161 lines
4.4 KiB
C
161 lines
4.4 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT 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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FLINT 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 FLINT; 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 <stdio.h>
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#include <stdlib.h>
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#include <float.h>
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#include <mpfr.h>
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#include "ulong_extras.h"
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#include "double_extras.h"
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#define ONE_OVER_E ldexp(6627126856707895.0, -54)
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int
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main()
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{
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double x, w, tol;
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slong iter, prec = 70;
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mpfr_t xx, ww, wnew, t, u, v, p, q, max_err;
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FLINT_TEST_INIT(state);
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flint_printf("lambertw....");
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fflush(stdout);
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mpfr_init2(xx, prec);
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mpfr_init2(ww, prec);
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mpfr_init2(wnew, prec);
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mpfr_init2(t, prec);
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mpfr_init2(u, prec);
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mpfr_init2(v, prec);
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mpfr_init2(p, prec);
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mpfr_init2(q, prec);
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mpfr_init2(max_err, prec);
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mpfr_set_ui(max_err, 0, MPFR_RNDN);
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for (iter = 0; iter < 10000 * flint_test_multiplier(); iter++)
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{
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x = d_randtest(state);
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switch (n_randint(state, 3))
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{
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/* singularity near -1/e */
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case 0:
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x = ldexp(x, -n_randint(state, -DBL_MIN_EXP+1));
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x = -ONE_OVER_E + x;
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tol = 50 * DBL_EPSILON;
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break;
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/* negative, not close to -1/e */
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case 1:
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x = d_randtest(state);
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x = ldexp(x, -n_randint(state, -DBL_MIN_EXP+1));
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x = x * -(1./4);
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tol = 2 * DBL_EPSILON;
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break;
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/* positive */
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default:
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x = d_randtest(state);
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x = ldexp(x, (int) n_randint(state, DBL_MAX_EXP-DBL_MIN_EXP-1)
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+ DBL_MIN_EXP);
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tol = 2 * DBL_EPSILON;
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break;
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}
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w = d_lambertw(x);
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mpfr_set_d(xx, x, MPFR_RNDN);
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mpfr_set_d(ww, w, MPFR_RNDN);
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/* t = exp(w) */
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mpfr_exp(t, ww, MPFR_RNDN);
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/* u = 2*w + 2 */
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mpfr_mul_ui(u, ww, 2, MPFR_RNDN);
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mpfr_add_ui(u, u, 2, MPFR_RNDN);
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/* v = w*t - x */
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mpfr_mul(v, t, ww, MPFR_RNDN);
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mpfr_sub(v, v, xx, MPFR_RNDN);
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/* p = u * v */
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mpfr_mul(p, u, v, MPFR_RNDN);
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/* q = (u*t*(w+1) - (w+2)*v) */
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mpfr_mul(q, u, t, MPFR_RNDN);
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mpfr_add_ui(t, ww, 1, MPFR_RNDN);
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mpfr_mul(q, q, t, MPFR_RNDN);
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mpfr_add_ui(t, ww, 2, MPFR_RNDN);
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mpfr_mul(t, t, v, MPFR_RNDN);
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mpfr_sub(q, q, t, MPFR_RNDN);
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/* wnew = w - p / q */
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mpfr_div(p, p, q, MPFR_RNDN);
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mpfr_sub(wnew, ww, p, MPFR_RNDN);
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/* relative error */
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mpfr_sub(t, ww, wnew, MPFR_RNDA);
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mpfr_div(t, t, wnew, MPFR_RNDA);
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mpfr_abs(t, t, MPFR_RNDA);
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if (mpfr_get_d(t, MPFR_RNDA) > tol)
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{
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flint_printf("FAIL\n");
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flint_printf("x = %.17g, w = %.17g, error = %g\n", x, w,
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mpfr_get_d(t, MPFR_RNDA));
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abort();
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}
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#if 0
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if (mpfr_cmp(t, max_err) > 0)
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{
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flint_printf("new record: ");
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flint_printf("x=%.20g w=%.20g wnew=%.20g relative error: %g\n",
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x, w, mpfr_get_d(wnew, MPFR_RNDN), mpfr_get_d(t, MPFR_RNDN));
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mpfr_set(max_err, t, MPFR_RNDN);
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}
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#endif
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}
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mpfr_clear(xx);
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mpfr_clear(ww);
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mpfr_clear(wnew);
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mpfr_clear(t);
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mpfr_clear(u);
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mpfr_clear(v);
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mpfr_clear(p);
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mpfr_clear(q);
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mpfr_clear(max_err);
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mpfr_free_cache();
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FLINT_TEST_CLEANUP(state);
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flint_printf("PASS\n");
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return EXIT_SUCCESS;
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}
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