public long Evaluate(long n)
{
if (n <= 0)
{
return(0);
}
this.n = n;
u = Math.Max((long)IntegerMath.FloorPower((BigInteger)n, 2, 3) * C1 / C2, IntegerMath.CeilingSquareRoot(n));
imax = n / u;
this.mobius = new MobiusRange(u + 1, threads);
var batchSize = Math.Min(u, maximumBatchSize);
m = new int[batchSize];
mx = new long[imax + 1];
var m0 = 0;
for (var x = (long)1; x <= u; x += maximumBatchSize)
{
var xstart = x;
var xend = Math.Min(xstart + maximumBatchSize - 1, u);
m0 = mobius.GetSums(xstart, xend + 1, m, m0);
ProcessBatch(xstart, xend);
}
ComputeMx();
return(mx[1]);
}
public long Evaluate(long n)
{
if (n <= 0)
{
return(0);
}
this.n = n;
u = Math.Max((long)IntegerMath.FloorPower((BigInteger)n, 2, 3) * C1 / C2, IntegerMath.CeilingSquareRoot(n));
u = DownToOdd(u);
imax = n / u;
this.mobius = new MobiusRange(imax + 1, threads);
this.mobiusOdd = new MobiusOddRange(u + 2, threads);
var batchSize = Math.Min(u + 1, maximumBatchSize);
mu = new sbyte[imax];
m = new int[batchSize >> 1];
sum = 0;
mobius.GetValues(1, imax + 1, mu);
var m0 = 0;
for (var x = (long)1; x <= u; x += maximumBatchSize)
{
var xstart = x;
var xend = Math.Min(xstart + maximumBatchSize - 2, u);
m0 = mobiusOdd.GetSums(xstart, xend + 2, m, m0);
ProcessBatch(xstart, xend);
}
return(mi1 - sum);
}
public BigInteger Evaluate(BigInteger n)
{
this.n = n;
if (n == 1)
{
return(1);
}
sum = 0;
imax = (long)IntegerMath.FloorRoot(n, 5) / C1;
xmax = imax != 0 ? Xi(imax) : (long)IntegerMath.FloorPower(n, 1, 2);
mobius = new MobiusRange(xmax + 1, 0);
mertens = new MertensRangeDR(mobius, Xi(1));
xi = new long[imax + 1];
mx = new long[imax + 1];
// Initialize xi (mx already initialized to zeros).
for (var i = 1; i <= imax; i++)
{
xi[i] = Xi(i);
}
if (threads <= 1)
{
var values = new sbyte[maximumBatchSize];
var m = new long[maximumBatchSize];
Evaluate(1, xmax, values, m);
}
else
{
EvaluateParallel(1, xmax);
}
EvaluateTail();
return(sum);
}
public MertensRangeBasic(MobiusRange mobius, long nmax)
{
this.mobius = mobius;
this.nmax = nmax;
threads = mobius.Threads;
u = Math.Max((long)IntegerMath.FloorPower((BigInteger)nmax, 2, 3) * C1 / C2, IntegerMath.CeilingSquareRoot(nmax));
ulo = Math.Min(u, maximumBatchSize);
mlo = new int[ulo];
mobius.GetSums(1, ulo + 1, mlo, 0);
}
public MertensRangeDR(MobiusRange mobius, long nmax)
{
this.mobius = mobius;
this.nmax = nmax;
threads = mobius.Threads;
u = Math.Max((long)IntegerMath.FloorPower((BigInteger)nmax, 2, 3) * C1 / C2, IntegerMath.CeilingSquareRoot(nmax));
ulo = Math.Max(Math.Min(u, maximumBatchSize), minimumLowSize);
mlo = new int[ulo];
values = new sbyte[ulo];
mobius.GetValuesAndSums(1, ulo + 1, values, mlo, 0);
}
private void ConsumeSumTwoToTheOmegaItems(int thread, BlockingCollection <WorkItem> queue, MobiusRange mobius, UInt128 x, ref int sum)
{
var values = new sbyte[blockSize];
var item = default(WorkItem);
while (queue.TryTake(out item, Timeout.Infinite))
{
if (item.Max == item.Min + 1 && item.Min < (ulong)mobiusSmall.Length)
