flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2010 William Hart
    Copyright (C) 2012 Sebastian Pancratz

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "ulong_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"

void
_nmod_poly_compose_horner(nn_ptr res, nn_srcptr poly1, slong len1,
                                      nn_srcptr poly2, slong len2, nmod_t mod)
{
    if (len1 == 1)
    {
        res[0] = poly1[0];
    }
    else if (len2 == 1)
    {
        res[0] = _nmod_poly_evaluate_nmod(poly1, len1, poly2[0], mod);
    }
    else if (len1 == 2)
    {
        _nmod_vec_scalar_mul_nmod(res, poly2, len2, poly1[1], mod);
        res[0] = n_addmod(res[0], poly1[0], mod.n);
    }
    else
    {
        const slong alloc = (len1 - 1) * (len2 - 1) + 1;
        slong i = len1 - 1, lenr = len2;
        nn_ptr t, t1, t2;
        TMP_INIT;

        TMP_START;
        t = TMP_ALLOC(alloc * sizeof(ulong));

        if (len1 % 2 == 0)
        {
            t1 = res;
            t2 = t;
        }
        else
        {
            t1 = t;
            t2 = res;
        }

        /*  Perform the first two steps as one,
            "res = a(m) * poly2 + a(m-1)".      */
        {
            _nmod_vec_scalar_mul_nmod(t1, poly2, len2, poly1[i], mod);
            i--;
            t1[0] = n_addmod(t1[0], poly1[i], mod.n);
        }
        while (i--)
        {
            _nmod_poly_mul(t2, t1, lenr, poly2, len2, mod);
            lenr += len2 - 1;
            FLINT_SWAP(nn_ptr, t1, t2);
            t1[0] = n_addmod(t1[0], poly1[i], mod.n);
        }

        TMP_END;
    }
}

void nmod_poly_compose_horner(nmod_poly_t res,
                              const nmod_poly_t poly1, const nmod_poly_t poly2)
{
    const slong len1 = poly1->length;
    const slong len2 = poly2->length;

    if (len1 == 0)
    {
        nmod_poly_zero(res);
    }
    else if (len1 == 1 || len2 == 0)
    {
        nmod_poly_fit_length(res, 1);
        res->coeffs[0] = poly1->coeffs[0];
        res->length = (res->coeffs[0] != 0);
    }
    else
    {
        const slong lenr = (len1 - 1) * (len2 - 1) + 1;

        if (res != poly1 && res != poly2)
        {
            nmod_poly_fit_length(res, lenr);
            _nmod_poly_compose_horner(res->coeffs, poly1->coeffs, len1,
                                                   poly2->coeffs, len2, poly1->mod);
        }
        else
        {
            nmod_poly_t t;
            nmod_poly_init2(t, poly1->mod.n, lenr);
            _nmod_poly_compose_horner(t->coeffs, poly1->coeffs, len1,
                                                 poly2->coeffs, len2, poly1->mod);
            nmod_poly_swap(res, t);
            nmod_poly_clear(t);
        }

        res->length = lenr;
        _nmod_poly_normalise(res);
    }
}