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Diff for /OpenXM_contrib/gmp/mpfr/Attic/log2.c between version 1.1.1.1 and 1.1.1.2

version 1.1.1.1, 2000/09/09 14:12:19 version 1.1.1.2, 2003/08/25 16:06:08
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 /* mpfr_log2 -- compute natural logarithm of 2  /* mpfr_log2 -- log base 2
   
 Copyright (C) 1999 PolKA project, Inria Lorraine and Loria  Copyright 2001, 2002 Free Software Foundation, Inc.
   
 This file is part of the MPFR Library.  This file is part of the MPFR Library.
   
 The MPFR Library is free software; you can redistribute it and/or modify  The MPFR Library is free software; you can redistribute it and/or modify
 it under the terms of the GNU Library General Public License as published by  it under the terms of the GNU Lesser General Public License as published by
 the Free Software Foundation; either version 2 of the License, or (at your  the Free Software Foundation; either version 2.1 of the License, or (at your
 option) any later version.  option) any later version.
   
 The MPFR Library is distributed in the hope that it will be useful, but  The MPFR Library is distributed in the hope that it will be useful, but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 License for more details.  License for more details.
   
 You should have received a copy of the GNU Library General Public License  You should have received a copy of the GNU Lesser General Public License
 along with the MPFR Library; see the file COPYING.LIB.  If not, write to  along with the MPFR Library; see the file COPYING.LIB.  If not, write to
 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,  the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 MA 02111-1307, USA. */  MA 02111-1307, USA. */
   
 #include <stdio.h>  #include <stdio.h>
 #include <math.h>  
 #include "gmp.h"  #include "gmp.h"
 #include "gmp-impl.h"  #include "gmp-impl.h"
 #include "longlong.h"  
 #include "mpfr.h"  #include "mpfr.h"
   #include "mpfr-impl.h"
   
 mpfr_t __mpfr_log2; /* stored value of log(2) with rnd_mode=GMP_RNDZ */   /* The computation of r=log2(a)
 int __mpfr_log2_prec=0; /* precision of stored value */  
   
 /* set x to log(2) rounded to precision PREC(x) with direction rnd_mode      r=log2(a)=log(a)/log(2)
    */
   
    use formula log(2) = sum(1/k/2^k, k=1..infinity)  int
   mpfr_log2 (mpfr_ptr r, mpfr_srcptr a, mp_rnd_t rnd_mode)
   {
     int inexact = 0;
   
    whence 2^N*log(2) = S(N) + R(N)    /* If a is NaN, the result is NaN */
     if (MPFR_IS_NAN(a))
       {
         MPFR_SET_NAN(r);
         MPFR_RET_NAN;
       }
   
    where S(N) = sum(2^(N-k)/k, k=1..N-1)    MPFR_CLEAR_NAN(r);
    and   R(N) = sum(1/k/2^(k-N), k=N..infinity) < 2/N  
   
    Let S'(N) = sum(floor(2^(N-k)/k), k=1..N-1)    /* check for infinity before zero */
     if (MPFR_IS_INF(a))
       {
         if (MPFR_SIGN(a) < 0) /* log(-Inf) = NaN */
           {
             MPFR_SET_NAN(r);
             MPFR_RET_NAN;
           }
         else /* log(+Inf) = +Inf */
           {
             MPFR_SET_INF(r);
             MPFR_SET_POS(r);
             MPFR_RET(0);
           }
       }
   
    Then 2^N*log(2)-S'(N) <= N-1+2/N <= N for N>=2.    /* Now we can clear the flags without damage even if r == a */
 */    MPFR_CLEAR_INF(r);
 void  
 #if __STDC__  
 mpfr_log2(mpfr_ptr x, unsigned char rnd_mode)  
 #else  
 mpfr_log2(x, rnd_mode) mpfr_ptr x; unsigned char rnd_mode;  
 #endif  
 {  
   int N, oldN, k, precx; mpz_t s, t, u;  
   
   precx = PREC(x);    if (MPFR_IS_ZERO(a))
       {
         MPFR_SET_INF(r);
         MPFR_SET_NEG(r);
         MPFR_RET(0); /* log2(0) is an exact -infinity */
       }
   
