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?
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.