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/* mpn_powlo -- Compute R = U^E mod R^n, where R is the limb base.
Copyright 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"
#define getbit(p,bi) \
((p[(bi - 1) / GMP_LIMB_BITS] >> (bi - 1) % GMP_LIMB_BITS) & 1)
static inline mp_limb_t
getbits (const mp_limb_t *p, unsigned long bi, int nbits)
{
int nbits_in_r;
mp_limb_t r;
mp_size_t i;
if (bi < nbits)
{
return p[0] & (((mp_limb_t) 1 << bi) - 1);
}
else
{
bi -= nbits; /* bit index of low bit to extract */
i = bi / GMP_LIMB_BITS; /* word index of low bit to extract */
bi %= GMP_LIMB_BITS; /* bit index in low word */
r = p[i] >> bi; /* extract (low) bits */
nbits_in_r = GMP_LIMB_BITS - bi; /* number of bits now in r */
if (nbits_in_r < nbits) /* did we get enough bits? */
r += p[i + 1] << nbits_in_r; /* prepend bits from higher word */
return r & (((mp_limb_t ) 1 << nbits) - 1);
}
}
static inline int
win_size (unsigned long eb)
{
int k;
static unsigned long x[] = {1,7,25,81,241,673,1793,4609,11521,28161,~0ul};
for (k = 0; eb > x[k]; k++)
;
return k;
}
/* rp[n-1..0] = bp[n-1..0] ^ ep[en-1..0] mod R^n, R is the limb base.
Requires that ep[en-1] is non-zero.
Uses scratch space tp[3n-1..0], i.e., 3n words. */
void
mpn_powlo (mp_ptr rp, mp_srcptr bp,
mp_srcptr ep, mp_size_t en,
mp_size_t n, mp_ptr tp)
{
int cnt;
long ebi;
int windowsize, this_windowsize;
mp_limb_t expbits;
mp_limb_t *pp, *this_pp, *last_pp;
mp_limb_t *b2p;
long i;
TMP_DECL;
ASSERT (en > 1 || (en == 1 && ep[0] > 1));
TMP_MARK;
count_leading_zeros (cnt, ep[en - 1]);
ebi = en * GMP_LIMB_BITS - cnt;
windowsize = win_size (ebi);
pp = TMP_ALLOC_LIMBS ((n << (windowsize - 1)) + n); /* + n is for mullow ign part */
this_pp = pp;
MPN_COPY (this_pp, bp, n);
b2p = tp + 2*n;
/* Store b^2 in b2. */
mpn_sqr_n (tp, bp, n); /* FIXME: Use "mpn_sqrlo" */
MPN_COPY (b2p, tp, n);
/* Precompute odd powers of b and put them in the temporary area at pp. */
for (i = (1 << (windowsize - 1)) - 1; i > 0; i--)
{
last_pp = this_pp;
this_pp += n;
mpn_mullow_n (this_pp, last_pp, b2p, n);
}
expbits = getbits (ep, ebi, windowsize);
ebi -= windowsize;
if (ebi < 0)
ebi = 0;
count_trailing_zeros (cnt, expbits);
ebi += cnt;
expbits >>= cnt;
MPN_COPY (rp, pp + n * (expbits >> 1), n);
while (ebi != 0)
{
while (getbit (ep, ebi) == 0)
{
mpn_sqr_n (tp, rp, n); /* FIXME: Use "mpn_sqrlo" */
MPN_COPY (rp, tp, n);
ebi--;
if (ebi == 0)
goto done;
}
/* The next bit of the exponent is 1. Now extract the largest block of
bits <= windowsize, and such that the least significant bit is 1. */
expbits = getbits (ep, ebi, windowsize);
ebi -= windowsize;
this_windowsize = windowsize;
if (ebi < 0)
{
this_windowsize += ebi;
ebi = 0;
}
count_trailing_zeros (cnt, expbits);
this_windowsize -= cnt;
ebi += cnt;
expbits >>= cnt;
do
{
mpn_sqr_n (tp, rp, n);
MPN_COPY (rp, tp, n);
this_windowsize--;
}
while (this_windowsize != 0);
mpn_mullow_n (tp, rp, pp + n * (expbits >> 1), n);
MPN_COPY (rp, tp, n);
}
done:
TMP_FREE;
}
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