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

1.1     ! ohara       1: /* mpfr_ui_pow -- power of n function n^x
        !             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: #include "gmp.h"
        !            23: #include "gmp-impl.h"
        !            24: #include "mpfr.h"
        !            25: #include "mpfr-impl.h"
        !            26:
        !            27:
        !            28:  /* The computation of y=pow(n,z) is done by
        !            29:
        !            30:     y=exp(z*log(n))=n^z
        !            31:  */
        !            32:
        !            33: int
        !            34: mpfr_ui_pow (mpfr_ptr y, unsigned long int n, mpfr_srcptr x, mp_rnd_t rnd_mode)
        !            35: {
        !            36:     int inexact;
        !            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_CLEAR_INF(y);
        !            51:             MPFR_SET_ZERO(y);
        !            52:           }
        !            53:         else
        !            54:           {
        !            55:             MPFR_SET_INF(y);
        !            56:           }
        !            57:         MPFR_SET_POS(y);
        !            58:         MPFR_RET(0);
        !            59:       }
        !            60:
        !            61:     /* n^0 = 1 */
        !            62:     if (MPFR_IS_ZERO(x))
        !            63:       {
        !            64:         return mpfr_set_ui(y,1,rnd_mode);
        !            65:       }
        !            66:
        !            67:     /* General case */
        !            68:     {
        !            69:     /* Declaration of the intermediary variable */
        !            70:       mpfr_t t, te, ti;
        !            71:
        !            72:       /* Declaration of the size variable */
        !            73:       mp_prec_t Nx = MPFR_PREC(x);   /* Precision of input variable */
        !            74:       mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */
        !            75:
        !            76:       mp_prec_t Nt;   /* Precision of the intermediary variable */
        !            77:       long int err;  /* Precision of error */
        !            78:
        !            79:       /* compute the precision of intermediary variable */
        !            80:       Nt=MAX(Nx,Ny);
        !            81:       /* the optimal number of bits : see algorithms.ps */
        !            82:       Nt=Nt+5+_mpfr_ceil_log2(Nt);
        !            83:
        !            84:       /* initialise of intermediary    variable */
        !            85:       mpfr_init(t);
        !            86:       mpfr_init2(ti,sizeof(unsigned long int)*8); /* 8 = CHAR_BIT */
        !            87:       mpfr_init(te);
        !            88:
        !            89:       do {
        !            90:
        !            91:        /* reactualisation of the precision */
        !            92:        mpfr_set_prec(t,Nt);
        !            93:        mpfr_set_prec(te,Nt);
        !            94:
        !            95:        /* compute   exp(x*ln(n))*/
        !            96:         mpfr_set_ui(ti,n,GMP_RNDN);      /* ti <- n*/
        !            97:         mpfr_log(t,ti,GMP_RNDU);         /* ln(n) */
        !            98:         mpfr_mul(te,x,t,GMP_RNDU);       /* x*ln(n) */
        !            99:         mpfr_exp(t,te,GMP_RNDN);         /* exp(x*ln(n))*/
        !           100:
        !           101:        /* estimation of the error -- see pow function in algorithms.ps*/
        !           102:        err = Nt - (MPFR_EXP(te)+3);
        !           103:
        !           104:        /* actualisation of the precision */
        !           105:        Nt += 10;
        !           106:
        !           107:       } while (err<0 || !mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
        !           108:
        !           109:       inexact = mpfr_set(y,t,rnd_mode);
        !           110:       mpfr_clear(t);
        !           111:       mpfr_clear(ti);
        !           112:       mpfr_clear(te);
        !           113:     }
        !           114:     return inexact;
        !           115:
        !           116: }