Precision testing module. More...

Namespaces
	distance
	Distance functions for use in prec::equals.

	estimator
	Precision estimators.

	fail
	Fail functions for use in prec::estimate.

	property
	Property testing of functions.

Classes
class	interval
	An interval on the real numbers. More...

class	estimate_result
	A structure holding the result of precision estimation. More...

class	estimate_options
	A structure holding the options for precision estimation. More...

class	equation_result
	A structure holding the result of an evaluation. More...

class	equation_options
	Structure holding options for equivalence evaluation. More...

class	prec_settings
	of the precision testing module. More...

class	prec_results
	of the precision testing module. More...

Typedefs
using	FailFunction = std::function< bool(const estimate_result &)>
	A function which determines whether an estimation failed.

template<typename Type >
using	DistanceFunction = std::function< long double(Type, Type)>
	Distance function between two elements.

template<typename R , typename ... Args>
using	Estimator = typename estimate_options< R, Args... >::Estimator_t
	Generic precision estimator function signature.

Functions
void	setup (std::string moduleName, int argc=0, const char **argv=nullptr)
	Setup the precision testing environment. More...

void	terminate (bool exit=true)
	Terminate the precision testing environment, printing the results to standard output and output files. More...

template<typename R , typename ... Args, typename Function1 = std::function<R(Args...)>, typename Function2 = Function1>
void	estimate (const std::string &name, Function1 funcApprox, Function2 funcExpected, estimate_options< R, Args... > opt)
	Estimate error integrals over a function with respect to an exact function, with the given options. More...

template<typename R , typename ... Args, typename Function1 = std::function<R(Args...)>, typename Function2 = Function1>
void	estimate (const std::string &name, Function1 funcApprox, Function2 funcExpected, std::vector< interval > domain, long double tolerance, unsigned int iterations, FailFunction fail, Estimator< R, Args... > estimator, bool quiet=false)
	Estimate error integrals over a function with respect to an exact function. More...

void	estimate (const std::string &name, EndoFunction< double > funcApprox, EndoFunction< double > funcExpected, interval domain, long double tolerance=settings.defaultTolerance, unsigned int iterations=settings.defaultIterations, FailFunction fail=fail::fail_on_max_err(), Estimator< double, double > estimator=estimator::quadrature1D< double >(), bool quiet=false)
	Estimate error integrals over a real function of real variable, with respect to an exact function. More...

template<typename T = double>
void	equals (const std::string &name, const T &evaluated, const T &expected, equation_options< T > opt=equation_options< T >())
	Test an equivalence up to a tolerance, with the given options (e.g. More...

template<typename T = double>
void	equals (const std::string &name, const T &evaluated, const T &expected, long double tolerance, DistanceFunction< T > distance, bool quiet=false)
	Test an equivalence up to a tolerance, with the given options (e.g. More...

void	equals (const std::string &name, long double evaluated, long double expected, long double tolerance=settings.defaultTolerance, bool quiet=false)
	Test an equivalence up to a tolerance, with the given options (e.g. More...

template<typename T >
void	equals (const std::string &name, std::vector< std::array< T, 2 >> values, long double tolerance=settings.defaultTolerance, bool quiet=false)
	Evaluate multiple pairs of values for equivalence up to the given tolerance (e.g. More...

Variables
struct chebyshev::prec::prec_settings	settings

struct chebyshev::prec::prec_results	results

Detailed Description

Precision testing module.

This module provides functions to estimate the precision and accuracy of mathematical approximations, over an entire domain using prec::estimate or at single points using prec:equals. For estimates over a domain, precision estimators are used.

Function Documentation

◆ equals() [1/4]

template<typename T = double>

void chebyshev::prec::equals	(	const std::string &	name,
		const T &	evaluated,
		const T &	expected,
		equation_options< T >	opt = `equation_options<T>()`
	)

inline

Test an equivalence up to a tolerance, with the given options (e.g.

for residual testing).

Parameters

name	The name of the test case
evaluate	The evaluated value
expected	The expected value
opt	The options for the evaluation

◆ equals() [2/4]

template<typename T = double>

void chebyshev::prec::equals	(	const std::string &	name,
		const T &	evaluated,
		const T &	expected,
		long double	tolerance,
		DistanceFunction< T >	distance,
		bool	quiet = `false`
	)

inline

Test an equivalence up to a tolerance, with the given options (e.g.

for residual testing).

