Régis Crelier
ba75b6939d
Change-Id: I60e7e34559d11d80fde7955dec98b21b7029e199 Reviewed-on: https://dart-review.googlesource.com/40962 Commit-Queue: Régis Crelier <regis@google.com> Reviewed-by: Alexander Markov <alexmarkov@google.com>
2123 lines
70 KiB
Dart
2123 lines
70 KiB
Dart
// Copyright (c) 2017, the Dart project authors. Please see the AUTHORS file
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// for details. All rights reserved. Use of this source code is governed by a
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// BSD-style license that can be found in the LICENSE file.
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// part of dart.core;
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// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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/*
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* Copyright (c) 2003-2005 Tom Wu
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* Copyright (c) 2012 Adam Singer (adam@solvr.io)
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* All Rights Reserved.
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*
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
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* WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
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*
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* IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
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* INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
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* RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
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* THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
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* OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*
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* In addition, the following condition applies:
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*
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* All redistributions must retain an intact copy of this copyright notice
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* and disclaimer.
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*/
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@patch
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class BigInt implements Comparable<BigInt> {
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@patch
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static BigInt get zero => _BigIntImpl.zero;
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@patch
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static BigInt get one => _BigIntImpl.one;
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@patch
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static BigInt get two => _BigIntImpl.two;
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@patch
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static BigInt parse(String source, {int radix}) =>
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_BigIntImpl.parse(source, radix: radix);
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@patch
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factory BigInt.from(num value) => new _BigIntImpl.from(value);
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}
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int _max(int a, int b) => a > b ? a : b;
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int _min(int a, int b) => a < b ? a : b;
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/**
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* An implementation for the arbitrarily large integer.
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*
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* The integer number is represented by a sign, an array of 16-bit unsigned
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* integers in little endian format, and a number of used digits in that array.
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*/
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class _BigIntImpl implements BigInt {
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// Bits per digit.
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static const int _digitBits = 32;
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static const int _digitBase = 1 << _digitBits;
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static const int _digitMask = (1 << _digitBits) - 1;
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// Bits per half digit.
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static const int _halfDigitBits = _digitBits >> 1;
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static const int _halfDigitMask = (1 << _halfDigitBits) - 1;
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static final _BigIntImpl zero = new _BigIntImpl._fromInt(0);
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static final _BigIntImpl one = new _BigIntImpl._fromInt(1);
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static final _BigIntImpl two = new _BigIntImpl._fromInt(2);
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static final _BigIntImpl _minusOne = -one;
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static final _BigIntImpl _oneBillion = new _BigIntImpl._fromInt(1000000000);
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static const int _minInt = -0x8000000000000000;
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static const int _maxInt = 0x7fffffffffffffff;
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// Result cache for last _divRem call.
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// Result cache for last _divRem call.
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static Uint32List _lastDividendDigits;
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static int _lastDividendUsed;
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static Uint32List _lastDivisorDigits;
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static int _lastDivisorUsed;
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static Uint32List _lastQuoRemDigits;
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static int _lastQuoRemUsed;
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static int _lastRemUsed;
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static int _lastRem_nsh;
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/// Whether this bigint is negative.
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final bool _isNegative;
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/// The unsigned digits of this bigint.
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///
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/// The least significant digit is in slot 0.
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/// The list may have more digits than needed. That is, `_digits.length` may
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/// be strictly greater than `_used`.
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final Uint32List _digits;
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/// The number of used entries in [_digits].
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///
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/// To avoid reallocating [Uint32List]s, lists that are too big are not
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/// replaced.
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final int _used;
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/**
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* Parses [source] as a, possibly signed, integer literal and returns its
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* value.
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*
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* The [source] must be a non-empty sequence of base-[radix] digits,
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* optionally prefixed with a minus or plus sign ('-' or '+').
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*
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* The [radix] must be in the range 2..36. The digits used are
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* first the decimal digits 0..9, and then the letters 'a'..'z' with
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* values 10 through 35. Also accepts upper-case letters with the same
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* values as the lower-case ones.
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*
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* If no [radix] is given then it defaults to 10. In this case, the [source]
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* digits may also start with `0x`, in which case the number is interpreted
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* as a hexadecimal literal, which effectively means that the `0x` is ignored
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* and the radix is instead set to 16.
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*
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* For any int `n` and radix `r`, it is guaranteed that
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* `n == int.parse(n.toRadixString(r), radix: r)`.
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*
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* Throws a [FormatException] if the [source] is not a valid integer literal,
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* optionally prefixed by a sign.
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*/
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static _BigIntImpl parse(String source, {int radix}) {
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var result = _tryParse(source, radix: radix);
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if (result == null) {
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throw new FormatException("Could not parse BigInt", source);
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}
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return result;
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}
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/// Parses a decimal bigint literal.
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///
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/// The [source] must not contain leading or trailing whitespace.
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static _BigIntImpl _parseDecimal(String source, bool isNegative) {
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const _0 = 48;
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int part = 0;
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_BigIntImpl result = zero;
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// Read in the source 9 digits at a time.
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// The first part may have a few leading virtual '0's to make the remaining
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// parts all have exactly 9 digits.
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int digitInPartCount = 9 - source.length.remainder(9);
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if (digitInPartCount == 9) digitInPartCount = 0;
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for (int i = 0; i < source.length; i++) {
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part = part * 10 + source.codeUnitAt(i) - _0;
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if (++digitInPartCount == 9) {
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result = result * _oneBillion + new _BigIntImpl._fromInt(part);
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part = 0;
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digitInPartCount = 0;
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}
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}
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if (isNegative) return -result;
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return result;
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}
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/// Returns the value of a given source digit.
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///
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/// Source digits between "0" and "9" (inclusive) return their decimal value.
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///
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/// Source digits between "a" and "z", or "A" and "Z" (inclusive) return
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/// 10 + their position in the ASCII alphabet.
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///
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/// The incoming [codeUnit] must be an ASCII code-unit.
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static int _codeUnitToRadixValue(int codeUnit) {
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// We know that the characters must be ASCII as otherwise the
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// regexp wouldn't have matched. Lowercasing by doing `| 0x20` is thus
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// guaranteed to be a safe operation, since it preserves digits
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// and lower-cases ASCII letters.
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const int _0 = 48;
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const int _9 = 57;
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const int _a = 97;
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if (_0 <= codeUnit && codeUnit <= _9) return codeUnit - _0;
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codeUnit |= 0x20;
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var result = codeUnit - _a + 10;
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return result;
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}
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/// Parses the given [source] string, starting at [startPos], as a hex
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/// literal.
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///
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/// If [isNegative] is true, negates the result before returning it.
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///
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/// The [source] (substring) must be a valid hex literal.
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static _BigIntImpl _parseHex(String source, int startPos, bool isNegative) {
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int hexDigitsPerChunk = _digitBits ~/ 4;
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int sourceLength = source.length - startPos;
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int chunkCount =
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(sourceLength + hexDigitsPerChunk - 1) ~/ hexDigitsPerChunk;
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var digits = new Uint32List(chunkCount);
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int lastDigitLength = sourceLength - (chunkCount - 1) * hexDigitsPerChunk;
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int digitIndex = digits.length - 1;
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int i = startPos;
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int chunk = 0;
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for (int j = 0; j < lastDigitLength; j++) {
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var digitValue = _codeUnitToRadixValue(source.codeUnitAt(i++));
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if (digitValue >= 16) return null;
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chunk = chunk * 16 + digitValue;
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}
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digits[digitIndex--] = chunk;
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while (i < source.length) {
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chunk = 0;
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for (int j = 0; j < hexDigitsPerChunk; j++) {
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var digitValue = _codeUnitToRadixValue(source.codeUnitAt(i++));
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if (digitValue >= 16) return null;
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chunk = chunk * 16 + digitValue;
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}
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digits[digitIndex--] = chunk;
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}
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if (digits.length == 1 && digits[0] == 0) return zero;
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return new _BigIntImpl._(isNegative, digits.length, digits);
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}
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/// Parses the given [source] as a [radix] literal.
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///
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/// The [source] will be checked for invalid characters. If it is invalid,
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/// this function returns `null`.
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static _BigIntImpl _parseRadix(String source, int radix, bool isNegative) {
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var result = zero;
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var base = new _BigIntImpl._fromInt(radix);
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for (int i = 0; i < source.length; i++) {
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var digitValue = _codeUnitToRadixValue(source.codeUnitAt(i));
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if (digitValue >= radix) return null;
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result = result * base + new _BigIntImpl._fromInt(digitValue);
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}
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if (isNegative) return -result;
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return result;
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}
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/// Tries to parse the given [source] as a [radix] literal.
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///
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/// Returns the parsed big integer, or `null` if it failed.
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///
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/// If the [radix] is `null` accepts decimal literals or `0x` hex literals.
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static _BigIntImpl _tryParse(String source, {int radix}) {
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if (source == "") return null;
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var re = new RegExp(r'^\s*([+-]?)((0x[a-f0-9]+)|(\d+)|([a-z0-9]+))\s*$',
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caseSensitive: false);
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var match = re.firstMatch(source);
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int signIndex = 1;
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int hexIndex = 3;
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int decimalIndex = 4;
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int nonDecimalHexIndex = 5;
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if (match == null) return null;
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bool isNegative = match[signIndex] == "-";
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String decimalMatch = match[decimalIndex];
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String hexMatch = match[hexIndex];
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String nonDecimalMatch = match[nonDecimalHexIndex];
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if (radix == null) {
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if (decimalMatch != null) {
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// Cannot fail because we know that the digits are all decimal.
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return _parseDecimal(decimalMatch, isNegative);
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}
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if (hexMatch != null) {
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// Cannot fail because we know that the digits are all hex.
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return _parseHex(hexMatch, 2, isNegative);
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}
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return null;
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}
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if (radix is! int) {
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throw new ArgumentError.value(radix, 'radix', 'is not an integer');
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}
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if (radix < 2 || radix > 36) {
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throw new RangeError.range(radix, 2, 36, 'radix');
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}
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if (radix == 10 && decimalMatch != null) {
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return _parseDecimal(decimalMatch, isNegative);
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}
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if (radix == 16 && (decimalMatch != null || nonDecimalMatch != null)) {
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return _parseHex(decimalMatch ?? nonDecimalMatch, 0, isNegative);
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}
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return _parseRadix(
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decimalMatch ?? nonDecimalMatch ?? hexMatch, radix, isNegative);
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}
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/// Finds the amount significant digits in the provided [digits] array.
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static int _normalize(int used, Uint32List digits) {
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while (used > 0 && digits[used - 1] == 0) used--;
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return used;
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}
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/// Factory returning an instance initialized with the given field values.
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/// If the [digits] array contains leading 0s, the [used] value is adjusted
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/// accordingly. The [digits] array is not modified.
