if (obj->IsBigInt()) {
return Handle<BigInt>::cast(obj);
}
if (obj->IsString()) {
Handle<BigInt> n;
if (!StringToBigInt(isolate, Handle<String>::cast(obj)).ToHandle(&n)) {
THROW_NEW_ERROR(isolate,
NewSyntaxError(MessageTemplate::kBigIntFromObject, obj),
BigInt);
}
return n;
}
THROW_NEW_ERROR(
isolate, NewTypeError(MessageTemplate::kBigIntFromObject, obj), BigInt);
}
Handle<Object> BigInt::ToNumber(Isolate* isolate, Handle<BigInt> x) {
if (x->is_zero()) return Handle<Smi>(Smi::zero(), isolate);
if (x->length() == 1 && x->digit(0) < Smi::kMaxValue) {
int value = static_cast<int>(x->digit(0));
if (x->sign()) value = -value;
return Handle<Smi>(Smi::FromInt(value), isolate);
}
double result = MutableBigInt::ToDouble(x);
return isolate->factory()->NewHeapNumber(result);
}
double MutableBigInt::ToDouble(Handle<BigIntBase> x) {
if (x->is_zero()) return 0.0;
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;
if (x_bitlength > 1024) return x->sign() ? -V8_INFINITY : V8_INFINITY;
uint64_t exponent = x_bitlength - 1;
// We need the most significant bit shifted to the position of a double's
// "hidden bit". We also need to hide that MSB, so we shift it out.
uint64_t current_digit = x_msd;
int digit_index = x_length - 1;
int shift = msd_leading_zeros + 1 + (64 - kDigitBits);
DCHECK_LE(1, shift);
DCHECK_LE(shift, 64);
uint64_t mantissa = (shift == 64) ? 0 : current_digit << shift;
mantissa >>= 12;
int mantissa_bits_unset = shift - 12;
// If not all mantissa bits are defined yet, get more digits as needed.
if (mantissa_bits_unset >= kDigitBits && digit_index > 0) {
digit_index--;
current_digit = static_cast<uint64_t>(x->digit(digit_index));
mantissa |= (current_digit << (mantissa_bits_unset - kDigitBits));
mantissa_bits_unset -= kDigitBits;
}
if (mantissa_bits_unset > 0 && digit_index > 0) {
DCHECK_LT(mantissa_bits_unset, kDigitBits);
digit_index--;
current_digit = static_cast<uint64_t>(x->digit(digit_index));
mantissa |= (current_digit >> (kDigitBits - mantissa_bits_unset));
mantissa_bits_unset -= kDigitBits;
}
// If there are unconsumed digits left, we may have to round.
Rounding rounding =
DecideRounding(x, mantissa_bits_unset, digit_index, current_digit);
if (rounding == kRoundUp || (rounding == kTie && (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 >> Double::kPhysicalSignificandSize) != 0) {
mantissa = 0;
exponent++;
// Incrementing the exponent can overflow too.
if (exponent > 1023) {
return x->sign() ? -V8_INFINITY : V8_INFINITY;
}
}
}
// Assemble the result.
uint64_t sign_bit = x->sign() ? (static_cast<uint64_t>(1) << 63) : 0;
exponent = (exponent + 0x3FF) << Double::kPhysicalSignificandSize;
uint64_t double_bits = sign_bit | exponent | mantissa;
return bit_cast<double>(double_bits);
}
// This is its own function to keep control flow sane. The meaning of the
// parameters is defined by {ToDouble}'s local variable usage.
MutableBigInt::Rounding MutableBigInt::DecideRounding(Handle<BigIntBase> x,
int mantissa_bits_unset,
int digit_index,
uint64_t current_digit) {
if (mantissa_bits_unset > 0) return kRoundDown;
int top_unconsumed_bit;
if (mantissa_bits_unset < 0) {
// There are unconsumed bits in {current_digit}.
top_unconsumed_bit = -mantissa_bits_unset - 1;
} else {
DCHECK_EQ(mantissa_bits_unset, 0);
// {current_digit} fit the mantissa exactly; look at the next digit.
if (digit_index == 0) return kRoundDown;
digit_index--;
current_digit = static_cast<uint64_t>(x->digit(digit_index));
top_unconsumed_bit = kDigitBits - 1;
}
// If the most significant remaining bit is 0, round down.
uint64_t bitmask = static_cast<uint64_t>(1) << top_unconsumed_bit;
if ((current_digit & bitmask) == 0) {
return kRoundDown;
}
// If any other remaining bit is set, round up.
bitmask -= 1;
if ((current_digit & bitmask) != 0) return kRoundUp;
while (digit_index > 0) {
digit_index--;
if (x->digit(digit_index) != 0) return kRoundUp;
}
return kTie;
}
void BigInt::BigIntShortPrint(std::ostream& os) {
if (sign()) os << "-";
int len = length();
if (len == 0) {
os << "0";
return;
}
if (len > 1) os << "...";
os << digit(0);
}
// Internal helpers.
MaybeHandle<BigInt> MutableBigInt::AbsoluteAdd(Isolate* isolate,
Handle<BigInt> x,
Handle<BigInt> y,
bool result_sign) {
if (x->length() < y->length()) return AbsoluteAdd(isolate, y, x, result_sign);
if (x->is_zero()) {
DCHECK(y->is_zero());
return x;
}
if (y->is_zero()) {
return result_sign == x->sign() ? x : BigInt::UnaryMinus(isolate, x);
}
Handle<MutableBigInt> result;
if (!New(isolate, x->length() + 1).ToHandle(&result)) {
return MaybeHandle<BigInt>();
}
digit_t carry = 0;
int i = 0;
for (; i < y->length(); i++) {
digit_t new_carry = 0;
digit_t sum = digit_add(x->digit(i), y->digit(i), &new_carry);
sum = digit_add(sum, carry, &new_carry);
result->set_digit(i, sum);
carry = new_carry;
}
for (; i < x->length(); i++) {
digit_t new_carry = 0;
digit_t sum = digit_add(x->digit(i), carry, &new_carry);
result->set_digit(i, sum);
carry = new_carry;
}
result->set_digit(i, carry);
result->set_sign(result_sign);
return MakeImmutable(result);
}
Handle<BigInt> MutableBigInt::AbsoluteSub(Isolate* isolate, Handle<BigInt> x,
Handle<BigInt> y, bool result_sign) {
DCHECK(x->length() >= y->length());
SLOW_DCHECK(AbsoluteCompare(x, y) >= 0);
if (x->is_zero()) {
DCHECK(y->is_zero());
return x;
}
if (y->is_zero()) {
return result_sign == x->sign() ? x : BigInt::UnaryMinus(isolate, x);
}
Handle<MutableBigInt> result = New(isolate, x->length()).ToHandleChecked();
digit_t borrow = 0;
int i = 0;
for (; i < y->length(); i++) {
digit_t new_borrow = 0;
digit_t difference = digit_sub(x->digit(i), y->digit(i), &new_borrow);
difference = digit_sub(difference, borrow, &new_borrow);
result->set_digit(i, difference);
borrow = new_borrow;
}
for (; i < x->length(); i++) {
digit_t new_borrow = 0;
digit_t difference = digit_sub(x->digit(i), borrow, &new_borrow);
result->set_digit(i, difference);
borrow = new_borrow;
}
DCHECK_EQ(0, borrow);
result->set_sign(result_sign);
return MakeImmutable(result);
}
// Adds 1 to the absolute value of {x} and sets the result's sign to {sign}.
