divrem_1.c
上传用户:qaz666999
上传日期:2022-08-06
资源大小:2570k
文件大小:7k
- /* mpn_divrem_1 -- mpn by limb division.
- Copyright 1991, 1993, 1994, 1996, 1998, 1999, 2000, 2002, 2003 Free Software
- Foundation, Inc.
- This file is part of the GNU MP Library.
- The GNU MP Library 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.
- The GNU MP 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 Lesser General Public
- License for more details.
- You should have received a copy of the GNU Lesser General Public License
- along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
- #include "gmp.h"
- #include "gmp-impl.h"
- #include "longlong.h"
- /* The size where udiv_qrnnd_preinv should be used rather than udiv_qrnnd,
- meaning the quotient size where that should happen, the quotient size
- being how many udiv divisions will be done.
- The default is to use preinv always, CPUs where this doesn't suit have
- tuned thresholds. Note in particular that preinv should certainly be
- used if that's the only division available (USE_PREINV_ALWAYS). */
- #ifndef DIVREM_1_NORM_THRESHOLD
- #define DIVREM_1_NORM_THRESHOLD 0
- #endif
- #ifndef DIVREM_1_UNNORM_THRESHOLD
- #define DIVREM_1_UNNORM_THRESHOLD 0
- #endif
- /* If the cpu only has multiply-by-inverse division (eg. alpha), then NORM
- and UNNORM thresholds are 0 and only the inversion code is included.
- If multiply-by-inverse is never viable, then NORM and UNNORM thresholds
- will be MP_SIZE_T_MAX and only the plain division code is included.
- Otherwise mul-by-inverse is better than plain division above some
- threshold, and best results are obtained by having code for both present.
- The main reason for separating the norm and unnorm cases is that not all
- CPUs give zero for "n0 >> GMP_LIMB_BITS" which would arise in the unnorm
- code used on an already normalized divisor.
- If UDIV_NEEDS_NORMALIZATION is false then plain division uses the same
- non-shifting code for both the norm and unnorm cases, though with
- different criteria for skipping a division, and with different thresholds
- of course. And in fact if inversion is never viable, then that simple
- non-shifting division would be all that's left.
- The NORM and UNNORM thresholds might not differ much, but if there's
- going to be separate code for norm and unnorm then it makes sense to have
- separate thresholds. One thing that's possible is that the
- mul-by-inverse might be better only for normalized divisors, due to that
- case not needing variable bit shifts.
- Notice that the thresholds are tested after the decision to possibly skip
- one divide step, so they're based on the actual number of divisions done.
- For the unnorm case, it would be possible to call mpn_lshift to adjust
- the dividend all in one go (into the quotient space say), rather than
- limb-by-limb in the loop. This might help if mpn_lshift is a lot faster
- than what the compiler can generate for EXTRACT. But this is left to CPU
- specific implementations to consider, especially since EXTRACT isn't on
- the dependent chain. */
- mp_limb_t
- mpn_divrem_1 (mp_ptr qp, mp_size_t qxn,
- mp_srcptr up, mp_size_t un, mp_limb_t d)
- {
- mp_size_t n;
- mp_size_t i;
- mp_limb_t n1, n0;
- mp_limb_t r = 0;
- ASSERT (qxn >= 0);
- ASSERT (un >= 0);
- ASSERT (d != 0);
- /* FIXME: What's the correct overlap rule when qxn!=0? */
- ASSERT (MPN_SAME_OR_SEPARATE_P (qp+qxn, up, un));
- n = un + qxn;
- if (n == 0)
- return 0;
- d <<= GMP_NAIL_BITS;
- qp += (n - 1); /* Make qp point at most significant quotient limb */
- if ((d & GMP_LIMB_HIGHBIT) != 0)
- {
- if (un != 0)
- {
- /* High quotient limb is 0 or 1, skip a divide step. */
- mp_limb_t q;
- r = up[un - 1] << GMP_NAIL_BITS;
- q = (r >= d);
- *qp-- = q;
- r -= (d & -q);
- r >>= GMP_NAIL_BITS;
- n--;
- un--;
- }
- if (BELOW_THRESHOLD (n, DIVREM_1_NORM_THRESHOLD))
- {
- plain:
- for (i = un - 1; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd (*qp, r, r, n0, d);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- for (i = qxn - 1; i >= 0; i--)
- {
- udiv_qrnnd (*qp, r, r, CNST_LIMB(0), d);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- return r;
- }
- else
- {
- /* Multiply-by-inverse, divisor already normalized. */
- mp_limb_t dinv;
- invert_limb (dinv, d);
- for (i = un - 1; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd_preinv (*qp, r, r, n0, d, dinv);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- for (i = qxn - 1; i >= 0; i--)
- {
- udiv_qrnnd_preinv (*qp, r, r, CNST_LIMB(0), d, dinv);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- return r;
- }
- }
- else
- {
- /* Most significant bit of divisor == 0. */
- int norm;
- /* Skip a division if high < divisor (high quotient 0). Testing here
- before normalizing will still skip as often as possible. */
- if (un != 0)
- {
- n1 = up[un - 1] << GMP_NAIL_BITS;
- if (n1 < d)
- {
- r = n1 >> GMP_NAIL_BITS;
- *qp-- = 0;
- n--;
- if (n == 0)
- return r;
- un--;
- }
- }
- if (! UDIV_NEEDS_NORMALIZATION
- && BELOW_THRESHOLD (n, DIVREM_1_UNNORM_THRESHOLD))
- goto plain;
- count_leading_zeros (norm, d);
- d <<= norm;
- r <<= norm;
- if (UDIV_NEEDS_NORMALIZATION
- && BELOW_THRESHOLD (n, DIVREM_1_UNNORM_THRESHOLD))
- {
- if (un != 0)
- {
- n1 = up[un - 1] << GMP_NAIL_BITS;
- r |= (n1 >> (GMP_LIMB_BITS - norm));
- for (i = un - 2; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd (*qp, r, r,
- (n1 << norm) | (n0 >> (GMP_NUMB_BITS - norm)),
- d);
- r >>= GMP_NAIL_BITS;
- qp--;
- n1 = n0;
- }
- udiv_qrnnd (*qp, r, r, n1 << norm, d);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- for (i = qxn - 1; i >= 0; i--)
- {
- udiv_qrnnd (*qp, r, r, CNST_LIMB(0), d);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- return r >> norm;
- }
- else
- {
- mp_limb_t dinv;
- invert_limb (dinv, d);
- if (un != 0)
- {
- n1 = up[un - 1] << GMP_NAIL_BITS;
- r |= (n1 >> (GMP_LIMB_BITS - norm));
- for (i = un - 2; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd_preinv (*qp, r, r,
- ((n1 << norm) | (n0 >> (GMP_NUMB_BITS - norm))),
- d, dinv);
- r >>= GMP_NAIL_BITS;
- qp--;
- n1 = n0;
- }
- udiv_qrnnd_preinv (*qp, r, r, n1 << norm, d, dinv);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- for (i = qxn - 1; i >= 0; i--)
- {
- udiv_qrnnd_preinv (*qp, r, r, CNST_LIMB(0), d, dinv);
- r >>= GMP_NAIL_BITS;
- qp--;
- }
- return r >> norm;
- }
- }
- }