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_BigIntImpl._(bool isNegative, int used, Uint32List digits)
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: this._normalized(isNegative, _normalize(used, digits), digits);
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_BigIntImpl._normalized(bool isNegative, this._used, this._digits)
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: _isNegative = _used == 0 ? false : isNegative;
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/// Whether this big integer is zero.
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bool get _isZero => _used == 0;
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/// Allocates an array of the given [length] and copies the [digits] in the
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/// range [from] to [to-1], starting at index 0, followed by leading zero
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/// digits.
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static Uint32List _cloneDigits(
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Uint32List digits, int from, int to, int length) {
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var resultDigits = new Uint32List(length);
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var n = to - from;
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for (var i = 0; i < n; i++) {
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resultDigits[i] = digits[from + i];
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}
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return resultDigits;
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}
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/// Allocates a big integer from the provided [value] number.
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factory _BigIntImpl.from(num value) {
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if (value == 0) return zero;
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if (value == 1) return one;
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if (value == 2) return two;
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if (value.abs() < 0x100000000)
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return new _BigIntImpl._fromInt(value.toInt());
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if (value is double) return new _BigIntImpl._fromDouble(value);
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return new _BigIntImpl._fromInt(value);
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}
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factory _BigIntImpl._fromInt(int value) {
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bool isNegative = value < 0;
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assert(_digitBits == 32);
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if (isNegative) {
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// Handle the min 64-bit value differently, since its negation is not
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// positive.
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if (value == _minInt) {
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var digits = new Uint32List(2);
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digits[1] = 0x80000000;
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return new _BigIntImpl._(true, 2, digits);
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}
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value = -value;
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}
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if (value < _digitBase) {
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var digits = new Uint32List(1);
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digits[0] = value;
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return new _BigIntImpl._(isNegative, 1, digits);
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}
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var digits = new Uint32List(2);
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digits[0] = value & _digitMask;
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digits[1] = value >> _digitBits;
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return new _BigIntImpl._(isNegative, 2, digits);
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}
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/// An 8-byte Uint8List we can reuse for [_fromDouble] to avoid generating
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/// garbage.
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static final Uint8List _bitsForFromDouble = new Uint8List(8);
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factory _BigIntImpl._fromDouble(double value) {
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const int exponentBias = 1075;
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if (value.isNaN || value.isInfinite) {
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throw new ArgumentError("Value must be finite: $value");
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}
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bool isNegative = value < 0;
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if (isNegative) value = -value;
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value = value.floorToDouble();
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if (value == 0) return zero;
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var bits = _bitsForFromDouble;
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for (int i = 0; i < 8; i++) {
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bits[i] = 0;
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}
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bits.buffer.asByteData().setFloat64(0, value, Endian.little);
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// The exponent is in bits 53..63.
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var biasedExponent = (bits[7] << 4) + (bits[6] >> 4);
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var exponent = biasedExponent - exponentBias;
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assert(_digitBits == 32);
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// The significant bits are in 0 .. 52.
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var unshiftedDigits = new Uint32List(2);
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unshiftedDigits[0] =
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(bits[3] << 24) + (bits[2] << 16) + (bits[1] << 8) + bits[0];
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// Don't forget to add the hidden bit.
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unshiftedDigits[1] =
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((0x10 | (bits[6] & 0xF)) << 16) + (bits[5] << 8) + bits[4];
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var unshiftedBig = new _BigIntImpl._normalized(false, 2, unshiftedDigits);
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_BigIntImpl absResult;
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if (exponent < 0) {
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absResult = unshiftedBig >> -exponent;
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} else if (exponent > 0) {
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absResult = unshiftedBig << exponent;
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}
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if (isNegative) return -absResult;
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return absResult;
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}
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/**
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* Return the negative value of this integer.
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*
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* The result of negating an integer always has the opposite sign, except
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* for zero, which is its own negation.
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*/
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_BigIntImpl operator -() {
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if (_used == 0) return this;
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return new _BigIntImpl._(!_isNegative, _used, _digits);
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}
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/**
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* Returns the absolute value of this integer.
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*
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* For any integer `x`, the result is the same as `x < 0 ? -x : x`.
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*/
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_BigIntImpl abs() => _isNegative ? -this : this;
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/// Returns this << n *_DIGIT_BITS.
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_BigIntImpl _dlShift(int n) {
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final used = _used;
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if (used == 0) {
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return zero;
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}
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final resultUsed = used + n;
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final digits = _digits;
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final resultDigits = new Uint32List(resultUsed);
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for (int i = used - 1; i >= 0; i--) {
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resultDigits[i + n] = digits[i];
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}
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return new _BigIntImpl._(_isNegative, resultUsed, resultDigits);
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}
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/// Same as [_dlShift] but works on the decomposed big integers.
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///
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/// Returns `resultUsed`.
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///
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/// `resultDigits[0..resultUsed-1] = xDigits[0..xUsed-1] << n*_DIGIT_BITS`.
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static int _dlShiftDigits(
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Uint32List xDigits, int xUsed, int n, Uint32List resultDigits) {
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if (xUsed == 0) {
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return 0;
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}
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if (n == 0 && identical(resultDigits, xDigits)) {
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return xUsed;
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}
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final resultUsed = xUsed + n;
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for (int i = xUsed - 1; i >= 0; i--) {
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resultDigits[i + n] = xDigits[i];
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}
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for (int i = n - 1; i >= 0; i--) {
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resultDigits[i] = 0;
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}
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return resultUsed;
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}
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/// Returns `this >> n*_DIGIT_BITS`.
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_BigIntImpl _drShift(int n) {
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final used = _used;
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if (used == 0) {
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return zero;
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}
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final resultUsed = used - n;
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if (resultUsed <= 0) {
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return _isNegative ? _minusOne : zero;
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}
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final digits = _digits;
|
|
final resultDigits = new Uint32List(resultUsed);
|
|
for (var i = n; i < used; i++) {
|
|
resultDigits[i - n] = digits[i];
|
|
}
|
|
final result = new _BigIntImpl._(_isNegative, resultUsed, resultDigits);
|
|
if (_isNegative) {
|
|
// Round down if any bit was shifted out.
|
|
for (var i = 0; i < n; i++) {
|
|
if (digits[i] != 0) {
|
|
return result - one;
|
|
}
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/// Shifts the digits of [xDigits] into the right place in [resultDigits].
|
|
///
|
|
/// `resultDigits[ds..xUsed+ds] = xDigits[0..xUsed-1] << (n % _DIGIT_BITS)`
|
|
/// where `ds = ceil(n / _DIGIT_BITS)`
|
|
///
|
|
/// Does *not* clear digits below ds.
|
|
static void _lsh(
|
|
Uint32List xDigits, int xUsed, int n, Uint32List resultDigits) {
|
|
final digitShift = n ~/ _digitBits;
|
|
final bitShift = n % _digitBits;
|
|
final carryBitShift = _digitBits - bitShift;
|
|
final bitMask = (1 << carryBitShift) - 1;
|
|
var carry = 0;
|
|
for (int i = xUsed - 1; i >= 0; i--) {
|
|
final digit = xDigits[i];
|
|
resultDigits[i + digitShift + 1] = (digit >> carryBitShift) | carry;
|
|
carry = (digit & bitMask) << bitShift;
|
|
}
|
|
resultDigits[digitShift] = carry;
|
|
}
|
|
|
|
/**
|
|
* Shift the bits of this integer to the left by [shiftAmount].
|
|
*
|
|
* Shifting to the left makes the number larger, effectively multiplying
|
|
* the number by `pow(2, shiftIndex)`.
|
|
*
|
|
* There is no limit on the size of the result. It may be relevant to
|
|
* limit intermediate values by using the "and" operator with a suitable
|
|
* mask.
|
|
*
|
|
* It is an error if [shiftAmount] is negative.
|
|
*/
|
|
_BigIntImpl operator <<(int shiftAmount) {
|
|
if (shiftAmount < 0) {
|
|
throw new ArgumentError("shift-amount must be posititve $shiftAmount");
|
|
}
|
|
final digitShift = shiftAmount ~/ _digitBits;
|
|
final bitShift = shiftAmount % _digitBits;
|
|
if (bitShift == 0) {
|
|
return _dlShift(digitShift);
|
|
}
|
|
var resultUsed = _used + digitShift + 1;
|
|
var resultDigits = new Uint32List(resultUsed);
|
|
_lsh(_digits, _used, shiftAmount, resultDigits);
|
|
return new _BigIntImpl._(_isNegative, resultUsed, resultDigits);
|
|
}
|
|
|
|
// resultDigits[0..resultUsed-1] = xDigits[0..xUsed-1] << n.
|
|
// Returns resultUsed.
|
|
static int _lShiftDigits(
|
|
Uint32List xDigits, int xUsed, int n, Uint32List resultDigits) {
|
|
final digitsShift = n ~/ _digitBits;
|
|
final bitShift = n % _digitBits;
|
|
if (bitShift == 0) {
|
|
return _dlShiftDigits(xDigits, xUsed, digitsShift, resultDigits);
|
|
}
|
|
var resultUsed = xUsed + digitsShift + 1;
|
|
_lsh(xDigits, xUsed, n, resultDigits);
|
|
var i = digitsShift;
|
|
while (--i >= 0) {
|
|
resultDigits[i] = 0;
|
|
}
|
|
if (resultDigits[resultUsed - 1] == 0) {
|
|
resultUsed--; // Clamp result.
|
|
}
|
|
return resultUsed;
|
|
}
|
|
|
|
// resultDigits[0..resultUsed-1] = xDigits[0..xUsed-1] >> n.
|
|
static void _rsh(
|
|
Uint32List xDigits, int xUsed, int n, Uint32List resultDigits) {
|
|
final digitsShift = n ~/ _digitBits;
|
|
final bitShift = n % _digitBits;
|
|
final carryBitShift = _digitBits - bitShift;
|
|
final bitMask = (1 << bitShift) - 1;
|
|
var carry = xDigits[digitsShift] >> bitShift;
|
|
final last = xUsed - digitsShift - 1;
|
|
for (var i = 0; i < last; i++) {
|
|
final digit = xDigits[i + digitsShift + 1];
|
|
resultDigits[i] = ((digit & bitMask) << carryBitShift) | carry;
|
|
carry = digit >> bitShift;
|
|
}
|
|
resultDigits[last] = carry;
|
|
}
|
|
|
|
/**
|
|
* Shift the bits of this integer to the right by [shiftAmount].
|
|
*
|
|
* Shifting to the right makes the number smaller and drops the least
|
|
* significant bits, effectively doing an integer division by
|
|
*`pow(2, shiftIndex)`.
|
|
*
|
|
* It is an error if [shiftAmount] is negative.
|
|
*/
|
|
_BigIntImpl operator >>(int shiftAmount) {
|
|
if (shiftAmount < 0) {
|
|
throw new ArgumentError("shift-amount must be posititve $shiftAmount");
|
|
}
|
|
final digitShift = shiftAmount ~/ _digitBits;
|
|
final bitShift = shiftAmount % _digitBits;
|
|
if (bitShift == 0) {
|
|
return _drShift(digitShift);
|
|
}
|
|
final used = _used;
|
|
final resultUsed = used - digitShift;
|
|
if (resultUsed <= 0) {
|
|
return _isNegative ? _minusOne : zero;
|
|
}
|
|
final digits = _digits;
|
|
final resultDigits = new Uint32List(resultUsed);
|
|
_rsh(digits, used, shiftAmount, resultDigits);
|
|
final result = new _BigIntImpl._(_isNegative, resultUsed, resultDigits);
|
|
if (_isNegative) {
|
|
// Round down if any bit was shifted out.
|
|
if ((digits[digitShift] & ((1 << bitShift) - 1)) != 0) {
|
|
return result - one;
|
|
}
|
|
for (var i = 0; i < digitShift; i++) {
|
|
if (digits[i] != 0) {
|
|
return result - one;
|
|
}
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/// Compares this to [other] taking the absolute value of both operands.
|
|
///
|
|
/// Returns 0 if abs(this) == abs(other); a positive number if
|
|
/// abs(this) > abs(other); and a negative number if abs(this) < abs(other).
|
|
int _absCompare(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
return _compareDigits(_digits, _used, other._digits, other._used);
|
|
}
|
|
|
|
/**
|
|
* Compares this to `other`.
|
|
*
|
|
* Returns a negative number if `this` is less than `other`, zero if they are
|
|
* equal, and a positive number if `this` is greater than `other`.
|
|
*/
|
|
int compareTo(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (_isNegative == other._isNegative) {
|
|
var result = _absCompare(other);
|
|
// Use 0 - result to avoid negative zero in JavaScript.
|
|
return _isNegative ? 0 - result : result;
|
|
}
|
|
return _isNegative ? -1 : 1;
|
|
}
|
|
|
|
/// Compares `digits[0..used-1]` with `otherDigits[0..otherUsed-1]`.
|
|
///
|
|
/// Returns 0 if equal; a positive number if larger;
|
|
/// and a negative number if smaller.
|
|
static int _compareDigits(
|
|
Uint32List digits, int used, Uint32List otherDigits, int otherUsed) {
|
|
var result = used - otherUsed;
|
|
if (result == 0) {
|
|
for (int i = used - 1; i >= 0; i--) {
|
|
result = digits[i] - otherDigits[i];
|
|
if (result != 0) return result;
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
// resultDigits[0..used] = digits[0..used-1] + otherDigits[0..otherUsed-1].
|
|
// used >= otherUsed > 0.
|
|
static void _absAdd(Uint32List digits, int used, Uint32List otherDigits,
|
|
int otherUsed, Uint32List resultDigits) {
|
|
assert(used >= otherUsed && otherUsed > 0);
|
|
var carry = 0;
|
|
for (var i = 0; i < otherUsed; i++) {
|
|
carry += digits[i] + otherDigits[i];
|
|
resultDigits[i] = carry & _digitMask;
|
|
carry >>= _digitBits;
|
|
}
|
|
for (var i = otherUsed; i < used; i++) {
|
|
carry += digits[i];
|
|
resultDigits[i] = carry & _digitMask;
|
|
carry >>= _digitBits;
|
|
}
|
|
resultDigits[used] = carry;
|
|
}
|
|
|
|
// resultDigits[0..used-1] = digits[0..used-1] - otherDigits[0..otherUsed-1].
|
|
// used >= otherUsed > 0.
|
|
static void _absSub(Uint32List digits, int used, Uint32List otherDigits,
|
|
int otherUsed, Uint32List resultDigits) {
|
|
assert(used >= otherUsed && otherUsed > 0);
|
|
|
|
var carry = 0;
|
|
for (var i = 0; i < otherUsed; i++) {
|
|
carry += digits[i] - otherDigits[i];
|
|
resultDigits[i] = carry & _digitMask;
|
|
carry >>= _digitBits;
|
|
}
|
|
for (var i = otherUsed; i < used; i++) {
|
|
carry += digits[i];
|
|
resultDigits[i] = carry & _digitMask;
|
|
carry >>= _digitBits;
|
|
}
|
|
}
|
|
|
|
/// Returns `abs(this) + abs(other)` with sign set according to [isNegative].
|
|
_BigIntImpl _absAddSetSign(_BigIntImpl other, bool isNegative) {
|
|
var used = _used;
|
|
var otherUsed = other._used;
|
|
if (used < otherUsed) {
|
|
return other._absAddSetSign(this, isNegative);
|
|
}
|
|
if (used == 0) {
|
|
assert(!isNegative);
|
|
return zero;
|
|
}
|
|
if (otherUsed == 0) {
|
|
return _isNegative == isNegative ? this : -this;
|
|
}
|
|
var resultUsed = used + 1;
|
|
var resultDigits = new Uint32List(resultUsed);
|
|
_absAdd(_digits, used, other._digits, otherUsed, resultDigits);
|
|
return new _BigIntImpl._(isNegative, resultUsed, resultDigits);
|
|
}
|
|
|
|
/// Returns `abs(this) - abs(other)` with sign set according to [isNegative].
|
|
///
|
|
/// Requirement: `abs(this) >= abs(other)`.
|
|
_BigIntImpl _absSubSetSign(_BigIntImpl other, bool isNegative) {
|
|
assert(_absCompare(other) >= 0);
|
|
var used = _used;
|
|
if (used == 0) {
|
|
assert(!isNegative);
|
|
return zero;
|
|
}
|
|
var otherUsed = other._used;
|
|
if (otherUsed == 0) {
|
|
return _isNegative == isNegative ? this : -this;
|
|
}
|
|
var resultDigits = new Uint32List(used);
|
|
_absSub(_digits, used, other._digits, otherUsed, resultDigits);
|
|
return new _BigIntImpl._(isNegative, used, resultDigits);
|
|
}
|
|
|
|
/// Returns `abs(this) & abs(other)` with sign set according to [isNegative].
|
|
_BigIntImpl _absAndSetSign(_BigIntImpl other, bool isNegative) {
|
|
var resultUsed = _min(_used, other._used);
|
|
var digits = _digits;
|
|
var otherDigits = other._digits;
|
|
var resultDigits = new Uint32List(resultUsed);
|
|
for (var i = 0; i < resultUsed; i++) {
|
|
resultDigits[i] = digits[i] & otherDigits[i];
|
|
}
|
|
return new _BigIntImpl._(isNegative, resultUsed, resultDigits);
|
|
}
|
|
|
|
/// Returns `abs(this) &~ abs(other)` with sign set according to [isNegative].
|
|
_BigIntImpl _absAndNotSetSign(_BigIntImpl other, bool isNegative) {
|
|
var resultUsed = _used;
|
|
var digits = _digits;
|
|
var otherDigits = other._digits;
|
|
var resultDigits = new Uint32List(resultUsed);
|
|
var m = _min(resultUsed, other._used);
|
|
for (var i = 0; i < m; i++) {
|
|
resultDigits[i] = digits[i] & ~otherDigits[i];
|
|
}
|
|
for (var i = m; i < resultUsed; i++) {
|
|
resultDigits[i] = digits[i];
|
|
}
|
|
return new _BigIntImpl._(isNegative, resultUsed, resultDigits);
|
|
}
|
|
|
|
/// Returns `abs(this) | abs(other)` with sign set according to [isNegative].
|
|
_BigIntImpl _absOrSetSign(_BigIntImpl other, bool isNegative) {
|
|
var used = _used;
|
|
var otherUsed = other._used;
|
|
var resultUsed = _max(used, otherUsed);
|
|
var digits = _digits;
|
|
var otherDigits = other._digits;
|
|
var resultDigits = new Uint32List(resultUsed);
|
|
var l, m;
|
|
if (used < otherUsed) {
|
|
l = other;
|
|
m = used;
|
|
} else {
|
|
l = this;
|
|
m = otherUsed;
|
|
}
|
|
for (var i = 0; i < m; i++) {
|
|
resultDigits[i] = digits[i] | otherDigits[i];
|
|
}
|
|
var lDigits = l._digits;
|
|
for (var i = m; i < resultUsed; i++) {
|
|
resultDigits[i] = lDigits[i];
|
|
}
|
|
return new _BigIntImpl._(isNegative, resultUsed, resultDigits);
|
|
}
|
|
|
|
/// Returns `abs(this) ^ abs(other)` with sign set according to [isNegative].
|
|
_BigIntImpl _absXorSetSign(_BigIntImpl other, bool isNegative) {
|
|
var used = _used;
|
|
var otherUsed = other._used;
|
|
var resultUsed = _max(used, otherUsed);
|
|
var digits = _digits;
|
|
var otherDigits = other._digits;
|
|
var resultDigits = new Uint32List(resultUsed);
|
|
var l, m;
|
|
if (used < otherUsed) {
|
|
l = other;
|
|
m = used;
|
|
} else {
|
|
l = this;
|
|
m = otherUsed;
|
|
}
|
|
for (var i = 0; i < m; i++) {
|
|
resultDigits[i] = digits[i] ^ otherDigits[i];
|
|
}
|
|
var lDigits = l._digits;
|
|
for (var i = m; i < resultUsed; i++) {
|
|
resultDigits[i] = lDigits[i];
|
|
}
|
|
return new _BigIntImpl._(isNegative, resultUsed, resultDigits);
|
|
}
|
|
|
|
/**
|
|
* Bit-wise and operator.
|
|
*
|
|
* Treating both `this` and [other] as sufficiently large two's component
|
|
* integers, the result is a number with only the bits set that are set in
|
|
* both `this` and [other]
|
|
*
|
|
* Of both operands are negative, the result is negative, otherwise
|
|
* the result is non-negative.
|
|
*/
|
|
_BigIntImpl operator &(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (_isNegative == other._isNegative) {
|
|
if (_isNegative) {
|
|
// (-this) & (-other) == ~(this-1) & ~(other-1)
|
|
// == ~((this-1) | (other-1))
|
|
// == -(((this-1) | (other-1)) + 1)
|
|
_BigIntImpl this1 = _absSubSetSign(one, true);
|
|
_BigIntImpl other1 = other._absSubSetSign(one, true);
|
|
// Result cannot be zero if this and other are negative.
|
|
return this1._absOrSetSign(other1, true)._absAddSetSign(one, true);
|
|
}
|
|
return _absAndSetSign(other, false);
|
|
}
|
|
// _isNegative != other._isNegative
|
|
var p, n;
|
|
if (_isNegative) {
|
|
p = other;
|
|
n = this;
|
|
} else {
|
|
// & is symmetric.
|
|
p = this;
|
|
n = other;
|
|
}
|
|
// p & (-n) == p & ~(n-1) == p &~ (n-1)
|
|
var n1 = n._absSubSetSign(one, false);
|
|
return p._absAndNotSetSign(n1, false);
|
|
}
|
|
|
|
/**
|
|
* Bit-wise or operator.
