Question

Is there any difference between the computation of small floats – that are close to 0 – and big floats – that are far from 0?

Answer 1

It depends what kind of computation you are talking about. Adding two numbers together is likely to take the same length of time regardless of the magnitude of the number. In the case of division, the size of the operand can make a difference – for instance, see Intel reference manual page C.34:

If you try compiling the following code, you can see this in action:

// Compile with -O0 to avoid optimising out loop!
#include <iostream>
#include <sys/time.h>
#include <limits>

void test(float a, float b)
{
        struct timeval start, end;
        gettimeofday(&start, NULL);
        for (size_t i=0; i<500000; ++i)
        {
                float result = a/b;
        }
        gettimeofday(&end, NULL);
        long  seconds, useconds; 
        seconds  = end.tv_sec  - start.tv_sec;
        useconds = end.tv_usec - start.tv_usec;
        double ms = ((seconds) * 1000 + useconds/1000.0); 
        std::cout  << a << "/" << b << " takes " << ms << "ms" << std::endl;
}

int main()
{
        test(1,2);
        test(0.0005,1.0e+35);
}

Gives the following output for me

1/2 takes 1.032ms

0.0005/1e+35 takes 32.287ms