How to compute 1/(2*i)?

[Francogrex]

Hi, I have a problem with this very simple program:

#include <iostream>
#include <cmath>
using namespace std;

int main(){
double n=16;
double t=2.78;
double x;
x=(t/sqrt(n));
int i=0;
double u[9];
while(i<8){
u[0]=1;
i=i+1;
u[i]=u[i-1]*((1-(1/(2*i)))/(1+(x*x)));
cout <<"Iteration " <<i<<" is: "<<u[i]<<"\n";
}
system("PAUSE") ;
return 0;
}

OUTPUT IS:
Iteration 1 is: 0.674297
Iteration 2 is: 0.454677
Iteration 3 is: 0.306588
Iteration 4 is: 0.206731
Iteration 5 is: 0.139398
Iteration 6 is: 0.093996
Iteration 7 is: 0.0633812
Iteration 8 is: 0.0427378
Press any key to continue . .

But the output should read:
0.337148733
0.170503902
0.095808624
0.056528074
0.034305063
0.021204166
0.013276636
0.008392877

the problem is that C++ is not doing this calculation 1/(2*i)
correctly. Is there a way to force him to do this division other than
using the brackets? Thanks.

[Alan Johnson]

Re: How to compute 1/(2*i)?

Francogrex wrote:

Hi, I have a problem with this very simple program:
>
#include <iostream>
#include <cmath>
using namespace std;
>
int main(){
double n=16;
double t=2.78;
double x;
x=(t/sqrt(n));
int i=0;
double u[9];
while(i<8){
u[0]=1;
i=i+1;
u[i]=u[i-1]*((1-(1/(2*i)))/(1+(x*x)));
cout <<"Iteration " <<i<<" is: "<<u[i]<<"\n";
}
system("PAUSE") ;
return 0;
}
>
OUTPUT IS:
Iteration 1 is: 0.674297
Iteration 2 is: 0.454677
Iteration 3 is: 0.306588
Iteration 4 is: 0.206731
Iteration 5 is: 0.139398
Iteration 6 is: 0.093996
Iteration 7 is: 0.0633812
Iteration 8 is: 0.0427378
Press any key to continue . .
>
But the output should read:
0.337148733
0.170503902
0.095808624
0.056528074
0.034305063
0.021204166
0.013276636
0.008392877
>
the problem is that C++ is not doing this calculation 1/(2*i)
correctly. Is there a way to force him to do this division other than
using the brackets? Thanks.

1 and 2 are int literals, and i is defined as an int, so the expression
1/(2*i) performs integer division. The easiest way to force floating
point division is to make one of your literals a floating point number.
That is: 1/(2.*i)

--
Alan Johnson

[Francogrex]

Re: How to compute 1/(2*i)?

On Apr 6, 11:34 am, Francogrex <fra...@grex.or gwrote:

Hi, I have a problem with this very simple program:
>
#include <iostream>
#include <cmath>
using namespace std;
>
int main(){
double n=16;
double t=2.78;
double x;
x=(t/sqrt(n));
int i=0;
double u[9];
while(i<8){
u[0]=1;
i=i+1;
u[i]=u[i-1]*((1-(1/(2*i)))/(1+(x*x)));
cout <<"Iteration " <<i<<" is: "<<u[i]<<"\n";}
>
system("PAUSE") ;
return 0;
>
}
>
OUTPUT IS:
Iteration 1 is: 0.674297
Iteration 2 is: 0.454677
Iteration 3 is: 0.306588
Iteration 4 is: 0.206731
Iteration 5 is: 0.139398
Iteration 6 is: 0.093996
Iteration 7 is: 0.0633812
Iteration 8 is: 0.0427378
Press any key to continue . .
>
But the output should read:
0.337148733
0.170503902
0.095808624
0.056528074
0.034305063
0.021204166
0.013276636
0.008392877
>
the problem is that C++ is not doing this calculation 1/(2*i)
correctly. Is there a way to force him to do this division other than
using the brackets? Thanks.

ok i figured it out: if it's written 1.0/(2.0*i) it works. strange
that you have to specify the points after the values, so by default c+
+ considers them as integers

[ciccio]

Re: How to compute 1/(2*i)?