|
|
*
|
|
* Treating both `this` and [other] as sufficiently large two's component
|
|
* integers, the result is a number with the bits set that are set in either
|
|
* of `this` and [other]
|
|
*
|
|
* If both operands are non-negative, the result is non-negative,
|
|
* otherwise the result us negative.
|
|
*/
|
|
_BigIntImpl operator |(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (_isNegative == other._isNegative) {
|
|
if (_isNegative) {
|
|
// (-this) | (-other) == ~(this-1) | ~(other-1)
|
|
// == ~((this-1) & (other-1))
|
|
// == -(((this-1) & (other-1)) + 1)
|
|
var this1 = _absSubSetSign(one, true);
|
|
var other1 = other._absSubSetSign(one, true);
|
|
// Result cannot be zero if this and a are negative.
|
|
return this1._absAndSetSign(other1, true)._absAddSetSign(one, true);
|
|
}
|
|
return _absOrSetSign(other, false);
|
|
}
|
|
// _neg != a._neg
|
|
var p, n;
|
|
if (_isNegative) {
|
|
p = other;
|
|
n = this;
|
|
} else {
|
|
// | is symmetric.
|
|
p = this;
|
|
n = other;
|
|
}
|
|
// p | (-n) == p | ~(n-1) == ~((n-1) &~ p) == -(~((n-1) &~ p) + 1)
|
|
var n1 = n._absSubSetSign(one, true);
|
|
// Result cannot be zero if only one of this or a is negative.
|
|
return n1._absAndNotSetSign(p, true)._absAddSetSign(one, true);
|
|
}
|
|
|
|
/**
|
|
* Bit-wise exclusive-or operator.
|
|
*
|
|
* Treating both `this` and [other] as sufficiently large two's component
|
|
* integers, the result is a number with the bits set that are set in one,
|
|
* but not both, of `this` and [other]
|
|
*
|
|
* If the operands have the same sign, the result is non-negative,
|
|
* otherwise the result is negative.
|
|
*/
|
|
_BigIntImpl operator ^(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (_isNegative == other._isNegative) {
|
|
if (_isNegative) {
|
|
// (-this) ^ (-other) == ~(this-1) ^ ~(other-1) == (this-1) ^ (other-1)
|
|
var this1 = _absSubSetSign(one, true);
|
|
var other1 = other._absSubSetSign(one, true);
|
|
return this1._absXorSetSign(other1, false);
|
|
}
|
|
return _absXorSetSign(other, false);
|
|
}
|
|
// _isNegative != a._isNegative
|
|
var p, n;
|
|
if (_isNegative) {
|
|
p = other;
|
|
n = this;
|
|
} else {
|
|
// ^ is symmetric.
|
|
p = this;
|
|
n = other;
|
|
}
|
|
// p ^ (-n) == p ^ ~(n-1) == ~(p ^ (n-1)) == -((p ^ (n-1)) + 1)
|
|
var n1 = n._absSubSetSign(one, true);
|
|
// Result cannot be zero if only one of this or a is negative.
|
|
return p._absXorSetSign(n1, true)._absAddSetSign(one, true);
|
|
}
|
|
|
|
/**
|
|
* The bit-wise negate operator.
|
|
*
|
|
* Treating `this` as a sufficiently large two's component integer,
|
|
* the result is a number with the opposite bits set.
|
|
*
|
|
* This maps any integer `x` to `-x - 1`.
|
|
*/
|
|
_BigIntImpl operator ~() {
|
|
if (_isNegative) {
|
|
// ~(-this) == ~(~(this-1)) == this-1
|
|
return _absSubSetSign(one, false);
|
|
}
|
|
// ~this == -this-1 == -(this+1)
|
|
// Result cannot be zero if this is positive.
|
|
return _absAddSetSign(one, true);
|
|
}
|
|
|
|
/// Addition operator.
|
|
_BigIntImpl operator +(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
var isNegative = _isNegative;
|
|
if (isNegative == other._isNegative) {
|
|
// this + other == this + other
|
|
// (-this) + (-other) == -(this + other)
|
|
return _absAddSetSign(other, isNegative);
|
|
}
|
|
// this + (-other) == this - other == -(this - other)
|
|
// (-this) + other == other - this == -(this - other)
|
|
if (_absCompare(other) >= 0) {
|
|
return _absSubSetSign(other, isNegative);
|
|
}
|
|
return other._absSubSetSign(this, !isNegative);
|
|
}
|
|
|
|
/// Subtraction operator.
|
|
_BigIntImpl operator -(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
var isNegative = _isNegative;
|
|
if (isNegative != other._isNegative) {
|
|
// this - (-other) == this + other
|
|
// (-this) - other == -(this + other)
|
|
return _absAddSetSign(other, isNegative);
|
|
}
|
|
// this - other == this - a == -(this - other)
|
|
// (-this) - (-other) == other - this == -(this - other)
|
|
if (_absCompare(other) >= 0) {
|
|
return _absSubSetSign(other, isNegative);
|
|
}
|
|
return other._absSubSetSign(this, !isNegative);
|
|
}
|
|
|
|
/// Multiplies [x] with [multiplicandDigits] and adds the result to
|
|
/// [accumulatorDigits].
|
|
///
|
|
/// The [multiplicandDigits] in the range [i] to [i]+[n]-1 are the
|
|
/// multiplicand digits.
|
|
///
|
|
/// The [acculumatorDigits] in the range [j] to [j]+[n]-1 are the accumulator
|
|
/// digits.
|
|
///
|
|
/// Adds the result of the multiplicand-digits * [x] to the accumulator.
|
|
///
|
|
/// Concretely: `accumulatorDigits[j..j+n] += x * m_digits[i..i+n-1]`.
|
|
static void _mulAdd(int x, Uint32List multiplicandDigits, int i,
|
|
Uint32List accumulatorDigits, int j, int n) {
|
|
if (x == 0) {
|
|
// No-op if x is 0.
|
|
return;
|
|
}
|
|
int carry = 0;
|
|
int xl = x & _halfDigitMask;
|
|
int xh = x >> _halfDigitBits;
|
|
while (--n >= 0) {
|
|
int ml = multiplicandDigits[i] & _halfDigitMask;
|
|
int mh = multiplicandDigits[i++] >> _halfDigitBits;
|
|
int ph = xh * ml + mh * xl;
|
|
int pl = xl * ml +
|
|
((ph & _halfDigitMask) << _halfDigitBits) +
|
|
accumulatorDigits[j] +
|
|
carry;
|
|
carry = (pl >> _digitBits) + (ph >> _halfDigitBits) + xh * mh;
|
|
accumulatorDigits[j++] = pl & _digitMask;
|
|
}
|
|
while (carry != 0) {
|
|
int l = accumulatorDigits[j] + carry;
|
|
carry = l >> _digitBits;
|
|
accumulatorDigits[j++] = l & _digitMask;
|
|
}
|
|
}
|
|
|
|
/// Multiplication operator.
|
|
_BigIntImpl operator *(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
var used = _used;
|
|
var otherUsed = other._used;
|
|
if (used == 0 || otherUsed == 0) {
|
|
return zero;
|
|
}
|
|
var resultUsed = used + otherUsed;
|
|
var digits = _digits;
|
|
var otherDigits = other._digits;
|
|
var resultDigits = new Uint32List(resultUsed);
|
|
var i = 0;
|
|
while (i < otherUsed) {
|
|
_mulAdd(otherDigits[i], digits, 0, resultDigits, i, used);
|
|
i++;
|
|
}
|
|
return new _BigIntImpl._(
|
|
_isNegative != other._isNegative, resultUsed, resultDigits);
|
|
}
|
|
|
|
// r_digits[0..rUsed-1] = xDigits[0..xUsed-1]*otherDigits[0..otherUsed-1].
|
|
// Return resultUsed = xUsed + otherUsed.
|
|
static int _mulDigits(Uint32List xDigits, int xUsed, Uint32List otherDigits,
|
|
int otherUsed, Uint32List resultDigits) {
|
|
var resultUsed = xUsed + otherUsed;
|
|
var i = resultUsed;
|
|
assert(resultDigits.length >= i);
|
|
while (--i >= 0) {
|
|
resultDigits[i] = 0;
|
|
}
|
|
i = 0;
|
|
while (i < otherUsed) {
|
|
_mulAdd(otherDigits[i], xDigits, 0, resultDigits, i, xUsed);
|
|
i++;
|
|
}
|
|
return resultUsed;
|
|
}
|
|
|
|
/// Returns an estimate of `digits[i-1..i] ~/ topDigitDivisor`.
|
|
static int _estimateQuotientDigit(
|
|
int topDigitDivisor, Uint32List digits, int i) {
|
|
if (digits[i] == topDigitDivisor) return _digitMask;
|
|
// Chop off one bit, since a Mint cannot hold 2 digits.
|
|
var quotientDigit =
|
|
((digits[i] << (_digitBits - 1)) | (digits[i - 1] >> 1)) ~/
|
|
(topDigitDivisor >> 1);
|
|
if (quotientDigit > _digitMask) return _digitMask;
|
|
return quotientDigit;
|
|
}
|
|
|
|
/// Returns `trunc(this / other)`, with `other != 0`.
|
|
_BigIntImpl _div(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
assert(other._used > 0);
|
|
if (_used < other._used) {
|
|
return zero;
|
|
}
|
|
_divRem(other);
|
|
// Return quotient, i.e.
|
|
// _lastQuoRem_digits[_lastRem_used.._lastQuoRem_used-1] with proper sign.
|
|
var lastQuo_used = _lastQuoRemUsed - _lastRemUsed;
|
|
var quo_digits = _cloneDigits(
|
|
_lastQuoRemDigits, _lastRemUsed, _lastQuoRemUsed, lastQuo_used);
|
|
var quo = new _BigIntImpl._(false, lastQuo_used, quo_digits);
|
|
if ((_isNegative != other._isNegative) && (quo._used > 0)) {
|
|
quo = -quo;
|
|
}
|
|
return quo;
|
|
}
|
|
|
|
/// Returns `this - other * trunc(this / other)`, with `other != 0`.
|
|
_BigIntImpl _rem(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
assert(other._used > 0);
|
|
if (_used < other._used) {
|
|
return this;
|
|
}
|
|
_divRem(other);
|
|
// Return remainder, i.e.
|
|
// denormalized _lastQuoRem_digits[0.._lastRem_used-1] with proper sign.
|
|
var remDigits =
|
|
_cloneDigits(_lastQuoRemDigits, 0, _lastRemUsed, _lastRemUsed);
|
|
var rem = new _BigIntImpl._(false, _lastRemUsed, remDigits);
|
|
if (_lastRem_nsh > 0) {
|
|
rem = rem >> _lastRem_nsh; // Denormalize remainder.
