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/* mpfr_ui_pow_ui -- compute the power between two machine integers
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"
int
mpfr_ui_pow_ui (mpfr_ptr x, unsigned long int y, unsigned long int n,
mpfr_rnd_t rnd)
{
mpfr_exp_t err;
unsigned long m;
mpfr_t res;
mpfr_prec_t prec;
int size_n;
int inexact;
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY (n <= 1))
{
if (n == 1)
return mpfr_set_ui (x, y, rnd); /* y^1 = y */
else
return mpfr_set_ui (x, 1, rnd); /* y^0 = 1 for any y */
}
else if (MPFR_UNLIKELY (y <= 1))
{
if (y == 1)
return mpfr_set_ui (x, 1, rnd); /* 1^n = 1 for any n > 0 */
else
return mpfr_set_ui (x, 0, rnd); /* 0^n = 0 for any n > 0 */
}
for (size_n = 0, m = n; m; size_n++, m >>= 1);
MPFR_SAVE_EXPO_MARK (expo);
prec = MPFR_PREC (x) + 3 + size_n;
mpfr_init2 (res, prec);
MPFR_ZIV_INIT (loop, prec);
for (;;)
{
int i = size_n;
inexact = mpfr_set_ui (res, y, MPFR_RNDU);
err = 1;
/* now 2^(i-1) <= n < 2^i: i=1+floor(log2(n)) */
for (i -= 2; i >= 0; i--)
{
inexact |= mpfr_sqr (res, res, MPFR_RNDU);
err++;
if (n & (1UL << i))
inexact |= mpfr_mul_ui (res, res, y, MPFR_RNDU);
}
/* since the loop is executed floor(log2(n)) times,
we have err = 1+floor(log2(n)).
Since prec >= MPFR_PREC(x) + 4 + floor(log2(n)), prec > err */
err = prec - err;
if (MPFR_LIKELY (inexact == 0
|| MPFR_CAN_ROUND (res, err, MPFR_PREC (x), rnd)))
break;
/* Actualisation of the precision */
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (res, prec);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (x, res, rnd);
mpfr_clear (res);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (x, inexact, rnd);
}
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