using System;
namespace Legalsoft.Truffer
{
public class Bessik
{
#region Constants
private readonly double[] i0p = { 9.999999999999997e-1, 2.466405579426905e-1, 1.478980363444585e-2, 3.826993559940360e-4, 5.395676869878828e-6, 4.700912200921704e-8, 2.733894920915608e-10, 1.115830108455192e-12, 3.301093025084127e-15, 7.209167098020555e-18, 1.166898488777214e-20, 1.378948246502109e-23, 1.124884061857506e-26, 5.498556929587117e-30 };
private readonly double[] i0q = { 4.463598170691436e-1, 1.702205745042606e-3, 2.792125684538934e-6, 2.369902034785866e-9, 8.965900179621208e-13 };
private readonly double[] i0pp = { 1.192273748120670e-1, 1.947452015979746e-1, 7.629241821600588e-2, 8.474903580801549e-3, 2.023821945835647e-4 };
private readonly double[] i0qq = { 2.962898424533095e-1, 4.866115913196384e-1, 1.938352806477617e-1, 2.261671093400046e-2, 6.450448095075585e-4, 1.529835782400450e-6 };
private readonly double[] i1p = { 5.000000000000000e-1, 6.090824836578078e-2, 2.407288574545340e-3, 4.622311145544158e-5, 5.161743818147913e-7, 3.712362374847555e-9, 1.833983433811517e-11, 6.493125133990706e-14, 1.693074927497696e-16, 3.299609473102338e-19, 4.813071975603122e-22, 5.164275442089090e-25, 3.846870021788629e-28, 1.712948291408736e-31 };
private readonly double[] i1q = { 4.665973211630446e-1, 1.677754477613006e-3, 2.583049634689725e-6, 2.045930934253556e-9, 7.166133240195285e-13 };
private readonly double[] i1pp = { 1.286515211317124e-1, 1.930915272916783e-1, 6.965689298161343e-2, 7.345978783504595e-3, 1.963602129240502e-4 };
private readonly double[] i1qq = { 3.309385098860755e-1, 4.878218424097628e-1, 1.663088501568696e-1, 1.473541892809522e-2, 1.964131438571051e-4, -1.034524660214173e-6 };
private readonly double[] k0pi = { 1.0, 2.346487949187396e-1, 1.187082088663404e-2, 2.150707366040937e-4, 1.425433617130587e-6 };
private readonly double[] k0qi = { 9.847324170755358e-1, 1.518396076767770e-2, 8.362215678646257e-5 };
private readonly double[] k0p = { 1.159315156584126e-1, 2.770731240515333e-1, 2.066458134619875e-2, 4.574734709978264e-4, 3.454715527986737e-6 };
private readonly double[] k0q = { 9.836249671709183e-1, 1.627693622304549e-2, 9.809660603621949e-5 };
private readonly double[] k0pp = { 1.253314137315499, 1.475731032429900e1, 6.123767403223466e1, 1.121012633939949e2, 9.285288485892228e1, 3.198289277679660e1, 3.595376024148513, 6.160228690102976e-2 };
private readonly double[] k0qq = { 1.0, 1.189963006673403e1, 5.027773590829784e1, 9.496513373427093e1, 8.318077493230258e1, 3.181399777449301e1, 4.443672926432041, 1.408295601966600e-1 };
private readonly double[] k1pi = { 0.5, 5.598072040178741e-2, 1.818666382168295e-3, 2.397509908859959e-5, 1.239567816344855e-7 };
private readonly double[] k1qi = { 9.870202601341150e-1, 1.292092053534579e-2, 5.881933053917096e-5 };
private readonly double[] k1p = { -3.079657578292062e-1, -8.109417631822442e-2, -3.477550948593604e-3, -5.385594871975406e-5, -3.110372465429008e-7 };
private readonly double[] k1q = { 9.861813171751389e-1, 1.375094061153160e-2, 6.774221332947002e-5 };
private readonly double[] k1pp = { 1.253314137315502, 1.457171340220454e1, 6.063161173098803e1, 1.147386690867892e2, 1.040442011439181e2, 4.356596656837691e1, 7.265230396353690, 3.144418558991021e-1 };
private readonly double[] k1qq = { 1.0, 1.125154514806458e1, 4.427488496597630e1, 7.616113213117645e1, 5.863377227890893e1, 1.850303673841586e1, 1.857244676566022, 2.538540887654872e-2 };
#endregion
private double y { get; set; }
private double z { get; set; }
private double ax { get; set; }
private double term { get; set; }
public double i0(double x)
{
if ((ax = Math.Abs(x)) < 15.0)
{
y = x * x;
return poly(i0p, 13, y) / poly(i0q, 4, 225.0 - y);
}
else
{
z = 1.0 - 15.0 / ax;
return Math.Exp(ax) * poly(i0pp, 4, z) / (poly(i0qq, 5, z) * Math.Sqrt(ax));
}
}
public double i1(double x)
{
if ((ax = Math.Abs(x)) < 15.0)
{
y = x * x;
return x * poly(i1p, 13, y) / poly(i1q, 4, 225.0 - y);
}
else
{
z = 1.0 - 15.0 / ax;
double ans = Math.Exp(ax) * poly(i1pp, 4, z) / (poly(i1qq, 5, z) * Math.Sqrt(ax));
return x > 0.0 ? ans : -ans;
}
}
public double k0(double x)
{
if (x <= 1.0)
{
z = x * x;
term = poly(k0pi, 4, z) * Math.Log(x) / poly(k0qi, 2, 1.0 - z);
return poly(k0p, 4, z) / poly(k0q, 2, 1.0 - z) - term;
}
else
{
z = 1.0 / x;
return Math.Exp(-x) * poly(k0pp, 7, z) / (poly(k0qq, 7, z) * Math.Sqrt(x));
}
}
public double k1(double x)
{
if (x <= 1.0)
{
z = x * x;
term = poly(k1pi, 4, z) * Math.Log(x) / poly(k1qi, 2, 1.0 - z);
return x * (poly(k1p, 4, z) / poly(k1q, 2, 1.0 - z) + term) + 1.0 / x;
}
else
{
z = 1.0 / x;
return Math.Exp(-x) * poly(k1pp, 7, z) / (poly(k1qq, 7, z) * Math.Sqrt(x));
}
}
public double poly(double[] cof, int n, double x)
{
double ans = cof[n];
for (int i = n - 1; i >= 0; i--)
{
ans = ans * x + cof[i];
}
return ans;
}
public double kn(int n, double x)
{
if (n == 0)
{
return k0(x);
}
if (n == 1)
{
return k1(x);
}
double tox = 2.0 / x;
double bkm = k0(x);
double bk = k1(x);
for (int j = 1; j < n; j++)
{
double bkp = bkm + j * tox * bk;
bkm = bk;
bk = bkp;
}
return bk;
}
public double xin(int n, double x)
{
const double ACC = 200.0;
const int IEXP = int.MaxValue / 2;// numeric_limits<double>.max_exponent / 2;
if (n == 0)
{
return i0(x);
}
if (n == 1)
{
return i1(x);
}
double ans = 0.0;
if (x * x <= 8.0 * float.Epsilon)
{
return 0.0;
}
else
{
double tox = 2.0 / Math.Abs(x);
double bip = ans = 0.0;
double bi = 1.0;
for (int j = 2 * (n + (int)Math.Sqrt(ACC * n)); j > 0; j--)
{
double bim = bip + j * tox * bi;
bip = bi;
bi = bim;
double dum = Globals.frexp(bi, out int k);
if (k > IEXP)
{
ans = Globals.ldexp(ans, -IEXP);
bi = Globals.ldexp(bi, -IEXP);
bip = Globals.ldexp(bip, -IEXP);
}
if (j == n)
{
ans = bip;
}
}
ans *= i0(x) / bi;
return x < 0.0 && (n & 1) != 0 ? -ans : ans;
}
}
}
}