private int F2SmallParallel(long x1, long x2)
{
var xmin = UpToOdd(Math.Max(1, x1));
var xmax = DownToOdd(Math.Min((long)IntegerMath.FloorSquareRoot(n), x2));
if (threads <= 1)
{
return(F2SmallParallel(0, xmin, xmax, x1, 2));
}
var xsmall = DownToOdd(Math.Max(xmin, Math.Min(smallCutoff, xmax)));
var s = 0;
for (var x = xmin; x < xsmall; x += 2)
{
s += IntegerMath.Mobius(x) * T2Parallel(n / ((UInt128)x * (UInt128)x));
}
var tasks = new Task <int> [threads];
var increment = 2 * threads;
for (var thread = 0; thread < threads; thread++)
{
var worker = thread;
var offset = 2 * thread;
tasks[thread] = Task.Factory.StartNew(() => F2SmallParallel(worker, xsmall + offset, xmax, x1, increment));
}
Task.WaitAll(tasks);
s += tasks.Select(task => task.Result).Sum();
return(s & 3);
}
private int Pi2Small(long x1, long x2)
{
var s = F2SmallParallel(x1, x2);
for (var k = 2; k <= kmax; k++)
{
var mu = IntegerMath.Mobius(k);
if (mu != 0)
{
s += mu * F2Small((UInt128)IntegerMath.FloorRoot((BigInteger)n, k), x1, x2);
}
}
return(s & 3);
}
private int FinishBlock(long k0, int length, sbyte[] products, sbyte[] values, long kmin, int[] sums, int sum0)
{
// Each product of a squareful number is less than zero.
// Each product of a square-free number can have at most one
// more prime factor. It has that factor if the value of
// the product is less half than the full value.
var k = k0;
var kmax = k + 2 * length;
var log2 = IntegerMath.CeilingLogBaseTwo(k) - 1;
var next = Math.Min((long)1 << (log2 + 1), kmax - 2);
if (sums == null)
{
while (k < kmax)
{
while (k <= next)
{
// Look ma, no branching.
Debug.Assert(log2 == IntegerMath.CeilingLogBaseTwo(k) - 1);
var p = (int)products[(k - k0) >> 1];
var flip = (log2 - p) >> 31; // flip = -1 if log2 < p, zero otherwise
values[(k - kmin) >> 1] = (sbyte)((((((p & 1) << 1) - 1) ^ flip) - flip) & ~(p >> 31));
Debug.Assert(values[(k - kmin) >> 1] == (sbyte)(p <0 ? 0 : p> log2 ? 1 - 2 * (p & 1) : 2 * (p & 1) - 1));
k += 2;
}
++log2;
next = Math.Min(next << 1, kmax - 2);
}
}
else if (values == null)
{
while (k < kmax)
{
while (k <= next)
{
// Look ma, no branching.
Debug.Assert(log2 == IntegerMath.CeilingLogBaseTwo(k) - 1);
var p = (int)products[(k - k0) >> 1];
var flip = (log2 - p) >> 31; // flip = -1 if log2 < p, zero otherwise
sums[(k - kmin) >> 1] = sum0 += (((((p & 1) << 1) - 1) ^ flip) - flip) & ~(p >> 31);
Debug.Assert(k == k0 || sums[(k - kmin) >> 1] - sums[(k - kmin - 2) >> 1] == (sbyte)(p <0 ? 0 : p> log2 ? 1 - 2 * (p & 1) : 2 * (p & 1) - 1));
k += 2;
}
++log2;
next = Math.Min(next << 1, kmax - 2);
}
}
else
{
while (k < kmax)
{
while (k <= next)
{
// Look ma, no branching.
Debug.Assert(log2 == IntegerMath.CeilingLogBaseTwo(k) - 1);
var p = (int)products[(k - k0) >> 1];
var flip = (log2 - p) >> 31; // flip = -1 if log2 < p, zero otherwise
var value = (((((p & 1) << 1) - 1) ^ flip) - flip) & ~(p >> 31);
var kk = (k - kmin) >> 1;
sums[kk] = sum0 += value;
values[kk] = (sbyte)value;
Debug.Assert(values[(k - kmin) >> 1] == (sbyte)(p <0 ? 0 : p> log2 ? 1 - 2 * (p & 1) : 2 * (p & 1) - 1));
Debug.Assert(values[(k - kmin) >> 1] == IntegerMath.Mobius(k));
k += 2;
}
++log2;
next = Math.Min(next << 1, kmax - 2);
}
}
return(sum0);
}
public MertensFunctionWheel(int threads)
{
this.threads = threads;
wheelSubtotal = new int[wheelSize];
wheelInclude = new bool[wheelSize >> 1];
wheelNext = new byte[wheelSize >> 1];
wheelPrev = new byte[wheelSize >> 1];
var total = 0;
for (var i = 0; i < wheelSize; i++)
{
var include = IntegerMath.GreatestCommonDivisor(i, wheelSize) == 1;
if (include)
{
++total;
}
wheelSubtotal[i] = total;
wheelInclude[i >> 1] = include;
}
Debug.Assert(total == wheelCount);
var next = 0;
for (var i = (wheelSize >> 1) - 1; i >= 0; i--)
{
next += 2;
wheelNext[i] = (byte)next;
if (wheelInclude[i])
{
next = 0;
}
}
var prev = 0;
for (var i = 0; i < (wheelSize >> 1); i++)
{
prev += 2;
wheelPrev[i] = (byte)prev;
if (wheelInclude[i])
{
prev = 0;
}
}
#if DEBUG
for (var i = 1; i < wheelSize; i += 2)
{
var skip = wheelNext[i >> 1];
for (var j = 2; j < skip; j += 2)
{
if (wheelInclude[((i + j) % wheelSize) >> 1])
{
Debugger.Break();
}
}
if (!wheelInclude[((i + skip) % wheelSize) >> 1])
{
Debugger.Break();
}
}
for (var i = 1; i < wheelSize; i += 2)
{
var skip = wheelPrev[i >> 1];
for (var j = 2; j < skip; j += 2)
{
if (wheelInclude[((i - j + wheelSize) % wheelSize) >> 1])
{
Debugger.Break();
}
}
if (!wheelInclude[((i - skip + wheelSize) % wheelSize) >> 1])
{
Debugger.Break();
}
}
#endif
wheelFactors = IntegerMath.Factors(wheelSize).ToArray();
wheelMobius = wheelFactors.Select(factor => IntegerMath.Mobius(factor)).ToArray();
}
