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Annotation of OpenXM_contrib/gmp/mpfr/sinh.c, Revision 1.1

1.1     ! ohara       1: /* mpfr_sinh -- hyperbolic sine
        !             2:
        !             3: Copyright 2001, 2002 Free Software Foundation, Inc.
        !             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:
        !            23: #include "gmp.h"
        !            24: #include "gmp-impl.h"
        !            25: #include "mpfr.h"
        !            26: #include "mpfr-impl.h"
        !            27:
        !            28:  /* The computation of sinh is done by
        !            29:
        !            30:     sinh(x) = 1/2 [e^(x)-e^(-x)]
        !            31:  */
        !            32:
        !            33: int
        !            34: mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mp_rnd_t rnd_mode)
        !            35: {
        !            36:     /****** Declarations ******/
        !            37:     mpfr_t x;
        !            38:     mp_prec_t Nxt = MPFR_PREC(xt);
        !            39:     int flag_neg=0, inexact =0;
        !            40:
        !            41:     if (MPFR_IS_NAN(xt))
        !            42:       {
        !            43:         MPFR_SET_NAN(y);
        !            44:         MPFR_RET_NAN;
        !            45:       }
        !            46:     MPFR_CLEAR_NAN(y);
        !            47:
        !            48:     if (MPFR_IS_INF(xt))
        !            49:       {
        !            50:         MPFR_SET_INF(y);
        !            51:         MPFR_SET_SAME_SIGN(y, xt);
        !            52:         MPFR_RET(0);
        !            53:       }
        !            54:
        !            55:     MPFR_CLEAR_INF(y);
        !            56:
        !            57:     if (MPFR_IS_ZERO(xt))
        !            58:       {
        !            59:         MPFR_SET_ZERO(y);   /* sinh(0) = 0 */
        !            60:         MPFR_SET_SAME_SIGN(y, xt);
        !            61:         MPFR_RET(0);
        !            62:       }
        !            63:
        !            64:     mpfr_init2 (x, Nxt);
        !            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:       int d;
        !            78:
        !            79:       /* Declaration of the size variable */
        !            80:       mp_prec_t Nx = Nxt;   /* Precision of input variable */
        !            81:       mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */
        !            82:
        !            83:       mp_prec_t Nt;   /* Precision of the intermediary variable */
        !            84:       long int err;  /* Precision of error */
        !            85:
        !            86:       /* compute the precision of intermediary variable */
        !            87:       Nt = MAX(Nx, Ny);
        !            88:       /* the optimal number of bits : see algorithms.ps */
        !            89:       Nt = Nt + _mpfr_ceil_log2 (5) + _mpfr_ceil_log2 (Nt);
        !            90:
        !            91:       /* initialise of intermediary    variable */
        !            92:       mpfr_init (t);
        !            93:       mpfr_init (te);
        !            94:       mpfr_init (ti);
        !            95:
        !            96:       /* First computation of sinh */
        !            97:       do {
        !            98:
        !            99:        /* reactualisation of the precision */
        !           100:
        !           101:        mpfr_set_prec (t, Nt);
        !           102:        mpfr_set_prec (te, Nt);
        !           103:        mpfr_set_prec (ti, Nt);
        !           104:
        !           105:        /* compute sinh */
        !           106:        mpfr_exp (te, x, GMP_RNDD);        /* exp(x) */
        !           107:        mpfr_ui_div (ti, 1, te, GMP_RNDU); /* 1/exp(x) */
        !           108:         mpfr_sub (t, te, ti, GMP_RNDN);    /* exp(x) - 1/exp(x) */
        !           109:        mpfr_div_2ui (t, t, 1, GMP_RNDN);  /* 1/2(exp(x) - 1/exp(x)) */
        !           110:
        !           111:         /* it may be that t is zero (in fact, it can only occur when te=1,
        !           112:            and thus ti=1 too) */
        !           113:
        !           114:         if (MPFR_IS_ZERO(t))
        !           115:           err = -1;
        !           116:         else
        !           117:           {
        !           118:             /* calculation of the error */
        !           119:             d = MPFR_EXP(te) - MPFR_EXP(t) + 2;
        !           120:
        !           121:             /* estimation of the error */
        !           122:             /* err = Nt-(_mpfr_ceil_log2(1+pow(2,d)));*/
        !           123:             err = Nt - (MAX(d,0) + 1);
        !           124:           }
        !           125:
        !           126:        /* actualisation of the precision */
        !           127:         Nt += 10;
        !           128:
        !           129:       } while ((err < 0) || !mpfr_can_round(t, err, GMP_RNDN, rnd_mode, Ny));
        !           130:
        !           131:       if (flag_neg == 1)
        !           132:           MPFR_CHANGE_SIGN(t);
        !           133:
        !           134:       inexact = mpfr_set (y, t, rnd_mode);
        !           135:       mpfr_clear (t);
        !           136:       mpfr_clear (ti);
        !           137:       mpfr_clear (te);
        !           138:     }
        !           139:     mpfr_clear (x);
        !           140:
        !           141:     return inexact;
        !           142: }