public static MutableInteger SetGreatestCommonDivisor(this MutableInteger c, MutableInteger a, MutableInteger b, MutableIntegerStore store)
{
var reg1 = store.Allocate();
if (a.IsZero)
c.Set(b);
else if (b.IsZero)
c.Set(a);
else
{
reg1.Set(a);
c.Set(b);
while (true)
{
reg1.Modulo(c);
if (reg1.IsZero)
break;
c.Modulo(reg1);
if (c.IsZero)
{
c.Set(reg1);
break;
}
}
}
store.Release(reg1);
return c;
}
public static MutableInteger SetModularInverse(this MutableInteger c, MutableInteger a, MutableInteger b, MutableIntegerStore store)
{
var p = store.Allocate().Set(a);
var q = store.Allocate().Set(b);
var x0 = store.Allocate().Set(1);
var x1 = store.Allocate().Set(0);
var quotient = store.Allocate();
var remainder = store.Allocate();
var product = store.Allocate();
while (!q.IsZero)
{
remainder.Set(p).ModuloWithQuotient(q, quotient);
var tmpp = p;
p = q;
q = tmpp.Set(remainder);
var tmpx = x1;
x1 = x0.Subtract(product.SetProduct(quotient, x1));
x0 = tmpx;
}
c.Set(x0);
if (c.Sign == -1)
c.Add(b);
store.Release(p);
store.Release(q);
store.Release(x0);
store.Release(x1);
store.Release(quotient);
store.Release(remainder);
return c;
}
public static MutableInteger SetModularInversePowerOfTwoModulus(this MutableInteger c, MutableInteger d, int n, MutableIntegerStore store)
{
// See 9.2 in: http://gmplib.org/~tege/divcnst-pldi94.pdf
c.Set(d);
var two = store.Allocate().Set(2);
var reg1 = store.Allocate();
var reg2 = store.Allocate();
for (int m = 3; m < n; m *= 2)
{
reg1.Set(c);
reg2.SetProduct(reg1, d);
reg2.Mask(n);
reg2.SetDifference(two, reg2);
c.SetProduct(reg1, reg2);
c.Mask(n);
}
if (c.Sign == -1)
c.Add(reg1.Set(1).LeftShift(n));
store.Release(two);
store.Release(reg1);
store.Release(reg2);
return c;
}
private int TauSumInnerWorkerLarge(UInt128 y, ulong imin, ulong imax)
{
#if false
var sum = (uint)0;
for (var i = imin; i < imax; i++)
sum ^= (uint)(y / i);
return (int)(sum & 1);
#endif
#if false
var yRep = (MutableInteger)y;
var xRep = yRep.Copy();
var iRep = (MutableInteger)imin;
var store = new MutableIntegerStore(4);
var sum = (uint)0;
for (var i = imin; i < imax; i++)
{
sum ^= xRep.Set(yRep).Divide(iRep, store).LeastSignificantWord;
iRep.Increment();
}
return (int)(sum & 1);
#endif
#if false
// The quantity floor(y/d) is odd iff y mod 2d >= d.
var sum = (ulong)0;
for (var i = imin; i < imax; i++)
sum ^= y % (i << 1) - i;
sum >>= 63;
if (((imax - imin) & 1) != 0)
sum ^= 1;
return (int)(sum & 1);
#endif
#if false
if (y.IsPowerOfTwo)
{
var uBits = y.GetBitLength() - 32;
var sum = (uint)0;
var y0 = (UInt128)y.LeastSignificantWord;
var y12 = (ulong)(y >> 32);
for (var i = imin; i < imax; i++)
{
var y12mod = y12 % i;
var yPrime = y0 + ((y12 % i) << 32);
var shift = 64 - i.GetBitCount();
sum ^= (uint)(y / i);
}
return (int)(sum & 1);
}
#endif
#if false
var sum = (uint)0;
var i = imax - 1;
var current = (ulong)(y / (i + 1));
var delta = (ulong)(y / i - current);
var mod = (long)(y - (UInt128)current * (i + 1));
var imid = Math.Max(imin, (ulong)(y >> (64 - safetyBits)));
while (i >= imid)
{
mod += (long)(current - delta * i);
current += delta;
if (mod >= (long)i)
{
++delta;
++current;
mod -= (long)i;
if (mod >= (long)i)
break;
}
else if (mod < 0)
{
--delta;
--current;
mod += (long)i;
}
Debug.Assert(y / i == current);
sum ^= (uint)current;
--i;
}
while (i >= imin)
{
sum ^= (uint)(y / i);
--i;
}
return (int)(sum & 1);
#endif
#if true
var sum = (uint)0;
var i = imax - 1;
var current = (ulong)(y / (i + 1));
var delta = (ulong)(y / i) - current;
var mod = (long)(y - (UInt128)current * (i + 1));
var imid = Math.Max(imin, (ulong)(y >> (64 - safetyBits)));
var deltai = delta * (i + 1);
while (i >= imid)
{
deltai -= delta;
mod += (long)(current - deltai);
if (mod >= (long)i)
{
++delta;
deltai += i;
mod -= (long)i;
if (mod >= (long)i)
break;
}
else if (mod < 0)
{
--delta;
deltai -= i;
mod += (long)i;
}
current += delta;
Debug.Assert(y / i == current);
sum ^= (uint)current;
--i;
}
while (i >= imin)
{
sum ^= (uint)(y / i);
--i;
}
return (int)(sum & 1);
#endif
}