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/* mpfr_exp2 -- power of 2 function 2^y
Copyright 2001, 2002, 2003 Free Software Foundation.
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 <limits.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of y = 2^z is done by
y = exp(z*log(2)). The result is exact iff z is an integer.
*/
int
mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int inexact;
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) ))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x))
{
if (MPFR_IS_POS(x))
MPFR_SET_INF(y);
else
MPFR_SET_ZERO(y);
MPFR_SET_POS(y);
MPFR_RET(0);
}
/* 2^0 = 1 */
else if (MPFR_IS_ZERO(x))
return mpfr_set_ui (y, 1, rnd_mode);
else
MPFR_ASSERTN(0);
}
/* Useless due to mpfr_set
MPFR_CLEAR_FLAGS(y);*/
/* since the smallest representable non-zero float is 1/2*2^__gmpfr_emin,
if x < __gmpfr_emin - 1, the result is either 1/2*2^__gmpfr_emin or 0 */
MPFR_ASSERTN(MPFR_EMIN_MIN - 2 >= LONG_MIN);
if (mpfr_cmp_si_2exp (x, __gmpfr_emin - 1, 0) < 0)
{
mp_rnd_t rnd2 = rnd_mode;
/* in round to nearest mode, round to zero when x <= __gmpfr_emin-2 */
if (rnd_mode == GMP_RNDN &&
mpfr_cmp_si_2exp (x, __gmpfr_emin - 2, 0) <= 0)
rnd2 = GMP_RNDZ;
return mpfr_set_underflow (y, rnd2, 1);
}
if (mpfr_integer_p (x)) /* we know that x >= 2^(emin-1) */
{
double xd;
MPFR_ASSERTN(MPFR_EMAX_MAX <= LONG_MAX);
if (mpfr_cmp_si_2exp (x, __gmpfr_emax, 0) > 0)
return mpfr_set_overflow (y, rnd_mode, 1);
xd = mpfr_get_d1 (x);
mpfr_set_ui (y, 1, GMP_RNDZ);
return mpfr_mul_2si (y, y, (long) xd, rnd_mode);
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te;
/* 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 + __gmpfr_ceil_log2 (Nt);
/* initialise of intermediary variable */
mpfr_init (t);
mpfr_init (te);
/* First computation */
do
{
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
/* compute exp(x*ln(2))*/
mpfr_const_log2 (t, GMP_RNDU); /* ln(2) */
mpfr_mul (te, x, t, GMP_RNDU); /* x*ln(2) */
mpfr_exp (t, te, GMP_RNDN); /* exp(x*ln(2))*/
/* estimate of the error -- see pow function in algorithms.ps*/
err = Nt - (MPFR_GET_EXP (te) + 2);
/* actualisation of the precision */
Nt += __gmpfr_isqrt (Nt) + 10;
}
while ((err < 0) || !mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
Ny + (rnd_mode == GMP_RNDN)));
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (te);
}
return inexact;
}
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