113 lines
2.9 KiB
C
113 lines
2.9 KiB
C
/* mpz_divexact_gcd -- exact division optimized for GCDs.
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THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE AND ARE ALMOST CERTAIN TO
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BE SUBJECT TO INCOMPATIBLE CHANGES IN FUTURE GNU MP RELEASES.
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Copyright 2000, 2005 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP 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 Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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/* Set q to a/d, expecting d to be from a GCD and therefore usually small.
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The distribution of GCDs of random numbers can be found in Knuth volume 2
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section 4.5.2 theorem D.
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GCD chance
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1 60.8%
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2^k 20.2% (1<=k<32)
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3*2^k 9.0% (1<=k<32)
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other 10.1%
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Only the low limb is examined for optimizations, since GCDs bigger than
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2^32 (or 2^64) will occur very infrequently.
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Future: This could change to an mpn_divexact_gcd, possibly partly
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inlined, if/when the relevant mpq functions change to an mpn based
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implementation. */
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static void
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mpz_divexact_by3 (mpz_ptr q, mpz_srcptr a)
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{
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mp_size_t size = SIZ(a);
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if (size == 0)
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{
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SIZ(q) = 0;
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return;
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}
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else
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{
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mp_size_t abs_size = ABS(size);
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mp_ptr qp;
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MPZ_REALLOC (q, abs_size);
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qp = PTR(q);
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mpn_divexact_by3 (qp, PTR(a), abs_size);
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abs_size -= (qp[abs_size-1] == 0);
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SIZ(q) = (size>0 ? abs_size : -abs_size);
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}
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}
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void
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mpz_divexact_gcd (mpz_ptr q, mpz_srcptr a, mpz_srcptr d)
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{
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ASSERT (mpz_sgn (d) > 0);
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if (SIZ(d) == 1)
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{
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mp_limb_t dl = PTR(d)[0];
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int twos;
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if (dl == 1)
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{
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if (q != a)
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mpz_set (q, a);
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return;
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}
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if (dl == 3)
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{
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mpz_divexact_by3 (q, a);
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return;
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}
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count_trailing_zeros (twos, dl);
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dl >>= twos;
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if (dl == 1)
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{
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mpz_tdiv_q_2exp (q, a, twos);
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return;
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}
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if (dl == 3)
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{
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mpz_tdiv_q_2exp (q, a, twos);
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mpz_divexact_by3 (q, q);
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return;
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}
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}
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mpz_divexact (q, a, d);
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}
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