mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
91 lines
2.2 KiB
C
91 lines
2.2 KiB
C
/*
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Copyright (C) 2016 Pascal Molin
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_dirichlet.h"
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/* assume xs has size >= len * step */
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void
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_acb_vec_set_powers_step(acb_ptr xs, slong n, slong len, slong step, slong prec)
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{
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slong i, j;
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prec += n_clog(n, 2);
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for (i = 0, j = 0; i < len; i++, j += step)
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{
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if (i == 0)
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acb_one(xs + j);
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else if (i == 1)
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acb_dirichlet_nth_root(xs + j, n, prec);
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else if (i % 2 == 0)
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acb_mul(xs + j, xs + j / 2, xs + j / 2, prec);
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else
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acb_mul(xs + j, xs + j - step, xs + step, prec);
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}
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}
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/* assume len = p^e and z has size >= len * step */
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void
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_acb_vec_roots_pe(acb_ptr z, slong p, slong e, slong len, slong step, slong prec)
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{
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if (e <= 1)
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{
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_acb_vec_set_powers_step(z, p, len, step, prec);
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}
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else
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{
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slong q, r;
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_acb_vec_roots_pe(z, p, e - 1, len / p, step * p, prec);
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_acb_vec_set_powers_step(z, n_pow(p, e), p, step, prec);
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for (q = p; q < len; q += p)
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for (r = 1; r < p; r++)
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acb_mul(z + (q + r) * step, z + q * step, z + r * step, prec);
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}
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}
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void
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acb_dirichlet_vec_nth_roots(acb_ptr z, slong len, slong prec)
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{
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slong i, q;
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n_factor_t fac;
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acb_one(z + 0);
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n_factor_init(&fac);
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n_factor(&fac, len, 0);
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q = 1;
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for (i = 0; i < fac.num; i++)
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{
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slong p, e, pe, mp, mq;
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p = fac.p[i];
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e = fac.exp[i];
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pe = n_pow(p, e);
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mp = len / pe;
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mq = len / q;
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_acb_vec_roots_pe(z, p, e, pe, mp, prec);
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if (i > 0)
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{
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slong k, l;
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for (k = mp; k < len; k += mp)
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{
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for (l = mq; l < len - k; l += mq)
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acb_mul(z + k + l, z + k, z + l, prec);
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for (; l < len; l += mq)
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acb_mul(z + k + l - len, z + k, z + l, prec);
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}
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}
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q *= pe;
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}
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}
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