public BigInteger ProcessRegionManual(int thread, BigInteger w, BigInteger a1, BigInteger b1, BigInteger c1, BigInteger a2, BigInteger b2, BigInteger c2)
{
if (w <= 1)
{
return(0);
}
var s = (BigInteger)0;
var umax = (long)w - 1;
var t1 = (a1 * b2 + b1 * a2) << 1;
var t2 = (c1 << 1) - a1 - b1;
var t3 = (t2 << 2) + 12;
var t4 = (a1 * b1) << 2;
var t5 = t1 * (1 + c1) - a1 + b1 - t4 * c2;
var t6 = IntegerMath.Square(t2 + 2) - t4 * n;
var store = stores[thread];
var sRep = store.Allocate().Set(0);
var t1Rep = store.Allocate().Set(t1);
var t3Rep = store.Allocate().Set(t3);
var t4Rep = store.Allocate().Set(t4);
var t5Rep = store.Allocate().Set(t5);
var t6Rep = store.Allocate().Set(t6);
var t7Rep = store.Allocate();
var t8Rep = store.Allocate();
var u = (long)1;
while (true)
{
t8Rep.SetUnsignedDifference(t5Rep, t7Rep.SetCeilingSquareRoot(t6Rep, store))
.ModuloWithQuotient(t4Rep, t7Rep);
sRep.SetUnsignedSum(sRep, t7Rep);
if (u >= umax)
{
break;
}
t5Rep.SetUnsignedSum(t5Rep, t1Rep);
t6Rep.SetUnsignedSum(t6Rep, t3Rep);
t3Rep.SetUnsignedSum(t3Rep, 8);
++u;
}
s = sRep;
store.Release(sRep);
store.Release(t1Rep);
store.Release(t3Rep);
store.Release(t4Rep);
store.Release(t6Rep);
store.Release(t7Rep);
store.Release(t8Rep);
Debug.Assert(s == ProcessRegionHorizontal(w, 0, a1, b1, c1, a2, b2, c2));
#if DIAG
Console.WriteLine("ProcessRegionManual: s = {0}", s);
#endif
return(s);
}
public void VFloor2(BigInteger u1, BigInteger a1, BigInteger b1, BigInteger c1, BigInteger c2, BigInteger abba, BigInteger ab2, out BigInteger v1, out BigInteger v2)
{
var uu = (u1 + c1) << 1;
var t1 = ab2 << 1;
var t2 = abba * uu - a1 + b1 - t1 * c2;
var t3 = uu - a1 - b1;
var t4 = IntegerMath.Square(t3) - t1 * n;
v1 = (t2 - IntegerMath.CeilingSquareRoot(t4)) / t1;
v2 = (t2 + (abba << 1) - IntegerMath.CeilingSquareRoot(t4 + ((t3 + 1) << 2))) / t1;
}
public ulong ProcessRegionManual(int thread, ulong w, ulong a1, ulong b1, ulong c1, ulong a2, ulong b2, ulong c2)
{
if (w <= 1)
{
return(0);
}
var s = (ulong)0;
var umax = w - 1;
var t1 = (a1 * b2 + b1 * a2) << 1;
var t2 = (c1 << 1) - a1 - b1;
var t3 = (t2 << 2) + 12;
var t4 = (a1 * b1) << 2;
var t5 = t1 * (1 + c1) - a1 + b1 - t4 * c2;
var t6 = IntegerMath.Square(t2 + 2) - t4 * n;
Debug.Assert(t6 == UInt128.Square(t2 + 2) - t4 * (UInt128)n);
var u = (ulong)1;
while (true)
{
Debug.Assert((t5 - IntegerMath.CeilingSquareRoot(t6)) / t4 == VFloor(u, a1, b1, c1, a2, b2, c2));
s += (t5 - IntegerMath.CeilingSquareRoot(t6)) / t4;
if (u >= umax)
{
break;
}
t5 += t1;
t6 += t3;
t3 += 8;
++u;
}
Debug.Assert(s == ProcessRegionHorizontal(w, 0, a1, b1, c1, a2, b2, c2));
#if DIAG
Console.WriteLine("ProcessRegionManual: s = {0}", s);
#endif
return(s);
}
public int Evaluate(UInt128 n)
{
this.n = n;
var sum = 0;
sqrtn = (long)IntegerMath.FloorSquareRoot(n);
kmax = (int)IntegerMath.FloorLog(n, 2);
imax = (long)IntegerMath.FloorPower(n, 1, 5) * C1 / C2;
xmax = DownToOdd(imax != 0 ? Xi(imax) : sqrtn);
xmed = DownToOdd(Math.Min((long)(IntegerMath.FloorPower(n, 2, 7) * C3 / C4), xmax));
var dmax = (long)IntegerMath.Min(n / IntegerMath.Square((UInt128)xmed) + 1, n);
mobius = new MobiusOddRangeAdditive((xmax + 2) | 1, threads);
divisors = new DivisorOddRangeAdditive((dmax + 2) | 1, threads);
xi = new long[imax + 1];
mx = new long[imax + 1];
// Initialize xi.
