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