horner.h File Reference

Horner implementation for Monomial polynomials. More...

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Functions
MPS_BEGIN_DECLS void	mps_parhorner (mps_context *st, int n, mpc_t x, mpc_t p[], mps_boolean b[], mpc_t s, int n_thread)
void	mps_aparhorner (mps_context *st, int n, rdpe_t x, rdpe_t p[], mps_boolean b[], rdpe_t s, int n_thread)
void	mps_fhorner (mps_context *s, mps_monomial_poly *p, cplx_t x, cplx_t value)
	Evaluate the polynomial p in the point x.
void	mps_fhorner_with_error (mps_context *s, mps_monomial_poly *p, cplx_t x, cplx_t value, double *relative_error)
	Evaluate the polynomial p in the point x, and give also a bound to the relative error occured in the computation.
void	mps_dhorner (mps_context *s, mps_monomial_poly *p, cdpe_t x, cdpe_t value)
	Evaluate the polynomial p in the point x.
void	mps_dhorner_with_error (mps_context *s, mps_monomial_poly *p, cdpe_t x, cdpe_t value, rdpe_t relative_error)
	Evaluate the polynomial p in the point x, and give also a bound to the relative error occured in the computation.
void	mps_mhorner (mps_context *s, mps_monomial_poly *p, mpc_t x, mpc_t value)
	Compute the value of the polynomial p in the point x and save it in value. If you need a bound to the relative error, try mps_mhorner_with_error().
void	mps_mhorner_with_error (mps_context *s, mps_monomial_poly *p, mpc_t x, mpc_t value, rdpe_t relative_error, long int wp)
	Compute the value of the polynomial p in the point x and save it in value.
void	mps_mhorner_with_error2 (mps_context *s, mps_monomial_poly *p, mpc_t x, mpc_t value, rdpe_t relative_error, long int wp)
	Compute the value of the polynomial p in the point x and save it in value.

Detailed Description

Horner implementation for Monomial polynomials.

Function Documentation

mps_dhorner()

void mps_dhorner	(	mps_context *	s,
		mps_monomial_poly *	p,
		cdpe_t	x,
		cdpe_t	value )

Evaluate the polynomial p in the point x.

Parameters

s	The mps_context of the computation.
p	The mps_monomial_poly to evaluate.
x	The point where the polynomial will be evaluated.
value	The value computed by the function.

mps_dhorner_with_error()

void mps_dhorner_with_error	(	mps_context *	s,
		mps_monomial_poly *	p,
		cdpe_t	x,
		cdpe_t	value,
		rdpe_t	error )

Evaluate the polynomial p in the point x, and give also a bound to the relative error occured in the computation.

Parameters

s	The mps_context of the computation.
p	The mps_monomial_poly to evaluate.
x	The point where the polynomial will be evaluated.
value	The value computed by the function.
error	A bound to the absolute error of the computation.

mps_fhorner()

void mps_fhorner	(	mps_context *	s,
		mps_monomial_poly *	p,
		cplx_t	x,
		cplx_t	value )

Evaluate the polynomial p in the point x.

Parameters

s	The mps_context of the computation.
p	The mps_monomial_poly to evaluate.
x	The point where the polynomial will be evaluated.
value	The value computed by the function.

mps_fhorner_with_error()

void mps_fhorner_with_error	(	mps_context *	s,
		mps_monomial_poly *	p,
		cplx_t	x,
		cplx_t	value,
		double *	error )

Evaluate the polynomial p in the point x, and give also a bound to the relative error occured in the computation.

Parameters

s	The mps_context of the computation.
p	The mps_monomial_poly to evaluate.
x	The point where the polynomial will be evaluated.
error	A pointer to the location when an upper bound to the computation error will be stored.
value	The value computed by the function.

mps_mhorner()

void mps_mhorner	(	mps_context *	s,
		mps_monomial_poly *	p,
		mpc_t	x,
		mpc_t	value )

Compute the value of the polynomial p in the point x and save it in value. If you need a bound to the relative error, try mps_mhorner_with_error().

Parameters

s	The mps_context of the computation.
p	The monomial_poly to evaluate.
x	The point where the polynomial will be evaluated.
value	The multiprecision complex variable where the result will be stored.

mps_mhorner_with_error()

void mps_mhorner_with_error	(	mps_context *	s,
		mps_monomial_poly *	p,
		mpc_t	x,
		mpc_t	value,
		rdpe_t	relative_error,
		long int	wp )

Compute the value of the polynomial p in the point x and save it in value.

A upper bound to the relative error of the evaluation will be stored in relative_error.

Parameters

s	The mps_context of the computation.
p	The monomial_poly to evaluate.
x	The point where the polynomial will be evaluated.
value	The multiprecision complex variable where the result will be stored.
relative_error	The RDPE where the relative error will be saved.
wp	The working precision to use for the computation. If this value is 0 then s->mpwp will be used.

mps_mhorner_with_error2()

void mps_mhorner_with_error2	(	mps_context *	s,
		mps_monomial_poly *	p,
		mpc_t	x,
		mpc_t	value,
		rdpe_t	error,
		long int	wp )

Compute the value of the polynomial p in the point x and save it in value.

A upper bound to the relative error of the evaluation will be stored in relative_error. The error is computed using the formula

where is the polynomial with the coefficients equal to the moduli of the coefficients of .

Parameters

s	The mps_context of the computation.
p	The monomial_poly to evaluate.
x	The point where the polynomial will be evaluated.
value	The multiprecision complex variable where the result will be stored.
error	The RDPE where the absolute error will be saved.
wp	The working precision to use for the computation. If this value is 0 then s->mpwp will be used.