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>()); } }