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mpir/mpn/generic/divrem_euclidean_r_1.c

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/*
dnl Copyright 2009 Jason Moxham
dnl This file is part of the MPIR Library.
dnl The MPIR Library is free software; you can redistribute it and/or modify
dnl it under the terms of the GNU Lesser General Public License as published
dnl by the Free Software Foundation; either version 2.1 of the License, or (at
dnl your option) any later version.
dnl The MPIR Library is distributed in the hope that it will be useful, but
dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
dnl License for more details.
dnl You should have received a copy of the GNU Lesser General Public License
dnl along with the MPIR Library; see the file COPYING.LIB. If not, write
dnl to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
dnl Boston, MA 02110-1301, USA.
*/
#include "mpir.h"
#include "gmp-impl.h"
#include "longlong.h"
/* in each round we remove one limb from the body, i.e. k = 1 */
mp_limb_t mpn_mod_1_1_wrap(mp_srcptr xp, mp_size_t xn, mp_limb_t d)
{
mp_limb_t dummy, h, l, sh, sl, ret, i, c, ds, db[2], rem[2];
mp_size_t j;
ASSERT_MPN(xp, xn);
if (xn == 0)
return 0;
if (xn == 1)
return xp[0]%d;
ASSERT(d - 1 <= GMP_LIMB_HIGHBIT);
count_leading_zeros(c, d);
ds = d<<c;
invert_limb(i, ds);
udiv_qrnnd_preinv(dummy, db[0], ((mp_limb_t) 1)<<c, 0, ds, i); /* this is B%ds */
udiv_qrnnd_preinv(dummy, db[1], db[0], 0, ds, i); /* this is B^2%ds, could calc. indep. of db[0] */
db[0] >>= c;
db[1] >>= c; /* these are now B^i %d */
mpn_mod_1_1(rem, xp, xn, db);
sh = rem[1];
sl = rem[0];
ASSERT(sh < d);
udiv_qrnnd_preinv(dummy, ret, (sh<<c) | ((sl>>(GMP_LIMB_BITS - 1 - c))>>1), sl<<c, ds, i);
return ret>>c;
}
/* in each round we remove two limbs from the body, i.e. k = 2 */
mp_limb_t mpn_mod_1_2_wrap(mp_srcptr xp, mp_size_t xn, mp_limb_t d)
{
mp_limb_t dummy, h, l, sh, sl, th, tl, i, ret, ds, c, db[3], rem[2];
mp_size_t j;
ASSERT_MPN(xp, xn);
if (xn == 0)
return 0;
if (xn == 1)
return xp[0]%d;
umul_ppmm(h, l, d - 1, 3);
ASSERT(h == 0 || (h == 1 && l == 0)); /* i.e. (k + 1)(d - 1) <= B */
count_leading_zeros(c, d);
ds = d<<c;
invert_limb(i, ds);
udiv_qrnnd_preinv(dummy, db[0], ((mp_limb_t) 1)<<c, 0, ds, i);
udiv_qrnnd_preinv(dummy, db[1], db[0], 0, ds, i);
db[0]>>=c;
udiv_qrnnd_preinv(dummy, db[2], db[1], 0, ds, i);
db[1]>>=c;
db[2]>>=c;
mpn_mod_1_2(rem, xp, xn, db);
h = rem[1];
l = rem[0];
ASSERT(h < d);
