eval.h File Reference

Definition of polynomial evaluator with arbitary precision coefficients. More...

Go to the source code of this file.

Data Structures
struct	eval_struct
	Evaluator of polynomials with multi-precision floating point coefficients. More...

Macros
#define	MIN_EVAL_PREC   8
	Minimum prcision for evaluators.
#define	MIN_EVAL_PREC_STR   "8"
#define	eval_lastValError(ev)   (ev->valErr)
	The [approximative] upper bound for the error of the last evaluation, in bits. Not reported by the Newton term computation.
#define	eval_lastDerError(ev)   (ev->derErr)
	The [approximative] upper bound for the error of the last derivative evaluation, in bits. Not reported by the Newton term computation.

Typedefs
typedef eval_struct	eval_t[1]
	Practical wrapper for eval_struct. More...
typedef eval_struct *	eval
	Convenience pointer to eval_struct.

Functions
eval	eval_new (poly P, prec_t prec)
	Returns a new evaluator of the complex polynomial P. More...
eval	eval_new_r (polyr Q, prec_t prec)
	Returns a new evaluator of the real polynomial Q. More...
bool	eval_free (eval ev)
	Frees all the memory used by the evaluator ev, assuming the struct has been allocated with malloc(), for example with eval_new() or with eval_new_r(). More...
bool	eval_val (comp v, eval ev, comp z)
	Evaluates ev->P(z) (or ev->Q(z)) using the method described in [1]. More...
bool	eval_der (comp d, eval ev, comp z)
	Evaluates ev->P'(z) (or ev->Q'(z)) using the method described in [1]. More...
bool	eval_val_der (comp v, comp d, eval ev, comp z)
	Evaluates ev->P(z) and ev->P'(z) (or ev->Q(z) and ev->Q'(z)) using the method described in [1]. More...
bool	eval_newton (comp nt, eval ev, comp z)
	Computes the Newthon method step of ev->P (or ev->Q) using the method described in [1]. More...
bool	eval_analyse (eval ev)
	Analyses the complex polynomial ev->P, after some of its coefficients have been changed. More...
bool	eval_analyse_r (eval ev)
	Analyses the real polynomial ev->Q, after some of its coefficients have been changed. More...
bool	eval_val_cc (comp v, eval ev, comp z)
	Evaluates ev->P(x) using the method described in [1]. More...
bool	eval_der_cc (comp d, eval ev, comp z)
	Evaluates ev->P'(x) using the method described in [1]. More...
bool	eval_val_der_cc (comp v, comp d, eval ev, comp z)
	Evaluates ev->P(x) and ev->P'(x) using the method described in [1]. More...
bool	eval_newton_cc (comp nt, eval ev, comp z)
	Computes the Newthon method step of ev->P using the method described in [1]. More...
bool	eval_val_cr (comp v, eval ev, mpfr_t x)
	Evaluates ev->P(x) using the method described in [1]. More...
bool	eval_der_cr (comp d, eval ev, mpfr_t x)
	Evaluates ev->P'(x) using the method described in [1]. More...
bool	eval_val_der_cr (comp v, comp d, eval ev, mpfr_t x)
	Evaluates ev->P(x) and ev->P'(x) using the method described in [1]. More...
bool	eval_newton_cr (comp nt, eval ev, mpfr_t x)
	Computes the Newthon method step of ev->P using the method described in [1]. More...
bool	eval_val_rc (comp v, eval ev, comp z)
	Evaluates ev->Q(x) using the method described in [1]. More...
bool	eval_der_rc (comp d, eval ev, comp z)
	Evaluates ev->Q'(x) using the method described in [1]. More...
bool	eval_val_der_rc (comp v, comp d, eval ev, comp z)
	Evaluates ev->Q(x) and ev->Q'(x) using the method described in [1]. More...
bool	eval_newton_rc (comp nt, eval ev, comp z)
	Computes the Newthon method step of ev->Q using the method described in [1]. More...
bool	eval_val_rr (mpfr_t v, eval ev, mpfr_t x)
	Evaluates the real polynomial ev->Q(x) using the method described in [1]. More...
bool	eval_der_rr (mpfr_t d, eval ev, mpfr_t x)
	Evaluates the derivative of real polynomial ev->Q'(x) using the method described in [1]. More...
bool	eval_val_der_rr (mpfr_t v, mpfr_t d, eval ev, mpfr_t x)
	Evaluates ev->Q(x) and ev->Q'(x) using the method described in [1]. More...
bool	eval_newton_rr (mpfr_t nt, eval ev, mpfr_t x)
	Computes the Newthon method step of the real polynomial ev->Q using the method described in [1]. More...

Detailed Description

Definition of polynomial evaluator with arbitary precision coefficients.

Definition in file eval.h.

Typedef Documentation

eval_t

typedef eval_struct eval_t[1]

Practical wrapper for eval_struct.

To avoid the constant use * and & the type eval_t is a pointer.

Definition at line 60 of file eval.h.

Function Documentation

eval_analyse()

bool eval_analyse

(

eval

ev

)

Analyses the complex polynomial ev->P, after some of its coefficients have been changed.

Note

The general functions eval_val(), eval_der(), eval_val_der() and eval_newton() automatically analyse the appropriate polynomial. Use this function only with the optimized versions like eval_val_cx().

Parameters

ev	the evaluator

Returns

true if ev is ready to use, false otherwise.

eval_analyse_r()

bool eval_analyse_r

(

eval

ev

)

Analyses the real polynomial ev->Q, after some of its coefficients have been changed.

Note

The general functions eval_val(), eval_der(), eval_val_der() and eval_newton() automatically analyse the appropriate polynomial. Use this function only with the optimized versions like eval_val_rx().

