/* mpfr_asinh -- inverse hyperbolic sine Copyright 2001, 2002, 2003 Free Software Foundation. This file is part of the MPFR Library. The 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 2.1 of the License, or (at your option) any later version. The 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 MPFR Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include "gmp.h" #include "gmp-impl.h" #include "mpfr.h" #include "mpfr-impl.h" /* The computation of asinh is done by asinh = ln(x + sqrt(x^2 + 1)) */ int mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) { int inexact; int neg = 0; mp_prec_t Nx, Ny, Nt; mpfr_t t, te, ti; /* auxiliary variables */ long int err; 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)) { MPFR_SET_INF(y); MPFR_SET_SAME_SIGN(y, x); MPFR_RET(0); } else if (MPFR_IS_ZERO(x)) { MPFR_SET_ZERO(y); /* asinh(0) = 0 */ MPFR_SET_SAME_SIGN(y, x); MPFR_RET(0); } else MPFR_ASSERTN(0); } MPFR_CLEAR_FLAGS(y); Nx = MPFR_PREC(x); /* Precision of input variable */ Ny = MPFR_PREC(y); /* Precision of output variable */ neg = MPFR_IS_NEG(x); /* General case */ /* compute the precision of intermediary variable */ Nt = MAX(Nx, Ny); /* the optimal number of bits : see algorithms.ps */ Nt = Nt + 4 + __gmpfr_ceil_log2 (Nt); /* initialize intermediary variables */ mpfr_init2 (t, 2); mpfr_init2 (te, 2); mpfr_init2 (ti, 2); mpfr_save_emin_emax (); /* First computation of asinh */ do { /* reactualisation of the precision */ mpfr_set_prec (t, Nt); mpfr_set_prec (te, Nt); mpfr_set_prec (ti, Nt); /* compute asinh */ mpfr_mul (te, x, x, GMP_RNDD); /* x^2 */ mpfr_add_ui (ti, te, 1, GMP_RNDD); /* x^2+1 */ mpfr_sqrt (t, ti, GMP_RNDN); /* sqrt(x^2+1) */ (neg ? mpfr_sub : mpfr_add) (t, t, x, GMP_RNDN); /* sqrt(x^2+1)+x */ mpfr_log (t, t, GMP_RNDN); /* ln(sqrt(x^2+1)+x)*/ /* error estimate -- see algorithms.ps */ err = Nt - (MAX(3 - MPFR_GET_EXP (t), 0) + 1); /* actualisation of the precision */ Nt += 10; } while ((err < 0) || (!mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ, Ny + (rnd_mode == GMP_RNDN)) || MPFR_IS_ZERO(t))); mpfr_restore_emin_emax (); if (neg) MPFR_CHANGE_SIGN(t); inexact = mpfr_set (y, t, rnd_mode); mpfr_clear (t); mpfr_clear (ti); mpfr_clear (te); return mpfr_check_range (y, inexact, rnd_mode); }