mirror of
https://github.com/Obfuscator-Collections/VMProtect.git
synced 2024-12-28 01:09:28 +03:00
1530 lines
35 KiB
C#
1530 lines
35 KiB
C#
// ==++==
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//
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// Copyright (c) Microsoft Corporation. All rights reserved.
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//
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// ==--==
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using System;
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using Contracts = System.Diagnostics.Debug;
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using Contract = System.Diagnostics.Debug;
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using Conditional = System.Diagnostics.ConditionalAttribute;
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// ReSharper disable once CheckNamespace
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namespace Numerics
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{
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/// <summary>
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/// BigIntegerBuilder holds a multiprecision unsigned integer value. It is mutable and
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/// supports common arithmetic operations. Be careful NOT to simply assign one
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/// BigIntegerBuilder to another, unless you really know what you are doing. The proper
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/// way to replicate a BigIntegerBuilder is via the constructor "BigIntegerBuilder(ref BigIntegerBuilder reg)",
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/// or with reg1.Load(ref reg2). Using the ctor marks the buffer as shared so changing the
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/// value of one register will not affect the other. Using Load copies the contents from
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/// one to the other. Either way, the internal buffer isn't aliased incorrectly.
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/// </summary>
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internal struct BigIntegerBuilder
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{
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// ReSharper disable once InconsistentNaming
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private const int kcbitUint = 32;
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// For a single uint, _iuLast is 0.
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private int _iuLast;
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// Used if _iuLast == 0.
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private uint _uSmall;
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// Used if _iuLast > 0.
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private uint[] _rgu;
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// This is false whenever _rgu is null or is shared with a NewBigInteger
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// or with another BigIntegerBuilder.
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private bool _fWritable;
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[Conditional("DEBUG")]
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// ReSharper disable once UnusedParameter.Local
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private void AssertValid(bool fTrimmed)
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{
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if (_iuLast <= 0)
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{
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Contract.Assert(_iuLast == 0);
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Contract.Assert(!_fWritable || _rgu != null);
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}
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else
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{
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Contract.Assert(_rgu != null && _rgu.Length > _iuLast);
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Contract.Assert(!fTrimmed || _rgu[_iuLast] != 0);
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}
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}
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#if CONTRACTS_FULL
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[ContractInvariantMethod]
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private void ObjectInvariant()
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{
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Contract.Invariant(_iuLast >=0);
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Contract.Invariant(!(_iuLast == 0) || (!_fWritable || _rgu != null));
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Contract.Invariant(!(_iuLast > 0) || (_rgu != null && _rgu.Length > _iuLast));
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}
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#endif
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/*
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internal BigIntegerBuilder(ref BigIntegerBuilder reg)
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{
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reg.AssertValid(true);
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this = reg;
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if (_fWritable)
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{
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_fWritable = false;
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if (_iuLast == 0)
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_rgu = null;
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else
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reg._fWritable = false;
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}
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AssertValid(true);
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}
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*/
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internal BigIntegerBuilder(int cuAlloc)
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{
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_iuLast = 0;
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_uSmall = 0;
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if (cuAlloc > 1)
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{
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_rgu = new uint[cuAlloc];
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_fWritable = true;
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}
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else
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{
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_rgu = null;
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_fWritable = false;
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}
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AssertValid(true);
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}
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/*
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internal BigIntegerBuilder(BigInteger bn)
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{
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_fWritable = false;
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_rgu = bn._Bits;
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if (_rgu == null)
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{
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_iuLast = 0;
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_uSmall = NumericsHelpers.Abs(bn._Sign);
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}
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else
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{
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_iuLast = _rgu.Length - 1;
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_uSmall = _rgu[0];
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while (_iuLast > 0 && _rgu[_iuLast] == 0)
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--_iuLast;
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}
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AssertValid(true);
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}
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*/
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internal BigIntegerBuilder(BigInteger bn, ref int sign)
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{
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Contract.Assert(sign == +1 || sign == -1);
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_fWritable = false;
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_rgu = bn._Bits;
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int n = bn._Sign;
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int mask = n >> (kcbitUint - 1);
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sign = (sign ^ mask) - mask;
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if (_rgu == null)
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{
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_iuLast = 0;
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_uSmall = (uint)((n ^ mask) - mask);
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}
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else
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{
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_iuLast = _rgu.Length - 1;
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_uSmall = _rgu[0];
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while (_iuLast > 0 && _rgu[_iuLast] == 0)
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--_iuLast;
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}
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AssertValid(true);
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}
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internal BigInteger GetInteger(int sign)
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{
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Contract.Assert(sign == +1 || sign == -1);
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AssertValid(true);
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uint[] bits;
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GetIntegerParts(sign, out sign, out bits);
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return new BigInteger(sign, bits);
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}
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private void GetIntegerParts(int signSrc, out int sign, out uint[] bits)
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{
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Contract.Assert(signSrc == +1 || signSrc == -1);
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AssertValid(true);
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if (_iuLast == 0)
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{
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if (_uSmall <= int.MaxValue)
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{
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sign = signSrc * (int)_uSmall;
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bits = null;
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return;
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}
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if (_rgu == null)
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_rgu = new[] { _uSmall };
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else if (_fWritable)
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_rgu[0] = _uSmall;
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else if (_rgu[0] != _uSmall)
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_rgu = new[] { _uSmall };
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}
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// The sign is +/- 1.
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sign = signSrc;
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int cuExtra = _rgu.Length - _iuLast - 1;
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Contract.Assert(cuExtra >= 0);
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if (cuExtra <= 1)
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{
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if (cuExtra == 0 || _rgu[_iuLast + 1] == 0)
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{
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_fWritable = false;
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bits = _rgu;
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return;
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}
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if (_fWritable)
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{
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_rgu[_iuLast + 1] = 0;
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_fWritable = false;
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bits = _rgu;
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return;
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}
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// The buffer isn't writable, but has an extra uint that is non-zero,
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// so we have to allocate a new buffer.
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}
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// Keep the bigger buffer (if it is writable), but create a smaller one for the BigInteger.
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bits = _rgu;
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Array.Resize(ref bits, _iuLast + 1);
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if (!_fWritable)
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_rgu = bits;
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}
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private void Set(uint u)
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{
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_uSmall = u;
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_iuLast = 0;
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AssertValid(true);
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}
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private void Set(ulong uu)
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{
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uint uHi = NumericsHelpers.GetHi(uu);
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if (uHi == 0)
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{
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_uSmall = NumericsHelpers.GetLo(uu);
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_iuLast = 0;
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}
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else
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{
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SetSizeLazy(2);
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_rgu[0] = (uint) uu;
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_rgu[1] = uHi;
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}
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}
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internal int Size { get { return _iuLast + 1; } }
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//internal uint High { get { return _iuLast == 0 ? _uSmall : _rgu[_iuLast]; } }
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/*internal void GetApproxParts(out int exp, out ulong man)
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{
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AssertValid(true);
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if (_iuLast == 0)
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{
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man = _uSmall;
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exp = 0;
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return;
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}
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int cuLeft = _iuLast - 1;
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man = NumericsHelpers.MakeUlong(_rgu[cuLeft + 1], _rgu[cuLeft]);
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exp = cuLeft * kcbitUint;
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int cbit;
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if (cuLeft > 0 && (cbit = NumericsHelpers.CbitHighZero(_rgu[cuLeft + 1])) > 0)
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{
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// Get 64 bits.
