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_acb_vec_nth_roots: simpler, better algorithm

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This commit is contained in:
Fredrik Johansson 2016-11-20 05:09:02 +01:00
parent 54e6ed1607
commit dfc7965898
3 changed files with 125 additions and 91 deletions
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63
acb/test/t-vec_nth_roots.c Normal file
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/*
Copyright (C) 2016 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("vec_nth_roots....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100; iter++)
{
acb_ptr vec;
fmpq_t q;
acb_t t;
slong k;
slong prec = 53;
vec = _acb_vec_init(iter);
acb_init(t);
fmpq_init(q);
_acb_vec_nth_roots(vec, iter, prec);
for (k = 0; k < iter; k++)
{
fmpq_set_si(q, 2 * k, iter);
arb_sin_cos_pi_fmpq(acb_imagref(t), acb_realref(t), q, prec);
if (!acb_overlaps(vec + k, t))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu k = %wd\n\n", iter, k);
flint_printf("vec = "); acb_printn(vec + k, 30, 0); flint_printf("\n\n");
flint_printf("t = "); acb_printn(t, 30, 0); flint_printf("\n\n");
abort();
}
}
_acb_vec_clear(vec, iter);
acb_clear(t);
fmpq_clear(q);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}

91
acb/vec_nth_root.c
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/*
Copyright (C) 2016 Pascal Molin
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
/* assume xs has size >= len * step */
void
_acb_vec_set_powers_step(acb_ptr xs, slong n, slong len, slong step, slong prec)
{
slong i, j;
prec += n_clog(n, 2);
for (i = 0, j = 0; i < len; i++, j += step)
{
if (i == 0)
acb_one(xs + j);
else if (i == 1)
acb_nth_root(xs + j, n, prec);
else if (i % 2 == 0)
acb_mul(xs + j, xs + j / 2, xs + j / 2, prec);
else
acb_mul(xs + j, xs + j - step, xs + step, prec);
}
}
/* assume len = p^e and z has size >= len * step */
void
_acb_vec_nth_roots_pe(acb_ptr z, slong p, slong e, slong len, slong step, slong prec)
{
if (e <= 1)
{
_acb_vec_set_powers_step(z, p, len, step, prec);
}
else
{
slong q, r;
_acb_vec_nth_roots_pe(z, p, e - 1, len / p, step * p, prec);
_acb_vec_set_powers_step(z, n_pow(p, e), p, step, prec);
for (q = p; q < len; q += p)
for (r = 1; r < p; r++)
acb_mul(z + (q + r) * step, z + q * step, z + r * step, prec);
}
}
void
_acb_vec_nth_roots(acb_ptr z, slong len, slong prec)
{
slong i, q;
n_factor_t fac;
acb_one(z + 0);
n_factor_init(&fac);
n_factor(&fac, len, 0);
q = 1;
for (i = 0; i < fac.num; i++)
{
slong p, e, pe, mp, mq;
p = fac.p[i];
e = fac.exp[i];
pe = n_pow(p, e);
mp = len / pe;
mq = len / q;
_acb_vec_nth_roots_pe(z, p, e, pe, mp, prec);
if (i > 0)
{
slong k, l;
for (k = mp; k < len; k += mp)
{
for (l = mq; l < len - k; l += mq)
acb_mul(z + k + l, z + k, z + l, prec);
for (; l < len; l += mq)
acb_mul(z + k + l - len, z + k, z + l, prec);
}
}
q *= pe;
}
}

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acb/vec_nth_roots.c Normal file
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/*
Copyright (C) 2016 Pascal Molin
Copyright (C) 2016 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
void
_acb_vec_nth_roots(acb_ptr res, slong n, slong prec)
{
slong k, len, wp;
acb_t t;
if (n <= 0)
return;
if (n % 4 == 0)
len = n / 8 + 1;
else if (n % 2 == 0)
len = n / 4 + 1;
else
len = n / 2 + 1;
wp = prec + 6 + 2 * FLINT_BIT_COUNT(len);
acb_init(t);
acb_nth_root(t, n, wp);
_acb_vec_set_powers(res, t, len, wp);
acb_clear(t);
_acb_vec_set_round(res, res, len, prec);
if (n % 4 == 0)
{
for (k = n / 8 + 1; k <= n / 4; k++)
{
arb_set(acb_realref(res + k), acb_imagref(res + n / 4 - k));
arb_set(acb_imagref(res + k), acb_realref(res + n / 4 - k));
}
for (k = n / 4 + 1; k <= n / 2; k++)
acb_mul_onei(res + k, res + k - n / 4);
}
else if (n % 2 == 0)
{
for (k = n / 4 + 1; k <= n / 2; k++)
{
acb_set(res + k, res + n / 2 - k);
arb_neg(acb_realref(res + k), acb_realref(res + k));
}
}
for (k = n / 2 + 1; k < n; k++)
acb_conj(res + k, res + n - k);
}