VMProtect/runtime/VMProtect.Runtime/Numerics/BigIntegerBuilder.cs

// ==++==
// 
//   Copyright (c) Microsoft Corporation.  All rights reserved.
// 
// ==--==

using System;

using Contracts = System.Diagnostics.Debug;
using Contract = System.Diagnostics.Debug;
using Conditional = System.Diagnostics.ConditionalAttribute;

// ReSharper disable once CheckNamespace
namespace Numerics
{
	/// <summary>
	/// BigIntegerBuilder holds a multiprecision unsigned integer value. It is mutable and
	/// supports common arithmetic operations. Be careful NOT to simply assign one
	/// BigIntegerBuilder to another, unless you really know what you are doing. The proper
	/// way to replicate a BigIntegerBuilder is via the constructor "BigIntegerBuilder(ref BigIntegerBuilder reg)",
	/// or with reg1.Load(ref reg2). Using the ctor marks the buffer as shared so changing the
	/// value of one register will not affect the other. Using Load copies the contents from
	/// one to the other. Either way, the internal buffer isn't aliased incorrectly.
	/// </summary>
	internal struct BigIntegerBuilder
	{
		// ReSharper disable once InconsistentNaming
		private const int kcbitUint = 32;

		// For a single uint, _iuLast is 0.
		private int _iuLast;

		// Used if _iuLast == 0.
		private uint _uSmall;

		// Used if _iuLast > 0.
		private uint[] _rgu;

		// This is false whenever _rgu is null or is shared with a NewBigInteger
		// or with another BigIntegerBuilder.
		private bool _fWritable;

		[Conditional("DEBUG")]
		// ReSharper disable once UnusedParameter.Local
		private void AssertValid(bool fTrimmed)
		{
			if (_iuLast <= 0)
			{
				Contract.Assert(_iuLast == 0);
				Contract.Assert(!_fWritable || _rgu != null);
			}
			else
			{
				Contract.Assert(_rgu != null && _rgu.Length > _iuLast);
				Contract.Assert(!fTrimmed || _rgu[_iuLast] != 0);
			}
		}

#if CONTRACTS_FULL
    [ContractInvariantMethod]
    private void ObjectInvariant()
    {
      Contract.Invariant(_iuLast >=0);
      Contract.Invariant(!(_iuLast == 0) || (!_fWritable || _rgu != null));
      Contract.Invariant(!(_iuLast > 0) || (_rgu != null && _rgu.Length > _iuLast));
    }
#endif

/*
		internal BigIntegerBuilder(ref BigIntegerBuilder reg)
		{
			reg.AssertValid(true);
			this = reg;
			if (_fWritable)
			{
				_fWritable = false;
				if (_iuLast == 0)
					_rgu = null;
				else
					reg._fWritable = false;
			}
			AssertValid(true);
		}
*/

		internal BigIntegerBuilder(int cuAlloc)
		{
			_iuLast = 0;
			_uSmall = 0;
			if (cuAlloc > 1)
			{
				_rgu = new uint[cuAlloc];
				_fWritable = true;
			}
			else
			{
				_rgu = null;
				_fWritable = false;
			}
			AssertValid(true);
		}

/*
		internal BigIntegerBuilder(BigInteger bn)
		{
			_fWritable = false;
			_rgu = bn._Bits;
			if (_rgu == null)
			{
				_iuLast = 0;
				_uSmall = NumericsHelpers.Abs(bn._Sign);
			}
			else
			{
				_iuLast = _rgu.Length - 1;
				_uSmall = _rgu[0];
				while (_iuLast > 0 && _rgu[_iuLast] == 0)
					--_iuLast;
			}
			AssertValid(true);
		}
*/

		internal BigIntegerBuilder(BigInteger bn, ref int sign)
		{
			Contract.Assert(sign == +1 || sign == -1);