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Contract.Assert(cbit < kcbitUint);
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man = (man << cbit) | (_rgu[cuLeft - 1] >> (kcbitUint - cbit));
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exp -= cbit;
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}
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}*/
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private void Trim()
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{
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AssertValid(false);
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if (_iuLast > 0 && _rgu[_iuLast] == 0)
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{
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_uSmall = _rgu[0];
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while (--_iuLast > 0 && _rgu[_iuLast] == 0)
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{
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}
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}
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AssertValid(true);
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}
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private int CuNonZero
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{
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get
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{
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Contract.Assert(_iuLast > 0);
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int cu = 0;
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for (int iu = _iuLast; iu >= 0; --iu)
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{
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if (_rgu[iu] != 0)
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cu++;
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}
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return cu;
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}
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}
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// Sets the size to cu and makes sure the buffer is writable (if cu > 1),
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// but makes no guarantees about the contents of the buffer.
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private void SetSizeLazy(int cu)
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{
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Contract.Assert(cu > 0);
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AssertValid(false);
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if (cu <= 1)
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{
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_iuLast = 0;
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return;
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}
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if (!_fWritable || _rgu.Length < cu)
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{
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_rgu = new uint[cu];
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_fWritable = true;
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}
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_iuLast = cu - 1;
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AssertValid(false);
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}
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// Sets the size to cu, makes sure the buffer is writable (if cu > 1),
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// and set the contents to all zero.
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private void SetSizeClear(int cu)
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{
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Contract.Assert(cu > 0);
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AssertValid(false);
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if (cu <= 1)
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{
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_iuLast = 0;
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_uSmall = 0;
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return;
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}
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if (!_fWritable || _rgu.Length < cu)
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{
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_rgu = new uint[cu];
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_fWritable = true;
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}
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else
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Array.Clear(_rgu, 0, cu);
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_iuLast = cu - 1;
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AssertValid(false);
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}
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// Sets the size to cu, makes sure the buffer is writable (if cu > 1),
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// and maintains the contents. If the buffer is reallocated, cuExtra
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// uints are also allocated.
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private void SetSizeKeep(int cu, int cuExtra)
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{
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Contract.Assert(cu > 0 && cuExtra >= 0);
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AssertValid(false);
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if (cu <= 1)
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{
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if (_iuLast > 0)
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_uSmall = _rgu[0];
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_iuLast = 0;
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return;
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}
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if (!_fWritable || _rgu.Length < cu)
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{
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uint[] rgu = new uint[cu + cuExtra];
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if (_iuLast == 0)
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rgu[0] = _uSmall;
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else
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Array.Copy(_rgu, rgu, Math.Min(cu, _iuLast + 1));
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_rgu = rgu;
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_fWritable = true;
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}
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else if (_iuLast + 1 < cu)
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{
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Array.Clear(_rgu, _iuLast + 1, cu - _iuLast - 1);
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if (_iuLast == 0)
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_rgu[0] = _uSmall;
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}
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_iuLast = cu - 1;
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AssertValid(false);
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}
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// Makes sure the buffer is writable and can support cu uints.
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// Preserves the contents of the buffer up to min(_iuLast + 1, cu).
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// Changes the size if cu <= _iuLast and the buffer needs to be allocated.
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/*
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internal void EnsureWritable(int cu, int cuExtra)
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{
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Contract.Assert(cu > 1 && cuExtra >= 0);
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AssertValid(false);
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if (_fWritable && _rgu.Length >= cu)
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return;
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uint[] rgu = new uint[cu + cuExtra];
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if (_iuLast > 0)
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{
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if (_iuLast >= cu)
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_iuLast = cu - 1;
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Array.Copy(_rgu, rgu, _iuLast + 1);
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}
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_rgu = rgu;
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_fWritable = true;
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AssertValid(false);
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}
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*/
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// Makes sure the buffer is writable and can support _iuLast + 1 uints.
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// Preserves the contents of the buffer.
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private void EnsureWritable(int cuExtra = 0)
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{
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Contract.Assert(cuExtra >= 0);
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AssertValid(false);
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Contract.Assert(_iuLast > 0);
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if (_fWritable)
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return;
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uint[] rgu = new uint[_iuLast + 1 + cuExtra];
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Array.Copy(_rgu, rgu, _iuLast + 1);
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_rgu = rgu;
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_fWritable = true;
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AssertValid(false);
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}
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// Loads the value of reg into this register.
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/*internal void Load(ref BigIntegerBuilder reg)
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{
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Load(ref reg, 0);
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}*/
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// Loads the value of reg into this register. If we need to allocate memory
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// to perform the load, allocate cuExtra elements.
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private void Load(ref BigIntegerBuilder reg, int cuExtra)
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{
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Contract.Assert(cuExtra >= 0);
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AssertValid(false);
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reg.AssertValid(true);
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if (reg._iuLast == 0)
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{
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_uSmall = reg._uSmall;
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_iuLast = 0;
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}
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else
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{
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if (!_fWritable || _rgu.Length <= reg._iuLast)
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{
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_rgu = new uint[reg._iuLast + 1 + cuExtra];
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_fWritable = true;
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}
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_iuLast = reg._iuLast;
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Array.Copy(reg._rgu, _rgu, _iuLast + 1);
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}
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AssertValid(true);
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}
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/*internal void Add(uint u)
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{
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AssertValid(true);
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if (_iuLast == 0)
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{
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if ((_uSmall += u) >= u)
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return;
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SetSizeLazy(2);
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_rgu[0] = _uSmall;
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_rgu[1] = 1;
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return;
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}
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if (u == 0)
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return;
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uint uNew = _rgu[0] + u;
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if (uNew < u)
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{
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// Have carry.