udiv_qrnnd_preinv(dummy, ret, (h<<c) | ((l>>(GMP_LIMB_BITS - 1 - c))>>1), l<<c, ds, i);
return ret>>c;
}
/* in each round we remove 3 limbs from the body */
mp_limb_t mpn_mod_1_3_wrap(mp_srcptr xp, mp_size_t xn, mp_limb_t d)
{
mp_limb_t dummy, h, l, sh, sl, th, tl, i, ret, ds, c, db[4], rem[2];
mp_size_t j, jj;
ASSERT_MPN(xp, xn);
if (xn == 0)
return 0;
if (xn == 1)
return xp[0]%d;
umul_ppmm(h, l, d - 1, 4);
ASSERT(h == 0 || (h == 1 && l == 0)); /* i.e. (k + 1)(d - 1) <= B */
count_leading_zeros(c, d);
ds = d<<c;
invert_limb(i, ds);
udiv_qrnnd_preinv(dummy, db[0], ((mp_limb_t) 1)<<c, 0, ds, i);
udiv_qrnnd_preinv(dummy, db[1], db[0], 0, ds, i);
db[0]>>=c;
udiv_qrnnd_preinv(dummy, db[2], db[1], 0, ds, i);
db[1]>>=c;
udiv_qrnnd_preinv(dummy, db[3], db[2], 0, ds, i);
db[2]>>=c;
db[3]>>=c;
mpn_mod_1_3(rem, xp, xn, db);
h = rem[1];
l = rem[0];
ASSERT(h < d);
udiv_qrnnd_preinv(dummy, ret, (h<<c) | ((l>>(GMP_LIMB_BITS - 1 - c))>>1), l<<c, ds, i);
return ret>>c;
}
/*
This is a generic version for k >= 2
In each round we remove k limbs from the body
*/
mp_limb_t mpn_mod_1_k(mp_srcptr xp, mp_size_t xn, mp_limb_t d, mp_size_t k)
{
mp_limb_t dummy, h, l, sh, sl, th, tl, i, ret, ds, c, db[30]; /* need k + 1 entries in array */
mp_size_t j,jj;
ASSERT_MPN(xp, xn);
if (xn == 0)
return 0;
if (xn == 1)
return xp[0]%d;
ASSERT(k >= 2);
umul_ppmm(h, l, d - 1, k + 1);
ASSERT(h == 0 || (h == 1 && l == 0)); /* i.e. (k + 1)(d - 1) <= B */
count_leading_zeros(c, d);
ds = d<<c;
invert_limb(i, ds);
udiv_qrnnd_preinv(dummy, db[0], ((mp_limb_t) 1)<<c, 0, ds, i);
ASSERT_ALWAYS(k + 1 <= numberof(db));
for (j = 1; j <= k; j++)
{
udiv_qrnnd_preinv(dummy, db[j], db[j - 1], 0, ds, i);
db[j - 1]>>=c;
}
/* now db[j] = B^j % d */
db[k]>>=c;
tl = xp[xn - 2];
th = xp[xn - 1];
for (j = xn - k - 2; j >= 0; j -= k)
{
umul_ppmm(sh, sl, xp[j + 1], db[0]);
add_ssaaaa(sh, sl, sh, sl, 0, xp[j]);
for (jj = 2; jj <= k - 1; jj++)
{
umul_ppmm(h, l, xp[j + jj], db[jj - 1]);
add_ssaaaa(sh, sl, sh, sl, h, l);
}
umul_ppmm(h, l, tl, db[k - 1]);
add_ssaaaa(sh, sl, sh, sl, h, l);
umul_ppmm(th, tl, th, db[k]);
add_ssaaaa(th, tl, th, tl, sh, sl);
}
if (j + k > 0) /* we have at least three limbs to do i.e. xp[0], ..., tl, th */
{
sh = 0;
sl = xp[0];
for (jj = 1; jj < j + k; jj++)
{
umul_ppmm(h, l, xp[jj], db[jj - 1]);
add_ssaaaa(sh, sl, sh, sl, h, l);
}
umul_ppmm(h, l, tl, db[jj - 1]);
add_ssaaaa(sh, sl, sh, sl, h, l);
umul_ppmm(th, tl, th, db[jj]);
add_ssaaaa(th, tl, th, tl, sh, sl);
}
umul_ppmm(h, l, th, db[0]);
add_ssaaaa(h, l, h, l, 0, tl);
ASSERT(h < d);