			_fWritable = false;
			_rgu = bn._Bits;
			int n = bn._Sign;
			int mask = n >> (kcbitUint - 1);
			sign = (sign ^ mask) - mask;
			if (_rgu == null)
			{
				_iuLast = 0;
				_uSmall = (uint)((n ^ mask) - mask);
			}
			else
			{
				_iuLast = _rgu.Length - 1;
				_uSmall = _rgu[0];
				while (_iuLast > 0 && _rgu[_iuLast] == 0)
					--_iuLast;
			}
			AssertValid(true);
		}

		internal BigInteger GetInteger(int sign)
		{
			Contract.Assert(sign == +1 || sign == -1);
			AssertValid(true);

			uint[] bits;
			GetIntegerParts(sign, out sign, out bits);
			return new BigInteger(sign, bits);
		}

		private void GetIntegerParts(int signSrc, out int sign, out uint[] bits)
		{
			Contract.Assert(signSrc == +1 || signSrc == -1);
			AssertValid(true);

			if (_iuLast == 0)
			{
				if (_uSmall <= int.MaxValue)
				{
					sign = signSrc * (int)_uSmall;
					bits = null;
					return;
				}
				if (_rgu == null)
					_rgu = new[] { _uSmall };
				else if (_fWritable)
					_rgu[0] = _uSmall;
				else if (_rgu[0] != _uSmall)
					_rgu = new[] { _uSmall };
			}

			// The sign is +/- 1.
			sign = signSrc;

			int cuExtra = _rgu.Length - _iuLast - 1;
			Contract.Assert(cuExtra >= 0);
			if (cuExtra <= 1)
			{
				if (cuExtra == 0 || _rgu[_iuLast + 1] == 0)
				{
					_fWritable = false;
					bits = _rgu;
					return;
				}
				if (_fWritable)
				{
					_rgu[_iuLast + 1] = 0;
					_fWritable = false;
					bits = _rgu;
					return;
				}
				// The buffer isn't writable, but has an extra uint that is non-zero,
				// so we have to allocate a new buffer.
			}

			// Keep the bigger buffer (if it is writable), but create a smaller one for the BigInteger.
			bits = _rgu;
			Array.Resize(ref bits, _iuLast + 1);
			if (!_fWritable)
				_rgu = bits;
		}

		private void Set(uint u)
		{
			_uSmall = u;
			_iuLast = 0;
			AssertValid(true);
		}

		private void Set(ulong uu)
		{
			uint uHi = NumericsHelpers.GetHi(uu);
			if (uHi == 0)
			{
				_uSmall = NumericsHelpers.GetLo(uu);
				_iuLast = 0;
			}
			else
			{
				SetSizeLazy(2);
				_rgu[0] = (uint) uu;
				_rgu[1] = uHi;
			}
		}

		internal int Size { get { return _iuLast + 1; } }

		//internal uint High { get { return _iuLast == 0 ? _uSmall : _rgu[_iuLast]; } }


		/*internal void GetApproxParts(out int exp, out ulong man)
		{
			AssertValid(true);
			if (_iuLast == 0)
			{
				man = _uSmall;
				exp = 0;
				return;
			}

			int cuLeft = _iuLast - 1;
			man = NumericsHelpers.MakeUlong(_rgu[cuLeft + 1], _rgu[cuLeft]);
			exp = cuLeft * kcbitUint;

			int cbit;
			if (cuLeft > 0 && (cbit = NumericsHelpers.CbitHighZero(_rgu[cuLeft + 1])) > 0)
			{
				// Get 64 bits.
				Contract.Assert(cbit < kcbitUint);
				man = (man << cbit) | (_rgu[cuLeft - 1] >> (kcbitUint - cbit));
				exp -= cbit;
			}
		}*/

		private void Trim()
		{
			AssertValid(false);
			if (_iuLast > 0 && _rgu[_iuLast] == 0)
			{
				_uSmall = _rgu[0];
				while (--_iuLast > 0 && _rgu[_iuLast] == 0)
				{
				}
			}
			AssertValid(true);
		}

		private int CuNonZero
		{
			get
			{
				Contract.Assert(_iuLast > 0);
				int cu = 0;
				for (int iu = _iuLast; iu >= 0; --iu)
				{
					if (_rgu[iu] != 0)
						cu++;
				}
				return cu;
			}
		}

