arb/fmprb_poly.h

/*=============================================================================

    This file is part of ARB.

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

    ARB 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 General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with ARB; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2012 Fredrik Johansson

******************************************************************************/

#ifndef FMPRB_POLY_H
#define FMPRB_POLY_H

#include "fmprb.h"
#include "fmpz_poly.h"
#include "fmpq_poly.h"

typedef struct
{
    fmprb_struct * coeffs;
    long length;
    long alloc;
}
fmprb_poly_struct;

typedef fmprb_poly_struct fmprb_poly_t[1];


/* Memory management */

void fmprb_poly_init(fmprb_poly_t poly);

void fmprb_poly_init2(fmprb_poly_t poly, long len);

void fmprb_poly_clear(fmprb_poly_t poly);

void fmprb_poly_fit_length(fmprb_poly_t poly, long len);

void _fmprb_poly_set_length(fmprb_poly_t poly, long len);

void _fmprb_poly_normalise(fmprb_poly_t poly);

static __inline__ void
fmprb_poly_swap(fmprb_poly_t poly1, fmprb_poly_t poly2)
{
    fmprb_poly_struct t = *poly1;
    *poly1 = *poly2;
    *poly2 = t;
}

void fmprb_poly_set(fmprb_poly_t poly, const fmprb_poly_t src);

/* Basic manipulation */

static __inline__ long fmprb_poly_length(const fmprb_poly_t poly)
{
    return poly->length;
}

static __inline__ void fmprb_poly_zero(fmprb_poly_t poly)
{
    poly->length = 0;
}

static __inline__ void
fmprb_poly_one(fmprb_poly_t poly)
{
    fmprb_poly_fit_length(poly, 1);
    fmprb_one(poly->coeffs);
    _fmprb_poly_set_length(poly, 1);
}

void _fmprb_poly_reverse(fmprb_struct * res, const fmprb_struct * poly, long len, long n);

/* Conversions */

void fmprb_poly_set_fmpz_poly(fmprb_poly_t poly, const fmpz_poly_t src, long prec);

void fmprb_poly_set_fmpq_poly(fmprb_poly_t poly, const fmpq_poly_t src, long prec);

static __inline__ void
fmprb_poly_set_fmprb(fmprb_poly_t poly, const fmprb_t c)
{
    fmprb_poly_fit_length(poly, 1);
    fmprb_set(poly->coeffs, c);
    _fmprb_poly_set_length(poly, !fmprb_is_zero(poly->coeffs));
}

/* Comparisons */

int fmprb_poly_contains_fmpq_poly(const fmprb_poly_t poly1, const fmpq_poly_t poly2);

int fmprb_poly_equal(const fmprb_poly_t A, const fmprb_poly_t B);

int _fmprb_poly_overlaps(const fmprb_struct * poly1, long len1, const fmprb_struct * poly2, long len2);

int fmprb_poly_overlaps(const fmprb_poly_t poly1, const fmprb_poly_t poly2);

/* IO */

void fmprb_poly_printd(const fmprb_poly_t poly, long digits);

/* Random generation */

void fmprb_poly_randtest(fmprb_poly_t poly, flint_rand_t state, long len, long prec, long mag_bits);

/* Arithmetic */

void
_fmprb_poly_add(fmprb_struct * res, const fmprb_struct * poly1, long len1,
    const fmprb_struct * poly2, long len2, long prec);

void fmprb_poly_add(fmprb_poly_t res, const fmprb_poly_t poly1,
              const fmprb_poly_t poly2, long prec);

void _fmprb_poly_mullow_ztrunc(fmprb_struct * res,
    const fmprb_struct * poly1, long len1,
    const fmprb_struct * poly2, long len2, long n, long prec);

void fmprb_poly_mullow_ztrunc(fmprb_poly_t res, const fmprb_poly_t poly1,
                                            const fmprb_poly_t poly2,
                                                long n, long prec);

void _fmprb_poly_mullow_classical(fmprb_struct * res,
    const fmprb_struct * poly1, long len1,
    const fmprb_struct * poly2, long len2, long n, long prec);

void fmprb_poly_mullow_classical(fmprb_poly_t res, const fmprb_poly_t poly1,
                                            const fmprb_poly_t poly2,
                                                long n, long prec);

