Minimum floating point number (closest to zero)

Question

I'm trying to find the minimum value (closest to zero) that I can store in a single precission floating point number. Using the <limits> header I can get the value, but if I make it much smaller, the float can still hold it and it gives the right result. Here is a test program, compiled with g++ 5.3.0.

#include <limits>
#include <iostream>
#include <math.h>

using namespace std;

int main()
{
    float a = numeric_limits<float>::max();    
    float b = numeric_limits<float>::min(); 

    a = a*2;
    b = b/pow(2,23);


    cout << a << endl;
    cout << b << endl;
}

As I expected, "a" gives infinity, but "b" keeps holding the good result even after dividing the minimum value by 2^23, after that it gives 0.

The value that gives numeric_limits<float>::min() is 2^(-126) which I belive is the correct answer, but why is the float on my progam holding such small numbers?

Answer 1

std::numeric_limits::min for floating-point types gives the smallest non-zero value that can be represented without loss of precision. std::numeric_limits::lowest gives the smallest representable value. With IEEE representations that's a subnormal value (previously called denormalized).