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/* mpfr_exp -- exponential of a floating-point number
Copyright (C) 1999 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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library 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 <math.h>
#include "gmp.h"
#include "mpfr.h"
#include "gmp-impl.h"
/* #define DEBUG */
#define LOG2 0.69314718055994528622 /* log(2) rounded to zero on 53 bits */
extern int mpfr_exp2 _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t));
extern int mpfr_exp3 _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t));
/* 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
#if __STDC__
mpfr_exp(mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
#else
mpfr_exp(y, x, rnd_mode)
mpfr_ptr y;
mpfr_srcptr x;
mp_rnd_t rnd_mode;
#endif
{
int expx, precy;
if (MPFR_IS_NAN(x)) { MPFR_SET_NAN(y); return 1; }
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) > 0)
{ MPFR_SET_INF(y); if (MPFR_SIGN(y) == -1) { MPFR_CHANGE_SIGN(y); } }
else
{ MPFR_SET_ZERO(y); if (MPFR_SIGN(y) == -1) { MPFR_CHANGE_SIGN(y); } }
/* TODO: conflits entre infinis et zeros ? */
}
if (!MPFR_NOTZERO(x)) { mpfr_set_ui(y, 1, GMP_RNDN); return 0; }
expx = MPFR_EXP(x);
precy = MPFR_PREC(y);
/* if x > (2^31-1)*ln(2), then exp(x) > 2^(2^31-1) i.e. gives +infinity */
if (expx > 30) {
if (MPFR_SIGN(x)>0) { printf("+infinity"); return 1; }
else { MPFR_SET_ZERO(y); return 1; }
}
/* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
if (expx < -precy) { int signx = MPFR_SIGN(x);
mpfr_set_ui(y, 1, rnd_mode);
if (signx>0 && rnd_mode==GMP_RNDU) mpfr_add_one_ulp(y);
else if (signx<0 && (rnd_mode==GMP_RNDD || rnd_mode==GMP_RNDZ))
mpfr_sub_one_ulp(y);
return 1; }
if (precy > 13000) mpfr_exp3(y, x, rnd_mode); /* O(M(n) log(n)^2) */
else mpfr_exp2(y, x, rnd_mode); /* O(n^(1/3) M(n)) */
return 1;
}
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