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/* mpfr_pow_si -- power function x^y with y a signed int
Copyright 2001, 2002, 2003, 2004, 2005, 2006 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., 51 Franklin Place, Fifth Floor, Boston,
MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* The computation of y=pow(x,z) is done by
* y=pow_ui(x,z) if z>0
* else
* y=1/pow_ui(x,z) if z<0
*/
int
mpfr_pow_si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd_mode)
{
if (n >= 0)
return mpfr_pow_ui (y, x, n, rnd_mode);
else
{
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))
{
MPFR_SET_ZERO (y);
if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0)
MPFR_SET_POS (y);
else
MPFR_SET_NEG (y);
MPFR_RET (0);
}
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_INF(y);
if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0)
MPFR_SET_POS (y);
else
MPFR_SET_NEG (y);
MPFR_RET(0);
}
}
MPFR_CLEAR_FLAGS (y);
/* detect exact powers: x^(-n) is exact iff x is a power of 2 */
if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0)
{
mp_exp_t expx = MPFR_EXP (x); /* warning: x and y may be the same
variable */
mpfr_set_si (y, (n % 2) ? MPFR_INT_SIGN(x) : 1, rnd_mode);
expx --;
MPFR_ASSERTD (n < 0);
/* Warning n*expx may overflow!
Some systems abort with LONG_MIN / 1 or LONG_MIN/-1*/
if (n != -1 && expx > 0 && -expx < MPFR_EXP_MIN / (-n))
MPFR_EXP (y) = MPFR_EMIN_MIN - 1; /* Underflow */
else if (n != -1 && expx < 0 && -expx > MPFR_EXP_MAX / (-n))
MPFR_EXP (y) = MPFR_EMAX_MAX + 1; /* Overflow */
else
MPFR_EXP (y) += n * expx;
return mpfr_check_range (y, 0, rnd_mode);
}
n = -n;
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t;
/* Declaration of the size variable */
mp_prec_t Ny = MPFR_PREC (y); /* target precision */
mp_prec_t Nt; /* working precision */
mp_exp_t err; /* error */
int inexact;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
MPFR_SAVE_EXPO_MARK (expo);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute 1/(x^n) n>0*/
mpfr_pow_ui (t, x, (unsigned long int) n, GMP_RNDN);
inexact = MPFR_IS_ZERO (t) || MPFR_IS_INF (t);
mpfr_ui_div (t, 1, t, GMP_RNDN);
inexact = inexact || MPFR_IS_ZERO (t) || MPFR_IS_INF (t);
/* error estimate -- see pow function in algorithms.ps */
err = Nt - 3;
if (MPFR_LIKELY (inexact != 0
|| MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
/* actualisation of the precision */
Nt += BITS_PER_MP_LIMB;
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
}
}
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