can_i_add.cpp

#include <iostream>
#include <cmath>

bool ok_to_sum(float a, float b)
{
    int exp_a, exp_b;
    std::frexp(a, &exp_a);
    std::frexp(b, &exp_b);

    return std::abs(exp_a - exp_b) <= 23;
}

float r = 12.543f;
float u0 = 12.543f + 0.1f;
float u1 = 12.543f + 0.01f;
float u2 = 12.543f + 0.001f;
float u3 = 12.543f + 0.0001f;
float u4 = 12.543f + 0.00001f;
float u5 = 12.543f + 0.000001f;
float u6 = 12.543f + 0.0000001f;

int main()
{
    std::cout << std::boolalpha << ok_to_sum(12.543f,0.1f) << "\n";
    std::cout << std::boolalpha << ok_to_sum(12.543f,0.01f) << "\n";
    std::cout << std::boolalpha << ok_to_sum(12.543f,0.001f) << "\n";
    std::cout << std::boolalpha << ok_to_sum(12.543f,0.0001f) << "\n";
    std::cout << std::boolalpha << ok_to_sum(12.543f,0.00001f) << "\n";
    std::cout << std::boolalpha << ok_to_sum(12.543f,0.000001f) << "\n";
    std::cout << std::boolalpha << ok_to_sum(12.543f,0.0000001f) << "\n";

}