/* mpn_fib2m -- calculate Fibonacci numbers, modulo m.

Contributed to the GNU project by Marco Bodrato, based on the previous

fib2_ui.c file.

   THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST

   CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN

   FUTURE GNU MP RELEASES.

Copyright 2001, 2002, 2005, 2009, 2018 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-impl.h"

#include "longlong.h"

/* Stores |{ap,n}-{bp,n}| in {rp,n},

   returns the sign of {ap,n}-{bp,n}. */

static int

abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)

{

  mp_limb_t  x, y;

  while (--n >= 0)

    {

      x = ap[n];

      y = bp[n];

      if (x != y)

        {

          ++n;

          if (x > y)

            {

              ASSERT_NOCARRY (mpn_sub_n (rp, ap, bp, n));

              return 1;

            }

          else

            {

              ASSERT_NOCARRY (mpn_sub_n (rp, bp, ap, n));

              return -1;

            }

        }

      rp[n] = 0;

    }

  return 0;

}

/* Store F[n] at fp and F[n-1] at f1p.  Both are computed modulo m.

   fp and f1p should have room for mn*2+1 limbs.

   The sign of one or both the values may be flipped (n-F, instead of F),

   the return value is 0 (zero) if the signs are coherent (both positive

   or both negative) and 1 (one) otherwise.

   Notes:

   In F[2k+1] with k even, +2 is applied to 4*F[k]^2 just by ORing into the

   low limb.

   In F[2k+1] with k odd, -2 is applied to F[k-1]^2 just by ORing into the

   low limb.

   TODO: Should {tp, 2 * mn} be passed as a scratch pointer?

   Should the call to mpn_fib2_ui() obtain (up to) 2*mn limbs?

*/

int

mpn_fib2m (mp_ptr fp, mp_ptr f1p, mp_srcptr np, mp_size_t nn, mp_srcptr mp, mp_size_t mn)

{

  unsigned long nfirst;

  mp_limb_t nh;

  mp_bitcnt_t nbi;

  mp_size_t sn, fn;

  int   fcnt, ncnt;

  ASSERT (! MPN_OVERLAP_P (fp, MAX(2*mn+1,5), f1p, MAX(2*mn+1,5)));

  ASSERT (nn > 0 && np[nn - 1] != 0);

  /* Estimate the maximal n such that fibonacci(n) fits in mn limbs. */

#if GMP_NUMB_BITS % 16 == 0

  if (UNLIKELY (ULONG_MAX / (23 * (GMP_NUMB_BITS / 16)) <= mn))

    nfirst = ULONG_MAX;

  else

    nfirst = mn * (23 * (GMP_NUMB_BITS / 16));

#else

  {

    mp_bitcnt_t mbi;

    mbi = (mp_bitcnt_t) mn * GMP_NUMB_BITS;

    if (UNLIKELY (ULONG_MAX / 23 < mbi))

      {

  if (UNLIKELY (ULONG_MAX / 23 * 16 <= mbi))

    nfirst = ULONG_MAX;

  else

    nfirst = mbi / 16 * 23;

      }

    else

      nfirst = mbi * 23 / 16;

  }

#endif

  sn = nn - 1;

  nh = np[sn];

  count_leading_zeros (ncnt, nh);

  count_leading_zeros (fcnt, nfirst);

  if (fcnt >= ncnt)

    {

      ncnt = fcnt - ncnt;

      nh >>= ncnt;

    }

  else if (sn > 0)

    {

      ncnt -= fcnt;

      nh <<= ncnt;

      ncnt = GMP_NUMB_BITS - ncnt;

      --sn;

      nh |= np[sn] >> ncnt;

    }

  else

    ncnt = 0;

  nbi = sn * GMP_NUMB_BITS + ncnt;

  if (nh > nfirst)

    {

      nh >>= 1;

      ++nbi;

    }

  ASSERT (nh <= nfirst);

  /* Take a starting pair from mpn_fib2_ui. */

  fn = mpn_fib2_ui (fp, f1p, nh);

