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Diffstat (limited to 'src/cosh.c')
| -rw-r--r-- | src/cosh.c | 128 |
1 files changed, 128 insertions, 0 deletions
diff --git a/src/cosh.c b/src/cosh.c new file mode 100644 index 0000000..dbef5aa --- /dev/null +++ b/src/cosh.c @@ -0,0 +1,128 @@ +/* mpfr_cosh -- hyperbolic cosine + +Copyright 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. +Contributed by the AriC 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 cosh is done by * + * cosh= 1/2[e^(x)+e^(-x)] */ + +int +mpfr_cosh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) +{ + mpfr_t x; + int inexact; + MPFR_SAVE_EXPO_DECL (expo); + + MPFR_LOG_FUNC ( + ("x[%Pu]=%*.Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode), + ("y[%Pu]=%*.Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, + inexact)); + + if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(xt))) + { + if (MPFR_IS_NAN(xt)) + { + MPFR_SET_NAN(y); + MPFR_RET_NAN; + } + else if (MPFR_IS_INF(xt)) + { + MPFR_SET_INF(y); + MPFR_SET_POS(y); + MPFR_RET(0); + } + else + { + MPFR_ASSERTD(MPFR_IS_ZERO(xt)); + return mpfr_set_ui (y, 1, rnd_mode); /* cosh(0) = 1 */ + } + } + + MPFR_SAVE_EXPO_MARK (expo); + + /* cosh(x) = 1+x^2/2 + ... <= 1+x^2 for x <= 2.9828..., + thus the error < 2^(2*EXP(x)). If x >= 1, then EXP(x) >= 1, + thus the following will always fail. */ + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, -2 * MPFR_GET_EXP (xt), 0, + 1, rnd_mode, inexact = _inexact; goto end); + + MPFR_TMP_INIT_ABS(x, xt); + /* General case */ + { + /* Declaration of the intermediary variable */ + mpfr_t t, te; + /* Declaration of the size variable */ + mpfr_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */ + mpfr_prec_t Nt; /* Precision of the intermediary variable */ + long int err; /* Precision of error */ + MPFR_ZIV_DECL (loop); + MPFR_GROUP_DECL (group); + + /* compute the precision of intermediary variable */ + /* The optimal number of bits : see algorithms.tex */ + Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny); + + /* initialise of intermediary variables */ + MPFR_GROUP_INIT_2 (group, Nt, t, te); + + /* First computation of cosh */ + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + MPFR_BLOCK_DECL (flags); + + /* Compute cosh */ + MPFR_BLOCK (flags, mpfr_exp (te, x, MPFR_RNDD)); /* exp(x) */ + /* exp can overflow (but not underflow since x>0) */ + if (MPFR_OVERFLOW (flags)) + /* cosh(x) > exp(x), cosh(x) underflows too */ + { + inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW); + break; + } + mpfr_ui_div (t, 1, te, MPFR_RNDU); /* 1/exp(x) */ + mpfr_add (t, te, t, MPFR_RNDU); /* exp(x) + 1/exp(x)*/ + mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* 1/2(exp(x) + 1/exp(x))*/ + + /* Estimation of the error */ + err = Nt - 3; + /* Check if we can round */ + if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) + { + inexact = mpfr_set (y, t, rnd_mode); + break; + } + + /* Actualisation of the precision */ + MPFR_ZIV_NEXT (loop, Nt); + MPFR_GROUP_REPREC_2 (group, Nt, t, te); + } + MPFR_ZIV_FREE (loop); + MPFR_GROUP_CLEAR (group); + } + + end: + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd_mode); +} |