public Int128 Evaluate(UInt128 n)
{
if (n == 0)
return 0;
this.n = n;
u = (long)IntegerMath.Max(IntegerMath.FloorPower(n, 2, 3) * C1 / C2, IntegerMath.CeilingSquareRoot(n));
imax = (int)(n / (ulong)u);
mobius = new MobiusRangeAdditive(u + 1, threads);
var batchSize = Math.Min(u, maximumBatchSize);
mu = new sbyte[maximumSmallBatchSize];
m = new int[batchSize];
mx = new Int128[imax + 1];
r = new int[imax + 1];
var lmax = 0;
for (var i = 1; i <= imax; i += 2)
{
if (wheelInclude[(i % wheelSize) >> 1])
r[lmax++] = i;
}
Array.Resize(ref r, lmax);
niLarge = new UInt128[imax + 1];
niSmall = new long[imax + 1];
var buckets = Math.Max(1, threads);
var costs = new double[buckets];
var bucketListsLarge = Enumerable.Range(0, buckets).Select(i => new List<int>()).ToArray();
var bucketListsSmall = Enumerable.Range(0, buckets).Select(i => new List<int>()).ToArray();
for (var l = 0; l < lmax; l++)
{
var i = r[l];
var ni = n / (uint)i;
var large = ni > largeLimit;
var cost = Math.Sqrt((double)n / i) * (large ? C7 : 1);
var addto = 0;
var mincost = costs[0];
for (var bucket = 0; bucket < buckets; bucket++)
{
if (costs[bucket] < mincost)
{
mincost = costs[bucket];
addto = bucket;
}
}
niLarge[i] = ni;
if (large)
bucketListsLarge[addto].Add(i);
else
{
niSmall[i] = (long)ni;
bucketListsSmall[addto].Add(i);
}
costs[addto] += cost;
}
bucketsLarge = bucketListsLarge.Select(bucket => bucket.ToArray()).ToArray();
bucketsSmall = bucketListsSmall.Select(bucket => bucket.ToArray()).ToArray();
var m0 = 0;
var xmed = Math.Min((long)IntegerMath.FloorRoot(n, 2) * C5 / C6, u);
for (var x = (long)1; x <= xmed; x += maximumSmallBatchSize)
{
var xstart = x;
var xend = Math.Min(xstart + maximumSmallBatchSize - 1, xmed);
m0 = mobius.GetValuesAndSums(xstart, xend + 1, mu, m, m0);
ProcessBatch(xstart, xend);
}
for (var x = xmed + 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 Int128 Evaluate(UInt128 n)
{
if (n == 0)
{
return(0);
}
this.n = n;
u = (long)IntegerMath.Max(IntegerMath.FloorPower(n, 2, 3) * C1 / C2, IntegerMath.CeilingSquareRoot(n));
imax = (int)(n / (ulong)u);
mobius = new MobiusRangeAdditive(u + 1, threads);
var batchSize = Math.Min(u, maximumBatchSize);
mu = new sbyte[maximumSmallBatchSize];
m = new int[batchSize];
mx = new Int128[imax + 1];
r = new int[imax + 1];
var lmax = 0;
for (var i = 1; i <= imax; i += 2)
{
if (wheelInclude[(i % wheelSize) >> 1])
{
r[lmax++] = i;
}
}
Array.Resize(ref r, lmax);
niLarge = new UInt128[imax + 1];
niSmall = new long[imax + 1];
var buckets = Math.Max(1, threads);
var costs = new double[buckets];
var bucketListsLarge = Enumerable.Range(0, buckets).Select(i => new List <int>()).ToArray();
var bucketListsSmall = Enumerable.Range(0, buckets).Select(i => new List <int>()).ToArray();
for (var l = 0; l < lmax; l++)
{
var i = r[l];
var ni = n / (uint)i;
var large = ni > largeLimit;
var cost = Math.Sqrt((double)n / i) * (large ? C7 : 1);
var addto = 0;
var mincost = costs[0];
for (var bucket = 0; bucket < buckets; bucket++)
{
if (costs[bucket] < mincost)
{
mincost = costs[bucket];
addto = bucket;
}
}
niLarge[i] = ni;
if (large)
{
bucketListsLarge[addto].Add(i);
}
else
{
niSmall[i] = (long)ni;
bucketListsSmall[addto].Add(i);
}
costs[addto] += cost;
}
bucketsLarge = bucketListsLarge.Select(bucket => bucket.ToArray()).ToArray();
bucketsSmall = bucketListsSmall.Select(bucket => bucket.ToArray()).ToArray();
var m0 = 0;
var xmed = Math.Min((long)IntegerMath.FloorRoot(n, 2) * C5 / C6, u);
for (var x = (long)1; x <= xmed; x += maximumSmallBatchSize)
{
var xstart = x;
var xend = Math.Min(xstart + maximumSmallBatchSize - 1, xmed);
m0 = mobius.GetValuesAndSums(xstart, xend + 1, mu, m, m0);
ProcessBatch(xstart, xend);
}
for (var x = xmed + 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]);
}
