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 void PrimitiveRootTemplateTest()
{
MathUtil.IsPrimitiveRoot(2, InternalMath.PrimitiveRoot <Mod2>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(3, InternalMath.PrimitiveRoot <Mod3>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(5, InternalMath.PrimitiveRoot <Mod5>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(7, InternalMath.PrimitiveRoot <Mod7>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(11, InternalMath.PrimitiveRoot <Mod11>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(998244353, InternalMath.PrimitiveRoot <Mod998244353>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(1000000007, InternalMath.PrimitiveRoot <Mod1000000007>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(469762049, InternalMath.PrimitiveRoot <Mod469762049>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(167772161, InternalMath.PrimitiveRoot <Mod167772161>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(754974721, InternalMath.PrimitiveRoot <Mod754974721>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(324013369, InternalMath.PrimitiveRoot <Mod324013369>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(831143041, InternalMath.PrimitiveRoot <Mod831143041>()).Should().BeTrue();
MathUtil.IsPrimitiveRoot(1685283601, InternalMath.PrimitiveRoot <Mod1685283601>()).Should().BeTrue();
}
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);
}