  MPN_ZERO (fp + fn, mn - fn);

  MPN_ZERO (f1p + fn, mn - fn);

  if (nbi == 0)

    {

      if (fn == mn)

  {

    mp_limb_t qp[2];

    mpn_tdiv_qr (qp, fp, 0, fp, fn, mp, mn);

    mpn_tdiv_qr (qp, f1p, 0, f1p, fn, mp, mn);

  }

      return 0;

    }

  else

    {

      mp_ptr  tp;

      unsigned  pb = nh & 1;

      int neg;

      TMP_DECL;

      TMP_MARK;

      tp = TMP_ALLOC_LIMBS (2 * mn + (mn < 2));

      do

  {

    mp_ptr  rp;

    /* Here fp==F[k] and f1p==F[k-1], with k being the bits of n from

       nbi upwards.

       Based on the next bit of n, we'll double to the pair

       fp==F[2k],f1p==F[2k-1] or fp==F[2k+1],f1p==F[2k], according as

       that bit is 0 or 1 respectively.  */

    mpn_sqr (tp, fp,  mn);

    mpn_sqr (fp, f1p, mn);

    /* Calculate F[2k-1] = F[k]^2 + F[k-1]^2. */

    f1p[2 * mn] = mpn_add_n (f1p, tp, fp, 2 * mn);

    /* Calculate F[2k+1] = 4*F[k]^2 - F[k-1]^2 + 2*(-1)^k.

       pb is the low bit of our implied k.  */

    /* fp is F[k-1]^2 == 0 or 1 mod 4, like all squares. */

    ASSERT ((fp[0] & 2) == 0);

    ASSERT (pb == (pb & 1));

    ASSERT ((fp[0] + (pb ? 2 : 0)) == (fp[0] | (pb << 1)));

    fp[0] |= pb << 1;   /* possible -2 */

#if HAVE_NATIVE_mpn_rsblsh2_n

    fp[2 * mn] = 1 + mpn_rsblsh2_n (fp, fp, tp, 2 * mn);

    MPN_INCR_U(fp, 2 * mn + 1, (1 ^ pb) << 1);  /* possible +2 */

    fp[2 * mn] = (fp[2 * mn] - 1) & GMP_NUMB_MAX;

#else

    {

      mp_limb_t  c;

      c = mpn_lshift (tp, tp, 2 * mn, 2);

      tp[0] |= (1 ^ pb) << 1; /* possible +2 */

      c -= mpn_sub_n (fp, tp, fp, 2 * mn);

      fp[2 * mn] = c & GMP_NUMB_MAX;

    }

#endif

    neg = fp[2 * mn] == GMP_NUMB_MAX;

    /* Calculate F[2k-1] = F[k]^2 + F[k-1]^2 */

    /* Calculate F[2k+1] = 4*F[k]^2 - F[k-1]^2 + 2*(-1)^k */

    /* Calculate F[2k] = F[2k+1] - F[2k-1], replacing the unwanted one of

       F[2k+1] and F[2k-1].  */

    --nbi;

    pb = (np [nbi / GMP_NUMB_BITS] >> (nbi % GMP_NUMB_BITS)) & 1;

    rp = pb ? f1p : fp;

    if (neg)

      {

        /* Calculate -(F[2k+1] - F[2k-1]) */

        rp[2 * mn] = f1p[2 * mn] + 1 - mpn_sub_n (rp, f1p, fp, 2 * mn);

        neg = ! pb;

        if (pb) /* fp not overwritten, negate it. */

    fp [2 * mn] = 1 ^ mpn_neg (fp, fp, 2 * mn);

      }

    else

      {

        neg = abs_sub_n (rp, fp, f1p, 2 * mn + 1) < 0;

      }

    mpn_tdiv_qr (tp, fp, 0, fp, 2 * mn + 1, mp, mn);

    mpn_tdiv_qr (tp, f1p, 0, f1p, 2 * mn + 1, mp, mn);

  }

      while (nbi != 0);

      TMP_FREE;

      return neg;

    }

}