?? d6r4.cpp
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# include<math.h>
# include<iomanip.h>
# include<iostream.h>
double fnc(double x1, double x2, double x3, double x4)
{
double temp;
temp = sqrt(x1 *x1 + x2 *x2 + x3 *x3 + x4 *x4);
return temp;
}
void main()
{
//program d6r4
//driver for routine ran3
//calculates pi statistically using volume of unit n-sphere
double yprob[4],a,b,pi,x1,x2,x3,x4;
int iy[4],idum,j,i,m,k;
idum = -1;
pi = 3.1415926;
a=0.0;
b=0.0;
for (i = 1; i<=3; i++)
iy[i] = 0;
cout<<"Volume of unit n-sphere, n=2,3,4"<<endl;
cout<<" # points pi [4/3]*pi [1/2]*pi^2"<<endl;
for (j = 1; j<=15; j++)
{
for (k =int( pow(2,(j - 1))); int(k<= pow(2,j)); k++)
{
x1=ran3(idum);
x2=ran3(idum);
x3=ran3(idum);
x4=ran3(idum);
if (fnc(x1, x2, a, b) < 1.0) iy[1] = iy[1] + 1;
if (fnc(x1, x2, x3, a) < 1.0) iy[2] = iy[2] + 1;
if (fnc(x1, x2, x3, x4) < 1.0) iy[3] = iy[3] + 1;
}
for (i = 1; i<=3; i++)
yprob[i] = 1.0 * pow(2,(i + 1)) * iy[i] / pow(2 , j);
cout<< setw(10)<<setprecision(0)<<setiosflags(ios::fixed)<<pow(2 , j);
for (m = 1; m<=3; m++)
cout<< setprecision(6)<<setiosflags(ios::fixed)<<setw(13)<<yprob[m];
cout<<endl;
}
cout<< " actual"<<setprecision(6)<<setiosflags(ios::fixed)<<setw(13)<<pi;
cout<<setprecision(6)<<setiosflags(ios::fixed)<<setw(13)<<4.0 * pi / 3.0;
cout<<setprecision(6)<<setiosflags(ios::fixed)<<setw(13)<<0.5*pow(pi,2)<<endl;
}
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