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/* mpfr_ui_pow -- power of n function n^x
Copyright 2001, 2002, 2003 Free Software Foundation, Inc.
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 <limits.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.h"
static int mpfr_ui_pow_is_exact _PROTO((unsigned long int, mpfr_srcptr));
/* return non zero iff x^y is exact.
Assumes y is a non-zero ordinary number (neither NaN nor Inf).
*/
static int
mpfr_ui_pow_is_exact (unsigned long int x, mpfr_srcptr y)
{
mp_exp_t d;
unsigned long i, c;
mp_limb_t *yp;
mp_size_t ysize;
if (mpfr_sgn (y) < 0) /* exact iff x = 2^k */
{
count_leading_zeros(c, x);
c = BITS_PER_MP_LIMB - c; /* number of bits of x */
return x == 1UL << (c - 1);
}
/* compute d such that y = c*2^d with c odd integer */
ysize = 1 + (MPFR_PREC(y) - 1) / BITS_PER_MP_LIMB;
d = MPFR_GET_EXP (y) - ysize * BITS_PER_MP_LIMB;
/* since y is not zero, necessarily one of the mantissa limbs is not zero,
thus we can simply loop until we find a non zero limb */
yp = MPFR_MANT(y);
for (i = 0; yp[i] == 0; i++, d += BITS_PER_MP_LIMB);
/* now yp[i] is not zero */
count_trailing_zeros (c, yp[i]);
d += c;
if (d < 0)
{
mpz_t a;
mp_exp_t b;
mpz_init_set_ui (a, x);
b = 0; /* x = a * 2^b */
c = mpz_scan1 (a, 0);
mpz_div_2exp (a, a, c);
b += c;
/* now a is odd */
while (d != 0)
{
if (mpz_perfect_square_p (a))
{
d++;
mpz_sqrt (a, a);
}
else
{
mpz_clear (a);
return 0;
}
}
mpz_clear (a);
}
return 1;
}
/* The computation of y=pow(n,z) is done by
y=exp(z*log(n))=n^z
*/
int
mpfr_ui_pow (mpfr_ptr y, unsigned long int n, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int inexact;
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y);
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) < 0)
{
MPFR_CLEAR_INF(y);
MPFR_SET_ZERO(y);
}
else
{
MPFR_SET_INF(y);
}
MPFR_SET_POS(y);
MPFR_RET(0);
}
/* n^0 = 1 */
if (MPFR_IS_ZERO(x))
return mpfr_set_ui (y, 1, rnd_mode);
inexact = mpfr_ui_pow_is_exact (n, x) == 0;
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te, ti;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
/* compute the precision of intermediary variable */
Nt = MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + 5 + __gmpfr_ceil_log2 (Nt);
/* initialise of intermediary variable */
mpfr_init2 (t, MPFR_PREC_MIN);
mpfr_init2 (ti, sizeof(unsigned long int) * CHAR_BIT);
mpfr_init2 (te, MPFR_PREC_MIN);
do
{
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
/* compute exp(x*ln(n)) */
mpfr_set_ui (ti, n, GMP_RNDN); /* ti <- n */
mpfr_log (t, ti, GMP_RNDU); /* ln(n) */
mpfr_mul (te, x, t, GMP_RNDU); /* x*ln(n) */
mpfr_exp (t, te, GMP_RNDN); /* exp(x*ln(n)) */
/* error estimate -- see pow function in algorithms.ps */
err = Nt - (MPFR_GET_EXP (te) + 3);
/* actualisation of the precision */
Nt += 10;
}
while (inexact &&
(err < 0 || !mpfr_can_round (t, err, GMP_RNDN, rnd_mode, Ny)));
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
}
return inexact;
}
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