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EnsureWritable(1);
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ApplyCarry(1);
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}
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else if (!_fWritable)
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EnsureWritable();
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_rgu[0] = uNew;
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AssertValid(true);
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}
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internal void Add(ref BigIntegerBuilder reg)
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{
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AssertValid(true);
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reg.AssertValid(true);
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if (reg._iuLast == 0)
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{
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Add(reg._uSmall);
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return;
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}
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if (_iuLast == 0)
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{
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uint u = _uSmall;
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if (u == 0)
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this = new BigIntegerBuilder(ref reg);
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else
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{
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Load(ref reg, 1);
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Add(u);
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}
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return;
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}
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EnsureWritable(Math.Max(_iuLast, reg._iuLast) + 1, 1);
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int cuAdd = reg._iuLast + 1;
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if (_iuLast < reg._iuLast)
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{
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cuAdd = _iuLast + 1;
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Array.Copy(reg._rgu, _iuLast + 1, _rgu, _iuLast + 1, reg._iuLast - _iuLast);
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Contract.Assert(_iuLast > 0);
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_iuLast = reg._iuLast;
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}
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// Add, tracking carry.
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uint uCarry = 0;
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for (int iu = 0; iu < cuAdd; iu++)
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{
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uCarry = AddCarry(ref _rgu[iu], reg._rgu[iu], uCarry);
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Contract.Assert(uCarry <= 1);
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}
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// Deal with extra carry.
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if (uCarry != 0)
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ApplyCarry(cuAdd);
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AssertValid(true);
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}
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internal void Sub(ref int sign, uint u)
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{
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Contract.Assert(sign == +1 || sign == -1);
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AssertValid(true);
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if (_iuLast == 0)
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{
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if (u <= _uSmall)
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_uSmall -= u;
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else
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{
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_uSmall = u - _uSmall;
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sign = -sign;
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}
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AssertValid(true);
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return;
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}
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if (u == 0)
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return;
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EnsureWritable();
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uint uTmp = _rgu[0];
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_rgu[0] = uTmp - u;
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if (uTmp < u)
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{
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ApplyBorrow(1);
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Trim();
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}
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AssertValid(true);
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}
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internal void Sub(ref int sign, ref BigIntegerBuilder reg)
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{
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Contract.Assert(sign == +1 || sign == -1);
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AssertValid(true);
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reg.AssertValid(true);
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if (reg._iuLast == 0)
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{
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Sub(ref sign, reg._uSmall);
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return;
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}
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if (_iuLast == 0)
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{
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uint u = _uSmall;
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if (u == 0)
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this = new BigIntegerBuilder(ref reg);
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else
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{
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Load(ref reg);
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Sub(ref sign, u);
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}
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sign = -sign;
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return;
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}
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if (_iuLast < reg._iuLast)
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{
|
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SubRev(ref reg);
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sign = -sign;
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return;
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}
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|
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int cuSub = reg._iuLast + 1;
|
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if (_iuLast == reg._iuLast)
|
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{
|
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// Determine which is larger.
|
|
_iuLast = BigInteger.GetDiffLength(_rgu, reg._rgu, _iuLast + 1) - 1;
|
|
if (_iuLast < 0)
|
|
{
|
|
_iuLast = 0;
|
|
_uSmall = 0;
|
|
return;
|
|
}
|
|
|
|
uint u1 = _rgu[_iuLast];
|
|
uint u2 = reg._rgu[_iuLast];
|
|
if (_iuLast == 0)
|
|
{
|
|
if (u1 < u2)
|
|
{
|
|
_uSmall = u2 - u1;
|
|
sign = -sign;
|
|
}
|
|
else
|
|
_uSmall = u1 - u2;
|
|
AssertValid(true);
|
|
return;
|
|
}
|
|
|
|
if (u1 < u2)
|
|
{
|
|
Contract.Assert(_iuLast > 0);
|
|
reg._iuLast = _iuLast;
|
|
SubRev(ref reg);
|
|
reg._iuLast = cuSub - 1;
|
|
Contract.Assert(reg._iuLast > 0);
|
|
sign = -sign;
|
|
return;
|
|
}
|
|
cuSub = _iuLast + 1;
|
|
}
|
|
|
|
EnsureWritable();
|
|
|
|
// Subtract, tracking borrow.
|
|
uint uBorrow = 0;
|
|
for (int iu = 0; iu < cuSub; iu++)
|
|
{
|
|
uBorrow = SubBorrow(ref _rgu[iu], reg._rgu[iu], uBorrow);
|
|
Contract.Assert(uBorrow <= 1);
|
|
}
|
|
if (uBorrow != 0)
|
|
{
|
|
Contract.Assert(uBorrow == 1 && cuSub <= _iuLast);
|
|
ApplyBorrow(cuSub);
|
|
}
|
|
Trim();
|
|
}
|
|
|
|
// Subtract this register from the given one and put the result in this one.
|
|
// Asserts that reg is larger in the most significant uint.
|
|
private void SubRev(ref BigIntegerBuilder reg)
|
|
{
|
|
Contract.Assert(0 < _iuLast && _iuLast <= reg._iuLast);
|
|
Contract.Assert(_iuLast < reg._iuLast || _rgu[_iuLast] < reg._rgu[_iuLast]);
|
|
|
|
EnsureWritable(reg._iuLast + 1, 0);
|
|
|
|
int cuSub = _iuLast + 1;
|
|
if (_iuLast < reg._iuLast)
|
|
{
|
|
Array.Copy(reg._rgu, _iuLast + 1, _rgu, _iuLast + 1, reg._iuLast - _iuLast);
|
|
Contract.Assert(_iuLast > 0);
|
|
_iuLast = reg._iuLast;
|
|
}
|
|
|
|
uint uBorrow = 0;
|
|
for (int iu = 0; iu < cuSub; iu++)
|
|
{
|
|
uBorrow = SubRevBorrow(ref _rgu[iu], reg._rgu[iu], uBorrow);
|
|
Contract.Assert(uBorrow <= 1);
|
|
}
|
|
if (uBorrow != 0)
|
|
{
|
|
Contract.Assert(uBorrow == 1);
|
|
ApplyBorrow(cuSub);
|
|
}
|
|
Trim();
|
|
}*/
|
|
|
|
private void Mul(uint u)
|
|
{
|
|
if (u == 0)
|
|
{
|
|
Set(0);
|
|
return;
|
|
}
|
|
if (u == 1)
|
|
return;
|
|
|
|
if (_iuLast == 0)
|
|
{
|
|
Set((ulong)_uSmall * u);
|
|
return;
|
|
}
|
|
|
|
EnsureWritable(1);
|
|
|
|
uint uCarry = 0;
|
|
for (int iu = 0; iu <= _iuLast; iu++)
|
|
uCarry = MulCarry(ref _rgu[iu], u, uCarry);
|
|
|
|
if (uCarry != 0)
|
|
{
|
|
SetSizeKeep(_iuLast + 2, 0);
|
|
_rgu[_iuLast] = uCarry;
|
|
}
|
|
}
|
|
|
|
// This version may share memory with regMul.
