flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2016 Pascal Molin

    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 "test_helpers.h"
#include "acb_dirichlet.h"

typedef void (*do_f) (acb_ptr w, acb_srcptr v, slong len, slong prec);

void
check_vec_eq_prec(acb_srcptr w1, acb_srcptr w2, slong len, slong prec, slong digits, ulong q, char f1[], char f2[])
{
    slong i;

    for (i = 0; i < len; i++)
    {
        if (!acb_overlaps(w1 + i, w2 + i))
        {
            flint_printf("FAIL\n\n");
            flint_printf("q = %wu, size = %wd\n", q, len);
            flint_printf("\nDFT differ from index %wd / %wd \n", i, len);
            flint_printf("\n%s =\n", f1);
            _acb_vec_printd(w1, len, digits);
            flint_printf("\n%s =\n", f2);
            _acb_vec_printd(w2, len, digits);
            flint_printf("\n\n");
            flint_abort();
        }
        else if (acb_rel_accuracy_bits(w1 + i) < 30
                || acb_rel_accuracy_bits(w2 + i) < 30)
        {
            flint_printf("FAIL\n\n");
            flint_printf("q = %wu\n", q);
            flint_printf("\nDFT inaccurate from index %wd / %wd \n", i, len);
            flint_printf("\nnaive =\n");
            acb_printd(w1 + i, digits);
            flint_printf("\nfast =\n");
            acb_printd(w2 + i, digits);
            flint_printf("\nerrors %wd & %wd [prec = %wd]\n",
                    acb_rel_accuracy_bits(w1 + i),
                    acb_rel_accuracy_bits(w2 + i), prec);
            flint_abort();
        }
    }
}

TEST_FUNCTION_START(acb_dirichlet_dft, state)
{
    slong k;
    slong prec = 100, digits = 30;
    slong nq = 13;
    ulong q[13] = { 2, 3, 4, 5, 6, 23, 10, 15, 30, 59, 308, 335, 961};

    /* Dirichlet group DFT */
    for (k = 0; k < nq; k++)
    {
        slong i, j, len;
        dirichlet_group_t G;
        dirichlet_char_t x, y;
        acb_dirichlet_roots_t roots;
        acb_t chiy;
        acb_ptr v, w1, w2;

        dirichlet_group_init(G, q[k]);

        len = G->phi_q;
        v = _acb_vec_init(len);
        w1 = _acb_vec_init(len);
        w2 = _acb_vec_init(len);
        acb_init(chiy);
        acb_dirichlet_roots_init(roots, G->expo, len, prec);

        dirichlet_char_init(x, G);
        dirichlet_char_init(y, G);

        for (i = 0; i < len; i++)
            acb_randtest_precise(v + i, state, prec, 0);

        /* naive */
        dirichlet_char_one(x, G);
        for (i = 0;  i < len; i++)
        {
            acb_zero(w1 + i);
            dirichlet_char_one(y, G);
            for (j = 0; j < len; j++)
            {
                acb_dirichlet_root(chiy, roots, dirichlet_pairing_char(G, x, y), prec);
                acb_conj(chiy, chiy);
                acb_addmul(w1 + i, chiy, v + j, prec);
                dirichlet_char_next(y, G);
            }
            dirichlet_char_next(x, G);
        }

        /* dft */
        acb_dirichlet_dft_index(w2, v, G, prec);

        check_vec_eq_prec(w1, w2, len, prec, digits, q[k], "naive", "group");

        _acb_vec_clear(v, len);
        _acb_vec_clear(w1, len);
        _acb_vec_clear(w2, len);
        acb_dirichlet_roots_clear(roots);

        dirichlet_char_clear(x);
        dirichlet_char_clear(y);
        dirichlet_group_clear(G);
        acb_clear(chiy);
    }

    TEST_FUNCTION_END(state);
}