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/* mpz_powm(res,base,exp,mod) -- Set RES to (base**exp) mod MOD.
Copyright (C) 1991, 1992 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 General Public License as published by
the Free Software Foundation; either version 2, 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with the GNU MP Library; see the file COPYING. If not, write to
the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#ifndef BERKELEY_MP
void
#ifdef __STDC__
mpz_powm (MP_INT *res, const MP_INT *base, const MP_INT *exp,
const MP_INT *mod)
#else
mpz_powm (res, base, exp, mod)
MP_INT *res;
const MP_INT *base;
const MP_INT *exp;
const MP_INT *mod;
#endif
#else /* BERKELEY_MP */
void
#ifdef __STDC__
pow (const MP_INT *base, const MP_INT *exp, const MP_INT *mod, MP_INT *res)
#else
pow (base, exp, mod, res)
const MP_INT *base;
const MP_INT *exp;
const MP_INT *mod;
MP_INT *res;
#endif
#endif /* BERKELEY_MP */
{
mp_ptr rp, ep, mp, bp;
mp_size esize, msize, bsize, rsize;
mp_size size;
int mod_shift_cnt;
int negative_result;
mp_limb *free_me = NULL;
size_t free_me_size;
esize = ABS (exp->size);
msize = ABS (mod->size);
size = 2 * msize;
rp = res->d;
ep = exp->d;
/* Normalize MOD (i.e. make its most significant bit set) as required by
mpn_div. 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) alloca (msize * BYTES_PER_MP_LIMB);
count_leading_zeros (mod_shift_cnt, mod->d[msize - 1]);
if (mod_shift_cnt != 0)
(void) mpn_lshift (mp, mod->d, msize, mod_shift_cnt);
else
MPN_COPY (mp, mod->d, msize);
bsize = ABS (base->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) alloca ((bsize + 1) * BYTES_PER_MP_LIMB);
MPN_COPY (bp, base->d, bsize);
/* We don't care about the quotient, store it above the remainder,
at BP + MSIZE. */
mpn_div (bp + msize, bp, bsize, mp, msize);
bsize = msize;
while (bsize > 0 && bp[bsize - 1] == 0)
bsize--;
}
else
{
bp = base->d;
bsize = ABS (base->size);
}
if (res->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->alloc;
}
else
(*_mp_free_func) (rp, res->alloc * BYTES_PER_MP_LIMB);
rp = (mp_ptr) (*_mp_allocate_func) (size * BYTES_PER_MP_LIMB);
res->alloc = size;
res->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) alloca (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) alloca (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) alloca (msize * BYTES_PER_MP_LIMB);
MPN_COPY (mp, rp, msize);
}
}
if (esize == 0)
{
rp[0] = 1;
res->size = 1;
return;
}
MPN_COPY (rp, bp, bsize);
rsize = bsize;
{
mp_size i;
mp_size xsize;
mp_ptr dummyp = (mp_ptr) alloca ((msize + 1) * BYTES_PER_MP_LIMB);
mp_ptr xp = (mp_ptr) alloca (2 * (msize + 1) * BYTES_PER_MP_LIMB);
int c;
mp_limb e;
mp_limb carry_limb;
negative_result = (ep[0] & 1) && base->size < 0;
i = esize - 1;
e = ep[i];
count_leading_zeros (c, e);
e <<= (c + 1); /* shift the exp bits to the left, loose msb */
c = BITS_PER_MP_LIMB - 1 - c;
/* Main loop.
Make the result be pointed to alternatingly by XP and RP. This
helps us avoid block copying, which would otherwise be necessary
with the overlap restrictions of mpn_div. With 50% probability
the result after this loop will be in the area originally pointed
by RP (==RES->D), and with 50% probability in the area originally
pointed to by XP. */
for (;;)
{
while (c != 0)
{
mp_ptr tp;
mp_size tsize;
xsize = mpn_mul (xp, rp, rsize, rp, rsize);
mpn_div (dummyp, xp, xsize, mp, msize);
/* Remove any leading zero words from the result. */
if (xsize > msize)
xsize = msize;
while (xsize > 0 && xp[xsize - 1] == 0)
xsize--;
tp = rp; rp = xp; xp = tp;
tsize = rsize; rsize = xsize; xsize = tsize;
if ((mp_limb_signed) e < 0)
{
if (rsize > bsize)
xsize = mpn_mul (xp, rp, rsize, bp, bsize);
else
xsize = mpn_mul (xp, bp, bsize, rp, rsize);
mpn_div (dummyp, xp, xsize, mp, msize);
/* Remove any leading zero words from the result. */
if (xsize > msize)
xsize = msize;
while (xsize > 0 && xp[xsize - 1] == 0)
xsize--;
tp = rp; rp = xp; xp = tp;
tsize = rsize; rsize = xsize; xsize = tsize;
}
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->D (where it already
might be, see above). */
carry_limb = mpn_lshift (res->d, rp, rsize, mod_shift_cnt);
rp = res->d;
if (carry_limb != 0)
{
rp[rsize] = carry_limb;
rsize++;
}
mpn_div (dummyp, rp, rsize, mp, msize);
/* Remove any leading zero words from the result. */
if (rsize > msize)
rsize = msize;
while (rsize > 0 && rp[rsize - 1] == 0)
rsize--;
rsize = mpn_rshift (rp, rp, rsize, mod_shift_cnt);
}
res->size = negative_result >= 0 ? rsize : -rsize;
if (free_me != NULL)
(*_mp_free_func) (free_me, free_me_size * BYTES_PER_MP_LIMB);
alloca (0);
}
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