/* mpfr_asinh -- Inverse Hyperbolic Sinus of Unsigned Integer Number Copyright 2001, 2002 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 xt, mp_rnd_t rnd_mode) { int inexact; mpfr_t x; int flag_neg=0; mp_prec_t Nx; if (MPFR_IS_NAN(xt)) { MPFR_SET_NAN(y); MPFR_RET_NAN; } MPFR_CLEAR_NAN(y); if (MPFR_IS_INF(xt)) { MPFR_SET_INF(y); MPFR_SET_SAME_SIGN(y, xt); MPFR_RET(0); } MPFR_CLEAR_INF(y); if (MPFR_IS_ZERO(xt)) { MPFR_SET_ZERO(y); /* asinh(0) = 0 */ MPFR_SET_SAME_SIGN(y, xt); MPFR_RET(0); } Nx = MPFR_PREC(xt); /* Precision of input variable */ mpfr_init2(x, Nx); mpfr_set(x, xt, GMP_RNDN); if (MPFR_SIGN(x) < 0) { MPFR_CHANGE_SIGN(x); flag_neg=1; } /* General case */ { /* Declaration of the intermediary variable */ mpfr_t t, te,ti; /* Declaration of the size variable */ mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */ mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */ mp_prec_t Nt; /* Precision of the intermediary variable */ long int err; /* Precision of error */ /* compute the precision of intermediary variable */ Nt=MAX(Nx,Ny); /* the optimal number of bits : see algorithms.ps */ Nt=Nt+4+_mpfr_ceil_log2(Nt); /* initialise of intermediary variable */ mpfr_init(t); mpfr_init(te); mpfr_init(ti); /* First computation of cosh */ 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) */ mpfr_add(t,t,x,GMP_RNDN); /* sqrt(x^2+1)+x */ mpfr_log(t,t,GMP_RNDN); /* ln(sqrt(x^2+1)+x)*/ /* estimation of the error see- algorithms.ps*/ /*err=Nt-_mpfr_ceil_log2(1+pow(2,3-MPFR_EXP(t)));*/ err=Nt-(MAX(3-MPFR_EXP(t),0)+1); /* actualisation of the precision */ Nt += 10; } while ((err < 0) || (!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny) || (MPFR_IS_ZERO(t)))); if(flag_neg) MPFR_CHANGE_SIGN(t); inexact = mpfr_set(y,t,rnd_mode); mpfr_clear(t); mpfr_clear(ti); mpfr_clear(te); } mpfr_clear(x); MPFR_RET(inexact); }