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Diffstat (limited to 'js/src/vm/BigIntType.cpp')
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diff --git a/js/src/vm/BigIntType.cpp b/js/src/vm/BigIntType.cpp new file mode 100644 index 0000000000..8382c641fa --- /dev/null +++ b/js/src/vm/BigIntType.cpp @@ -0,0 +1,3260 @@ +/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- + * This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ + +/* + * Portions of this code taken from WebKit, whose copyright is as follows: + * + * Copyright (C) 2017 Caio Lima <ticaiolima@gmail.com> + * Copyright (C) 2017-2018 Apple Inc. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY + * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR + * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY + * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + * + * Portions of this code taken from V8, whose copyright notice is as follows: + * + * Copyright 2017 the V8 project authors. All rights reserved. + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are + * met: + * * Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above + * copyright notice, this list of conditions and the following + * disclaimer in the documentation and/or other materials provided + * with the distribution. + * * Neither the name of Google Inc. nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR + * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT + * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT + * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + * + * Portions of this code taken from Dart, whose copyright notice is as follows: + * + * 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 + * + * Portions of this code taken from Go, whose copyright notice is as follows: + * + * 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 "vm/BigIntType.h" + +#include "mozilla/Casting.h" +#include "mozilla/FloatingPoint.h" +#include "mozilla/HashFunctions.h" +#include "mozilla/MathAlgorithms.h" +#include "mozilla/Maybe.h" +#include "mozilla/Range.h" +#include "mozilla/RangedPtr.h" +#include "mozilla/WrappingOperations.h" + +#include <functional> +#include <limits> +#include <math.h> +#include <memory> + +#include "jsapi.h" +#include "jsnum.h" +#include "jscntxt.h" + +#include "builtin/BigInt.h" +#include "gc/Allocator.h" +#include "js/Initialization.h" +#include "js/Utility.h" +#include "vm/SelfHosting.h" + +#include "vm/String.h" + +using namespace js; + +using mozilla::Abs; +using mozilla::AssertedCast; +using mozilla::BitwiseCast; +using mozilla::IsFinite; +using mozilla::Maybe; +using mozilla::NegativeInfinity; +using mozilla::Nothing; +using mozilla::PositiveInfinity; +using mozilla::Range; +using mozilla::RangedPtr; +using mozilla::Some; +using mozilla::WrapToSigned; + +static inline unsigned DigitLeadingZeroes(BigInt::Digit x) { + return sizeof(x) == 4 ? mozilla::CountLeadingZeroes32(x) + : mozilla::CountLeadingZeroes64(x); +} + +BigInt* BigInt::createUninitialized(ExclusiveContext* cx, size_t length, + bool isNegative) { + if (length > MaxDigitLength) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_TOO_LARGE); + } + return nullptr; + } + + UniquePtr<Digit[], JS::FreePolicy> heapDigits; + if (length > InlineDigitsLength) { + heapDigits = cx->make_pod_array<Digit>(length); + if (!heapDigits) { + return nullptr; + } + } else { + heapDigits = nullptr; + } + + BigInt* x = Allocate<BigInt>(cx); + if (!x) { + return nullptr; + } + + x->lengthSignAndReservedBits_ = + (length << LengthShift) | (isNegative ? SignBit : 0); + MOZ_ASSERT(x->digitLength() == length); + MOZ_ASSERT(x->isNegative() == isNegative); + + if (heapDigits) { + x->heapDigits_ = heapDigits.release(); + } + + return x; +} + +void BigInt::initializeDigitsToZero() { + auto digs = digits(); + std::uninitialized_fill_n(digs.begin(), digs.Length(), 0); +} + +void BigInt::finalize(js::FreeOp* fop) { + if (hasHeapDigits()) { + fop->free_(heapDigits_); + } +} + +js::HashNumber BigInt::hash() { + js::HashNumber h = + mozilla::HashBytes(digits().data(), digitLength() * sizeof(Digit)); + return mozilla::AddToHash(h, isNegative()); +} + +size_t BigInt::sizeOfExcludingThis(mozilla::MallocSizeOf mallocSizeOf) const { + return hasInlineDigits() ? 0 : mallocSizeOf(heapDigits_); +} + +BigInt* BigInt::zero(ExclusiveContext* cx) { + return createUninitialized(cx, 0, false); +} + +BigInt* BigInt::one(ExclusiveContext* cx) { + BigInt* ret = createUninitialized(cx, 1, false); + + if (!ret) { + return nullptr; + } + + ret->setDigit(0, 1); + + return ret; +} + +BigInt* BigInt::neg(ExclusiveContext* cx, HandleBigInt x) { + if (x->isZero()) { + return x; + } + + BigInt* result = copy(cx, x); + if (!result) { + return nullptr; + } + result->lengthSignAndReservedBits_ ^= SignBit; + return result; +} + +#if !defined(JS_64BIT) +#define HAVE_TWO_DIGIT 1 +using TwoDigit = uint64_t; +#elif defined(HAVE_INT128_SUPPORT) +#define HAVE_TWO_DIGIT 1 +using TwoDigit = __uint128_t; +#endif + +inline BigInt::Digit BigInt::digitMul(Digit a, Digit b, Digit* high) { +#if defined(HAVE_TWO_DIGIT) + TwoDigit result = static_cast<TwoDigit>(a) * static_cast<TwoDigit>(b); + *high = result >> DigitBits; + + return static_cast<Digit>(result); +#else + // Multiply in half-pointer-sized chunks. + // For inputs [AH AL]*[BH BL], the result is: + // + // [AL*BL] // rLow + // + [AL*BH] // rMid1 + // + [AH*BL] // rMid2 + // + [AH*BH] // rHigh + // = [R4 R3 R2 R1] // high = [R4 R3], low = [R2 R1] + // + // Where of course we must be careful with carries between the columns. + Digit aLow = a & HalfDigitMask; + Digit aHigh = a >> HalfDigitBits; + Digit bLow = b & HalfDigitMask; + Digit bHigh = b >> HalfDigitBits; + + Digit rLow = aLow * bLow; + Digit rMid1 = aLow * bHigh; + Digit rMid2 = aHigh * bLow; + Digit rHigh = aHigh * bHigh; + + Digit carry = 0; + Digit low = digitAdd(rLow, rMid1 << HalfDigitBits, &carry); + low = digitAdd(low, rMid2 << HalfDigitBits, &carry); + + *high = (rMid1 >> HalfDigitBits) + (rMid2 >> HalfDigitBits) + rHigh + carry; + + return low; +#endif +} + +BigInt::Digit BigInt::digitDiv(Digit high, Digit low, Digit divisor, + Digit* remainder) { + MOZ_ASSERT(high < divisor, "division must not overflow"); +#if defined(__x86_64__) + Digit quotient; + Digit rem; + __asm__("divq %[divisor]" + // Outputs: `quotient` will be in rax, `rem` in rdx. + : "=a"(quotient), "=d"(rem) + // Inputs: put `high` into rdx, `low` into rax, and `divisor` into + // any register or stack slot. + : "d"(high), "a"(low), [divisor] "rm"(divisor)); + *remainder = rem; + return quotient; +#elif defined(__i386__) + Digit quotient; + Digit rem; + __asm__("divl %[divisor]" + // Outputs: `quotient` will be in eax, `rem` in edx. + : "=a"(quotient), "=d"(rem) + // Inputs: put `high` into edx, `low` into eax, and `divisor` into + // any register or stack slot. + : "d"(high), "a"(low), [divisor] "rm"(divisor)); + *remainder = rem; + return quotient; +#else + static constexpr Digit HalfDigitBase = 1ull << HalfDigitBits; + // Adapted from Warren, Hacker's Delight, p. 152. + unsigned s = DigitLeadingZeroes(divisor); + // If `s` is DigitBits here, it causes an undefined behavior. + // But `s` is never DigitBits since `divisor` is never zero here. + MOZ_ASSERT(s != DigitBits); + divisor <<= s; + + Digit vn1 = divisor >> HalfDigitBits; + Digit vn0 = divisor & HalfDigitMask; + + // `sZeroMask` which is 0 if s == 0 and all 1-bits otherwise. + // + // `s` can be 0. If `s` is 0, performing "low >> (DigitBits - s)" must not + // be done since it causes an undefined behavior since `>> DigitBits` is + // undefined in C++. Quoted from C++ spec, "The type of the result is that of + // the promoted left operand. + // + // The behavior is undefined if the right operand is negative, or greater + // than or equal to the length in bits of the promoted left operand". We + // mask the right operand of the shift by `shiftMask` (`DigitBits - 1`), + // which makes `DigitBits - 0` zero. + // + // This shifting produces a value which covers 0 < `s` <= (DigitBits - 1) + // cases. `s` == DigitBits never happen as we asserted. Since `sZeroMask` + // clears the value in the case of `s` == 0, `s` == 0 case is also covered. + static_assert(sizeof(intptr_t) == sizeof(Digit), + "unexpected size of BigInt::Digit"); + Digit sZeroMask = + static_cast<Digit>((-static_cast<intptr_t>(s)) >> (DigitBits - 1)); + static constexpr unsigned shiftMask = DigitBits - 1; + Digit un32 = + (high << s) | ((low >> ((DigitBits - s) & shiftMask)) & sZeroMask); + + Digit un10 = low << s; + Digit un1 = un10 >> HalfDigitBits; + Digit un0 = un10 & HalfDigitMask; + Digit q1 = un32 / vn1; + Digit rhat = un32 - q1 * vn1; + + while (q1 >= HalfDigitBase || q1 * vn0 > rhat * HalfDigitBase + un1) { + q1--; + rhat += vn1; + if (rhat >= HalfDigitBase) { + break; + } + } + + Digit un21 = un32 * HalfDigitBase + un1 - q1 * divisor; + Digit q0 = un21 / vn1; + rhat = un21 - q0 * vn1; + + while (q0 >= HalfDigitBase || q0 * vn0 > rhat * HalfDigitBase + un0) { + q0--; + rhat += vn1; + if (rhat >= HalfDigitBase) { + break; + } + } + + *remainder = (un21 * HalfDigitBase + un0 - q0 * divisor) >> s; + return q1 * HalfDigitBase + q0; +#endif +} + +// Multiplies `source` with `factor` and adds `summand` to the result. +// `result` and `source` may be the same BigInt for inplace modification. +void BigInt::internalMultiplyAdd(BigInt* source, Digit factor, Digit summand, + unsigned n, BigInt* result) { + MOZ_ASSERT(source->digitLength() >= n); + MOZ_ASSERT(result->digitLength() >= n); + + Digit carry = summand; + Digit high = 0; + for (unsigned i = 0; i < n; i++) { + Digit current = source->digit(i); + Digit newCarry = 0; + + // Compute this round's multiplication. + Digit newHigh = 0; + current = digitMul(current, factor, &newHigh); + + // Add last round's carryovers. + current = digitAdd(current, high, &newCarry); + current = digitAdd(current, carry, &newCarry); + + // Store result and prepare for next round. + result->setDigit(i, current); + carry = newCarry; + high = newHigh; + } + + if (result->digitLength() > n) { + result->setDigit(n++, carry + high); + + // Current callers don't pass in such large results, but let's be robust. + while (n < result->digitLength()) { + result->setDigit(n++, 0); + } + } else { + MOZ_ASSERT(!