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

Contributed to the GNU project by Marco Bodrato.

   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"

#if HAVE_NATIVE_mpn_rsblsh1_n || HAVE_NATIVE_mpn_sublsh1_n

#else

/* 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;

}

#endif

/* Computes at most count terms of the sequence needed by the

   Lucas-Lehmer-Riesel test, indexing backward:

   L_i = L_{i+1}^2 - 2

   The sequence is computed modulo M = {mp, mn}.

   The starting point is given in L_{count+1} = {lp, mn}.

   The scratch pointed by sp, needs a space of at least 3 * mn + 1 limbs.

   Returns the index i>0 if L_i = 0 (mod M) is found within the

   computed count terms of the sequence.  Otherwise it returns zero.

   Note: (+/-2)^2-2=2, (+/-1)^2-2=-1, 0^2-2=-2

 */

static mp_bitcnt_t

mpn_llriter (mp_ptr lp, mp_srcptr mp, mp_size_t mn, mp_bitcnt_t count, mp_ptr sp)

{

  do

    {

      mpn_sqr (sp, lp, mn);

      mpn_tdiv_qr (sp + 2 * mn, lp, 0, sp, 2 * mn, mp, mn);

      if (lp[0] < 5)

  {

    /* If L^2 % M < 5, |L^2 % M - 2| <= 2 */

    if (mn == 1 || mpn_zero_p (lp + 1, mn - 1))

      return (lp[0] == 2) ? count : 0;

    else

      MPN_DECR_U (lp, mn, 2);

  }

      else

  lp[0] -= 2;

    } while (--count != 0);

  return 0;

}

/* Store the Lucas' number L[n] at lp (maybe), computed modulo m.  lp

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

   Returns the size of L[n] normally.

   If F[n] is zero modulo m, or L[n] is, returns 0 and lp is

   undefined.

*/

static mp_size_t

mpn_lucm (mp_ptr lp, mp_srcptr np, mp_size_t nn, mp_srcptr mp, mp_size_t mn, mp_ptr scratch)

{

  int   neg;

  mp_limb_t cy;

  ASSERT (! MPN_OVERLAP_P (lp, MAX(2*mn+1,5), scratch, MAX(2*mn+1,5)));

  ASSERT (nn > 0);

  neg = mpn_fib2m (lp, scratch, np, nn, mp, mn);

  /* F[n] = +/-{lp, mn}, F[n-1] = +/-{scratch, mn} */

  if (mpn_zero_p (lp, mn))

    return 0;

  if (neg) /* One sign is opposite, use sub instead of add. */

    {

#if HAVE_NATIVE_mpn_rsblsh1_n || HAVE_NATIVE_mpn_sublsh1_n

#if HAVE_NATIVE_mpn_rsblsh1_n

      cy = mpn_rsblsh1_n (lp, lp, scratch, mn); /* L[n] = +/-(2F[n-1]-(-F[n])) */

#else

      cy = mpn_sublsh1_n (lp, lp, scratch, mn); /* L[n] = -/+(F[n]-(-2F[n-1])) */

      if (cy != 0)

  cy = mpn_add_n (lp, lp, mp, mn) - cy;

#endif

      if (cy > 1)

  cy += mpn_add_n (lp, lp, mp, mn);

#else

      cy = mpn_lshift (scratch, scratch, mn, 1); /* 2F[n-1] */

      if (UNLIKELY (cy))

  cy -= mpn_sub_n (lp, scratch, lp, mn); /* L[n] = +/-(2F[n-1]-(-F[n])) */

      else

  abs_sub_n (lp, lp, scratch, mn);

#endif

      ASSERT (cy <= 1);

    }

  else

    {

#if HAVE_NATIVE_mpn_addlsh1_n

      cy = mpn_addlsh1_n (lp, lp, scratch, mn); /* L[n] = +/-(2F[n-1]+F[n])) */

#else

      cy = mpn_lshift (scratch, scratch, mn, 1);

      cy+= mpn_add_n (lp, lp, scratch, mn);

#endif

      ASSERT (cy <= 2);

    }

  while (cy || mpn_cmp (lp, mp, mn) >= 0)

    cy -= mpn_sub_n (lp, lp, mp, mn);

  MPN_NORMALIZE (lp, mn);

  return mn;

}

int

mpn_strongfibo (mp_srcptr mp, mp_size_t mn, mp_ptr scratch)

{

  mp_ptr  lp, sp;

  mp_size_t en;

  mp_bitcnt_t b0;

  TMP_DECL;

#if GMP_NUMB_BITS % 4 == 0

  b0 = mpn_scan0 (mp, 0);

#else

  {

    mpz_t m = MPZ_ROINIT_N(mp, mn);

    b0 = mpz_scan0 (m, 0);

  }

  if (UNLIKELY (b0 == mn * GMP_NUMB_BITS))

    {

      en = 1;

      scratch [0] = 1;

    }

  else

#endif

    {

      int cnt = b0 % GMP_NUMB_BITS;

      en = b0 / GMP_NUMB_BITS;

      if (LIKELY (cnt != 0))

  mpn_rshift (scratch, mp + en, mn - en, cnt);

      else

  MPN_COPY (scratch, mp + en, mn - en);

      en = mn - en;

      scratch [0] |= 1;

      en -= scratch [en - 1] == 0;

    }

  TMP_MARK;

  lp = TMP_ALLOC_LIMBS (4 * mn + 6);

  sp = lp + 2 * mn + 3;

  en = mpn_lucm (sp, scratch, en, mp, mn, lp);

  if (en != 0 && LIKELY (--b0 != 0))

    {

      mpn_sqr (lp, sp, en);

      lp [0] |= 2; /* V^2 + 2 */

      if (LIKELY (2 * en >= mn))

  mpn_tdiv_qr (sp, lp, 0, lp, 2 * en, mp, mn);

      else

  MPN_ZERO (lp + 2 * en, mn - 2 * en);

      if (! mpn_zero_p (lp, mn) && LIKELY (--b0 != 0))

  b0 = mpn_llriter (lp, mp, mn, b0, lp + mn + 1);

    }

  TMP_FREE;

  return (b0 != 0);

}