/* mpn_remove -- divide out all multiples of odd mpn number from another mpn number. Contributed to the GNU project by Torbjorn Granlund. THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE. Copyright 2009, 2012, 2013 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 either: * the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. or * the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. or both in parallel, as here. 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 copies of the GNU General Public License and the GNU Lesser General Public License along with the GNU MP Library. If not, see https://www.gnu.org/licenses/. */ #include "gmp.h" #include "gmp-impl.h" #if GMP_LIMB_BITS > 50 #define LOG 50 #else #define LOG GMP_LIMB_BITS #endif /* Input: U = {up,un}, V = {vp,vn} must be odd, cap Ouput W = {wp,*wn} allocation need is exactly *wn Set W = U / V^k, where k is the largest integer <= cap such that the division yields an integer. FIXME: We currently allow any operand overlap. This is quite non mpn-ish and might be changed, since it cost significant temporary space. * If we require W to have space for un + 1 limbs, we could save qp or qp2 (but we will still need to copy things into wp 50% of the time). * If we allow ourselves to clobber U, we could save the other of qp and qp2, and the initial COPY (but also here we would need un + 1 limbs). */ /* FIXME: We need to wrap mpn_bdiv_qr due to the itch interface. This need indicates a flaw in the current itch mechanism: Which operands not greater than un,un will incur the worst itch? We need a parallel foo_maxitch set of functions. */ static void mpn_bdiv_qr_wrap (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn) { mp_ptr scratch_out; TMP_DECL; TMP_MARK; scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (nn, dn)); mpn_bdiv_qr (qp, rp, np, nn, dp, dn, scratch_out); TMP_FREE; } mp_bitcnt_t mpn_remove (mp_ptr wp, mp_size_t *wn, mp_ptr up, mp_size_t un, mp_ptr vp, mp_size_t vn, mp_bitcnt_t cap) { mp_ptr pwpsp[LOG]; mp_size_t pwpsn[LOG]; mp_size_t npowers; mp_ptr tp, qp, np, pp, qp2; mp_size_t pn, nn, qn, i; mp_bitcnt_t pwr; TMP_DECL; ASSERT (un > 0); ASSERT (vn > 0); ASSERT (vp[0] % 2 != 0); /* 2-adic division wants odd numbers */ ASSERT (vn > 1 || vp[0] > 1); /* else we would loop indefinitely */ TMP_MARK; tp = TMP_ALLOC_LIMBS ((un + 1 + vn) / 2); /* remainder */ qp = TMP_ALLOC_LIMBS (un + 1); /* quotient, alternating */ qp2 = TMP_ALLOC_LIMBS (un + 1); /* quotient, alternating */ pp = vp; pn = vn; MPN_COPY (qp, up, un); qn = un; npowers = 0; while (qn >= pn) { qp[qn] = 0; mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pp, pn); if (!mpn_zero_p (tp, pn)) break; /* could not divide by V^npowers */ MP_PTR_SWAP (qp, qp2); qn = qn - pn; qn += qp[qn] != 0; pwpsp[npowers] = pp; pwpsn[npowers] = pn; npowers++; if (((mp_bitcnt_t) 2 << npowers) - 1 > cap) break; nn = 2 * pn - 1; /* next power will be at least this large */ if (nn > qn) break; /* next power would be overlarge */ if (npowers == 1) /* Alloc once, but only if it's needed */ np = TMP_ALLOC_LIMBS (qn + LOG); /* powers of V */ else np += pn; mpn_sqr (np, pp, pn); pn = nn + (np[nn] != 0); pp = np; } pwr = ((mp_bitcnt_t) 1 << npowers) - 1; for (i = npowers - 1; i >= 0; i--) { pn = pwpsn[i]; if (qn < pn) continue; if (pwr + ((mp_bitcnt_t) 1 << i) > cap) continue; /* V^i would bring us past cap */ qp[qn] = 0; mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pwpsp[i], pn); if (!mpn_zero_p (tp, pn)) continue; /* could not divide by V^i */ MP_PTR_SWAP (qp, qp2); qn = qn - pn; qn += qp[qn] != 0; pwr += (mp_bitcnt_t) 1 << i; } MPN_COPY (wp, qp, qn); *wn = qn; TMP_FREE; return pwr; }