(carry + high)); + } +} + +// Multiplies `this` with `factor` and adds `summand` to the result. +void BigInt::inplaceMultiplyAdd(Digit factor, Digit summand) { + internalMultiplyAdd(this, factor, summand, digitLength(), this); +} + +// Multiplies `multiplicand` with `multiplier` and adds the result to +// `accumulator`, starting at `accumulatorIndex` for the least-significant +// digit. Callers must ensure that `accumulator`'s digitLength and +// corresponding digit storage is long enough to hold the result. +void BigInt::multiplyAccumulate(BigInt* multiplicand, Digit multiplier, + BigInt* accumulator, + unsigned accumulatorIndex) { + MOZ_ASSERT(accumulator->digitLength() > + multiplicand->digitLength() + accumulatorIndex); + if (!multiplier) { + return; + } + + Digit carry = 0; + Digit high = 0; + for (unsigned i = 0; i < multiplicand->digitLength(); + i++, accumulatorIndex++) { + Digit acc = accumulator->digit(accumulatorIndex); + Digit newCarry = 0; + + // Add last round's carryovers. + acc = digitAdd(acc, high, &newCarry); + acc = digitAdd(acc, carry, &newCarry); + + // Compute this round's multiplication. + Digit multiplicandDigit = multiplicand->digit(i); + Digit low = digitMul(multiplier, multiplicandDigit, &high); + acc = digitAdd(acc, low, &newCarry); + + // Store result and prepare for next round. + accumulator->setDigit(accumulatorIndex, acc); + carry = newCarry; + } + + while (carry || high) { + MOZ_ASSERT(accumulatorIndex < accumulator->digitLength()); + Digit acc = accumulator->digit(accumulatorIndex); + Digit newCarry = 0; + acc = digitAdd(acc, high, &newCarry); + high = 0; + acc = digitAdd(acc, carry, &newCarry); + accumulator->setDigit(accumulatorIndex, acc); + carry = newCarry; + accumulatorIndex++; + } +} + +inline int8_t BigInt::absoluteCompare(BigInt* x, BigInt* y) { + MOZ_ASSERT(!x->digitLength() || x->digit(x->digitLength() - 1)); + MOZ_ASSERT(!y->digitLength() || y->digit(y->digitLength() - 1)); + + // Sanity checks to catch negative zeroes escaping to the wild. + MOZ_ASSERT(!x->isNegative() || !x->isZero()); + MOZ_ASSERT(!y->isNegative() || !y->isZero()); + + int diff = x->digitLength() - y->digitLength(); + if (diff) { + return diff < 0 ? -1 : 1; + } + + int i = x->digitLength() - 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; +} + +BigInt* BigInt::absoluteAdd(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y, + bool resultNegative) { + bool swap = x->digitLength() < y->digitLength(); + // Ensure `left` has at least as many digits as `right`. + HandleBigInt& left = swap ? y : x; + HandleBigInt& right = swap ? x : y; + + if (left->isZero()) { + MOZ_ASSERT(right->isZero()); + return left; + } + + if (right->isZero()) { + return resultNegative == left->isNegative() ? left : neg(cx, left); + } + + RootedBigInt result( + cx, createUninitialized(cx, left->digitLength() + 1, resultNegative)); + if (!result) { + return nullptr; + } + Digit carry = 0; + unsigned i = 0; + for (; i < right->digitLength(); i++) { + Digit newCarry = 0; + Digit sum = digitAdd(left->digit(i), right->digit(i), &newCarry); + sum = digitAdd(sum, carry, &newCarry); + result->setDigit(i, sum); + carry = newCarry; + } + + for (; i < left->digitLength(); i++) { + Digit newCarry = 0; + Digit sum = digitAdd(left->digit(i), carry, &newCarry); + result->setDigit(i, sum); + carry = newCarry; + } + + result->setDigit(i, carry); + + return destructivelyTrimHighZeroDigits(cx, result); +} + +BigInt* BigInt::absoluteSub(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y, + bool resultNegative) { + MOZ_ASSERT(x->digitLength() >= y->digitLength()); + + if (x->isZero()) { + MOZ_ASSERT(y->isZero()); + return x; + } + + if (y->isZero()) { + return resultNegative == x->isNegative() ? x : neg(cx, x); + } + + int8_t comparisonResult = absoluteCompare(x, y); + MOZ_ASSERT(comparisonResult >= 0); + if (comparisonResult == 0) { + return zero(cx); + } + + RootedBigInt result( + cx, createUninitialized(cx, x->digitLength(), resultNegative)); + if (!result) { + return nullptr; + } + Digit borrow = 0; + unsigned i = 0; + for (; i < y->digitLength(); i++) { + Digit newBorrow = 0; + Digit difference = digitSub(x->digit(i), y->digit(i), &newBorrow); + difference = digitSub(difference, borrow, &newBorrow); + result->setDigit(i, difference); + borrow = newBorrow; + } + + for (; i < x->digitLength(); i++) { + Digit newBorrow = 0; + Digit difference = digitSub(x->digit(i), borrow, &newBorrow); + result->setDigit(i, difference); + borrow = newBorrow; + } + + MOZ_ASSERT(!borrow); + return destructivelyTrimHighZeroDigits(cx, result); +} + +// 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 `Nothing()` if the caller is only interested in the remainder. +// +// This function returns false if `quotient` is an empty handle, but allocating +// the quotient failed. Otherwise it returns true, indicating success. +bool BigInt::absoluteDivWithDigitDivisor(ExclusiveContext* cx, HandleBigInt x, + Digit divisor, + const Maybe<MutableHandleBigInt>& quotient, + Digit* remainder, + bool quotientNegative) { + MOZ_ASSERT(divisor); + + MOZ_ASSERT(!x->isZero()); + *remainder = 0; + if (divisor == 1) { + if (quotient) { + BigInt* q; + if (x->isNegative() == quotientNegative) { + q = x; + } else { + q = neg(cx, x); + if (!q) { + return false; + } + } + quotient.value().set(q); + } + return true; + } + + unsigned length = x->digitLength(); + if (quotient) { + if (!quotient.value()) { + BigInt* q = createUninitialized(cx, length, quotientNegative); + if (!q) { + return false; + } + quotient.value().set(q); + } + + for (int i = length - 1; i >= 0; i--) { + Digit q = digitDiv(*remainder, x->digit(i), divisor, remainder); + quotient.value()->setDigit(i, q); + } + } else { + for (int i = length - 1; i >= 0; i--) { + digitDiv(*remainder, x->digit(i), divisor, remainder); + } + } + + return true; +} + +// Adds `summand` onto `this`, starting with `summand`'s 0th digit +// at `this`'s `startIndex`'th digit. Returns the "carry" (0 or 1). +BigInt::Digit BigInt::absoluteInplaceAdd(BigInt* summand, unsigned startIndex) { + Digit carry = 0; + unsigned n = summand->digitLength(); + MOZ_ASSERT(digitLength() > startIndex, + "must start adding at an in-range digit"); + MOZ_ASSERT(digitLength() - startIndex >= n, + "digits being added to must not extend above the digits in " + "this (except for the returned carry digit)"); + for (unsigned i = 0; i < n; i++) { + Digit newCarry = 0; + Digit sum = digitAdd(digit(startIndex + i), summand->digit(i), &newCarry); + sum = digitAdd(sum, carry, &newCarry); + setDigit(startIndex + i, sum); + carry = newCarry; + } + + return carry; +} + +// Subtracts `subtrahend` from this, starting with `subtrahend`'s 0th digit +// at `this`'s `startIndex`-th digit. Returns the "borrow" (0 or 1). +BigInt::Digit BigInt::absoluteInplaceSub(BigInt* subtrahend, + unsigned startIndex) { + Digit borrow = 0; + unsigned n = subtrahend->digitLength(); + MOZ_ASSERT(digitLength() > startIndex, + "must start subtracting from an in-range digit"); + MOZ_ASSERT(digitLength() - startIndex >= n, + "digits being subtracted from must not extend above the " + "digits in this (except for the returned borrow digit)"); + for (unsigned i = 0; i < n; i++) { + Digit newBorrow = 0; + Digit difference = + digitSub(digit(startIndex + i), subtrahend->digit(i), &newBorrow); + difference = digitSub(difference, borrow, &newBorrow); + setDigit(startIndex + i, difference); + borrow = newBorrow; + } + + return borrow; +} + +// Returns whether (factor1 * factor2) > (high << kDigitBits) + low. +inline bool BigInt::productGreaterThan(Digit factor1, Digit factor2, Digit high, + Digit low) { + Digit resultHigh; + Digit resultLow = digitMul(factor1, factor2, &resultHigh); + return resultHigh > high || (resultHigh == high && resultLow > low); +} + +void BigInt::inplaceRightShiftLowZeroBits(unsigned shift) { + MOZ_ASSERT(shift < DigitBits); + MOZ_ASSERT(!(digit(0) & ((static_cast<Digit>(1) << shift) - 1)), + "should only be shifting away zeroes"); + + if (!shift) { + return; + } + + Digit carry = digit(0) >> shift; + unsigned last = digitLength() - 1; + for (unsigned i = 0; i < last; i++) { + Digit d = digit(i + 1); + setDigit(i, (d << (DigitBits - shift)) | carry); + carry = d >> shift; + } + setDigit(last, carry); +} + +// Always copies the input, even when `shift` == 0. +BigInt* BigInt::absoluteLeftShiftAlwaysCopy(ExclusiveContext* cx, HandleBigInt x, + unsigned shift, + LeftShiftMode mode) { + MOZ_ASSERT(shift < DigitBits); + MOZ_ASSERT(!x->isZero()); + + unsigned n = x->digitLength(); + unsigned resultLength = mode == LeftShiftMode::AlwaysAddOneDigit ? n + 1 : n; + RootedBigInt result(cx, + createUninitialized(cx, resultLength, x->isNegative())); + if (!result) { + return nullptr; + } + + if (!shift) { + for (unsigned i = 0; i < n; i++) { + result->setDigit(i, x->digit(i)); + } + if (mode == LeftShiftMode::AlwaysAddOneDigit) { + result->setDigit(n, 0); + } + + return result; + } + + Digit carry = 0; + for (unsigned i = 0; i < n; i++) { + Digit d = x->digit(i); + result->setDigit(i, (d << shift) | carry); + carry = d >> (DigitBits - shift); + } + + if (mode == LeftShiftMode::AlwaysAddOneDigit) { + result->setDigit(n, carry); + } else { + MOZ_ASSERT(mode == LeftShiftMode::SameSizeResult); + MOZ_ASSERT(!carry); + } + + return result; +} + +// 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. +// Also see the overview of the algorithm by Jan Marthedal Rasmussen over at +// https://janmr.com/blog/2014/04/basic-multiple-precision-long-division/. +bool BigInt::absoluteDivWithBigIntDivisor(ExclusiveContext* cx, HandleBigInt dividend, + HandleBigInt divisor, + const Maybe<MutableHandleBigInt>& quotient, + const Maybe<MutableHandleBigInt>& remainder, + bool isNegative) { + MOZ_ASSERT(divisor->digitLength() >= 2); + MOZ_ASSERT(dividend->digitLength() >= divisor->digitLength()); + + // Any early error return is detectable by checking the quotient and/or + // remainder output values. + MOZ_ASSERT(!quotient || !quotient.value()); + MOZ_ASSERT(!remainder || !remainder.value()); + + // 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. + const unsigned n = divisor->digitLength(); + const unsigned m = dividend->digitLength() - n; + + // The quotient to be computed. + RootedBigInt q(cx); + if (quotient) { + q = createUninitialized(cx, m + 1, isNegative); + if (!q) { + return false; + } + } + + // In each iteration, `qhatv` holds `divisor` * `current quotient digit`. + // "v" is the book's name for `divisor`, `qhat` the current quotient digit. + RootedBigInt qhatv(cx, createUninitialized(cx, n + 1, isNegative)); + if (!