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+/* 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;
+}