Francogrex wrote:

On Apr 6, 11:34 am, Francogrex <fra...@grex.or gwrote:

>Hi, I have a problem with this very simple program:
>>
>#include <iostream>
>#include <cmath>
>using namespace std;
>>
>int main(){
>double n=16;
>double t=2.78;
>double x;
>x=(t/sqrt(n));
>int i=0;
>double u[9];
>while(i<8){
>u[0]=1;
>i=i+1;
>u[i]=u[i-1]*((1-(1/(2*i)))/(1+(x*x)));
>cout <<"Iteration " <<i<<" is: "<<u[i]<<"\n";}
>>
>system("PAUSE" );
>return 0;
>>
>}
>>
>OUTPUT IS:
>Iteration 1 is: 0.674297
>Iteration 2 is: 0.454677
>Iteration 3 is: 0.306588
>Iteration 4 is: 0.206731
>Iteration 5 is: 0.139398
>Iteration 6 is: 0.093996
>Iteration 7 is: 0.0633812
>Iteration 8 is: 0.0427378
>Press any key to continue . .
>>
>But the output should read:
>0.337148733
>0.170503902
>0.095808624
>0.056528074
>0.034305063
>0.021204166
>0.013276636
>0.008392877
>>
>the problem is that C++ is not doing this calculation 1/(2*i)
>correctly. Is there a way to force him to do this division other than
>using the brackets? Thanks.

>
ok i figured it out: if it's written 1.0/(2.0*i) it works. strange
that you have to specify the points after the values, so by default c+
+ considers them as integers

Yep,

And if you really want to get rid of the brackets, you type

0.5/i

The line you have
u[i]=u[i-1]*((1-(1/(2*i)))/(1+(x*x)));
Should be
u[i] = u[i-1]*(1.0-0.5/i)/(1.0+x*x);

If you work with floats or doubles, always define your constants as
floats or doubles, even if they can be represented as an integer.

The problem with yours was that 1/(2*i) = 0 (integer devisions)

Regards

[brian tyler]

Re: How to compute 1/(2*i)?

ok i figured it out: if it's written 1.0/(2.0*i) it works. strange

that you have to specify the points after the values, so by default c+
+ considers them as integers

It would be stranger if it didn't. These pages might help you
understand exactly what is going on

http://c.comsci.us/etymology/literals.html

http://en.wikipedia.org/wiki/Division_(mathematics)#Division_of_integers

Brian

[Francogrex]

Re: How to compute 1/(2*i)?

On Apr 6, 11:53 am, Alan Johnson <aw...@yahoo.co mwrote:

the problem is that C++ is not doing this calculation 1/(2*i)
correctly. Is there a way to force him to do this division other than
using the brackets? Thanks.

>
1 and 2 are int literals, and i is defined as an int, so the expression
1/(2*i) performs integer division.  The easiest way to force floating
point division is to make one of your literals a floating point number.
That is: 1/(2.*i)

Hi thanks all. I just figured it out right after I posted. Sometimes
it's worthwhile that I try and be patient before I post.

[stan]

Re: How to compute 1/(2*i)?

Francogrex wrote:

On Apr 6, 11:34 am, Francogrex <fra...@grex.or gwrote:

>Hi, I have a problem with this very simple program:
>>
>#include <iostream>
>#include <cmath>
>using namespace std;
>>
>int main(){
>double n=16;
>double t=2.78;
>double x;
>x=(t/sqrt(n));
>int i=0;
>double u[9];
>while(i<8){
>u[0]=1;
>i=i+1;
>u[i]=u[i-1]*((1-(1/(2*i)))/(1+(x*x)));
>cout <<"Iteration " <<i<<" is: "<<u[i]<<"\n";}
>>
>system("PAUSE" );
>return 0;
>>
>}
>>
>OUTPUT IS:
>Iteration 1 is: 0.674297
>Iteration 2 is: 0.454677
>Iteration 3 is: 0.306588
>Iteration 4 is: 0.206731
>Iteration 5 is: 0.139398
>Iteration 6 is: 0.093996
>Iteration 7 is: 0.0633812
>Iteration 8 is: 0.0427378
>Press any key to continue . .
>>
>But the output should read:
>0.337148733
>0.170503902
>0.095808624
>0.056528074
>0.034305063
>0.021204166
>0.013276636
>0.008392877
>>
>the problem is that C++ is not doing this calculation 1/(2*i)
>correctly. Is there a way to force him to do this division other than
>using the brackets? Thanks.

>
ok i figured it out: if it's written 1.0/(2.0*i) it works. strange
that you have to specify the points after the values, so by default c+
+ considers them as integers

You do know that you can/should also move u[0]=1; outside the loop?
Further, you can precalculate the denminator (1+(x*x)) since x isn't
modified in the loop. It's probably more typical to see this type of
thing written as a for loop vice a while.

for (int i=0; i<9; ++i) {
u[i] = ....
}