private static MultiPrecision <N> BesselKIntegerNuNearZero(int n, MultiPrecision <N> z)
{
Consts.BesselIntegerFiniteTermCoef finite_table = Consts.Bessel.IntegerFiniteTermCoef(n);
Consts.BesselIntegerConvergenceTermCoef convergence_table = Consts.Bessel.IntegerConvergenceTermCoef(n);
MultiPrecision <Double <N> > z_ex = z.Convert <Double <N> >();
MultiPrecision <Double <N> > u = 1;
MultiPrecision <Double <N> > w = z_ex * z_ex;
MultiPrecision <Double <N> > r
= MultiPrecisionSandbox <Double <N> > .BesselINearZero(n, z_ex).Convert <Double <N> >() * MultiPrecision <Double <N> > .Log(z_ex / 2);
long r_exponent = r.Exponent;
MultiPrecision <Double <N> > m = MultiPrecision <Double <N> > .Pow(z_ex / 2, n);
MultiPrecision <Double <N> > x = 0, y = 0;
Sign sign = Sign.Plus;
for (int k = 0; k < int.MaxValue; k++, u *= w)
{
MultiPrecision <Double <N> > c = u * convergence_table.Value(k);
y += c;
if (k < n)
{
if (sign == Sign.Plus)
{
x += u * finite_table.Value(k);
sign = Sign.Minus;
}
else
{
x -= u * finite_table.Value(k);
sign = Sign.Plus;
}
continue;
}
if (r.Exponent < -MultiPrecision <N> .Bits * 8 && (c.IsZero || y.Exponent - c.Exponent > MultiPrecision <Plus1 <N> > .Bits))
{
break;
}
if (c.IsZero || Math.Min(y.Exponent - c.Exponent, r_exponent - c.Exponent - m.Exponent) > MultiPrecision <Double <N> > .Bits)
{
break;
}
}
MultiPrecision <Double <N> > d = (x / m + ((n & 1) == 0 ? 1 : -1) * (y * m - 2 * r)) / 2;
return(d.Convert <N>());
}
private static MultiPrecision <N> BesselYIntegerNuNearZero(int n, MultiPrecision <N> z)
{
Consts.BesselIntegerFiniteTermCoef finite_table = Consts.Bessel.IntegerFiniteTermCoef(n);
Consts.BesselIntegerConvergenceTermCoef convergence_table = Consts.Bessel.IntegerConvergenceTermCoef(n);
MultiPrecision <Double <N> > z_ex = z.Convert <Double <N> >();
MultiPrecision <Double <N> > u = 1;
MultiPrecision <Double <N> > w = z_ex * z_ex;
MultiPrecision <Double <N> > r
= 2 * BesselJNearZero(n, z).Convert <Double <N> >() * MultiPrecision <Double <N> > .Log(z_ex / 2);
long r_exponent = MultiPrecision <Pow2.N4> .Sqrt(2 / (MultiPrecision <Pow2.N4> .PI * (z.Convert <Pow2.N4>() + MultiPrecision <Pow2.N4> .Point5))).Exponent;
MultiPrecision <Double <N> > m = MultiPrecision <Double <N> > .Pow(z_ex / 2, n);
MultiPrecision <Double <N> > x = 0, y = 0;
Sign sign = Sign.Plus;
for (int k = 0; k < int.MaxValue; k++, u *= w)
{
MultiPrecision <Double <N> > c = u * convergence_table.Value(k);
if (sign == Sign.Plus)
{
x += c;
sign = Sign.Minus;
}
else
{
x -= c;
sign = Sign.Plus;
}
if (k < n)
{
y += u * finite_table.Value(k);
continue;
}
if (c.IsZero || Math.Min(x.Exponent - c.Exponent, r_exponent - c.Exponent - m.Exponent) > MultiPrecision <Plus1 <N> > .Bits)
{
break;
}
}
MultiPrecision <Double <N> > d = (r - y / m - x * m) / MultiPrecision <Double <N> > .PI;
return(d.Convert <N>());
}
private static MultiPrecision <N> BesselKIntegerNuNearZero(int n, MultiPrecision <N> z)
{
Consts.BesselNearZeroCoef nearzero_table = Consts.Bessel.NearZeroCoef(n);
Consts.BesselIntegerFiniteTermCoef finite_table = Consts.Bessel.IntegerFiniteTermCoef(n);
Consts.BesselIntegerConvergenceTermCoef convergence_table = Consts.Bessel.IntegerConvergenceTermCoef(n);
MultiPrecision <Double <N> > z_ex = z.Convert <Double <N> >();
MultiPrecision <Double <N> > m = MultiPrecision <Double <N> > .Pow(z_ex / 2, n), inv_mm = 1 / (m * m);
MultiPrecision <Double <N> > u = m, v = 2 * m * MultiPrecision <Double <N> > .Log(z_ex / 2);
MultiPrecision <Double <N> > w = z_ex * z_ex;
MultiPrecision <Double <N> > x = 0;
bool probably_convergenced = false;
Sign sign = Sign.Plus;
for (int k = 0; k < int.MaxValue; k++, u *= w, v *= w)
{
MultiPrecision <Double <N> > c_pos = u * convergence_table.Value(k);
MultiPrecision <Double <N> > c_neg = v * nearzero_table.Value(k);
MultiPrecision <Double <N> > c = c_pos - c_neg;
if ((n & 1) == 0)
{
x += c;
}
else
{
x -= c;
}
if (k < n)
{
MultiPrecision <Double <N> > d = u * inv_mm * finite_table.Value(k);
if (sign == Sign.Plus)
{
x += d;
sign = Sign.Minus;
}
else
{
x -= d;
sign = Sign.Plus;
}
}
else
{
if (c.IsZero || x.Exponent - c.Exponent > MultiPrecision <Plus1 <N> > .Bits)
{
if (probably_convergenced)
{
break;
}
else
{
probably_convergenced = true;
continue;
}
}
probably_convergenced = false;
}
}
MultiPrecision <N> y = x.Convert <N>() / 2;
return(y);
}
