mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
94 lines
3 KiB
C
94 lines
3 KiB
C
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/*=============================================================================
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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) 2013 Fredrik Johansson
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******************************************************************************/
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#include "gamma.h"
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void
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gamma_stirling_bound_phase(fmpr_t bound, const fmpcb_t z, long prec)
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{
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fmpr_t x, y, t, u;
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int xsign;
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fmpr_init(x);
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fmpr_init(y);
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fmpr_init(t);
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fmpr_init(u);
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/* first compute x, y such that |arg(z)| <= arg(x+yi) */
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/* argument increases with smaller real parts */
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fmpr_sub(x, fmprb_midref(fmpcb_realref(z)),
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fmprb_radref(fmpcb_realref(z)), prec, FMPR_RND_FLOOR);
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xsign = fmpr_sgn(x);
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if (xsign >= 0) /* argument increases away from the real axis */
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fmprb_get_abs_ubound_fmpr(y, fmpcb_imagref(z), prec);
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else /* argument increases closer to the real axis */
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fmprb_get_abs_lbound_fmpr(y, fmpcb_imagref(z), prec);
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if (fmpr_is_zero(y))
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{
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if (xsign > 0)
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fmpr_one(bound);
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else
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fmpr_pos_inf(bound);
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}
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else
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{
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if (xsign >= 0)
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{
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/* compute upper bound for t = y / (sqrt(x^2 + y^2) + x) */
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fmpr_mul(t, x, x, prec, FMPR_RND_DOWN);
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fmpr_mul(u, y, y, prec, FMPR_RND_DOWN);
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fmpr_add(t, t, u, prec, FMPR_RND_DOWN);
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fmpr_sqrt(t, t, prec, FMPR_RND_DOWN);
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fmpr_add(t, t, x, prec, FMPR_RND_DOWN);
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fmpr_div(t, y, t, prec, FMPR_RND_UP);
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}
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else
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{
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/* compute upper bound for t = (sqrt(x^2 + y^2) - x) / y */
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fmpr_mul(t, x, x, prec, FMPR_RND_UP);
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fmpr_mul(u, y, y, prec, FMPR_RND_UP);
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fmpr_add(t, t, u, prec, FMPR_RND_UP);
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fmpr_sqrt(t, t, prec, FMPR_RND_UP);
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fmpr_sub(t, t, x, prec, FMPR_RND_UP);
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fmpr_div(t, t, y, prec, FMPR_RND_UP);
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}
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/* compute upper bound for sqrt(1 + t^2) */
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fmpr_mul(t, t, t, prec, FMPR_RND_UP);
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fmpr_add_ui(t, t, 1, prec, FMPR_RND_UP);
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fmpr_sqrt(bound, t, prec, FMPR_RND_UP);
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}
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fmpr_clear(x);
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fmpr_clear(y);
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fmpr_clear(t);
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fmpr_clear(u);
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}
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