mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
148 lines
3.4 KiB
C
148 lines
3.4 KiB
C
/*
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Copyright (C) 2012 Fredrik Johansson
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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_poly.h"
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/* we don't need any error bounding, so we define a few helper
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functions that ignore the radii */
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static __inline__ void
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acb_sub_mid(acb_t z, const acb_t x, const acb_t y, slong prec)
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{
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arf_sub(arb_midref(acb_realref(z)),
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arb_midref(acb_realref(x)),
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arb_midref(acb_realref(y)), prec, ARF_RND_DOWN);
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arf_sub(arb_midref(acb_imagref(z)),
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arb_midref(acb_imagref(x)),
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arb_midref(acb_imagref(y)), prec, ARF_RND_DOWN);
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}
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static __inline__ void
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acb_add_mid(acb_t z, const acb_t x, const acb_t y, slong prec)
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{
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arf_add(arb_midref(acb_realref(z)),
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arb_midref(acb_realref(x)),
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arb_midref(acb_realref(y)), prec, ARF_RND_DOWN);
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arf_add(arb_midref(acb_imagref(z)),
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arb_midref(acb_imagref(x)),
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arb_midref(acb_imagref(y)), prec, ARF_RND_DOWN);
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}
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static __inline__ void
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acb_mul_mid(acb_t z, const acb_t x, const acb_t y, slong prec)
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{
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#define a arb_midref(acb_realref(x))
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#define b arb_midref(acb_imagref(x))
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#define c arb_midref(acb_realref(y))
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#define d arb_midref(acb_imagref(y))
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#define e arb_midref(acb_realref(z))
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#define f arb_midref(acb_imagref(z))
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arf_complex_mul(e, f, a, b, c, d, prec, ARF_RND_DOWN);
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#undef a
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#undef b
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#undef c
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#undef d
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#undef e
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#undef f
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}
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static __inline__ void
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acb_inv_mid(acb_t z, const acb_t x, slong prec)
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{
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arf_t t;
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arf_init(t);
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#define a arb_midref(acb_realref(x))
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#define b arb_midref(acb_imagref(x))
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#define e arb_midref(acb_realref(z))
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#define f arb_midref(acb_imagref(z))
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arf_mul(t, a, a, prec, ARF_RND_DOWN);
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arf_addmul(t, b, b, prec, ARF_RND_DOWN);
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arf_div(e, a, t, prec, ARF_RND_DOWN);
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arf_div(f, b, t, prec, ARF_RND_DOWN);
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arf_neg(f, f);
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#undef a
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#undef b
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#undef e
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#undef f
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arf_clear(t);
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}
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void
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_acb_poly_evaluate_mid(acb_t res, acb_srcptr f, slong len,
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const acb_t a, slong prec)
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{
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slong i = len - 1;
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acb_t t;
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acb_init(t);
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acb_set(res, f + i);
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for (i = len - 2; i >= 0; i--)
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{
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acb_mul_mid(t, res, a, prec);
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acb_add_mid(res, f + i, t, prec);
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}
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acb_clear(t);
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}
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void
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_acb_poly_refine_roots_durand_kerner(acb_ptr roots,
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acb_srcptr poly, slong len, slong prec)
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{
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slong i, j;
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acb_t x, y, t;
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acb_init(x);
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acb_init(y);
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acb_init(t);
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for (i = 0; i < len - 1; i++)
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{
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_acb_poly_evaluate_mid(x, poly, len, roots + i, prec);
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acb_set(y, poly + len - 1);
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for (j = 0; j < len - 1; j++)
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{
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if (i != j)
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{
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acb_sub_mid(t, roots + i, roots + j, prec);
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acb_mul_mid(y, y, t, prec);
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}
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}
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mag_zero(arb_radref(acb_realref(y)));
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mag_zero(arb_radref(acb_imagref(y)));
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acb_inv_mid(t, y, prec);
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acb_mul_mid(t, t, x, prec);
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acb_sub_mid(roots + i, roots + i, t, prec);
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arf_get_mag(arb_radref(acb_realref(roots + i)), arb_midref(acb_realref(t)));
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arf_get_mag(arb_radref(acb_imagref(roots + i)), arb_midref(acb_imagref(t)));
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}
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acb_clear(x);
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acb_clear(y);
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acb_clear(t);
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}
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