mod_1.c
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上传日期:2022-08-06
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- /* mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) --
- Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
- Return the single-limb remainder.
- There are no constraints on the value of the divisor.
- Copyright 1991, 1993, 1994, 1999, 2000, 2002, 2007, 2008, 2009 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 MOD_1_NORM_THRESHOLD
- #define MOD_1_NORM_THRESHOLD 0
- #endif
- #ifndef MOD_1_UNNORM_THRESHOLD
- #define MOD_1_UNNORM_THRESHOLD 0
- #endif
- #ifndef MOD_1U_TO_MOD_1_1_THRESHOLD
- #define MOD_1U_TO_MOD_1_1_THRESHOLD MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */
- #endif
- #ifndef MOD_1N_TO_MOD_1_1_THRESHOLD
- #define MOD_1N_TO_MOD_1_1_THRESHOLD MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */
- #endif
- #ifndef MOD_1_1_TO_MOD_1_2_THRESHOLD
- #define MOD_1_1_TO_MOD_1_2_THRESHOLD 10
- #endif
- #ifndef MOD_1_2_TO_MOD_1_4_THRESHOLD
- #define MOD_1_2_TO_MOD_1_4_THRESHOLD 20
- #endif
- /* The comments in mpn/generic/divrem_1.c apply here too.
- As noted in the algorithms section of the manual, the shifts in the loop
- for the unnorm case can be avoided by calculating r = a%(d*2^n), followed
- by a final (r*2^n)%(d*2^n). In fact if it happens that a%(d*2^n) can
- skip a division where (a*2^n)%(d*2^n) can't then there's the same number
- of divide steps, though how often that happens depends on the assumed
- distributions of dividend and divisor. In any case this idea is left to
- CPU specific implementations to consider. */
- static mp_limb_t
- mpn_mod_1_unnorm (mp_srcptr up, mp_size_t un, mp_limb_t d)
- {
- mp_size_t i;
- mp_limb_t n1, n0, r;
- mp_limb_t dummy;
- int cnt;
- ASSERT (un > 0);
- ASSERT (d != 0);
- d <<= GMP_NAIL_BITS;
- /* Skip a division if high < divisor. Having the test here before
- normalizing will still skip as often as possible. */
- r = up[un - 1] << GMP_NAIL_BITS;
- if (r < d)
- {
- r >>= GMP_NAIL_BITS;
- un--;
- if (un == 0)
- return r;
- }
- else
- r = 0;
- /* If udiv_qrnnd doesn't need a normalized divisor, can use the simple
- code above. */
- if (! UDIV_NEEDS_NORMALIZATION
- && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD))
- {
- for (i = un - 1; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd (dummy, r, r, n0, d);
- r >>= GMP_NAIL_BITS;
- }
- return r;
- }
- count_leading_zeros (cnt, d);
- d <<= cnt;
- n1 = up[un - 1] << GMP_NAIL_BITS;
- r = (r << cnt) | (n1 >> (GMP_LIMB_BITS - cnt));
- if (UDIV_NEEDS_NORMALIZATION
- && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD))
- {
- for (i = un - 2; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd (dummy, r, r,
- (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt)),
- d);
- r >>= GMP_NAIL_BITS;
- n1 = n0;
- }
- udiv_qrnnd (dummy, r, r, n1 << cnt, d);
- r >>= GMP_NAIL_BITS;
- return r >> cnt;
- }
- else
- {
- mp_limb_t inv;
- invert_limb (inv, d);
- for (i = un - 2; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd_preinv (dummy, r, r,
- (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt)),
- d, inv);
- r >>= GMP_NAIL_BITS;
- n1 = n0;
- }
- udiv_qrnnd_preinv (dummy, r, r, n1 << cnt, d, inv);
- r >>= GMP_NAIL_BITS;
- return r >> cnt;
- }
- }
- static mp_limb_t
- mpn_mod_1_norm (mp_srcptr up, mp_size_t un, mp_limb_t d)
- {
- mp_size_t i;
- mp_limb_t n0, r;
- mp_limb_t dummy;
- ASSERT (un > 0);
- d <<= GMP_NAIL_BITS;
- ASSERT (d & GMP_LIMB_HIGHBIT);
- /* High limb is initial remainder, possibly with one subtract of
- d to get r<d. */
- r = up[un - 1] << GMP_NAIL_BITS;
- if (r >= d)
- r -= d;
- r >>= GMP_NAIL_BITS;
- un--;
- if (un == 0)
- return r;
- if (BELOW_THRESHOLD (un, MOD_1_NORM_THRESHOLD))
- {
- for (i = un - 1; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd (dummy, r, r, n0, d);
- r >>= GMP_NAIL_BITS;
- }
- return r;
- }
- else
- {
- mp_limb_t inv;
- invert_limb (inv, d);
- for (i = un - 1; i >= 0; i--)
- {
- n0 = up[i] << GMP_NAIL_BITS;
- udiv_qrnnd_preinv (dummy, r, r, n0, d, inv);
- r >>= GMP_NAIL_BITS;
- }
- return r;
- }
- }
- mp_limb_t
- mpn_mod_1 (mp_srcptr ap, mp_size_t n, mp_limb_t b)
- {
- ASSERT (n >= 0);
- ASSERT (b != 0);
- /* Should this be handled at all? Rely on callers? Note un==0 is currently
- required by mpz/fdiv_r_ui.c and possibly other places. */
- if (n == 0)
- return 0;
- if (UNLIKELY ((b & GMP_NUMB_HIGHBIT) != 0))
- {
- if (BELOW_THRESHOLD (n, MOD_1N_TO_MOD_1_1_THRESHOLD))
- {
- return mpn_mod_1_norm (ap, n, b);
- }
- else
- {
- mp_limb_t pre[4];
- mpn_mod_1_1p_cps (pre, b);
- return mpn_mod_1_1p (ap, n, b, pre);
- }
- }
- else
- {
- if (BELOW_THRESHOLD (n, MOD_1U_TO_MOD_1_1_THRESHOLD))
- {
- return mpn_mod_1_unnorm (ap, n, b);
- }
- else if (BELOW_THRESHOLD (n, MOD_1_1_TO_MOD_1_2_THRESHOLD))
- {
- mp_limb_t pre[4];
- mpn_mod_1_1p_cps (pre, b);
- return mpn_mod_1_1p (ap, n, b << pre[1], pre);
- }
- else if (BELOW_THRESHOLD (n, MOD_1_2_TO_MOD_1_4_THRESHOLD) || UNLIKELY (b > GMP_NUMB_MASK / 4))
- {
- mp_limb_t pre[5];
- mpn_mod_1s_2p_cps (pre, b);
- return mpn_mod_1s_2p (ap, n, b << pre[1], pre);
- }
- else
- {
- mp_limb_t pre[7];
- mpn_mod_1s_4p_cps (pre, b);
- return mpn_mod_1s_4p (ap, n, b << pre[1], pre);
- }
- }
- }