|
|
/*internal void Mul(ref BigIntegerBuilder regMul)
|
|
{
|
|
AssertValid(true);
|
|
regMul.AssertValid(true);
|
|
|
|
if (regMul._iuLast == 0)
|
|
Mul(regMul._uSmall);
|
|
else if (_iuLast == 0)
|
|
{
|
|
uint u = _uSmall;
|
|
if (u == 1)
|
|
this = new BigIntegerBuilder(ref regMul);
|
|
else if (u != 0)
|
|
{
|
|
Load(ref regMul, 1);
|
|
Mul(u);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
int cuBase = _iuLast + 1;
|
|
SetSizeKeep(cuBase + regMul._iuLast, 1);
|
|
|
|
for (int iu = cuBase; --iu >= 0; )
|
|
{
|
|
uint uMul = _rgu[iu];
|
|
_rgu[iu] = 0;
|
|
uint uCarry = 0;
|
|
for (int iuSrc = 0; iuSrc <= regMul._iuLast; iuSrc++)
|
|
uCarry = AddMulCarry(ref _rgu[iu + iuSrc], regMul._rgu[iuSrc], uMul, uCarry);
|
|
if (uCarry != 0)
|
|
{
|
|
for (int iuDst = iu + regMul._iuLast + 1; uCarry != 0 && iuDst <= _iuLast; iuDst++)
|
|
uCarry = AddCarry(ref _rgu[iuDst], 0, uCarry);
|
|
if (uCarry != 0)
|
|
{
|
|
SetSizeKeep(_iuLast + 2, 0);
|
|
_rgu[_iuLast] = uCarry;
|
|
}
|
|
}
|
|
}
|
|
AssertValid(true);
|
|
}
|
|
}*/
|
|
|
|
// Multiply reg1 times reg2, putting the result in 'this'. This version never shares memory
|
|
// with either of the operands. This is useful when performing a series of arithmetic operations
|
|
// and large working buffers are allocated up front.
|
|
internal void Mul(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2)
|
|
{
|
|
AssertValid(true);
|
|
reg1.AssertValid(true);
|
|
reg2.AssertValid(true);
|
|
|
|
if (reg1._iuLast == 0)
|
|
{
|
|
if (reg2._iuLast == 0)
|
|
Set((ulong)reg1._uSmall * reg2._uSmall);
|
|
else
|
|
{
|
|
Load(ref reg2, 1);
|
|
Mul(reg1._uSmall);
|
|
}
|
|
}
|
|
else if (reg2._iuLast == 0)
|
|
{
|
|
Load(ref reg1, 1);
|
|
Mul(reg2._uSmall);
|
|
}
|
|
else
|
|
{
|
|
Contract.Assert(reg1._iuLast > 0 && reg2._iuLast > 0);
|
|
SetSizeClear(reg1._iuLast + reg2._iuLast + 2);
|
|
|
|
uint[] rgu1, rgu2;
|
|
int cu1, cu2;
|
|
|
|
// We prefer more iterations on the inner loop and fewer on the outer.
|
|
if (reg1.CuNonZero <= reg2.CuNonZero)
|
|
{
|
|
rgu1 = reg1._rgu; cu1 = reg1._iuLast + 1;
|
|
rgu2 = reg2._rgu; cu2 = reg2._iuLast + 1;
|
|
}
|
|
else
|
|
{
|
|
rgu1 = reg2._rgu; cu1 = reg2._iuLast + 1;
|
|
rgu2 = reg1._rgu; cu2 = reg1._iuLast + 1;
|
|
}
|
|
|
|
for (int iu1 = 0; iu1 < cu1; iu1++)
|
|
{
|
|
uint uCur = rgu1[iu1];
|
|
if (uCur == 0)
|
|
continue;
|
|
|
|
uint uCarry = 0;
|
|
int iuRes = iu1;
|
|
for (int iu2 = 0; iu2 < cu2; iu2++, iuRes++)
|
|
uCarry = AddMulCarry(ref _rgu[iuRes], uCur, rgu2[iu2], uCarry);
|
|
while (uCarry != 0)
|
|
uCarry = AddCarry(ref _rgu[iuRes++], 0, uCarry);
|
|
}
|
|
Trim();
|
|
}
|
|
}
|
|
|
|
// Divide 'this' by uDen, leaving the quotient in 'this' and returning the remainder.
|
|
/*internal uint DivMod(uint uDen)
|
|
{
|
|
AssertValid(true);
|
|
|
|
if (uDen == 1)
|
|
return 0;
|
|
if (_iuLast == 0)
|
|
{
|
|
uint uTmp = _uSmall;
|
|
_uSmall = uTmp / uDen;
|
|
return uTmp % uDen;
|
|
}
|
|
|
|
EnsureWritable();
|
|
|
|
ulong uu = 0;
|
|
for (int iv = _iuLast; iv >= 0; iv--)
|
|
{
|
|
uu = NumericsHelpers.MakeUlong((uint)uu, _rgu[iv]);
|
|
_rgu[iv] = (uint)(uu / uDen);
|
|
uu %= uDen;
|
|
}
|
|
Trim();
|
|
return (uint)uu;
|
|
}*/
|
|
|
|
// Divide regNum by uDen, returning the remainder and tossing the quotient.
|
|
private static uint Mod(ref BigIntegerBuilder regNum, uint uDen)
|
|
{
|
|
regNum.AssertValid(true);
|
|
|
|
if (uDen == 1)
|
|
return 0;
|
|
if (regNum._iuLast == 0)
|
|
return regNum._uSmall % uDen;
|
|
|
|
ulong uu = 0;
|
|
for (int iv = regNum._iuLast; iv >= 0; iv--)
|
|
{
|
|
uu = NumericsHelpers.MakeUlong((uint)uu, regNum._rgu[iv]);
|
|
uu %= uDen;
|
|
}
|
|
return (uint)uu;
|
|
}
|
|
|
|
// Divide 'this' by regDen, leaving the remainder in 'this' and tossing the quotient.
|
|
internal void Mod(ref BigIntegerBuilder regDen)
|
|
{
|
|
AssertValid(true);
|
|
regDen.AssertValid(true);
|
|
|
|
if (regDen._iuLast == 0)
|
|
{
|
|
Set(Mod(ref this, regDen._uSmall));
|
|
return;
|
|
}
|
|
if (_iuLast == 0)
|
|
return;
|
|
|
|
BigIntegerBuilder regTmp = new BigIntegerBuilder();
|
|
ModDivCore(ref this, ref regDen, false, ref regTmp);
|
|
}
|
|
|
|
// Divide 'this' by regDen, leaving the quotient in 'this' and tossing the remainder.
