Floats and Doubles for Dummies: Understanding Floating Points

010_simple_near_equal.cpp

#include <cmath>
#include <iostream>

template<typename FP>
bool nearEqual(FP v1, FP v2, FP absTol)
{
    return std::abs(v1 - v2) <= absTol;
}

template<typename FP>
bool nearEqual(FP v1, FP v2, FP absTol, FP relTol)
{
    if ((v1 == v2) || std::abs(v1 - v2) <= absTol)
    {
        return true;
    }
    
    FP relDiff = 2*std::abs(v1 - v2)/(std::abs(v1) + std::abs(v2));
    return relDiff <= relTol;
}

int main()
{
    std::cout << nearEqual(0.2, 0.199999, 1e-6) << std::endl;
    std::cout << nearEqual(0.2, 0.199999, 1e-6, 1e-4) << std::endl;
    
    std::cout << nearEqual(0.2, 0.1999999, 1e-7) << std::endl;
    std::cout << nearEqual(0.2, 0.1999999, 1e-7, 1e-4) << std::endl;
    
    const float v0 = 0.2;
    const float v1 = 0.199999;
    const float v2 = 0.1999999;
    const float absTol1 = 1e-6;
    const float absTol2 = 1e-7;
    const float relTol = 1e-4;
    
    std::cout << nearEqual(v0, v1, absTol1) << std::endl;
    std::cout << nearEqual(v0, v1, absTol1, relTol) << std::endl;
    
    std::cout << nearEqual(v0, v2, absTol2) << std::endl;
    std::cout << nearEqual(v0, v2, absTol2, relTol) << std::endl;
    
    return 0;
}