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 digitDiv call below) from + // overflowing (they take a two digits wide input, and return a one digit + // result). + Digit lastDigit = divisor->digit(n - 1); + unsigned shift = DigitLeadingZeroes(lastDigit); + + RootedBigInt shiftedDivisor(cx); + if (shift > 0) { + shiftedDivisor = absoluteLeftShiftAlwaysCopy(cx, divisor, shift, + LeftShiftMode::SameSizeResult); + if (!shiftedDivisor) { + return false; + } + } else { + shiftedDivisor = divisor; + } + + // Holds the (continuously updated) remaining part of the dividend, which + // eventually becomes the remainder. + RootedBigInt u(cx, + absoluteLeftShiftAlwaysCopy(cx, dividend, shift, + LeftShiftMode::AlwaysAddOneDigit)); + if (!u) { + return false; + } + + // D2. + // Iterate over the dividend's digit (like the "grade school" algorithm). + // `vn1` is the divisor's most significant digit. + Digit vn1 = shiftedDivisor->digit(n - 1); + for (int j = m; j >= 0; j--) { + // D3. + // Estimate the current iteration's quotient digit (see Knuth for details). + // `qhat` is the current quotient digit. + Digit qhat = std::numeric_limits<Digit>::max(); + + // `ujn` is the dividend's most significant remaining digit. + Digit ujn = u->digit(j + n); + if (ujn != vn1) { + // `rhat` is the current iteration's remainder. + Digit rhat = 0; + // Estimate the current quotient digit by dividing the most significant + // digits of dividend and divisor. The result will not be too small, + // but could be a bit too large. + qhat = digitDiv(ujn, u->digit(j + n - 1), vn1, &rhat); + + // Decrement the quotient estimate as needed by looking at the next + // digit, i.e. by testing whether + // qhat * v_{n-2} > (rhat << DigitBits) + u_{j+n-2}. + Digit vn2 = shiftedDivisor->digit(n - 2); + Digit ujn2 = u->digit(j + n - 2); + while (productGreaterThan(qhat, vn2, rhat, ujn2)) { + qhat--; + Digit prevRhat = rhat; + rhat += vn1; + // v[n-1] >= 0, so this tests for overflow. + if (rhat < prevRhat) { + break; + } + } + } + + // D4. + // Multiply the divisor with the current quotient digit, and subtract + // it from the dividend. If there was "borrow", then the quotient digit + // was one too high, so we must correct it and undo one subtraction of + // the (shifted) divisor. + internalMultiplyAdd(shiftedDivisor, qhat, 0, n, qhatv); + Digit c = u->absoluteInplaceSub(qhatv, j); + if (c) { + c = u->absoluteInplaceAdd(shiftedDivisor, j); + u->setDigit(j + n, u->digit(j + n) + c); + qhat--; + } + + if (quotient) { + q->setDigit(j, qhat); + } + } + + if (quotient) { + BigInt* bi = destructivelyTrimHighZeroDigits(cx, q); + if (!bi) { + return false; + } + quotient.value().set(q); + } + + if (remainder) { + u->inplaceRightShiftLowZeroBits(shift); + remainder.value().set(u); + } + + return true; +} + +// 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, `kind` configures how +// remaining digits are handled. +// Example: +// y: [ y2 ][ y1 ][ y0 ] +// x: [ x3 ][ x2 ][ x1 ][ x0 ] +// | | | | +// (Fill) (op) (op) (op) +// | | | | +// v v v v +// result: [ 0 ][ x3 ][ r2 ][ r1 ][ r0 ] +template <BigInt::BitwiseOpKind kind, typename BitwiseOp> +inline BigInt* BigInt::absoluteBitwiseOp(ExclusiveContext* cx, HandleBigInt x, + HandleBigInt y, BitwiseOp&& op) { + unsigned xLength = x->digitLength(); + unsigned yLength = y->digitLength(); + unsigned numPairs = std::min(xLength, yLength); + unsigned resultLength; + if (kind == BitwiseOpKind::SymmetricTrim) { + resultLength = numPairs; + } else if (kind == BitwiseOpKind::SymmetricFill) { + resultLength = std::max(xLength, yLength); + } else { + MOZ_ASSERT(kind == BitwiseOpKind::AsymmetricFill); + resultLength = xLength; + } + bool resultNegative = false; + + RootedBigInt result(cx, + createUninitialized(cx, resultLength, resultNegative)); + if (!result) { + return nullptr; + } + + unsigned i = 0; + for (; i < numPairs; i++) { + result->setDigit(i, op(x->digit(i), y->digit(i))); + } + + if (kind != BitwiseOpKind::SymmetricTrim) { + HandleBigInt& source = + kind == BitwiseOpKind::AsymmetricFill ? x : xLength == i ? y : x; + for (; i < resultLength; i++) { + result->setDigit(i, source->digit(i)); + } + } + + MOZ_ASSERT(i == resultLength); + + return destructivelyTrimHighZeroDigits(cx, result); +} + +BigInt* BigInt::absoluteAnd(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + return absoluteBitwiseOp<BitwiseOpKind::SymmetricTrim>(cx, x, y, + std::bit_and<Digit>()); +} + +BigInt* BigInt::absoluteOr(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + return absoluteBitwiseOp<BitwiseOpKind::SymmetricFill>(cx, x, y, + std::bit_or<Digit>()); +} + +BigInt* BigInt::absoluteAndNot(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + auto digitOperation = [](Digit a, Digit b) { return a & ~b; }; + return absoluteBitwiseOp<BitwiseOpKind::AsymmetricFill>(cx, x, y, + digitOperation); +} + +BigInt* BigInt::absoluteXor(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + return absoluteBitwiseOp<BitwiseOpKind::SymmetricFill>(cx, x, y, + std::bit_xor<Digit>()); +} + +BigInt* BigInt::absoluteAddOne(ExclusiveContext* cx, HandleBigInt x, + bool resultNegative) { + unsigned inputLength = x->digitLength(); + // The addition will overflow into a new digit if all existing digits are + // at maximum. + bool willOverflow = true; + for (unsigned i = 0; i < inputLength; i++) { + if (std::numeric_limits<Digit>::max() != x->digit(i)) { + willOverflow = false; + break; + } + } + + unsigned resultLength = inputLength + willOverflow; + RootedBigInt result(cx, + createUninitialized(cx, resultLength, resultNegative)); + if (!result) { + return nullptr; + } + + Digit carry = 1; + for (unsigned i = 0; i < inputLength; i++) { + Digit newCarry = 0; + result->setDigit(i, digitAdd(x->digit(i), carry, &newCarry)); + carry = newCarry; + } + if (resultLength > inputLength) { + MOZ_ASSERT(carry == 1); + result->setDigit(inputLength, 1); + } else { + MOZ_ASSERT(!carry); + } + + return destructivelyTrimHighZeroDigits(cx, result); +} + +// Like the above, but you can specify that the allocated result should have +// length `resultLength`, which must be at least as large as `x->digitLength()`. +// The result will be unsigned. +BigInt* BigInt::absoluteSubOne(ExclusiveContext* cx, HandleBigInt x, + unsigned resultLength) { + MOZ_ASSERT(!x->isZero()); + MOZ_ASSERT(resultLength >= x->digitLength()); + bool resultNegative = false; + RootedBigInt result(cx, + createUninitialized(cx, resultLength, resultNegative)); + if (!result) { + return nullptr; + } + + unsigned length = x->digitLength(); + Digit borrow = 1; + for (unsigned i = 0; i < length; i++) { + Digit newBorrow = 0; + result->setDigit(i, digitSub(x->digit(i), borrow, &newBorrow)); + borrow = newBorrow; + } + MOZ_ASSERT(!borrow); + for (unsigned i = length; i < resultLength; i++) { + result->setDigit(i, 0); + } + + return destructivelyTrimHighZeroDigits(cx, result); +} + +// 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) + ","); } +static constexpr uint8_t maxBitsPerCharTable[] = { + 0, 0, 32, 51, 64, 75, 83, 90, 96, // 0..8 + 102, 107, 111, 115, 119, 122, 126, 128, // 9..16 + 131, 134, 136, 139, 141, 143, 145, 147, // 17..24 + 149, 151, 153, 154, 156, 158, 159, 160, // 25..32 + 162, 163, 165, 166, // 33..36 +}; + +static constexpr unsigned bitsPerCharTableShift = 5; +static constexpr size_t bitsPerCharTableMultiplier = 1u + << bitsPerCharTableShift; +static constexpr char radixDigits[] = "0123456789abcdefghijklmnopqrstuvwxyz"; + +static inline uint64_t CeilDiv(uint64_t numerator, uint64_t denominator) { + MOZ_ASSERT(numerator != 0); + return 1 + (numerator - 1) / denominator; +}; + +// Compute (an overapproximation of) the length of the string representation of +// a BigInt. In base B an X-digit number has maximum value: +// +// B**X - 1 +// +// We're trying to find N for an N-digit number in base |radix| full +// representing a |bitLength|-digit number in base 2, so we have: +// +// radix**N - 1 ≥ 2**bitLength - 1 +// radix**N ≥ 2**bitLength +// N ≥ log2(2**bitLength) / log2(radix) +// N ≥ bitLength / log2(radix) +// +// so the smallest N is: +// +// N = ⌈bitLength / log2(radix)⌉ +// +// We want to avoid floating-point computations and precompute the logarithm, so +// we multiply both sides of the division by |bitsPerCharTableMultiplier|: +// +// N = ⌈(bPCTM * bitLength) / (bPCTM * log2(radix))⌉ +// +// and then because |maxBitsPerChar| representing the denominator may have been +// rounded *up* -- which could produce an overall under-computation -- we reduce +// by one to undo any rounding and conservatively compute: +// +// N ≥ ⌈(bPCTM * bitLength) / (maxBitsPerChar - 1)⌉ +// +size_t BigInt::calculateMaximumCharactersRequired(HandleBigInt x, + unsigned radix) { + MOZ_ASSERT(!x->isZero()); + MOZ_ASSERT(radix >= 2 && radix <= 36); + + size_t length = x->digitLength(); + Digit lastDigit = x->digit(length - 1); + size_t bitLength = length * DigitBits - DigitLeadingZeroes(lastDigit); + + uint8_t maxBitsPerChar = maxBitsPerCharTable[radix]; + uint64_t maximumCharactersRequired = + CeilDiv(static_cast<uint64_t>(bitsPerCharTableMultiplier) * bitLength, + maxBitsPerChar - 1); + maximumCharactersRequired += x->isNegative(); + + return AssertedCast<size_t>(maximumCharactersRequired); +} + +JSLinearString* BigInt::toStringBasePowerOfTwo(ExclusiveContext* cx, HandleBigInt x, + unsigned radix) { + MOZ_ASSERT(mozilla::IsPowerOfTwo(radix)); + MOZ_ASSERT(radix >= 2 && radix <= 32); + MOZ_ASSERT(!x->isZero()); + + const unsigned length = x->digitLength(); + const bool sign = x->isNegative(); + const unsigned bitsPerChar = mozilla::CountTrailingZeroes32(radix); + const unsigned charMask = radix - 1; + // Compute the length of the resulting string: divide the bit length of the + // BigInt by the number of bits representable per character (rounding up). + const Digit msd = x->digit(length - 1); + + const size_t bitLength = length * DigitBits - DigitLeadingZeroes(msd); + const size_t charsRequired = CeilDiv(bitLength, bitsPerChar) + sign; + + if (charsRequired > JSString::MAX_LENGTH) { + ReportOutOfMemory(cx); + return nullptr; + } + + auto resultChars = cx->make_pod_array<char>(charsRequired); + if (!resultChars) { + return nullptr; + } + + Digit digit = 0; + // Keeps track of how many unprocessed bits there are in |digit|. + unsigned availableBits = 0; + size_t pos = charsRequired; + for (unsigned i = 0; i < length - 1; i++) { + Digit newDigit = x->digit(i); + // Take any leftover bits from the last iteration into account. + unsigned current = (digit | (newDigit << availableBits)) & charMask; + MOZ_ASSERT(pos); + resultChars[--pos] = radixDigits[current]; + unsigned consumedBits = bitsPerChar - availableBits; + digit = newDigit >> consumedBits; + availableBits = DigitBits - consumedBits; + while (availableBits >= bitsPerChar) { + MOZ_ASSERT(pos); + resultChars[--pos] = radixDigits[digit & charMask]; + digit >>= bitsPerChar; + availableBits -= bitsPerChar; + } + } + + // Write out the character containing the lowest-order bit of |msd|. + // + // This character may include leftover bits from the Digit below |msd|. For + // example, if |x === 2n**64n| and |radix == 32|: the preceding loop writes + // twelve zeroes for low-order bits 0-59 in |x->digit(0)| (and |x->digit(1)| + // on 32-bit); then the highest 4 bits of of |x->digit(0)| (or |x->digit(1)| + // on 32-bit) and bit 0 of |x->digit(1)| (|x->digit(2)| on 32-bit) will + // comprise the |current == 0b1'0000| computed below for the high-order 'g' + // character. + unsigned current = (digit | (msd << availableBits)) & charMask; + MOZ_ASSERT(pos); + resultChars[--pos] = radixDigits[current]; + + // Write out remaining characters represented by |msd|. (There may be none, + // as in the example above.) + digit = msd >> (bitsPerChar - availableBits); + while (digit != 0) { + MOZ_ASSERT(pos); + resultChars[--pos] = radixDigits[digit & charMask]; + digit >>= bitsPerChar; + } + + if (sign) { + MOZ_ASSERT(pos); + resultChars[--pos] = '-'; + } + + MOZ_ASSERT(pos == 0); + return NewStringCopyN<CanGC>(cx, resultChars.get(), charsRequired); +} + +static constexpr BigInt::Digit MaxPowerInDigit(uint8_t radix) { + BigInt::Digit result = 1; + while (result < BigInt::Digit(-1) / radix) { + result *= radix; + } + return result; +} + +static constexpr uint8_t MaxExponentInDigit(uint8_t radix) { + uint8_t exp = 0; + BigInt::Digit result = 1; + while (result < BigInt::Digit(-1) / radix) { + result *= radix; + exp += 1; + } + return exp; +} + +struct RadixInfo { + BigInt::Digit maxPowerInDigit; + uint8_t maxExponentInDigit; + + constexpr RadixInfo(BigInt::Digit maxPower, uint8_t maxExponent) + : maxPowerInDigit(maxPower), maxExponentInDigit(maxExponent) {} + + explicit constexpr RadixInfo(uint8_t radix) + : RadixInfo(MaxPowerInDigit(radix), MaxExponentInDigit(radix)) {} +}; + +static constexpr const RadixInfo toStringInfo[37] = { + {0, 0}, {0, 0}, RadixInfo(2), RadixInfo(3), RadixInfo(4), + RadixInfo(5), RadixInfo(6), RadixInfo(7), RadixInfo(8), RadixInfo(9), + RadixInfo(10), RadixInfo(11), RadixInfo(12), RadixInfo(13), RadixInfo(14), + RadixInfo(15), RadixInfo(16), RadixInfo(17), RadixInfo(18), RadixInfo(19), + RadixInfo(20), RadixInfo(21), RadixInfo(22), RadixInfo(23), RadixInfo(24), + RadixInfo(25), RadixInfo(26), RadixInfo(27), RadixInfo(28), RadixInfo(29), + RadixInfo(30), RadixInfo(31), RadixInfo(32), RadixInfo(33), RadixInfo(34), + RadixInfo(35), RadixInfo(36), +}; + +JSLinearString* BigInt::toStringGeneric(ExclusiveContext* cx, HandleBigInt x, + unsigned radix) { + MOZ_ASSERT(radix >= 2 && radix <= 36); + MOZ_ASSERT(!x->isZero()); + + size_t maximumCharactersRequired = + calculateMaximumCharactersRequired(x, radix); + if (maximumCharactersRequired > JSString::MAX_LENGTH) { + ReportOutOfMemory(cx); + return nullptr; + } + + UniqueChars resultString(js_pod_malloc<char>(maximumCharactersRequired)); + if (!resultString) { + ReportOutOfMemory(cx); + return nullptr; + } + + size_t writePos = maximumCharactersRequired; + unsigned length = x->digitLength(); + Digit lastDigit; + if (length == 1) { + lastDigit = x->digit(0); + } else { + unsigned chunkChars = toStringInfo[radix].maxExponentInDigit; + Digit chunkDivisor = toStringInfo[radix].maxPowerInDigit; + + unsigned nonZeroDigit = length - 1; + MOZ_ASSERT(x->digit(nonZeroDigit) != 0); + + // `rest` holds the part of the BigInt that we haven't looked at yet. + // Not to be confused with "remainder"! + RootedBigInt rest(cx); + + // In the first round, divide the input, allocating a new BigInt for + // the result == rest; from then on divide the rest in-place. + // + // FIXME: absoluteDivWithDigitDivisor doesn't + // destructivelyTrimHighZeroDigits for in-place divisions, leading to + // worse constant factors. See + // https://bugzilla.mozilla.org/show_bug.cgi?id=1510213. + RootedBigInt dividend(cx, x); + do { + Digit chunk; + if (!absoluteDivWithDigitDivisor(cx, dividend, chunkDivisor, Some(&rest), + &chunk, dividend->isNegative())) { + return nullptr; + } + + dividend = rest; + for (unsigned i = 0; i < chunkChars; i++) { + MOZ_ASSERT(writePos > 0); + resultString[--writePos] = radixDigits[chunk % radix]; + chunk /= radix; + } + MOZ_ASSERT(!chunk); + + if (!rest->digit(nonZeroDigit)) { + nonZeroDigit--; + } + + MOZ_ASSERT(rest->digit(nonZeroDigit) != 0, + "division by a single digit can't remove more than one " + "digit from a number"); + } while (nonZeroDigit > 0); + + lastDigit = rest->digit(0); + } + + do { + MOZ_ASSERT(writePos > 0); + resultString[--writePos] = radixDigits[lastDigit % radix]; + lastDigit /= radix; + } while (lastDigit > 0); + MOZ_ASSERT(writePos < maximumCharactersRequired); + MOZ_ASSERT(maximumCharactersRequired - writePos <= + static_cast<size_t>(maximumCharactersRequired)); + + // Remove leading zeroes. + while (writePos + 1 < maximumCharactersRequired && + resultString[writePos] == '0') { + writePos++; + } + + if (x->isNegative()) { + MOZ_ASSERT(writePos > 0); + resultString[--writePos] = '-'; + } + + MOZ_ASSERT(writePos < maximumCharactersRequired); + // Would be better to somehow adopt resultString directly. + return NewStringCopyN<CanGC>(cx, resultString.get() + writePos, + maximumCharactersRequired - writePos); +} + +BigInt* BigInt::trimHighZeroDigits(ExclusiveContext* cx, HandleBigInt x) { + if (x->isZero()) { + MOZ_ASSERT(!x->isNegative()); + return x; + } + MOZ_ASSERT(x->digitLength()); + + int nonZeroIndex = x->digitLength() - 1; + while (nonZeroIndex >= 0 && x->digit(nonZeroIndex) == 0) { + nonZeroIndex--; + } + + if (nonZeroIndex < 0) { + return zero(cx); + } + + if (nonZeroIndex == static_cast<int>(x->digitLength() - 1)) { + return x; + } + + unsigned newLength = nonZeroIndex + 1; + BigInt* trimmedBigInt = createUninitialized(cx, newLength, x->isNegative()); + if (!trimmedBigInt) { + return nullptr; + } + for (unsigned i = 0; i < newLength; i++) { + trimmedBigInt->setDigit(i, x->digit(i)); + } + + return trimmedBigInt; +} + +BigInt* BigInt::destructivelyTrimHighZeroDigits(ExclusiveContext* cx, HandleBigInt x) { + // TODO: Modify in place instead of allocating. + return trimHighZeroDigits(cx, x); +} + +// The maximum value `radix**charCount - 1` must be represented as a max number +// `2**(N * DigitBits) - 1` for `N` digits, so +// +// 2**(N * DigitBits) - 1 ≥ radix**charcount - 1 +// 2**(N * DigitBits) ≥ radix**charcount +// N * DigitBits ≥ log2(radix**charcount) +// N * DigitBits ≥ charcount * log2(radix) +// N ≥ ⌈charcount * log2(radix) / DigitBits⌉ (conservatively) +// +// or in the code's terms (all numbers promoted to exact mathematical values), +// +// N ≥ ⌈charcount * bitsPerChar / (DigitBits * bitsPerCharTableMultiplier)⌉ +// +// Note that `N` is computed even more conservatively here because `bitsPerChar` +// is rounded up. +bool BigInt::calculateMaximumDigitsRequired(ExclusiveContext* cx, uint8_t radix, + size_t charcount, size_t* result) { + MOZ_ASSERT(2 <= radix && radix <= 36); + + size_t bitsPerChar = maxBitsPerCharTable[radix]; + + MOZ_ASSERT(charcount > 0); + MOZ_ASSERT(charcount <= std::numeric_limits<size_t>::max() / bitsPerChar); + uint64_t n = + CeilDiv(charcount * bitsPerChar, DigitBits * bitsPerCharTableMultiplier); + if (n > MaxDigitLength) { + ReportAllocationOverflow(cx); + return false; + } + + *result = n; + return true; +} + +template <typename CharT> +BigInt* BigInt::parseLiteralDigits(ExclusiveContext* cx, + const Range<const CharT> chars, + unsigned radix, bool isNegative, + bool* haveParseError) { + MOZ_ASSERT(chars.length()); + + RangedPtr<const CharT> start = chars.begin(); + RangedPtr<const CharT> end = chars.end(); + + // Skipping leading zeroes. + while (start[0] == '0') { + start++; + if (start == end) { + return zero(cx); + } + } + + unsigned limit0 = '0' + std::min(radix, 10u); + unsigned limita = 'a' + (radix - 10); + unsigned limitA = 'A' + (radix - 10); + + size_t length; + if (!calculateMaximumDigitsRequired(cx, radix, end - start, &length)) { + return nullptr; + } + RootedBigInt result(cx, createUninitialized(cx, length, isNegative)); + if (!result) { + return nullptr; + } + + result->initializeDigitsToZero(); + + RangedPtr<const CharT> begin = start; + for (; start < end; start++) { + uint32_t digit; + CharT c = *start; + if (c == '_' && start > begin && start < end - 1) { + // skip over block delimiters unless at the very start or end + continue; + } else if (c >= '0' && c < limit0) { + digit = c - '0'; + } else if (c >= 'a' && c < limita) { + digit = c - 'a' + 10; + } else if (c >= 'A' && c < limitA) { + digit = c - 'A' + 10; + } else { + *haveParseError = true; + return nullptr; + } + + result->inplaceMultiplyAdd(static_cast<Digit>(radix), + static_cast<Digit>(digit)); + } + + return destructivelyTrimHighZeroDigits(cx, result); +} + +// BigInt proposal section 7.2 +template <typename CharT> +BigInt* BigInt::parseLiteral(ExclusiveContext* cx, const Range<const CharT> chars, + bool* haveParseError) { + RangedPtr<const CharT> start = chars.begin(); + const RangedPtr<const CharT> end = chars.end(); + bool isNegative = false; + + MOZ_ASSERT(chars.length()); + + if (end - start > 2 && start[0] == '0') { + if (start[1] == 'b' || start[1] == 'B') { + // StringNumericLiteral ::: BinaryIntegerLiteral + return parseLiteralDigits(cx, Range<const CharT>(start + 2, end), 2, + isNegative, haveParseError); + } + if (start[1] == 'x' || start[1] == 'X') { + // StringNumericLiteral ::: HexIntegerLiteral + return parseLiteralDigits(cx, Range<const CharT>(start + 2, end), 16, + isNegative, haveParseError); + } + if (start[1] == 'o' || start[1] == 'O') { + // StringNumericLiteral ::: OctalIntegerLiteral + return parseLiteralDigits(cx, Range<const CharT>(start + 2, end), 8, + isNegative, haveParseError); + } + } + + return parseLiteralDigits(cx, Range<const CharT>(start, end), 10, isNegative, + haveParseError); +} + +// BigInt proposal section 5.1.1 +static bool IsInteger(double d) { + // Step 1 is an assertion checked by the caller. + // Step 2. + if (!mozilla::IsFinite(d)) { + return false; + } + + // Step 3. + double i = JS::ToInteger(d); + + // Step 4. + if (i != d) { + return false; + } + + // Step 5. + return true; +} + +BigInt* BigInt::createFromDouble(ExclusiveContext* cx, double d) { + MOZ_ASSERT(::IsInteger(d), + "Only integer-valued doubles can convert to BigInt"); + + if (d == 0) { + return zero(cx); + } + + int exponent = mozilla::ExponentComponent(d); + MOZ_ASSERT(exponent >= 0); + int length = exponent / DigitBits + 1; + BigInt* result = createUninitialized(cx, length, d < 0); + if (!result) { + return nullptr; + } + + // We construct a BigInt from the double `d` 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 + // <--> <------> + // msdTopBits DigitBits + // + using Double = mozilla::FloatingPoint<double>; + uint64_t mantissa = + mozilla::BitwiseCast<uint64_t>(d) & Double::kSignificandBits; + // Add implicit high bit. + mantissa |= 1ull << Double::kSignificandWidth; + + const int mantissaTopBit = Double::kSignificandWidth; // 0-indexed. + + // 0-indexed position of `d`'s most significant bit within the `msd`. + int msdTopBit = exponent % DigitBits; + + // Next digit under construction. + Digit digit; + + // First, build the MSD by shifting the mantissa appropriately. + if (msdTopBit < mantissaTopBit) { + int remainingMantissaBits = mantissaTopBit - msdTopBit; + digit = mantissa >> remainingMantissaBits; + mantissa = mantissa << (64 - remainingMantissaBits); + } else { + MOZ_ASSERT(msdTopBit >= mantissaTopBit); + digit = mantissa << (msdTopBit - mantissaTopBit); + mantissa = 0; + } + result->setDigit(--length, digit); + + // Fill in digits containing mantissa contributions. + while (mantissa) { + MOZ_ASSERT(length > 0, + "double bits were all non-fractional, so there must be " + "digits present to hold them"); + + if (DigitBits == 64) { + result->setDigit(--length, mantissa); + break; + } + + MOZ_ASSERT(DigitBits == 32); + Digit current = mantissa >> 32; + mantissa = mantissa << 32; + result->setDigit(--length, current); + } + + // Fill in low-order zeroes. + for (int i = length - 1; i >= 0; i--) { + result->setDigit(i, 0); + } + + return result; +} + +BigInt* BigInt::createFromUint64(ExclusiveContext* cx, uint64_t n) { + if (n == 0) { + return zero(cx); + } + + const bool isNegative = false; + + if (DigitBits == 32) { + Digit low = n; + Digit high = n >> 32; + size_t length = high ? 2 : 1; + + BigInt* res = createUninitialized(cx, length, isNegative); + if (!res) { + return nullptr; + } + res->setDigit(0, low); + if (high) { + res->setDigit(1, high); + } + return res; + } + + BigInt* res = createUninitialized(cx, 1, isNegative); + if (!res) { + return nullptr; + } + + res->setDigit(0, n); + return res; +} + +BigInt* BigInt::createFromInt64(ExclusiveContext* cx, int64_t n) { + BigInt* res = createFromUint64(cx, Abs(n)); + if (!res) { + return nullptr; + } + + if (n < 0) { + res->lengthSignAndReservedBits_ |= SignBit; + } + MOZ_ASSERT(res->isNegative() == (n < 0)); + + return res; +} + +// BigInt proposal section 5.1.2 +BigInt* js::NumberToBigInt(ExclusiveContext* cx, double d) { + // Step 1 is an assertion checked by the caller. + // Step 2. + if (!::IsInteger(d)) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_NUMBER_TO_BIGINT); + } + return nullptr; + } + + // Step 3. + return BigInt::createFromDouble(cx, d); +} + +BigInt* BigInt::copy(ExclusiveContext* cx, HandleBigInt x) { + if (x->isZero()) { + return zero(cx); + } + + BigInt* result = createUninitialized(cx, x->digitLength(), x->isNegative()); + if (!result) { + return nullptr; + } + for (size_t i = 0; i < x->digitLength(); i++) { + result->setDigit(i, x->digit(i)); + } + return result; +} + +// BigInt proposal section 1.1.7 +BigInt* BigInt::add(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + bool xNegative = x->isNegative(); + + // x + y == x + y + // -x + -y == -(x + y) + if (xNegative == y->isNegative()) { + return absoluteAdd(cx, x, y, xNegative); + } + + // x + -y == x - y == -(y - x) + // -x + y == y - x == -(x - y) + if (absoluteCompare(x, y) >= 0) { + return absoluteSub(cx, x, y, xNegative); + } + + return absoluteSub(cx, y, x, !xNegative); +} + +// BigInt proposal section 1.1.8 +BigInt* BigInt::sub(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + bool xNegative = x->isNegative(); + if (xNegative != y->isNegative()) { + // x - (-y) == x + y + // (-x) - y == -(x + y) + return absoluteAdd(cx, x, y, xNegative); + } + // x - y == -(y - x) + // (-x) - (-y) == y - x == -(x - y) + if (absoluteCompare(x, y) >= 0) { + return absoluteSub(cx, x, y, xNegative); + } + + return absoluteSub(cx, y, x, !xNegative); +} + +// BigInt proposal section 1.1.4 +BigInt* BigInt::mul(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (x->isZero()) { + return x; + } + if (y->isZero()) { + return y; + } + + unsigned resultLength = x->digitLength() + y->digitLength(); + bool resultNegative = x->isNegative() != y->isNegative(); + RootedBigInt result(cx, + createUninitialized(cx, resultLength, resultNegative)); + if (!result) { + return nullptr; + } + result->initializeDigitsToZero(); + + for (size_t i = 0; i < x->digitLength(); i++) { + multiplyAccumulate(y, x->digit(i), result, i); + } + + return destructivelyTrimHighZeroDigits(cx, result); +} + +// BigInt proposal section 1.1.5 +BigInt* BigInt::div(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + // 1. If y is 0n, throw a RangeError exception. + if (y->isZero()) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_DIVISION_BY_ZERO); + } + return nullptr; + } + + // 2. Let quotient be the mathematical value of x divided by y. + // 3. Return a BigInt representing quotient rounded towards 0 to the next + // integral value. + if (x->isZero()) { + return x; + } + + if (absoluteCompare(x, y) < 0) { + return zero(cx); + } + + RootedBigInt quotient(cx); + bool resultNegative = x->isNegative() != y->isNegative(); + if (y->digitLength() == 1) { + Digit divisor = y->digit(0); + if (divisor == 1) { + return resultNegative == x->isNegative() ? x : neg(cx, x); + } + + Digit remainder; + if (!absoluteDivWithDigitDivisor(cx, x, divisor, Some("ient), + &remainder, resultNegative)) { + return nullptr; + } + } else { + if (!absoluteDivWithBigIntDivisor(cx, x, y, Some("ient), Nothing(), + resultNegative)) { + return nullptr; + } + } + + return destructivelyTrimHighZeroDigits(cx, quotient); +} + +// BigInt proposal section 1.1.6 +BigInt* BigInt::mod(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + // 1. If y is 0n, throw a RangeError exception. + if (y->isZero()) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_DIVISION_BY_ZERO); + } + return nullptr; + } + + // 2. If x is 0n, return x. + if (x->isZero()) { + return x; + } + // 3. Let r be the BigInt defined by the mathematical relation r = x - (y × + // q) where q is a BigInt that is negative only if x/y is negative and + // positive only if x/y is positive, and whose magnitude is as large as + // possible without exceeding the magnitude of the true mathematical + // quotient of x and y. + if (absoluteCompare(x, y) < 0) { + return x; + } + + if (y->digitLength() == 1) { + Digit divisor = y->digit(0); + if (divisor == 1) { + return zero(cx); + } + + Digit remainderDigit; + bool unusedQuotientNegative = false; + if (!absoluteDivWithDigitDivisor(cx, x, divisor, Nothing(), &remainderDigit, + unusedQuotientNegative)) { + MOZ_CRASH("BigInt div by digit failed unexpectedly"); + } + + if (!remainderDigit) { + return zero(cx); + } + + BigInt* remainder = createUninitialized(cx, 1, x->isNegative()); + if (!remainder) { + return nullptr; + } + remainder->setDigit(0, remainderDigit); + return remainder; + } else { + RootedBigInt remainder(cx); + if (!absoluteDivWithBigIntDivisor(cx, x, y, Nothing(), Some(&remainder), + x->isNegative())) { + return nullptr; + } + MOZ_ASSERT(remainder); + return destructivelyTrimHighZeroDigits(cx, remainder); + } +} + +// BigInt proposal section 1.1.3 +BigInt* BigInt::pow(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + // 1. If exponent is < 0, throw a RangeError exception. + if (y->isNegative()) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_NEGATIVE_EXPONENT); + } + return nullptr; + } + + // 2. If base is 0n and exponent is 0n, return 1n. + if (y->isZero()) { + return one(cx); + } + + if (x->isZero()) { + return x; + } + + // 3. Return a BigInt representing the mathematical value of base raised + // to the power exponent. + if (x->digitLength() == 1 && x->digit(0) == 1) { + // (-1) ** even_number == 1. + if (x->isNegative() && (y->digit(0) & 1) == 0) { + return neg(cx, x); + } + // (-1) ** odd_number == -1; 1 ** anything == 1. + return x; + } + + // For all bases >= 2, very large exponents would lead to unrepresentable + // results. + static_assert(MaxBitLength < std::numeric_limits<Digit>::max(), + "unexpectedly large MaxBitLength"); + if (y->digitLength() > 1) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_TOO_LARGE); + } + return nullptr; + } + Digit exponent = y->digit(0); + if (exponent == 1) { + return x; + } + if (exponent >= MaxBitLength) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_TOO_LARGE); + } + return nullptr; + } + + static_assert(MaxBitLength <= std::numeric_limits<int>::max(), + "unexpectedly large MaxBitLength"); + int n = static_cast<int>(exponent); + if (x->digitLength() == 1 && x->digit(0) == 2) { + // Fast path for 2^n. + int length = 1 + (n / DigitBits); + // Result is negative for odd powers of -2n. + bool resultNegative = x->isNegative() && (n & 1); + RootedBigInt result(cx, createUninitialized(cx, length, resultNegative)); + if (!result) { + return nullptr; + } + result->initializeDigitsToZero(); + result->setDigit(length - 1, static_cast<Digit>(1) << (n % DigitBits)); + return result; + } + + // This implicitly sets the result's sign correctly. + RootedBigInt result(cx, (n & 1) ? x : nullptr); + RootedBigInt runningSquare(cx, x); + for (n /= 2; n; n /= 2) { + runningSquare = mul(cx, runningSquare, runningSquare); + if (!runningSquare) { + return nullptr; + } + if (n & 1) { + if (!result) { + result = runningSquare; + } else { + result = mul(cx, result, runningSquare); + if (!result) { + return nullptr; + } + } + } + } + return result; +} + +BigInt* BigInt::lshByAbsolute(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (x->isZero() || y->isZero()) { + return x; + } + + if (y->digitLength() > 1 || y->digit(0) > MaxBitLength) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_TOO_LARGE); + } + return nullptr; + } + Digit shift = y->digit(0); + int digitShift = static_cast<int>(shift / DigitBits); + int bitsShift = static_cast<int>(shift % DigitBits); + int length = x->digitLength(); + bool grow = bitsShift && (x->digit(length - 1) >> (DigitBits - bitsShift)); + int resultLength = length + digitShift + grow; + RootedBigInt result(cx, + createUninitialized(cx, resultLength, x->isNegative())); + if (!result) { + return nullptr; + } + + int i = 0; + for (; i < digitShift; i++) { + result->setDigit(i, 0); + } + + if (bitsShift == 0) { + for (int j = 0; i < resultLength; i++, j++) { + result->setDigit(i, x->digit(j)); + } + } else { + Digit carry = 0; + for (int j = 0; j < length; i++, j++) { + Digit d = x->digit(j); + result->setDigit(i, (d << bitsShift) | carry); + carry = d >> (DigitBits - bitsShift); + } + if (grow) { + result->setDigit(i, carry); + } else { + MOZ_ASSERT(!carry); + } + } + return result; +} + +BigInt* BigInt::rshByMaximum(ExclusiveContext* cx, bool isNegative) { + if (isNegative) { + RootedBigInt negativeOne(cx, createUninitialized(cx, 1, isNegative)); + if (!negativeOne) { + return nullptr; + } + negativeOne->setDigit(0, 1); + return negativeOne; + } + return zero(cx); +} + +BigInt* BigInt::rshByAbsolute(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (x->isZero() || y->isZero()) { + return x; + } + + if (y->digitLength() > 1 || y->digit(0) >= MaxBitLength) { + return rshByMaximum(cx, x->isNegative()); + } + Digit shift = y->digit(0); + int length = x->digitLength(); + int digitShift = static_cast<int>(shift / DigitBits); + int bitsShift = static_cast<int>(shift % DigitBits); + int resultLength = length - digitShift; + if (resultLength <= 0) { + return rshByMaximum(cx, x->isNegative()); + } + // For negative numbers, round down if any bit was shifted out (so that e.g. + // -5n >> 1n == -3n and not -2n). Check now whether this will happen and + // whether it can cause overflow into a new digit. If we allocate the result + // large enough up front, it avoids having to do a second allocation later. + bool mustRoundDown = false; + if (x->isNegative()) { + const Digit mask = (static_cast<Digit>(1) << bitsShift) - 1; + if ((x->digit(digitShift) & mask)) { + mustRoundDown = true; + } else { + for (int i = 0; i < digitShift; i++) { + if (x->digit(i)) { + mustRoundDown = true; + break; + } + } + } + } + // If bits_shift is non-zero, it frees up bits, preventing overflow. + if (mustRoundDown && bitsShift == 0) { + // Overflow cannot