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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/exp2.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/exp2.c')
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diff --git a/src/exp2.c b/src/exp2.c
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+/* mpfr_exp2 -- power of 2 function 2^y
+
+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 y = 2^z is done by *
+ * y = exp(z*log(2)). The result is exact iff z is an integer. */
+
+int
+mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
+{
+ int inexact;
+ long xint;
+ mpfr_t xfrac;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ {
+ if (MPFR_IS_NAN (x))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ else if (MPFR_IS_INF (x))
+ {
+ if (MPFR_IS_POS (x))
+ MPFR_SET_INF (y);
+ else
+ MPFR_SET_ZERO (y);
+ MPFR_SET_POS (y);
+ MPFR_RET (0);
+ }
+ else /* 2^0 = 1 */
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO(x));
+ return mpfr_set_ui (y, 1, rnd_mode);
+ }
+ }
+
+ /* since the smallest representable non-zero float is 1/2*2^__gmpfr_emin,
+ if x < __gmpfr_emin - 1, the result is either 1/2*2^__gmpfr_emin or 0 */
+ MPFR_ASSERTN (MPFR_EMIN_MIN >= LONG_MIN + 2);
+ if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emin - 1) < 0))
+ {
+ mpfr_rnd_t rnd2 = rnd_mode;
+ /* in round to nearest mode, round to zero when x <= __gmpfr_emin-2 */
+ if (rnd_mode == MPFR_RNDN &&
+ mpfr_cmp_si_2exp (x, __gmpfr_emin - 2, 0) <= 0)
+ rnd2 = MPFR_RNDZ;
+ return mpfr_underflow (y, rnd2, 1);
+ }
+
+ MPFR_ASSERTN (MPFR_EMAX_MAX <= LONG_MAX);
+ if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax) >= 0))
+ return mpfr_overflow (y, rnd_mode, 1);
+
+ /* We now know that emin - 1 <= x < emax. */
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ /* 2^x = 1 + x*log(2) + O(x^2) for x near zero, and for |x| <= 1 we have
+ |2^x - 1| <= x < 2^EXP(x). If x > 0 we must round away from 0 (dir=1);
+ if x < 0 we must round toward 0 (dir=0). */
+ MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, __gmpfr_one, - MPFR_GET_EXP (x), 0,
+ MPFR_SIGN(x) > 0, rnd_mode, expo, {});
+
+ xint = mpfr_get_si (x, MPFR_RNDZ);
+ mpfr_init2 (xfrac, MPFR_PREC (x));
+ mpfr_sub_si (xfrac, x, xint, MPFR_RNDN); /* exact */
+
+ if (MPFR_IS_ZERO (xfrac))
+ {
+ mpfr_set_ui (y, 1, MPFR_RNDN);
+ inexact = 0;
+ }
+ else
+ {
+ /* Declaration of the intermediary variable */
+ mpfr_t t;
+
+ /* Declaration of the size variable */
+ mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */
+ mpfr_prec_t Nt; /* working precision */
+ mpfr_exp_t err; /* error */
+ MPFR_ZIV_DECL (loop);
+
+ /* compute the precision of intermediary variable */
+ /* the optimal number of bits : see algorithms.tex */
+ Nt = Ny + 5 + MPFR_INT_CEIL_LOG2 (Ny);
+
+ /* initialise of intermediary variable */
+ mpfr_init2 (t, Nt);
+
+ /* First computation */
+ MPFR_ZIV_INIT (loop, Nt);
+ for (;;)
+ {
+ /* compute exp(x*ln(2))*/
+ mpfr_const_log2 (t, MPFR_RNDU); /* ln(2) */
+ mpfr_mul (t, xfrac, t, MPFR_RNDU); /* xfrac * ln(2) */
+ err = Nt - (MPFR_GET_EXP (t) + 2); /* Estimate of the error */
+ mpfr_exp (t, t, MPFR_RNDN); /* exp(xfrac * ln(2)) */
+
+ if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
+ break;
+
+ /* Actualisation of the precision */
+ MPFR_ZIV_NEXT (loop, Nt);
+ mpfr_set_prec (t, Nt);
+ }
+ MPFR_ZIV_FREE (loop);
+
+ inexact = mpfr_set (y, t, rnd_mode);
+
+ mpfr_clear (t);
+ }
+
+ mpfr_clear (xfrac);
+ mpfr_clear_flags ();
+ mpfr_mul_2si (y, y, xint, MPFR_RNDN); /* exact or overflow */
+ /* Note: We can have an overflow only when t was rounded up to 2. */
+ MPFR_ASSERTD (MPFR_IS_PURE_FP (y) || inexact > 0);
+ MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (y, inexact, rnd_mode);
+}