259 lines
7.2 KiB
C
259 lines
7.2 KiB
C
/* mpn_divrem_1 -- mpn by limb division.
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Copyright 1991, 1993, 1994, 1996, 1998, 1999, 2000, 2002, 2003 Free Software
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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 "mpir.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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/* The size where udiv_qrnnd_preinv should be used rather than udiv_qrnnd,
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meaning the quotient size where that should happen, the quotient size
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being how many udiv divisions will be done.
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The default is to use preinv always, CPUs where this doesn't suit have
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tuned thresholds. Note in particular that preinv should certainly be
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used if that's the only division available (USE_PREINV_ALWAYS). */
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#ifndef DIVREM_1_NORM_THRESHOLD
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#define DIVREM_1_NORM_THRESHOLD 0
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#endif
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#ifndef DIVREM_1_UNNORM_THRESHOLD
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#define DIVREM_1_UNNORM_THRESHOLD 0
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#endif
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/* If the cpu only has multiply-by-inverse division (eg. alpha), then NORM
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and UNNORM thresholds are 0 and only the inversion code is included.
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If multiply-by-inverse is never viable, then NORM and UNNORM thresholds
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will be MP_SIZE_T_MAX and only the plain division code is included.
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Otherwise mul-by-inverse is better than plain division above some
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threshold, and best results are obtained by having code for both present.
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The main reason for separating the norm and unnorm cases is that not all
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CPUs give zero for "n0 >> BITS_PER_MP_LIMB" which would arise in the
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unnorm code used on an already normalized divisor.
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If UDIV_NEEDS_NORMALIZATION is false then plain division uses the same
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non-shifting code for both the norm and unnorm cases, though with
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different criteria for skipping a division, and with different thresholds
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of course. And in fact if inversion is never viable, then that simple
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non-shifting division would be all that's left.
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The NORM and UNNORM thresholds might not differ much, but if there's
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going to be separate code for norm and unnorm then it makes sense to have
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separate thresholds. One thing that's possible is that the
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mul-by-inverse might be better only for normalized divisors, due to that
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case not needing variable bit shifts.
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Notice that the thresholds are tested after the decision to possibly skip
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one divide step, so they're based on the actual number of divisions done.
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For the unnorm case, it would be possible to call mpn_lshift to adjust
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the dividend all in one go (into the quotient space say), rather than
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limb-by-limb in the loop. This might help if mpn_lshift is a lot faster
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than what the compiler can generate for EXTRACT. But this is left to CPU
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specific implementations to consider, especially since EXTRACT isn't on
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the dependent chain. */
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mp_limb_t
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mpn_divrem_1 (mp_ptr qp, mp_size_t qxn,
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mp_srcptr up, mp_size_t un, mp_limb_t d)
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{
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mp_size_t n;
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mp_size_t i;
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mp_limb_t n1, n0;
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mp_limb_t r = 0;
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ASSERT (qxn >= 0);
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ASSERT (un >= 0);
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ASSERT (d != 0);
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/* FIXME: What's the correct overlap rule when qxn!=0? */
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ASSERT (MPN_SAME_OR_SEPARATE_P (qp+qxn, up, un));
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n = un + qxn;
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if (n == 0)
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return 0;
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d <<= GMP_NAIL_BITS;
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if(qxn==0)
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{
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if(d<=GMP_LIMB_HIGHBIT/2+1 && ABOVE_THRESHOLD(un,DIVREM_EUCLID_HENSEL_THRESHOLD))
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{r=mpn_divrem_euclidean_r_1(up,un,d);
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count_trailing_zeros(i,d);
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mpn_rsh_divrem_hensel_qr_1(qp,up,un,d>>i,i,r);
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return r;}
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#if HAVE_NATIVE_mpn_divrem_euclidean_qr_1
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return mpn_divrem_euclidean_qr_1(qp,0,up,un,d);
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#endif
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}
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qp += (n - 1); /* Make qp point at most significant quotient limb */
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if ((d & GMP_LIMB_HIGHBIT) != 0)
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{
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if (un != 0)
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{
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/* High quotient limb is 0 or 1, skip a divide step. */
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mp_limb_t q;
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r = up[un - 1] << GMP_NAIL_BITS;
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q = (r >= d);
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*qp-- = q;
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r -= (d & -q);
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r >>= GMP_NAIL_BITS;
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n--;
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un--;
