Author: Robert Hyatt
Date: 20:08:37 09/09/02
Go up one level in this thread
On September 09, 2002 at 13:32:42, Ed Panek wrote:
>Red Hat Linux release 6.0 (Hedwig)
>Kernel 2.2.5-15 on an i686
>
>Here is just one example of unpredictable floating point behavior. I ran the
>following program on RH and on my Mac G4:
>
That's actually not unpredictable. It is perfectly normal and is a problem
in _all_ FP math where you want exact answers. Many base 10 fractions have
no exact IEEE fp conversions, so that you start getting errors before you
do the first math operation.
>#include <stdlib.h>
>#include <stdio.h>
>#include <math.h>
>
>void main( void )
>{
> double a,b,c,d;
> double a_int, a_fract;
> double b_int, b_fract;
> double c_int, c_fract;
>
> int i,j;
>
> for( i = 8; i < 13; ++i )
> {
> a = (double)i;
> b = a / 1000.0;
>
> d = 1000.0;
> c = b * d;
> j = (int)(b * d);
>
>
> a_fract = modf(a, &a_int);
> b_fract = modf(b, &b_int);
> c_fract = modf(c, &c_int);
>
> printf("i = %d, a = %35.30f, b = %35.30f, c = %35.30f, j =
>%d\n",i,a,b,c,j);
> printf("a = %35.30f + %35.30f\n", a_int, a_fract);
> printf("b = %35.30f + %35.30f\n", b_int, b_fract);
> printf("c = %35.30f + %35.30f\n", c_int, c_fract);
>
> }
>
> return;
>
>}
>
>The output on RH is as follows:
>
>
>
>testit
>i = 8, a = 8.000000000000000000000000000000, b =
>0.008000000000000000166533453694, c = 8.000000000000000000000000000000, j =
>8
>a = 8.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.008000000000000000166533453694
>c = 8.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>i = 9, a = 9.000000000000000000000000000000, b =
>0.008999999999999999319988397417, c = 9.000000000000000000000000000000, j =
>8
>a = 9.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.008999999999999999319988397417
>c = 9.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>i = 10, a = 10.000000000000000000000000000000, b =
>0.010000000000000000208166817117, c = 10.000000000000000000000000000000, j =
>10
>a = 10.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.010000000000000000208166817117
>c = 10.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>i = 11, a = 11.000000000000000000000000000000, b =
>0.010999999999999999361621760841, c = 11.000000000000000000000000000000, j =
>10
>a = 11.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.010999999999999999361621760841
>c = 11.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>In the above case, the cast to int truncates and leaves the integer too small by
>1 in some cases. But, suprisingly, the modf() routine returns data that is
>corrected for the error.
> Where is the correction happenning? In modf()? By the CPU when the result is
>stored back?
>
>On my mac, the CPU and/or libraries do some magic to correct this so that the
>underlying data IS whole number data before the cast, or else the cast is very
>smart. In this case, the cast and the printf() agree. I will note that it is
>possible the compiler is very smart and factored the divide and multiply by 1000
>out of the equation... But I doubt it.
>
>Power PC G4 output:
>
>
>testit
>i = 8, a = 8.000000000000000000000000000000, b =
>0.008000000000000000166533453694, c = 8.000000000000000000000000000000, j =
>8
>a = 8.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.008000000000000000166533453694
>c = 8.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>i = 9, a = 9.000000000000000000000000000000, b =
>0.008999999999999999319988397417, c = 9.000000000000000000000000000000, j =
>9
>a = 9.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.008999999999999999319988397417
>c = 9.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>i = 10, a = 10.000000000000000000000000000000, b =
>0.010000000000000000208166817117, c = 10.000000000000000000000000000000, j =
>10
>a = 10.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.010000000000000000208166817117
>c = 10.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>i = 11, a = 11.000000000000000000000000000000, b =
>0.010999999999999999361621760841, c = 11.000000000000000000000000000000, j =
>11
>a = 11.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.010999999999999999361621760841
>c = 11.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>i = 12, a = 12.000000000000000000000000000000, b =
>0.012000000000000000249800180541, c = 12.000000000000000000000000000000, j =
>12
>a = 12.000000000000000000000000000000 + 0.000000000000000000000000000000
>b = 0.000000000000000000000000000000 + 0.012000000000000000249800180541
>c = 12.000000000000000000000000000000 + 0.000000000000000000000000000000
>
>
>All very interesting to me... But the bottom line is that floating point is
>spooky.
>
>
>Comments?
>
>
>Ed
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