{
values[0] = (sbyte)mobiusSmall[item.Min];
}
else
{
mobius.GetValues((long)item.Min, (long)item.Max, values);
}
Interlocked.Add(ref sum, SumTwoToTheOmega(values, x, item.Min, item.Max));
}
}
private int SumTwoToTheOmega(UInt128 x, ulong limit)
{
var sum = 0;
ulong d;
for (d = 1; d < singleLimit1; d++)
{
var mu = mobiusSmall[d];
if (mu != 0)
{
var tau = TauSumParallel(x / (d * d));
if (mu == 1)
{
sum += tau;
}
else
{
sum += 4 - tau;
}
}
}
var mobius = new MobiusRange((long)limit + 1, 0);
var queue = new BlockingCollection <WorkItem>();
var units = limit < (1 << 16) ? 1 : 100;
var consumers = Math.Max(1, threads);
var tasks = new Task[consumers];
for (var consumer = 0; consumer < consumers; consumer++)
{
var thread = consumer;
tasks[consumer] = Task.Factory.StartNew(() => ConsumeSumTwoToTheOmegaItems(thread, queue, mobius, x, ref sum));
}
for (d = singleLimit1; d < singleLimit2; d++)
{
if (mobiusSmall[d] != 0)
{
queue.Add(new WorkItem {
Min = d, Max = d + 1
});
}
}
for (var unit = 0; unit < units; unit++)
{
var dmin = d;
var dmax = unit == units - 1 ? limit + 1 : (ulong)Math.Exp((unit + 1) * Math.Log(limit + 1) / units);
if (dmin >= dmax)
{
continue;
}
if (dmax - dmin > blockSize)
{
break;
}
queue.Add(new WorkItem {
Min = dmin, Max = dmax
});
d = dmax;
}
while (d < limit + 1)
{
var dmin = d;
var dmax = Math.Min(dmin + blockSize, limit + 1);
queue.Add(new WorkItem {
Min = dmin, Max = dmax
});
d = dmax;
}
queue.CompleteAdding();
Task.WaitAll(tasks);
return(sum & 3);
}
public long Evaluate(long n)
{
if (n <= 0)
{
return(0);
}
this.n = n;
u = Math.Max((long)IntegerMath.FloorPower((BigInteger)n, 2, 3) * C1 / C2, IntegerMath.CeilingSquareRoot(n));
if (u <= wheelSize)
{
return(new MertensFunctionDR(threads).Evaluate(n));
}
imax = (int)(n / u);
mobius = new MobiusRange(u + 1, threads);
var batchSize = Math.Min(u, maximumBatchSize);
m = new int[batchSize];
mx = new long[imax + 1];
r = new int[imax + 1];
lmax = 0;
for (var i = 1; i <= imax; i += 2)
{
if (wheelInclude[(i % wheelSize) >> 1])
{
r[lmax++] = i;
}
}
Array.Resize(ref r, lmax);
if (threads > 1)
{
var costs = new double[threads];
var bucketLists = new List <int> [threads];
for (var thread = 0; thread < threads; thread++)
{
bucketLists[thread] = new List <int>();
}
for (var l = 0; l < lmax; l++)
{
var i = r[l];
var cost = Math.Sqrt(n / i);
var addto = 0;
var mincost = costs[0];
for (var thread = 0; thread < threads; thread++)
{
if (costs[thread] < mincost)
{
mincost = costs[thread];
addto = thread;
}
}
bucketLists[addto].Add(i);
costs[addto] += cost;
}
buckets = new int[threads][];
for (var thread = 0; thread < threads; thread++)
{
buckets[thread] = bucketLists[thread].ToArray();
}
}
var m0 = 0;
for (var x = (long)1; x <= u; x += maximumBatchSize)
{
var xstart = x;
var xend = Math.Min(xstart + maximumBatchSize - 1, u);
m0 = mobius.GetSums(xstart, xend + 1, m, m0);
ProcessBatch(xstart, xend);
}
ComputeMx();
return(mx[1]);
}