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authorvlefevre <vlefevre@280ebfd0-de03-0410-8827-d642c229c3f4>2010-08-17 09:10:13 +0000
committervlefevre <vlefevre@280ebfd0-de03-0410-8827-d642c229c3f4>2010-08-17 09:10:13 +0000
commitc9583bdfe064e1069828e518533f7bc29a8fdddb (patch)
tree2400842d4095628b8486fbeabaf7bc7b8af4ed02 /src/atanh.c
parent50ac5b5985174201c7fa6e20496cd2b096107001 (diff)
downloadmpfr-c9583bdfe064e1069828e518533f7bc29a8fdddb.tar.gz
Source reorganization. In short:
* Added directories and moved related files into them: - src for the MPFR source files (to build the library). - doc for documentation files (except INSTALL, README...). - tools for various tools (scripts) and mbench. - tune for tuneup-related source files. - other for other source files (not distributed in tarballs). Existing directories: - tests for the source files of the test suite (make check). - examples for examples. - m4 for m4 files. * Renamed configure.in to configure.ac. * Added/updated Makefile.am files where needed. * Updated acinclude.m4 and configure.ac (AC_CONFIG_FILES line). * Updated the documentation (INSTALL, README, doc/README.dev and doc/mpfr.texi). * Updated NEWS and TODO. * Updated the scripts now in tools. The following script was used: #!/usr/bin/env zsh svn mkdir doc other src tools tune svn mv ${${(M)$(sed -n '/libmpfr_la_SOURCES/,/[^\]$/p' \ Makefile.am):#*.[ch]}:#get_patches.c} mparam_h.in \ round_raw_generic.c jyn_asympt.c src svn mv mbench check_inits_clears coverage get_patches.sh mpfrlint \ nightly-test update-patchv update-version tools svn mv bidimensional_sample.c speed.c tuneup.c tune svn mv *.{c,h} other svn mv FAQ.html README.dev algorithm* faq.xsl fdl.texi mpfr.texi \ update-faq doc svn mv configure.in configure.ac svn cp Makefile.am src/Makefile.am svn rm replace_all [Modifying some files, see above] svn add doc/Makefile.am svn add tune/Makefile.am git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@7087 280ebfd0-de03-0410-8827-d642c229c3f4
Diffstat (limited to 'src/atanh.c')
-rw-r--r--src/atanh.c127
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diff --git a/src/atanh.c b/src/atanh.c
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+/* mpfr_atanh -- Inverse Hyperbolic Tangente
+
+Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
+Contributed by the Arenaire and Caramel projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU MPFR Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+The GNU MPFR Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
+http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
+51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
+
+#define MPFR_NEED_LONGLONG_H
+#include "mpfr-impl.h"
+
+ /* The computation of atanh is done by
+ atanh= 1/2*ln(x+1)-1/2*ln(1-x) */
+
+int
+mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
+{
+ int inexact;
+ mpfr_t x, t, te;
+ mpfr_prec_t Nx, Ny, Nt;
+ mpfr_exp_t err;
+ MPFR_ZIV_DECL (loop);
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode),
+ ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+ /* Special cases */
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
+ {
+ /* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result
+ between -1 and 1 */
+ if (MPFR_IS_NAN (xt) || MPFR_IS_INF (xt))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ else /* necessarily xt is 0 */
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO (xt));
+ MPFR_SET_ZERO (y); /* atanh(0) = 0 */
+ MPFR_SET_SAME_SIGN (y,xt);
+ MPFR_RET (0);
+ }
+ }
+
+ /* atanh (x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */
+ if (MPFR_UNLIKELY (MPFR_EXP (xt) > 0))
+ {
+ if (MPFR_EXP (xt) == 1 && mpfr_powerof2_raw (xt))
+ {
+ MPFR_SET_INF (y);
+ MPFR_SET_SAME_SIGN (y, xt);
+ MPFR_RET (0);
+ }
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+
+ /* atanh(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
+ MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 1,
+ rnd_mode, {});
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ /* Compute initial precision */
+ Nx = MPFR_PREC (xt);
+ MPFR_TMP_INIT_ABS (x, xt);
+ Ny = MPFR_PREC (y);
+ Nt = MAX (Nx, Ny);
+ /* the optimal number of bits : see algorithms.ps */
+ Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
+
+ /* initialise of intermediary variable */
+ mpfr_init2 (t, Nt);
+ mpfr_init2 (te, Nt);
+
+ /* First computation of cosh */
+ MPFR_ZIV_INIT (loop, Nt);
+ for (;;)
+ {
+ /* compute atanh */
+ mpfr_ui_sub (te, 1, x, MPFR_RNDU); /* (1-xt)*/
+ mpfr_add_ui (t, x, 1, MPFR_RNDD); /* (xt+1)*/
+ mpfr_div (t, t, te, MPFR_RNDN); /* (1+xt)/(1-xt)*/
+ mpfr_log (t, t, MPFR_RNDN); /* ln((1+xt)/(1-xt))*/
+ mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* (1/2)*ln((1+xt)/(1-xt))*/
+
+ /* error estimate: see algorithms.tex */
+ /* FIXME: this does not correspond to the value in algorithms.tex!!! */
+ /* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
+ err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
+
+ if (MPFR_LIKELY (MPFR_IS_ZERO (t)
+ || MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
+ break;
+
+ /* reactualisation of the precision */
+ MPFR_ZIV_NEXT (loop, Nt);
+ mpfr_set_prec (t, Nt);
+ mpfr_set_prec (te, Nt);
+ }
+ MPFR_ZIV_FREE (loop);
+
+ inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
+
+ mpfr_clear(t);
+ mpfr_clear(te);
+
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (y, inexact, rnd_mode);
+}
+