|
|
/*internal void Div(ref BigIntegerBuilder regDen)
|
|
{
|
|
AssertValid(true);
|
|
regDen.AssertValid(true);
|
|
|
|
if (regDen._iuLast == 0)
|
|
{
|
|
DivMod(regDen._uSmall);
|
|
return;
|
|
}
|
|
if (_iuLast == 0)
|
|
{
|
|
_uSmall = 0;
|
|
return;
|
|
}
|
|
|
|
BigIntegerBuilder regTmp = new BigIntegerBuilder();
|
|
ModDivCore(ref this, ref regDen, true, ref regTmp);
|
|
NumericsHelpers.Swap(ref this, ref regTmp);
|
|
}*/
|
|
|
|
// Divide regNum by regDen, leaving the remainder in regNum and the quotient in regQuo (if fQuo is true).
|
|
/*
|
|
internal void ModDiv(ref BigIntegerBuilder regDen, ref BigIntegerBuilder regQuo)
|
|
{
|
|
if (regDen._iuLast == 0)
|
|
{
|
|
regQuo.Set(DivMod(regDen._uSmall));
|
|
NumericsHelpers.Swap(ref this, ref regQuo);
|
|
return;
|
|
}
|
|
if (_iuLast == 0)
|
|
return;
|
|
|
|
ModDivCore(ref this, ref regDen, true, ref regQuo);
|
|
}
|
|
*/
|
|
|
|
private static void ModDivCore(ref BigIntegerBuilder regNum, ref BigIntegerBuilder regDen, bool fQuo, ref BigIntegerBuilder regQuo)
|
|
{
|
|
Contract.Assert(regNum._iuLast > 0 && regDen._iuLast > 0);
|
|
|
|
regQuo.Set(0);
|
|
if (regNum._iuLast < regDen._iuLast)
|
|
return;
|
|
|
|
Contract.Assert(0 < regDen._iuLast && regDen._iuLast <= regNum._iuLast);
|
|
int cuDen = regDen._iuLast + 1;
|
|
int cuDiff = regNum._iuLast - regDen._iuLast;
|
|
|
|
// Determine whether the result will have cuDiff "digits" or cuDiff+1 "digits".
|
|
int cuQuo = cuDiff;
|
|
for (int iu = regNum._iuLast; ; iu--)
|
|
{
|
|
if (iu < cuDiff)
|
|
{
|
|
cuQuo++;
|
|
break;
|
|
}
|
|
if (regDen._rgu[iu - cuDiff] != regNum._rgu[iu])
|
|
{
|
|
if (regDen._rgu[iu - cuDiff] < regNum._rgu[iu])
|
|
cuQuo++;
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (cuQuo == 0)
|
|
return;
|
|
|
|
if (fQuo)
|
|
regQuo.SetSizeLazy(cuQuo);
|
|
|
|
// Get the uint to use for the trial divisions. We normalize so the high bit is set.
|
|
uint uDen = regDen._rgu[cuDen - 1];
|
|
uint uDenNext = regDen._rgu[cuDen - 2];
|
|
int cbitShiftLeft = NumericsHelpers.CbitHighZero(uDen);
|
|
int cbitShiftRight = kcbitUint - cbitShiftLeft;
|
|
if (cbitShiftLeft > 0)
|
|
{
|
|
uDen = (uDen << cbitShiftLeft) | (uDenNext >> cbitShiftRight);
|
|
uDenNext <<= cbitShiftLeft;
|
|
if (cuDen > 2)
|
|
uDenNext |= regDen._rgu[cuDen - 3] >> cbitShiftRight;
|
|
}
|
|
Contract.Assert((uDen & 0x80000000) != 0);
|
|
|
|
// Allocate and initialize working space.
|
|
Contract.Assert(cuQuo + cuDen == regNum._iuLast + 1 || cuQuo + cuDen == regNum._iuLast + 2);
|
|
regNum.EnsureWritable();
|
|
|
|
for (int iu = cuQuo; --iu >= 0; )
|
|
{
|
|
// Get the high (normalized) bits of regNum.
|
|
uint uNumHi = iu + cuDen <= regNum._iuLast ? regNum._rgu[iu + cuDen] : 0;
|
|
Contract.Assert(uNumHi <= regDen._rgu[cuDen - 1]);
|
|
|
|
ulong uuNum = NumericsHelpers.MakeUlong(uNumHi, regNum._rgu[iu + cuDen - 1]);
|
|
uint uNumNext = regNum._rgu[iu + cuDen - 2];
|
|
if (cbitShiftLeft > 0)
|
|
{
|
|
uuNum = (uuNum << cbitShiftLeft) | (uNumNext >> cbitShiftRight);
|
|
uNumNext <<= cbitShiftLeft;
|
|
if (iu + cuDen >= 3)
|
|
uNumNext |= regNum._rgu[iu + cuDen - 3] >> cbitShiftRight;
|
|
}
|
|
|
|
// Divide to get the quotient digit.
|
|
ulong uuQuo = uuNum / uDen;
|
|
ulong uuRem = (uint)(uuNum % uDen);
|
|
Contract.Assert(uuQuo <= (ulong)uint.MaxValue + 2);
|
|
if (uuQuo > uint.MaxValue)
|
|
{
|
|
uuRem += uDen * (uuQuo - uint.MaxValue);
|
|
uuQuo = uint.MaxValue;
|
|
}
|
|
while (uuRem <= uint.MaxValue && uuQuo * uDenNext > NumericsHelpers.MakeUlong((uint)uuRem, uNumNext))
|
|
{
|
|
uuQuo--;
|
|
uuRem += uDen;
|
|
}
|
|
|
|
// Multiply and subtract. Note that uuQuo may be 1 too large. If we have a borrow
|
|
// at the end, we'll add the denominator back on and decrement uuQuo.
|
|
if (uuQuo > 0)
|
|
{
|
|
ulong uuBorrow = 0;
|
|
for (int iu2 = 0; iu2 < cuDen; iu2++)
|
|
{
|
|
uuBorrow += regDen._rgu[iu2] * uuQuo;
|
|
uint uSub = (uint)uuBorrow;
|
|
uuBorrow >>= kcbitUint;
|
|
if (regNum._rgu[iu + iu2] < uSub)
|
|
uuBorrow++;
|
|
regNum._rgu[iu + iu2] -= uSub;
|
|
}
|
|
|
|
Contract.Assert(uNumHi == uuBorrow || uNumHi == uuBorrow - 1);
|
|
if (uNumHi < uuBorrow)
|
|
{
|
|
// Add, tracking carry.
