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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003, 2004, 2005, 2007 StatPro Italia srl
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
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 license for more details.
*/
/*! \file comparison.hpp
\brief floating-point comparisons
*/
#ifndef quantlib_comparison_hpp
#define quantlib_comparison_hpp
#include <ql/types.hpp>
#include <ql/shared_ptr.hpp>
namespace QuantLib {
/*! Follows somewhat the advice of Knuth on checking for floating-point
equality. The closeness relationship is:
\f[
\mathrm{close}(x,y,n) \equiv |x-y| \leq \varepsilon |x|
\wedge |x-y| \leq \varepsilon |y|
\f]
where \f$ \varepsilon \f$ is \f$ n \f$ times the machine accuracy;
\f$ n \f$ equals 42 if not given.
*/
bool close(Real x, Real y);
bool close(Real x, Real y, Size n);
/*! Follows somewhat the advice of Knuth on checking for floating-point
equality. The closeness relationship is:
\f[
\mathrm{close}(x,y,n) \equiv |x-y| \leq \varepsilon |x|
\vee |x-y| \leq \varepsilon |y|
\f]
where \f$ \varepsilon \f$ is \f$ n \f$ times the machine accuracy;
\f$ n \f$ equals 42 if not given.
*/
bool close_enough(Real x, Real y);
bool close_enough(Real x, Real y, Size n);
// inline definitions
inline bool close(Real x, Real y) {
// we're duplicating the code here instead of calling close(x,y,42)
// for optimization; this allows us to make tolerance constexpr
// and shave a few more cycles.
// Deals with +infinity and -infinity representations etc.
if (x == y)
return true;
Real diff = std::fabs(x-y);
constexpr double tolerance = 42 * QL_EPSILON;
if (x == 0.0 || y == 0.0)
return diff < (tolerance * tolerance);
return diff <= tolerance*std::fabs(x) &&
diff <= tolerance*std::fabs(y);
}
inline bool close(Real x, Real y, Size n) {
// Deals with +infinity and -infinity representations etc.
if (x == y)
return true;
Real diff = std::fabs(x-y), tolerance = n * QL_EPSILON;
if (x == 0.0 || y == 0.0)
return diff < (tolerance * tolerance);
return diff <= tolerance*std::fabs(x) &&
diff <= tolerance*std::fabs(y);
}
inline bool close_enough(Real x, Real y) {
// see close() for a note on duplication
// Deals with +infinity and -infinity representations etc.
if (x == y)
return true;
Real diff = std::fabs(x-y);
constexpr double tolerance = 42 * QL_EPSILON;
if (x == 0.0 || y == 0.0) // x or y = 0.0
return diff < (tolerance * tolerance);
return diff <= tolerance*std::fabs(x) ||
diff <= tolerance*std::fabs(y);
}
inline bool close_enough(Real x, Real y, Size n) {
// Deals with +infinity and -infinity representations etc.
if (x == y)
return true;
Real diff = std::fabs(x-y), tolerance = n * QL_EPSILON;
if (x == 0.0 || y == 0.0)
return diff < (tolerance * tolerance);
return diff <= tolerance*std::fabs(x) ||
diff <= tolerance*std::fabs(y);
}
//! compare two objects by date
/*! There is no generic implementation of this struct.
Template specializations will have to be defined for
each needed type (see CashFlow for an example.)
*/
template <class T> struct earlier_than;
/* partial specialization for shared pointers, forwarding to their
pointees. */
template <class T>
struct earlier_than<ext::shared_ptr<T> > {
bool operator()(const ext::shared_ptr<T>& x,
const ext::shared_ptr<T>& y) const {
return earlier_than<T>()(*x,*y);
}
};
}
#endif
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