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/*
* Author: Sven Gothel <sgothel@jausoft.com>
* Copyright (c) 2020 Gothel Software e.K.
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
#ifndef JAU_BASIC_FLOAT_MATH_HPP_
#define JAU_BASIC_FLOAT_MATH_HPP_
#include <cmath>
#include <type_traits>
#include <algorithm>
namespace jau {
/** @defgroup Floats Float types and arithmetic
* Float types and arithmetic
* @{
*/
/**
// *************************************************
// *************************************************
// *************************************************
*/
/**
* Returns true, if both integer point values differ less than the given delta.
* @tparam T an integral type
* @param a value to compare
* @param b value to compare
* @param delta the maximum difference both values may differ
*/
template<class T>
bool in_range(const T& a, const T& b, const T& delta)
{
const T diff = std::fabs(a-b);
return diff <= delta ||
diff < std::numeric_limits<T>::min(); // subnormal limit
}
/**
* Calculates the smallest floating point value approximation
* the given type T can represent, the machine epsilon of T.
* @tparam T a non integer float type
* @return machine epsilon of T
*/
template<class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, T>::type
machineEpsilon() {
const T one(1);
const T two(2);
T x = one, res;
do {
res = x;
} while (one + (x /= two) > one);
return res;
}
/**
* Returns true, if both floating point values are equal
* in the sense that their potential difference is less or equal <code>epsilon * ulp</code>.
* @tparam T a non integer float type
* @param a value to compare
* @param b value to compare
* @param ulp desired precision in ULPs (units in the last place), defaults to 1
* @param epsilon the machine epsilon of type T, defaults to <code>std::numeric_limits<T>::epsilon()</code>
*/
template<class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
machine_equal(const T& a, const T& b, int ulp=1, const T& epsilon=std::numeric_limits<T>::epsilon())
{
const T diff = std::fabs(a-b);
return diff <= epsilon * ulp ||
diff < std::numeric_limits<T>::min(); // subnormal limit
}
/**
* Returns true, if both floating point values are equal
* in the sense that their potential difference is less or equal <code>epsilon * |a+b| * ulp</code>,
* where <code>|a+b|</code> scales epsilon to the magnitude of used values.
* @tparam T a non integer float type
* @param a value to compare
* @param b value to compare
* @param ulp desired precision in ULPs (units in the last place), defaults to 1
* @param epsilon the machine epsilon of type T, defaults to <code>std::numeric_limits<T>::epsilon()</code>
*/
template<class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
almost_equal(const T& a, const T& b, int ulp=1, const T& epsilon=std::numeric_limits<T>::epsilon())
{
const T diff = std::fabs(a-b);
return diff <= epsilon * std::fabs(a+b) * ulp ||
diff < std::numeric_limits<T>::min(); // subnormal limit
}
/**@}*/
} // namespace jau
#endif /* JAU_BASIC_FLOAT_MATH_HPP_ */
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