|
|
}
|
|
if (_isNegative && (rem._used > 0)) {
|
|
rem = -rem;
|
|
}
|
|
return rem;
|
|
}
|
|
|
|
/// Computes this ~/ other and this.remainder(other).
|
|
///
|
|
/// Stores the result in [_lastQuoRemDigits], [_lastQuoRemUsed] and
|
|
/// [_lastRemUsed]. The [_lastQuoRemDigits] contains the digits of *both*, the
|
|
/// quotient and the remainder.
|
|
///
|
|
/// Caches the input to avoid doing the work again when users write
|
|
/// `a ~/ b` followed by a `a % b`.
|
|
void _divRem(_BigIntImpl other) {
|
|
// Check if result is already cached.
|
|
if ((this._used == _lastDividendUsed) &&
|
|
(other._used == _lastDivisorUsed) &&
|
|
identical(this._digits, _lastDividendDigits) &&
|
|
identical(other._digits, _lastDivisorDigits)) {
|
|
return;
|
|
}
|
|
assert(_used >= other._used);
|
|
|
|
var nsh = _digitBits - other._digits[other._used - 1].bitLength;
|
|
// Concatenated positive quotient and normalized positive remainder.
|
|
// The resultDigits can have at most one more digit than the dividend.
|
|
Uint32List resultDigits;
|
|
int resultUsed;
|
|
// Normalized positive divisor.
|
|
// The normalized divisor has the most-significant bit of its most
|
|
// significant digit set.
|
|
// This makes estimating the quotient easier.
|
|
Uint32List yDigits;
|
|
int yUsed;
|
|
if (nsh > 0) {
|
|
yDigits = new Uint32List(other._used + 5);
|
|
yUsed = _lShiftDigits(other._digits, other._used, nsh, yDigits);
|
|
resultDigits = new Uint32List(_used + 5);
|
|
resultUsed = _lShiftDigits(_digits, _used, nsh, resultDigits);
|
|
} else {
|
|
yDigits = other._digits;
|
|
yUsed = other._used;
|
|
resultDigits = _cloneDigits(_digits, 0, _used, _used + 2);
|
|
resultUsed = _used;
|
|
}
|
|
var topDigitDivisor = yDigits[yUsed - 1];
|
|
var i = resultUsed;
|
|
var j = i - yUsed;
|
|
// tmpDigits is a temporary array of i (resultUsed) digits.
|
|
var tmpDigits = new Uint32List(i);
|
|
var tmpUsed = _dlShiftDigits(yDigits, yUsed, j, tmpDigits);
|
|
// Explicit first division step in case normalized dividend is larger or
|
|
// equal to shifted normalized divisor.
|
|
if (_compareDigits(resultDigits, resultUsed, tmpDigits, tmpUsed) >= 0) {
|
|
assert(i == resultUsed);
|
|
resultDigits[resultUsed++] = 1; // Quotient = 1.
|
|
// Subtract divisor from remainder.
|
|
_absSub(resultDigits, resultUsed, tmpDigits, tmpUsed, resultDigits);
|
|
} else {
|
|
// Account for possible carry in _mulAdd step.
|
|
resultDigits[resultUsed++] = 0;
|
|
}
|
|
|
|
// Negate y so we can later use _mulAdd instead of non-existent _mulSub.
|
|
var nyDigits = new Uint32List(yUsed + 2);
|
|
nyDigits[yUsed] = 1;
|
|
_absSub(nyDigits, yUsed + 1, yDigits, yUsed, nyDigits);
|
|
// nyDigits is read-only and has yUsed digits (possibly including several
|
|
// leading zeros).
|
|
// resultDigits is modified during iteration.
|
|
// resultDigits[0..yUsed-1] is the current remainder.
|
|
// resultDigits[yUsed..resultUsed-1] is the current quotient.
|
|
--i;
|
|
|
|
while (j > 0) {
|
|
var estimatedQuotientDigit =
|
|
_estimateQuotientDigit(topDigitDivisor, resultDigits, i);
|
|
j--;
|
|
_mulAdd(estimatedQuotientDigit, nyDigits, 0, resultDigits, j, yUsed);
|
|
if (resultDigits[i] < estimatedQuotientDigit) {
|
|
// Reusing the already existing tmpDigits array.
|
|
var tmpUsed = _dlShiftDigits(nyDigits, yUsed, j, tmpDigits);
|
|
_absSub(resultDigits, resultUsed, tmpDigits, tmpUsed, resultDigits);
|
|
while (resultDigits[i] < --estimatedQuotientDigit) {
|
|
_absSub(resultDigits, resultUsed, tmpDigits, tmpUsed, resultDigits);
|
|
}
|
|
}
|
|
i--;
|
|
}
|
|
// Cache result.
|
|
_lastDividendDigits = _digits;
|
|
_lastDividendUsed = _used;
|
|
_lastDivisorDigits = other._digits;
|
|
_lastDivisorUsed = other._used;
|
|
_lastQuoRemDigits = resultDigits;
|
|
_lastQuoRemUsed = resultUsed;
|
|
_lastRemUsed = yUsed;
|
|
_lastRem_nsh = nsh;
|
|
}
|
|
|
|
int get hashCode {
|
|
// This is the [Jenkins hash function][1] but using masking to keep
|
|
// values in SMI range.
|
|
//
|
|
// [1]: http://en.wikipedia.org/wiki/Jenkins_hash_function
|
|
|
|
int combine(int hash, int value) {
|
|
hash = 0x1fffffff & (hash + value);
|
|
hash = 0x1fffffff & (hash + ((0x0007ffff & hash) << 10));
|
|
return hash ^ (hash >> 6);
|
|
}
|
|
|
|
int finish(int hash) {
|
|
hash = 0x1fffffff & (hash + ((0x03ffffff & hash) << 3));
|
|
hash = hash ^ (hash >> 11);
|
|
return 0x1fffffff & (hash + ((0x00003fff & hash) << 15));
|
|
}
|
|
|
|
if (_isZero) return 6707; // Just a random number.
|
|
var hash = _isNegative ? 83585 : 429689; // Also random.
|
|
for (int i = 0; i < _used; i++) {
|
|
hash = combine(hash, _digits[i]);
|
|
}
|
|
return finish(hash);
|
|
}
|
|
|
|
/**
|
|
* Test whether this value is numerically equal to `other`.
|
|
*
|
|
* If [other] is a [_BigIntImpl] returns whether the two operands have the same
|
|
* value.
|
|
*
|
|
* Returns false if `other` is not a [_BigIntImpl].
|
|
*/
|
|
bool operator ==(Object other) =>
|
|
other is _BigIntImpl && compareTo(other) == 0;
|
|
|
|
/**
|
|
* Returns the minimum number of bits required to store this big integer.
|
|
*
|
|
* The number of bits excludes the sign bit, which gives the natural length
|
|
* for non-negative (unsigned) values. Negative values are complemented to
|
|
* return the bit position of the first bit that differs from the sign bit.
|
|
*
|
|
* To find the number of bits needed to store the value as a signed value,
|
|
* add one, i.e. use `x.bitLength + 1`.
|
|
*
|
|
* ```
|
|
* x.bitLength == (-x-1).bitLength
|
|
*
|
|
* new BigInt.from(3).bitLength == 2; // 00000011
|
|
* new BigInt.from(2).bitLength == 2; // 00000010
|
|
* new BigInt.from(1).bitLength == 1; // 00000001
|
|
* new BigInt.from(0).bitLength == 0; // 00000000
|
|
* new BigInt.from(-1).bitLength == 0; // 11111111
|
|
* new BigInt.from(-2).bitLength == 1; // 11111110
|
|
* new BigInt.from(-3).bitLength == 2; // 11111101
|
|
* new BigInt.from(-4).bitLength == 2; // 11111100
|
|
* ```
|
|
*/
|
|
int get bitLength {
|
|
if (_used == 0) return 0;
|
|
if (_isNegative) return (~this).bitLength;
|
|
return _digitBits * (_used - 1) + _digits[_used - 1].bitLength;
|
|
}
|
|
|
|
/**
|
|
* Truncating division operator.
|
|
*
|
|
* Performs a truncating integer division, where the remainder is discarded.
|
|
*
|
|
* The remainder can be computed using the [remainder] method.
|
|
*
|
|
* Examples:
|
|
* ```
|
|
* var seven = new BigInt.from(7);
|
|
* var three = new BigInt.from(3);
|
|
* seven ~/ three; // => 2
|
|
* (-seven) ~/ three; // => -2
|
|
* seven ~/ -three; // => -2
|
|
* seven.remainder(three); // => 1
|
|
* (-seven).remainder(three); // => -1
|
|
* seven.remainder(-three); // => 1
|
|
* ```
|
|
*/
|
|
_BigIntImpl operator ~/(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (other._used == 0) {
|
|
throw const IntegerDivisionByZeroException();
|
|
}
|
|
return _div(other);
|
|
}
|
|
|
|
/**
|
|
* Returns the remainder of the truncating division of `this` by [other].
|
|
*
|
|
* The result `r` of this operation satisfies:
|
|
* `this == (this ~/ other) * other + r`.
|
|
* As a consequence the remainder `r` has the same sign as the divider `this`.
|
|
*/
|
|
_BigIntImpl remainder(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (other._used == 0) {
|
|
throw const IntegerDivisionByZeroException();
|
|
}
|
|
return _rem(other);
|
|
}
|
|
|
|
/// Division operator.
|
|
double operator /(BigInt other) => this.toDouble() / other.toDouble();
|
|
|
|
/** Relational less than operator. */
|
|
bool operator <(BigInt other) => compareTo(other) < 0;
|
|
|
|
/** Relational less than or equal operator. */
|
|
bool operator <=(BigInt other) => compareTo(other) <= 0;
|
|
|
|
/** Relational greater than operator. */
|
|
bool operator >(BigInt other) => compareTo(other) > 0;
|
|
|
|
/** Relational greater than or equal operator. */
|
|
bool operator >=(BigInt other) => compareTo(other) >= 0;
|
|
|
|
/**
|
|
* Euclidean modulo operator.
|
|
*
|
|
* Returns the remainder of the Euclidean division. The Euclidean division of
|
|
* two integers `a` and `b` yields two integers `q` and `r` such that
|
|
* `a == b * q + r` and `0 <= r < b.abs()`.
|
|
*
|
|
* The sign of the returned value `r` is always positive.
|
|
*
|
|
* See [remainder] for the remainder of the truncating division.
|
|
*/
|
|
_BigIntImpl operator %(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (other._used == 0) {
|
|
throw const IntegerDivisionByZeroException();
|
|
}
|
|
var result = _rem(other);
|
|
if (result._isNegative) {
|
|
if (other._isNegative) {
|
|
result = result - other;
|
|
} else {
|
|
result = result + other;
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Returns the sign of this big integer.
|
|
*
|
|
* Returns 0 for zero, -1 for values less than zero and
|
|
* +1 for values greater than zero.
