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git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@29042 a95241bf-73f2-0310-859d-f6bbb57e9c96
126 lines
4.0 KiB
C
126 lines
4.0 KiB
C
/* mpfr_cosh -- hyperbolic cosine
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Copyright 2001, 2002, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the MPFR Library.
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The MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the MPFR Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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/* The computation of cosh is done by *
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* cosh= 1/2[e^(x)+e^(-x)] */
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int
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mpfr_cosh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
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{
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mpfr_t x;
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int inexact;
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode),
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("y[%#R]=%R inexact=%d", y, y, inexact));
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if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(xt)))
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{
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if (MPFR_IS_NAN(xt))
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{
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MPFR_SET_NAN(y);
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MPFR_RET_NAN;
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}
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else if (MPFR_IS_INF(xt))
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{
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MPFR_SET_INF(y);
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MPFR_SET_POS(y);
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MPFR_RET(0);
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}
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else
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{
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MPFR_ASSERTD(MPFR_IS_ZERO(xt));
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return mpfr_set_ui (y, 1, rnd_mode); /* cosh(0) = 1 */
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}
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}
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MPFR_SAVE_EXPO_MARK (expo);
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/* cosh(x) = 1+x^2/2 + ... <= 1+x^2 for x <= 2.9828...,
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thus the error < 2^(2*EXP(x)). If x >= 1, then EXP(x) >= 1,
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thus the following will always fail. */
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MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, -2 * MPFR_GET_EXP (xt), 0,
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1, rnd_mode, inexact = _inexact; goto end);
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MPFR_TMP_INIT_ABS(x, xt);
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/* General case */
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{
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/* Declaration of the intermediary variable */
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mpfr_t t, te;
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/* Declaration of the size variable */
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mp_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */
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mp_prec_t Nt; /* Precision of the intermediary variable */
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long int err; /* Precision of error */
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MPFR_ZIV_DECL (loop);
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MPFR_GROUP_DECL (group);
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/* compute the precision of intermediary variable */
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/* The optimal number of bits : see algorithms.tex */
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Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
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/* initialise of intermediary variables */
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MPFR_GROUP_INIT_2 (group, Nt, t, te);
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/* First computation of cosh */
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MPFR_ZIV_INIT (loop, Nt);
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for (;;)
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{
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/* Compute cosh */
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mpfr_clear_flags ();
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mpfr_exp (te, x, GMP_RNDD); /* exp(x) */
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/* exp can overflow (but not underflow since x>0) */
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/* BUG/TODO/FIXME: exp can overflow but cosh may be representable! */
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if (MPFR_UNLIKELY (mpfr_overflow_p ()))
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{
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inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
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MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
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break;
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}
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mpfr_ui_div (t, 1, te, GMP_RNDU); /* 1/exp(x) */
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mpfr_add (t, te, t, GMP_RNDU); /* exp(x) + 1/exp(x)*/
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mpfr_div_2ui (t, t, 1, GMP_RNDN); /* 1/2(exp(x) + 1/exp(x))*/
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/* Estimation of the error */
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err = Nt - 3;
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/* Check if we can round */
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if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
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{
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inexact = mpfr_set (y, t, rnd_mode);
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break;
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}
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/* Actualisation of the precision */
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MPFR_ZIV_NEXT (loop, Nt);
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MPFR_GROUP_REPREC_2 (group, Nt, t, te);
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}
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MPFR_ZIV_FREE (loop);
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MPFR_GROUP_CLEAR (group);
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}
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end:
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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_check_range (y, inexact, rnd_mode);
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}
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