udiv_qrnnd_preinv(dummy, ret, (h<<c) | (l>>(GMP_LIMB_BITS - c)), l<<c, ds, i);
return ret>>c;
}
/* d is mormalized */
#define udiv_inverse(i,d) \
do { \
mp_limb_t __X; \
udiv_qrnnd(i, __X, ~(d), GMP_LIMB_MAX, d); \
} while(0)
/*
note double length inverse can easily be calculated from single length inverse
d is normalised
*/
#define udiv_double_inverse(ih,il,d) \
do { \
mp_limb_t __X; \
udiv_qrnnd(ih, __X, ~(d), GMP_LIMB_MAX, d); \
udiv_qrnnd(il, __X, __X, GMP_LIMB_MAX, d); \
} while(0)
/* set to 1 = store or 0 = not store */
#define STORE_QUOTIENT 0
/* set to 0 = udiv, 1 = gmp-preinv, 2 = barrett */
#define UDIV_METHOD 1
#if UDIV_NEEDS_NORMALIZATION == 1 || UDIV_METHOD == 1
#define NORMALIZE 1
#else
#define NORMALIZE 0
#endif
#if UDIV_METHOD == 0
#define UDIV(q,r,h,l,d,i) udiv_qrnnd(q,r,h,l,d)
#endif
#if UDIV_METHOD == 1
#define UDIV udiv_qrnnd_preinv
#endif
#if UDIV_METHOD == 2
#define UDIV udiv_qrnnd_barrett
#endif
/*
(xp, n) = (qp, n)*d + r and 0 <= r < d
In hensel-div we use shiftout which means we can use mmx shifting and
dont need to always use it
In euclid-div shiftout needs a final div for the remainder
*/
#if STORE_QUOTIENT
mp_limb_t mpn_divrem_euclidean_qr_1(mp_ptr qp, mp_size_t qxn,
mp_srcptr xp, mp_size_t n, mp_limb_t d)
#else
mp_limb_t mpn_divrem_euclidean_r_1(mp_srcptr xp, mp_size_t n, mp_limb_t d)
#endif
{
mp_size_t j;
mp_limb_t r = 0, s = 0, h, l, q, i;
#if STORE_QUOTIENT
ASSET_ALWAYS(qxn == 0);
#endif
ASSERT(n > 0);
ASSERT(d != 0);
ASSERT_MPN(xp, n);
#if STORE_QUOTIENT
ASSERT(MPN_SAME_OR_SEPARATE_P(qp, xp, n));
#endif
if (d <= GMP_LIMB_HIGHBIT/2 + 1 && ABOVE_THRESHOLD(n, MOD_1_3_THRESHOLD))
return mpn_mod_1_3_wrap(xp, n, d);
if (d <= MP_LIMB_T_MAX/3 + 1 && ABOVE_THRESHOLD(n, MOD_1_2_THRESHOLD))
return mpn_mod_1_2_wrap(xp, n, d);
if (d <= GMP_LIMB_HIGHBIT + 1 && ABOVE_THRESHOLD(n, MOD_1_1_THRESHOLD))
return mpn_mod_1_1_wrap(xp, n, d);
/* for n = 1 or n = 2 probably faster to do a special case */
#if NORMALIZE == 1
count_leading_zeros(s, d);
d = d<<s;
invert_limb(i, d);
#endif
for (j = n - 1; j >= 0; j--)
{
l = xp[j]; /* out dlimb is (h = r, l) */
h = (l>>((GMP_LIMB_BITS - 1 - s))>>1);
l = l<<s; /* shift dlimb left by s */
h = h + r; /* carry in */
UDIV(q, r, h, l, d, i); /* carry out, carry-out to carry-in is the critical latency bottleneck */
#if STORE_QUOTIENT
qp[j] = q;
#endif
}
ASSERT((r<<(GMP_LIMB_BITS - 1 - s)<<1) == 0); /* ie bottom s bits of r are zero */
r>>=s;
return r;
}
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