|
|
*/
|
|
int get sign {
|
|
if (_used == 0) return 0;
|
|
return _isNegative ? -1 : 1;
|
|
}
|
|
|
|
/// Whether this big integer is even.
|
|
bool get isEven => _used == 0 || (_digits[0] & 1) == 0;
|
|
|
|
/// Whether this big integer is odd.
|
|
bool get isOdd => !isEven;
|
|
|
|
/// Whether this number is negative.
|
|
bool get isNegative => _isNegative;
|
|
|
|
_BigIntImpl pow(int exponent) {
|
|
if (exponent < 0) {
|
|
throw new ArgumentError("Exponent must not be negative: $exponent");
|
|
}
|
|
if (exponent == 0) return one;
|
|
|
|
// Exponentiation by squaring.
|
|
var result = one;
|
|
var base = this;
|
|
while (exponent != 0) {
|
|
if ((exponent & 1) == 1) {
|
|
result *= base;
|
|
}
|
|
exponent >>= 1;
|
|
// Skip unnecessary operation.
|
|
if (exponent != 0) {
|
|
base *= base;
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Returns this integer to the power of [exponent] modulo [modulus].
|
|
*
|
|
* The [exponent] must be non-negative and [modulus] must be
|
|
* positive.
|
|
*/
|
|
_BigIntImpl modPow(BigInt bigExponent, BigInt bigModulus) {
|
|
_BigIntImpl exponent = bigExponent;
|
|
_BigIntImpl modulus = bigModulus;
|
|
if (exponent._isNegative) {
|
|
throw new ArgumentError("exponent must be positive: $exponent");
|
|
}
|
|
if (modulus <= zero) {
|
|
throw new ArgumentError("modulus must be strictly positive: $modulus");
|
|
}
|
|
if (exponent._isZero) return one;
|
|
|
|
final modulusUsed = modulus._used;
|
|
final modulusUsed2p4 = 2 * modulusUsed + 4;
|
|
final exponentBitlen = exponent.bitLength;
|
|
if (exponentBitlen <= 0) return one;
|
|
_BigIntReduction z = new _BigIntClassic(modulus);
|
|
var resultDigits = new Uint32List(modulusUsed2p4);
|
|
var result2Digits = new Uint32List(modulusUsed2p4);
|
|
var gDigits = new Uint32List(modulusUsed);
|
|
var gUsed = z.convert(this, gDigits);
|
|
// Initialize result with g.
|
|
// Copy leading zero if any.
|
|
for (int j = gUsed - 1; j >= 0; j--) {
|
|
resultDigits[j] = gDigits[j];
|
|
}
|
|
var resultUsed = gUsed;
|
|
var result2Used;
|
|
for (int i = exponentBitlen - 2; i >= 0; i--) {
|
|
result2Used = z.sqr(resultDigits, resultUsed, result2Digits);
|
|
if (!(exponent & (one << i))._isZero) {
|
|
resultUsed =
|
|
z.mul(result2Digits, result2Used, gDigits, gUsed, resultDigits);
|
|
} else {
|
|
// Swap result and result2.
|
|
var tmpDigits = resultDigits;
|
|
var tmpUsed = resultUsed;
|
|
resultDigits = result2Digits;
|
|
resultUsed = result2Used;
|
|
result2Digits = tmpDigits;
|
|
result2Used = tmpUsed;
|
|
}
|
|
}
|
|
return z.revert(resultDigits, resultUsed);
|
|
}
|
|
|
|
// If inv is false, returns gcd(x, y).
|
|
// If inv is true and gcd(x, y) = 1, returns d, so that c*x + d*y = 1.
|
|
// If inv is true and gcd(x, y) != 1, throws Exception("Not coprime").
|
|
static _BigIntImpl _binaryGcd(_BigIntImpl x, _BigIntImpl y, bool inv) {
|
|
var xDigits = x._digits;
|
|
var yDigits = y._digits;
|
|
var xUsed = x._used;
|
|
var yUsed = y._used;
|
|
var maxUsed = xUsed > yUsed ? xUsed : yUsed;
|
|
var unshiftedMaxUsed = maxUsed; // Keep
|
|
xDigits = _cloneDigits(xDigits, 0, xUsed, maxUsed);
|
|
yDigits = _cloneDigits(yDigits, 0, yUsed, maxUsed);
|
|
int shiftAmount = 0;
|
|
if (inv) {
|
|
if ((yUsed == 1) && (yDigits[0] == 1)) return one;
|
|
if ((yUsed == 0) || (yDigits[0].isEven && xDigits[0].isEven)) {
|
|
throw new Exception("Not coprime");
|
|
}
|
|
} else {
|
|
if (x._isZero) {
|
|
throw new ArgumentError.value(0, "this", "must not be zero");
|
|
}
|
|
if (y._isZero) {
|
|
throw new ArgumentError.value(0, "other", "must not be zero");
|
|
}
|
|
if (((xUsed == 1) && (xDigits[0] == 1)) ||
|
|
((yUsed == 1) && (yDigits[0] == 1))) return one;
|
|
while (((xDigits[0] & 1) == 0) && ((yDigits[0] & 1) == 0)) {
|
|
_rsh(xDigits, xUsed, 1, xDigits);
|
|
_rsh(yDigits, yUsed, 1, yDigits);
|
|
shiftAmount++;
|
|
}
|
|
if (shiftAmount >= _digitBits) {
|
|
var digitShiftAmount = shiftAmount ~/ _digitBits;
|
|
xUsed -= digitShiftAmount;
|
|
yUsed -= digitShiftAmount;
|
|
maxUsed -= digitShiftAmount;
|
|
}
|
|
if ((yDigits[0] & 1) == 1) {
|
|
// Swap x and y.
|
|
var tmpDigits = xDigits;
|
|
var tmpUsed = xUsed;
|
|
xDigits = yDigits;
|
|
xUsed = yUsed;
|
|
yDigits = tmpDigits;
|
|
yUsed = tmpUsed;
|
|
}
|
|
}
|
|
var uDigits = _cloneDigits(xDigits, 0, xUsed, unshiftedMaxUsed);
|
|
var vDigits =
|
|
_cloneDigits(yDigits, 0, yUsed, unshiftedMaxUsed + 2); // +2 for lsh.
|
|
final bool ac = (xDigits[0] & 1) == 0;
|
|
|
|
// Variables a, b, c, and d require one more digit.
|
|
final abcdUsed = maxUsed + 1;
|
|
final abcdLen = abcdUsed + 2; // +2 to satisfy _absAdd.
|
|
var aDigits, bDigits, cDigits, dDigits;
|
|
bool aIsNegative, bIsNegative, cIsNegative, dIsNegative;
|
|
if (ac) {
|
|
aDigits = new Uint32List(abcdLen);
|
|
aIsNegative = false;
|
|
aDigits[0] = 1;
|
|
cDigits = new Uint32List(abcdLen);
|
|
cIsNegative = false;
|
|
}
|
|
bDigits = new Uint32List(abcdLen);
|
|
bIsNegative = false;
|
|
dDigits = new Uint32List(abcdLen);
|
|
dIsNegative = false;
|
|
dDigits[0] = 1;
|
|
|
|
while (true) {
|
|
while ((uDigits[0] & 1) == 0) {
|
|
_rsh(uDigits, maxUsed, 1, uDigits);
|
|
if (ac) {
|
|
if (((aDigits[0] & 1) == 1) || ((bDigits[0] & 1) == 1)) {
|
|
if (aIsNegative) {
|
|
if ((aDigits[maxUsed] != 0) ||
|
|
(_compareDigits(aDigits, maxUsed, yDigits, maxUsed)) > 0) {
|
|
_absSub(aDigits, abcdUsed, yDigits, maxUsed, aDigits);
|
|
} else {
|
|
_absSub(yDigits, maxUsed, aDigits, maxUsed, aDigits);
|
|
aIsNegative = false;
|
|
}
|
|
} else {
|
|
_absAdd(aDigits, abcdUsed, yDigits, maxUsed, aDigits);
|
|
}
|
|
if (bIsNegative) {
|
|
_absAdd(bDigits, abcdUsed, xDigits, maxUsed, bDigits);
|
|
} else if ((bDigits[maxUsed] != 0) ||
|
|
(_compareDigits(bDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(bDigits, abcdUsed, xDigits, maxUsed, bDigits);
|
|
} else {
|
|
_absSub(xDigits, maxUsed, bDigits, maxUsed, bDigits);
|
|
bIsNegative = true;
|
|
}
|
|
}
|
|
_rsh(aDigits, abcdUsed, 1, aDigits);
|
|
} else if ((bDigits[0] & 1) == 1) {
|
|
if (bIsNegative) {
|
|
_absAdd(bDigits, abcdUsed, xDigits, maxUsed, bDigits);
|
|
} else if ((bDigits[maxUsed] != 0) ||
|
|
(_compareDigits(bDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(bDigits, abcdUsed, xDigits, maxUsed, bDigits);
|
|
} else {
|
|
_absSub(xDigits, maxUsed, bDigits, maxUsed, bDigits);
|
|
bIsNegative = true;
|
|
}
|
|
}
|
|
_rsh(bDigits, abcdUsed, 1, bDigits);
|
|
}
|
|
while ((vDigits[0] & 1) == 0) {
|
|
_rsh(vDigits, maxUsed, 1, vDigits);
|
|
if (ac) {
|
|
if (((cDigits[0] & 1) == 1) || ((dDigits[0] & 1) == 1)) {
|
|
if (cIsNegative) {
|
|
if ((cDigits[maxUsed] != 0) ||
|
|
(_compareDigits(cDigits, maxUsed, yDigits, maxUsed) > 0)) {
|
|
_absSub(cDigits, abcdUsed, yDigits, maxUsed, cDigits);
|
|
} else {
|
|
_absSub(yDigits, maxUsed, cDigits, maxUsed, cDigits);
|
|
cIsNegative = false;
|
|
}
|
|
} else {
|
|
_absAdd(cDigits, abcdUsed, yDigits, maxUsed, cDigits);
|
|
}
|
|
if (dIsNegative) {
|
|
_absAdd(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
} else if ((dDigits[maxUsed] != 0) ||
|
|
(_compareDigits(dDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
} else {
|
|
_absSub(xDigits, maxUsed, dDigits, maxUsed, dDigits);
|
|
dIsNegative = true;
|
|
}
|
|
}
|
|
_rsh(cDigits, abcdUsed, 1, cDigits);
|
|
} else if ((dDigits[0] & 1) == 1) {
|
|
if (dIsNegative) {
|
|
_absAdd(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
} else if ((dDigits[maxUsed] != 0) ||
|
|
(_compareDigits(dDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
} else {
|
|
_absSub(xDigits, maxUsed, dDigits, maxUsed, dDigits);
|
|
dIsNegative = true;
|
|
}
|
|
}
|
|
_rsh(dDigits, abcdUsed, 1, dDigits);
|
|
}
|
|
if (_compareDigits(uDigits, maxUsed, vDigits, maxUsed) >= 0) {
|
|
_absSub(uDigits, maxUsed, vDigits, maxUsed, uDigits);
|
|
if (ac) {
|
|
if (aIsNegative == cIsNegative) {
|
|
var a_cmp_c = _compareDigits(aDigits, abcdUsed, cDigits, abcdUsed);
|
|
if (a_cmp_c > 0) {
|
|
_absSub(aDigits, abcdUsed, cDigits, abcdUsed, aDigits);
|
|
} else {
|
|
_absSub(cDigits, abcdUsed, aDigits, abcdUsed, aDigits);
|
|
aIsNegative = !aIsNegative && (a_cmp_c != 0);
|
|
}
|
|
} else {
|
|
_absAdd(aDigits, abcdUsed, cDigits, abcdUsed, aDigits);
|
|
}
|
|
}
|
|
if (bIsNegative == dIsNegative) {
|
|
var b_cmp_d = _compareDigits(bDigits, abcdUsed, dDigits, abcdUsed);
|
|
if (b_cmp_d > 0) {
|
|
_absSub(bDigits, abcdUsed, dDigits, abcdUsed, bDigits);
|
|
} else {
|
|
_absSub(dDigits, abcdUsed, bDigits, abcdUsed, bDigits);
|
|
bIsNegative = !bIsNegative && (b_cmp_d != 0);
|
|
}
|
|
} else {
|
|
_absAdd(bDigits, abcdUsed, dDigits, abcdUsed, bDigits);
|
|
}
|
|
} else {
|
|
_absSub(vDigits, maxUsed, uDigits, maxUsed, vDigits);
|
|
if (ac) {
|
|
if (cIsNegative == aIsNegative) {
|
|
var c_cmp_a = _compareDigits(cDigits, abcdUsed, aDigits, abcdUsed);
|
|
if (c_cmp_a > 0) {
|
|
_absSub(cDigits, abcdUsed, aDigits, abcdUsed, cDigits);
|
|
} else {
|
|
_absSub(aDigits, abcdUsed, cDigits, abcdUsed, cDigits);
|
|
cIsNegative = !cIsNegative && (c_cmp_a != 0);
|
|
}
|
|
} else {
|
|
_absAdd(cDigits, abcdUsed, aDigits, abcdUsed, cDigits);
|
|
}
|
|
}
|
|
if (dIsNegative == bIsNegative) {
|
|
var d_cmp_b = _compareDigits(dDigits, abcdUsed, bDigits, abcdUsed);
|
|
if (d_cmp_b > 0) {
|
|
_absSub(dDigits, abcdUsed, bDigits, abcdUsed, dDigits);
|
|
} else {
|
|
_absSub(bDigits, abcdUsed, dDigits, abcdUsed, dDigits);
|
|
dIsNegative = !dIsNegative && (d_cmp_b != 0);
|
|
}
|
|
} else {
|
|
_absAdd(dDigits, abcdUsed, bDigits, abcdUsed, dDigits);
|
|
}
|
|
}
|
|
// Exit loop if u == 0.
