apps.h File Reference

The implementation of the mini-apps with MPFR numbers. More...

Go to the source code of this file.

Functions
array	app_join (long prec, array z1, array z2)
	Joins the real parts of the sequences z1 and z2 as the real parts and imaginary parts of a new list. More...
array	app_grid (long prec, array z1, array z2)
	Computes the set product of the real parts of two sequences z1 and z2. More...
array	app_exp (long prec, array z)
	Computes the complex exponential of a sequence z. More...
array	app_rot (long prec, array z)
	Computes a*exp(ib) for each term a+ib of a sequence z of complex numbers. More...
array	app_polar (long prec, array z)
	Computes the complex numbers given by a sequence z of their polar coordinates on the sphere. More...
array	app_unif (long prec, ulong n, mpfr_t st, mpfr_t en)
	Returns the list of n real numbers that split the interval [st,en] in n-1 equal intervals. More...
array	app_rand (long prec, ulong n, mpfr_t st, mpfr_t en)
	Returns the list of n random real numbers in the interval [st,en], uniformly distributed. More...
array	app_normal (long prec, ulong n, mpfr_t cent, mpfr_t var)
	Returns the list of n random real numbers, normally distributed with center cent and variance var. More...
array	app_sphere (long prec, ulong n)
	Returns a list of n compelx numbers, uniformly distributed on the Riemann sphere. More...
bool	app_compare (long prec, array z1, array z2, char *output)
	Compares two list of complex values and reports the eventual errors. More...
array	app_re (long prec, array z)
	Returns the real parts of the numbers in the sequence z. More...
array	app_im (long prec, array z)
	Returns the imaginary parts of the numbers in the sequence z. More...
array	app_conj (long prec, array z)
	Returns the conjugates of the numbers in the sequence z. More...
array	app_tensor (long prec, array z1, array z2)
	Computes tensor (or piontwise) product of the sequences z1 and z2. More...
bool	app_eval_p (long prec, poly P, array z, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the polynomial P in all points in the list z, using the FPE algorithm. More...
bool	app_eval_d (long prec, poly P, array z, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the derivative of the polynomial P in all points in the list z, using the FPE algorithm. More...
bool	app_eval_n (long prec, poly P, array z, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the Newton terms of the polynomial P in all points in the list z, using the FPE algorithm. More...
bool	app_eval_r (long prec, poly P, array z, ulong maxIter, char *outFile, char *outError, long count, char *outHorner, long countHorner, const char **inFiles)
	Evaluates the Newton iterates of the polynomial P in all points in the list z, using the FPE algorithm. More...
bool	app_analyse (long prec, poly P, char *outFile, char *outChange)
	Analyses the polynomail P and outputs its concave cover, ignored coefficients and (optionally) the modules of complex numbers for which the reduced polynomial changes. More...

Detailed Description

The implementation of the mini-apps with MPFR numbers.

Definition in file apps.h.

Function Documentation

app_analyse()

bool app_analyse	(	long	prec,
		poly	P,
		char *	outFile,
		char *	outChange
	)

Analyses the polynomail P and outputs its concave cover, ignored coefficients and (optionally) the modules of complex numbers for which the reduced polynomial changes.

These analysis is performed for the evaluations of the P with prec bits of precision. The concave cover corresponds to the pre-processing phase of the FPE algortihm. The map k->log_2|a_k| is considered.

Parameters

prec	the precision of evaluations
P	the polynomial
outFile	the output file containing the concave cover and the ognored coefficients
outChange	the output file containing the intervals for log_2|z| and the corresponding reduced polynomials of P

Returns

true if the analysis is complete, false if some error occurred.

app_compare()

bool app_compare	(	long	prec,
		array	z1,
		array	z2,
		char *	output
	)

Compares two list of complex values and reports the eventual errors.

Parameters

prec	the precision of the result
z1	the fist list
z2	the second list
output	a file name for the output file, NULL if not used

Returns

true if the comparison is complete, false if some error occurred.

app_conj()

array app_conj	(	long	prec,
		array	z
	)

Returns the conjugates of the numbers in the sequence z.

Parameters

prec	the precision of the result
z	the list of points

Returns

the conjugates of z, NULL if some error occurred.

app_eval_d()

bool app_eval_d	(	long	prec,
		poly	P,
		array	z,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the derivative of the polynomial P in all points in the list z, using the FPE algorithm.

Parameters

prec	the precision of intermediary computations and of the result
P	the polynomial
z	the list of evaluation points
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

app_eval_n()

bool app_eval_n	(	long	prec,
		poly	P,
		array	z,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the Newton terms of the polynomial P in all points in the list z, using the FPE algorithm.

Parameters

prec	the precision of intermediary computations and of the result
P	the polynomial
z	the list of evaluation points
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

app_eval_p()

bool app_eval_p	(	long	prec,
		poly	P,
		array	z,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the polynomial P in all points in the list z, using the FPE algorithm.

Parameters

prec	the precision of intermediary computations and of the result
P	the polynomial
z	the list of evaluation points
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

app_eval_r()

bool app_eval_r	(	long	prec,
		poly	P,
		array	z,
		ulong	maxIter,
		char *	outFile,
		char *	outError,
		long	count,
		char *	outHorner,
		long	countHorner,
		const char **	inFiles
	)

Evaluates the Newton iterates of the polynomial P in all points in the list z, using the FPE algorithm.

This is a method to approximate the roots of P, but there are no guarantees for the convergence. If the iterates escape far from the origin, the alogrith stops (for those starting points).

Parameters

prec	the precision of intermediary computations and of the result
P	the polynomial
z	the list of evaluation points
maxIter	the maximum iterates for each starting point
outFile	the results output file name
outError	the errors list file name
count	the number of repetitions of the computing task
outHorner	the results output file name, computed by Horner's method
countHorner	the number of repetitions of the computing task by Horner's method
inFiles	a vector with the names of input files, for printing stats only

Returns

true if the evaluaion is complete, false if some error occurred.

app_exp()

array app_exp	(	long	prec,
		array	z
	)

Computes the complex exponential of a sequence z.

Parameters

prec	the precision of the result
z	the list of points

Returns

the image by the complex exponential, NULL if some error occurred.

app_grid()

array app_grid	(	long	prec,
		array	z1,
		array	z2
	)

Computes the set product of the real parts of two sequences z1 and z2.

Parameters

prec	the precision of the result
z1	the first list
z2	the second list

Returns

the set product, NULL if some error occurred.

app_im()

array app_im	(	long	prec,
		array	z
	)

Returns the imaginary parts of the numbers in the sequence z.

Parameters

prec	the precision of the result
z	the list of points

Returns

the imaginary parts in z, NULL if some error occurred.

app_join()

array app_join	(	long	prec,
		array	z1,
		array	z2
	)

Joins the real parts of the sequences z1 and z2 as the real parts and imaginary parts of a new list.

Parameters

prec	the precision of the result
z1	the first list
z2	the second list

Returns

the joint list, NULL if some error occurred.

app_normal()

array app_normal	(	long	prec,
		ulong	n,
		mpfr_t	cent,
		mpfr_t	var
	)

Returns the list of n random real numbers, normally distributed with center cent and variance var.

Parameters

prec	the precision of the result
n	the number of points, at least 2
cent	the center of the normal distribution
var	the variance of the normal distribution

Returns

the list of random real numbers (in complex format), NULL if some error occurred.

app_polar()

array app_polar	(	long	prec,
		array	z
	)

Computes the complex numbers given by a sequence z of their polar coordinates on the sphere.

Parameters

prec	the precision of the result
z	the list of polar coordinates

Returns

the complex numbers given by their polar coordinates, NULL if some error occurred.

app_rand()

array app_rand	(	long	prec,
		ulong	n,
		mpfr_t	st,
		mpfr_t	en
	)

Returns the list of n random real numbers in the interval [st,en], uniformly distributed.

Parameters

prec	the precision of the result
n	the number of points, at least 2
st	the start point
en	the end point

Returns

the list of random real numbers (in complex format), NULL if some error occurred.

app_re()

array app_re	(	long	prec,
		array	z
	)

Returns the real parts of the numbers in the sequence z.

Parameters

prec	the precision of the result
z	the list of points

Returns

the real parts in z, NULL if some error occurred.

app_rot()

array app_rot	(	long	prec,
		array	z
	)

Computes a*exp(ib) for each term a+ib of a sequence z of complex numbers.

Parameters

prec	the precision of the result
z	the list of points

Returns

the image by a+ib->a*exp(ib), NULL if some error occurred.

app_sphere()

array app_sphere	(	long	prec,
		ulong	n
	)

Returns a list of n compelx numbers, uniformly distributed on the Riemann sphere.

Parameters

prec	the precision of the result
n	the number of points, at least 2

Returns

the list of points uniformly distributed on the sphere, NULL if some error occurred.

app_tensor()

array app_tensor	(	long	prec,
		array	z1,
		array	z2
	)

Computes tensor (or piontwise) product of the sequences z1 and z2.

Parameters

prec	the precision of the result
z1	the first list
z2	the second list

Returns

the tensor product, NULL if some error occurred.

app_unif()

array app_unif	(	long	prec,
		ulong	n,
		mpfr_t	st,
		mpfr_t	en
	)

Returns the list of n real numbers that split the interval [st,en] in n-1 equal intervals.

Parameters

prec	the precision of the result
n	the number of points, at least 2
st	the start point
en	the end point

Returns

the list of real numbers (in complex format), NULL if some error occurred.