|
|
uint uCarry = 0;
|
|
for (int iu2 = 0; iu2 < cuDen; iu2++)
|
|
{
|
|
uCarry = AddCarry(ref regNum._rgu[iu + iu2], regDen._rgu[iu2], uCarry);
|
|
Contract.Assert(uCarry <= 1);
|
|
}
|
|
Contract.Assert(uCarry == 1);
|
|
uuQuo--;
|
|
}
|
|
regNum._iuLast = iu + cuDen - 1;
|
|
}
|
|
|
|
if (fQuo)
|
|
{
|
|
if (cuQuo == 1)
|
|
regQuo._uSmall = (uint)uuQuo;
|
|
else
|
|
regQuo._rgu[iu] = (uint)uuQuo;
|
|
}
|
|
}
|
|
|
|
Contract.Assert(cuDen > 1 && regNum._iuLast > 0);
|
|
regNum._iuLast = cuDen - 1;
|
|
regNum.Trim();
|
|
}
|
|
|
|
//private static readonly double kdblLn2To32 = 32 * Math.Log(2);
|
|
|
|
/*internal void ShiftRight(int cbit)
|
|
{
|
|
AssertValid(true);
|
|
if (cbit <= 0)
|
|
{
|
|
if (cbit < 0)
|
|
ShiftLeft(-cbit);
|
|
return;
|
|
}
|
|
ShiftRight(cbit / kcbitUint, cbit % kcbitUint);
|
|
}
|
|
|
|
internal void ShiftRight(int cuShift, int cbitShift)
|
|
{
|
|
Contract.Assert(cuShift >= 0);
|
|
Contract.Assert(0 <= cbitShift);
|
|
Contract.Assert(cbitShift < kcbitUint);
|
|
AssertValid(true);
|
|
|
|
if ((cuShift | cbitShift) == 0)
|
|
return;
|
|
if (cuShift > _iuLast)
|
|
{
|
|
Set(0);
|
|
return;
|
|
}
|
|
if (_iuLast == 0)
|
|
{
|
|
_uSmall >>= cbitShift;
|
|
AssertValid(true);
|
|
return;
|
|
}
|
|
|
|
uint[] rguSrc = _rgu;
|
|
int cuSrc = _iuLast + 1;
|
|
_iuLast -= cuShift;
|
|
if (_iuLast == 0)
|
|
_uSmall = rguSrc[cuShift] >> cbitShift;
|
|
else
|
|
{
|
|
Contract.Assert(_rgu.Length > _iuLast);
|
|
if (!_fWritable)
|
|
{
|
|
_rgu = new uint[_iuLast + 1];
|
|
_fWritable = true;
|
|
}
|
|
if (cbitShift > 0)
|
|
{
|
|
for (int iuSrc = cuShift + 1, iuDst = 0; iuSrc < cuSrc; iuSrc++, iuDst++)
|
|
_rgu[iuDst] = (rguSrc[iuSrc - 1] >> cbitShift) | (rguSrc[iuSrc] << (kcbitUint - cbitShift));
|
|
_rgu[_iuLast] = rguSrc[cuSrc - 1] >> cbitShift;
|
|
Trim();
|
|
}
|
|
else
|
|
Array.Copy(rguSrc, cuShift, _rgu, 0, _iuLast + 1);
|
|
}
|
|
AssertValid(true);
|
|
}*/
|
|
|
|
/*internal void ShiftLeft(int cbit)
|
|
{
|
|
AssertValid(true);
|
|
if (cbit <= 0)
|
|
{
|
|
if (cbit < 0)
|
|
ShiftRight(-cbit);
|
|
return;
|
|
}
|
|
ShiftLeft(cbit / kcbitUint, cbit % kcbitUint);
|
|
}
|
|
|
|
internal void ShiftLeft(int cuShift, int cbitShift)
|
|
{
|
|
Contract.Assert(cuShift >= 0);
|
|
Contract.Assert(0 <= cbitShift);
|
|
Contract.Assert(cbitShift < kcbitUint);
|
|
AssertValid(true);
|
|
|
|
int iuLastNew = _iuLast + cuShift;
|
|
uint uHigh = 0;
|
|
if (cbitShift > 0)
|
|
{
|
|
uHigh = High >> (kcbitUint - cbitShift);
|
|
if (uHigh != 0)
|
|
iuLastNew++;
|
|
}
|
|
if (iuLastNew == 0)
|
|
{
|
|
_uSmall <<= cbitShift;
|
|
return;
|
|
}
|
|
|
|
uint[] rguSrc = _rgu;
|
|
bool fClearLow = cuShift > 0;
|
|
if (!_fWritable || _rgu.Length <= iuLastNew)
|
|
{
|
|
_rgu = new uint[iuLastNew + 1];
|
|
_fWritable = true;
|
|
fClearLow = false;
|
|
}
|
|
if (_iuLast == 0)
|
|
{
|
|
if (uHigh != 0)
|
|
_rgu[cuShift + 1] = uHigh;
|
|
_rgu[cuShift] = _uSmall << cbitShift;
|
|
}
|
|
else if (cbitShift == 0)
|
|
Array.Copy(rguSrc, 0, _rgu, cuShift, _iuLast + 1);
|
|
else
|
|
{
|
|
int iuSrc = _iuLast;
|
|
int iuDst = _iuLast + cuShift;
|
|
if (iuDst < iuLastNew)
|
|
_rgu[iuLastNew] = uHigh;
|
|
for (; iuSrc > 0; iuSrc--, iuDst--)
|
|
_rgu[iuDst] = (rguSrc[iuSrc] << cbitShift) | (rguSrc[iuSrc - 1] >> (kcbitUint - cbitShift));
|
|
_rgu[cuShift] = rguSrc[0] << cbitShift;
|
|
}
|
|
_iuLast = iuLastNew;
|
|
if (fClearLow)
|
|
Array.Clear(_rgu, 0, cuShift);
|
|
}*/
|
|
|
|
// Get the high two uints, combined into a ulong, zero extending to
|
|
// length cu if necessary. Asserts cu > _iuLast and _iuLast > 0.
|
|
/*
|
|
private ulong GetHigh2(int cu)
|
|
{
|
|
Contract.Assert(cu >= 2);
|
|
Contract.Assert(_iuLast > 0);
|
|
Contract.Assert(cu > _iuLast);
|
|
|
|
if (cu - 1 <= _iuLast)
|
|
return NumericsHelpers.MakeUlong(_rgu[cu - 1], _rgu[cu - 2]);
|
|
if (cu - 2 == _iuLast)
|
|
return _rgu[cu - 2];
|
|
return 0;
|
|
}
|
|
*/
|
|
|
|
// Apply a single carry starting at iu, extending the register
|
|
// if needed.
|
|
/*
|
|
private void ApplyCarry(int iu)
|
|
{
|
|
Contract.Assert(0 <= iu);
|
|
Contract.Assert(_fWritable && _iuLast > 0);
|
|
Contract.Assert(iu <= _iuLast + 1);
|
|
|
|
for (; ; iu++)
|
|
{
|
|
if (iu > _iuLast)
|
|
{
|
|
if (_iuLast + 1 == _rgu.Length)
|
|
Array.Resize(ref _rgu, _iuLast + 2);
|
|
_rgu[++_iuLast] = 1;
|
|
break;
|
|
}
|
|
if (++_rgu[iu] > 0)
|
|
break;
|
|
}
|
|
}
|
|
*/
|
|
|
|
// Apply a single borrow starting at iu. This does NOT trim the result.