void _fmprb_poly_mullow(fmprb_struct * C,
    const fmprb_struct * A, long lenA,
    const fmprb_struct * B, long lenB, long n, long prec);

void fmprb_poly_mullow(fmprb_poly_t res, const fmprb_poly_t poly1,
              const fmprb_poly_t poly2, long len, long prec);

void _fmprb_poly_mul(fmprb_struct * C,
    const fmprb_struct * A, long lenA,
    const fmprb_struct * B, long lenB, long prec);

void fmprb_poly_mul(fmprb_poly_t res, const fmprb_poly_t poly1,
              const fmprb_poly_t poly2, long prec);

static __inline__ void
_fmprb_poly_mul_monic(fmprb_struct * res, const fmprb_struct * poly1, long len1,
    const fmprb_struct * poly2, long len2, long prec)
{
    if (len1 + len2 - 2 > 0)
        _fmprb_poly_mullow(res, poly1, len1, poly2, len2, len1 + len2 - 2, prec);
    fmprb_one(res + len1 + len2 - 2);
}

void _fmprb_poly_inv_series(fmprb_struct * Qinv, const fmprb_struct * Q, long len, long prec);

void fmprb_poly_inv_series(fmprb_poly_t Qinv, const fmprb_poly_t Q, long n, long prec);

void
_fmprb_poly_div(fmprb_struct * Q,
    const fmprb_struct * A, long lenA,
    const fmprb_struct * B, long lenB, long prec);

void _fmprb_poly_divrem(fmprb_struct * Q, fmprb_struct * R,
    const fmprb_struct * A, long lenA,
    const fmprb_struct * B, long lenB, long prec);

void _fmprb_poly_rem(fmprb_struct * R,
    const fmprb_struct * A, long lenA,
    const fmprb_struct * B, long lenB, long prec);

void fmprb_poly_divrem(fmprb_poly_t Q, fmprb_poly_t R,
                             const fmprb_poly_t A, const fmprb_poly_t B, long prec);

void _fmprb_poly_div_root(fmprb_struct * Q, fmprb_t R, const fmprb_struct * A,
    long len, const fmprb_t c, long prec);

/* Product trees */

void _fmprb_poly_product_roots(fmprb_struct * poly, const fmprb_struct * xs, long n, long prec);

void fmprb_poly_product_roots(fmprb_poly_t poly, fmprb_struct * xs, long n, long prec);

fmprb_struct ** _fmprb_poly_tree_alloc(long len);

void _fmprb_poly_tree_free(fmprb_struct ** tree, long len);

void _fmprb_poly_tree_build(fmprb_struct ** tree, const fmprb_struct * roots, long len, long prec);

/* Composition */

void _fmprb_poly_compose(fmprb_struct * res,
    const fmprb_struct * poly1, long len1,
    const fmprb_struct * poly2, long len2, long prec);

void fmprb_poly_compose(fmprb_poly_t res,
              const fmprb_poly_t poly1, const fmprb_poly_t poly2, long prec);

void _fmprb_poly_compose_horner(fmprb_struct * res,
    const fmprb_struct * poly1, long len1,
    const fmprb_struct * poly2, long len2, long prec);

void fmprb_poly_compose_horner(fmprb_poly_t res,
              const fmprb_poly_t poly1, const fmprb_poly_t poly2, long prec);

void _fmprb_poly_compose_divconquer(fmprb_struct * res,
    const fmprb_struct * poly1, long len1,
    const fmprb_struct * poly2, long len2, long prec);

void fmprb_poly_compose_divconquer(fmprb_poly_t res,
              const fmprb_poly_t poly1, const fmprb_poly_t poly2, long prec);

void _fmprb_poly_compose_series_horner(fmprb_struct * res, const fmprb_struct * poly1, long len1,
                            const fmprb_struct * poly2, long len2, long n, long prec);

void fmprb_poly_compose_series_horner(fmprb_poly_t res,
                    const fmprb_poly_t poly1,
                    const fmprb_poly_t poly2, long n, long prec);

void _fmprb_poly_compose_series_brent_kung(fmprb_struct * res, const fmprb_struct * poly1, long len1,
                            const fmprb_struct * poly2, long len2, long n, long prec);

void fmprb_poly_compose_series_brent_kung(fmprb_poly_t res,
                    const fmprb_poly_t poly1,
                    const fmprb_poly_t poly2, long n, long prec);

void _fmprb_poly_compose_series(fmprb_struct * res, const fmprb_struct * poly1, long len1,
                            const fmprb_struct * poly2, long len2, long n, long prec);

void fmprb_poly_compose_series(fmprb_poly_t res,
                    const fmprb_poly_t poly1,
                    const fmprb_poly_t poly2, long n, long prec);

