gcc/gmp/mpz/fib_ui.c

/* mpz_fib_ui -- calculate Fibonacci numbers.

Copyright 2000, 2001, 2002, 2005 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 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.

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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */

#include <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"


/* change to "#define TRACE(x) x" to get some traces */
#define TRACE(x)


/* In the F[2k+1] below for k odd, the -2 won't give a borrow from the low
   limb because the result F[2k+1] is an F[4m+3] and such numbers are always
   == 1, 2 or 5 mod 8, whereas an underflow would leave 6 or 7.  (This is
   the same as in mpn_fib2_ui.)

   In the F[2k+1] for k even, the +2 won't give a carry out of the low limb
   in normal circumstances.  This is an F[4m+1] and we claim that F[3*2^b+1]
   == 1 mod 2^b is the first F[4m+1] congruent to 0 or 1 mod 2^b, and hence
   if n < 2^GMP_NUMB_BITS then F[n] cannot have a low limb of 0 or 1.  No
   proof for this claim, but it's been verified up to b==32 and has such a
   nice pattern it must be true :-).  Of interest is that F[3*2^b] == 0 mod
   2^(b+1) seems to hold too.

   When n >= 2^GMP_NUMB_BITS, which can arise in a nails build, then the low
   limb of F[4m+1] can certainly be 1, and an mpn_add_1 must be used.  */

void
mpz_fib_ui (mpz_ptr fn, unsigned long n)
{
  mp_ptr         fp, xp, yp;
  mp_size_t      size, xalloc;
  unsigned long  n2;
  mp_limb_t      c, c2;
  TMP_DECL;

  if (n <= FIB_TABLE_LIMIT)
    {
      PTR(fn)[0] = FIB_TABLE (n);
      SIZ(fn) = (n != 0);      /* F[0]==0, others are !=0 */
      return;
    }

  n2 = n/2;
  xalloc = MPN_FIB2_SIZE (n2) + 1;
  MPZ_REALLOC (fn, 2*xalloc+1);
  fp = PTR (fn);

  TMP_MARK;
  TMP_ALLOC_LIMBS_2 (xp,xalloc, yp,xalloc);
  size = mpn_fib2_ui (xp, yp, n2);

  TRACE (printf ("mpz_fib_ui last step n=%lu size=%ld bit=%lu\n",
                 n >> 1, size, n&1);
         mpn_trace ("xp", xp, size);
         mpn_trace ("yp", yp, size));

  if (n & 1)
    {
      /* F[2k+1] = (2F[k]+F[k-1])*(2F[k]-F[k-1]) + 2*(-1)^k  */
      mp_size_t  xsize, ysize;

#if HAVE_NATIVE_mpn_addsub_n
      xp[size] = mpn_lshift (xp, xp, size, 1);
      yp[size] = 0;
      ASSERT_NOCARRY (mpn_addsub_n (xp, yp, xp, yp, size+1));
      xsize = size + (xp[size] != 0);
      ysize = size + (yp[size] != 0);
#else
      c2 = mpn_lshift (fp, xp, size, 1);
      c = c2 + mpn_add_n (xp, fp, yp, size);
      xp[size] = c;
      xsize = size + (c != 0);
      c2 -= mpn_sub_n (yp, fp, yp, size);
      yp[size] = c2;
      ASSERT (c2 <= 1);
      ysize = size + c2;
#endif

      size = xsize + ysize;
      c = mpn_mul (fp, xp, xsize, yp, ysize);

#if GMP_NUMB_BITS >= BITS_PER_ULONG
      /* no overflow, see comments above */
      ASSERT (n & 2 ? fp[0] >= 2 : fp[0] <= GMP_NUMB_MAX-2);
      fp[0] += (n & 2 ? -CNST_LIMB(2) : CNST_LIMB(2));
#else
      if (n & 2)
        {
          ASSERT (fp[0] >= 2);
          fp[0] -= 2;
        }
      else
        {
          ASSERT (c != GMP_NUMB_MAX); /* because it's the high of a mul */
          c += mpn_add_1 (fp, fp, size-1, CNST_LIMB(2));
          fp[size-1] = c;
        }
#endif
    }
  else
    {
      /* F[2k] = F[k]*(F[k]+2F[k-1]) */

      mp_size_t  xsize, ysize;
      c = mpn_lshift (yp, yp, size, 1);
      c += mpn_add_n (yp, yp, xp, size);
      yp[size] = c;
      xsize = size;
      ysize = size + (c != 0);
      size += ysize;
      c = mpn_mul (fp, yp, ysize, xp, xsize);
    }

  /* one or two high zeros */
  size -= (c == 0);
  size -= (fp[size-1] == 0);
  SIZ(fn) = size;

  TRACE (printf ("done special, size=%ld\n", size);
         mpn_trace ("fp ", fp, size));

  TMP_FREE;
}