/* mpz_fib_ui -- calculate Fibonacci numbers.

Copyright 2000-2002, 2005, 2012, 2014 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.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;

  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;

  fp = MPZ_NEWALLOC (fn, 2 * xalloc);

  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_add_n_sub_n

      xp[size] = mpn_lshift (xp, xp, size, 1);

      yp[size] = 0;

      ASSERT_NOCARRY (mpn_add_n_sub_n (xp, yp, xp, yp, size+1));

      xsize = size + (xp[size] != 0);

      ASSERT (yp[size] <= 1);

      ysize = size + yp[size];

#else

      mp_limb_t  c2;

      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;

#if HAVE_NATIVE_mpn_addlsh1_n

      c = mpn_addlsh1_n (yp, xp, yp, size);

#else

      c = mpn_lshift (yp, yp, size, 1);

      c += mpn_add_n (yp, yp, xp, size);

#endif

      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;

}