Add Chromium-only Blender WebEngine parity work
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mes123456
282
blender-5.2.0/extern/gmp-source/mpz/powm.c
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282
blender-5.2.0/extern/gmp-source/mpz/powm.c
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/* mpz_powm(res,base,exp,mod) -- Set R to (U^E) mod M.
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Contributed to the GNU project by Torbjorn Granlund.
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Copyright 1991, 1993, 1994, 1996, 1997, 2000-2002, 2005, 2008, 2009,
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2011, 2012, 2015, 2019 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 either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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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 General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp-impl.h"
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#include "longlong.h"
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/* TODO
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* Improve handling of buffers. It is pretty ugly now.
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* For even moduli, we compute a binvert of its odd part both here and in
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mpn_powm. How can we avoid this recomputation?
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*/
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/*
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b ^ e mod m res
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0 0 0 ?
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0 e 0 ?
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0 0 m ?
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0 e m 0
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b 0 0 ?
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b e 0 ?
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b 0 m 1 mod m
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b e m b^e mod m
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*/
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#define HANDLE_NEGATIVE_EXPONENT 1
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void
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mpz_powm (mpz_ptr r, mpz_srcptr b, mpz_srcptr e, mpz_srcptr m)
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{
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mp_size_t n, nodd, ncnt;
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int cnt;
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mp_ptr rp, tp;
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mp_srcptr bp, ep, mp;
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mp_size_t rn, bn, es, en, itch;
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mpz_t new_b; /* note: value lives long via 'b' */
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TMP_DECL;
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n = ABSIZ(m);
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if (UNLIKELY (n == 0))
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DIVIDE_BY_ZERO;
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mp = PTR(m);
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TMP_MARK;
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es = SIZ(e);
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if (UNLIKELY (es <= 0))
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{
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if (es == 0)
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{
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/* b^0 mod m, b is anything and m is non-zero.
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Result is 1 mod m, i.e., 1 or 0 depending on if m = 1. */
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SIZ(r) = n != 1 || mp[0] != 1;
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MPZ_NEWALLOC (r, 1)[0] = 1;
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TMP_FREE; /* we haven't really allocated anything here */
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return;
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}
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#if HANDLE_NEGATIVE_EXPONENT
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MPZ_TMP_INIT (new_b, n + 1);
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if (UNLIKELY (! mpz_invert (new_b, b, m)))
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DIVIDE_BY_ZERO;
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b = new_b;
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es = -es;
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#else
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DIVIDE_BY_ZERO;
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#endif
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}
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en = es;
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bn = ABSIZ(b);
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if (UNLIKELY (bn == 0))
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{
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SIZ(r) = 0;
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TMP_FREE;
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return;
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}
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ep = PTR(e);
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/* Handle (b^1 mod m) early, since mpn_pow* do not handle that case. */
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if (UNLIKELY (en == 1 && ep[0] == 1))
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{
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rp = TMP_ALLOC_LIMBS (n);
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bp = PTR(b);
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if (bn >= n)
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{
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mp_ptr qp = TMP_ALLOC_LIMBS (bn - n + 1);
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mpn_tdiv_qr (qp, rp, 0L, bp, bn, mp, n);
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rn = n;
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MPN_NORMALIZE (rp, rn);
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if (rn != 0 && SIZ(b) < 0)
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{
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mpn_sub (rp, mp, n, rp, rn);
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rn = n;
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MPN_NORMALIZE_NOT_ZERO (rp, rn);
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}
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}
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else
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{
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if (SIZ(b) < 0)
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{
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mpn_sub (rp, mp, n, bp, bn);
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rn = n;
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MPN_NORMALIZE_NOT_ZERO (rp, rn);
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}
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else
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{
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MPN_COPY (rp, bp, bn);
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rn = bn;
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}
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}
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goto ret;
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}
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/* Remove low zero limbs from M. This loop will terminate for correctly
