public BigInteger Evaluate(BigInteger n)
{
t3Map.Clear();
var jmax = IntegerMath.FloorLog(n, 2);
var dmax = IntegerMath.FloorRoot(n, 3);
mobius = new MobiusCollection((int)(IntegerMath.Max(jmax, dmax) + 1), 0);
return(Pi3(n));
}
public BigInteger Pi3(BigInteger n)
{
var kmax = IntegerMath.FloorLog(n, 2);
var sum = (BigInteger)0;
for (var k = 1; k <= kmax; k++)
{
if (k % 3 != 0 && mobius[k] != 0)
{
sum += k * mobius[k] * F3(IntegerMath.FloorRoot(n, k));
}
}
return((sum + 1) % 3);
}
public static T PerfectPower <T>(T a)
{
// See: Sieve Algorithms for Perfect Power Testing,
// E. Bach and J. Sorenson, Algorithmica 9 (1993) 313-328.
// Algorithm B (modified).
var absA = Number <T> .Abs(a);
var bits = IntegerMath.FloorLog((T)absA, 2);
var logA = Number <T> .Log(absA).Real;
var smallPrimes = GetSmallPrimes();
foreach (var p in smallPrimes)
{
if (absA != a && p == 2)
{
continue;
}
var b = (Number <T>)p;
if (b > bits)
{
break;
}
if (!IsPossiblePerfectPower(a, p))
{
continue;
}
Number <T> power;
var c = FloorRootCore <T>(absA, logA, b, out power);
if (power == absA)
{
return(b * PerfectPower <T>(absA == a ? c : -c));
}
}
return(Number <T> .One);
}
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);
}