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Annotation of OpenXM_contrib/gmp/mpfr/exp2.c, Revision 1.1.1.1

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: }