Can multiplication of non-zero floats yield exactly zero?

Question

Suppose I have a series of small random floating point numbers in either double or float format which are guaranteed to be non-zero, in a CPU which follows the IEEE754 standard, and I make multiplications between two of these small numbers.

If both numbers are different from zero but very small (below machine epsilon), is it possible that a multiplication result would yield zero or negative zero, such that if I interpret the result as a C++ boolean, it would translate into false?

Answer 1

Yes. You can demonstrate that by experiment:

#include <stdio.h>

int main()
{
    float x = 0.1 ;
    int it = 0 ;
    
    while( x *= x )
    {
        it++ ;
        printf( "%d %f\n", it, x ) ;
    }

    return 0;
}

Outputs:

1 0.010000                                                                                                                                                                                    
2 0.000100                                                                                                                                                                                    
3 0.000000                                                                                                                                                                                    
4 0.000000                                                                                                                                                                                    
5 0.000000 

The fact that the loop terminates, indicates that x is zero and implicitly casts to false.

The test runs for 8 iterations for double, and 12 for long double on Linux.

The result is the same for while( -(x *= x) ) - to address the part of your question referring to negative-zero.