mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
126 lines
2.6 KiB
C
126 lines
2.6 KiB
C
/*
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Copyright (C) 2017 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 "mag.h"
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#include "arb.h" /* for atan table */
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static double
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mag_atan_d(double x)
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{
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double t, u, v;
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int p, q, flip;
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t = x;
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flip = 0;
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if (t > 1.0)
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{
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t = 1.0 / t;
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flip = 1;
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}
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q = ldexp(1.0, ARB_ATAN_TAB1_BITS);
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p = t * (1 << ARB_ATAN_TAB1_BITS);
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if (p == (1 << ARB_ATAN_TAB1_BITS))
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p--;
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#if FLINT_BITS == 64
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v = arb_atan_tab1[p][ARB_ATAN_TAB1_LIMBS - 1] * ldexp(1.0, -FLINT_BITS);
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#else
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v = arb_atan_tab1[p][ARB_ATAN_TAB1_LIMBS - 1] * ldexp(1.0, -FLINT_BITS)
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+ arb_atan_tab1[p][ARB_ATAN_TAB1_LIMBS - 2] * ldexp(1.0, -2 * FLINT_BITS);
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#endif
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t = (q * t - p) / (p * t + q);
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/* t - t^3/3 + t^5/5 */
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u = t * t;
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t = (t * (1.0 / 15.0)) * (15.0 - 5.0 * u + 3.0 * (u * u));
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v += t;
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if (flip)
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v = 1.5707963267948966192 - v;
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return v;
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}
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void
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mag_atan(mag_t res, const mag_t x)
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{
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if (mag_is_zero(x))
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{
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mag_zero(res);
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}
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else if (mag_cmp_2exp_si(x, MAG_BITS) > 0)
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{
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mag_const_pi(res);
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mag_mul_2exp_si(res, res, -1);
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}
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else if (mag_cmp_2exp_si(x, -(MAG_BITS / 2)) < 0)
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{
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mag_set(res, x);
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}
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else
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{
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double t;
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t = ldexp(MAG_MAN(x), MAG_EXP(x) - MAG_BITS);
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t = mag_atan_d(t);
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t = t * (1.0 + 1e-12);
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mag_set_d(res, t);
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}
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}
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void
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mag_atan_lower(mag_t res, const mag_t x)
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{
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if (mag_is_zero(x))
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{
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mag_zero(res);
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}
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else if (mag_is_inf(x))
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{
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mag_const_pi_lower(res);
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mag_mul_2exp_si(res, res, -1);
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}
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else if (mag_cmp_2exp_si(x, MAG_BITS) > 0)
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{
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/* atan(x) > pi/2 - 1/x */
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mag_t t;
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mag_init(t);
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mag_one(t);
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mag_div(t, t, x);
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mag_const_pi_lower(res);
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mag_mul_2exp_si(res, res, -1);
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mag_sub_lower(res, res, t);
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mag_clear(t);
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}
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else if (mag_cmp_2exp_si(x, -MAG_BITS) < 0)
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{
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/* atan(x) > x - x^2 */
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mag_t t;
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mag_init(t);
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mag_mul(t, x, x);
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mag_sub_lower(res, x, t);
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mag_clear(t);
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}
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else
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{
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double t;
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t = ldexp(MAG_MAN(x), MAG_EXP(x) - MAG_BITS);
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t = mag_atan_d(t);
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t = t * (1.0 - 1e-12);
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mag_set_d_lower(res, t);
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}
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}
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