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Annotation of OpenXM_contrib/gmp/mpfr/asinh.c, Revision 1.1.1.1

1.1       ohara       1: /* mpfr_asinh -- Inverse Hyperbolic Sinus of Unsigned Integer Number
                      2:
                      3: Copyright 2001, 2002 Free Software Foundation.
                      4:
                      5: This file is part of the MPFR Library.
                      6:
                      7: The MPFR Library is free software; you can redistribute it and/or modify
                      8: it under the terms of the GNU Lesser General Public License as published by
                      9: the Free Software Foundation; either version 2.1 of the License, or (at your
                     10: option) any later version.
                     11:
                     12: The MPFR Library is distributed in the hope that it will be useful, but
                     13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
                     14: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
                     15: License for more details.
                     16:
                     17: You should have received a copy of the GNU Lesser General Public License
                     18: along with the MPFR Library; see the file COPYING.LIB.  If not, write to
                     19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
                     20: MA 02111-1307, USA. */
                     21:
                     22: #include "gmp.h"
                     23: #include "gmp-impl.h"
                     24: #include "mpfr.h"
                     25: #include "mpfr-impl.h"
                     26:
                     27:  /* The computation of asinh is done by
                     28:
                     29:     asinh= ln(x+sqrt(x^2+1))
                     30:  */
                     31: int
                     32: mpfr_asinh (mpfr_ptr y, mpfr_srcptr xt, mp_rnd_t rnd_mode)
                     33: {
                     34:   int inexact;
                     35:   mpfr_t x;
                     36:   int flag_neg=0;
                     37:   mp_prec_t Nx;
                     38:
                     39:   if (MPFR_IS_NAN(xt))
                     40:     {
                     41:       MPFR_SET_NAN(y);
                     42:       MPFR_RET_NAN;
                     43:     }
                     44:
                     45:   MPFR_CLEAR_NAN(y);
                     46:
                     47:   if (MPFR_IS_INF(xt))
                     48:     {
                     49:       MPFR_SET_INF(y);
                     50:       MPFR_SET_SAME_SIGN(y, xt);
                     51:       MPFR_RET(0);
                     52:     }
                     53:
                     54:   MPFR_CLEAR_INF(y);
                     55:
                     56:   if (MPFR_IS_ZERO(xt))
                     57:     {
                     58:       MPFR_SET_ZERO(y);   /* asinh(0) = 0 */
                     59:       MPFR_SET_SAME_SIGN(y, xt);
                     60:       MPFR_RET(0);
                     61:     }
                     62:
                     63:   Nx = MPFR_PREC(xt);   /* Precision of input variable */
                     64:   mpfr_init2(x, Nx);
                     65:   mpfr_set(x, xt, GMP_RNDN);
                     66:
                     67:   if (MPFR_SIGN(x) < 0)
                     68:     {
                     69:       MPFR_CHANGE_SIGN(x);
                     70:       flag_neg=1;
                     71:     }
                     72:
                     73:   /* General case */
                     74:   {
                     75:     /* Declaration of the intermediary variable */
                     76:     mpfr_t t, te,ti;
                     77:
                     78:     /* Declaration of the size variable */
                     79:     mp_prec_t Nx = MPFR_PREC(x);   /* Precision of input variable */
                     80:     mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */
                     81:
                     82:     mp_prec_t Nt;   /* Precision of the intermediary variable */
                     83:     long int err;  /* Precision of error */
                     84:
                     85:     /* compute the precision of intermediary variable */
                     86:     Nt=MAX(Nx,Ny);
                     87:     /* the optimal number of bits : see algorithms.ps */
                     88:     Nt=Nt+4+_mpfr_ceil_log2(Nt);
                     89:
                     90:     /* initialise of intermediary      variable */
                     91:     mpfr_init(t);
                     92:     mpfr_init(te);
                     93:     mpfr_init(ti);
                     94:
                     95:     /* First computation of cosh */
                     96:     do {
                     97:
                     98:       /* reactualisation of the precision */
                     99:       mpfr_set_prec(t,Nt);
                    100:       mpfr_set_prec(te,Nt);
                    101:       mpfr_set_prec(ti,Nt);
                    102:
                    103:       /* compute asinh */
                    104:       mpfr_mul(te,x,x,GMP_RNDD);  /* (x^2) */
                    105:       mpfr_add_ui(ti,te,1,GMP_RNDD);  /* (x^2+1) */
                    106:       mpfr_sqrt(t,ti,GMP_RNDN);     /* sqrt(x^2+1) */
                    107:       mpfr_add(t,t,x,GMP_RNDN);    /* sqrt(x^2+1)+x */
                    108:       mpfr_log(t,t,GMP_RNDN);        /* ln(sqrt(x^2+1)+x)*/
                    109:
                    110:       /* estimation of the error see- algorithms.ps*/
                    111:       /*err=Nt-_mpfr_ceil_log2(1+pow(2,3-MPFR_EXP(t)));*/
                    112:       err=Nt-(MAX(3-MPFR_EXP(t),0)+1);
                    113:
                    114:       /* actualisation of the precision */
                    115:       Nt += 10;
                    116:
                    117:     } while ((err < 0) || (!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny) || (MPFR_IS_ZERO(t))));
                    118:
                    119:     if(flag_neg)
                    120:       MPFR_CHANGE_SIGN(t);
                    121:
                    122:     inexact = mpfr_set(y,t,rnd_mode);
                    123:
                    124:     mpfr_clear(t);
                    125:     mpfr_clear(ti);
                    126:     mpfr_clear(te);
                    127:   }
                    128:   mpfr_clear(x);
                    129:   MPFR_RET(inexact);
                    130: }