|
|
/*
|
|
private void ApplyBorrow(int iuMin)
|
|
{
|
|
Contract.Assert(0 < iuMin);
|
|
Contract.Assert(_fWritable && _iuLast > 0);
|
|
Contract.Assert(iuMin <= _iuLast);
|
|
|
|
for (int iu = iuMin; iu <= _iuLast; iu++)
|
|
{
|
|
uint u = _rgu[iu]--;
|
|
if (u > 0)
|
|
return;
|
|
}
|
|
// Borrowed off the end!
|
|
Contract.Assert(false, "Invalid call to ApplyBorrow");
|
|
}
|
|
*/
|
|
|
|
private static uint AddCarry(ref uint u1, uint u2, uint uCarry)
|
|
{
|
|
ulong uu = (ulong)u1 + u2 + uCarry;
|
|
u1 = (uint)uu;
|
|
return (uint)(uu >> kcbitUint);
|
|
}
|
|
|
|
/*private static uint SubBorrow(ref uint u1, uint u2, uint uBorrow)
|
|
{
|
|
ulong uu = (ulong)u1 - u2 - uBorrow;
|
|
u1 = (uint)uu;
|
|
return (uint)-(int)(uu >> kcbitUint);
|
|
}
|
|
|
|
private static uint SubRevBorrow(ref uint u1, uint u2, uint uBorrow)
|
|
{
|
|
ulong uu = (ulong)u2 - u1 - uBorrow;
|
|
u1 = (uint)uu;
|
|
return (uint)-(int)(uu >> kcbitUint);
|
|
}*/
|
|
|
|
private static uint MulCarry(ref uint u1, uint u2, uint uCarry)
|
|
{
|
|
// This is guaranteed not to overflow.
|
|
ulong uuRes = (ulong)u1 * u2 + uCarry;
|
|
u1 = (uint)uuRes;
|
|
return (uint)(uuRes >> kcbitUint);
|
|
}
|
|
|
|
private static uint AddMulCarry(ref uint uAdd, uint uMul1, uint uMul2, uint uCarry)
|
|
{
|
|
// This is guaranteed not to overflow.
|
|
ulong uuRes = (ulong)uMul1 * uMul2 + uAdd + uCarry;
|
|
uAdd = (uint)uuRes;
|
|
return (uint)(uuRes >> kcbitUint);
|
|
}
|
|
|
|
// ReSharper disable once InconsistentNaming
|
|
/*
|
|
internal static void GCD(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2)
|
|
{
|
|
// Use Lehmer's GCD, with improvements, after eliminating common powers of 2.
|
|
if (reg1._iuLast > 0 && reg1._rgu[0] == 0 || reg2._iuLast > 0 && reg2._rgu[0] == 0)
|
|
{
|
|
int cbit1 = reg1.MakeOdd();
|
|
int cbit2 = reg2.MakeOdd();
|
|
LehmerGcd(ref reg1, ref reg2);
|
|
int cbitMin = Math.Min(cbit1, cbit2);
|
|
if (cbitMin > 0)
|
|
reg1.ShiftLeft(cbitMin);
|
|
}
|
|
else
|
|
LehmerGcd(ref reg1, ref reg2);
|
|
}
|
|
*/
|
|
|
|
// This leaves the GCD in reg1 and trash in reg2.
|
|
// This uses Lehmer's method, with test due to Jebelean / Belnkiy and Vidunas.
|
|
// See Knuth, vol 2, page 345; Jebelean (1993) "Improving the Multiprecision Euclidean Algorithm";
|
|
// and Belenkiy & Vidunas (1998) "A Greatest Common Divisor Algorithm".
|
|
/*
|
|
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2)
|
|
{
|
|
// This value has no real significance. Occ----ionally we want to subtract
|
|
// the two registers and keep the absolute value of the difference. To do
|
|
// so we need to pass a ref sign to Sub.
|
|
int signTmp = +1;
|
|
|
|
for (; ; )
|
|
{
|
|
reg1.AssertValid(true);
|
|
reg2.AssertValid(true);
|
|
|
|
int cuMax = reg1._iuLast + 1;
|
|
int cuMin = reg2._iuLast + 1;
|
|
if (cuMax < cuMin)
|
|
{
|
|
NumericsHelpers.Swap(ref reg1, ref reg2);
|
|
NumericsHelpers.Swap(ref cuMax, ref cuMin);
|
|
}
|
|
Contract.Assert(cuMax == reg1._iuLast + 1);
|
|
Contract.Assert(cuMin == reg2._iuLast + 1);
|
|
|
|
if (cuMin == 1)
|
|
{
|
|
if (cuMax == 1)
|
|
reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall);
|
|
else if (reg2._uSmall != 0)
|
|
reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall));
|
|
return;
|
|
}
|
|
|
|
if (cuMax == 2)
|
|
{
|
|
reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2)));
|
|
return;
|
|
}
|
|
|
|
if (cuMin <= cuMax - 2)
|
|
{
|
|
// reg1 is much larger than reg2, so just mod.
|
|
reg1.Mod(ref reg2);
|
|
continue;
|
|
}
|
|
|
|
ulong uu1 = reg1.GetHigh2(cuMax);
|
|
ulong uu2 = reg2.GetHigh2(cuMax);
|
|
Contract.Assert(uu1 != 0 && uu2 != 0);
|
|
|
|
int cbit = NumericsHelpers.CbitHighZero(uu1 | uu2);
|
|
if (cbit > 0)
|
|
{
|
|
uu1 = (uu1 << cbit) | (reg1._rgu[cuMax - 3] >> (kcbitUint - cbit));
|
|
// Note that [cuMax - 3] is correct, NOT [cuMin - 3].
|
|
uu2 = (uu2 << cbit) | (reg2._rgu[cuMax - 3] >> (kcbitUint - cbit));
|
|
}
|
|
if (uu1 < uu2)
|
|
{
|
|
NumericsHelpers.Swap(ref uu1, ref uu2);
|
|
NumericsHelpers.Swap(ref reg1, ref reg2);
|
|
}
|
|
|
|
// Make sure we don't overflow.
|
|
if (uu1 == ulong.MaxValue || uu2 == ulong.MaxValue)
|
|
{
|
|
uu1 >>= 1;
|
|
uu2 >>= 1;
|
|
}
|
|
Contract.Assert(uu1 >= uu2); // We ensured this above.
|
|
if (uu1 == uu2)
|
|
{
|
|
// The high bits are the same, so we don't know which
|
|
// is larger. No matter, just subtract one from the other
|
|
// and keep the absolute value of the result.
