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
      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  }