📄 d6r2.cpp
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# include<iostream.h>
# include<math.h>
# include<iomanip.h>
# include<stdlib.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;
}
static double r[98];
static int iff,ix1,ix2,ix3;
double ran1(int& idum)
{
double rm1,rm2,t;
int m1,m2,m3,ia1,ia2,ia3,ic1,ic2,ic3,j;
m1 = 259200, ia1 = 7141, ic1 = 54773, rm1 = 0.0000038580247,
m2 = 134456, ia2 = 8121, ic2 = 28411, rm2 = 0.0000074373773,
m3 = 243000, ia3= 4561, ic3 = 51349;
if ((idum < 0) || (iff == 0))
{
iff = 1;
ix1 = (ic1 - idum) % m1;
ix1 = (ia1 * ix1 + ic1) % m1;
ix2 = ix1 % m2;
ix1 = (ia1 * ix1 + ic1) % m1;
ix3 = ix1 % m3;
for (j = 1; j<=97; j++)
{
ix1 = (ia1 * ix1 + ic1)% m1;
ix2 = (ia2 * ix2 + ic2)% m2;
r[j] = (double(ix1) + double(ix2) * rm2) * rm1;
}
idum = 1;
}
ix1 = (ia1 * ix1 + ic1) % m1;
ix2 = (ia2 * ix2 + ic2) % m2;
ix3 = (ia3 * ix3 + ic3) % m3;
j = 1 + int((97 * ix3) / m3);
if ((j > 97) || (j < 1))
{
cout<< "abnormal exit"<<endl;
return 1;
}
t = r[j];
r[j] = (float(ix1) + float(ix2) * rm2) * rm1;
return t;
}
void main()
{
//program d6r2
//driver for routine ran1
//calculates pi statistically using volume of unit n-sphere
double yprob[4],a,b,pi,x1,x2,k,x3,x4;
int iy[4],idum,j,i,m;
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 = pow(2,(j - 1)); k<= pow(2,j); k++)
{
x1 = ran1(idum);
x2 = ran1(idum);
x3 = ran1(idum);
x4 = ran1(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<<setprecision(0)<<setiosflags(ios::fixed)<<setw(8)<<pow(2 , j);
for (m = 1; m<=3; m++)
cout<< setprecision(6)<<setiosflags(ios::fixed)<<setw(14)<<yprob[m];
cout<<endl;
}
cout<<setprecision(6)<<setiosflags(ios::fixed)<<setw(8)<<" actual "<<pi;
cout<<setprecision(6)<<setiosflags(ios::fixed)<<setw(14)<<4.0 * pi / 3.0;
cout<<setprecision(6)<<setiosflags(ios::fixed)<<setw(14)<<0.5 * pow(pi,2)<<endl;
}
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