175 lines
4.7 KiB
C
175 lines
4.7 KiB
C
/* 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 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 2.1 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; see the file COPYING.LIB. If not, write to
|
|
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
|
|
MA 02110-1301, USA. */
|
|
|
|
#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
|
|
|
|
|
|
/* 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. */
|
|
|
|
mp_limb_t
|
|
mpn_mod_1 (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;
|
|
|
|
ASSERT (un >= 0);
|
|
ASSERT (d != 0);
|
|
|
|
/* Botch: Should this be handled at all? Rely on callers?
|
|
But note un==0 is currently required by mpz/fdiv_r_ui.c and possibly
|
|
other places. */
|
|
if (un == 0)
|
|
return 0;
|
|
|
|
d <<= GMP_NAIL_BITS;
|
|
|
|
if ((d & GMP_LIMB_HIGHBIT) != 0)
|
|
{
|
|
/* 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))
|
|
{
|
|
plain:
|
|
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;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
int norm;
|
|
|
|
/* 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))
|
|
goto plain;
|
|
|
|
count_leading_zeros (norm, d);
|
|
d <<= norm;
|
|
|
|
n1 = up[un - 1] << GMP_NAIL_BITS;
|
|
r = (r << norm) | (n1 >> (GMP_LIMB_BITS - norm));
|
|
|
|
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 << norm) | (n0 >> (GMP_NUMB_BITS - norm)),
|
|
d);
|
|
r >>= GMP_NAIL_BITS;
|
|
n1 = n0;
|
|
}
|
|
udiv_qrnnd (dummy, r, r, n1 << norm, d);
|
|
r >>= GMP_NAIL_BITS;
|
|
return r >> norm;
|
|
}
|
|
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 << norm) | (n0 >> (GMP_NUMB_BITS - norm)),
|
|
d, inv);
|
|
r >>= GMP_NAIL_BITS;
|
|
n1 = n0;
|
|
}
|
|
udiv_qrnnd_preinv (dummy, r, r, n1 << norm, d, inv);
|
|
r >>= GMP_NAIL_BITS;
|
|
return r >> norm;
|
|
}
|
|
}
|
|
}
|