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/* kara_sqrtrem -- Karatsuba square root
Copyright (C) 1999-2000 PolKA project, Inria Lorraine and Loria
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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library 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. */
/* Reference: Karatsuba Square Root, Paul Zimmermann, Research Report 3805,
INRIA, November 1999. */
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#define SQRT_LIMIT KARATSUBA_MUL_THRESHOLD /* must be at least 3, should be
near from optimal */
/* n must be even */
mp_size_t kara_sqrtrem(mp_limb_t *s, mp_limb_t *r, mp_limb_t *op, mp_size_t n)
{
if (n<SQRT_LIMIT) return mpn_sqrtrem(s, r, op, n);
else {
mp_size_t nn, rn, rrn, sn, qn; mp_limb_t *q, tmp;
TMP_DECL (marker);
TMP_MARK (marker);
nn = n/4; /* block size 'b' corresponds to nn limbs */
rn = kara_sqrtrem(s+nn, r+nn, op+2*nn, n-2*nn);
/* rn <= ceil(n-2*nn, 2) + 1 <= ceil(2*nn+3, 2) + 1 <= nn+3 */
/* to divide by 2*s', first divide by 2, to ensure the dividend is
less than b^2 */
sn=(n-2*nn+1)/2; /* sn >= nn */
MPN_COPY(r, op+nn, nn); /* copy a_1 */
tmp = mpn_rshift(r, r, nn+rn, 1);
if (r[nn+rn-1]==0) rn--;
q = (mp_limb_t*) TMP_ALLOC(2*(sn+1)*sizeof(mp_limb_t));
if (nn+rn < 2*sn) MPN_ZERO(r+nn+rn, 2*sn-nn-rn);
qn = sn; if (mpn_cmp(r+sn, s+nn, sn)>=0) {
q[qn++]=1; mpn_sub_n(r+sn, r+sn, s+nn, sn);
}
mpn_divrem(q, 0, r, 2*sn, s+nn, sn);
while (qn>nn && q[qn-1]==0) qn--;
MPN_COPY(s, q, nn);
if (nn+rn > 2*sn) {
tmp=mpn_add_n(s+sn, s+sn, q+sn, nn+rn-2*sn);
if (tmp) mpn_add_1(s+nn+rn-sn, s+nn+rn-sn, (n+1)/2-nn-rn+sn, tmp);
}
/* multiply remainder by two and add low bit of a_1 */
rrn = nn+sn; /* size of output remainder */
rrn += mpn_lshift(r+nn, r, sn, 1);
r[nn] |= (op[nn] & 1);
sn += nn;
if (qn>nn) {
MPN_COPY(r, s+nn, qn-nn); /* save the qn-nn limbs from s */
MPN_COPY(s+nn, q+nn, qn-nn); /* replace by those of q */
}
mpn_mul_n(q, s, s, qn);
if (qn>nn) { /* restore the limbs from s, adding them to those of q */
mp_limb_t cy;
cy = mpn_add_n(s+nn, s+nn, r, qn-nn);
if (qn<sn) cy = mpn_add_1(s+qn, s+qn, sn-qn, cy);
if (cy) s[sn++]=1;
}
MPN_COPY(r, op, nn); /* copy a_0 */
qn = 2*qn;
if (qn<sn) MPN_ZERO(q+qn, sn-qn);
if (rrn<sn) MPN_ZERO(r+rrn, sn-rrn);
if (mpn_sub_n(r, r, q, sn) || (qn>sn)) {
if (rrn>sn) rrn=sn;
else {
/* one shift and one add is faster than two add's */
r[sn] = mpn_lshift(q, s, sn, 1) + mpn_add_n(r, r, q, sn)
- mpn_sub_1(r, r, sn, 1) - 1;
rrn = sn + r[sn];
mpn_sub_1(s, s, sn, 1);
}
}
else if (rrn>sn) r[sn]=1;
TMP_FREE (marker);
MPN_NORMALIZE(r, rrn);
return rrn;
}
}
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