// {result_storage} is optional; if present, it will be used to store the
// result, otherwise a new BigInt will be allocated for the result.
// {result_storage} and {x} may refer to the same BigInt for in-place
// modification.
MaybeHandle<MutableBigInt> MutableBigInt::AbsoluteAddOne(
Isolate* isolate, Handle<BigIntBase> x, bool sign,
MutableBigInt result_storage) {
int input_length = x->length();
// The addition will overflow into a new digit if all existing digits are
// at maximum.
bool will_overflow = true;
for (int i = 0; i < input_length; i++) {
if (!digit_ismax(x->digit(i))) {
will_overflow = false;
break;
}
}
int result_length = input_length + will_overflow;
Handle<MutableBigInt> result(result_storage, isolate);
if (result_storage.is_null()) {
if (!New(isolate, result_length).ToHandle(&result)) {
return MaybeHandle<MutableBigInt>();
}
} else {
DCHECK(result->length() == result_length);
}
digit_t carry = 1;
for (int i = 0; i < input_length; i++) {
digit_t new_carry = 0;
result->set_digit(i, digit_add(x->digit(i), carry, &new_carry));
carry = new_carry;
}
if (result_length > input_length) {
result->set_digit(input_length, carry);
} else {
DCHECK_EQ(carry, 0);
}
result->set_sign(sign);
return result;
}
// Subtracts 1 from the absolute value of {x}. {x} must not be zero.
Handle<MutableBigInt> MutableBigInt::AbsoluteSubOne(Isolate* isolate,
Handle<BigIntBase> x) {
DCHECK(!x->is_zero());
// Requesting a result length identical to an existing BigInt's length
// cannot overflow the limit.
return AbsoluteSubOne(isolate, x, x->length()).ToHandleChecked();
}
// Like the above, but you can specify that the allocated result should have
// length {result_length}, which must be at least as large as {x->length()}.
MaybeHandle<MutableBigInt> MutableBigInt::AbsoluteSubOne(Isolate* isolate,
Handle<BigIntBase> x,
int result_length) {
DCHECK(!x->is_zero());
DCHECK(result_length >= x->length());
Handle<MutableBigInt> result;
if (!New(isolate, result_length).ToHandle(&result)) {
return MaybeHandle<MutableBigInt>();
}
int length = x->length();
digit_t borrow = 1;
for (int i = 0; i < length; i++) {
digit_t new_borrow = 0;
result->set_digit(i, digit_sub(x->digit(i), borrow, &new_borrow));
borrow = new_borrow;
}
DCHECK_EQ(borrow, 0);
for (int i = length; i < result_length; i++) {
result->set_digit(i, borrow);
}
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, {extra_digits} configures how
// remaining digits in the longer input (if {symmetric} == kSymmetric, in
// {x} otherwise) are handled: copied to the result or ignored.
// If {result_storage} is non-nullptr, it will be used for the result and
// any extra digits in it will be zeroed out, otherwise a new BigInt (with
// the same length as the longer input) will be allocated.
// {result_storage} may alias {x} or {y} for in-place modification.
// Example:
// y: [ y2 ][ y1 ][ y0 ]
// x: [ x3 ][ x2 ][ x1 ][ x0 ]
// | | | |
// (kCopy) (op) (op) (op)
// | | | |
// v v v v
// result_storage: [ 0 ][ x3 ][ r2 ][ r1 ][ r0 ]
inline Handle<MutableBigInt> 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) {
int x_length = x->length();
int y_length = y->length();
int num_pairs = y_length;
if (x_length < y_length) {
num_pairs = x_length;
if (symmetric == kSymmetric) {
std::swap(x, y);
std::swap(x_length, y_length);
}
}
DCHECK(num_pairs == Min(x_length, y_length));
Handle<MutableBigInt> result(result_storage, isolate);
int result_length = extra_digits == kCopy ? x_length : num_pairs;
if (result_storage.is_null()) {
result = New(isolate, result_length).ToHandleChecked();
} else {
DCHECK(result_storage->length() >= result_length);
result_length = result_storage->length();
}
int i = 0;
for (; i < num_pairs; i++) {
result->set_digit(i, op(x->digit(i), y->digit(i)));
}
if (extra_digits == kCopy) {
for (; i < x_length; i++) {
result->set_digit(i, x->digit(i));
}
}
for (; i < result_length; i++) {
result->set_digit(i, 0);
}
return result;
}
// If {result_storage} is non-nullptr, it will be used for the result,
// otherwise a new BigInt of appropriate length will be allocated.
// {result_storage} may alias {x} or {y} for in-place modification.
Handle<MutableBigInt> MutableBigInt::AbsoluteAnd(Isolate* isolate,
Handle<BigIntBase> x,
Handle<BigIntBase> y,
MutableBigInt result_storage) {
return AbsoluteBitwiseOp(isolate, x, y, result_storage, kSkip, kSymmetric,
[](digit_t a, digit_t b) { return a & b; });
}
// If {result_storage} is non-nullptr, it will be used for the result,
// otherwise a new BigInt of appropriate length will be allocated.
// {result_storage} may alias {x} or {y} for in-place modification.
Handle<MutableBigInt> MutableBigInt::AbsoluteAndNot(
Isolate* isolate, Handle<BigIntBase> x, Handle<BigIntBase> y,
MutableBigInt result_storage) {
return AbsoluteBitwiseOp(isolate, x, y, result_storage, kCopy, kNotSymmetric,
[](digit_t a, digit_t b) { return a & ~b; });
}
// If {result_storage} is non-nullptr, it will be used for the result,
// otherwise a new BigInt of appropriate length will be allocated.
// {result_storage} may alias {x} or {y} for in-place modification.
Handle<MutableBigInt> MutableBigInt::AbsoluteOr(Isolate* isolate,
Handle<BigIntBase> x,
Handle<BigIntBase> y,
MutableBigInt result_storage) {
return AbsoluteBitwiseOp(isolate, x, y, result_storage, kCopy, kSymmetric,
[](digit_t a, digit_t b) { return a | b; });
}
// If {result_storage} is non-nullptr, it will be used for the result,
// otherwise a new BigInt of appropriate length will be allocated.
// {result_storage} may alias {x} or {y} for in-place modification.
Handle<MutableBigInt> MutableBigInt::AbsoluteXor(Isolate* isolate,
Handle<BigIntBase> x,
Handle<BigIntBase> y,
MutableBigInt result_storage) {
return AbsoluteBitwiseOp(isolate, x, y, result_storage, kCopy, kSymmetric,
[](digit_t a, digit_t b) { return a ^ b; });
}
// Returns a positive value if abs(x) > abs(y), a negative value if
// abs(x) < abs(y), or zero if abs(x) == abs(y).
int MutableBigInt::AbsoluteCompare(Handle<BigIntBase> x, Handle<BigIntBase> y) {
int diff = x->length() - y->length();
if (diff != 0) return diff;
int i = x->length() - 1;
while (i >= 0 && x->digit(i) == y->digit(i)) i--;
if (i < 0) return 0;
return x->digit(i) > y->digit(i) ? 1 : -1;
}
// Multiplies {multiplicand} with {multiplier} and adds the result to
// {accumulator}, starting at {accumulator_index} for the least-significant
// digit.
// Callers must ensure that {accumulator} is big enough to hold the result.
void MutableBigInt::MultiplyAccumulate(Handle<BigIntBase> multiplicand,
digit_t multiplier,
Handle<MutableBigInt> accumulator,
int accumulator_index) {
// This is a minimum requirement; the DCHECK in the second loop below
// will enforce more as needed.
DCHECK(accumulator->length() > multiplicand->length() + accumulator_index);
if (multiplier == 0L) return;
digit_t carry = 0;
digit_t high = 0;
for (int i = 0; i < multiplicand->length(); i++, accumulator_index++) {
digit_t acc = accumulator->digit(accumulator_index);
digit_t new_carry = 0;
// Add last round's carryovers.
acc = digit_add(acc, high, &new_carry);
acc = digit_add(acc, carry, &new_carry);
// Compute this round's multiplication.
digit_t m_digit = multiplicand->digit(i);
digit_t low = digit_mul(multiplier, m_digit, &high);
acc = digit_add(acc, low, &new_carry);
// Store result and prepare for next round.
accumulator->set_digit(accumulator_index, acc);
carry = new_carry;
}
for (; carry != 0 || high != 0; accumulator_index++) {
DCHECK(accumulator_index < accumulator->length());
digit_t acc = accumulator->digit(accumulator_index);
digit_t new_carry = 0;
acc = digit_add(acc, high, &new_carry);
high = 0;
acc = digit_add(acc, carry, &new_carry);
accumulator->set_digit(accumulator_index, acc);
carry = new_carry;
}
}
// Multiplies {source} with {factor} and adds {summand} to the result.
// {result} and {source} may be the same BigInt for inplace modification.
void MutableBigInt::InternalMultiplyAdd(BigIntBase source, digit_t factor,
digit_t summand, int n,
MutableBigInt result) {
DCHECK(source->length() >= n);
DCHECK(result->length() >= n);
digit_t carry = summand;
digit_t high = 0;
for (int i = 0; i < n; i++) {
digit_t current = source->digit(i);
digit_t new_carry = 0;
// Compute this round's multiplication.
digit_t new_high = 0;
current = digit_mul(current, factor, &new_high);
// Add last round's carryovers.
current = digit_add(current, high, &new_carry);
current = digit_add(current, carry, &new_carry);
// Store result and prepare for next round.
result->set_digit(i, current);
carry = new_carry;
high = new_high;
}
if (result->length() > n) {
result->set_digit(n++, carry + high);
// Current callers don't pass in such large results, but let's be robust.
while (n < result->length()) {
result->set_digit(n++, 0);
}
} else {
CHECK_EQ(carry + high, 0);
}
}
// Multiplies {x} with {factor} and then adds {summand} to it.
void BigInt::InplaceMultiplyAdd(Handle<FreshlyAllocatedBigInt> x,
uintptr_t factor, uintptr_t summand) {
STATIC_ASSERT(sizeof(factor) == sizeof(digit_t));
STATIC_ASSERT(sizeof(summand) == sizeof(digit_t));
Handle<MutableBigInt> bigint = MutableBigInt::Cast(x);
MutableBigInt::InternalMultiplyAdd(*bigint, factor, summand, bigint->length(),
*bigint);
}
// Divides {x} by {divisor}, returning the result in {quotient} and {remainder}.
// Mathematically, the contract is:
// quotient = (x - remainder) / divisor, with 0 <= remainder < divisor.
// If {quotient} is an empty handle, an appropriately sized BigInt will be
// allocated for it; otherwise the caller must ensure that it is big enough.
// {quotient} can be the same as {x} for an in-place division. {quotient} can
// also be nullptr if the caller is only interested in the remainder.
void MutableBigInt::AbsoluteDivSmall(Isolate* isolate, Handle<BigIntBase> x,
digit_t divisor,
Handle<MutableBigInt>* quotient,
digit_t* remainder) {
DCHECK_NE(divisor, 0);
DCHECK(!x->is_zero()); // Callers check anyway, no need to handle this.