		// Sets the size to cu and makes sure the buffer is writable (if cu > 1),
		// but makes no guarantees about the contents of the buffer.
		private void SetSizeLazy(int cu)
		{
			Contract.Assert(cu > 0);
			AssertValid(false);
			if (cu <= 1)
			{
				_iuLast = 0;
				return;
			}
			if (!_fWritable || _rgu.Length < cu)
			{
				_rgu = new uint[cu];
				_fWritable = true;
			}
			_iuLast = cu - 1;
			AssertValid(false);
		}

		// Sets the size to cu, makes sure the buffer is writable (if cu > 1),
		// and set the contents to all zero.
		private void SetSizeClear(int cu)
		{
			Contract.Assert(cu > 0);
			AssertValid(false);
			if (cu <= 1)
			{
				_iuLast = 0;
				_uSmall = 0;
				return;
			}
			if (!_fWritable || _rgu.Length < cu)
			{
				_rgu = new uint[cu];
				_fWritable = true;
			}
			else
				Array.Clear(_rgu, 0, cu);
			_iuLast = cu - 1;
			AssertValid(false);
		}

		// Sets the size to cu, makes sure the buffer is writable (if cu > 1),
		// and maintains the contents. If the buffer is reallocated, cuExtra
		// uints are also allocated.
		private void SetSizeKeep(int cu, int cuExtra)
		{
			Contract.Assert(cu > 0 && cuExtra >= 0);
			AssertValid(false);

			if (cu <= 1)
			{
				if (_iuLast > 0)
					_uSmall = _rgu[0];
				_iuLast = 0;
				return;
			}
			if (!_fWritable || _rgu.Length < cu)
			{
				uint[] rgu = new uint[cu + cuExtra];
				if (_iuLast == 0)
					rgu[0] = _uSmall;
				else
					Array.Copy(_rgu, rgu, Math.Min(cu, _iuLast + 1));
				_rgu = rgu;
				_fWritable = true;
			}
			else if (_iuLast + 1 < cu)
			{
				Array.Clear(_rgu, _iuLast + 1, cu - _iuLast - 1);
				if (_iuLast == 0)
					_rgu[0] = _uSmall;
			}
			_iuLast = cu - 1;
			AssertValid(false);
		}

		// Makes sure the buffer is writable and can support cu uints.
		// Preserves the contents of the buffer up to min(_iuLast + 1, cu).
		// Changes the size if cu <= _iuLast and the buffer needs to be allocated.
/*
		internal void EnsureWritable(int cu, int cuExtra)
		{
			Contract.Assert(cu > 1 && cuExtra >= 0);
			AssertValid(false);

			if (_fWritable && _rgu.Length >= cu)
				return;

			uint[] rgu = new uint[cu + cuExtra];
			if (_iuLast > 0)
			{
				if (_iuLast >= cu)
					_iuLast = cu - 1;
				Array.Copy(_rgu, rgu, _iuLast + 1);
			}
			_rgu = rgu;
			_fWritable = true;
			AssertValid(false);
		}
*/

		// Makes sure the buffer is writable and can support _iuLast + 1 uints.
		// Preserves the contents of the buffer.
		private void EnsureWritable(int cuExtra = 0)
		{
			Contract.Assert(cuExtra >= 0);
			AssertValid(false);
			Contract.Assert(_iuLast > 0);

			if (_fWritable)
				return;

			uint[] rgu = new uint[_iuLast + 1 + cuExtra];
			Array.Copy(_rgu, rgu, _iuLast + 1);
			_rgu = rgu;
			_fWritable = true;
			AssertValid(false);
		}

		// Loads the value of reg into this register.
		/*internal void Load(ref BigIntegerBuilder reg)
		{
			Load(ref reg, 0);
		}*/