|
|
Contract.Assert(cuMax == cuMin);
|
|
reg1.Sub(ref signTmp, ref reg2);
|
|
Contract.Assert(reg1._iuLast < cuMin - 1);
|
|
continue;
|
|
}
|
|
if (NumericsHelpers.GetHi(uu2) == 0)
|
|
{
|
|
// reg1 is much larger than reg2, so just mod.
|
|
reg1.Mod(ref reg2);
|
|
continue;
|
|
}
|
|
|
|
// These are the coefficients to apply to reg1 and reg2 to get
|
|
// the new values, using: a * reg1 - b * reg2 and -c * reg1 + d * reg2.
|
|
uint a = 1, b = 0;
|
|
uint c = 0, d = 1;
|
|
|
|
for (; ; )
|
|
{
|
|
Contract.Assert(uu1 + a > a); // no overflow
|
|
Contract.Assert(uu2 + d > d);
|
|
Contract.Assert(uu1 > b);
|
|
Contract.Assert(uu2 > c);
|
|
Contract.Assert(uu2 + d <= uu1 - b);
|
|
|
|
uint uQuo = 1;
|
|
ulong uuNew = uu1 - uu2;
|
|
while (uuNew >= uu2 && uQuo < 32)
|
|
{
|
|
uuNew -= uu2;
|
|
uQuo++;
|
|
}
|
|
if (uuNew >= uu2)
|
|
{
|
|
ulong uuQuo = uu1 / uu2;
|
|
if (uuQuo > uint.MaxValue)
|
|
break;
|
|
uQuo = (uint)uuQuo;
|
|
uuNew = uu1 - uQuo * uu2;
|
|
}
|
|
ulong uuAdNew = a + (ulong)uQuo * c;
|
|
ulong uuBcNew = b + (ulong)uQuo * d;
|
|
if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
|
|
break;
|
|
// Jebelean / Belenkiy-Vidunas conditions
|
|
if (uuNew < uuBcNew || uuNew + uuAdNew > uu2 - c)
|
|
break;
|
|
|
|
Contract.Assert(uQuo == (uu1 + a - 1) / (uu2 - c));
|
|
Contract.Assert(uQuo == (uu1 - b) / (uu2 + d));
|
|
|
|
a = (uint)uuAdNew;
|
|
b = (uint)uuBcNew;
|
|
uu1 = uuNew;
|
|
|
|
if (uu1 <= b)
|
|
{
|
|
Contract.Assert(uu1 == b);
|
|
break;
|
|
}
|
|
|
|
Contract.Assert(uu1 + a > a); // no overflow
|
|
Contract.Assert(uu2 + d > d);
|
|
Contract.Assert(uu2 > c);
|
|
Contract.Assert(uu1 > b);
|
|
Contract.Assert(uu1 + a <= uu2 - c);
|
|
|
|
uQuo = 1;
|
|
uuNew = uu2 - uu1;
|
|
while (uuNew >= uu1 && uQuo < 32)
|
|
{
|
|
uuNew -= uu1;
|
|
uQuo++;
|
|
}
|
|
if (uuNew >= uu1)
|
|
{
|
|
ulong uuQuo = uu2 / uu1;
|
|
if (uuQuo > uint.MaxValue)
|
|
break;
|
|
uQuo = (uint)uuQuo;
|
|
uuNew = uu2 - uQuo * uu1;
|
|
}
|
|
uuAdNew = d + (ulong)uQuo * b;
|
|
uuBcNew = c + (ulong)uQuo * a;
|
|
if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
|
|
break;
|
|
// Jebelean / Belenkiy-Vidunas conditions
|
|
if (uuNew < uuBcNew || uuNew + uuAdNew > uu1 - b)
|
|
break;
|
|
|
|
Contract.Assert(uQuo == (uu2 + d - 1) / (uu1 - b));
|
|
Contract.Assert(uQuo == (uu2 - c) / (uu1 + a));
|
|
|
|
d = (uint)uuAdNew;
|
|
c = (uint)uuBcNew;
|
|
uu2 = uuNew;
|
|
|
|
if (uu2 <= c)
|
|
{
|
|
Contract.Assert(uu2 == c);
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (b == 0)
|
|
{
|
|
Contract.Assert(a == 1 && c == 0 && d == 1);
|
|
Contract.Assert(uu1 > uu2); // We ensured this above.
|
|
if (uu1 / 2 >= uu2)
|
|
reg1.Mod(ref reg2);
|
|
else
|
|
reg1.Sub(ref signTmp, ref reg2);
|
|
}
|
|
else
|
|
{
|
|
// Replace reg1 with a * reg1 - b * reg2.
|
|
// Replace reg2 with -c * reg1 + d * reg2.
|
|
// Do everything mod cuMin uint's.
|
|
reg1.SetSizeKeep(cuMin, 0);
|
|
reg2.SetSizeKeep(cuMin, 0);
|
|
int nCarry1 = 0;
|
|
int nCarry2 = 0;
|
|
for (int iu = 0; iu < cuMin; iu++)
|
|
{
|
|
uint u1 = reg1._rgu[iu];
|
|
uint u2 = reg2._rgu[iu];
|
|
long nn1 = (long)u1 * a - (long)u2 * b + nCarry1;
|
|
long nn2 = (long)u2 * d - (long)u1 * c + nCarry2;
|
|
nCarry1 = (int)(nn1 >> kcbitUint);
|
|
nCarry2 = (int)(nn2 >> kcbitUint);
|
|
reg1._rgu[iu] = (uint)nn1;
|
|
reg2._rgu[iu] = (uint)nn2;
|
|
}
|
|
reg1.Trim();
|
|
reg2.Trim();
|
|
}
|
|
}
|
|
}
|
|
*/
|
|
|
|
/*internal int CbitLowZero()
|
|
{
|
|
AssertValid(true);
|
|
if (_iuLast == 0)
|
|
{
|
|
if ((_uSmall & 1) != 0 || _uSmall == 0)
|
|
return 0;
|
|
return NumericsHelpers.CbitLowZero(_uSmall);
|
|
}
|
|
|
|
int iuMin = 0;
|
|
while (_rgu[iuMin] == 0)
|
|
iuMin++;
|
|
int cbit = NumericsHelpers.CbitLowZero(_rgu[iuMin]);
|
|
return cbit + iuMin * kcbitUint;
|
|
}*/
|
|
|
|
// Shift right until the number is odd. Return the number of bits
|
|
// shifted. Asserts that the register is trimmed.
|
|
/*
|
|
internal int MakeOdd()
|
|
{
|
|
AssertValid(true);
|
|
int cbit = CbitLowZero();
|
|
if (cbit > 0)
|
|
ShiftRight(cbit);
|
|
return cbit;
|
|
}
|
|
*/
|
|
}
|
|
}
|