mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
125 lines
3.7 KiB
C
125 lines
3.7 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Fredrik Johansson
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******************************************************************************/
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#include "fmpcb.h"
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void
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fmpcb_invroot_newton(fmpcb_t r, const fmpcb_t a, ulong m,
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const fmpcb_t r0, long startprec, long prec)
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{
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long iters, precs[FLINT_BITS];
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long i, extra, wp, rad_prec;
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fmpr_t en, enew, zlo, zhi, v;
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fmpcb_t t, z, z_exact;
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/* stay clear of overflow */
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if (m + 2 < m) abort();
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fmpr_init(en);
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fmpr_init(enew);
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fmpr_init(zlo);
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fmpr_init(zhi);
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fmpr_init(v);
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fmpcb_init(t);
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fmpcb_init(z);
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fmpcb_init(z_exact);
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fmpcb_set(z, r0);
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rad_prec = FMPRB_RAD_PREC;
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extra = 10 + FLINT_BIT_COUNT(m);
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precs[0] = prec + extra;
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iters = 1;
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while ((iters < FLINT_BITS) && (precs[iters-1] + extra > 2*startprec))
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{
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precs[iters] = (precs[iters-1] / 2) + extra;
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iters++;
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}
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for (i = iters - 1; i >= 0; i--)
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{
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wp = precs[i];
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/* printf("lifting to precision %ld\n", wp); */
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/* bounds for old error */
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fmpcb_get_rad_ubound_fmpr(en, z, rad_prec);
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fmpcb_get_abs_lbound_fmpr(zlo, z, rad_prec);
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fmpcb_get_abs_ubound_fmpr(zhi, z, rad_prec);
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/* to improve, we require |z| > 0, i.e. en < |z| */
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if (fmpr_cmp(en, zlo) >= 0)
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break;
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/* z[n+1] = z[n] * (m + 1 - a * z[n]^m) / m */
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fmpcb_set(z_exact, z);
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fmpr_zero(fmprb_radref(fmpcb_realref(z_exact)));
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fmpr_zero(fmprb_radref(fmpcb_imagref(z_exact)));
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fmpcb_pow_ui(t, z_exact, m, wp);
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fmpcb_mul(t, t, a, wp);
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fmpcb_neg(t, t);
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fmpcb_add_ui(t, t, m + 1, wp);
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fmpcb_mul(t, t, z_exact, wp);
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fmpcb_div_ui(t, t, m, wp);
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/* new error bound = en^2 * (m+1) / (|zn| / (|zn| - en))^(m+2) / |zn| */
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fmpr_mul(enew, en, en, rad_prec, FMPR_RND_UP);
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fmpr_mul_ui(enew, enew, m + 1, rad_prec, FMPR_RND_UP);
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fmpr_mul(enew, enew, zhi, rad_prec, FMPR_RND_UP);
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fmpr_sub(v, zlo, en, rad_prec, FMPR_RND_DOWN);
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fmpr_div(v, zhi, v, rad_prec, FMPR_RND_UP);
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fmpr_pow_sloppy_ui(v, v, m + 2, rad_prec, FMPR_RND_UP);
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fmpr_div(v, v, zlo, rad_prec, FMPR_RND_UP);
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fmpr_mul(enew, enew, v, rad_prec, FMPR_RND_UP);
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/* quit if there was no improvement */
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if (fmpr_cmp(enew, en) >= 0)
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break;
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fmpcb_set(z, t);
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/* add upper bound for new radius */
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fmprb_add_error_fmpr(fmpcb_realref(z), enew);
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fmprb_add_error_fmpr(fmpcb_imagref(z), enew);
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}
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fmpcb_set(r, z);
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fmpcb_clear(t);
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fmpcb_clear(z);
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fmpcb_clear(z_exact);
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fmpr_clear(en);
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fmpr_clear(enew);
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fmpr_clear(zlo);
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fmpr_clear(zhi);
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fmpr_clear(v);
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}
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