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include/it/poly.h

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/*
   libit - Library for basic source and channel coding functions
   Copyright (C) 2005-2008 Francois Cayre, Vivien Chappelier, Herve Jegou

   This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Library General Public
   License as published by the Free Software Foundation; either
   version 2 of the License, or (at your option) any later version.

   This library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Library General Public License for more details.

   You should have received a copy of the GNU Library General Public
   License along with this library; if not, write to the Free
   Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/

/*
  Polynomial functions
  Copyright (C) 2005-2007 Vivien Chappelier
*/

#ifndef __it_poly_h
#define __it_poly_h

#include <it/types.h>
#include <it/vec.h>
#include <it/mat.h>

/*---------------------------------------------------------------------------*/
/*! \defgroup poly Polynomial functions                                      */
/* @{                                                                        */
/*---------------------------------------------------------------------------*/

/* matrix of polynomials */
typedef vec **pmat;

static inline pmat pmat_new (int W, int H) {
  return ((pmat) Mat_new (vec, W, H));
}
static inline void pmat_delete (pmat m) {
  Mat_delete ((Mat) m);
}

/* vector of polynomials */
typedef vec *pvec;

static inline pvec pvec_new (int N) {
  return ((pvec) Vec_new (vec, N));
}
static inline void pvec_delete (pvec v) {
  Vec_delete ((Vec) v);
}

/* polynomial function */
it_function_args (itf_polynomial) {
  vec  poly;
};
extern it_function_t itf_polynomial;

/* the degree of a polynomial */
#define poly_deg(p) (vec_length(p) - 1)

/* remove null factors from the polynomial */
void poly_normalize (vec v);

/* check if the polynomial is null. */
int  poly_is_null (vec v);

/* evaluate the polynomial in 'x' */
static inline double poly_eval (vec v, double x) {
  it_function_args (itf_polynomial) itf_polynomial_args;
  itf_polynomial_args.poly = v;
  return (itf_polynomial (x, &itf_polynomial_args));
}

/*-----------------------------------------------------------------*/
/* Arithmetic operations                                           */
/*-----------------------------------------------------------------*/

void poly_shift (vec v, int shift);

/* polynomial addition */
vec  poly_add (vec a, vec b);

/* polynomial subtraction */
vec  poly_sub (vec a, vec b);

/* polynomial multiplication */
static inline vec poly_mul (vec a, vec b) {
  return (vec_conv (a, b));
}

/* Laurent polynomial Euclidean division of a by b */
/* This finds Q and R such that A = B Q + R X^deg_x */
/* for classical polynomial division, deg_x = 0. */
vec  lpoly_ediv (vec _a, vec _b, int deg_x, vec * _q);

/* polynomial Euclidean division */
#define poly_ediv(a, b, _q) lpoly_ediv(a, b, 0, _q)

/* returns the quotient of the Euclidean division of a by b */
static inline vec poly_div (vec a, vec b) {
  vec  q, r;
  r = poly_ediv (a, b, &q);
  vec_delete (r);
  return (q);
}

/* returns the remainder of the Euclidean division of a by b */
static inline vec poly_mod (vec a, vec b) {
  vec  q, r;
  r = poly_ediv (a, b, &q);
  vec_delete (q);
  return (r);
}

/* returns the greatest common divider of a and b */
vec  poly_gcd (vec a, vec b);

/* @} */


#endif

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