/* mpn_jacobi_base -- limb/limb Jacobi symbol with restricted arguments.

   THIS INTERFACE IS PRELIMINARY AND MIGHT DISAPPEAR OR BE SUBJECT TO

   INCOMPATIBLE CHANGES IN A FUTURE RELEASE OF GMP.

Copyright 1999-2002, 2010 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 "gmp.h"

#include "gmp-impl.h"

#include "longlong.h"

/* Use the simple loop by default.  The generic count_trailing_zeros is not

   very fast, and the extra trickery of method 3 has proven to be less use

   than might have been though.  */

#ifndef JACOBI_BASE_METHOD

#define JACOBI_BASE_METHOD  2

#endif

/* Use count_trailing_zeros.  */

#if JACOBI_BASE_METHOD == 1

#define PROCESS_TWOS_ANY                                \

  {                                                     \

    mp_limb_t  twos;                                    \

    count_trailing_zeros (twos, a);                     \

    result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b);        \

    a >>= twos;                                         \

  }

#define PROCESS_TWOS_EVEN  PROCESS_TWOS_ANY

#endif

/* Use a simple loop.  A disadvantage of this is that there's a branch on a

   50/50 chance of a 0 or 1 low bit.  */

#if JACOBI_BASE_METHOD == 2

#define PROCESS_TWOS_EVEN               \

  {                                     \

    int  two;                           \

    two = JACOBI_TWO_U_BIT1 (b);        \

    do                                  \

      {                                 \

	a >>= 1;                        \

	result_bit1 ^= two;             \

	ASSERT (a != 0);                \

      }                                 \

    while ((a & 1) == 0);               \

  }

#define PROCESS_TWOS_ANY        \

  if ((a & 1) == 0)             \

    PROCESS_TWOS_EVEN;

#endif

/* Process one bit arithmetically, then a simple loop.  This cuts the loop

   condition down to a 25/75 chance, which should branch predict better.

   The CPU will need a reasonable variable left shift.  */

#if JACOBI_BASE_METHOD == 3

#define PROCESS_TWOS_EVEN               \

  {                                     \

    int  two, mask, shift;              \

					\

    two = JACOBI_TWO_U_BIT1 (b);        \

    mask = (~a & 2);                    \

    a >>= 1;                            \

					\

    shift = (~a & 1);                   \

    a >>= shift;                        \

    result_bit1 ^= two ^ (two & mask);  \

					\

    while ((a & 1) == 0)                \

      {                                 \

	a >>= 1;                        \

	result_bit1 ^= two;             \

	ASSERT (a != 0);                \

      }                                 \

  }

#define PROCESS_TWOS_ANY                \

  {                                     \

    int  two, mask, shift;              \

					\

    two = JACOBI_TWO_U_BIT1 (b);        \

    shift = (~a & 1);                   \

    a >>= shift;                        \

					\

    mask = shift << 1;                  \

    result_bit1 ^= (two & mask);        \

					\

    while ((a & 1) == 0)                \

      {                                 \

	a >>= 1;                        \

	result_bit1 ^= two;             \

	ASSERT (a != 0);                \

      }                                 \

  }

#endif

#if JACOBI_BASE_METHOD < 4

/* Calculate the value of the Jacobi symbol (a/b) of two mp_limb_t's, but

   with a restricted range of inputs accepted, namely b>1, b odd.

   The initial result_bit1 is taken as a parameter for the convenience of

   mpz_kronecker_ui() et al.  The sign changes both here and in those

   routines accumulate nicely in bit 1, see the JACOBI macros.

   The return value here is the normal +1, 0, or -1.  Note that +1 and -1

   have bit 1 in the "BIT1" sense, which could be useful if the caller is

   accumulating it into some extended calculation.

   Duplicating the loop body to avoid the MP_LIMB_T_SWAP(a,b) would be

   possible, but a couple of tests suggest it's not a significant speedup,

   and may even be a slowdown, so what's here is good enough for now. */

int

mpn_jacobi_base (mp_limb_t a, mp_limb_t b, int result_bit1)

{

  ASSERT (b & 1);  /* b odd */

  ASSERT (b != 1);

  if (a == 0)

    return 0;

  PROCESS_TWOS_ANY;

  if (a == 1)

    goto done;

  if (a >= b)

    goto a_gt_b;

  for (;;)

    {

      result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b);

      MP_LIMB_T_SWAP (a, b);

    a_gt_b:

      do

	{

	  /* working on (a/b), a,b odd, a>=b */

	  ASSERT (a & 1);

	  ASSERT (b & 1);

	  ASSERT (a >= b);

	  if ((a -= b) == 0)

	    return 0;

	  PROCESS_TWOS_EVEN;

	  if (a == 1)

	    goto done;

	}

      while (a >= b);

    }

 done:

  return JACOBI_BIT1_TO_PN (result_bit1);

}

#endif

#if JACOBI_BASE_METHOD == 4

/* Computes (a/b) for odd b > 1 and any a. The initial bit is taken as a

 * parameter. We have no need for the convention that the sign is in

 * bit 1, internally we use bit 0. */

/* FIXME: Could try table-based count_trailing_zeros. */

int

mpn_jacobi_base (mp_limb_t a, mp_limb_t b, int bit)

{

  int c;

  ASSERT (b & 1);

  ASSERT (b > 1);

  if (a == 0)

    /* This is the only line which depends on b > 1 */

    return 0;

  bit >>= 1;

  /* Below, we represent a and b shifted right so that the least

     significant one bit is implicit. */

  b >>= 1;

  count_trailing_zeros (c, a);

  bit ^= c & (b ^ (b >> 1));

  /* We may have c==GMP_LIMB_BITS-1, so we can't use a>>c+1. */

  a >>= c;

  a >>= 1;

  do

    {

      mp_limb_t t = a - b;

      mp_limb_t bgta = LIMB_HIGHBIT_TO_MASK (t);

      if (t == 0)

	return 0;

      /* If b > a, invoke reciprocity */

      bit ^= (bgta & a & b);

      /* b <-- min (a, b) */

      b += (bgta & t);

      /* a <-- |a - b| */

      a = (t ^ bgta) - bgta;

      /* Number of trailing zeros is the same no matter if we look at

       * t or a, but using t gives more parallelism. */

      count_trailing_zeros (c, t);

      c ++;

      /* (2/b) = -1 if b = 3 or 5 mod 8 */

      bit ^= c & (b ^ (b >> 1));

      a >>= c;

    }

  while (b > 0);

  return 1-2*(bit & 1);

}

#endif /* JACOBI_BASE_METHOD == 4 */