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

1.1       ohara       1: /* mpfr_tanh -- hyperbolic tangent
                      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 cosh is done by
                     28:
                     29:     tanh= [e^(x)^2-1]/+[e^(x)^2+1]
                     30:  */
                     31:
                     32: int
                     33: #if __STDC__
                     34: mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
                     35: #else
                     36: mpfr_tanh (y, xt, rnd_mode)
                     37:      mpfr_ptr y;
                     38:      mpfr_srcptr xt;
                     39:      mp_rnd_t rnd_mode;
                     40: #endif
                     41: {
                     42:
                     43:     /****** Declaration ******/
                     44:     mpfr_t x;
                     45:     mp_prec_t Nxt = MPFR_PREC(xt);
                     46:     int flag_neg=0, inexact=0;
                     47:
                     48:     /* Special value checking */
                     49:
                     50:     if (MPFR_IS_NAN(xt))
                     51:       {
                     52:         MPFR_SET_NAN(y);
                     53:         MPFR_RET_NAN;
                     54:       }
                     55:     MPFR_CLEAR_NAN(y);
                     56:
                     57:     if (MPFR_IS_INF(xt))
                     58:       {
                     59:         if (MPFR_SIGN(xt) > 0)
                     60:           return mpfr_set_si(y,1,rnd_mode); /* tanh(inf) = 1 */
                     61:         else
                     62:           return mpfr_set_si(y,-1,rnd_mode); /* tanh(-inf) = -1 */
                     63:       }
                     64:     MPFR_CLEAR_INF(y);
                     65:
                     66:     /* tanh(0) = 0 */
                     67:     if (MPFR_IS_ZERO(xt))
                     68:       {
                     69:         MPFR_SET_ZERO(y);
                     70:         MPFR_SET_SAME_SIGN(y,xt);
                     71:         MPFR_RET(0);
                     72:       }
                     73:
                     74:     mpfr_init2(x,Nxt);
                     75:     mpfr_set(x,xt,GMP_RNDN);
                     76:
                     77:     if (MPFR_SIGN(x) < 0)
                     78:       {
                     79:         MPFR_CHANGE_SIGN(x);
                     80:         flag_neg=1;
                     81:       }
                     82:
                     83:     /* General case */
                     84:     {
                     85:       /* Declaration of the intermediary variable */
                     86:       mpfr_t t, te, ta,tb;
                     87:       int d;
                     88:
                     89:       /* Declaration of the size variable */
                     90:       mp_prec_t Nx = Nxt;   /* Precision of input variable */
                     91:       mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */
                     92:
                     93:       mp_prec_t Nt;   /* Precision of the intermediary variable */
                     94:       long int err;  /* Precision of error */
                     95:
                     96:       /* compute the precision of intermediary variable */
                     97:       Nt=MAX(Nx,Ny);
                     98:       /* the optimal number of bits : see algorithms.ps */
                     99:       Nt = Nt+_mpfr_ceil_log2(9)+_mpfr_ceil_log2(Nt);
                    100:
                    101:       /* initialise of intermediary    variable */
                    102:       mpfr_init(t);
                    103:       mpfr_init(te);
                    104:       mpfr_init(ta);
                    105:       mpfr_init(tb);
                    106:
                    107:
                    108:       /* First computation of cosh */
                    109:       do {
                    110:
                    111:        /* reactualisation of the precision */
                    112:        mpfr_set_prec(t,Nt);
                    113:        mpfr_set_prec(te,Nt);
                    114:        mpfr_set_prec(ta,Nt);
                    115:        mpfr_set_prec(tb,Nt);
                    116:
                    117:         /* compute tanh */
                    118:         mpfr_mul_2ui(te,x,1,GMP_RNDN);  /* 2x */
                    119:         mpfr_exp(te,te,GMP_RNDN);       /* exp(2x) */
                    120:         mpfr_add_ui(ta,te,1,GMP_RNDD);  /* exp(2x) + 1*/
                    121:         mpfr_sub_ui(tb,te,1,GMP_RNDU);  /* exp(2x) - 1*/
                    122:         mpfr_div(t,tb,ta,GMP_RNDN);     /* (exp(2x)-1)/(exp(2x)+1)*/
                    123:
                    124:
                    125:         /* calculation of the error*/
                    126:         d = MPFR_EXP(te)-MPFR_EXP(t);
                    127:
                    128:        /* estimation of the error */
                    129:         /*err = Nt-(_mpfr_ceil_log2(7+pow(2,d+1)));*/
                    130:         err = Nt-(MAX(d+1,3)+1);
                    131:
                    132:        /* actualisation of the precision */
                    133:         Nt += 10;
                    134:
                    135:       } while ((err <0)||!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
                    136:
                    137:       if (flag_neg==1)
                    138:           MPFR_CHANGE_SIGN(t);
                    139:
                    140:       inexact = mpfr_set(y,t,rnd_mode);
                    141:       mpfr_clear(t);
                    142:       mpfr_clear(te);
                    143:       mpfr_clear(ta);
                    144:       mpfr_clear(tb);
                    145:     }
                    146:     mpfr_clear(x);
                    147:     return inexact;
                    148:
                    149: }
                    150: