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/* mpfr_ui_pow -- power of n function n^x
Copyright 2001, 2002 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
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
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of y=pow(n,z) is done by
y=exp(z*log(n))=n^z
*/
int
mpfr_ui_pow (mpfr_ptr y, unsigned long int n, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int inexact;
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y);
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) < 0)
{
MPFR_CLEAR_INF(y);
MPFR_SET_ZERO(y);
}
else
{
MPFR_SET_INF(y);
}
MPFR_SET_POS(y);
MPFR_RET(0);
}
/* n^0 = 1 */
if (MPFR_IS_ZERO(x))
{
return mpfr_set_ui(y,1,rnd_mode);
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te, ti;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* 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+5+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init2(ti,sizeof(unsigned long int)*8); /* 8 = CHAR_BIT */
mpfr_init(te);
do {
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
/* compute exp(x*ln(n))*/
mpfr_set_ui(ti,n,GMP_RNDN); /* ti <- n*/
mpfr_log(t,ti,GMP_RNDU); /* ln(n) */
mpfr_mul(te,x,t,GMP_RNDU); /* x*ln(n) */
mpfr_exp(t,te,GMP_RNDN); /* exp(x*ln(n))*/
/* estimation of the error -- see pow function in algorithms.ps*/
err = Nt - (MPFR_EXP(te)+3);
/* actualisation of the precision */
Nt += 10;
} while (err<0 || !mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
inexact = mpfr_set(y,t,rnd_mode);
mpfr_clear(t);
mpfr_clear(ti);
mpfr_clear(te);
}
return inexact;
}
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