Float comparison

math.hpp

#pragma once

#include <cfloat>
#include <cmath>
#include <cstdlib>

/**
 * @brief Math related utility functions
 */
namespace Math {

    /**
     * @brief Union type for getting the integer representation of a float.
     * Used for calculating the ULP distance between to floats. More information on
     * comparing floats:
     * https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
     */
    union Float {
        int32_t i;
        float f;

        constexpr Float(float val = 0.0f) : f(val) {}

        constexpr bool isNegative() const {
            return i < 0;
        }
    };

    /**
     * @brief Compare two floats relatively to each other based on a max epsilon
     * distance.
     * @param lhs Left hand side value.
     * @param rhs Right hand side value.
     * @param epsilon Max epsilon distance.
     */
    constexpr bool EqualRel(float lhs, float rhs, float epsilon = FLT_EPSILON) {
        float diff = std::abs(lhs - rhs);
        float largest = std::max(std::abs(lhs), std::abs(rhs));
        return diff <= largest * epsilon;
    }

    /**
     * Compare two floats to each other based on a max ULP distance.
     * https://en.wikipedia.org/wiki/Unit_in_the_last_place
     * @param lhs Left hand side value.
     * @param rhs Right hand side value.
     * @param epsilon Max epsilon distance.
     */
    constexpr bool EqualULP(float lhs, float rhs, int max_ulp_diff = 1) {
        Float _lhs(lhs);
        Float _rhs(rhs);

        // Compare signs, in case they are different the values do not match.
        if (_lhs.isNegative() != _rhs.isNegative()) {
            // Check to make sure +0==-0
            return lhs == rhs;
        }

        // Get the ULP distance
        int ulp_diff = std::abs(_lhs.i - _rhs.i);
        return ulp_diff <= max_ulp_diff;
    }

}  // namespace Math