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

1.1       ohara       1: /* mpfr_atanh -- Inverse Hyperbolic Tangente 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 acosh is done by
                     28:
                     29:     atanh= 1/2*ln(x+1)-1/2*ln(1-x)
                     30:  */
                     31:
                     32: int
                     33: mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
                     34: {
                     35:   int inexact =0;
                     36:   mpfr_t x;
                     37:   int flag_neg=0;
                     38:
                     39:   mp_prec_t Nx=MPFR_PREC(xt);   /* Precision of input variable */
                     40:   mpfr_init2(x,Nx);
                     41:   mpfr_set(x,xt,GMP_RNDN);
                     42:
                     43:   if (MPFR_SIGN(x) < 0)
                     44:     {
                     45:       MPFR_CHANGE_SIGN(x);
                     46:       flag_neg=1;
                     47:     }
                     48:
                     49:   if (MPFR_IS_NAN(x))
                     50:     {
                     51:       MPFR_SET_NAN(y);
                     52:       mpfr_clear(x);
                     53:       MPFR_RET_NAN;
                     54:     }
                     55:   MPFR_CLEAR_NAN(y);
                     56:
                     57:
                     58:   if (MPFR_IS_INF(x))
                     59:     {
                     60:       MPFR_SET_INF(y);
                     61:       MPFR_SET_SAME_SIGN(y,x);
                     62:       if(flag_neg)
                     63:        MPFR_CHANGE_SIGN(y);
                     64:       mpfr_clear(x);
                     65:       MPFR_RET(0);
                     66:     }
                     67:
                     68:   MPFR_CLEAR_INF(y);
                     69:
                     70:   if (MPFR_IS_ZERO(x))
                     71:     {
                     72:       MPFR_SET_ZERO(y);   /* atanh(0) = 0 */
                     73:       MPFR_SET_SAME_SIGN(y,x);
                     74:       if(flag_neg)
                     75:        MPFR_CHANGE_SIGN(y);
                     76:       mpfr_clear(x);
                     77:       MPFR_RET(0);
                     78:     }
                     79:
                     80:   /* General case */
                     81:   {
                     82:     /* Declaration of the intermediary variable */
                     83:     mpfr_t t, te,ti;
                     84:
                     85:     /* Declaration of the size variable */
                     86:     mp_prec_t Nx = MPFR_PREC(x);   /* Precision of input variable */
                     87:     mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */
                     88:
                     89:     mp_prec_t Nt;   /* Precision of the intermediary variable */
                     90:     long int err;  /* Precision of error */
                     91:
                     92:     /* compute the precision of intermediary variable */
                     93:     Nt=MAX(Nx,Ny);
                     94:     /* the optimal number of bits : see algorithms.ps */
                     95:     Nt=Nt+4+_mpfr_ceil_log2(Nt);
                     96:
                     97:     /* initialise of intermediary      variable */
                     98:     mpfr_init(t);
                     99:     mpfr_init(te);
                    100:     mpfr_init(ti);
                    101:
                    102:     /* First computation of cosh */
                    103:     do {
                    104:
                    105:       /* reactualisation of the precision */
                    106:       mpfr_set_prec(t,Nt);
                    107:       mpfr_set_prec(te,Nt);
                    108:       mpfr_set_prec(ti,Nt);
                    109:
                    110:       /* compute atanh */
                    111:       mpfr_ui_sub(te,1,x,GMP_RNDU);   /* (1-xt)*/
                    112:       mpfr_add_ui(ti,x,1,GMP_RNDD);   /* (xt+1)*/
                    113:       mpfr_div(te,ti,te,GMP_RNDN);    /* (1+xt)/(1-xt)*/
                    114:       mpfr_log(te,te,GMP_RNDN);       /* ln((1+xt)/(1-xt))*/
                    115:       mpfr_div_2ui(t,te,1,GMP_RNDN);  /* (1/2)*ln((1+xt)/(1-xt))*/
                    116:
                    117:       /* estimation of the error see- algorithms.ps*/
                    118:       /* err=Nt-_mpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
                    119:       err=Nt-(MAX(4-MPFR_EXP(t),0)+1);
                    120:
                    121:       /* actualisation of the precision */
                    122:       Nt += 10;
                    123:
                    124:     } while ((err < 0) || (!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny) || (MPFR_IS_ZERO(t))));
                    125:
                    126:     if(flag_neg)
                    127:       MPFR_CHANGE_SIGN(t);
                    128:
                    129:     inexact = mpfr_set(y,t,rnd_mode);
                    130:
                    131:     mpfr_clear(t);
                    132:     mpfr_clear(ti);
                    133:     mpfr_clear(te);
                    134:   }
                    135:   mpfr_clear(x);
                    136:   return inexact;
                    137: }
                    138:
                    139:
                    140:
                    141:
                    142: