evalf.h File Reference

Definition of polynomials evaluator with machine floating point coefficients. More...

Go to the source code of this file.

Data Structures
struct	evalf_struct
	Evaluator of polynomials with machine floating point coefficients. More...

Macros
#define	evalf_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	evalf_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 evalf_struct	evalf_t[1]
	Practical wrapper for evalf_struct. More...
typedef evalf_struct *	evalf
	Convenience pointer to evalf_struct.

Functions
evalf	evalf_new (polyf P)
	Returns a new evaluator of the complex polynomial P. More...
evalf	evalf_new_r (polyfr Q)
	Returns a new evaluator of the real polynomial Q. More...
bool	evalf_free (evalf ev)
	Frees all the memory used by the evaluator ev, assuming the struct has been allocated with malloc(), for example with evalf_new() or with evalf_new_r(). More...
bool	evalf_val (compf v, evalf ev, compf z)
	Evaluates ev->P(z) (or ev->Q(z)) using the method described in [1]. More...
bool	evalf_der (compf d, evalf ev, compf z)
	Evaluates ev->P'(z) (or ev->Q'(z)) using the method described in [1]. More...
bool	evalf_val_der (compf v, compf d, evalf ev, compf 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	evalf_newton (compf nt, evalf ev, compf z)
	Computes the Newthon method step of ev->P (or ev->Q) using the method described in [1]. More...
bool	evalf_analyse (evalf ev)
	Analyses the complex polynomial ev->P, after some of its coefficients have been changed. More...
bool	evalf_analyse_r (evalf ev)
	Analyses the real polynomial ev->Q, after some of its coefficients have been changed. More...
bool	evalf_val_cc (compf v, evalf ev, compf z)
	Evaluates ev->P(x) using the method described in [1]. More...
bool	evalf_der_cc (compf d, evalf ev, compf z)
	Evaluates ev->P'(x) using the method described in [1]. More...
bool	evalf_val_der_cc (compf v, compf d, evalf ev, compf z)
	Evaluates ev->P(x) and ev->P'(x) using the method described in [1]. More...
bool	evalf_newton_cc (compf nt, evalf ev, compf z)
	Computes the Newthon method step of ev->P using the method described in [1]. More...
bool	evalf_val_cr (compf v, evalf ev, coeff_t x)
	Evaluates ev->P(x) using the method described in [1]. More...
bool	evalf_der_cr (compf d, evalf ev, coeff_t x)
	Evaluates ev->P'(x) using the method described in [1]. More...
bool	evalf_val_der_cr (compf v, compf d, evalf ev, coeff_t x)
	Evaluates ev->P(x) and ev->P'(x) using the method described in [1]. More...
bool	evalf_newton_cr (compf nt, evalf ev, coeff_t x)
	Computes the Newthon method step of ev->P using the method described in [1]. More...
bool	evalf_val_rc (compf v, evalf ev, compf z)
	Evaluates ev->Q(x) using the method described in [1]. More...
bool	evalf_der_rc (compf d, evalf ev, compf z)
	Evaluates ev->Q'(x) using the method described in [1]. More...
bool	evalf_val_der_rc (compf v, compf d, evalf ev, compf z)
	Evaluates ev->Q(x) and ev->Q'(x) using the method described in [1]. More...
bool	evalf_newton_rc (compf nt, evalf ev, compf z)
	Computes the Newthon method step of ev->Q using the method described in [1]. More...
coeff_t	evalf_val_rr (evalf ev, coeff_t x)
	Evaluates the real polynomial ev->Q(x) using the method described in [1]. More...
coeff_t	evalf_der_rr (evalf ev, coeff_t x)
	Evaluates the derivative of real polynomial ev->Q'(x) using the method described in [1]. More...
bool	evalf_val_der_rr (coeff_t *v, coeff_t *d, evalf ev, coeff_t x)
	Evaluates ev->Q(x) and ev->Q'(x) using the method described in [1]. More...
coeff_t	evalf_newton_rr (evalf ev, coeff_t x)
	Computes the Newthon method step of the real polynomial ev->Q using the method described in [1]. More...

Detailed Description

Definition of polynomials evaluator with machine floating point coefficients.

