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