		// Loads the value of reg into this register. If we need to allocate memory
		// to perform the load, allocate cuExtra elements.
		private void Load(ref BigIntegerBuilder reg, int cuExtra)
		{
			Contract.Assert(cuExtra >= 0);
			AssertValid(false);
			reg.AssertValid(true);

			if (reg._iuLast == 0)
			{
				_uSmall = reg._uSmall;
				_iuLast = 0;
			}
			else
			{
				if (!_fWritable || _rgu.Length <= reg._iuLast)
				{
					_rgu = new uint[reg._iuLast + 1 + cuExtra];
					_fWritable = true;
				}
				_iuLast = reg._iuLast;
				Array.Copy(reg._rgu, _rgu, _iuLast + 1);
			}
			AssertValid(true);
		}

		/*internal void Add(uint u)
		{
			AssertValid(true);
			if (_iuLast == 0)
			{
				if ((_uSmall += u) >= u)
					return;
				SetSizeLazy(2);
				_rgu[0] = _uSmall;
				_rgu[1] = 1;
				return;
			}

			if (u == 0)
				return;

			uint uNew = _rgu[0] + u;
			if (uNew < u)
			{
				// Have carry.
				EnsureWritable(1);
				ApplyCarry(1);
			}
			else if (!_fWritable)
				EnsureWritable();
			_rgu[0] = uNew;
			AssertValid(true);
		}

		internal void Add(ref BigIntegerBuilder reg)
		{
			AssertValid(true);
			reg.AssertValid(true);

			if (reg._iuLast == 0)
			{
				Add(reg._uSmall);
				return;
			}
			if (_iuLast == 0)
			{
				uint u = _uSmall;
				if (u == 0)
					this = new BigIntegerBuilder(ref reg);
				else
				{
					Load(ref reg, 1);
					Add(u);
				}
				return;
			}

			EnsureWritable(Math.Max(_iuLast, reg._iuLast) + 1, 1);

			int cuAdd = reg._iuLast + 1;
			if (_iuLast < reg._iuLast)
			{
				cuAdd = _iuLast + 1;
				Array.Copy(reg._rgu, _iuLast + 1, _rgu, _iuLast + 1, reg._iuLast - _iuLast);
				Contract.Assert(_iuLast > 0);
				_iuLast = reg._iuLast;
			}

			// Add, tracking carry.
			uint uCarry = 0;
			for (int iu = 0; iu < cuAdd; iu++)
			{
				uCarry = AddCarry(ref _rgu[iu], reg._rgu[iu], uCarry);
				Contract.Assert(uCarry <= 1);
			}

			// Deal with extra carry.
			if (uCarry != 0)
				ApplyCarry(cuAdd);
			AssertValid(true);
		}

		internal void Sub(ref int sign, uint u)
		{
			Contract.Assert(sign == +1 || sign == -1);
			AssertValid(true);
			if (_iuLast == 0)
			{
				if (u <= _uSmall)
					_uSmall -= u;
				else
				{
					_uSmall = u - _uSmall;
					sign = -sign;
				}
				AssertValid(true);
				return;
			}

			if (u == 0)
				return;

			EnsureWritable();

			uint uTmp = _rgu[0];
			_rgu[0] = uTmp - u;
			if (uTmp < u)
			{
				ApplyBorrow(1);
				Trim();
			}
			AssertValid(true);
		}

		internal void Sub(ref int sign, ref BigIntegerBuilder reg)
		{
			Contract.Assert(sign == +1 || sign == -1);
			AssertValid(true);
			reg.AssertValid(true);

			if (reg._iuLast == 0)
			{
				Sub(ref sign, reg._uSmall);
				return;
			}
			if (_iuLast == 0)
			{
				uint u = _uSmall;
				if (u == 0)
					this = new BigIntegerBuilder(ref reg);
				else
				{
					Load(ref reg);
					Sub(ref sign, u);
				}
				sign = -sign;
				return;
			}

			if (_iuLast < reg._iuLast)
			{
				SubRev(ref reg);
				sign = -sign;
				return;
			}

			int cuSub = reg._iuLast + 1;
			if (_iuLast == reg._iuLast)
			{
				// 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;
		}
*/
	}
}