public Reducer(MutableIntegerReduction reduction, BigInteger n)
: base(reduction, n)
{
length = (n.GetBitLength() + 31) / 32 * 2 + 1;
store = new MutableIntegerStore(length);
nRep = store.Allocate();
nRep.Set(n);
}
public DivisorSummatoryFunctionOddBigInteger(int threads)
{
this.threads = threads;
queue = new BlockingCollection <Region>();
finished = new ManualResetEventSlim();
manualAlgorithm = new DivisionFreeDivisorSummatoryFunction(threads, false, true);
stores = new IStore <MutableInteger> [Math.Max(threads, 1)];
for (var i = 0; i < Math.Max(threads, 1); i++)
{
stores[i] = new MutableIntegerStore(8);
}
}
public Reducer(IReductionAlgorithm <BigInteger> reduction, BigInteger p)
{
this.reduction = reduction;
this.p = p;
bLength = 32;
b = BigInteger.One << bLength;
var pLength = p.GetBitLength();
k = (pLength - 1) / bLength + 1;
mu = BigInteger.Pow(b, 2 * k) / p;
var muLength = mu.GetBitLength();
length = (pLength + 31) / 32 * 2 + (muLength + 31) / 32;
store = new MutableIntegerStore(length);
muRep = store.Allocate();
pRep = store.Allocate();
muRep.Set(mu);
pRep.Set(p);
bToTheKMinusOneLength = bLength * (k - 1);
bToTheKPlusOneLength = bLength * (k + 1);
}
public Reducer(BigIntegerMontgomeryReduction reduction, BigInteger modulus)
: base(reduction, modulus)
{
if (modulus.IsEven)
{
throw new InvalidOperationException("not relatively prime");
}
var rLength = (modulus.GetBitLength() + 31) / 32 * 32;
length = (int)(2 * rLength / 32 + 1);
store = new MutableIntegerStore(length);
nRep = store.Allocate().Set(modulus);
var rRep = store.Allocate().Set(1).LeftShift((int)rLength);
var nInv = store.Allocate().SetModularInversePowerOfTwoModulus(nRep, (int)rLength, store);
var kRep = store.Allocate().Set(rRep).Subtract(nInv);
k0 = kRep.LeastSignificantWord;
rSquaredModNRep = store.Allocate().SetSquare(rRep).Modulo(nRep);
oneRep = store.Allocate().Set(1).Multiply(rSquaredModNRep, store);
store.Release(rRep);
store.Release(nInv);
store.Release(kRep);
Reduce(oneRep);
}
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 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);
}
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);
}
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
}