*remainder = 0;
int length = x->length();
if (quotient != nullptr) {
if ((*quotient).is_null()) {
*quotient = New(isolate, length).ToHandleChecked();
}
for (int i = length - 1; i >= 0; i--) {
digit_t q = digit_div(*remainder, x->digit(i), divisor, remainder);
(*quotient)->set_digit(i, q);
}
} else {
for (int i = length - 1; i >= 0; i--) {
digit_div(*remainder, x->digit(i), divisor, remainder);
}
}
}
// Divides {dividend} by {divisor}, returning the result in {quotient} and
// {remainder}. Mathematically, the contract is:
// quotient = (dividend - remainder) / divisor, with 0 <= remainder < divisor.
// Both {quotient} and {remainder} are optional, for callers that are only
// interested in one of them.
// See Knuth, Volume 2, section 4.3.1, Algorithm D.
bool MutableBigInt::AbsoluteDivLarge(Isolate* isolate,
Handle<BigIntBase> dividend,
Handle<BigIntBase> divisor,
Handle<MutableBigInt>* quotient,
Handle<MutableBigInt>* remainder) {
DCHECK_GE(divisor->length(), 2);
DCHECK(dividend->length() >= divisor->length());
// 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.
int n = divisor->length();
int m = dividend->length() - n;
// The quotient to be computed.
Handle<MutableBigInt> q;
if (quotient != nullptr) q = New(isolate, m + 1).ToHandleChecked();
// In each iteration, {qhatv} holds {divisor} * {current quotient digit}.
// "v" is the book's name for {divisor}, "qhat" the current quotient digit.
Handle<MutableBigInt> qhatv;
if (!New(isolate, n + 1).ToHandle(&qhatv)) return false;
// 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).
int shift = base::bits::CountLeadingZeros(divisor->digit(n - 1));
if (shift > 0) {
divisor = SpecialLeftShift(isolate, divisor, shift, kSameSizeResult)
.ToHandleChecked();
}
// Holds the (continuously updated) remaining part of the dividend, which
// eventually becomes the remainder.
Handle<MutableBigInt> u;
if (!SpecialLeftShift(isolate, dividend, shift, kAlwaysAddOneDigit)
.ToHandle(&u)) {
return false;
}
// D2.
// Iterate over the dividend's digit (like the "grad school" algorithm).
// {vn1} is the divisor's most significant digit.
digit_t 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_t qhat = std::numeric_limits<digit_t>::max();
// {ujn} is the dividend's most significant remaining digit.
digit_t ujn = u->digit(j + n);
if (ujn != vn1) {
// {rhat} is the current iteration's remainder.
digit_t 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 = digit_div(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 << kDigitBits) + u_{j+n-2}.
digit_t vn2 = divisor->digit(n - 2);
digit_t ujn2 = u->digit(j + n - 2);
while (ProductGreaterThan(qhat, vn2, rhat, ujn2)) {
qhat--;
digit_t prev_rhat = rhat;
rhat += vn1;
// v[n-1] >= 0, so this tests for overflow.
if (rhat < prev_rhat) break;
}
}
// D4.
// Multiply the divisor with the current quotient digit, and subtract
// it from the dividend. If there was "borrow", then the quotient digit
// was one too high, so we must correct it and undo one subtraction of
// the (shifted) divisor.
InternalMultiplyAdd(*divisor, qhat, 0, n, *qhatv);
digit_t c = u->InplaceSub(qhatv, j);
if (c != 0) {
c = u->InplaceAdd(divisor, j);
u->set_digit(j + n, u->digit(j + n) + c);
qhat--;
}
if (quotient != nullptr) q->set_digit(j, qhat);
}
if (quotient != nullptr) {
*quotient = q; // Caller will right-trim.
}
if (remainder != nullptr) {
u->InplaceRightShift(shift);
*remainder = u;
}
return true;
}
// Returns whether (factor1 * factor2) > (high << kDigitBits) + low.
bool MutableBigInt::ProductGreaterThan(digit_t factor1, digit_t factor2,
digit_t high, digit_t low) {
digit_t result_high;
digit_t result_low = digit_mul(factor1, factor2, &result_high);
return result_high > high || (result_high == high && result_low > low);
}
// Adds {summand} onto {this}, starting with {summand}'s 0th digit
// at {this}'s {start_index}'th digit. Returns the "carry" (0 or 1).
BigInt::digit_t MutableBigInt::InplaceAdd(Handle<BigIntBase> summand,
int start_index) {
digit_t carry = 0;
int n = summand->length();
DCHECK(length() >= start_index + n);
for (int i = 0; i < n; i++) {
digit_t new_carry = 0;
digit_t sum =
digit_add(digit(start_index + i), summand->digit(i), &new_carry);
sum = digit_add(sum, carry, &new_carry);
set_digit(start_index + i, sum);
carry = new_carry;
}
return carry;
}
// Subtracts {subtrahend} from {this}, starting with {subtrahend}'s 0th digit
// at {this}'s {start_index}-th digit. Returns the "borrow" (0 or 1).
BigInt::digit_t MutableBigInt::InplaceSub(Handle<BigIntBase> subtrahend,
int start_index) {
digit_t borrow = 0;
int n = subtrahend->length();
DCHECK(length() >= start_index + n);
for (int i = 0; i < n; i++) {
digit_t new_borrow = 0;
digit_t difference =
digit_sub(digit(start_index + i), subtrahend->digit(i), &new_borrow);
difference = digit_sub(difference, borrow, &new_borrow);
set_digit(start_index + i, difference);
borrow = new_borrow;
}
return borrow;
}
void MutableBigInt::InplaceRightShift(int shift) {
DCHECK_GE(shift, 0);
DCHECK_LT(shift, kDigitBits);
DCHECK_GT(length(), 0);
DCHECK_EQ(digit(0) & ((static_cast<digit_t>(1) << shift) - 1), 0);
if (shift == 0) return;
digit_t carry = digit(0) >> shift;
int last = length() - 1;
for (int i = 0; i < last; i++) {
digit_t d = digit(i + 1);
set_digit(i, (d << (kDigitBits - shift)) | carry);
carry = d >> shift;
}
set_digit(last, carry);
}
// Always copies the input, even when {shift} == 0.
// {shift} must be less than kDigitBits, {x} must be non-zero.