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represented mpz numbers. */
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ncnt = 0;
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while (UNLIKELY (mp[0] == 0))
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{
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mp++;
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ncnt++;
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}
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nodd = n - ncnt;
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cnt = 0;
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if (mp[0] % 2 == 0)
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{
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mp_ptr newmp = TMP_ALLOC_LIMBS (nodd);
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count_trailing_zeros (cnt, mp[0]);
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mpn_rshift (newmp, mp, nodd, cnt);
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nodd -= newmp[nodd - 1] == 0;
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mp = newmp;
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ncnt++;
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}
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if (ncnt != 0)
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{
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/* We will call both mpn_powm and mpn_powlo. */
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/* rp needs n, mpn_powlo needs 4n, the 2 mpn_binvert might need more */
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mp_size_t n_largest_binvert = MAX (ncnt, nodd);
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mp_size_t itch_binvert = mpn_binvert_itch (n_largest_binvert);
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itch = 3 * n + MAX (itch_binvert, 2 * n);
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}
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else
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{
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/* We will call just mpn_powm. */
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mp_size_t itch_binvert = mpn_binvert_itch (nodd);
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itch = n + MAX (itch_binvert, 2 * n);
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}
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tp = TMP_ALLOC_LIMBS (itch);
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rp = tp; tp += n;
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bp = PTR(b);
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mpn_powm (rp, bp, bn, ep, en, mp, nodd, tp);
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rn = n;
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if (ncnt != 0)
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{
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mp_ptr r2, xp, yp, odd_inv_2exp;
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unsigned long t;
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int bcnt;
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if (bn < ncnt)
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{
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mp_ptr newbp = TMP_ALLOC_LIMBS (ncnt);
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MPN_COPY (newbp, bp, bn);
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MPN_ZERO (newbp + bn, ncnt - bn);
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bp = newbp;
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}
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r2 = tp;
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if (bp[0] % 2 == 0)
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{
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if (en > 1)
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{
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MPN_ZERO (r2, ncnt);
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goto zero;
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}
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ASSERT (en == 1);
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t = (ncnt - (cnt != 0)) * GMP_NUMB_BITS + cnt;
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/* Count number of low zero bits in B, up to 3. */
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bcnt = (0x1213 >> ((bp[0] & 7) << 1)) & 0x3;
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/* Note that ep[0] * bcnt might overflow, but that just results
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in a missed optimization. */
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if (ep[0] * bcnt >= t)
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{
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MPN_ZERO (r2, ncnt);
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goto zero;
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}
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}
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mpn_powlo (r2, bp, ep, en, ncnt, tp + ncnt);
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zero:
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if (nodd < ncnt)
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{
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mp_ptr newmp = TMP_ALLOC_LIMBS (ncnt);
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MPN_COPY (newmp, mp, nodd);
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MPN_ZERO (newmp + nodd, ncnt - nodd);
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mp = newmp;
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}
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odd_inv_2exp = tp + n;
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mpn_binvert (odd_inv_2exp, mp, ncnt, tp + 2 * n);
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mpn_sub (r2, r2, ncnt, rp, nodd > ncnt ? ncnt : nodd);
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xp = tp + 2 * n;
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mpn_mullo_n (xp, odd_inv_2exp, r2, ncnt);
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if (cnt != 0)
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xp[ncnt - 1] &= (CNST_LIMB(1) << cnt) - 1;
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yp = tp;
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if (ncnt > nodd)
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mpn_mul (yp, xp, ncnt, mp, nodd);
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else
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mpn_mul (yp, mp, nodd, xp, ncnt);
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mpn_add (rp, yp, n, rp, nodd);
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ASSERT (nodd + ncnt >= n);
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ASSERT (nodd + ncnt <= n + 1);
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}
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MPN_NORMALIZE (rp, rn);
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if ((ep[0] & 1) && SIZ(b) < 0 && rn != 0)
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{
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mpn_sub (rp, PTR(m), n, rp, rn);
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rn = n;
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MPN_NORMALIZE (rp, rn);
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}
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ret:
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MPZ_NEWALLOC (r, rn);
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SIZ(r) = rn;
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MPN_COPY (PTR(r), rp, rn);
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TMP_FREE;
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}
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