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Posted-Date: Fri, 9 Jan 1998 16:35:34 +0100 (MET)
Date: Fri, 9 Jan 1998 16:35:34 +0100 (MET)
From: Dirk-Willem van Gulik <Dirk.vanGulik@jrc.it>
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To: Yingjun He <hey@tuns.ca>
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On Fri, 9 Jan 1998, Yingjun He wrote:

> I am running FreeBSD2.25 and 2.05 and I found that the numerical calculation
> results of the same program is different. Is this caused by the difference of
> the operating systems? Or something wrong with my hardware?

Most propably not; it is not uncommon for numerical calculation to
be somewhat unstable. After many iterations a very small difference,
well below the accuracy margnin propagates through.

Check out for example 'Numerical Reciepes' for a good discussion.

As an example consider the output of the programme below; a small
conceptual thing, the order of the loop, not the formula, causes
an increduble difference. Such a difference can by caused by compiler
optimizations and couldless other small things.

D1=1235325026304.000000
D2=1235334987776.000000

Dw.

int main( int a, char * * b) {
        float d;
        int i;
#define M 10000000
        printf("start\n");
        d=1234567890123.0;
        for( i=1; i <M; i++)
                d += 1.0*i/(1+i*i);
        printf("D1=%f\n",d);
 
        d=1234567890123.0;
        for( i=M-1; i >0; i--)
                d += 1.0*i/(1+i*i);
        printf("D2=%f\n",d);
 
        exit(0);
        }