Date: Fri, 9 Jan 1998 16:35:34 +0100 (MET) From: Dirk-Willem van Gulik <Dirk.vanGulik@jrc.it> To: Yingjun He <hey@tuns.ca> Cc: questions@FreeBSD.ORG Subject: Re: your mail Message-ID: <Pine.SOL.3.96.980109161654.8962C-100000@elect6.jrc.it> In-Reply-To: <3.0.1.32.19980109091508.00969330@newton.ccs.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);
}
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