#include <iostream.h>
#include <math.h>
#include <iomanip.h>
#include <stdlib.h>
#include <fstream.h>
#include <string>
#include <process.h>

double bessi0(double x)
{
	double p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7,q8,q9;
	double y,aaa,bbb,ax,temp;
    p1 = 1.0;             p2 = 3.5156229;
    p3 = 3.0899424;       p4 = 1.2067492;
    p5 = 0.2659732;       p6 = 0.0360768;
    p7 = 0.0045813;
    q1 = 0.39894228;      q2 = 0.01328592;
    q3 = 0.00225319;      q4 = -0.00157565;
    q5 = 0.00916281;      q6 = -0.02057706;
    q7 = 0.02635537;      q8 = -0.01647633;
    q9 = 0.00392377;
    if( fabs(x) < 3.75)
	{
        y = (x / 3.75)*(x / 3.75);
        aaa = y * (p5 + y * (p6 + y * p7));
        temp = p1 + y * (p2 + y * (p3 + y * (p4 + aaa)));
	}
    else
	{
        ax = fabs(x);
        y = 3.75 / ax;
        aaa = exp(ax) / sqrt(ax);
        bbb = q4 + y * (q5 + y * (q6 + y * (q7 + y * (q8 + y * q9))));
        temp = aaa * (q1 + y * (q2 + y * (q3 + y * bbb)));
	}
	return temp;
}

double bessk0(double x)
{
	double p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7;
	double y,aaa,bbb,temp;
    p1 = -0.57721566;      p2 = 0.4227842;
    p3 = 0.23069756;       p4 = 0.0348859;
    p5 = 0.00262698;       p6 = 0.0001075;
    p7 = 0.0000074;
    q1 = 1.25331414;       q2 = -0.07832358;
    q3 = 0.02189568;       q4 = -0.01062446;
    q5 = 0.00587872;       q6 = -0.0025154;
    q7 = 0.00053208;
    if( x <= 2.0)
	{
        y = x * x / 4.0;
        bbb = y * (p5 + y * (p6 + y * p7));
        aaa= p1 + y * (p2 + y * (p3 + y * (p4 + bbb)));
        temp = (-log(x / 2.0) * bessi0(x)) + aaa;
	}
    else
	{
        y = (2.0 / x);
        bbb = y * (q5 + y * (q6 + y * q7));
        aaa = q1 + y * (q2 + y * (q3 + y * (q4 + bbb)));
        temp = (exp(-x) / sqrt(x)) * aaa;
	}
	return temp;
}

void main()
{
    //program d4r21
    //driver for routine bessk0
    int i;
	char text[20];
    double nval,value,x; 
    const double pi = 3.1415926;
    fstream fin;
    fin.open("d:\\vc常用數值算法集\\data\\fncval.dat",ios::in);
    while ( strcmp(text,"K0")!=0) 
	{
      fin>>text;
	}
    fin>>nval;
	fin>>text;
    cout<<"Modified Bessel Function K0 "<<endl;
    cout<<endl;
    cout<<"      x            actual          bessk0(x)"<<endl;
    for( i = 1;i<=nval;i++)
	{
        fin>>x;
		fin>>value;           
		cout<<setprecision(2)<<setw(8)<<x;
        cout<<setprecision(8)<<setw(18)<<value;
		cout<<setprecision(8)<<setw(18)<<bessk0(x)<<endl;			          
    }
}