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

1.1     ! ohara       1: /* mpfr_acosh -- Inverse Hyperbolic Cosine 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:     acosh= ln(x+sqrt(x-1)*sqrt(x+1))
        !            30:  */
        !            31:
        !            32: int
        !            33: mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
        !            34: {
        !            35:
        !            36:   int inexact =0;
        !            37:   int comp;
        !            38:
        !            39:   if (MPFR_IS_NAN(x))
        !            40:     {
        !            41:       MPFR_SET_NAN(y);
        !            42:       MPFR_RET_NAN;
        !            43:     }
        !            44:
        !            45:   comp=mpfr_cmp_ui(x,1);
        !            46:
        !            47:   if(comp < 0)
        !            48:     {
        !            49:       MPFR_SET_NAN(y);
        !            50:       MPFR_RET_NAN;
        !            51:     }
        !            52:   MPFR_CLEAR_NAN(y);
        !            53:
        !            54:   if(comp == 0)
        !            55:     {
        !            56:       MPFR_SET_ZERO(y); /* acosh(1) = 0 */
        !            57:       MPFR_SET_POS(y);
        !            58:       MPFR_RET(0);
        !            59:     }
        !            60:
        !            61:   if (MPFR_IS_INF(x))
        !            62:     {
        !            63:       MPFR_SET_INF(y);
        !            64:       MPFR_SET_POS(y);
        !            65:       MPFR_RET(0);
        !            66:     }
        !            67:
        !            68:   MPFR_CLEAR_INF(y);
        !            69:
        !            70:   /* General case */
        !            71:   {
        !            72:     /* Declaration of the intermediary variable */
        !            73:     mpfr_t t, te,ti;
        !            74:
        !            75:     /* Declaration of the size variable */
        !            76:     mp_prec_t Nx = MPFR_PREC(x);   /* Precision of input variable */
        !            77:     mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */
        !            78:
        !            79:     mp_prec_t Nt;   /* Precision of the intermediary variable */
        !            80:     int err;  /* Precision of error */
        !            81:
        !            82:     /* compute the precision of intermediary variable */
        !            83:     Nt=MAX(Nx,Ny);
        !            84:     /* the optimal number of bits : see algorithms.ps */
        !            85:     Nt=Nt+4+_mpfr_ceil_log2(Nt);
        !            86:
        !            87:     /* initialise of intermediary      variable */
        !            88:     mpfr_init(t);
        !            89:     mpfr_init(te);
        !            90:     mpfr_init(ti);
        !            91:
        !            92:     /* First computation of cosh */
        !            93:     do {
        !            94:
        !            95:       /* reactualisation of the precision */
        !            96:       mpfr_set_prec(t,Nt);
        !            97:       mpfr_set_prec(te,Nt);
        !            98:       mpfr_set_prec(ti,Nt);
        !            99:
        !           100:       /* compute acosh */
        !           101:       mpfr_mul(te,x,x,GMP_RNDD);  /* (x^2) */
        !           102:       mpfr_sub_ui(ti,te,1,GMP_RNDD);  /* (x^2-1) */
        !           103:       mpfr_sqrt(t,ti,GMP_RNDN);     /* sqrt(x^2-1) */
        !           104:       mpfr_add(t,t,x,GMP_RNDN);    /* sqrt(x^2-1)+x */
        !           105:       mpfr_log(t,t,GMP_RNDN);        /* ln(sqrt(x^2-1)+x)*/
        !           106:
        !           107:       /* estimation of the error see- algorithms.ps*/
        !           108:       /*err=Nt-_mpfr_ceil_log2(0.5+pow(2,2-MPFR_EXP(t))+pow(2,1+MPFR_EXP(te)-MPFR_EXP(ti)-MPFR_EXP(t)));*/
        !           109:       err=Nt-(-1+2*MAX(2+MAX(2-MPFR_EXP(t),1+MPFR_EXP(te)-MPFR_EXP(ti)-MPFR_EXP(t)),0));
        !           110:
        !           111:       /* actualisation of the precision */
        !           112:       Nt += 10;
        !           113:
        !           114:     } while ((err<0) ||!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
        !           115:
        !           116:     inexact = mpfr_set(y,t,rnd_mode);
        !           117:
        !           118:     mpfr_clear(t);
        !           119:     mpfr_clear(ti);
        !           120:     mpfr_clear(te);
        !           121:   }
        !           122:   return inexact;
        !           123: }
        !           124:
        !           125:
        !           126:
        !           127:
        !           128:
        !           129:
        !           130:
        !           131:
        !           132:
        !           133:
        !           134: