mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
88 lines
2.6 KiB
C
88 lines
2.6 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 "partitions.h"
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static void
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_fmpr_sinh(fmpr_t y, const fmpr_t x, long prec)
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{
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fmprb_t t;
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fmprb_init(t);
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fmprb_set_fmpr(t, x);
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fmprb_sinh(t, t, prec);
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fmpr_add(y, fmprb_midref(t), fmprb_radref(t), prec, FMPR_RND_UP);
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fmprb_clear(t);
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}
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/* Equation (1.8) in the paper */
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void
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partitions_rademacher_bound(fmpr_t b, ulong n, ulong N)
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{
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fmpr_t A, B, C, t, u;
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fmpr_init(A);
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fmpr_init(B);
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fmpr_init(C);
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fmpr_init(t);
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fmpr_init(u);
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/* bound for 44*pi^2/(225*sqrt(3)) */
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fmpr_set_si_2exp_si(A, 18695160, -24);
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/* bound for pi*sqrt(2)/75 */
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fmpr_set_si_2exp_si(B, 993857, -24);
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/* bound for pi*sqrt(2/3) */
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fmpr_set_si_2exp_si(C, 43035232, -24);
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/* first term: A / sqrt(N) */
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fmpr_sqrt_ui(t, N, FMPRB_RAD_PREC, FMPR_RND_DOWN);
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fmpr_div(b, A, t, FMPRB_RAD_PREC, FMPR_RND_UP);
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/* B * sqrt(N/(n-1)) */
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fmpr_set_ui(t, N);
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fmpr_div_ui(t, t, n - 1, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_sqrt(t, t, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_mul(t, B, t, FMPRB_RAD_PREC, FMPR_RND_UP);
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/* sinh(C*sqrt(n)/N) */
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fmpr_sqrt_ui(u, n, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_div_ui(u, u, N, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_mul(u, C, u, FMPRB_RAD_PREC, FMPR_RND_UP);
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_fmpr_sinh(u, u, FMPRB_RAD_PREC);
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/* second term: B * ... * sinh... */
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fmpr_mul(t, t, u, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_add(b, b, t, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_clear(A);
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fmpr_clear(B);
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fmpr_clear(C);
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fmpr_clear(t);
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fmpr_clear(u);
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}
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