$Id: why_reals_arent.txt,v 1.2 2011/01/22 01:28:38 db Exp db $

Invariably, some new C programmer comes asking why a float or even
a double calculation does not come up with an answer they expect.
That's because floats and doubles are _not_ real. That is, they
are only clever integer approximations to the real number line.

Here's an illustration of what can happen:

#include <stdio.h>
#include <math.h>

int
main()
{
        float a;

        a = (0.1 / 3.0);
        printf("a= %f\n", a);
        a = a * 3.0;
        printf("a= %f\n", a);
        if (a == 0.1)
                printf("a is equal to 0.1\n");
        else
                printf("a is not equal to 0.1\n");
}

cc -o f f.c -lm
./f
a= 0.033333
a= 0.100000
a is not equal to 0.1

The number 1.0 / 3.0 should work out to exactly 1/3. In C, the best we
can do is a decimal representation. Since we can only use binary and
a fixed number of bits to represent the part after the '.' (Mantissa), it
is not an exact equivalent to the real number 1/3.


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