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/* mpfr_exp -- exponential of a floating-point number
Copyright 1999, 2000, 2001, 2002, 2003, 2004 Free Software Foundation.
Contributed by the Spaces project.
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 "mpfr-impl.h"
/* #define DEBUG */
/* use Brent's formula exp(x) = (1+r+r^2/2!+r^3/3!+...)^(2^K)*2^n
where x = n*log(2)+(2^K)*r
number of operations = O(K+prec(r)/K)
*/
int
mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int expx, precy, inexact;
double d;
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
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, GMP_RNDN);
}
}
MPFR_CLEAR_FLAGS(y);
expx = MPFR_GET_EXP (x);
precy = MPFR_PREC(y);
/* result is +Inf when exp(x) >= 2^(__gmpfr_emax), i.e.
x >= __gmpfr_emax * log(2) */
d = mpfr_get_d1 (x);
if (MPFR_UNLIKELY(d >= (double) __gmpfr_emax * LOG2))
return mpfr_set_overflow (y, rnd_mode, 1);
/* result is 0 when exp(x) < 1/2*2^(__gmpfr_emin), i.e.
x < (__gmpfr_emin-1) * LOG2 */
if (MPFR_UNLIKELY(d < ((double) __gmpfr_emin - 1.0) * LOG2))
{
/* warning: mpfr_set_underflow rounds away for RNDN */
if (rnd_mode == GMP_RNDN && d < ((double) __gmpfr_emin - 2.0) * LOG2)
rnd_mode = GMP_RNDZ;
return mpfr_set_underflow (y, rnd_mode, 1);
}
/* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
if (MPFR_UNLIKELY(expx < -precy))
{
int signx = MPFR_SIGN(x);
if (MPFR_IS_NEG_SIGN(signx) && (rnd_mode == GMP_RNDD))
{
MPFR_SET_POS(y);
mpfr_setmax (y, 0); /* y = 1 - epsilon */
return -1;
}
mpfr_setmin (y, 1); /* y = 1 */
if (MPFR_IS_POS_SIGN(signx) && rnd_mode == GMP_RNDU)
{
mp_size_t yn;
int sh;
yn = 1 + (MPFR_PREC(y) - 1) / BITS_PER_MP_LIMB;
sh = (mp_prec_t) yn * BITS_PER_MP_LIMB - MPFR_PREC(y);
MPFR_MANT(y)[0] += MPFR_LIMB_ONE << sh;
return 1;
}
return -MPFR_FROM_SIGN_TO_INT(signx);
}
mpfr_save_emin_emax ();
if (MPFR_UNLIKELY(precy > MPFR_EXP_THRESHOLD))
inexact = mpfr_exp_3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
else
inexact = mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
mpfr_restore_emin_emax ();
return mpfr_check_range (y, inexact, rnd_mode);
}
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