   /* has stored value enough precision ? */    /* If a is negative, the result is NaN */
   if (precx <= __mpfr_log2_prec) {    if (MPFR_SIGN(a) < 0)
     if (rnd_mode==GMP_RNDZ || rnd_mode==GMP_RNDD ||      {
         mpfr_can_round(__mpfr_log2, __mpfr_log2_prec, GMP_RNDZ, rnd_mode, precx))        MPFR_SET_NAN(r);
       {        MPFR_RET_NAN;
         mpfr_set(x, __mpfr_log2, rnd_mode); return;      }
       }  
   }  
   
   /* need to recompute */    /* If a is 1, the result is 0 */
   N=2;    if (mpfr_cmp_ui(a, 1) == 0)
   do {      {
     oldN = N;        MPFR_SET_ZERO(r);
     N = precx + (int)ceil(log((double)N)/log(2.0));        MPFR_SET_POS(r);
   } while (N != oldN);        MPFR_RET(0); /* only "normal" case where the result is exact */
   mpz_init_set_ui(s,0);      }
   mpz_init(u);  
   mpz_init_set_ui(t,1);  
 #if 0  
   /* use log(2) = sum(1/k/2^k, k=1..infinity) */  
   mpz_mul_2exp(t, t, N);  
   for (k=1;k<N;k++) {  
     mpz_div_2exp(t, t, 1);  
     mpz_fdiv_q_ui(u, t, k);  
     mpz_add(s, s, u);  
   }  
 #else  
   /* use log(2) = sum((6*k-1)/(2*k^2-k)/2^(2*k+1), k=1..infinity) */  
   mpz_mul_2exp(t, t, N-1);  
   for (k=1;k<N/2;k++) {  
     mpz_div_2exp(t, t, 2);  
     mpz_mul_ui(u, t, 6*k-1);  
     mpz_fdiv_q_ui(u, u, k*(2*k-1));  
     mpz_add(s, s, u);  
   }  
 #endif  
   mpfr_set_z(x, s, rnd_mode);  
   EXP(x) -= N;  
   
   /* stored computed value */    /* If a is integer, log2(a) is exact*/
   if (__mpfr_log2_prec==0) mpfr_init2(__mpfr_log2, precx);    if (mpfr_cmp_ui_2exp(a,1,MPFR_EXP(a)-1) == 0)
   else mpfr_set_prec(__mpfr_log2, precx);        return mpfr_set_si(r,MPFR_EXP(a)-1,rnd_mode);
   mpfr_set(__mpfr_log2, x, GMP_RNDZ);  
   __mpfr_log2_prec=precx;  
   
   mpz_clear(s); mpz_clear(t); mpz_clear(u);  
    /* General case */
     {
       /* Declaration of the intermediary variable */
       mpfr_t t, tt;
   
       /* Declaration of the size variable */
       mp_prec_t Nx = MPFR_PREC(a);   /* Precision of input variable */
       mp_prec_t Ny = MPFR_PREC(r);   /* Precision of input variable */
   
       mp_prec_t Nt;   /* Precision of the intermediary variable */
       long int err;  /* Precision of error */
   
   
       /* compute the precision of intermediary variable */
       Nt=MAX(Nx,Ny);
       /* the optimal number of bits : see algorithms.ps */
       Nt=Nt+3+_mpfr_ceil_log2(Nt);
   
       /* initialise of intermediary       variable */
       mpfr_init(t);
       mpfr_init(tt);
   
   
       /* First computation of log2 */
       do {
   
         /* reactualisation of the precision */
         mpfr_set_prec(t,Nt);
         mpfr_set_prec(tt,Nt);
   
         /* compute log2 */
         mpfr_const_log2(t,GMP_RNDD); /* log(2) */
         mpfr_log(tt,a,GMP_RNDN);     /* log(a) */
         mpfr_div(t,tt,t,GMP_RNDN); /* log(a)/log(2) */
   
   
         /* estimation of the error */
         err=Nt-3;
   
         /* actualisation of the precision */
         Nt += 10;
       } while ((err<0) || !mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
   
         inexact = mpfr_set(r,t,rnd_mode);
   
         mpfr_clear(t);
         mpfr_clear(tt);
     }
     return inexact;
 }  }
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