Initial Commit
This commit is contained in:
Jordan Sherer
@@ -0,0 +1,315 @@
|
||||
// (C) Copyright Gennadiy Rozental 2001.
|
||||
// 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
|
||||
Reference in New Issue
Block a user