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}
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if (BELOW_THRESHOLD (n, DIVREM_1_NORM_THRESHOLD))
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{
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plain:
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for (i = un - 1; i >= 0; i--)
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{
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n0 = up[i] << GMP_NAIL_BITS;
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udiv_qrnnd (*qp, r, r, n0, d);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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for (i = qxn - 1; i >= 0; i--)
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{
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udiv_qrnnd (*qp, r, r, CNST_LIMB(0), d);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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return r;
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}
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else
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{
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/* Multiply-by-inverse, divisor already normalized. */
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mp_limb_t dinv;
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invert_limb (dinv, d);
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for (i = un - 1; i >= 0; i--)
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{
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n0 = up[i] << GMP_NAIL_BITS;
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udiv_qrnnd_preinv (*qp, r, r, n0, d, dinv);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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for (i = qxn - 1; i >= 0; i--)
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{
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udiv_qrnnd_preinv (*qp, r, r, CNST_LIMB(0), d, dinv);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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return r;
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}
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}
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else
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{
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/* Most significant bit of divisor == 0. */
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int norm;
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/* Skip a division if high < divisor (high quotient 0). Testing here
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before normalizing will still skip as often as possible. */
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if (un != 0)
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{
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n1 = up[un - 1] << GMP_NAIL_BITS;
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if (n1 < d)
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{
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r = n1 >> GMP_NAIL_BITS;
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*qp-- = 0;
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n--;
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if (n == 0)
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return r;
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un--;
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}
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}
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if (! UDIV_NEEDS_NORMALIZATION
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&& BELOW_THRESHOLD (n, DIVREM_1_UNNORM_THRESHOLD))
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goto plain;
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count_leading_zeros (norm, d);
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d <<= norm;
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r <<= norm;
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if (UDIV_NEEDS_NORMALIZATION
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&& BELOW_THRESHOLD (n, DIVREM_1_UNNORM_THRESHOLD))
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{
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if (un != 0)
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{
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n1 = up[un - 1] << GMP_NAIL_BITS;
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r |= (n1 >> (GMP_LIMB_BITS - norm));
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for (i = un - 2; i >= 0; i--)
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{
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n0 = up[i] << GMP_NAIL_BITS;
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udiv_qrnnd (*qp, r, r,
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(n1 << norm) | (n0 >> (GMP_NUMB_BITS - norm)),
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d);
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r >>= GMP_NAIL_BITS;
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qp--;
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n1 = n0;
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}
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udiv_qrnnd (*qp, r, r, n1 << norm, d);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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for (i = qxn - 1; i >= 0; i--)
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{
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udiv_qrnnd (*qp, r, r, CNST_LIMB(0), d);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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return r >> norm;
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}
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else
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{
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mp_limb_t dinv;
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invert_limb (dinv, d);
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if (un != 0)
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{
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n1 = up[un - 1] << GMP_NAIL_BITS;
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r |= (n1 >> (GMP_LIMB_BITS - norm));
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for (i = un - 2; i >= 0; i--)
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{
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n0 = up[i] << GMP_NAIL_BITS;
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udiv_qrnnd_preinv (*qp, r, r,
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((n1 << norm) | (n0 >> (GMP_NUMB_BITS - norm))),
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d, dinv);
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r >>= GMP_NAIL_BITS;
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qp--;
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n1 = n0;
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}
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udiv_qrnnd_preinv (*qp, r, r, n1 << norm, d, dinv);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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for (i = qxn - 1; i >= 0; i--)
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{
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udiv_qrnnd_preinv (*qp, r, r, CNST_LIMB(0), d, dinv);
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r >>= GMP_NAIL_BITS;
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qp--;
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}
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return r >> norm;
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}
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}
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}
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