Parameters

ev	the evaluator

Returns

true if ev is ready to use, false otherwise.

eval_der()

bool eval_der	(	comp	d,
		eval	ev,
		comp	z
	)

Evaluates ev->P'(z) (or ev->Q'(z)) using the method described in [1].

Note

This function chooses the quickest variant to compute, depending if the polynomial of ev and / or z are real.

Parameters

d	the result
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_der_cc()

bool eval_der_cc	(	comp	d,
		eval	ev,
		comp	z
	)

Evaluates ev->P'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

d	the result
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_der_cr()

bool eval_der_cr	(	comp	d,
		eval	ev,
		mpfr_t	x
	)

Evaluates ev->P'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

d	the result
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.

eval_der_rc()

bool eval_der_rc	(	comp	d,
		eval	ev,
		comp	z
	)

Evaluates ev->Q'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

d	the result
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_der_rr()

bool eval_der_rr	(	mpfr_t	d,
		eval	ev,
		mpfr_t	x
	)

Evaluates the derivative of real polynomial ev->Q'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

d	the derivative
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.

eval_free()

bool eval_free

(

eval

ev

)

Frees all the memory used by the evaluator ev, assuming the struct has been allocated with malloc(), for example with eval_new() or with eval_new_r().

Parameters

ev	the evaluator

Returns

true if successfull, false otherwise.

eval_new()

eval eval_new	(	poly	P,
		prec_t	prec
	)

Returns a new evaluator of the complex polynomial P.

Parameters

P	the complex polynomial
prec	the precision of evaluations, in bits

Returns

the new evaluator, NULL if some error occurred.

eval_new_r()

eval eval_new_r	(	polyr	Q,
		prec_t	prec
	)

Returns a new evaluator of the real polynomial Q.

Parameters

Q	the real polynomial
prec	the precision of evaluations, in bits

Returns

the new evaluator, NULL if some error occurred.

eval_newton()

bool eval_newton	(	comp	nt,
		eval	ev,
		comp	z
	)

Computes the Newthon method step of ev->P (or ev->Q) using the method described in [1].

Note

This function chooses the quickest variant to compute, depending if the polynomial of ev and / or z are real.

Parameters

nt	the Newton term
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_newton_cc()

bool eval_newton_cc	(	comp	nt,
		eval	ev,
		comp	z
	)

Computes the Newthon method step of ev->P using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

nt	the Newton term
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_newton_cr()

bool eval_newton_cr	(	comp	nt,
		eval	ev,
		mpfr_t	x
	)

Computes the Newthon method step of ev->P using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

nt	the Newton term
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.

eval_newton_rc()

bool eval_newton_rc	(	comp	nt,
		eval	ev,
		comp	z
	)

Computes the Newthon method step of ev->Q using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

nt	the Newton term
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_newton_rr()

bool eval_newton_rr	(	mpfr_t	nt,
		eval	ev,
		mpfr_t	x
	)

Computes the Newthon method step of the real polynomial ev->Q using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

nt	the Newton term
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.

eval_val()

bool eval_val	(	comp	v,
		eval	ev,
		comp	z
	)

Evaluates ev->P(z) (or ev->Q(z)) using the method described in [1].

Note

This function chooses the quickest variant to compute, depending if the polynomial of ev and / or z are real.

Parameters

v	the result
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_val_cc()

bool eval_val_cc	(	comp	v,
		eval	ev,
		comp	z
	)

Evaluates ev->P(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the result
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_val_cr()

bool eval_val_cr	(	comp	v,
		eval	ev,
		mpfr_t	x
	)

Evaluates ev->P(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the result
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.

eval_val_der()

bool eval_val_der	(	comp	v,
		comp	d,
		eval	ev,
		comp	z
	)

Evaluates ev->P(z) and ev->P'(z) (or ev->Q(z) and ev->Q'(z)) using the method described in [1].

Note

This function chooses the quickest variant to compute, depending if the polynomial of ev and / or z are real.

Parameters

v	the value
d	the derivative
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_val_der_cc()

bool eval_val_der_cc	(	comp	v,
		comp	d,
		eval	ev,
		comp	z
	)

Evaluates ev->P(x) and ev->P'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the value
d	the derivative
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_val_der_cr()

bool eval_val_der_cr	(	comp	v,
		comp	d,
		eval	ev,
		mpfr_t	x
	)

Evaluates ev->P(x) and ev->P'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the value
d	the derivative
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.

eval_val_der_rc()

bool eval_val_der_rc	(	comp	v,
		comp	d,
		eval	ev,
		comp	z
	)

Evaluates ev->Q(x) and ev->Q'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the value
d	the derivative
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_val_der_rr()

bool eval_val_der_rr	(	mpfr_t	v,
		mpfr_t	d,
		eval	ev,
		mpfr_t	x
	)

Evaluates ev->Q(x) and ev->Q'(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the value
d	the derivative
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.

eval_val_rc()

bool eval_val_rc	(	comp	v,
		eval	ev,
		comp	z
	)

Evaluates ev->Q(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the result
ev	the evaluator
z	the complex argument

Returns

true if successfull, false otherwise.

eval_val_rr()

bool eval_val_rr	(	mpfr_t	v,
		eval	ev,
		mpfr_t	x
	)

Evaluates the real polynomial ev->Q(x) using the method described in [1].

Warning

For maximum speed, no checks are performed on the parameters, on the type of polynomial represented by ev nor if the polynomial has been pre-conditionned after the last coefficient update.

Parameters

v	the value
ev	the evaluator
x	the real argument

Returns

true if successfull, false otherwise.