MaybeHandle<MutableBigInt> MutableBigInt::SpecialLeftShift(
Isolate* isolate, Handle<BigIntBase> x, int shift,
SpecialLeftShiftMode mode) {
DCHECK_GE(shift, 0);
DCHECK_LT(shift, kDigitBits);
DCHECK_GT(x->length(), 0);
int n = x->length();
int result_length = mode == kAlwaysAddOneDigit ? n + 1 : n;
Handle<MutableBigInt> result;
if (!New(isolate, result_length).ToHandle(&result)) {
return MaybeHandle<MutableBigInt>();
}
if (shift == 0) {
for (int i = 0; i < n; i++) result->set_digit(i, x->digit(i));
if (mode == kAlwaysAddOneDigit) result->set_digit(n, 0);
return result;
}
DCHECK_GT(shift, 0);
digit_t carry = 0;
for (int i = 0; i < n; i++) {
digit_t d = x->digit(i);
result->set_digit(i, (d << shift) | carry);
carry = d >> (kDigitBits - shift);
}
if (mode == kAlwaysAddOneDigit) {
result->set_digit(n, carry);
} else {
DCHECK_EQ(mode, kSameSizeResult);
DCHECK_EQ(carry, 0);
}
return result;
}
MaybeHandle<BigInt> MutableBigInt::LeftShiftByAbsolute(Isolate* isolate,
Handle<BigIntBase> x,
Handle<BigIntBase> y) {
Maybe<digit_t> maybe_shift = ToShiftAmount(y);
if (maybe_shift.IsNothing()) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig),
BigInt);
}
digit_t shift = maybe_shift.FromJust();
int digit_shift = static_cast<int>(shift / kDigitBits);
int bits_shift = static_cast<int>(shift % kDigitBits);
int length = x->length();
bool grow = bits_shift != 0 &&
(x->digit(length - 1) >> (kDigitBits - bits_shift)) != 0;
int result_length = length + digit_shift + grow;
if (result_length > kMaxLength) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig),
BigInt);
}
Handle<MutableBigInt> result;
if (!New(isolate, result_length).ToHandle(&result)) {
return MaybeHandle<BigInt>();
}
if (bits_shift == 0) {
int i = 0;
for (; i < digit_shift; i++) result->set_digit(i, 0ul);
for (; i < result_length; i++) {
result->set_digit(i, x->digit(i - digit_shift));
}
} else {
digit_t carry = 0;
for (int i = 0; i < digit_shift; i++) result->set_digit(i, 0ul);
for (int i = 0; i < length; i++) {
digit_t d = x->digit(i);
result->set_digit(i + digit_shift, (d << bits_shift) | carry);
carry = d >> (kDigitBits - bits_shift);
}
if (grow) {
result->set_digit(length + digit_shift, carry);
} else {
DCHECK_EQ(carry, 0);
}
}
result->set_sign(x->sign());
return MakeImmutable(result);
}
Handle<BigInt> MutableBigInt::RightShiftByAbsolute(Isolate* isolate,
Handle<BigIntBase> x,
Handle<BigIntBase> y) {
int length = x->length();
bool sign = x->sign();
Maybe<digit_t> maybe_shift = ToShiftAmount(y);
if (maybe_shift.IsNothing()) {
return RightShiftByMaximum(isolate, sign);
}
digit_t shift = maybe_shift.FromJust();
int digit_shift = static_cast<int>(shift / kDigitBits);
int bits_shift = static_cast<int>(shift % kDigitBits);
int result_length = length - digit_shift;
if (result_length <= 0) {
return RightShiftByMaximum(isolate, 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 must_round_down = false;
if (sign) {
const digit_t mask = (static_cast<digit_t>(1) << bits_shift) - 1;
if ((x->digit(digit_shift) & mask) != 0) {
must_round_down = true;
} else {
for (int i = 0; i < digit_shift; i++) {
if (x->digit(i) != 0) {
must_round_down = true;
break;
}
}
}
}
// If bits_shift is non-zero, it frees up bits, preventing overflow.
if (must_round_down && bits_shift == 0) {
// Overflow cannot happen if the most significant digit has unset bits.
digit_t msd = x->digit(length - 1);
bool rounding_can_overflow = digit_ismax(msd);
if (rounding_can_overflow) result_length++;
}
DCHECK_LE(result_length, length);
Handle<MutableBigInt> result = New(isolate, result_length).ToHandleChecked();
if (bits_shift == 0) {
for (int i = digit_shift; i < length; i++) {
result->set_digit(i - digit_shift, x->digit(i));
}
} else {
digit_t carry = x->digit(digit_shift) >> bits_shift;
int last = length - digit_shift - 1;
for (int i = 0; i < last; i++) {
digit_t d = x->digit(i + digit_shift + 1);
result->set_digit(i, (d << (kDigitBits - bits_shift)) | carry);
carry = d >> bits_shift;
}
result->set_digit(last, carry);
}
if (sign) {
result->set_sign(true);
if (must_round_down) {
// Since the result is negative, rounding down means adding one to
// its absolute value. This cannot overflow.
result = AbsoluteAddOne(isolate, result, true, *result).ToHandleChecked();
}
}
return MakeImmutable(result);
}
Handle<BigInt> MutableBigInt::RightShiftByMaximum(Isolate* isolate, bool sign) {
if (sign) {
// TODO(jkummerow): Consider caching a canonical -1n BigInt.
return NewFromInt(isolate, -1);
} else {
return Zero(isolate);
}
}
// Returns the value of {x} if it is less than the maximum bit length of
// a BigInt, or Nothing otherwise.
