mirror of https://github.com/macssh/macssh.git
103 lines
3.4 KiB
C
Executable File
103 lines
3.4 KiB
C
Executable File
/* kara_sqrtrem -- Karatsuba square root
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Copyright (C) 1999-2000 PolKA project, Inria Lorraine and Loria
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This file is part of the MPFR Library.
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The MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Library General Public License as published by
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the Free Software Foundation; either version 2 of the License, or (at your
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option) any later version.
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The MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
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License for more details.
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You should have received a copy of the GNU Library General Public License
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along with the MPFR Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
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MA 02111-1307, USA. */
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/* Reference: Karatsuba Square Root, Paul Zimmermann, Research Report 3805,
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INRIA, November 1999. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "mpfr.h"
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#define SQRT_LIMIT KARATSUBA_MUL_THRESHOLD /* must be at least 3, should be
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near from optimal */
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/* n must be even */
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mp_size_t kara_sqrtrem(mp_limb_t *s, mp_limb_t *r, mp_limb_t *op, mp_size_t n)
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{
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if (n<SQRT_LIMIT) return mpn_sqrtrem(s, r, op, n);
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else {
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mp_size_t nn, rn, rrn, sn, qn; mp_limb_t *q, tmp;
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TMP_DECL (marker);
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TMP_MARK (marker);
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nn = n/4; /* block size 'b' corresponds to nn limbs */
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rn = kara_sqrtrem(s+nn, r+nn, op+2*nn, n-2*nn);
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/* rn <= ceil(n-2*nn, 2) + 1 <= ceil(2*nn+3, 2) + 1 <= nn+3 */
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/* to divide by 2*s', first divide by 2, to ensure the dividend is
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less than b^2 */
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sn=(n-2*nn+1)/2; /* sn >= nn */
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MPN_COPY(r, op+nn, nn); /* copy a_1 */
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tmp = mpn_rshift(r, r, nn+rn, 1);
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if (r[nn+rn-1]==0) rn--;
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q = (mp_limb_t*) TMP_ALLOC(2*(sn+1)*sizeof(mp_limb_t));
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if (nn+rn < 2*sn) MPN_ZERO(r+nn+rn, 2*sn-nn-rn);
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qn = sn; if (mpn_cmp(r+sn, s+nn, sn)>=0) {
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q[qn++]=1; mpn_sub_n(r+sn, r+sn, s+nn, sn);
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}
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#if 0
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mpn_divrem(q, 0, r, 2*sn, s+nn, sn);
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#else
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mpn_divrem_n(q, r, s+nn, sn);
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#endif
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while (qn>nn && q[qn-1]==0) qn--;
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MPN_COPY(s, q, nn);
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if (nn+rn > 2*sn) {
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tmp=mpn_add_n(s+sn, s+sn, q+sn, nn+rn-2*sn);
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if (tmp) mpn_add_1(s+nn+rn-sn, s+nn+rn-sn, (n+1)/2-nn-rn+sn, tmp);
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}
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/* multiply remainder by two and add low bit of a_1 */
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rrn = nn+sn; /* size of output remainder */
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rrn += mpn_lshift(r+nn, r, sn, 1);
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r[nn] |= (op[nn] & 1);
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sn += nn;
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if (qn>nn) {
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MPN_COPY(r, s+nn, qn-nn); /* save the qn-nn limbs from s */
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MPN_COPY(s+nn, q+nn, qn-nn); /* replace by those of q */
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}
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mpn_mul_n(q, s, s, qn);
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if (qn>nn) { /* restore the limbs from s, adding them to those of q */
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mp_limb_t cy;
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cy = mpn_add_n(s+nn, s+nn, r, qn-nn);
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if (qn<sn) cy = mpn_add_1(s+qn, s+qn, sn-qn, cy);
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if (cy) s[sn++]=1;
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}
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MPN_COPY(r, op, nn); /* copy a_0 */
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qn = 2*qn;
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if (qn<sn) MPN_ZERO(q+qn, sn-qn);
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if (rrn<sn) MPN_ZERO(r+rrn, sn-rrn);
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if (mpn_sub_n(r, r, q, sn) || (qn>sn)) {
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if (rrn>sn) rrn=sn;
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else {
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/* one shift and one add is faster than two add's */
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r[sn] = mpn_lshift(q, s, sn, 1) + mpn_add_n(r, r, q, sn)
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- mpn_sub_1(r, r, sn, 1) - 1;
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rrn = sn + r[sn];
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mpn_sub_1(s, s, sn, 1);
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}
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}
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else if (rrn>sn) r[sn]=1;
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TMP_FREE (marker);
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MPN_NORMALIZE(r, rrn);
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return rrn;
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}
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}
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