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// ==++==
//
// Copyright (c) Microsoft Corporation. All rights reserved.
//
// ==--==
using System;
using System.Diagnostics.Contracts;
using System.Runtime.InteropServices;
using Conditional = System.Diagnostics.ConditionalAttribute;
namespace System.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 {
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")]
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
public BigIntegerBuilder(ref BigIntegerBuilder reg) {
reg.AssertValid(true);
this = reg;
if (_fWritable) {
_fWritable = false;
if (_iuLast == 0)
_rgu = null;
else
reg._fWritable = false;
}
AssertValid(true);
}
public BigIntegerBuilder(int cuAlloc) {
_iuLast = 0;
_uSmall = 0;
if (cuAlloc > 1) {
_rgu = new uint[cuAlloc];
_fWritable = true;
}
else {
_rgu = null;
_fWritable = false;
}
AssertValid(true);
}
public 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);
}
public BigIntegerBuilder(BigInteger bn, ref int sign) {
Contract.Requires(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);
}
public BigInteger GetInteger(int sign) {
Contract.Requires(sign == +1 || sign == -1);
AssertValid(true);
uint[] bits;
GetIntegerParts(sign, out sign, out bits);
return new BigInteger(sign, bits);
}
internal void GetIntegerParts(int signSrc, out int sign, out uint[] bits) {
Contract.Requires(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 uint[1] { _uSmall };
else if (_fWritable)
_rgu[0] = _uSmall;
else if (_rgu[0] != _uSmall)
_rgu = new uint[1] { _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;
}
public void Set(uint u) {
_uSmall = u;
_iuLast = 0;
AssertValid(true);
}
public 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;
}
AssertValid(true);
}
public int Size { get { return _iuLast + 1; } }
public uint High { get { return _iuLast == 0 ? _uSmall : _rgu[_iuLast]; } }
public void GetApproxParts(out int exp, out ulong man) {
AssertValid(true);
if (_iuLast == 0) {
man = (ulong)_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.Requires(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.Requires(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.Requires(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.
public void EnsureWritable(int cu, int cuExtra) {
Contract.Requires(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.
public void EnsureWritable(int cuExtra) {
Contract.Requires(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);
}
public void EnsureWritable() {
EnsureWritable(0);
}
// Loads the value of reg into this register.
public 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.
public void Load(ref BigIntegerBuilder reg, int cuExtra) {
Contract.Requires(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);
}
public 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);
}
public 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);
}
public void Sub(ref int sign, uint u) {
Contract.Requires(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);
}
public void Sub(ref int sign, ref BigIntegerBuilder reg) {
Contract.Requires(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();
}
public 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.
public 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.
public 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.
public 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.
public 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.
public 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.
public 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).
public 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);
public void ShiftRight(int cbit) {
AssertValid(true);
if (cbit <= 0) {
if (cbit < 0)
ShiftLeft(-cbit);
return;
}
ShiftRight(cbit / kcbitUint, cbit % kcbitUint);
}
public void ShiftRight(int cuShift, int cbitShift) {
Contract.Requires(cuShift >= 0);
Contract.Requires(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);
}
public void ShiftLeft(int cbit) {
AssertValid(true);
if (cbit <= 0) {
if (cbit < 0)
ShiftRight(-cbit);
return;
}
ShiftLeft(cbit / kcbitUint, cbit % kcbitUint);
}
public void ShiftLeft(int cuShift, int cbitShift) {
Contract.Requires(cuShift >= 0);
Contract.Requires(0 <= cbitShift);
Contract.Assert(cbitShift < kcbitUint);
AssertValid(true);
int iuLastNew = _iuLast + cuShift;
uint uHigh = 0;
if (cbitShift > 0) {
uHigh = this.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.Requires(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.Requires(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.Requires(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);
}
public 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();
}
}
}
public 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.
public int MakeOdd() {
AssertValid(true);
int cbit = CbitLowZero();
if (cbit > 0)
ShiftRight(cbit);
return cbit;
}
private static readonly byte[] _rgbInv = new byte[128] {
0x01, 0xAB, 0xCD, 0xB7, 0x39, 0xA3, 0xC5, 0xEF,
0xF1, 0x1B, 0x3D, 0xA7, 0x29, 0x13, 0x35, 0xDF,
0xE1, 0x8B, 0xAD, 0x97, 0x19, 0x83, 0xA5, 0xCF,
0xD1, 0xFB, 0x1D, 0x87, 0x09, 0xF3, 0x15, 0xBF,
0xC1, 0x6B, 0x8D, 0x77, 0xF9, 0x63, 0x85, 0xAF,
0xB1, 0xDB, 0xFD, 0x67, 0xE9, 0xD3, 0xF5, 0x9F,
0xA1, 0x4B, 0x6D, 0x57, 0xD9, 0x43, 0x65, 0x8F,
0x91, 0xBB, 0xDD, 0x47, 0xC9, 0xB3, 0xD5, 0x7F,
0x81, 0x2B, 0x4D, 0x37, 0xB9, 0x23, 0x45, 0x6F,
0x71, 0x9B, 0xBD, 0x27, 0xA9, 0x93, 0xB5, 0x5F,
0x61, 0x0B, 0x2D, 0x17, 0x99, 0x03, 0x25, 0x4F,
0x51, 0x7B, 0x9D, 0x07, 0x89, 0x73, 0x95, 0x3F,
0x41, 0xEB, 0x0D, 0xF7, 0x79, 0xE3, 0x05, 0x2F,
0x31, 0x5B, 0x7D, 0xE7, 0x69, 0x53, 0x75, 0x1F,
0x21, 0xCB, 0xED, 0xD7, 0x59, 0xC3, 0xE5, 0x0F,
0x11, 0x3B, 0x5D, 0xC7, 0x49, 0x33, 0x55, 0xFF
};
}
}
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