Parameters

name	The name of the test case
evaluate	The evaluated value
expected	The expected value
distance	The distance function to use
tolerance	The tolerance for the evaluation
quiet	Whether to output the result

◆ equals() [3/4]

void chebyshev::prec::equals	(	const std::string &	name,
		long double	evaluated,
		long double	expected,
		long double	tolerance = `settings.defaultTolerance`,
		bool	quiet = `false`
	)

inline

Test an equivalence up to a tolerance, with the given options (e.g.

for residual testing).

Parameters

name	The name of the test case
evaluate	The evaluated value
expected	The expected value
tolerance	The tolerance for the evaluation
quiet	Whether to output the result

◆ equals() [4/4]

template<typename T >

void chebyshev::prec::equals	(	const std::string &	name,
		std::vector< std::array< T, 2 >>	values,
		long double	tolerance = `settings.defaultTolerance`,
		bool	quiet = `false`
	)

inline

Evaluate multiple pairs of values for equivalence up to the given tolerance (e.g.

for residual testing).

Parameters

name	The name of the function or test case
values	A list of values to equate
tolerance	The tolerance for the evaluation
quiet	Whether to output the result

◆ estimate() [1/3]

void chebyshev::prec::estimate	(	const std::string &	name,
		EndoFunction< double >	funcApprox,
		EndoFunction< double >	funcExpected,
		interval	domain,
		long double	tolerance = `settings.defaultTolerance`,
		unsigned int	iterations = `settings.defaultIterations`,
		FailFunction	fail = `fail::fail_on_max_err()`,
		Estimator< double, double >	estimator = `estimator::quadrature1D<double>()`,
		bool	quiet = `false`
	)

inline

Estimate error integrals over a real function of real variable, with respect to an exact function.

Parameters

name	The name of the test case.
funcApprox	The approximation to test.
funcExpected	The expected result.
intervals	The (potentially multidimensional) domain of estimation.
iterations	The number of function evaluations.
fail	The fail function to determine whether the test failed (defaults to fail_on_max_err).
estimator	The precision estimator to use (defaults to the trapezoid<double> estimator).
quiet	Whether to output the result.

◆ estimate() [2/3]

template<typename R , typename ... Args, typename Function1 = std::function<R(Args...)>, typename Function2 = Function1>

void chebyshev::prec::estimate	(	const std::string &	name,
		Function1	funcApprox,
		Function2	funcExpected,
		estimate_options< R, Args... >	opt
	)

inline

Estimate error integrals over a function with respect to an exact function, with the given options.

Parameters

name	The name of the test case
funcApprox	The approximation to test
funcExpected	The expected result
opt	The options for the estimation

◆ estimate() [3/3]

template<typename R , typename ... Args, typename Function1 = std::function<R(Args...)>, typename Function2 = Function1>

void chebyshev::prec::estimate	(	const std::string &	name,
		Function1	funcApprox,
		Function2	funcExpected,
		std::vector< interval >	domain,
		long double	tolerance,
		unsigned int	iterations,
		FailFunction	fail,
		Estimator< R, Args... >	estimator,
		bool	quiet = `false`
	)

inline

Estimate error integrals over a function with respect to an exact function.

Parameters

name	The name of the test case.
funcApprox	The approximation to test.
funcExpected	The expected result.
intervals	The (potentially multidimensional) domain of estimation.
iterations	The number of function evaluations.
fail	The fail function to determine whether the test failed.
estimator	The precision estimator to use.
quiet	Whether to output the result.

◆ setup()

void chebyshev::prec::setup	(	std::string	moduleName,
		int	argc = `0`,
		const char **	argv = `nullptr`
	)

inline

Setup the precision testing environment.

Parameters

moduleName	Name of the module under test.
argc	The number of command line arguments
argv	A list of C-style strings containing the command line arguments.

◆ terminate()

void chebyshev::prec::terminate ( bool exit = true )

inline

Terminate the precision testing environment, printing the results to standard output and output files.

Parameters

exit	Whether to exit after terminating the module.

Namespaces

Classes

Typedefs

Functions

Variables

Detailed Description

Function Documentation

◆ equals() [1/4]

◆ equals() [2/4]

◆ equals() [3/4]

◆ equals() [4/4]

◆ estimate() [1/3]

◆ estimate() [2/3]

◆ estimate() [3/3]

◆ setup()

◆ terminate()