Maybe<BigInt::digit_t> MutableBigInt::ToShiftAmount(Handle<BigIntBase> x) {
if (x->length() > 1) return Nothing<digit_t>();
digit_t value = x->digit(0);
STATIC_ASSERT(kMaxLengthBits < std::numeric_limits<digit_t>::max());
if (value > kMaxLengthBits) return Nothing<digit_t>();
return Just(value);
}
// 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 kMaxBitsPerChar[] = {
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 const int kBitsPerCharTableShift = 5;
static const size_t kBitsPerCharTableMultiplier = 1u << kBitsPerCharTableShift;
MaybeHandle<FreshlyAllocatedBigInt> BigInt::AllocateFor(
Isolate* isolate, int radix, int charcount, ShouldThrow should_throw,
PretenureFlag pretenure) {
DCHECK(2 <= radix && radix <= 36);
DCHECK_GE(charcount, 0);
size_t bits_per_char = kMaxBitsPerChar[radix];
size_t chars = static_cast<size_t>(charcount);
const int roundup = kBitsPerCharTableMultiplier - 1;
if (chars <= (std::numeric_limits<size_t>::max() - roundup) / bits_per_char) {
size_t bits_min = bits_per_char * chars;
// Divide by 32 (see table), rounding up.
bits_min = (bits_min + roundup) >> kBitsPerCharTableShift;
if (bits_min <= static_cast<size_t>(kMaxInt)) {
// Divide by kDigitsBits, rounding up.
int length = (static_cast<int>(bits_min) + kDigitBits - 1) / kDigitBits;
if (length <= kMaxLength) {
Handle<MutableBigInt> result =
MutableBigInt::New(isolate, length, pretenure).ToHandleChecked();
result->InitializeDigits(length);
return result;
}
}
}
// All the overflow/maximum checks above fall through to here.
if (should_throw == kThrowOnError) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig),
FreshlyAllocatedBigInt);
} else {
return MaybeHandle<FreshlyAllocatedBigInt>();
}
}
Handle<BigInt> BigInt::Finalize(Handle<FreshlyAllocatedBigInt> x, bool sign) {
Handle<MutableBigInt> bigint = MutableBigInt::Cast(x);
bigint->set_sign(sign);
return MutableBigInt::MakeImmutable(bigint);
}
// The serialization format MUST NOT CHANGE without updating the format
// version in value-serializer.cc!
uint32_t BigInt::GetBitfieldForSerialization() const {
// In order to make the serialization format the same on 32/64 bit builds,
// we convert the length-in-digits to length-in-bytes for serialization.
// Being able to do this depends on having enough LengthBits:
STATIC_ASSERT(kMaxLength * kDigitSize <= LengthBits::kMax);
int bytelength = length() * kDigitSize;
return SignBits::encode(sign()) | LengthBits::encode(bytelength);
}
int BigInt::DigitsByteLengthForBitfield(uint32_t bitfield) {
return LengthBits::decode(bitfield);
}
// The serialization format MUST NOT CHANGE without updating the format
// version in value-serializer.cc!
void BigInt::SerializeDigits(uint8_t* storage) {
void* digits =
reinterpret_cast<void*>(ptr() + kDigitsOffset - kHeapObjectTag);
#if defined(V8_TARGET_LITTLE_ENDIAN)
int bytelength = length() * kDigitSize;
memcpy(storage, digits, bytelength);
#elif defined(V8_TARGET_BIG_ENDIAN)
digit_t* digit_storage = reinterpret_cast<digit_t*>(storage);
const digit_t* digit = reinterpret_cast<const digit_t*>(digits);
for (int i = 0; i < length(); i++) {
*digit_storage = ByteReverse(*digit);
digit_storage++;
digit++;
}
#endif // V8_TARGET_BIG_ENDIAN
}
// The serialization format MUST NOT CHANGE without updating the format
// version in value-serializer.cc!
MaybeHandle<BigInt> BigInt::FromSerializedDigits(
Isolate* isolate, uint32_t bitfield, Vector<const uint8_t> digits_storage,
PretenureFlag pretenure) {
int bytelength = LengthBits::decode(bitfield);
DCHECK(digits_storage.length() == bytelength);
bool sign = SignBits::decode(bitfield);
int length = (bytelength + kDigitSize - 1) / kDigitSize; // Round up.
Handle<MutableBigInt> result =
MutableBigInt::Cast(isolate->factory()->NewBigInt(length, pretenure));
result->initialize_bitfield(sign, length);
void* digits =
reinterpret_cast<void*>(result->ptr() + kDigitsOffset - kHeapObjectTag);
#if defined(V8_TARGET_LITTLE_ENDIAN)
memcpy(digits, digits_storage.start(), bytelength);
void* padding_start =
reinterpret_cast<void*>(reinterpret_cast<Address>(digits) + bytelength);
memset(padding_start, 0, length * kDigitSize - bytelength);
#elif defined(V8_TARGET_BIG_ENDIAN)
digit_t* digit = reinterpret_cast<digit_t*>(digits);
const digit_t* digit_storage =
reinterpret_cast<const digit_t*>(digits_storage.start());
for (int i = 0; i < bytelength / kDigitSize; i++) {
*digit = ByteReverse(*digit_storage);
digit_storage++;
digit++;
}
if (bytelength % kDigitSize) {
*digit = 0;
byte* digit_byte = reinterpret_cast<byte*>(digit);
digit_byte += sizeof(*digit) - 1;
const byte* digit_storage_byte =
reinterpret_cast<const byte*>(digit_storage);
for (int i = 0; i < bytelength % kDigitSize; i++) {
*digit_byte = *digit_storage_byte;
digit_byte--;
digit_storage_byte++;
}
}
#endif // V8_TARGET_BIG_ENDIAN
return MutableBigInt::MakeImmutable(result);
}
static const char kConversionChars[] = "0123456789abcdefghijklmnopqrstuvwxyz";
MaybeHandle<String> MutableBigInt::ToStringBasePowerOfTwo(
Isolate* isolate, Handle<BigIntBase> x, int radix,
ShouldThrow should_throw) {
STATIC_ASSERT(base::bits::IsPowerOfTwo(kDigitBits));
DCHECK(base::bits::IsPowerOfTwo(radix));
DCHECK(radix >= 2 && radix <= 32);
DCHECK(!x->is_zero());
const int length = x->length();
const bool sign = x->sign();
const int bits_per_char = base::bits::CountTrailingZeros(radix);
const int char_mask = 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_t msd = x->digit(length - 1);
const int msd_leading_zeros = base::bits::CountLeadingZeros(msd);
const size_t bit_length = length * kDigitBits - msd_leading_zeros;
const size_t chars_required =
(bit_length + bits_per_char - 1) / bits_per_char + sign;
if (chars_required > String::kMaxLength) {
if (should_throw == kThrowOnError) {
THROW_NEW_ERROR(isolate, NewInvalidStringLengthError(), String);
} else {
return MaybeHandle<String>();
}
}
Handle<SeqOneByteString> result =
isolate->factory()
->NewRawOneByteString(static_cast<int>(chars_required))
.ToHandleChecked();
DisallowHeapAllocation no_gc;
uint8_t* buffer = result->GetChars(no_gc);
// Print the number into the string, starting from the last position.
