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/* mpfr_exp2 -- power of 2 function 2^y
Copyright 2001, 2002, 2003, 2004, 2005, 2006 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., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include <limits.h>
#define MPFR_NEED_LONGLONG_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;
MPFR_SAVE_EXPO_DECL (expo);
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);
}
else /* 2^0 = 1 */
{
MPFR_ASSERTD (MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, rnd_mode);
}
}
/* 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_ASSERTD (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_underflow (y, rnd2, 1);
}
MPFR_SAVE_EXPO_MARK (expo);
if (mpfr_integer_p (x)) /* we know that x >= 2^(emin-1) */
{
long xd;
MPFR_ASSERTD (MPFR_EMAX_MAX <= LONG_MAX);
if (mpfr_cmp_si_2exp (x, __gmpfr_emax, 0) > 0)
return mpfr_overflow (y, rnd_mode, 1);
/* x <= __gmpfr_emax */
MPFR_ASSERTN (__gmpfr_emax <= LONG_MAX);
xd = mpfr_get_si (x, GMP_RNDN);
mpfr_set_ui (y, 1, GMP_RNDZ);
inexact = mpfr_mul_2si (y, y, xd, rnd_mode);
}
else /* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* Declaration of the size variable */
mp_prec_t Ny = MPFR_PREC(y); /* target precision */
mp_prec_t Nt; /* working precision */
mp_exp_t err; /* error */
MPFR_ZIV_DECL (loop);
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Ny + 5 + MPFR_INT_CEIL_LOG2 (Ny);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
/* First computation */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute exp(x*ln(2))*/
mpfr_const_log2 (t, GMP_RNDU); /* ln(2) */
mpfr_mul (t, x, t, GMP_RNDU); /* x*ln(2) */
err = Nt - (MPFR_GET_EXP (t) + 2); /* Estimate of the error */
mpfr_exp (t, t, GMP_RNDN); /* exp(x*ln(2))*/
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
/* Actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
}
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
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