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Annotation of OpenXM_contrib/gmp/mpfr/exp2.c, Revision 1.1

1.1     ! ohara       1: /* mpfr_exp2 -- power of 2 function 2^y
        !             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 y=pow(2,z) is done by
        !            28:
        !            29:     y=exp(z*log(2))=2^z
        !            30:  */
        !            31:
        !            32: int
        !            33: mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
        !            34: {
        !            35:
        !            36:     int inexact =0;
        !            37:
        !            38:     if (MPFR_IS_NAN(x))
        !            39:       {
        !            40:         MPFR_SET_NAN(y);
        !            41:         MPFR_RET_NAN;
        !            42:       }
        !            43:
        !            44:     MPFR_CLEAR_NAN(y);
        !            45:
        !            46:     if (MPFR_IS_INF(x))
        !            47:       {
        !            48:         if (MPFR_SIGN(x) > 0)
        !            49:           {
        !            50:             MPFR_SET_INF(y);
        !            51:           }
        !            52:         else
        !            53:           {
        !            54:             MPFR_CLEAR_INF(y);
        !            55:             MPFR_SET_ZERO(y);
        !            56:           }
        !            57:         MPFR_SET_POS(y);
        !            58:         MPFR_RET(0);
        !            59:       }
        !            60:
        !            61:     /* 2^0 = 1 */
        !            62:     if (MPFR_IS_ZERO(x))
        !            63:       return mpfr_set_ui (y, 1, rnd_mode);
        !            64:
        !            65:     /* since the smallest representable non-zero float is 1/2*2^__mpfr_emin,
        !            66:        if x < __mpfr_emin - 1, the result is either 1/2*2^__mpfr_emin or 0 */
        !            67:     if (mpfr_cmp_si_2exp (x, __mpfr_emin - 1, 0) < 0)
        !            68:       return mpfr_set_underflow (y, rnd_mode, 1);
        !            69:
        !            70:     /* General case */
        !            71:     {
        !            72:     /* Declaration of the intermediary variable */
        !            73:       mpfr_t t, te;
        !            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:       long 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 + 5 + _mpfr_ceil_log2 (Nt);
        !            86:
        !            87:
        !            88:       /* initialise of intermediary    variable */
        !            89:       mpfr_init (t);
        !            90:       mpfr_init (te);
        !            91:
        !            92:       /* First computation */
        !            93:       do {
        !            94:
        !            95:        /* reactualisation of the precision */
        !            96:        mpfr_set_prec (t, Nt);
        !            97:        mpfr_set_prec (te, Nt);
        !            98:
        !            99:        /* compute   exp(x*ln(2))*/
        !           100:         mpfr_const_log2 (t, GMP_RNDU);    /* ln(2) */
        !           101:         mpfr_mul (te, x, t, GMP_RNDU);    /* x*ln(2) */
        !           102:         mpfr_exp (t, te, GMP_RNDN);       /* exp(x*ln(2))*/
        !           103:
        !           104:        /* estimate of the error -- see pow function in algorithms.ps*/
        !           105:        err = Nt - (MPFR_EXP(te) + 2);
        !           106:
        !           107:        /* actualisation of the precision */
        !           108:        Nt += _mpfr_isqrt (Nt) + 10;
        !           109:
        !           110:       } while ((err < 0) || !mpfr_can_round (t, err, GMP_RNDN, rnd_mode, Ny));
        !           111:
        !           112:       inexact = mpfr_set (y, t, rnd_mode);
        !           113:
        !           114:       mpfr_clear (t);
        !           115:       mpfr_clear (te);
        !           116:     }
        !           117:     return inexact;
        !           118:
        !           119: }