happen if the most significant digit has unset bits. + Digit msd = x->digit(length - 1); + bool roundingCanOverflow = msd == std::numeric_limits<Digit>::max(); + if (roundingCanOverflow) { + resultLength++; + } + } + + MOZ_ASSERT(resultLength <= length); + RootedBigInt result(cx, + createUninitialized(cx, resultLength, x->isNegative())); + if (!result) { + return nullptr; + } + if (!bitsShift) { + // If roundingCanOverflow, manually initialize the overflow digit. + result->setDigit(resultLength - 1, 0); + for (int i = digitShift; i < length; i++) { + result->setDigit(i - digitShift, x->digit(i)); + } + } else { + Digit carry = x->digit(digitShift) >> bitsShift; + int last = length - digitShift - 1; + for (int i = 0; i < last; i++) { + Digit d = x->digit(i + digitShift + 1); + result->setDigit(i, (d << (DigitBits - bitsShift)) | carry); + carry = d >> bitsShift; + } + result->setDigit(last, carry); + } + + if (mustRoundDown) { + MOZ_ASSERT(x->isNegative()); + // Since the result is negative, rounding down means adding one to + // its absolute value. This cannot overflow. TODO: modify the result in + // place. + return absoluteAddOne(cx, result, x->isNegative()); + } + return destructivelyTrimHighZeroDigits(cx, result); +} + +// BigInt proposal section 1.1.9. BigInt::leftShift ( x, y ) +BigInt* BigInt::lsh(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (y->isNegative()) { + return rshByAbsolute(cx, x, y); + } + return lshByAbsolute(cx, x, y); +} + +// BigInt proposal section 1.1.10. BigInt::signedRightShift ( x, y ) +BigInt* BigInt::rsh(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (y->isNegative()) { + return lshByAbsolute(cx, x, y); + } + return rshByAbsolute(cx, x, y); +} + +// BigInt proposal section 1.1.17. BigInt::bitwiseAND ( x, y ) +BigInt* BigInt::bitAnd(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (x->isZero()) { + return x; + } + + if (y->isZero()) { + return y; + } + + if (!x->isNegative() && !y->isNegative()) { + return absoluteAnd(cx, x, y); + } + + if (x->isNegative() && y->isNegative()) { + int resultLength = std::max(x->digitLength(), y->digitLength()) + 1; + // (-x) & (-y) == ~(x-1) & ~(y-1) == ~((x-1) | (y-1)) + // == -(((x-1) | (y-1)) + 1) + RootedBigInt x1(cx, absoluteSubOne(cx, x, resultLength)); + if (!x1) { + return nullptr; + } + RootedBigInt y1(cx, absoluteSubOne(cx, y, y->digitLength())); + if (!y1) { + return nullptr; + } + RootedBigInt result(cx, absoluteOr(cx, x1, y1)); + if (!result) { + return nullptr; + } + bool resultNegative = true; + return absoluteAddOne(cx, result, resultNegative); + } + + MOZ_ASSERT(x->isNegative() != y->isNegative()); + HandleBigInt& pos = x->isNegative() ? y : x; + HandleBigInt& neg = x->isNegative() ? x : y; + + RootedBigInt neg1(cx, absoluteSubOne(cx, neg, neg->digitLength())); + if (!neg1) { + return nullptr; + } + + // x & (-y) == x & ~(y-1) == x & ~(y-1) + return absoluteAndNot(cx, pos, neg1); +} + +// BigInt proposal section 1.1.18. BigInt::bitwiseXOR ( x, y ) +BigInt* BigInt::bitXor(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (x->isZero()) { + return y; + } + + if (y->isZero()) { + return x; + } + + if (!x->isNegative() && !y->isNegative()) { + return absoluteXor(cx, x, y); + } + + if (x->isNegative() && y->isNegative()) { + int resultLength = std::max(x->digitLength(), y->digitLength()); + + // (-x) ^ (-y) == ~(x-1) ^ ~(y-1) == (x-1) ^ (y-1) + RootedBigInt x1(cx, absoluteSubOne(cx, x, resultLength)); + if (!x1) { + return nullptr; + } + RootedBigInt y1(cx, absoluteSubOne(cx, y, y->digitLength())); + if (!y1) { + return nullptr; + } + return absoluteXor(cx, x1, y1); + } + MOZ_ASSERT(x->isNegative() != y->isNegative()); + int resultLength = std::max(x->digitLength(), y->digitLength()) + 1; + + HandleBigInt& pos = x->isNegative() ? y : x; + HandleBigInt& neg = x->isNegative() ? x : y; + + // x ^ (-y) == x ^ ~(y-1) == ~(x ^ (y-1)) == -((x ^ (y-1)) + 1) + RootedBigInt result(cx, absoluteSubOne(cx, neg, resultLength)); + if (!result) { + return nullptr; + } + result = absoluteXor(cx, result, pos); + if (!result) { + return nullptr; + } + bool resultNegative = true; + return absoluteAddOne(cx, result, resultNegative); +} + +// BigInt proposal section 1.1.19. BigInt::bitwiseOR ( x, y ) +BigInt* BigInt::bitOr(ExclusiveContext* cx, HandleBigInt x, HandleBigInt y) { + if (x->isZero()) { + return y; + } + + if (y->isZero()) { + return x; + } + + unsigned resultLength = std::max(x->digitLength(), y->digitLength()); + bool resultNegative = x->isNegative() || y->isNegative(); + + if (!resultNegative) { + return absoluteOr(cx, x, y); + } + + if (x->isNegative() && y->isNegative()) { + // (-x) | (-y) == ~(x-1) | ~(y-1) == ~((x-1) & (y-1)) + // == -(((x-1) & (y-1)) + 1) + RootedBigInt result(cx, absoluteSubOne(cx, x, resultLength)); + if (!result) { + return nullptr; + } + RootedBigInt y1(cx, absoluteSubOne(cx, y, y->digitLength())); + if (!y1) { + return nullptr; + } + result = absoluteAnd(cx, result, y1); + if (!result) { + return nullptr; + } + return absoluteAddOne(cx, result, resultNegative); + } + + MOZ_ASSERT(x->isNegative() != y->isNegative()); + HandleBigInt& pos = x->isNegative() ? y : x; + HandleBigInt& neg = x->isNegative() ? x : y; + + // x | (-y) == x | ~(y-1) == ~((y-1) &~ x) == -(((y-1) &~ x) + 1) + RootedBigInt result(cx, absoluteSubOne(cx, neg, resultLength)); + if (!result) { + return nullptr; + } + result = absoluteAndNot(cx, result, pos); + if (!result) { + return nullptr; + } + return absoluteAddOne(cx, result, resultNegative); +} + +// BigInt proposal section 1.1.2. BigInt::bitwiseNOT ( x ) +BigInt* BigInt::bitNot(ExclusiveContext* cx, HandleBigInt x) { + if (x->isNegative()) { + // ~(-x) == ~(~(x-1)) == x-1 + return absoluteSubOne(cx, x, x->digitLength()); + } else { + // ~x == -x-1 == -(x+1) + bool resultNegative = true; + return absoluteAddOne(cx, x, resultNegative); + } +} + +int64_t BigInt::toInt64(BigInt* x) { return WrapToSigned(toUint64(x)); } + +uint64_t BigInt::toUint64(BigInt* x) { + if (x->isZero()) { + return 0; + } + + uint64_t digit = x->digit(0); + + if (DigitBits == 32 && x->digitLength() > 1) { + digit |= static_cast<uint64_t>(x->digit(1)) << 32; + } + + // Return the two's complement if x is negative. + if (x->isNegative()) { + return ~(digit - 1); + } + + return digit; +} + +bool BigInt::isInt64(BigInt* x, int64_t* result) { + MOZ_MAKE_MEM_UNDEFINED(result, sizeof(*result)); + + size_t length = x->digitLength(); + if (length > (DigitBits == 32 ? 2 : 1)) { + return false; + } + + if (length == 0) { + *result = 0; + return true; + } + + uint64_t magnitude = x->digit(0); + if (DigitBits == 32 && length > 1) { + magnitude |= static_cast<uint64_t>(x->digit(1)) << 32; + } + + if (x->isNegative()) { + constexpr uint64_t Int64MinMagnitude = uint64_t(1) << 63; + if (magnitude <= Int64MinMagnitude) { + *result = magnitude == Int64MinMagnitude + ? std::numeric_limits<int64_t>::min() + : -AssertedCast<int64_t>(magnitude); + return true; + } + } else { + if (magnitude <= + static_cast<uint64_t>(std::numeric_limits<int64_t>::max())) { + *result = AssertedCast<int64_t>(magnitude); + return true; + } + } + + return false; +} + +// Compute `2**bits - (x & (2**bits - 1))`. Used when treating BigInt values as +// arbitrary-precision two's complement signed integers. +BigInt* BigInt::truncateAndSubFromPowerOfTwo(ExclusiveContext* cx, HandleBigInt x, + uint64_t bits, + bool resultNegative) { + MOZ_ASSERT(bits != 0); + MOZ_ASSERT(!x->isZero()); + + size_t resultLength = CeilDiv(bits, DigitBits); + RootedBigInt result(cx, + createUninitialized(cx, resultLength, resultNegative)); + if (!result) { + return nullptr; + } + + // Process all digits except the MSD. + size_t xLength = x->digitLength(); + Digit borrow = 0; + // Take digits from `x` until its length is exhausted. + for (size_t i = 0; i < std::min(resultLength - 1, xLength); i++) { + Digit newBorrow = 0; + Digit difference = digitSub(0, x->digit(i), &newBorrow); + difference = digitSub(difference, borrow, &newBorrow); + result->setDigit(i, difference); + borrow = newBorrow; + } + // Then simulate leading zeroes in `x` as needed. + for (size_t i = xLength; i < resultLength - 1; i++) { + Digit newBorrow = 0; + Digit difference = digitSub(0, borrow, &newBorrow); + result->setDigit(i, difference); + borrow = newBorrow; + } + + // The MSD might contain extra bits that we don't want. + Digit xMSD = resultLength <= xLength ? x->digit(resultLength - 1) : 0; + Digit resultMSD; + if (bits % DigitBits == 0) { + Digit newBorrow = 0; + resultMSD = digitSub(0, xMSD, &newBorrow); + resultMSD = digitSub(resultMSD, borrow, &newBorrow); + } else { + size_t drop = DigitBits - (bits % DigitBits); + xMSD = (xMSD << drop) >> drop; + Digit minuendMSD = Digit(1) << (DigitBits - drop); + Digit newBorrow = 0; + resultMSD = digitSub(minuendMSD, xMSD, &newBorrow); + resultMSD = digitSub(resultMSD, borrow, &newBorrow); + MOZ_ASSERT(newBorrow == 0, "result < 2^bits"); + // If all subtracted bits were zero, we have to get rid of the + // materialized minuendMSD again. + resultMSD &= (minuendMSD - 1); + } + result->setDigit(resultLength - 1, resultMSD); + + return trimHighZeroDigits(cx, result); +} + +BigInt* BigInt::asUintN(ExclusiveContext* cx, HandleBigInt x, uint64_t bits) { + if (x->isZero()) { + return x; + } + + if (bits == 0) { + return zero(cx); + } + + // When truncating a negative number, simulate two's complement. + if (x->isNegative()) { + bool resultNegative = false; + return truncateAndSubFromPowerOfTwo(cx, x, bits, resultNegative); + } + + if (bits <= 64) { + uint64_t u64 = toUint64(x); + uint64_t mask = uint64_t(-1) >> (64 - bits); + return createFromUint64(cx, u64 & mask); + } + + if (bits >= MaxBitLength) { + return x; + } + + Digit msd = x->digit(x->digitLength() - 1); + size_t msdBits = DigitBits - DigitLeadingZeroes(msd); + size_t bitLength = msdBits + (x->digitLength() - 1) * DigitBits; + + if (bits >= bitLength) { + return x; + } + + size_t length = CeilDiv(bits, DigitBits); + bool isNegative = false; + + BigInt* res = createUninitialized(cx, length, isNegative); + if (!res) { + return nullptr; + } + + MOZ_ASSERT(length >= 2, "single-digit cases should be handled above"); + MOZ_ASSERT(length <= x->digitLength()); + for (size_t i = 0; i < length - 1; i++) { + res->setDigit(i, x->digit(i)); + } + + Digit mask = Digit(-1) >> (DigitBits - (bits % DigitBits)); + res->setDigit(length - 1, x->digit(length - 1) & mask); + + return res; +} + +BigInt* BigInt::asIntN(ExclusiveContext* cx, HandleBigInt x, uint64_t bits) { + if (x->isZero()) { + return x; + } + + if (bits == 0) { + return zero(cx); + } + + if (bits == 64) { + return createFromInt64(cx, toInt64(x)); + } + + if (bits > MaxBitLength) { + return x; + } + + Digit msd = x->digit(x->digitLength() - 1); + size_t msdBits = DigitBits - DigitLeadingZeroes(msd); + size_t bitLength = msdBits + (x->digitLength() - 1) * DigitBits; + + if (bits > bitLength) { + return x; + } + + Digit signBit = Digit(1) << ((bits - 1) % DigitBits); + if (bits == bitLength && msd < signBit) { + return x; + } + + // All the cases above were the trivial cases: truncating zero, or to zero + // bits, or to more bits than are in `x` (so we return `x` directly), or we + // already have the 64-bit fast path. If we get here, follow the textbook + // algorithm from the specification. + + // BigInt.asIntN step 3: Let `mod` be `x` modulo `2**bits`. + RootedBigInt mod(cx, asUintN(cx, x, bits)); + if (!mod) { + return nullptr; + } + + // Step 4: If `mod >= 2**(bits - 1)`, return `mod - 2**bits`; otherwise, + // return `mod`. + if (mod->digitLength() == CeilDiv(bits, DigitBits) && + (mod->digit(mod->digitLength() - 1) & signBit) != 0) { + bool resultNegative = true; + return truncateAndSubFromPowerOfTwo(cx, mod, bits, resultNegative); + } + + return mod; +} + +static bool ValidBigIntOperands(ExclusiveContext* cx, HandleValue lhs, + HandleValue rhs) { + MOZ_ASSERT(lhs.isBigInt() || rhs.isBigInt()); + + if (!lhs.isBigInt() || !rhs.isBigInt()) { + if (cx->isJSContext()) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_TO_NUMBER); + } + return false; + } + + return true; +} + +bool BigInt::add(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::add(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::sub(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::sub(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::mul(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::mul(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::div(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::div(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::mod(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::mod(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::pow(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::pow(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::neg(ExclusiveContext* cx, HandleValue operand, MutableHandleValue res) { + MOZ_ASSERT(operand.isBigInt()); + + RootedBigInt operandBigInt(cx, operand.toBigInt()); + BigInt* resBigInt = BigInt::neg(cx, operandBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::lsh(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::lsh(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::rsh(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::rsh(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::bitAnd(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::bitAnd(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::bitXor(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::bitXor(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::bitOr(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + MutableHandleValue res) { + if (!ValidBigIntOperands(cx, lhs, rhs)) { + return false; + } + + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + BigInt* resBigInt = BigInt::bitOr(cx, lhsBigInt, rhsBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +bool BigInt::bitNot(ExclusiveContext* cx, HandleValue operand, + MutableHandleValue res) { + MOZ_ASSERT(operand.isBigInt()); + + RootedBigInt operandBigInt(cx, operand.toBigInt()); + BigInt* resBigInt = BigInt::bitNot(cx, operandBigInt); + if (!resBigInt) { + return false; + } + res.setBigInt(resBigInt); + return true; +} + +// BigInt proposal section 7.3 +BigInt* js::ToBigInt(ExclusiveContext* cx, HandleValue val) { + RootedValue v(cx, val); + + if(cx->isJSContext()) { + // Step 1. + if (!ToPrimitive(cx->asJSContext(), JSTYPE_NUMBER, &v)) { + return nullptr; + } + + // Step 2. + if (v.isBigInt()) { + return v.toBigInt(); + } + + if (v.isBoolean()) { + return v.toBoolean() ? BigInt::one(cx) : BigInt::zero(cx); + } + + if (v.isString()) { + BigInt* bi = nullptr; + RootedString str(cx, v.toString()); + JS_TRY_VAR_OR_RETURN_NULL(cx, bi, StringToBigInt(cx, str)); + if (!bi) { + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, + JSMSG_BIGINT_INVALID_SYNTAX); + return nullptr; + } + return bi; + } + + JS_ReportErrorNumberASCII(cx->asJSContext(), GetErrorMessage, nullptr, JSMSG_NOT_BIGINT); + } + return nullptr; +} + +JS::Result<int64_t> js::ToBigInt64(JSContext* cx, HandleValue v) { + BigInt* bi = ToBigInt(cx, v); + if (!bi) { + return cx->alreadyReportedError(); + } + return BigInt::toInt64(bi); +} + +JS::Result<uint64_t> js::ToBigUint64(JSContext* cx, HandleValue v) { + BigInt* bi = ToBigInt(cx, v); + if (!bi) { + return cx->alreadyReportedError(); + } + return BigInt::toUint64(bi); +} + +double BigInt::numberValue(BigInt* x) { + if (x->isZero()) { + return 0.0; + } + + using Double = mozilla::FloatingPoint<double>; + constexpr uint8_t ExponentShift = Double::kExponentShift; + constexpr uint8_t SignificandWidth = Double::kSignificandWidth; + constexpr unsigned ExponentBias = Double::kExponentBias; + constexpr uint8_t SignShift = Double::kExponentWidth + SignificandWidth; + + size_t length = x->digitLength(); + MOZ_ASSERT(length != 0); + + // Fast path for the likely-common case of up to a uint64_t of magnitude + // that doesn't exceed integral precision in IEEE-754. + if (length <= 64 / DigitBits) { + uint64_t magnitude = x->digit(0); + if (DigitBits == 32 && length > 1) { + magnitude |= static_cast<uint64_t>(x->digit(1)) << 32; + } + const uint64_t MaxIntegralPrecisionDouble = uint64_t(1) + << (SignificandWidth + 1); + if (magnitude <= MaxIntegralPrecisionDouble) { + return x->isNegative() ? -double(magnitude) : +double(magnitude); + } + } + + Digit msd = x->digit(length - 1); + uint8_t msdLeadingZeroes = DigitLeadingZeroes(msd); + + // `2**ExponentBias` is the largest power of two in a finite IEEE-754 + // double. If this bigint has a greater power of two, it'll round to + // infinity. + uint64_t exponent = length * DigitBits - msdLeadingZeroes - 1; + if (exponent > ExponentBias) { + return x->isNegative() ? mozilla::NegativeInfinity<double>() + : mozilla::PositiveInfinity<double>(); + } + + // Otherwise munge the most significant bits of the number into proper + // position in an IEEE-754 double and go to town. + + // Omit the most significant bit: the IEEE-754 format includes this bit + // implicitly for all double-precision integers. + const uint8_t msdIgnoredBits = msdLeadingZeroes + 1; + const uint8_t msdIncludedBits = DigitBits - msdIgnoredBits; + + uint8_t bitsFilled = msdIncludedBits; + + // Shift `msd`'s contributed bits upward to remove high-order zeroes and + // the highest set bit (which is implicit in IEEE-754 integral values so + // must be removed) and to add low-order zeroes. + uint64_t shiftedMantissa = + msdIncludedBits == 0 ? 0 : uint64_t(msd) << (64 - msdIncludedBits); + + // Add in bits from the next one or two digits if `msd` didn't contain all + // bits necessary to define the result. (The extra bit allows us to + // properly round an inexact overall result.) Any lower bits that are + // uselessly set will be shifted away when `shiftedMantissa` is converted to + // a real mantissa. + if (bitsFilled < SignificandWidth + 1) { + MOZ_ASSERT(length >= 2, + "single-Digit numbers with this few bits should have been " + "handled by the fast-path above"); + + Digit second = x->digit(length - 2); + if (DigitBits == 32) { + shiftedMantissa |= uint64_t(second) << msdIgnoredBits; + bitsFilled += DigitBits; + + // Add in bits from another digit, if any, if we still have unfilled + // significand bits. + if (bitsFilled < SignificandWidth + 1 && length >= 3) { + Digit third = x->digit(length - 3); + shiftedMantissa |= uint64_t(third) >> msdIncludedBits; + // The second and third 32-bit digits contributed 64 bits total, filling + // well beyond the mantissa. + bitsFilled = 64; + } + } else { + shiftedMantissa |= second >> msdIncludedBits; + // A full 64-bit digit's worth of bits (some from the most significant + // digit, the rest from the next) fills well beyond the mantissa. + bitsFilled = 64; + } + } + + // Round the overall result, if necessary. (It's possible we don't need to + // round -- the number might not have enough bits to round.) + if (bitsFilled >= SignificandWidth + 1) { + constexpr uint64_t LeastSignificantBit = uint64_t(1) + << (64 - SignificandWidth); + constexpr uint64_t ExtraBit = LeastSignificantBit >> 1; + + // When the first bit outside the significand is set, the overall value + // is rounded: downward (i.e. no change to the bits) if the least + // significant bit in the significand is zero, upward if it instead is + // one. + if ((shiftedMantissa & ExtraBit) && + (shiftedMantissa & LeastSignificantBit)) { + // We're rounding upward: add to the significand bits. If they + // overflow, the exponent must also be increased. If *that* + // overflows, return the appropriate infinity. + uint64_t before = shiftedMantissa; + shiftedMantissa += ExtraBit; + if (shiftedMantissa < before) { + exponent++; + if (exponent > ExponentBias) { + return x->isNegative() ? NegativeInfinity<double>() + : PositiveInfinity<double>(); + } + } + } + } + + uint64_t significandBits = shiftedMantissa >> (64 - SignificandWidth); + uint64_t signBit = uint64_t(x->isNegative() ? 1 : 0) << SignShift; + uint64_t exponentBits = (exponent + ExponentBias) << ExponentShift; + return mozilla::BitwiseCast<double>(signBit | exponentBits | significandBits); +} + +int8_t BigInt::compare(BigInt* x, BigInt* y) { + // Sanity checks to catch negative zeroes escaping to the wild. + MOZ_ASSERT(!x->isNegative() || !x->isZero()); + MOZ_ASSERT(!y->isNegative() || !y->isZero()); + + bool xSign = x->isNegative(); + + if (xSign != y->isNegative()) { + return xSign ? -1 : 1; + } + + if (xSign) { + mozilla::Swap(x, y); + } + + return absoluteCompare(x, y); +} + +bool BigInt::equal(BigInt* lhs, BigInt* rhs) { + if (lhs == rhs) { + return true; + } + if (lhs->digitLength() != rhs->digitLength()) { + return false; + } + if (lhs->isNegative() != rhs->isNegative()) { + return false; + } + for (size_t i = 0; i < lhs->digitLength(); i++) { + if (lhs->digit(i) != rhs->digit(i)) { + return false; + } + } + return true; +} + +int8_t BigInt::compare(BigInt* x, double y) { + MOZ_ASSERT(!mozilla::IsNaN(y)); + + constexpr int LessThan = -1, Equal = 0, GreaterThan = 1; + + // ±Infinity exceeds a finite bigint value. + if (!mozilla::IsFinite(y)) { + return y > 0 ? LessThan : GreaterThan; + } + + // Handle `x === 0n` and `y == 0` special cases. + if (x->isZero()) { + if (y == 0) { + // -0 and +0 are treated identically. + return Equal; + } + + return y > 0 ? LessThan : GreaterThan; + } + + const bool xNegative = x->isNegative(); + if (y == 0) { + return xNegative ? LessThan : GreaterThan; + } + + // Nonzero `x` and `y` with different signs are trivially compared. + const bool yNegative = y < 0; + if (xNegative != yNegative) { + return xNegative ? LessThan : GreaterThan; + } + + // `x` and `y` are same-signed. Determine which has greater magnitude, + // then combine that with the signedness just computed to reach a result. + const int exponent = mozilla::ExponentComponent(y); + if (exponent < 0) { + // `y` is a nonzero fraction of