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