/* Evaluation and interpolation */

void
_fmprb_poly_evaluate(fmprb_t res, const fmprb_struct * f, long len,
                           const fmprb_t a, long prec);

void fmprb_poly_evaluate(fmprb_t res, const fmprb_poly_t f, const fmprb_t a, long prec);

void _fmprb_poly_evaluate_vec_iter(fmprb_struct * ys, const fmprb_struct * poly, long plen,
    const fmprb_struct * xs, long n, long prec);

void fmprb_poly_evaluate_vec_iter(fmprb_struct * ys,
        const fmprb_poly_t poly, const fmprb_struct * xs, long n, long prec);

void _fmprb_poly_evaluate_vec_fast_precomp(fmprb_struct * vs, const fmprb_struct * poly,
    long plen, fmprb_struct ** tree, long len, long prec);

void _fmprb_poly_evaluate_vec_fast(fmprb_struct * ys, const fmprb_struct * poly, long plen,
    const fmprb_struct * xs, long n, long prec);

void fmprb_poly_evaluate_vec_fast(fmprb_struct * ys,
        const fmprb_poly_t poly, const fmprb_struct * xs, long n, long prec);

void _fmprb_poly_interpolate_newton(fmprb_struct * poly, const fmprb_struct * xs,
    const fmprb_struct * ys, long n, long prec);

void fmprb_poly_interpolate_newton(fmprb_poly_t poly,
    const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec);

void
_fmprb_poly_interpolate_barycentric(fmprb_struct * poly,
    const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec);

void fmprb_poly_interpolate_barycentric(fmprb_poly_t poly,
    const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec);

void _fmprb_poly_interpolation_weights(fmprb_struct * w,
    fmprb_struct ** tree, long len, long prec);

void _fmprb_poly_interpolate_fast_precomp(fmprb_struct * poly,
    const fmprb_struct * ys, fmprb_struct ** tree, const fmprb_struct * weights,
    long len, long prec);

void _fmprb_poly_interpolate_fast(fmprb_struct * poly,
    const fmprb_struct * xs, const fmprb_struct * ys, long len, long prec);

void fmprb_poly_interpolate_fast(fmprb_poly_t poly,
        const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec);

/* Derivative and integral */

void _fmprb_poly_derivative(fmprb_struct * res, const fmprb_struct * poly, long len, long prec);

void fmprb_poly_derivative(fmprb_poly_t res, const fmprb_poly_t poly, long prec);

void _fmprb_poly_integral(fmprb_struct * res, const fmprb_struct * poly, long len, long prec);

void fmprb_poly_integral(fmprb_poly_t res, const fmprb_poly_t poly, long prec);

/* Special functions */

void _fmprb_poly_log_series(fmprb_struct * res, fmprb_struct * f, long n, long prec);

void fmprb_poly_log_series(fmprb_poly_t res, const fmprb_poly_t f, long n, long prec);

void _fmprb_poly_exp_series_basecase(fmprb_struct * f,
        const fmprb_struct * h, long hlen, long n, long prec);

void fmprb_poly_exp_series_basecase(fmprb_poly_t f, const fmprb_poly_t h, long n, long prec);

void _fmprb_poly_exp_series(fmprb_struct * f, const fmprb_struct * h, long hlen, long n, long prec);

void fmprb_poly_exp_series(fmprb_poly_t f, const fmprb_poly_t h, long n, long prec);

void fmprb_poly_log_gamma_series(fmprb_poly_t z, long n, long prec);

void _fmprb_poly_rfac_series_ui(fmprb_struct * res, const fmprb_struct * f, long flen, ulong r, long trunc, long prec);

void fmprb_poly_rfac_series_ui(fmprb_poly_t res, const fmprb_poly_t f, ulong r, long trunc, long prec);

#endif