|
|
var i = maxUsed;
|
|
while ((i > 0) && (uDigits[i - 1] == 0)) --i;
|
|
if (i == 0) break;
|
|
}
|
|
if (!inv) {
|
|
if (shiftAmount > 0) {
|
|
maxUsed = _lShiftDigits(vDigits, maxUsed, shiftAmount, vDigits);
|
|
}
|
|
return new _BigIntImpl._(false, maxUsed, vDigits);
|
|
}
|
|
// No inverse if v != 1.
|
|
var i = maxUsed - 1;
|
|
while ((i > 0) && (vDigits[i] == 0)) --i;
|
|
if ((i != 0) || (vDigits[0] != 1)) {
|
|
throw new Exception("Not coprime");
|
|
}
|
|
|
|
if (dIsNegative) {
|
|
if ((dDigits[maxUsed] != 0) ||
|
|
(_compareDigits(dDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
if ((dDigits[maxUsed] != 0) ||
|
|
(_compareDigits(dDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
} else {
|
|
_absSub(xDigits, maxUsed, dDigits, maxUsed, dDigits);
|
|
dIsNegative = false;
|
|
}
|
|
} else {
|
|
_absSub(xDigits, maxUsed, dDigits, maxUsed, dDigits);
|
|
dIsNegative = false;
|
|
}
|
|
} else if ((dDigits[maxUsed] != 0) ||
|
|
(_compareDigits(dDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
if ((dDigits[maxUsed] != 0) ||
|
|
(_compareDigits(dDigits, maxUsed, xDigits, maxUsed) > 0)) {
|
|
_absSub(dDigits, abcdUsed, xDigits, maxUsed, dDigits);
|
|
}
|
|
}
|
|
return new _BigIntImpl._(false, maxUsed, dDigits);
|
|
}
|
|
|
|
/**
|
|
* Returns the modular multiplicative inverse of this big integer
|
|
* modulo [modulus].
|
|
*
|
|
* The [modulus] must be positive.
|
|
*
|
|
* It is an error if no modular inverse exists.
|
|
*/
|
|
// Returns 1/this % modulus, with modulus > 0.
|
|
_BigIntImpl modInverse(BigInt bigInt) {
|
|
_BigIntImpl modulus = bigInt;
|
|
if (modulus <= zero) {
|
|
throw new ArgumentError("Modulus must be strictly positive: $modulus");
|
|
}
|
|
if (modulus == one) return zero;
|
|
var tmp = this;
|
|
if (tmp._isNegative || (tmp._absCompare(modulus) >= 0)) {
|
|
tmp %= modulus;
|
|
}
|
|
return _binaryGcd(modulus, tmp, true);
|
|
}
|
|
|
|
/**
|
|
* Returns the greatest common divisor of this big integer and [other].
|
|
*
|
|
* If either number is non-zero, the result is the numerically greatest
|
|
* integer dividing both `this` and `other`.
|
|
*
|
|
* The greatest common divisor is independent of the order,
|
|
* so `x.gcd(y)` is always the same as `y.gcd(x)`.
|
|
*
|
|
* For any integer `x`, `x.gcd(x)` is `x.abs()`.
|
|
*
|
|
* If both `this` and `other` is zero, the result is also zero.
|
|
*/
|
|
_BigIntImpl gcd(BigInt bigInt) {
|
|
_BigIntImpl other = bigInt;
|
|
if (_isZero) return other.abs();
|
|
if (other._isZero) return this.abs();
|
|
return _binaryGcd(this, other, false);
|
|
}
|
|
|
|
/**
|
|
* Returns the least significant [width] bits of this big integer as a
|
|
* non-negative number (i.e. unsigned representation). The returned value has
|
|
* zeros in all bit positions higher than [width].
|
|
*
|
|
* ```
|
|
* new BigInt.from(-1).toUnsigned(5) == 31 // 11111111 -> 00011111
|
|
* ```
|
|
*
|
|
* This operation can be used to simulate arithmetic from low level languages.
|
|
* For example, to increment an 8 bit quantity:
|
|
*
|
|
* ```
|
|
* q = (q + 1).toUnsigned(8);
|
|
* ```
|
|
*
|
|
* `q` will count from `0` up to `255` and then wrap around to `0`.
|
|
*
|
|
* If the input fits in [width] bits without truncation, the result is the
|
|
* same as the input. The minimum width needed to avoid truncation of `x` is
|
|
* given by `x.bitLength`, i.e.
|
|
*
|
|
* ```
|
|
* x == x.toUnsigned(x.bitLength);
|
|
* ```
|
|
*/
|
|
_BigIntImpl toUnsigned(int width) {
|
|
return this & ((one << width) - one);
|
|
}
|
|
|
|
/**
|
|
* Returns the least significant [width] bits of this integer, extending the
|
|
* highest retained bit to the sign. This is the same as truncating the value
|
|
* to fit in [width] bits using an signed 2-s complement representation. The
|
|
* returned value has the same bit value in all positions higher than [width].
|
|
*
|
|
* ```
|
|
* var big15 = new BigInt.from(15);
|
|
* var big16 = new BigInt.from(16);
|
|
* var big239 = new BigInt.from(239);
|
|
* V--sign bit-V
|
|
* big16.toSigned(5) == -big16 // 00010000 -> 11110000
|
|
* big239.toSigned(5) == big15 // 11101111 -> 00001111
|
|
* ^ ^
|
|
* ```
|
|
*
|
|
* This operation can be used to simulate arithmetic from low level languages.
|
|
* For example, to increment an 8 bit signed quantity:
|
|
*
|
|
* ```
|
|
* q = (q + 1).toSigned(8);
|
|
* ```
|
|
*
|
|
* `q` will count from `0` up to `127`, wrap to `-128` and count back up to
|
|
* `127`.
|
|
*
|
|
* If the input value fits in [width] bits without truncation, the result is
|
|
* the same as the input. The minimum width needed to avoid truncation of `x`
|
|
* is `x.bitLength + 1`, i.e.
|
|
*
|
|
* ```
|
|
* x == x.toSigned(x.bitLength + 1);
|
|
* ```
|
|
*/
|
|
_BigIntImpl toSigned(int width) {
|
|
// The value of binary number weights each bit by a power of two. The
|
|
// twos-complement value weights the sign bit negatively. We compute the
|
|
// value of the negative weighting by isolating the sign bit with the
|
|
// correct power of two weighting and subtracting it from the value of the
|
|
// lower bits.
|
|
var signMask = one << (width - 1);
|
|
return (this & (signMask - one)) - (this & signMask);
|
|
}
|
|
|
|
bool get isValidInt {
|
|
assert(_digitBits == 32);
|
|
return _used < 2 ||
|
|
(_used == 2 &&
|
|
(_digits[1] < 0x80000000 ||
|
|
(_isNegative && _digits[1] == 0x80000000 && _digits[0] == 0)));
|
|
}
|
|
|
|
int toInt() {
|
|
assert(_digitBits == 32);
|
|
if (_used == 0) return 0;
|
|
if (_used == 1) return _isNegative ? -_digits[0] : _digits[0];
|
|
if (_used == 2 && _digits[1] < 0x80000000) {
|
|
var result = (_digits[1] << _digitBits) | _digits[0];
|
|
return _isNegative ? -result : result;
|
|
}
|
|
return _isNegative ? _minInt : _maxInt;
|
|
}
|
|
|
|
/**
|
|
* Returns this [_BigIntImpl] as a [double].
|
|
*
|
|
* If the number is not representable as a [double], an
|
|
* approximation is returned. For numerically large integers, the
|
|
* approximation may be infinite.
|
|
*/
|
|
double toDouble() {
|
|
const int exponentBias = 1075;
|
|
// There are 11 bits for the exponent.
|
|
// 2047 (all bits set to 1) is reserved for infinity and NaN.
|
|
// When storing the exponent in the 11 bits, it is biased by exponentBias
|
|
// to support negative exponents.
