IEEE floating point Numbers

Question

I studied IEEE floating point number from the following link

In the above article, I am not clear behind the logic of special operation. Why they have decided the special operation in this way (means why Infinity-Infinity is Nan) and all the others also.

If anyone know, Please help me.

score 0 · Answer 1 · edited May 23 '17 at 12:28

NaN is something like “error” or “unknown”. Every operation with NaN results in NaN. Infinity and -Infinity are introduced to handle overflow in a well-defined way. When overflow happens, you cannot be sure about how much it happened. Therefore two infinite values can be in fact different. Therefore Infinity - Infinity does not have any well-defined value, which is handled by NaN.

C example:

#include <stdio.h>
#include <float.h>

int main() {
    double e, f;

    /* floats are always implicitly converted to doubles for computation */
    /* but intermediate values can be larger */
    e = DBL_MAX * 2.0;
    f = DBL_MAX * 2.5;
    printf("%-12s%e\n", "DBL_MAX",    DBL_MAX);
    printf("%-12s%e\n", "e",          e);
    printf("%-12s%e\n", "f",          f);
    printf("%-12s%e\n", "f - e",      f - e);
    printf("%-12s%e\n", "f - e expr", DBL_MAX * 2.5 - DBL_MAX * 2.0);

    return 0;
}

Output (GCC 4.3.2, Linux 2.6.26-2-686):

DBL_MAX     1.79769e+308
e           inf
f           inf
f - e       nan
f - e expr  8.98847e+307

The last expression is a tricky one. Why this happens is described elsewhere. Basically the intermediate calculation is done in a larger type.

IEEE floating point Numbers

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