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authorDuncan Wilkie <antigravityd@gmail.com>2023-11-18 06:11:09 -0600
committerDuncan Wilkie <antigravityd@gmail.com>2023-11-18 06:11:09 -0600
commit11da511c784eca003deb90c23570f0873954e0de (patch)
treee14fdd3d5d6345956d67e79ae771d0633d28362b /gmp-6.3.0/mpn/generic/strongfibo.c
Initial commit.
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+/* mpn_fib2m -- calculate Fibonacci numbers, modulo m.
+
+Contributed to the GNU project by Marco Bodrato.
+
+ THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
+ CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
+ FUTURE GNU MP RELEASES.
+
+Copyright 2001, 2002, 2005, 2009, 2018, 2022 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 <stdio.h>
+#include "gmp-impl.h"
+
+
+#if ! HAVE_NATIVE_mpn_rsblsh1_n && ! HAVE_NATIVE_mpn_sublsh1_n
+/* Stores |{ap,n}-{bp,n}| in {rp,n},
+ returns the sign of {ap,n}-{bp,n}. */
+static int
+abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+{
+ mp_limb_t x, y;
+ while (--n >= 0)
+ {
+ x = ap[n];
+ y = bp[n];
+ if (x != y)
+ {
+ ++n;
+ if (x > y)
+ {
+ ASSERT_NOCARRY (mpn_sub_n (rp, ap, bp, n));
+ return 1;
+ }
+ else
+ {
+ ASSERT_NOCARRY (mpn_sub_n (rp, bp, ap, n));
+ return -1;
+ }
+ }
+ rp[n] = 0;
+ }
+ return 0;
+}
+#endif
+
+/* Computes at most count terms of the sequence needed by the
+ Lucas-Lehmer-Riesel test, indexing backward:
+ L_i = L_{i+1}^2 - 2
+
+ The sequence is computed modulo M = {mp, mn}.
+ The starting point is given in L_{count+1} = {lp, mn}.
+ The scratch pointed by sp, needs a space of at least 3 * mn + 1 limbs.
+
+ Returns the index i>0 if L_i = 0 (mod M) is found within the
+ computed count terms of the sequence. Otherwise it returns zero.
+
+ Note: (+/-2)^2-2=2, (+/-1)^2-2=-1, 0^2-2=-2
+ */
+
+static mp_bitcnt_t
+mpn_llriter (mp_ptr lp, mp_srcptr mp, mp_size_t mn, mp_bitcnt_t count, mp_ptr sp)
+{
+ do
+ {
+ mpn_sqr (sp, lp, mn);
+ mpn_tdiv_qr (sp + 2 * mn, lp, 0, sp, 2 * mn, mp, mn);
+ if (lp[0] < 5)
+ {
+ /* If L^2 % M < 5, |L^2 % M - 2| <= 2 */
+ if (mn == 1 || mpn_zero_p (lp + 1, mn - 1))
+ return (lp[0] == 2) ? count : 0;
+ else
+ MPN_DECR_U (lp, mn, 2);
+ }
+ else
+ lp[0] -= 2;
+ } while (--count != 0);
+ return 0;
+}
+
+/* Store the Lucas' number L[n] at lp (maybe), computed modulo m. lp
+ and scratch should have room for mn*2+1 limbs.
+
+ Returns the size of L[n] normally.
+
+ If F[n] is zero modulo m, or L[n] is, returns 0 and lp is
+ undefined.