int pos = static_cast<int>(chars_required - 1);
digit_t digit = 0;
// Keeps track of how many unprocessed bits there are in {digit}.
int available_bits = 0;
for (int i = 0; i < length - 1; i++) {
digit_t new_digit = x->digit(i);
// Take any leftover bits from the last iteration into account.
int current = (digit | (new_digit << available_bits)) & char_mask;
buffer[pos--] = kConversionChars[current];
int consumed_bits = bits_per_char - available_bits;
digit = new_digit >> consumed_bits;
available_bits = kDigitBits - consumed_bits;
while (available_bits >= bits_per_char) {
buffer[pos--] = kConversionChars[digit & char_mask];
digit >>= bits_per_char;
available_bits -= bits_per_char;
}
}
// Take any leftover bits from the last iteration into account.
int current = (digit | (msd << available_bits)) & char_mask;
buffer[pos--] = kConversionChars[current];
digit = msd >> (bits_per_char - available_bits);
while (digit != 0) {
buffer[pos--] = kConversionChars[digit & char_mask];
digit >>= bits_per_char;
}
if (sign) buffer[pos--] = '-';
DCHECK_EQ(pos, -1);
return result;
}
MaybeHandle<String> MutableBigInt::ToStringGeneric(Isolate* isolate,
Handle<BigIntBase> x,
int radix,
ShouldThrow should_throw) {
DCHECK(radix >= 2 && radix <= 36);
DCHECK(!x->is_zero());
Heap* heap = isolate->heap();
const int length = x->length();
const bool sign = x->sign();
// Compute (an overapproximation of) the length of the resulting string:
// Divide bit length of the BigInt by bits representable per character.
const size_t bit_length =
length * kDigitBits - base::bits::CountLeadingZeros(x->digit(length - 1));
// Maximum number of bits we can represent with one character. We'll use this
// to find an appropriate chunk size below.
const uint8_t max_bits_per_char = kMaxBitsPerChar[radix];
// For estimating result length, we have to be pessimistic and work with
// the minimum number of bits one character can represent.
const uint8_t min_bits_per_char = max_bits_per_char - 1;
// Perform the following computation with uint64_t to avoid overflows.
uint64_t chars_required = bit_length;
chars_required *= kBitsPerCharTableMultiplier;
chars_required += min_bits_per_char - 1; // Round up.
chars_required /= min_bits_per_char;
chars_required += sign;
if (chars_required > String::kMaxLength) {
if (should_throw == kThrowOnError) {
THROW_NEW_ERROR(isolate, NewInvalidStringLengthError(), String);
} else {
return MaybeHandle<String>();
}
}
Handle<SeqOneByteString> result =
isolate->factory()
->NewRawOneByteString(static_cast<int>(chars_required))
.ToHandleChecked();
#if DEBUG
// Zap the string first.
{
DisallowHeapAllocation no_gc;
uint8_t* chars = result->GetChars(no_gc);
for (int i = 0; i < static_cast<int>(chars_required); i++) chars[i] = '?';
}
#endif
// We assemble the result string in reverse order, and then reverse it.
// TODO(jkummerow): Consider building the string from the right, and
// left-shifting it if the length estimate was too large.
int pos = 0;
digit_t last_digit;
if (length == 1) {
last_digit = x->digit(0);
} else {
int chunk_chars =
kDigitBits * kBitsPerCharTableMultiplier / max_bits_per_char;
digit_t chunk_divisor = digit_pow(radix, chunk_chars);
// By construction of chunk_chars, there can't have been overflow.
DCHECK_NE(chunk_divisor, 0);
int nonzero_digit = length - 1;
DCHECK_NE(x->digit(nonzero_digit), 0);
// {rest} holds the part of the BigInt that we haven't looked at yet.
// Not to be confused with "remainder"!
Handle<MutableBigInt> rest;
// In the first round, divide the input, allocating a new BigInt for
// the result == rest; from then on divide the rest in-place.
Handle<BigIntBase>* dividend = &x;
do {
digit_t chunk;
AbsoluteDivSmall(isolate, *dividend, chunk_divisor, &rest, &chunk);
DCHECK(!rest.is_null());
dividend = reinterpret_cast<Handle<BigIntBase>*>(&rest);
DisallowHeapAllocation no_gc;
uint8_t* chars = result->GetChars(no_gc);
for (int i = 0; i < chunk_chars; i++) {
chars[pos++] = kConversionChars[chunk % radix];
chunk /= radix;
}
DCHECK_EQ(chunk, 0);
if (rest->digit(nonzero_digit) == 0) nonzero_digit--;
// We can never clear more than one digit per iteration, because
// chunk_divisor is smaller than max digit value.
DCHECK_GT(rest->digit(nonzero_digit), 0);
} while (nonzero_digit > 0);
last_digit = rest->digit(0);
}
DisallowHeapAllocation no_gc;
uint8_t* chars = result->GetChars(no_gc);
do {
chars[pos++] = kConversionChars[last_digit % radix];
last_digit /= radix;
} while (last_digit > 0);
DCHECK_GE(pos, 1);
DCHECK(pos <= static_cast<int>(chars_required));
// Remove leading zeroes.
while (pos > 1 && chars[pos - 1] == '0') pos--;
if (sign) chars[pos++] = '-';
// Trim any over-allocation (which can happen due to conservative estimates).
if (pos < static_cast<int>(chars_required)) {
result->synchronized_set_length(pos);
int string_size =
SeqOneByteString::SizeFor(static_cast<int>(chars_required));
int needed_size = SeqOneByteString::SizeFor(pos);
if (needed_size < string_size) {
Address new_end = result->address() + needed_size;
heap->CreateFillerObjectAt(new_end, (string_size - needed_size),
ClearRecordedSlots::kNo);
}
}
// Reverse the string.
for (int i = 0, j = pos - 1; i < j; i++, j--) {
uint8_t tmp = chars[i];
chars[i] = chars[j];
chars[j] = tmp;
}
#if DEBUG
// Verify that all characters have been written.
