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/* mpfr_exp -- exponential of a floating-point number
Copyright 1999-2021 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 3 of the License, or (at your
option) any later version.
The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#include "mpfr-impl.h"
/* Cache for emin and emax bounds.
Contrary to other caches, it uses a fixed size for the mantissa,
so there is no dynamic allocation, and no need to free them. */
static MPFR_THREAD_ATTR mpfr_exp_t previous_emin;
static MPFR_THREAD_ATTR mp_limb_t bound_emin_limb[(32 - 1) / GMP_NUMB_BITS + 1];
static MPFR_THREAD_ATTR mpfr_t bound_emin;
static MPFR_THREAD_ATTR mpfr_exp_t previous_emax;
static MPFR_THREAD_ATTR mp_limb_t bound_emax_limb[(32 - 1) / GMP_NUMB_BITS + 1];
static MPFR_THREAD_ATTR mpfr_t bound_emax;
int
mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t expx;
mpfr_prec_t precy;
int inexact;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (y), mpfr_log_prec, 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);
}
}
/* First, let's detect most overflow and underflow cases. */
/* emax bound is cached. Check if the value in cache is ok */
if (MPFR_UNLIKELY (mpfr_get_emax() != previous_emax))
{
/* Recompute the emax bound */
mp_limb_t e_limb[MPFR_EXP_LIMB_SIZE];
mpfr_t e;
/* We extend the exponent range and save the flags. */
MPFR_SAVE_EXPO_MARK (expo);
MPFR_TMP_INIT1(e_limb, e, sizeof (mpfr_exp_t) * CHAR_BIT);
MPFR_TMP_INIT1(bound_emax_limb, bound_emax, 32);
inexact = mpfr_set_exp_t (e, expo.saved_emax, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
mpfr_mul (bound_emax, expo.saved_emax < 0 ?
__gmpfr_const_log2_RNDD : __gmpfr_const_log2_RNDU,
e, MPFR_RNDU);
previous_emax = expo.saved_emax;
MPFR_SAVE_EXPO_FREE (expo);
}
/* mpfr_cmp works even in reduced emin,emax range */
if (MPFR_UNLIKELY (mpfr_cmp (x, bound_emax) >= 0))
{
/* x > log(2^emax), thus exp(x) > 2^emax */
return mpfr_overflow (y, rnd_mode, 1);
}
/* emin bound is cached. Check if the value in cache is ok */
if (MPFR_UNLIKELY (mpfr_get_emin() != previous_emin))
{
mp_limb_t e_limb[MPFR_EXP_LIMB_SIZE];
mpfr_t e;
/* We extend the exponent range and save the flags. */
MPFR_SAVE_EXPO_MARK (expo);
/* avoid using a full limb since arithmetic might be slower */
MPFR_TMP_INIT1(e_limb, e, sizeof (mpfr_exp_t) * CHAR_BIT - 1);
MPFR_TMP_INIT1(bound_emin_limb, bound_emin, 32);
inexact = mpfr_set_exp_t (e, expo.saved_emin, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
inexact = mpfr_sub_ui (e, e, 2, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
mpfr_const_log2 (bound_emin, expo.saved_emin < 0 ? MPFR_RNDU : MPFR_RNDD);
mpfr_mul (bound_emin, bound_emin, e, MPFR_RNDD);
previous_emin = expo.saved_emin;
MPFR_SAVE_EXPO_FREE (expo);
}
if (MPFR_UNLIKELY (mpfr_cmp (x, bound_emin) <= 0))
{
/* x < log(2^(emin - 2)), thus exp(x) < 2^(emin - 2) */
return mpfr_underflow (y, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
1);
}
expx = MPFR_GET_EXP (x);
precy = MPFR_PREC (y);
/* if x < 2^(-precy), then exp(x) gives 1 +/- 1 ulp(1) */
if (MPFR_UNLIKELY (expx < 0 && (mpfr_uexp_t) (-expx) > precy))
{
mpfr_exp_t emin = __gmpfr_emin;
mpfr_exp_t emax = __gmpfr_emax;
int signx = MPFR_SIGN (x);
/* Make sure that the exponent range is large enough:
* [0,2] is sufficient in all precisions.
*/
__gmpfr_emin = 0;
__gmpfr_emax = 2;
MPFR_SET_POS (y);
if (MPFR_IS_NEG_SIGN (signx) && (rnd_mode == MPFR_RNDD ||
rnd_mode == MPFR_RNDZ))
{
mpfr_setmax (y, 0); /* y = 1 - epsilon */
inexact = -1;
}
else
{
mpfr_setmin (y, 1); /* y = 1 */
if (MPFR_IS_POS_SIGN (signx) && (rnd_mode == MPFR_RNDU ||
rnd_mode == MPFR_RNDA))
{
/* Warning: should work for precision 1 bit too! */
mpfr_nextabove (y);
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_UPDATE_FLAGS (expo, __gmpfr_flags);
MPFR_SAVE_EXPO_FREE (expo);
}
}
return mpfr_check_range (y, inexact, rnd_mode);
}
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