for (var i = 1; i <= imax; i++)
{
xi[i] = Xi(i);
}
values = new sbyte[mobiusBatchSize >> 1];
m = new int[mobiusBatchSize >> 1];
m0 = 0;
dsums = new ulong[divisorBatchSize >> 1];
d1 = d2 = 1;
// Process small x values.
for (var x = (long)1; x <= xmed; x += mobiusBatchSize)
{
var xfirst = x;
var xlast = Math.Min(xmed, xfirst + mobiusBatchSize - 2);
m0 = mobius.GetValuesAndSums(xfirst, xlast + 2, values, m, m0);
sum += Pi2Small(xfirst, xlast);
UpdateMx(xfirst, xlast);
}
// Process medium x values.
#if true
for (var x = xmed + 2; x <= xmax; x += mobiusBatchSize)
{
var xfirst = x;
var xlast = Math.Min(xmax, xfirst + mobiusBatchSize - 2);
m0 = mobius.GetValuesAndSums(xfirst, xlast + 2, values, m, m0);
sum += Pi2Medium(xfirst, xlast);
UpdateMx(xfirst, xlast);
}
#else
for (var x = xmax; x > xmed; x -= mobiusBatchSize)
{
var xlast = x;
var xfirst = Math.Max(xmed + 2, xlast - mobiusBatchSize + 2);
m0 = mobius.GetValuesAndSums(xfirst, xlast + 2, values, m, m0);
sum += Pi2Medium(xfirst, xlast);
UpdateMx(xfirst, xlast);
}
#endif
// Process large x values.
sum += Pi2Large();
// Adjust for final parity of F2.
sum -= IntegerMath.Mertens(kmax);
// Compute final result.
sum &= 3;
Debug.Assert((sum & 1) == 0);
sum >>= 1;
return((sum + (n >= 2 ? 1 : 0)) % 2);
}
public BigInteger VFloor(BigInteger u, BigInteger a1, BigInteger b1, BigInteger c1, BigInteger a2, BigInteger b2, BigInteger c2)
{
return((2 * (a1 * b2 + b1 * a2) * (u + c1) - a1 + b1 - IntegerMath.CeilingSquareRoot(IntegerMath.Square(2 * (u + c1) - a1 - b1) - 4 * a1 * b1 * n)) / (4 * a1 * b1) - c2);
}
public BigInteger UFloor(BigInteger v, BigInteger a1, BigInteger b1, BigInteger c1, BigInteger a2, BigInteger b2, BigInteger c2)
{
return((2 * (a1 * b2 + b1 * a2) * (v + c2) + a2 - b2 - IntegerMath.CeilingSquareRoot(IntegerMath.Square(2 * (v + c2) - a2 - b2) - 4 * a2 * b2 * n)) / (4 * a2 * b2) - c1);
}
public BigInteger UTan(BigInteger ab1, BigInteger abba, BigInteger ab2, BigInteger a3b3, BigInteger c1)
{
return((ab1 + IntegerMath.FloorSquareRoot(IntegerMath.Square(abba + ab2) * n / a3b3) - (c1 << 1)) / 2);
}