+*/
+
+static mp_size_t
+mpn_lucm (mp_ptr lp, mp_srcptr np, mp_size_t nn, mp_srcptr mp, mp_size_t mn, mp_ptr scratch)
+{
+ int neg;
+ mp_limb_t cy;
+
+ ASSERT (! MPN_OVERLAP_P (lp, MAX(2*mn+1,5), scratch, MAX(2*mn+1,5)));
+ ASSERT (nn > 0);
+
+ neg = mpn_fib2m (lp, scratch, np, nn, mp, mn);
+
+ /* F[n] = +/-{lp, mn}, F[n-1] = +/-{scratch, mn} */
+ if (mpn_zero_p (lp, mn))
+ return 0;
+
+ if (neg) /* One sign is opposite, use sub instead of add. */
+ {
+#if HAVE_NATIVE_mpn_rsblsh1_n || HAVE_NATIVE_mpn_sublsh1_n
+#if HAVE_NATIVE_mpn_rsblsh1_n
+ cy = mpn_rsblsh1_n (lp, lp, scratch, mn); /* L[n] = +/-(2F[n-1]-(-F[n])) */
+#else
+ cy = mpn_sublsh1_n (lp, lp, scratch, mn); /* L[n] = -/+(F[n]-(-2F[n-1])) */
+ if (cy != 0)
+ cy = mpn_add_n (lp, lp, mp, mn) - cy;
+#endif
+ if (cy > 1)
+ cy += mpn_add_n (lp, lp, mp, mn);
+#else
+ cy = mpn_lshift (scratch, scratch, mn, 1); /* 2F[n-1] */
+ if (UNLIKELY (cy))
+ cy -= mpn_sub_n (lp, scratch, lp, mn); /* L[n] = +/-(2F[n-1]-(-F[n])) */
+ else
+ abs_sub_n (lp, lp, scratch, mn);
+#endif
+ ASSERT (cy <= 1);
+ }
+ else
+ {
+#if HAVE_NATIVE_mpn_addlsh1_n
+ cy = mpn_addlsh1_n (lp, lp, scratch, mn); /* L[n] = +/-(2F[n-1]+F[n])) */
+#else
+ cy = mpn_lshift (scratch, scratch, mn, 1);
+ cy+= mpn_add_n (lp, lp, scratch, mn);
+#endif
+ ASSERT (cy <= 2);
+ }
+ while (cy || mpn_cmp (lp, mp, mn) >= 0)
+ cy -= mpn_sub_n (lp, lp, mp, mn);
+ MPN_NORMALIZE (lp, mn);
+ return mn;
+}
+
+int
+mpn_strongfibo (mp_srcptr mp, mp_size_t mn, mp_ptr scratch)
+{
+ mp_ptr lp, sp;
+ mp_size_t en;
+ mp_bitcnt_t b0;
+ TMP_DECL;
+
+#if GMP_NUMB_BITS % 4 == 0
+ b0 = mpn_scan0 (mp, 0);
+#else
+ {
+ mpz_t m = MPZ_ROINIT_N(mp, mn);
+ b0 = mpz_scan0 (m, 0);
+ }
+ if (UNLIKELY (b0 == mn * GMP_NUMB_BITS))
+ {
+ en = 1;
+ scratch [0] = 1;
+ }
+ else
+#endif
+ {
+ int cnt = b0 % GMP_NUMB_BITS;
+ en = b0 / GMP_NUMB_BITS;
+ if (LIKELY (cnt != 0))
+ mpn_rshift (scratch, mp + en, mn - en, cnt);
+ else
+ MPN_COPY (scratch, mp + en, mn - en);
+ en = mn - en;
+ scratch [0] |= 1;
+ en -= scratch [en - 1] == 0;
+ }
+ TMP_MARK;
+
+ lp = TMP_ALLOC_LIMBS (4 * mn + 6);
+ sp = lp + 2 * mn + 3;
+ en = mpn_lucm (sp, scratch, en, mp, mn, lp);
+ if (en != 0 && LIKELY (--b0 != 0))
+ {
+ mpn_sqr (lp, sp, en);
+ lp [0] |= 2; /* V^2 + 2 */
+ if (LIKELY (2 * en >= mn))
+ mpn_tdiv_qr (sp, lp, 0, lp, 2 * en, mp, mn);
+ else
+ MPN_ZERO (lp + 2 * en, mn - 2 * en);
+ if (! mpn_zero_p (lp, mn) && LIKELY (--b0 != 0))
+ b0 = mpn_llriter (lp, mp, mn, b0, lp + mn + 1);
+ }
+ TMP_FREE;
+ return (b0 != 0);
+}