Definition in file evalf.h.

Typedef Documentation

evalf_t

typedef evalf_struct evalf_t[1]

Practical wrapper for evalf_struct.

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

Definition at line 51 of file evalf.h.

Function Documentation

evalf_analyse()

bool evalf_analyse

(

evalf

ev

)

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

Note

The general functions evalf_val(), evalf_der(), evalf_val_der() and evalf_newton() automatically analyse the appropriate polynomial. Use this function only with the optimized versions like evalf_val_cx().

Parameters

ev	the evaluator

Returns

true if ev is ready to use, false otherwise.

evalf_analyse_r()

bool evalf_analyse_r

(

evalf

ev

)

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

Note

The general functions evalf_val(), evalf_der(), evalf_val_der() and evalf_newton() automatically analyse the appropriate polynomial. Use this function only with the optimized versions like evalf_val_rx().

Parameters

ev	the evaluator

Returns

true if ev is ready to use, false otherwise.

evalf_der()

bool evalf_der	(	compf	d,
		evalf	ev,
		compf	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.

evalf_der_cc()

bool evalf_der_cc	(	compf	d,
		evalf	ev,
		compf	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.

evalf_der_cr()

bool evalf_der_cr	(	compf	d,
		evalf	ev,
		coeff_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.

evalf_der_rc()

bool evalf_der_rc	(	compf	d,
		evalf	ev,
		compf	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.

evalf_der_rr()

coeff_t evalf_der_rr	(	evalf	ev,
		coeff_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

ev	the evaluator
x	the real argument

Returns

the result, NaN is some error occurred.

evalf_free()

bool evalf_free

(

evalf

ev

)

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

Parameters

ev	the evaluator

Returns

true if successfull, false otherwise.

evalf_new()

evalf evalf_new

(

polyf

P

)

Returns a new evaluator of the complex polynomial P.

Parameters

P	the complex polynomial

Returns

the new evaluator, NULL if some error occurred.

evalf_new_r()

evalf evalf_new_r

(

polyfr

Q

)

Returns a new evaluator of the real polynomial Q.

Parameters

Q	the real polynomial

Returns

the new evaluator, NULL if some error occurred.

evalf_newton()

bool evalf_newton	(	compf	nt,
		evalf	ev,
		compf	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.

evalf_newton_cc()

bool evalf_newton_cc	(	compf	nt,
		evalf	ev,
		compf	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.

evalf_newton_cr()

bool evalf_newton_cr	(	compf	nt,
		evalf	ev,
		coeff_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.

evalf_newton_rc()

bool evalf_newton_rc	(	compf	nt,
		evalf	ev,
		compf	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.

evalf_newton_rr()

coeff_t evalf_newton_rr	(	evalf	ev,
		coeff_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

ev	the evaluator
x	the real argument

Returns

the result, NaN is some error occurred.

evalf_val()

bool evalf_val	(	compf	v,
		evalf	ev,
		compf	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.

evalf_val_cc()

bool evalf_val_cc	(	compf	v,
		evalf	ev,
		compf	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.

evalf_val_cr()

bool evalf_val_cr	(	compf	v,
		evalf	ev,
		coeff_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.

evalf_val_der()

bool evalf_val_der	(	compf	v,
		compf	d,
		evalf	ev,
		compf	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.

evalf_val_der_cc()

bool evalf_val_der_cc	(	compf	v,
		compf	d,
		evalf	ev,
		compf	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.

evalf_val_der_cr()

bool evalf_val_der_cr	(	compf	v,
		compf	d,
		evalf	ev,
		coeff_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.

evalf_val_der_rc()

bool evalf_val_der_rc	(	compf	v,
		compf	d,
		evalf	ev,
		compf	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.

evalf_val_der_rr()

bool evalf_val_der_rr	(	coeff_t *	v,
		coeff_t *	d,
		evalf	ev,
		coeff_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.

evalf_val_rc()

bool evalf_val_rc	(	compf	v,
		evalf	ev,
		compf	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.

evalf_val_rr()

coeff_t evalf_val_rr	(	evalf	ev,
		coeff_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

ev	the evaluator
x	the real argument

Returns

the result, NaN is some error occurred.