static int plot(StreamWriter sw, decimal nu, int min_matchbits, decimal z)
{
MultiPrecision <N> t = MultiPrecisionSandbox <N> .BesselJ(nu, z);
MultiPrecision <Plus1 <N> > s = MultiPrecisionSandbox <Plus1 <N> > .BesselJ(nu, z);
sw.WriteLine($" z: {z}");
sw.WriteLine($" f : {t}");
sw.WriteLine($" {t.ToHexcode()}");
sw.WriteLine($" {s.ToHexcode()}");
MultiPrecision <N> err = MultiPrecision <N> .Abs(t - s.Convert <N>());
sw.WriteLine($" err : {err}");
for (int keepbits = MultiPrecision <N> .Bits; keepbits >= 0; keepbits--)
{
if (keepbits == 0)
{
min_matchbits = 0;
}
else if (MultiPrecision <N> .RoundMantissa(t, MultiPrecision <N> .Bits - keepbits) == MultiPrecision <N> .RoundMantissa(s.Convert <N>(), MultiPrecision <N> .Bits - keepbits))
{
sw.WriteLine($" matchbits : {keepbits}");
if (keepbits < min_matchbits)
{
min_matchbits = keepbits;
}
break;
}
}
return(min_matchbits);
}
public static MultiPrecision <N> BesselJ(MultiPrecision <N> nu, MultiPrecision <N> x)
{
if (MultiPrecision <N> .Abs(nu) > 64)
{
throw new ArgumentOutOfRangeException(
nameof(nu),
"In the calculation of the Bessel function, nu with an absolute value greater than 64 is not supported."
);
}
if (nu.IsNaN || x.IsNaN)
{
return(MultiPrecision <N> .NaN);
}
if (x.Sign == Sign.Minus)
{
if (nu != MultiPrecision <N> .Truncate(nu))
{
return(MultiPrecision <N> .NaN);
}
long n = (long)nu;
return(((n & 1L) == 0) ? BesselJ(nu, MultiPrecision <N> .Abs(x)) : -BesselJ(nu, MultiPrecision <N> .Abs(x)));
}
if (!x.IsFinite)
{
return(0);
}
if ((x / 2).IsZero && nu.IsZero)
{
return(1);
}
if (nu.Sign == Sign.Minus && nu == MultiPrecision <N> .Truncate(nu))
{
long n = (long)nu;
return(((n & 1L) == 0) ? BesselJ(MultiPrecision <N> .Abs(nu), x) : -BesselJ(MultiPrecision <N> .Abs(nu), x));
}
if (nu - MultiPrecision <N> .Point5 == MultiPrecision <N> .Floor(nu))
{
long n = (long)MultiPrecision <N> .Floor(nu);
if (n >= -2 && n < 2)
{
MultiPrecision <Plus1 <N> > x_ex = x.Convert <Plus1 <N> >();
MultiPrecision <Plus1 <N> > envelope = MultiPrecision <Plus1 <N> > .Sqrt(2 / (MultiPrecision <Plus1 <N> > .PI * x_ex));
if (n == -2)
{
return(-(envelope * (MultiPrecision <Plus1 <N> > .Cos(x_ex) / x_ex + MultiPrecision <Plus1 <N> > .Sin(x_ex))).Convert <N>());
}
if (n == -1)
{
return((envelope * MultiPrecision <Plus1 <N> > .Cos(x_ex)).Convert <N>());
}
if (n == 0)
{
MultiPrecision <N> y = (envelope * MultiPrecision <Plus1 <N> > .Sin(x_ex)).Convert <N>();
return(y.IsNormal ? y : 0);
}
if (n == 1)
{
MultiPrecision <N> y = (envelope * (MultiPrecision <Plus1 <N> > .Sin(x_ex) / x_ex - MultiPrecision <Plus1 <N> > .Cos(x_ex))).Convert <N>();
return(y.IsNormal ? y : 0);
}
}
}
if (MultiPrecision <N> .Length <= 4)
{
return(MultiPrecisionSandbox <Plus1 <N> > .BesselJ(nu.Convert <Plus1 <N> >(), x.Convert <Plus1 <N> >()).Convert <N>());
}
if (x < Consts.BesselJY.ApproxThreshold)
{
return(BesselJNearZero(nu, x).Convert <N>());
}
else
{
return(BesselJLimit(nu, x).Convert <N>());
}
}
