boost/test/tools/floating_point_comparison.hpp
// (C) Copyright Gennadiy Rozental 2001-2014.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
// See http://www.boost.org/libs/test for the library home page.
//
//!@file
//!@brief algorithms for comparing floating point values
// ***************************************************************************
#ifndef BOOST_TEST_FLOATING_POINT_COMPARISON_HPP_071894GER
#define BOOST_TEST_FLOATING_POINT_COMPARISON_HPP_071894GER
// Boost.Test
#include <boost/test/detail/global_typedef.hpp>
#include <boost/test/tools/assertion_result.hpp>
// Boost
#include <boost/limits.hpp> // for std::numeric_limits
#include <boost/static_assert.hpp>
#include <boost/assert.hpp>
#include <boost/mpl/bool.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/type_traits/is_array.hpp>
#include <boost/type_traits/conditional.hpp>
#include <boost/utility/enable_if.hpp>
// STL
#include <iosfwd>
#include <boost/test/detail/suppress_warnings.hpp>
//____________________________________________________________________________//
namespace boost {
namespace math {
namespace fpc {
// ************************************************************************** //
// ************** fpc::tolerance_based ************** //
// ************************************************************************** //
//! @internal
//! Protects the instanciation of std::numeric_limits from non-supported types (eg. T=array)
template <typename T, bool enabled>
struct tolerance_based_delegate;
template <typename T>
struct tolerance_based_delegate<T, false> : mpl::false_ {};
template <typename T>
struct tolerance_based_delegate<T, true>
: mpl::bool_<
is_floating_point<T>::value ||
(!std::numeric_limits<T>::is_integer && std::numeric_limits<T>::is_specialized && !std::numeric_limits<T>::is_exact)>
{};
/*!@brief Indicates if a type can be compared using a tolerance scheme
*
* This is a metafunction that should evaluate to @c mpl::true_ if the type
* @c T can be compared using a tolerance based method, typically for floating point
* types.
*
* This metafunction can be specialized further to declare user types that are
* floating point (eg. boost.multiprecision).
*/
template <typename T>
struct tolerance_based : tolerance_based_delegate<T, !is_array<T>::value >::type {};
// ************************************************************************** //
// ************** fpc::strength ************** //
// ************************************************************************** //
//! Method for comparing floating point numbers
enum strength {
FPC_STRONG, //!< "Very close" - equation 2' in docs, the default
FPC_WEAK //!< "Close enough" - equation 3' in docs.
};
// ************************************************************************** //
// ************** tolerance presentation types ************** //
// ************************************************************************** //
template<typename FPT>
struct percent_tolerance_t {
explicit percent_tolerance_t( FPT v ) : m_value( v ) {}
FPT m_value;
};
//____________________________________________________________________________//
template<typename FPT>
inline std::ostream& operator<<( std::ostream& out, percent_tolerance_t<FPT> t )
{
return out << t.m_value;
}
//____________________________________________________________________________//
template<typename FPT>
inline percent_tolerance_t<FPT>
percent_tolerance( FPT v )
{
return percent_tolerance_t<FPT>( v );
}
//____________________________________________________________________________//
// ************************************************************************** //
// ************** details ************** //
// ************************************************************************** //
namespace fpc_detail {
// FPT is Floating-Point Type: float, double, long double or User-Defined.
template<typename FPT>
inline FPT
fpt_abs( FPT fpv )
{
return fpv < static_cast<FPT>(0) ? -fpv : fpv;
}
//____________________________________________________________________________//
template<typename FPT>
struct fpt_specialized_limits
{
static FPT min_value() { return (std::numeric_limits<FPT>::min)(); }
static FPT max_value() { return (std::numeric_limits<FPT>::max)(); }
};
template<typename FPT>
struct fpt_non_specialized_limits
{
static FPT min_value() { return static_cast<FPT>(0); }
static FPT max_value() { return static_cast<FPT>(1000000); } // for our purposes it doesn't really matter what value is returned here
};
template<typename FPT>
struct fpt_limits : boost::conditional<std::numeric_limits<FPT>::is_specialized,
fpt_specialized_limits<FPT>,
fpt_non_specialized_limits<FPT>
>::type
{};
//____________________________________________________________________________//
// both f1 and f2 are unsigned here
template<typename FPT>
inline FPT
safe_fpt_division( FPT f1, FPT f2 )
{
// Avoid overflow.
if( (f2 < static_cast<FPT>(1)) && (f1 > f2*fpt_limits<FPT>::max_value()) )
return fpt_limits<FPT>::max_value();
// Avoid underflow.