DCHECK(result->length() == pos);
for (int i = 0; i < pos; i++) DCHECK_NE(chars[i], '?');
#endif
return result;
}
Handle<BigInt> BigInt::AsIntN(Isolate* isolate, uint64_t n, Handle<BigInt> x) {
if (x->is_zero()) return x;
if (n == 0) return MutableBigInt::Zero(isolate);
uint64_t needed_length = (n + kDigitBits - 1) / kDigitBits;
uint64_t x_length = static_cast<uint64_t>(x->length());
// If {x} has less than {n} bits, return it directly.
if (x_length < needed_length) return x;
DCHECK_LE(needed_length, kMaxInt);
digit_t top_digit = x->digit(static_cast<int>(needed_length) - 1);
digit_t compare_digit = static_cast<digit_t>(1) << ((n - 1) % kDigitBits);
if (x_length == needed_length && top_digit < compare_digit) return x;
// Otherwise we have to truncate (which is a no-op in the special case
// of x == -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 x->sign() xor "(n-1)th bit present".
// The only exception is when x 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 has_bit = (top_digit & compare_digit) == compare_digit;
DCHECK_LE(n, kMaxInt);
int N = static_cast<int>(n);
if (!has_bit) {
return MutableBigInt::TruncateToNBits(isolate, N, x);
}
if (!x->sign()) {
return MutableBigInt::TruncateAndSubFromPowerOfTwo(isolate, N, x, true);
}
// Negative numbers must subtract from 2^n, except for the special case
// described above.
if ((top_digit & (compare_digit - 1)) == 0) {
for (int i = static_cast<int>(needed_length) - 2; i >= 0; i--) {
if (x->digit(i) != 0) {
return MutableBigInt::TruncateAndSubFromPowerOfTwo(isolate, N, x,
false);
}
}
// Truncation is no-op if x == -2^(n-1).
if (x_length == needed_length && top_digit == compare_digit) return x;
return MutableBigInt::TruncateToNBits(isolate, N, x);
}
return MutableBigInt::TruncateAndSubFromPowerOfTwo(isolate, N, x, false);
}
MaybeHandle<BigInt> BigInt::AsUintN(Isolate* isolate, uint64_t n,
Handle<BigInt> x) {
if (x->is_zero()) return x;
if (n == 0) return MutableBigInt::Zero(isolate);
// If {x} is negative, simulate two's complement representation.
if (x->sign()) {
if (n > kMaxLengthBits) {
THROW_NEW_ERROR(isolate, NewRangeError(MessageTemplate::kBigIntTooBig),
BigInt);
}
return MutableBigInt::TruncateAndSubFromPowerOfTwo(
isolate, static_cast<int>(n), x, false);
}
// If {x} is positive and has up to {n} bits, return it directly.
if (n >= kMaxLengthBits) return x;
STATIC_ASSERT(kMaxLengthBits < kMaxInt - kDigitBits);
int needed_length = static_cast<int>((n + kDigitBits - 1) / kDigitBits);
if (x->length() < needed_length) return x;
int bits_in_top_digit = n % kDigitBits;
if (bits_in_top_digit == 0) {
if (x->length() == needed_length) return x;
} else {
digit_t top_digit = x->digit(needed_length - 1);
if ((top_digit >> bits_in_top_digit) == 0) return x;
}
// Otherwise, truncate.
DCHECK_LE(n, kMaxInt);
return MutableBigInt::TruncateToNBits(isolate, static_cast<int>(n), x);
}
Handle<BigInt> MutableBigInt::TruncateToNBits(Isolate* isolate, int n,
Handle<BigInt> x) {
// Only call this when there's something to do.
DCHECK_NE(n, 0);
DCHECK_GT(x->length(), n / kDigitBits);
int needed_digits = (n + (kDigitBits - 1)) / kDigitBits;
DCHECK_LE(needed_digits, x->length());
Handle<MutableBigInt> result = New(isolate, needed_digits).ToHandleChecked();
// Copy all digits except the MSD.
int last = needed_digits - 1;
for (int i = 0; i < last; i++) {
result->set_digit(i, x->digit(i));
}
// The MSD might contain extra bits that we don't want.
digit_t msd = x->digit(last);
if (n % kDigitBits != 0) {
int drop = kDigitBits - (n % kDigitBits);
msd = (msd << drop) >> drop;
}
result->set_digit(last, msd);
result->set_sign(x->sign());
return MakeImmutable(result);
}
// Subtracts the least significant n bits of abs(x) from 2^n.
Handle<BigInt> MutableBigInt::TruncateAndSubFromPowerOfTwo(Isolate* isolate,
int n,
Handle<BigInt> x,
bool result_sign) {
DCHECK_NE(n, 0);
DCHECK_LE(n, kMaxLengthBits);
int needed_digits = (n + (kDigitBits - 1)) / kDigitBits;
DCHECK_LE(needed_digits, kMaxLength); // Follows from n <= kMaxLengthBits.
Handle<MutableBigInt> result = New(isolate, needed_digits).ToHandleChecked();
// Process all digits except the MSD.
int i = 0;
int last = needed_digits - 1;
int x_length = x->length();
digit_t borrow = 0;
// Take digits from {x} unless its length is exhausted.
int limit = Min(last, x_length);
for (; i < limit; i++) {
digit_t new_borrow = 0;
digit_t difference = digit_sub(0, x->digit(i), &new_borrow);
difference = digit_sub(difference, borrow, &new_borrow);
result->set_digit(i, difference);
borrow = new_borrow;
}
// Then simulate leading zeroes in {x} as needed.
for (; i < last; i++) {
digit_t new_borrow = 0;
digit_t difference = digit_sub(0, borrow, &new_borrow);
result->set_digit(i, difference);
borrow = new_borrow;
}
// The MSD might contain extra bits that we don't want.
digit_t msd = last < x_length ? x->digit(last) : 0;
int msd_bits_consumed = n % kDigitBits;
digit_t result_msd;
if (msd_bits_consumed == 0) {
digit_t new_borrow = 0;
result_msd = digit_sub(0, msd, &new_borrow);
result_msd = digit_sub(result_msd, borrow, &new_borrow);
} else {
int drop = kDigitBits - msd_bits_consumed;
msd = (msd << drop) >> drop;
digit_t minuend_msd = static_cast<digit_t>(1) << (kDigitBits - drop);
digit_t new_borrow = 0;