magnitude less than 1. + return xNegative ? LessThan : GreaterThan; + } + + size_t xLength = x->digitLength(); + MOZ_ASSERT(xLength > 0); + + Digit xMSD = x->digit(xLength - 1); + const int shift = DigitLeadingZeroes(xMSD); + int xBitLength = xLength * DigitBits - shift; + + // Differing bit-length makes for a simple comparison. + int yBitLength = exponent + 1; + if (xBitLength < yBitLength) { + return xNegative ? GreaterThan : LessThan; + } + if (xBitLength > yBitLength) { + return xNegative ? LessThan : GreaterThan; + } + + // Compare the high 64 bits of both numbers. (Lower-order bits not present + // in either number are zeroed.) Either that distinguishes `x` and `y`, or + // `x` and `y` differ only if a subsequent nonzero bit in `x` means `x` has + // larger magnitude. + + using Double = mozilla::FloatingPoint<double>; + constexpr uint8_t SignificandWidth = Double::kSignificandWidth; + constexpr uint64_t SignificandBits = Double::kSignificandBits; + + const uint64_t doubleBits = mozilla::BitwiseCast<uint64_t>(y); + const uint64_t significandBits = doubleBits & SignificandBits; + + // Readd the implicit-one bit when constructing `y`'s high 64 bits. + const uint64_t yHigh64Bits = + ((uint64_t(1) << SignificandWidth) | significandBits) + << (64 - SignificandWidth - 1); + + // Cons up `x`'s high 64 bits, backfilling zeroes for binary fractions of 1 + // if `x` doesn't have 64 bits. + uint8_t xBitsFilled = DigitBits - shift; + uint64_t xHigh64Bits = uint64_t(xMSD) << (64 - xBitsFilled); + + // At this point we no longer need to look at the most significant digit. + xLength--; + + // The high 64 bits from `x` will probably not align to a digit boundary. + // `xHasNonZeroLeftoverBits` will be set to true if any remaining + // least-significant bit from the digit holding xHigh64Bits's + // least-significant bit is nonzero. + bool xHasNonZeroLeftoverBits = false; + + if (xBitsFilled < std::min(xBitLength, 64)) { + MOZ_ASSERT(xLength >= 1, + "If there are more bits to fill, there should be " + "more digits to fill them from"); + + Digit second = x->digit(--xLength); + if (DigitBits == 32) { + xBitsFilled += 32; + xHigh64Bits |= uint64_t(second) << (64 - xBitsFilled); + if (xBitsFilled < 64 && xLength >= 1) { + Digit third = x->digit(--xLength); + const uint8_t neededBits = 64 - xBitsFilled; + xHigh64Bits |= uint64_t(third) >> (DigitBits - neededBits); + xHasNonZeroLeftoverBits = (third << neededBits) != 0; + } + } else { + const uint8_t neededBits = 64 - xBitsFilled; + xHigh64Bits |= uint64_t(second) >> (DigitBits - neededBits); + xHasNonZeroLeftoverBits = (second << neededBits) != 0; + } + } + + // If high bits are unequal, the larger one has greater magnitude. + if (yHigh64Bits > xHigh64Bits) { + return xNegative ? GreaterThan : LessThan; + } + if (xHigh64Bits > yHigh64Bits) { + return xNegative ? LessThan : GreaterThan; + } + + // Otherwise the top 64 bits of both are equal. If the values differ, a + // lower-order bit in `x` is nonzero and `x` has greater magnitude than + // `y`; otherwise `x == y`. + if (xHasNonZeroLeftoverBits) { + return xNegative ? LessThan : GreaterThan; + } + while (xLength != 0) { + if (x->digit(--xLength) != 0) { + return xNegative ? LessThan : GreaterThan; + } + } + + return Equal; +} + +bool BigInt::equal(BigInt* lhs, double rhs) { + if (mozilla::IsNaN(rhs)) { + return false; + } + return compare(lhs, rhs) == 0; +} + +// BigInt proposal section 3.2.5 +JS::Result<bool> BigInt::looselyEqual(ExclusiveContext* cx, HandleBigInt lhs, + HandleValue rhs) { + // Step 1. + if (rhs.isBigInt()) { + return equal(lhs, rhs.toBigInt()); + } + + // Steps 2-5 (not applicable). + + // Steps 6-7. + if (rhs.isString()) { + RootedBigInt rhsBigInt(cx); + RootedString rhsString(cx, rhs.toString()); + MOZ_TRY_VAR(rhsBigInt, StringToBigInt(cx, rhsString)); + if (!rhsBigInt) { + return false; + } + return equal(lhs, rhsBigInt); + } + + // Steps 8-9 (not applicable). + + // Steps 10-11. + if (rhs.isObject()) { + RootedValue rhsPrimitive(cx, rhs); + if (!cx->isJSContext() || !ToPrimitive(cx->asJSContext(), &rhsPrimitive)) { + return cx->alreadyReportedError(); + } + return looselyEqual(cx, lhs, rhsPrimitive); + } + + // Step 12. + if (rhs.isNumber()) { + return equal(lhs, rhs.toNumber()); + } + + // Step 13. + return false; +} + +// BigInt proposal section 1.1.12. BigInt::lessThan ( x, y ) +bool BigInt::lessThan(BigInt* x, BigInt* y) { return compare(x, y) < 0; } + +Maybe<bool> BigInt::lessThan(BigInt* lhs, double rhs) { + if (mozilla::IsNaN(rhs)) { + return Maybe<bool>(Nothing()); + } + return Some(compare(lhs, rhs) < 0); +} + +Maybe<bool> BigInt::lessThan(double lhs, BigInt* rhs) { + if (mozilla::IsNaN(lhs)) { + return Maybe<bool>(Nothing()); + } + return Some(-compare(rhs, lhs) < 0); +} + +bool BigInt::lessThan(ExclusiveContext* cx, HandleBigInt lhs, HandleString rhs, + Maybe<bool>& res) { + RootedBigInt rhsBigInt(cx); + JS_TRY_VAR_OR_RETURN_FALSE(cx, rhsBigInt, StringToBigInt(cx, rhs)); + if (!rhsBigInt) { + res = Nothing(); + return true; + } + res = Some(lessThan(lhs, rhsBigInt)); + return true; +} + +bool BigInt::lessThan(ExclusiveContext* cx, HandleString lhs, HandleBigInt rhs, + Maybe<bool>& res) { + RootedBigInt lhsBigInt(cx); + JS_TRY_VAR_OR_RETURN_FALSE(cx, lhsBigInt, StringToBigInt(cx, lhs)); + if (!lhsBigInt) { + res = Nothing(); + return true; + } + res = Some(lessThan(lhsBigInt, rhs)); + return true; +} + +bool BigInt::lessThan(ExclusiveContext* cx, HandleValue lhs, HandleValue rhs, + Maybe<bool>& res) { + if (lhs.isBigInt()) { + if (rhs.isString()) { + RootedBigInt lhsBigInt(cx, lhs.toBigInt()); + RootedString rhsString(cx, rhs.toString()); + return lessThan(cx, lhsBigInt, rhsString, res); + } + + if (rhs.isNumber()) { + res = lessThan(lhs.toBigInt(), rhs.toNumber()); + return true; + } + + MOZ_ASSERT(rhs.isBigInt()); + res = Some(lessThan(lhs.toBigInt(), rhs.toBigInt())); + return true; + } + + MOZ_ASSERT(rhs.isBigInt()); + if (lhs.isString()) { + RootedString lhsString(cx, lhs.toString()); + RootedBigInt rhsBigInt(cx, rhs.toBigInt()); + return lessThan(cx, lhsString, rhsBigInt, res); + } + + MOZ_ASSERT(lhs.isNumber()); + res = lessThan(lhs.toNumber(), rhs.toBigInt()); + return true; +} + +JSLinearString* BigInt::toString(ExclusiveContext* cx, HandleBigInt x, uint8_t radix) { + MOZ_ASSERT(2 <= radix && radix <= 36); + + if (x->isZero()) { + return cx->staticStrings().getInt(0); + } + + if (mozilla::IsPowerOfTwo(radix)) { + return toStringBasePowerOfTwo(cx, x, radix); + } + + return toStringGeneric(cx, x, radix); +} + +template <typename CharT> +static inline BigInt* ParseStringBigIntLiteral(ExclusiveContext* cx, + Range<const CharT> range, + bool* haveParseError) { + auto start = range.begin(); + auto end = range.end(); + + while (start < end && unicode::IsSpace(start[0])) { + start++; + } + + while (start < end && unicode::IsSpace(end[-1])) { + end--; + } + + if (start == end) { + return BigInt::zero(cx); + } + + // StringNumericLiteral ::: StrDecimalLiteral, but without Infinity, decimal + // points, or exponents. Note that the raw '+' or '-' cases fall through + // because the string is too short, and eventually signal a parse error. + if (end - start > 1) { + if (start[0] == '+') { + bool isNegative = false; + start++; + return BigInt::parseLiteralDigits(cx, Range<const CharT>(start, end), 10, + isNegative, haveParseError); + } else if (start[0] == '-') { + bool isNegative = true; + start++; + return BigInt::parseLiteralDigits(cx, Range<const CharT>(start, end), 10, + isNegative, haveParseError); + } + } + + return BigInt::parseLiteral(cx, Range<const CharT>(start, end), + haveParseError); +} + +// Called from BigInt constructor. +JS::Result<BigInt*, JS::OOM&> js::StringToBigInt(ExclusiveContext* cx, + HandleString str) { + JSLinearString* linear = str->ensureLinear(cx); + if (!linear) { + return cx->alreadyReportedOOM(); + } + + BigInt* res = nullptr; + bool parseError = false; + + if(cx->isJSContext()) { + AutoStableStringChars chars(cx->asJSContext()); + if (!chars.init(cx->asJSContext(), str)) { + return cx->alreadyReportedOOM(); + } + + if (chars.isLatin1()) { + res = ParseStringBigIntLiteral(cx->asJSContext(), chars.latin1Range(), &parseError); + } else { + res = ParseStringBigIntLiteral(cx->asJSContext(), chars.twoByteRange(), &parseError); + } + } + + // A nullptr result can indicate either a parse error or out-of-memory. + if (!res && !parseError) { + return cx->alreadyReportedOOM(); + } + + return res; +} + +// Called from parser with already trimmed and validated token. +BigInt* js::ParseBigIntLiteral(ExclusiveContext* cx, + const Range<const char16_t>& chars) { + bool parseError = false; + BigInt* res = BigInt::parseLiteral(cx, chars, &parseError); + if (!res) { + return nullptr; + } + MOZ_RELEASE_ASSERT(!parseError); + return res; +} + +JSAtom* js::BigIntToAtom(ExclusiveContext* cx, HandleBigInt bi) { + JSString* str = BigInt::toString(cx, bi, 10); + if (!str) { + return nullptr; + } + return AtomizeString(cx, str); +} + +JS::ubi::Node::Size JS::ubi::Concrete<BigInt>::size( + mozilla::MallocSizeOf mallocSizeOf) const { + BigInt& bi = get(); + MOZ_ASSERT(bi.isTenured()); + size_t size = js::gc::Arena::thingSize(bi.asTenured().getAllocKind()); + size += bi.sizeOfExcludingThis(mallocSizeOf); + return size; +} + +template <XDRMode mode> +bool js::XDRBigInt(XDRState<mode>* xdr, MutableHandleBigInt bi) { + ExclusiveContext* cx = xdr->cx(); + + uint8_t sign; + uint32_t length; + + if (mode == XDR_ENCODE) { + sign = static_cast<uint8_t>(bi->isNegative()); + uint64_t sz = bi->digitLength() * sizeof(BigInt::Digit); + // As the maximum source code size is currently UINT32_MAX code units + // (see BytecodeCompiler::checkLength), any bigint literal's length in + // word-sized digits will be less than UINT32_MAX as well. That could + // change or FoldConstants could start creating these though, so leave + // this as a release-enabled assert. + MOZ_RELEASE_ASSERT(sz <= UINT32_MAX); + length = static_cast<uint32_t>(sz); + } + + if(!xdr->codeUint8(&sign)) + return false; + if(!xdr->codeUint32(&length)) + return false; + + MOZ_RELEASE_ASSERT(length % sizeof(BigInt::Digit) == 0); + uint32_t digitLength = length / sizeof(BigInt::Digit); + auto buf = cx->make_pod_array<BigInt::Digit>(digitLength); + if (!buf) { + return xdr->fail(JS::TranscodeResult_Throw); + } + + if (mode == XDR_ENCODE) { + std::uninitialized_copy_n(bi->digits().Elements(), digitLength, buf.get()); + } + + if(!xdr->codeBytes(buf.get(), length)) + return false; + + if (mode == XDR_DECODE) { + BigInt* res = BigInt::createUninitialized(cx, digitLength, sign); + if (!res) { + return xdr->fail(JS::TranscodeResult_Throw); + } + std::uninitialized_copy_n(buf.get(), digitLength, bi->digits().Elements()); + bi.set(res); + } + + return true; +} + +template bool js::XDRBigInt(XDRState<XDR_ENCODE>* xdr, MutableHandleBigInt bi); + +template bool js::XDRBigInt(XDRState<XDR_DECODE>* xdr, MutableHandleBigInt bi); + |