if( (f1 == static_cast<FPT>(0)) ||
((f2 > static_cast<FPT>(1)) && (f1 < f2*fpt_limits<FPT>::min_value())) )
return static_cast<FPT>(0);
return f1/f2;
}
//____________________________________________________________________________//
template<typename FPT, typename ToleranceType>
inline FPT
fraction_tolerance( ToleranceType tolerance )
{
return static_cast<FPT>(tolerance);
}
//____________________________________________________________________________//
template<typename FPT2, typename FPT>
inline FPT2
fraction_tolerance( percent_tolerance_t<FPT> tolerance )
{
return FPT2(tolerance.m_value)*FPT2(0.01);
}
//____________________________________________________________________________//
} // namespace fpc_detail
// ************************************************************************** //
// ************** close_at_tolerance ************** //
// ************************************************************************** //
/*!@brief Predicate for comparing floating point numbers
*
* This predicate is used to compare floating point numbers. In addition the comparison produces maximum
* related differnce, which can be used to generate detailed error message
* The methods for comparing floating points are detailed in the documentation. The method is chosen
* by the @ref boost::math::fpc::strength given at construction.
*/
template<typename FPT>
class close_at_tolerance {
public:
// Public typedefs
typedef bool result_type;
// Constructor
template<typename ToleranceType>
explicit close_at_tolerance( ToleranceType tolerance, fpc::strength fpc_strength = FPC_STRONG )
: m_fraction_tolerance( fpc_detail::fraction_tolerance<FPT>( tolerance ) )
, m_strength( fpc_strength )
, m_tested_rel_diff( 0 )
{
BOOST_ASSERT_MSG( m_fraction_tolerance >= FPT(0), "tolerance must not be negative!" ); // no reason for tolerance to be negative
}
// Access methods
//! Returns the tolerance
FPT fraction_tolerance() const { return m_fraction_tolerance; }
//! Returns the comparison method
fpc::strength strength() const { return m_strength; }
//! Returns the failing fraction
FPT tested_rel_diff() const { return m_tested_rel_diff; }
/*! Compares two floating point numbers a and b such that their "left" relative difference |a-b|/a and/or
* "right" relative difference |a-b|/b does not exceed specified relative (fraction) tolerance.
*
* @param[in] left first floating point number to be compared
* @param[in] right second floating point number to be compared
*
* What is reported by @c tested_rel_diff in case of failure depends on the comparison method:
* - for @c FPC_STRONG: the max of the two fractions
* - for @c FPC_WEAK: the min of the two fractions
* The rationale behind is to report the tolerance to set in order to make a test pass.
*/
bool operator()( FPT left, FPT right ) const
{
FPT diff = fpc_detail::fpt_abs<FPT>( left - right );
FPT fraction_of_right = fpc_detail::safe_fpt_division( diff, fpc_detail::fpt_abs( right ) );
FPT fraction_of_left = fpc_detail::safe_fpt_division( diff, fpc_detail::fpt_abs( left ) );
FPT max_rel_diff = (std::max)( fraction_of_left, fraction_of_right );
FPT min_rel_diff = (std::min)( fraction_of_left, fraction_of_right );
m_tested_rel_diff = m_strength == FPC_STRONG ? max_rel_diff : min_rel_diff;
return m_tested_rel_diff <= m_fraction_tolerance;
}
private:
// Data members
FPT m_fraction_tolerance;
fpc::strength m_strength;
mutable FPT m_tested_rel_diff;
};
// ************************************************************************** //
// ************** small_with_tolerance ************** //
// ************************************************************************** //
/*!@brief Predicate for comparing floating point numbers against 0
*
* Serves the same purpose as boost::math::fpc::close_at_tolerance, but used when one
* of the operand is null.
*/
template<typename FPT>
class small_with_tolerance {
public:
// Public typedefs
typedef bool result_type;
// Constructor
explicit small_with_tolerance( FPT tolerance ) // <= absolute tolerance
: m_tolerance( tolerance )
{
BOOST_ASSERT( m_tolerance >= FPT(0) ); // no reason for the tolerance to be negative
}
// Action method
bool operator()( FPT fpv ) const
{
return fpc::fpc_detail::fpt_abs( fpv ) < m_tolerance;
}
private:
// Data members
FPT m_tolerance;
};
// ************************************************************************** //
// ************** is_small ************** //
// ************************************************************************** //
template<typename FPT>
inline bool
is_small( FPT fpv, FPT tolerance )
{
return small_with_tolerance<FPT>( tolerance )( fpv );
}
//____________________________________________________________________________//
} // namespace fpc
} // namespace math
} // namespace boost
#include <boost/test/detail/enable_warnings.hpp>
#endif // BOOST_FLOATING_POINT_COMAPARISON_HPP_071894GER