// 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)
{
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
{
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 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);
}
// This version may share memory with regMul.
public void Mul(ref BigIntegerBuilder regMul)
{
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;
}
}
}
}
}
// Divide 'this' by regDen, leaving the remainder in 'this' and tossing the quotient.
public void Mod(ref BigIntegerBuilder regDen)
{
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);
}
public BigIntegerBuilder(ref BigIntegerBuilder reg)
{
this = reg;
if (_fWritable)
{
_fWritable = false;
if (_iuLast == 0)
{
_rgu = null;
}
else
{
reg._fWritable = false;
}
}
}
public void Add(ref BigIntegerBuilder reg)
{
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);
_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);
}
// Deal with extra carry.
if (uCarry != 0)
{
ApplyCarry(cuAdd);
}
}
// Divide 'this' by regDen, leaving the quotient in 'this' and tossing the remainder.
public void Div(ref BigIntegerBuilder regDen)
{
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);
}
// 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)
{
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);
}
}
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);
}
}
// Divide regNum by uDen, returning the remainder and tossing the quotient.
public static uint Mod(ref BigIntegerBuilder regNum, uint uDen)
{
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);
}
// 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)
{
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);
_iuLast = reg._iuLast;
}
uint uBorrow = 0;
for (int iu = 0; iu < cuSub; iu++)
{
uBorrow = SubRevBorrow(ref _rgu[iu], reg._rgu[iu], uBorrow);
}
if (uBorrow != 0)
{
ApplyBorrow(cuSub);
}
Trim();
}
private static void ModDivCore(ref BigIntegerBuilder regNum, ref BigIntegerBuilder regDen, bool fQuo, ref BigIntegerBuilder regQuo)
{
regQuo.Set(0);
if (regNum._iuLast < regDen._iuLast)
{
return;
}
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;
}
}
// Allocate and initialize working space.
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;
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);
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;
}
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);
}
uuQuo--;
}
regNum._iuLast = iu + cuDen - 1;
}
if (fQuo)
{
if (cuQuo == 1)
{
regQuo._uSmall = (uint)uuQuo;
}
else
{
regQuo._rgu[iu] = (uint)uuQuo;
}
}
}
regNum._iuLast = cuDen - 1;
regNum.Trim();
}
public void Sub(ref int sign, ref BigIntegerBuilder reg)
{
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;
}
return;
}
if (u1 < u2)
{
reg._iuLast = _iuLast;
SubRev(ref reg);
reg._iuLast = cuSub - 1;
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);
}
if (uBorrow != 0)
{
ApplyBorrow(cuSub);
}
Trim();
}
// Loads the value of reg into this register.
public void Load(ref BigIntegerBuilder reg)
{
Load(ref reg, 0);
}
// 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 (;;)
{
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);
}
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);
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;
}
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.
reg1.Sub(ref signTmp, ref reg2);
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 (;;)
{
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;
}
a = (uint)uuAdNew;
b = (uint)uuBcNew;
uu1 = uuNew;
if (uu1 <= b)
{
break;
}
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;
}
d = (uint)uuAdNew;
c = (uint)uuBcNew;
uu2 = uuNew;
if (uu2 <= c)
{
break;
}
}
if (b == 0)
{
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();
}
}
}