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/* mpfr_exp -- exponential of a floating-point number
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
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 "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)
{
mp_exp_t expx;
mp_prec_t precy;
int inexact;
double d;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
("y[%#R]=%R inexact=%d", y, y, 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);
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, rnd_mode);
}
}
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) */
/* TODO: Don't convert to double! */
d = mpfr_get_d1 (x);
if (MPFR_UNLIKELY (d >= (double) __gmpfr_emax * LOG2))
return mpfr_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_underflow rounds away for RNDN */
if (rnd_mode == GMP_RNDN && d < ((double) __gmpfr_emin - 2.0) * LOG2)
rnd_mode = GMP_RNDZ;
return mpfr_underflow (y, rnd_mode, 1);
}
/* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
if (MPFR_UNLIKELY (expx < 0 && (mpfr_uexp_t) (-expx) > precy))
{
mp_exp_t emin = __gmpfr_emin;
mp_exp_t emax = __gmpfr_emax;
int signx = MPFR_SIGN (x);
MPFR_SET_POS (y);
if (MPFR_IS_NEG_SIGN (signx) && (rnd_mode == GMP_RNDD ||
rnd_mode == GMP_RNDZ))
{
__gmpfr_emin = 0;
__gmpfr_emax = 0;
mpfr_setmax (y, 0); /* y = 1 - epsilon */
inexact = -1;
}
else
{
__gmpfr_emin = 1;
__gmpfr_emax = 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;
inexact = 1;
}
else
inexact = -MPFR_FROM_SIGN_TO_INT(signx);
}
__gmpfr_emin = emin;
__gmpfr_emax = emax;
}
else /* General case */
{
if (MPFR_UNLIKELY (precy > MPFR_EXP_THRESHOLD))
/* mpfr_exp_3 saves the exponent range and flags itself, otherwise
the flag changes in mpfr_exp_3 are lost */
inexact = mpfr_exp_3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
else
{
MPFR_SAVE_EXPO_MARK (expo);
inexact = mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
MPFR_SAVE_EXPO_FREE (expo);
}
}
return mpfr_check_range (y, inexact, rnd_mode);
}
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