1/* mpz_lucnum2_ui -- calculate Lucas numbers.
2
3Copyright 2001, 2003, 2005, 2012, 2015, 2016, 2018 Free Software
4Foundation, Inc.
5
6This file is part of the GNU MP Library.
7
8The GNU MP Library is free software; you can redistribute it and/or modify
9it 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
15or
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
21or both in parallel, as here.
22
23The GNU MP Library is distributed in the hope that it will be useful, but
24WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
25or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
26for more details.
27
28You should have received copies of the GNU General Public License and the
29GNU Lesser General Public License along with the GNU MP Library.  If not,
30see https://www.gnu.org/licenses/.  */
31
32#include <stdio.h>
33#include "gmp-impl.h"
34
35
36void
37mpz_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