Below I quote a simple but useful library (implemented in C++) which contains functions for comparing double precision floating point numbers.

Interface of library (arithmetictools.h):

/*
 *  arithmetictools.h -- floating point numbers comparison tools.
 *
 *  Copyright (C) 2010  Efstathios Chatzikyriakidis (stathis.chatzikyriakidis@gmail.com)
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program. If not, see <http://www.gnu.org/licenses/>.
 */

/* header defining the interface of the library. */
#ifndef ARITHMETICTOOLS_H
#define ARITHMETICTOOLS_H

/* include C++ library headers. */
#include <cmath>
#include <limits>

/* check if double a is less than double b. */
bool isLessThan (const double a, const double b);

/* check if double a is greater than double b. */
bool isGreaterThan (const double a, const double b);

/* check if double a is approximately equal to double b. */
bool isApproximatelyEqual (const double a, const double b);

/* check if double a is essentially equal to double b. */
bool isEssentiallyEqual (const double a, const double b);

#endif // ARITHMETICTOOLS_H

Implementation of library (arithmetictools.cpp):

/*
 *  arithmetictools.cpp -- floating point numbers comparison tools.
 *
 *  Copyright (C) 2010  Efstathios Chatzikyriakidis (stathis.chatzikyriakidis@gmail.com)
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program. If not, see <http://www.gnu.org/licenses/>.
 */

/* include header defining the interface of the library. */
#include "arithmetictools.h"

/* check if double a is less than double b. */
bool
isLessThan (const double a, const double b) {
    return (b - a) > ((fabs (a) < fabs (b) ? fabs (b) : fabs (a)) *
        std::numeric_limits<double>::epsilon ());
}

/* check if double a is greater than double b. */
bool
isGreaterThan (const double a, const double b) {
    return (a - b) > ((fabs (a) < fabs (b) ? fabs (b) : fabs (a)) *
        std::numeric_limits<double>::epsilon ());
}

/* check if double a is approximately equal to double b. */
bool
isApproximatelyEqual (const double a, const double b) {
    return fabs (a - b) <= ((fabs (a) < fabs (b) ? fabs (b) : fabs (a)) *
        std::numeric_limits<double>::epsilon ());
}

/* check if double a is essentially equal to double b. */
bool
isEssentiallyEqual(const double a, const double b) {
    return fabs (a - b) <= ((fabs (a) > fabs (b) ? fabs (b) : fabs (a)) *
        std::numeric_limits<double>::epsilon ());
}