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/* mpfr_exp -- exponential of a floating-point number
Copyright 1999, 2000, 2001, 2002, 2003 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 <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#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;
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 if (MPFR_IS_ZERO(x))
return mpfr_set_ui (y, 1, GMP_RNDN);
else
MPFR_ASSERTN(0);
}
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 (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 (d < ((double) __gmpfr_emin - 1.0) * LOG2)
return mpfr_set_underflow (y, rnd_mode, 1);
/* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
if (expx < -precy)
{
int signx = MPFR_SIGN(x);
if (MPFR_IS_NEG_SIGN(signx) && (rnd_mode == GMP_RNDD || rnd_mode == GMP_RNDZ))
{
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] += MP_LIMB_T_ONE << sh;
return 1;
}
return -MPFR_FROM_SIGN_TO_INT(signx);
}
if (precy > 13000)
return mpfr_exp3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
else
return mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
}
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