|
|
const int maxDoubleExponent = 2046 - exponentBias;
|
|
if (_isZero) return 0.0;
|
|
|
|
// We fill the 53 bits little-endian.
|
|
var resultBits = new Uint8List(8);
|
|
|
|
var length = _digitBits * (_used - 1) + _digits[_used - 1].bitLength;
|
|
if (length - 53 > maxDoubleExponent) return double.INFINITY;
|
|
|
|
// The most significant bit is for the sign.
|
|
if (_isNegative) resultBits[7] = 0x80;
|
|
|
|
// Write the exponent into bits 1..12:
|
|
var biasedExponent = length - 53 + exponentBias;
|
|
resultBits[6] = (biasedExponent & 0xF) << 4;
|
|
resultBits[7] |= biasedExponent >> 4;
|
|
|
|
int cachedBits = 0;
|
|
int cachedBitsLength = 0;
|
|
int digitIndex = _used - 1;
|
|
int readBits(int n) {
|
|
// Ensure that we have enough bits in [cachedBits].
|
|
while (cachedBitsLength < n) {
|
|
int nextDigit;
|
|
int nextDigitLength = _digitBits; // May get updated.
|
|
if (digitIndex < 0) {
|
|
nextDigit = 0;
|
|
digitIndex--;
|
|
} else {
|
|
nextDigit = _digits[digitIndex];
|
|
if (digitIndex == _used - 1) nextDigitLength = nextDigit.bitLength;
|
|
digitIndex--;
|
|
}
|
|
cachedBits = (cachedBits << nextDigitLength) + nextDigit;
|
|
cachedBitsLength += nextDigitLength;
|
|
}
|
|
// Read the top [n] bits.
|
|
var result = cachedBits >> (cachedBitsLength - n);
|
|
// Remove the bits from the cache.
|
|
cachedBits -= result << (cachedBitsLength - n);
|
|
cachedBitsLength -= n;
|
|
return result;
|
|
}
|
|
|
|
// The first leading 1 bit is implicit in the double-representation and can
|
|
// be discarded.
|
|
var leadingBits = readBits(5) & 0xF;
|
|
resultBits[6] |= leadingBits;
|
|
|
|
for (int i = 5; i >= 0; i--) {
|
|
// Get the remaining 48 bits.
|
|
resultBits[i] = readBits(8);
|
|
}
|
|
|
|
void roundUp() {
|
|
// Simply consists of adding 1 to the whole 64 bit "number".
|
|
// It will update the exponent, if necessary.
|
|
// It might even round up to infinity (which is what we want).
|
|
var carry = 1;
|
|
for (int i = 0; i < 8; i++) {
|
|
if (carry == 0) break;
|
|
var sum = resultBits[i] + carry;
|
|
resultBits[i] = sum & 0xFF;
|
|
carry = sum >> 8;
|
|
}
|
|
}
|
|
|
|
if (readBits(1) == 1) {
|
|
if (resultBits[0].isOdd) {
|
|
// Rounds to even all the time.
|
|
roundUp();
|
|
} else {
|
|
// Round up, if there is at least one other digit that is not 0.
|
|
if (cachedBits != 0) {
|
|
// There is already one in the cachedBits.
|
|
roundUp();
|
|
} else {
|
|
for (int i = digitIndex; digitIndex >= 0; i--) {
|
|
if (_digits[i] != 0) {
|
|
roundUp();
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return resultBits.buffer.asByteData().getFloat64(0, Endian.little);
|
|
}
|
|
|
|
/**
|
|
* Returns a String-representation of this integer.
|
|
*
|
|
* The returned string is parsable by [parse].
|
|
* For any `_BigIntImpl` `i`, it is guaranteed that
|
|
* `i == _BigIntImpl.parse(i.toString())`.
|
|
*/
|
|
String toString() {
|
|
if (_used == 0) return "0";
|
|
if (_used == 1) {
|
|
if (_isNegative) return (-_digits[0]).toString();
|
|
return _digits[0].toString();
|
|
}
|
|
|
|
// Generate in chunks of 9 digits.
|
|
// The chunks are in reversed order.
|
|
var decimalDigitChunks = <String>[];
|
|
var rest = isNegative ? -this : this;
|
|
while (rest._used > 1) {
|
|
var digits9 = rest.remainder(_oneBillion).toString();
|
|
decimalDigitChunks.add(digits9);
|
|
var zeros = 9 - digits9.length;
|
|
if (zeros == 8) {
|
|
decimalDigitChunks.add("00000000");
|
|
} else {
|
|
if (zeros >= 4) {
|
|
zeros -= 4;
|
|
decimalDigitChunks.add("0000");
|
|
}
|
|
if (zeros >= 2) {
|
|
zeros -= 2;
|
|
decimalDigitChunks.add("00");
|
|
}
|
|
if (zeros >= 1) {
|
|
decimalDigitChunks.add("0");
|
|
}
|
|
}
|
|
rest = rest ~/ _oneBillion;
|
|
}
|
|
decimalDigitChunks.add(rest._digits[0].toString());
|
|
if (_isNegative) decimalDigitChunks.add("-");
|
|
return decimalDigitChunks.reversed.join();
|
|
}
|
|
|
|
int _toRadixCodeUnit(int digit) {
|
|
const int _0 = 48;
|
|
const int _a = 97;
|
|
if (digit < 10) return _0 + digit;
|
|
return _a + digit - 10;
|
|
}
|
|
|
|
/**
|
|
* Converts [this] to a string representation in the given [radix].
|
|
*
|
|
* In the string representation, lower-case letters are used for digits above
|
|
* '9', with 'a' being 10 an 'z' being 35.
|
|
*
|
|
* The [radix] argument must be an integer in the range 2 to 36.
|
|
*/
|
|
String toRadixString(int radix) {
|
|
if (radix > 36) throw new RangeError.range(radix, 2, 36);
|
|
|
|
if (_used == 0) return "0";
|
|
|
|
if (_used == 1) {
|
|
var digitString = _digits[0].toRadixString(radix);
|
|
if (_isNegative) return "-" + digitString;
|
|
return digitString;
|
|
}
|
|
|
|
if (radix == 16) return _toHexString();
|
|
|
|
var base = new _BigIntImpl._fromInt(radix);
|
|
var reversedDigitCodeUnits = <int>[];
|
|
var rest = this.abs();
|
|
while (!rest._isZero) {
|
|
var digit = rest.remainder(base).toInt();
|
|
rest = rest ~/ base;
|
|
reversedDigitCodeUnits.add(_toRadixCodeUnit(digit));
|
|
}
|
|
var digitString = new String.fromCharCodes(reversedDigitCodeUnits.reversed);
|
|
if (_isNegative) return "-" + digitString;
|
|
return digitString;
|
|
}
|
|
|
|
String _toHexString() {
|
|
var chars = <int>[];
|
|
for (int i = 0; i < _used - 1; i++) {
|
|
int chunk = _digits[i];
|
|
for (int j = 0; j < (_digitBits ~/ 4); j++) {
|
|
chars.add(_toRadixCodeUnit(chunk & 0xF));
|
|
chunk >>= 4;
|
|
}
|
|
}
|
|
var msbChunk = _digits[_used - 1];
|
|
while (msbChunk != 0) {
|
|
chars.add(_toRadixCodeUnit(msbChunk & 0xF));
|
|
msbChunk >>= 4;
|
|
}
|
|
if (_isNegative) {
|
|
const _dash = 45;
|
|
chars.add(_dash);
|
|
}
|
|
return new String.fromCharCodes(chars.reversed);
|
|
}
|
|
}
|
|
|
|
// Interface for modular reduction.
|
|
abstract class _BigIntReduction {
|
|
// Return the number of digits used by r_digits.
|
|
int convert(_BigIntImpl x, Uint32List r_digits);
|
|
int mul(Uint32List xDigits, int xUsed, Uint32List yDigits, int yUsed,
|
|
Uint32List resultDigits);
|
|
int sqr(Uint32List xDigits, int xUsed, Uint32List resultDigits);
|
|
|
|
// Return x reverted to _BigIntImpl.
|
|
_BigIntImpl revert(Uint32List xDigits, int xUsed);
|
|
}
|
|
|
|
// Modular reduction using "classic" algorithm.
|
|
class _BigIntClassic implements _BigIntReduction {
|
|
final _BigIntImpl _modulus; // Modulus.
|
|
final _BigIntImpl _normalizedModulus; // Normalized _modulus.
|
|
|
|
_BigIntClassic(this._modulus)
|
|
: _normalizedModulus = _modulus <<
|
|
(_BigIntImpl._digitBits -
|
|
_modulus._digits[_modulus._used - 1].bitLength);
|
|
|
|
int convert(_BigIntImpl x, Uint32List resultDigits) {
|
|
var digits;
|
|
var used;
|
|
if (x._isNegative || x.compareTo(_modulus) >= 0) {
|
|
var remainder = x._rem(_modulus);
|
|
if (x._isNegative && !remainder._isNegative && remainder._used > 0) {
|
|
remainder = _modulus - remainder;
|
|
}
|
|
assert(!remainder._isNegative);
|
|
used = remainder._used;
|
|
digits = remainder._digits;
|
|
} else {
|
|
used = x._used;
|
|
digits = x._digits;
|
|
}
|
|
var i = used; // Copy leading zero if any.
|
|
while (--i >= 0) {
|
|
resultDigits[i] = digits[i];
|
|
}
|
|
return used;
|
|
}
|
|
|
|
_BigIntImpl revert(Uint32List xDigits, int xUsed) {
|
|
return new _BigIntImpl._(false, xUsed, xDigits);
|
|
}
|
|
|
|
int _reduce(Uint32List xDigits, int xUsed) {
|
|
if (xUsed < _modulus._used) {
|
|
return xUsed;
|
|
}
|
|
var reverted = revert(xDigits, xUsed);
|
|
var rem = reverted._rem(_normalizedModulus);
|
|
return convert(rem, xDigits);
|
|
}
|
|
|
|
int sqr(Uint32List xDigits, int xUsed, Uint32List resultDigits) {
|
|
var b = new _BigIntImpl._(false, xUsed, xDigits);
|
|
var b2 = b * b;
|
|
for (int i = 0; i < b2._used; i++) {
|
|
resultDigits[i] = b2._digits[i];
|
|
}
|
|
for (int i = b2._used; i < 2 * xUsed; i++) {
|
|
resultDigits[i] = 0;
|
|
}
|
|
return _reduce(resultDigits, 2 * xUsed);
|
|
}
|
|
|
|
int mul(Uint32List xDigits, int xUsed, Uint32List yDigits, int yUsed,
|
|
Uint32List resultDigits) {
|
|
var resultUsed =
|
|
_BigIntImpl._mulDigits(xDigits, xUsed, yDigits, yUsed, resultDigits);
|
|
return _reduce(resultDigits, resultUsed);
|
|
}
|
|
}
|