flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2016 Vincent Delecroix

    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 "nmod.h"
#include "nmod_vec.h"
#include "nmod_poly.h"

void
_nmod_poly_power_sums_to_poly(nn_ptr res, nn_srcptr poly, slong len,
                              nmod_t mod)
{
    if (mod.n <= 12 || poly[0] <= 10)
        _nmod_poly_power_sums_to_poly_naive(res, poly, len, mod);
    else
        _nmod_poly_power_sums_to_poly_schoenhage(res, poly, len, mod);
}

void
nmod_poly_power_sums_to_poly(nmod_poly_t res, const nmod_poly_t Q)
{
    if (Q->length == 0)
    {
        nmod_poly_fit_length(res, 1);
        res->coeffs[0] = 1;
        _nmod_poly_set_length(res, 1);
    }
    else
    {
        slong d = Q->coeffs[0];
        if (Q == res)
        {
            nmod_poly_t t;
            nmod_poly_init_preinv(t, Q->mod.n, Q->mod.ninv);
            nmod_poly_fit_length(t, d + 1);
            _nmod_poly_power_sums_to_poly(t->coeffs, Q->coeffs, Q->length,
                                          Q->mod);
            nmod_poly_swap(res, t);
            nmod_poly_clear(t);
        }
        else
        {
            nmod_poly_fit_length(res, d + 1);
            _nmod_poly_power_sums_to_poly(res->coeffs, Q->coeffs, Q->length,
                                          Q->mod);
        }
        _nmod_poly_set_length(res, d + 1);
        _nmod_poly_normalise(res);
    }
}

/* todo: should use dot products */
void
_nmod_poly_power_sums_to_poly_naive(nn_ptr res, nn_srcptr poly, slong len,
                                    nmod_t mod)
{
    slong i, k;
    slong d = poly[0];

    res[d] = 1;
    for (k = 1; k < FLINT_MIN(d + 1, len); k++)
    {
        res[d - k] = poly[k];
        for (i = 1; i < k; i++)
            res[d - k] = nmod_add(res[d - k],
                    nmod_mul(res[d - k + i], poly[i], mod),
                    mod);
        res[d - k] = nmod_div(res[d - k], k, mod);
        res[d - k] = nmod_neg(res[d - k], mod);
    }
    for (k = len; k <= d; k++)
    {
        res[d - k] = 0;
        for (i = 1; i < len; i++)
            res[d - k] = nmod_add(res[d - k],
                    nmod_mul(res[d - k + i], poly[i], mod),
                    mod);
        res[d - k] = nmod_div(res[d - k], k, mod);
        res[d - k] = nmod_neg(res[d - k], mod);
    }
}

void
nmod_poly_power_sums_to_poly_naive(nmod_poly_t res, const nmod_poly_t Q)
{
    if (Q->length == 0)
    {
        nmod_poly_fit_length(res, 1);
        res->coeffs[0] = 1;
        _nmod_poly_set_length(res, 1);
    }
    else
    {
        slong d = Q->coeffs[0];
        if (Q == res)
        {
            nmod_poly_t t;
            nmod_poly_init_preinv(t, Q->mod.n, Q->mod.ninv);
            nmod_poly_fit_length(t, d + 1);
            _nmod_poly_power_sums_to_poly_naive(t->coeffs, Q->coeffs,
                                                Q->length, Q->mod);
            nmod_poly_swap(res, t);
            nmod_poly_clear(t);
        }
        else
        {
            nmod_poly_fit_length(res, d + 1);
            _nmod_poly_power_sums_to_poly_naive(res->coeffs, Q->coeffs,
                                                Q->length, Q->mod);
        }
        _nmod_poly_set_length(res, d + 1);
        _nmod_poly_normalise(res);
    }
}

void
_nmod_poly_power_sums_to_poly_schoenhage(nn_ptr res, nn_srcptr poly, slong len,
                                         nmod_t mod)
{
    nn_ptr t;
    slong d = poly[0];

    if (len >= d + 1)
        len = d + 1;

    t = flint_malloc(len * sizeof(ulong));

    _nmod_vec_neg(t, poly + 1, len - 1, mod);
    _nmod_poly_integral(t, t, len, mod);
    _nmod_poly_exp_series(res, t, len, d + 1, mod);
    _nmod_poly_reverse(res, res, d + 1, d + 1);

    flint_free(t);
}

void
nmod_poly_power_sums_to_poly_schoenhage(nmod_poly_t res, const nmod_poly_t Q)
{
    if (Q->length == 0)
    {
        nmod_poly_fit_length(res, 1);
        (res->coeffs)[0] = 1;
        _nmod_poly_set_length(res, 1);
    }
    else
    {
        slong d = (Q->coeffs)[0];
        if (Q == res)
        {
            nmod_poly_t t;
            nmod_poly_init_preinv(t, Q->mod.n, Q->mod.ninv);
            nmod_poly_fit_length(t, d + 1);
            _nmod_poly_power_sums_to_poly_schoenhage(t->coeffs, Q->coeffs,
                                                     Q->length, Q->mod);
            nmod_poly_swap(res, t);
            nmod_poly_clear(t);
        }
        else
        {
            nmod_poly_fit_length(res, d + 1);
            _nmod_poly_power_sums_to_poly_schoenhage(res->coeffs, Q->coeffs,
                                                     Q->length, Q->mod);
        }
        _nmod_poly_set_length(res, d + 1);
        _nmod_poly_normalise(res);
    }
}