1 /* mpz_lucnum2_ui -- calculate Lucas numbers.
2
3 Copyright 2001, 2003, 2005, 2012, 2015, 2016, 2018 Free Software
4 Foundation, Inc.
5
6 This file is part of the GNU MP Library.
7
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of either:
10
11 * the GNU Lesser General Public License as published by the Free
12 Software Foundation; either version 3 of the License, or (at your
13 option) any later version.
14
15 or
16
17 * the GNU General Public License as published by the Free Software
18 Foundation; either version 2 of the License, or (at your option) any
19 later version.
20
21 or both in parallel, as here.
22
23 The GNU MP Library is distributed in the hope that it will be useful, but
24 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
25 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
26 for more details.
27
28 You should have received copies of the GNU General Public License and the
29 GNU Lesser General Public License along with the GNU MP Library. If not,
30 see https://www.gnu.org/licenses/. */
31
32 #include <stdio.h>
33 #include "gmp-impl.h"
34
35
36 void
mpz_lucnum2_ui(mpz_ptr ln,mpz_ptr lnsub1,unsigned long n)37 mpz_lucnum2_ui (mpz_ptr ln, mpz_ptr lnsub1, unsigned long n)
38 {
39 mp_ptr lp, l1p, f1p;
40 mp_size_t size;
41 mp_limb_t c;
42 TMP_DECL;
43
44 ASSERT (ln != lnsub1);
45
46 /* handle small n quickly, and hide the special case for L[-1]=-1 */
47 if (n <= FIB_TABLE_LUCNUM_LIMIT)
48 {
49 mp_limb_t f = FIB_TABLE (n);
50 mp_limb_t f1 = FIB_TABLE ((int) n - 1);
51
52 /* L[n] = F[n] + 2F[n-1] */
53 MPZ_NEWALLOC (ln, 1)[0] = f + 2*f1;
54 SIZ(ln) = 1;
55
56 /* L[n-1] = 2F[n] - F[n-1], but allow for L[-1]=-1 */
57 MPZ_NEWALLOC (lnsub1, 1)[0] = (n == 0 ? 1 : 2*f - f1);
58 SIZ(lnsub1) = (n == 0 ? -1 : 1);
59
60 return;
61 }
62
63 TMP_MARK;
64 size = MPN_FIB2_SIZE (n);
65 f1p = TMP_ALLOC_LIMBS (size);
66
67 lp = MPZ_NEWALLOC (ln, size+1);
68 l1p = MPZ_NEWALLOC (lnsub1, size+1);
69
70 size = mpn_fib2_ui (l1p, f1p, n);
71
72 /* L[n] = F[n] + 2F[n-1] */
73 #if HAVE_NATIVE_mpn_addlsh1_n
74 c = mpn_addlsh1_n (lp, l1p, f1p, size);
75 #else
76 c = mpn_lshift (lp, f1p, size, 1);
77 c += mpn_add_n (lp, lp, l1p, size);
78 #endif
79 lp[size] = c;
80 SIZ(ln) = size + (c != 0);
81
82 /* L[n-1] = 2F[n] - F[n-1] */
83 #if HAVE_NATIVE_mpn_rsblsh1_n
84 c = mpn_rsblsh1_n (l1p, f1p, l1p, size);
85 #else
86 c = mpn_lshift (l1p, l1p, size, 1);
87 c -= mpn_sub_n (l1p, l1p, f1p, size);
88 #endif
89 ASSERT ((mp_limb_signed_t) c >= 0);
90 l1p[size] = c;
91 SIZ(lnsub1) = size + (c != 0);
92
93 TMP_FREE;
94 }
95