private static void Initialize()
{
_previousModulo = ModuloInteger.Modulo;
_sumE = new ModuloInteger[30];
_sumIe = new ModuloInteger[30];
var es = new ModuloInteger[30];
var ies = new ModuloInteger[30];
var bit = BitScanForward(_previousModulo - 1);
var e = ModuloInteger.Power(Mathematics.PrimitiveRoot(_previousModulo), (_previousModulo - 1) >> bit);
var ie = e.Inverse();
for (var i = bit; i >= 2; i--)
{
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
ModuloInteger now = 1;
ModuloInteger inow = 1;
for (var i = 0; i <= bit - 2; i++)
{
_sumE[i] = es[i] * now;
_sumIe[i] = ies[i] * inow;
now *= ies[i];
inow *= es[i];
}
}
public static ModuloInteger[] Execute(IEnumerable <ModuloInteger> source1, IEnumerable <ModuloInteger> source2)
{
if (source1 is null)
{
throw new ArgumentNullException(nameof(source1));
}
if (source2 is null)
{
throw new ArgumentNullException(nameof(source2));
}
var(a, b) = (source1.ToArray(), source2.ToArray());
if (a.Length == 0 || b.Length == 0)
{
return(Array.Empty <ModuloInteger>());
}
if (Math.Min(a.Length, b.Length) <= 60)
{
return(Naive(a, b));
}
var length = a.Length + b.Length - 1;
var z = 1 << CeilLog2(length);
if (ModuloInteger.Modulo != _previousModulo)
{
Initialize();
}
Array.Resize(ref a, z);
Butterfly(a);
Array.Resize(ref b, z);
Butterfly(b);
var result = new ModuloInteger[z];
for (var i = 0; i < z; i++)
{
result[i] = a[i] * b[i];
}
ButterflyInverse(result);
Array.Resize(ref result, length);
var iz = ModuloInteger.Inverse(z);
for (var i = 0; i < result.Length; i++)
{
result[i] *= iz;
}
return(result);
}
private static ModuloInteger[] Naive(ReadOnlySpan <ModuloInteger> source1, ReadOnlySpan <ModuloInteger> source2)
{
var length = source1.Length + source2.Length - 1;
var result = new ModuloInteger[length];
for (var i = 0; i < source1.Length; i++)
{
for (var j = 0; j < source2.Length; j++)
{
result[i + j] += source1[i] * source2[j];
}
}
return(result);
}
private static void ButterflyInverse(Span <ModuloInteger> items)
{
var h = CeilLog2(items.Length);
for (var ph = h; ph >= 1; ph--)
{
var w = 1 << (ph - 1);
var p = 1 << (h - ph);
ModuloInteger inow = 1;
for (var s = 0; s < w; s++)
{
var offset = s << (h - ph + 1);
for (var i = 0; i < p; i++)
{
var l = items[i + offset];
var r = items[i + offset + p];
items[i + offset] = l + r;
items[i + offset + p] = (l - r) * inow;
}
inow *= _sumIe[BitScanForward(~s)];
}
}
}
private static void Butterfly(Span <ModuloInteger> items)
{
var h = CeilLog2(items.Length);
for (var ph = 1; ph <= h; ph++)
{
var w = 1 << (ph - 1);
var p = 1 << (h - ph);
ModuloInteger now = 1;
for (var s = 0; s < w; s++)
{
var offset = s << (h - ph + 1);
for (var i = 0; i < p; i++)
{
var l = items[i + offset];
var r = items[i + offset + p] * now;
items[i + offset] = l + r;
items[i + offset + p] = l - r;
}
now *= _sumE[BitScanForward(~s)];
}
}
}
