diff options
author | vlefevre <vlefevre@280ebfd0-de03-0410-8827-d642c229c3f4> | 2010-08-17 09:10:13 +0000 |
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committer | vlefevre <vlefevre@280ebfd0-de03-0410-8827-d642c229c3f4> | 2010-08-17 09:10:13 +0000 |
commit | c9583bdfe064e1069828e518533f7bc29a8fdddb (patch) | |
tree | 2400842d4095628b8486fbeabaf7bc7b8af4ed02 /src/exp2.c | |
parent | 50ac5b5985174201c7fa6e20496cd2b096107001 (diff) | |
download | mpfr-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')
-rw-r--r-- | src/exp2.c | 146 |
1 files changed, 146 insertions, 0 deletions
diff --git a/src/exp2.c b/src/exp2.c new file mode 100644 index 000000000..bf0902c86 --- /dev/null +++ b/src/exp2.c @@ -0,0 +1,146 @@ +/* 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); +} |