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/* mpz_powm(res,base,exp,mod) -- Set RES to (base**exp) mod MOD.
Copyright (C) 1991, 1993, 1994, 1996 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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library General Public License
along with the GNU MP Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#ifndef BERKELEY_MP
void
#if __STDC__
mpz_powm (mpz_ptr res, mpz_srcptr base, mpz_srcptr exp, mpz_srcptr mod)
#else
mpz_powm (res, base, exp, mod)
mpz_ptr res;
mpz_srcptr base;
mpz_srcptr exp;
mpz_srcptr mod;
#endif
#else /* BERKELEY_MP */
void
#if __STDC__
pow (mpz_srcptr base, mpz_srcptr exp, mpz_srcptr mod, mpz_ptr res)
#else
pow (base, exp, mod, res)
mpz_srcptr base;
mpz_srcptr exp;
mpz_srcptr mod;
mpz_ptr res;
#endif
#endif /* BERKELEY_MP */
{
mp_ptr rp, ep, mp, bp;
mp_size_t esize, msize, bsize, rsize;
mp_size_t size;
int mod_shift_cnt;
int negative_result;
mp_limb_t *free_me = NULL;
size_t free_me_size;
TMP_DECL (marker);
esize = ABS (exp->_mp_size);
msize = ABS (mod->_mp_size);
size = 2 * msize;
rp = res->_mp_d;
ep = exp->_mp_d;
if (msize == 0)
msize = 1 / msize; /* provoke a signal */
if (esize == 0)
{
/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
depending on if MOD equals 1. */
rp[0] = 1;
res->_mp_size = (msize == 1 && (mod->_mp_d)[0] == 1) ? 0 : 1;
return;
}
TMP_MARK (marker);
/* Normalize MOD (i.e. make its most significant bit set) as required by
mpn_divmod. This will make the intermediate values in the calculation
slightly larger, but the correct result is obtained after a final
reduction using the original MOD value. */
mp = (mp_ptr) TMP_ALLOC (msize * BYTES_PER_MP_LIMB);
count_leading_zeros (mod_shift_cnt, mod->_mp_d[msize - 1]);
if (mod_shift_cnt != 0)
mpn_lshift (mp, mod->_mp_d, msize, mod_shift_cnt);
else
MPN_COPY (mp, mod->_mp_d, msize);
bsize = ABS (base->_mp_size);
if (bsize > msize)
{
/* The base is larger than the module. Reduce it. */
/* Allocate (BSIZE + 1) with space for remainder and quotient.
(The quotient is (bsize - msize + 1) limbs.) */
bp = (mp_ptr) TMP_ALLOC ((bsize + 1) * BYTES_PER_MP_LIMB);
MPN_COPY (bp, base->_mp_d, bsize);
/* We don't care about the quotient, store it above the remainder,
at BP + MSIZE. */
mpn_divmod (bp + msize, bp, bsize, mp, msize);
bsize = msize;
/* Canonicalize the base, since we are going to multiply with it
quite a few times. */
MPN_NORMALIZE (bp, bsize);
}
else
bp = base->_mp_d;
if (bsize == 0)
{
res->_mp_size = 0;
TMP_FREE (marker);
return;
}
if (res->_mp_alloc < size)
{
/* We have to allocate more space for RES. If any of the input
parameters are identical to RES, defer deallocation of the old
space. */
if (rp == ep || rp == mp || rp == bp)
{
free_me = rp;
free_me_size = res->_mp_alloc;
}
else
(*_mp_free_func) (rp, res->_mp_alloc * BYTES_PER_MP_LIMB);
rp = (mp_ptr) (*_mp_allocate_func) (size * BYTES_PER_MP_LIMB);
res->_mp_alloc = size;
res->_mp_d = rp;
}
else
{
/* Make BASE, EXP and MOD not overlap with RES. */
if (rp == bp)
{
/* RES and BASE are identical. Allocate temp. space for BASE. */
bp = (mp_ptr) TMP_ALLOC (bsize * BYTES_PER_MP_LIMB);
MPN_COPY (bp, rp, bsize);
}
if (rp == ep)
{
/* RES and EXP are identical. Allocate temp. space for EXP. */
ep = (mp_ptr) TMP_ALLOC (esize * BYTES_PER_MP_LIMB);
MPN_COPY (ep, rp, esize);
}
if (rp == mp)
{
/* RES and MOD are identical. Allocate temporary space for MOD. */
mp = (mp_ptr) TMP_ALLOC (msize * BYTES_PER_MP_LIMB);
MPN_COPY (mp, rp, msize);
}
}
MPN_COPY (rp, bp, bsize);
rsize = bsize;
{
mp_size_t i;
mp_ptr xp = (mp_ptr) TMP_ALLOC (2 * (msize + 1) * BYTES_PER_MP_LIMB);
int c;
mp_limb_t e;
mp_limb_t carry_limb;
negative_result = (ep[0] & 1) && base->_mp_size < 0;
i = esize - 1;
e = ep[i];
count_leading_zeros (c, e);
e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
c = BITS_PER_MP_LIMB - 1 - c;
/* Main loop.
Make the result be pointed to alternately by XP and RP. This
helps us avoid block copying, which would otherwise be necessary
with the overlap restrictions of mpn_divmod. With 50% probability
the result after this loop will be in the area originally pointed
by RP (==RES->_mp_d), and with 50% probability in the area originally
pointed to by XP. */
for (;;)
{
while (c != 0)
{
mp_ptr tp;
mp_size_t xsize;
mpn_mul_n (xp, rp, rp, rsize);
xsize = 2 * rsize;
if (xsize > msize)
{
mpn_divmod (xp + msize, xp, xsize, mp, msize);
xsize = msize;
}
tp = rp; rp = xp; xp = tp;
rsize = xsize;
if ((mp_limb_signed_t) e < 0)
{
mpn_mul (xp, rp, rsize, bp, bsize);
xsize = rsize + bsize;
if (xsize > msize)
{
mpn_divmod (xp + msize, xp, xsize, mp, msize);
xsize = msize;
}
tp = rp; rp = xp; xp = tp;
rsize = xsize;
}
e <<= 1;
c--;
}
i--;
if (i < 0)
break;
e = ep[i];
c = BITS_PER_MP_LIMB;
}
/* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
steps. Adjust the result by reducing it with the original MOD.
Also make sure the result is put in RES->_mp_d (where it already
might be, see above). */
if (mod_shift_cnt != 0)
{
carry_limb = mpn_lshift (res->_mp_d, rp, rsize, mod_shift_cnt);
rp = res->_mp_d;
if (carry_limb != 0)
{
rp[rsize] = carry_limb;
rsize++;
}
}
else
{
MPN_COPY (res->_mp_d, rp, rsize);
rp = res->_mp_d;
}
if (rsize >= msize)
{
mpn_divmod (rp + msize, rp, rsize, mp, msize);
rsize = msize;
}
/* Remove any leading zero words from the result. */
if (mod_shift_cnt != 0)
mpn_rshift (rp, rp, rsize, mod_shift_cnt);
MPN_NORMALIZE (rp, rsize);
}
if (negative_result && rsize != 0)
{
if (mod_shift_cnt != 0)
mpn_rshift (mp, mp, msize, mod_shift_cnt);
mpn_sub (rp, mp, msize, rp, rsize);
rsize = msize;
MPN_NORMALIZE (rp, rsize);
}
res->_mp_size = rsize;
if (free_me != NULL)
(*_mp_free_func) (free_me, free_me_size * BYTES_PER_MP_LIMB);
TMP_FREE (marker);
}
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