private static StaticModInt <T>[] CalcurateSumE()
{
int g = InternalMath.PrimitiveRoot((int)default(T).Mod);
int cnt2 = InternalBit.BSF(default(T).Mod - 1);
var e = new StaticModInt <T>(g).Pow((default(T).Mod - 1) >> cnt2);
var ie = e.Inv();
var sumE = new StaticModInt <T> [cnt2 - 2];
// es[i]^(2^(2+i)) == 1
Span <StaticModInt <T> > es = stackalloc StaticModInt <T> [cnt2 - 1];
Span <StaticModInt <T> > ies = stackalloc StaticModInt <T> [cnt2 - 1];
for (int i = es.Length - 1; i >= 0; i--)
{
// e^(2^(2+i)) == 1
es[i] = e;
ies[i] = ie;
e *= e;
ie *= ie;
}
var now = StaticModInt <T> .Raw(1);
for (int i = 0; i < sumE.Length; i++)
{
sumE[i] = es[i] * now;
now *= ies[i];
}
return(sumE);
}
public static void Calculate(Span <StaticModInt <T> > a)
{
var n = a.Length;
var h = InternalMath.CeilPow2(n);
for (int ph = 1; ph <= h; ph++)
{
// ブロックサイズの半分
int w = 1 << (ph - 1);
// ブロック数
int p = 1 << (h - ph);
var now = StaticModInt <T> .Raw(1);
// 各ブロックの s 段目
for (int s = 0; s < w; s++)
{
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++)
{
var l = a[i + offset];
var r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sumE[InternalBit.BSF(~(uint)s)];
}
}
}
public static void CalculateInv(Span <StaticModInt <T> > a)
{
var n = a.Length;
var h = InternalMath.CeilPow2(n);
for (int ph = h; ph >= 1; ph--)
{
// ブロックサイズの半分
int w = 1 << (ph - 1);
// ブロック数
int p = 1 << (h - ph);
var iNow = StaticModInt <T> .Raw(1);
// 各ブロックの s 段目
for (int s = 0; s < w; s++)
{
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++)
{
var l = a[i + offset];
var r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] = StaticModInt <T> .Raw(
unchecked ((int)((ulong)(default(T).Mod + l.Value - r.Value) * (ulong)iNow.Value % default(T).Mod)));
}
iNow *= sumIE[InternalBit.BSF(~(uint)s)];
}
}
}
private static StaticModInt <T>[] CalcurateSumIE()
{
int g = InternalMath.PrimitiveRoot <T>();
int cnt2 = InternalBit.BSF(default(T).Mod - 1);
var e = new StaticModInt <T>(g).Pow((default(T).Mod - 1) >> cnt2);
var ie = e.Inv();
var sumIE = new StaticModInt <T> [30];
// es[i]^(2^(2+i)) == 1
Span <StaticModInt <T> > es =
#if !NETCOREAPP3_0_OR_GREATER
new
#else
stackalloc
#endif
StaticModInt <T> [cnt2 - 1];
Span <StaticModInt <T> > ies =
#if !NETCOREAPP3_0_OR_GREATER
new
#else
stackalloc
#endif
StaticModInt <T> [cnt2 - 1];
for (int i = es.Length - 1; i >= 0; i--)
{
// e^(2^(2+i)) == 1
es[i] = e;
ies[i] = ie;
e *= e;
ie *= ie;
}
var now = StaticModInt <T> .Raw(1);
for (int i = 0; i <= cnt2 - 2; i++)
{
sumIE[i] = ies[i] * now;
now *= es[i];
}
return(sumIE);
}
public static void Calculate(Span <StaticModInt <T> > a)
{
CheckPow2(a.Length);
var n = a.Length;
var h = InternalBit.CeilPow2(n);
var regLength = Vector <uint> .Count;
#if !NETCOREAPP3_0_OR_GREATER
var copyTmp = new uint[regLength];
#endif
// 全要素がmodのVector<uint>を作成（比較および加減算用）
var modV = new Vector <uint>(default(T).Mod);
for (int ph = 1; ph <= h; ph++)
{
// ブロックサイズの半分
int w = 1 << (ph - 1);
// ブロック数
int p = 1 << (h - ph);
var now = StaticModInt <T> .Raw(1);
// 各ブロックの s 段目
for (int s = 0; s < w; s++)
{
int offset = s << (h - ph + 1);
var ls = a.Slice(offset, p);
var rs = a.Slice(offset + p, p);
if (p < regLength)
{
for (int i = 0; i < p; i++)
{
var l = ls[i];
var r = rs[i] * now;
ls[i] = l + r;
rs[i] = l - r;
}
}
else
{
foreach (ref var r in rs)
{
r *= now;
}
// uintとして再解釈
var lu = MemoryMarshal.Cast <StaticModInt <T>, uint>(ls);
var ru = MemoryMarshal.Cast <StaticModInt <T>, uint>(rs);
for (int i = 0; i < lu.Length; i += regLength)
{
var luSliced = lu.Slice(i);
var ruSliced = ru.Slice(i);
var u = new Vector <uint>(luSliced);
var v = new Vector <uint>(ruSliced);
var add = u + v;
var sub = u - v;
var ge = Vector.GreaterThanOrEqual(add, modV);
add = Vector.ConditionalSelect(ge, add - modV, add);
ge = Vector.GreaterThanOrEqual(sub, modV);
sub = Vector.ConditionalSelect(ge, sub + modV, sub);
#if !NETCOREAPP3_0_OR_GREATER
add.CopyTo(copyTmp);
copyTmp.CopyTo(luSliced);
sub.CopyTo(copyTmp);
copyTmp.CopyTo(ruSliced);
#else
add.CopyTo(luSliced);
sub.CopyTo(ruSliced);
#endif
}
}
now *= sumE[InternalBit.BSF(~(uint)s)];
}
}
}
public void BSF(uint input, int expected)
{
InternalBit.BSF(input).Should().Be(expected);
}
public void CeilPow2(int input, int expected)
{
InternalBit.CeilPow2(input).Should().Be(expected);
}
public void ExtractLowestSetBit(int input, uint expected)
{
InternalBit.ExtractLowestSetBit(input).Should().Be(expected);
(input & -input).Should().Be((int)expected);
}