public MobiusOddRangeAdditive(long size, int threads)
{
this.size = size;
this.threads = threads;
var limit = (int)Math.Ceiling(Math.Sqrt(size));
primes = new PrimeCollection(limit, 0).Select(p => (int)p).ToArray();
logPrimes = primes.Select(p => (sbyte)(IntegerMath.CeilingLogBaseTwo(p) | 1)).ToArray();
CreateCycle();
var arrayLength = Math.Max(1, threads);
queue = new ConcurrentQueue <Data>();
}
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);
}
private ulong FinishBlock(long k0, int length, sbyte[] products, ushort[] values, long kmin, ulong[] sums, long smin, ulong sum0, bool onlySums)
{
// Each product can have at most one more prime factor.
// It has that factor if the value of the product is
// less than the full value.
var k = k0;
var kmax = k + 2 * length;
var log2 = IntegerMath.CeilingLogBaseTwo(k);
var next = Math.Min((long)1 << log2, kmax - 2);
if (onlySums)
{
var kk = 0;
while (k < kmax)
{
while (k <= next)
{
// Look ma, no branching.
Debug.Assert(log2 == IntegerMath.CeilingLogBaseTwo(k));
var value = (uint)values[kk];
sums[(k - smin) >> 1] = sum0 += value + ((uint)((products[kk] - log2) >> 31) & value);
Debug.Assert(k == k0 || (int)(sums[(k - smin) >> 1] - sums[(k - smin - 2) >> 1]) == (products[kk] > log2 - 1 ? value : 2 * value));
k += 2;
++kk;
}
++log2;
next = Math.Min(next << 1, kmax - 2);
}
}
else if (sums == null)
{
while (k < kmax)
{
while (k <= next)
{
// Look ma, no branching.
Debug.Assert(log2 == IntegerMath.CeilingLogBaseTwo(k));
var kk = (k - kmin) >> 1;
var value = (uint)values[kk];
sum0 += values[kk] = (ushort)(value + ((uint)((products[(k - k0) >> 1] - log2) >> 31) & value));
Debug.Assert(values[kk] == (products[(k - k0) >> 1] > log2 - 1 ? value : 2 * value));
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));
var kk = (k - kmin) >> 1;
var value = (uint)values[kk];
sums[(k - smin) >> 1] = sum0 += values[kk] = (ushort)(value + ((uint)((products[(k - k0) >> 1] - log2) >> 31) & value));
Debug.Assert(values[kk] == (products[(k - k0) >> 1] > log2 - 1 ? value : 2 * value));
Debug.Assert(k == k0 || (int)(sums[(k - smin) >> 1] - sums[(k - smin - 2) >> 1]) == (products[(k - k0) >> 1] > log2 - 1 ? value : 2 * value));
k += 2;
}
++log2;
next = Math.Min(next << 1, kmax - 2);
}
}
return(sum0);
}
