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/* mpc_pow_ui -- Raise a complex number to an integer power.
Copyright (C) 2009, 2010, 2011, 2012 INRIA
This file is part of GNU MPC.
GNU MPC 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.
GNU MPC 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 this program. If not, see http://www.gnu.org/licenses/ .
*/
#include <limits.h> /* for CHAR_BIT */
#include "mpc-impl.h"
static int
mpc_pow_usi_naive (mpc_ptr z, mpc_srcptr x, unsigned long y, int sign,
mpc_rnd_t rnd)
{
int inex;
mpc_t t;
mpc_init3 (t, sizeof (unsigned long) * CHAR_BIT, MPFR_PREC_MIN);
if (sign > 0)
mpc_set_ui (t, y, MPC_RNDNN); /* exact */
else
mpc_set_si (t, - (signed long) y, MPC_RNDNN);
inex = mpc_pow (z, x, t, rnd);
mpc_clear (t);
return inex;
}
int
mpc_pow_usi (mpc_ptr z, mpc_srcptr x, unsigned long y, int sign,
mpc_rnd_t rnd)
/* computes z = x^(sign*y) */
{
int inex;
mpc_t t, x3;
mpfr_prec_t p, l, l0;
long unsigned int u;
int has3; /* non-zero if y has '11' in its binary representation */
int loop, done;
/* let mpc_pow deal with special values */
if (!mpc_fin_p (x) || mpfr_zero_p (mpc_realref (x)) || mpfr_zero_p (mpc_imagref(x))
|| y == 0)
return mpc_pow_usi_naive (z, x, y, sign, rnd);
/* easy special cases */
else if (y == 1) {
if (sign > 0)
return mpc_set (z, x, rnd);
else
return mpc_ui_div (z, 1ul, x, rnd);
}
else if (y == 2 && sign > 0)
return mpc_sqr (z, x, rnd);
/* let mpc_pow treat potential over- and underflows */
else {
mpfr_exp_t exp_r = mpfr_get_exp (mpc_realref (x)),
exp_i = mpfr_get_exp (mpc_imagref (x));
if ( MPC_MAX (exp_r, exp_i) > mpfr_get_emax () / (mpfr_exp_t) y
/* heuristic for overflow */
|| MPC_MAX (-exp_r, -exp_i) > (-mpfr_get_emin ()) / (mpfr_exp_t) y
/* heuristic for underflow */
)
return mpc_pow_usi_naive (z, x, y, sign, rnd);
}
has3 = (y & (y >> 1)) != 0;
for (l = 0, u = y; u > 3; l ++, u >>= 1);
/* l>0 is the number of bits of y, minus 2, thus y has bits:
y_{l+1} y_l y_{l-1} ... y_1 y_0 */
l0 = l + 2;
p = MPC_MAX_PREC(z) + l0 + 32; /* l0 ensures that y*2^{-p} <= 1 below */
mpc_init2 (t, p);
if (has3)
mpc_init2 (x3, p);
loop = 0;
done = 0;
while (!done) {
loop++;
mpc_sqr (t, x, MPC_RNDNN);
if (has3) {
mpc_mul (x3, t, x, MPC_RNDNN);
if ((y >> l) & 1) /* y starts with 11... */
mpc_set (t, x3, MPC_RNDNN);
}
while (l-- > 0) {
mpc_sqr (t, t, MPC_RNDNN);
if ((y >> l) & 1) {
if ((l > 0) && ((y >> (l-1)) & 1)) /* implies has3 <> 0 */ {
l--;
mpc_sqr (t, t, MPC_RNDNN);
mpc_mul (t, t, x3, MPC_RNDNN);
}
else
mpc_mul (t, t, x, MPC_RNDNN);
}
}
if (sign < 0)
mpc_ui_div (t, 1ul, t, MPC_RNDNN);
if (mpfr_zero_p (mpc_realref(t)) || mpfr_zero_p (mpc_imagref(t))) {
inex = mpc_pow_usi_naive (z, x, y, sign, rnd);
/* since mpfr_get_exp() is not defined for zero */
done = 1;
}
else {
/* see error bound in algorithms.tex; we use y<2^l0 instead of y-1
also when sign>0 */
mpfr_exp_t diff;
mpfr_prec_t er, ei;
diff = mpfr_get_exp (mpc_realref(t)) - mpfr_get_exp (mpc_imagref(t));
/* the factor on the real part is 2+2^(-diff+2) <= 4 for diff >= 1
and < 2^(-diff+3) for diff <= 0 */
er = (diff >= 1) ? l0 + 3 : l0 + (-diff) + 3;
/* the factor on the imaginary part is 2+2^(diff+2) <= 4 for diff <= -1
and < 2^(diff+3) for diff >= 0 */
ei = (diff <= -1) ? l0 + 3 : l0 + diff + 3;
if (mpfr_can_round (mpc_realref(t), p - er, GMP_RNDN, GMP_RNDZ,
MPC_PREC_RE(z) + (MPC_RND_RE(rnd) == GMP_RNDN))
&& mpfr_can_round (mpc_imagref(t), p - ei, GMP_RNDN, GMP_RNDZ,
MPC_PREC_IM(z) + (MPC_RND_IM(rnd) == GMP_RNDN))) {
inex = mpc_set (z, t, rnd);
done = 1;
}
else if (loop == 1 && SAFE_ABS(mpfr_prec_t, diff) < MPC_MAX_PREC(z)) {
/* common case, make a second trial at higher precision */
p += MPC_MAX_PREC(x);
mpc_set_prec (t, p);
if (has3)
mpc_set_prec (x3, p);
l = l0 - 2;
}
else {
/* stop the loop and use mpc_pow */
inex = mpc_pow_usi_naive (z, x, y, sign, rnd);
done = 1;
}
}
}
mpc_clear (t);
if (has3)
mpc_clear (x3);
return inex;
}
int
mpc_pow_ui (mpc_ptr z, mpc_srcptr x, unsigned long y, mpc_rnd_t rnd)
{
return mpc_pow_usi (z, x, y, 1, rnd);
}
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