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b58ddff026
* merged mpfr 3.0.0 and gmp 5.0.1 in buildtools trunk git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@37378 a95241bf-73f2-0310-859d-f6bbb57e9c96
118 lines
3.6 KiB
C
118 lines
3.6 KiB
C
/* mpfr_asinh -- inverse hyperbolic sine
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Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 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 GNU MPFR Library.
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The GNU 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 3 of the License, or (at your
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option) any later version.
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The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, 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 asinh is done by *
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* asinh = ln(x + sqrt(x^2 + 1)) */
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int
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mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
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{
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int inexact;
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int signx, neg;
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mpfr_prec_t Ny, Nt;
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mpfr_t t; /* auxiliary variables */
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mpfr_exp_t err;
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_ZIV_DECL (loop);
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MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
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("y[%#R]=%R inexact=%d", y, y, inexact));
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if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
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{
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if (MPFR_IS_NAN (x))
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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 (x))
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{
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MPFR_SET_INF (y);
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MPFR_SET_SAME_SIGN (y, x);
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MPFR_RET (0);
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}
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else /* x is necessarily 0 */
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{
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MPFR_ASSERTD (MPFR_IS_ZERO (x));
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MPFR_SET_ZERO (y); /* asinh(0) = 0 */
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MPFR_SET_SAME_SIGN (y, x);
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MPFR_RET (0);
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}
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}
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/* asinh(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
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MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0,
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rnd_mode, {});
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Ny = MPFR_PREC (y); /* Precision of output variable */
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signx = MPFR_SIGN (x);
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neg = MPFR_IS_NEG (x);
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/* General case */
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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 + 4 + MPFR_INT_CEIL_LOG2 (Ny);
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MPFR_SAVE_EXPO_MARK (expo);
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/* initialize intermediary variables */
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mpfr_init2 (t, Nt);
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/* First computation of asinh */
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MPFR_ZIV_INIT (loop, Nt);
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for (;;)
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{
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/* compute asinh */
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mpfr_mul (t, x, x, MPFR_RNDD); /* x^2 */
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mpfr_add_ui (t, t, 1, MPFR_RNDD); /* x^2+1 */
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mpfr_sqrt (t, t, MPFR_RNDN); /* sqrt(x^2+1) */
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(neg ? mpfr_sub : mpfr_add) (t, t, x, MPFR_RNDN); /* sqrt(x^2+1)+x */
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mpfr_log (t, t, MPFR_RNDN); /* ln(sqrt(x^2+1)+x)*/
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if (MPFR_LIKELY (MPFR_IS_PURE_FP (t)))
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{
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/* error estimate -- see algorithms.tex */
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err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
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if (MPFR_LIKELY (MPFR_IS_ZERO (t)
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|| MPFR_CAN_ROUND (t, err, Ny, 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_set_prec (t, Nt);
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}
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MPFR_ZIV_FREE (loop);
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inexact = mpfr_set4 (y, t, rnd_mode, signx);
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mpfr_clear (t);
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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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