public static uint[] Convolution <TMod>(ReadOnlySpan <uint> a, ReadOnlySpan <uint> b)
where TMod : struct, IStaticMod
{
var mod = default(TMod).Mod;
if (default(TMod).IsPrime && a.Length + b.Length - 1 <= (1 << InternalBit.BSF(mod - 1)))
{
// ACL で解けるならOK
return(MathLib.Convolution <TMod>(a, b));
}
unchecked
{
var n = a.Length;
var m = b.Length;
var la = new long[n];
for (int i = 0; i < la.Length; i++)
{
la[i] = a[i] % mod;
}
var lb = new long[m];
for (int i = 0; i < lb.Length; i++)
{
lb[i] = b[i] % mod;
}
if (n == 0 || m == 0)
{
return(Array.Empty <uint>());
}
const long Mod1 = 167772161;
const long Mod2 = 469762049;
const long Mod3 = 754974721;
const long M1i2 = 104391568;
const long M12i3 = 190329765;
long M12i = (long)(ulong)(Mod1 * Mod2) % mod;
Debug.Assert(default(FFTMod1).Mod == Mod1);
Debug.Assert(default(FFTMod2).Mod == Mod2);
Debug.Assert(default(FFTMod3).Mod == Mod3);
Debug.Assert(M1i2 == new StaticModInt <FFTMod2>(Mod1).Inv().Value);
Debug.Assert(M12i3 == new StaticModInt <FFTMod3>(Mod1 * Mod2).Inv().Value);
var c1 = MathLib.Convolution <FFTMod1>(la, lb);
var c2 = MathLib.Convolution <FFTMod2>(la, lb);
var c3 = MathLib.Convolution <FFTMod3>(la, lb);
var c = new uint[n + m - 1];
for (int i = 0; i < c.Length; i++)
{
var v1 = ((c2[i] - c1[i]) * M1i2) % Mod2;
if (v1 < 0)
{
v1 += Mod2;
}
var v2 = (c3[i] - (c1[i] + Mod1 * v1) % Mod3) * M12i3 % Mod3;
if (v2 < 0)
{
v2 += Mod3;
}
var x = (c1[i] + Mod1 * v1 + M12i * v2) % mod;
if (x < 0)
{
x += mod;
}
c[i] = (uint)x;
}
return(c);
}
}
