=================================================================== RCS file: /home/cvs/OpenXM_contrib/gmp/mpz/Attic/powm_ui.c,v retrieving revision 1.1 retrieving revision 1.1.1.3 diff -u -p -r1.1 -r1.1.1.3 --- OpenXM_contrib/gmp/mpz/Attic/powm_ui.c 2000/01/10 15:35:27 1.1 +++ OpenXM_contrib/gmp/mpz/Attic/powm_ui.c 2003/08/25 16:06:33 1.1.1.3 @@ -1,234 +1,197 @@ /* mpz_powm_ui(res,base,exp,mod) -- Set RES to (base**exp) mod MOD. -Copyright (C) 1991, 1993, 1994, 1996 Free Software Foundation, Inc. +Copyright 1991, 1993, 1994, 1996, 1997, 2000, 2001, 2002 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 +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 2.1 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 +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 Library General Public License +You should have received a copy of the GNU Lesser 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" -void -#if __STDC__ -mpz_powm_ui (mpz_ptr res, mpz_srcptr base, unsigned long int exp, mpz_srcptr mod) -#else -mpz_powm_ui (res, base, exp, mod) - mpz_ptr res; - mpz_srcptr base; - unsigned long int exp; - mpz_srcptr mod; -#endif +/* Compute t = a mod m, a is defined by (ap,an), m is defined by (mp,mn), and + t is defined by (tp,mn). */ +static void +reduce (mp_ptr tp, mp_srcptr ap, mp_size_t an, mp_srcptr mp, mp_size_t mn) { - mp_ptr rp, mp, bp; - mp_size_t 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; + mp_ptr qp; TMP_DECL (marker); - msize = ABS (mod->_mp_size); - size = 2 * msize; + TMP_MARK (marker); + qp = TMP_ALLOC_LIMBS (an - mn + 1); - rp = res->_mp_d; + mpn_tdiv_qr (qp, tp, 0L, ap, an, mp, mn); - if (msize == 0) - msize = 1 / msize; /* provoke a signal */ + TMP_FREE (marker); +} - if (exp == 0) +void +mpz_powm_ui (mpz_ptr r, mpz_srcptr b, unsigned long int el, mpz_srcptr m) +{ + mp_ptr xp, tp, qp, mp, bp; + mp_size_t xn, tn, mn, bn; + int m_zero_cnt; + int c; + mp_limb_t e; + TMP_DECL (marker); + + mp = PTR(m); + mn = ABSIZ(m); + if (mn == 0) + DIVIDE_BY_ZERO; + + if (el == 0) { - rp[0] = 1; - res->_mp_size = (msize == 1 && (mod->_mp_d)[0] == 1) ? 0 : 1; + /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0 + depending on if MOD equals 1. */ + SIZ(r) = (mn == 1 && mp[0] == 1) ? 0 : 1; + PTR(r)[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) + /* Normalize m (i.e. make its most significant bit set) as required by + division functions below. */ + count_leading_zeros (m_zero_cnt, mp[mn - 1]); + m_zero_cnt -= GMP_NAIL_BITS; + if (m_zero_cnt != 0) { - /* The base is larger than the module. Reduce it. */ + mp_ptr new_mp = TMP_ALLOC_LIMBS (mn); + mpn_lshift (new_mp, mp, mn, m_zero_cnt); + mp = new_mp; + } - /* 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); + bn = ABSIZ(b); + bp = PTR(b); + if (bn > mn) + { + /* Reduce possibly huge base. Use a function call to reduce, since we + don't want the quotient allocation to live until function return. */ + mp_ptr new_bp = TMP_ALLOC_LIMBS (mn); + reduce (new_bp, bp, bn, mp, mn); + bp = new_bp; + bn = mn; + /* Canonicalize the base, since we are potentially going to multiply with + it quite a few times. */ + MPN_NORMALIZE (bp, bn); } - else - bp = base->_mp_d; - if (bsize == 0) + if (bn == 0) { - res->_mp_size = 0; + SIZ(r) = 0; TMP_FREE (marker); return; } - if (res->_mp_alloc < size) + tp = TMP_ALLOC_LIMBS (2 * mn + 1); + xp = TMP_ALLOC_LIMBS (mn); + + qp = TMP_ALLOC_LIMBS (mn + 1); + + MPN_COPY (xp, bp, bn); + xn = bn; + + e = el; + 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. */ + + /* If m is already normalized (high bit of high limb set), and b is the + same size, but a bigger value, and e==1, then there's no modular + reductions done and we can end up with a result out of range at the + end. */ + if (c == 0) { - /* 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 (xn == mn && mpn_cmp (xp, mp, mn) >= 0) + mpn_sub_n (xp, xp, mp, mn); + goto finishup; + } - if (rp == mp || rp == bp) + while (c != 0) + { + mpn_sqr_n (tp, xp, xn); + tn = 2 * xn; tn -= tp[tn - 1] == 0; + if (tn < mn) { - free_me = rp; - free_me_size = res->_mp_alloc; + MPN_COPY (xp, tp, tn); + xn = tn; } else - (*_mp_free_func) (rp, res->_mp_alloc * BYTES_PER_MP_LIMB); + { + mpn_tdiv_qr (qp, xp, 0L, tp, tn, mp, mn); + xn = mn; + } - rp = (mp_ptr) (*_mp_allocate_func) (size * BYTES_PER_MP_LIMB); - res->_mp_alloc = size; - res->_mp_d = rp; + if ((mp_limb_signed_t) e < 0) + { + mpn_mul (tp, xp, xn, bp, bn); + tn = xn + bn; tn -= tp[tn - 1] == 0; + if (tn < mn) + { + MPN_COPY (xp, tp, tn); + xn = tn; + } + else + { + mpn_tdiv_qr (qp, xp, 0L, tp, tn, mp, mn); + xn = mn; + } + } + e <<= 1; + c--; } - else + + finishup: + /* We shifted m left m_zero_cnt steps. Adjust the result by reducing + it with the original MOD. */ + if (m_zero_cnt != 0) { - /* Make BASE, EXP and MOD not overlap with RES. */ - if (rp == bp) + mp_limb_t cy; + cy = mpn_lshift (tp, xp, xn, m_zero_cnt); + tp[xn] = cy; xn += cy != 0; + + if (xn < mn) { - /* 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); + MPN_COPY (xp, tp, xn); } - if (rp == mp) + else { - /* 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_tdiv_qr (qp, xp, 0L, tp, xn, mp, mn); + xn = mn; } + mpn_rshift (xp, xp, xn, m_zero_cnt); } + MPN_NORMALIZE (xp, xn); - MPN_COPY (rp, bp, bsize); - rsize = bsize; + if ((el & 1) != 0 && SIZ(b) < 0 && xn != 0) + { + mp = PTR(m); /* want original, unnormalized m */ + mpn_sub (xp, mp, mn, xp, xn); + xn = mn; + MPN_NORMALIZE (xp, xn); + } + MPZ_REALLOC (r, xn); + SIZ (r) = xn; + MPN_COPY (PTR(r), xp, xn); - { - 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 = (exp & 1) && base->_mp_size < 0; - - e = exp; - 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. */ - - 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--; - } - - /* 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); - } - - res->_mp_size = negative_result == 0 ? rsize : -rsize; - - if (free_me != NULL) - (*_mp_free_func) (free_me, free_me_size * BYTES_PER_MP_LIMB); TMP_FREE (marker); }