mpir/mpz/gcd.c

/* mpz/gcd.c:   Calculate the greatest common divisor of two integers.

Copyright 1991, 1993, 1994, 1996, 2000, 2001, 2002 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 2.1 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; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include "mpir.h"
#include "gmp-impl.h"
#include "longlong.h"
#ifdef BERKELEY_MP
# error BERKELEY_MP not supported
#endif

#define GCD_BODY(MPN_GCD)							\
{										\
  unsigned long int g_zero_bits, u_zero_bits, v_zero_bits;			\
  mp_size_t g_zero_limbs, u_zero_limbs, v_zero_limbs;				\
  mp_ptr tp;									\
  mp_ptr up = u->_mp_d;								\
  mp_size_t usize = ABS (u->_mp_size);						\
  mp_ptr vp = v->_mp_d;								\
  mp_size_t vsize = ABS (v->_mp_size);						\
  mp_size_t gsize;								\
  TMP_DECL;								        \
										\
  /* GCD(0, V) == V.  */							\
  if (usize == 0)								\
    {										\
      g->_mp_size = vsize;							\
      if (g == v)								\
	return;									\
      if (g->_mp_alloc < vsize)							\
	_mpz_realloc (g, vsize);						\
      MPN_COPY (g->_mp_d, vp, vsize);						\
      return;									\
    }										\
										\
  /* GCD(U, 0) == U.  */							\
  if (vsize == 0)								\
    {										\
      g->_mp_size = usize;							\
      if (g == u)								\
	return;									\
      if (g->_mp_alloc < usize)							\
	_mpz_realloc (g, usize);						\
      MPN_COPY (g->_mp_d, up, usize);						\
      return;									\
    }										\
										\
  if (usize == 1)								\
    {										\
      g->_mp_size = 1;								\
      g->_mp_d[0] = mpn_gcd_1 (vp, vsize, up[0]);				\
      return;									\
    }										\
										\
  if (vsize == 1)								\
    {										\
      g->_mp_size = 1;								\
      g->_mp_d[0] = mpn_gcd_1 (up, usize, vp[0]);				\
      return;									\
    }										\
										\
  TMP_MARK;      								\
										\
  /*  Eliminate low zero bits from U and V and move to temporary storage.  */	\
  while (*up == 0)								\
    up++;									\
  u_zero_limbs = up - u->_mp_d;							\
  usize -= u_zero_limbs;							\
  count_trailing_zeros (u_zero_bits, *up);					\
  tp = up;									\
  up = (mp_ptr) TMP_ALLOC (usize * BYTES_PER_MP_LIMB);				\
  if (u_zero_bits != 0)								\
    {										\
      mpn_rshift (up, tp, usize, u_zero_bits);					\
      usize -= up[usize - 1] == 0;						\
    }										\
  else										\
    MPN_COPY (up, tp, usize);							\
										\
  while (*vp == 0)								\
    vp++;									\
  v_zero_limbs = vp - v->_mp_d;							\
  vsize -= v_zero_limbs;							\
  count_trailing_zeros (v_zero_bits, *vp);					\
  tp = vp;									\
  vp = (mp_ptr) TMP_ALLOC (vsize * BYTES_PER_MP_LIMB);				\
  if (v_zero_bits != 0)								\
    {										\
      mpn_rshift (vp, tp, vsize, v_zero_bits);					\
      vsize -= vp[vsize - 1] == 0;						\
    }										\
  else										\
    MPN_COPY (vp, tp, vsize);							\
										\
  if (u_zero_limbs > v_zero_limbs)						\
    {										\
      g_zero_limbs = v_zero_limbs;						\
      g_zero_bits = v_zero_bits;						\
    }										\
  else if (u_zero_limbs < v_zero_limbs)						\
    {										\
      g_zero_limbs = u_zero_limbs;						\
      g_zero_bits = u_zero_bits;						\
    }										\
  else  /*  Equal.  */								\
    {										\
      g_zero_limbs = u_zero_limbs;						\
      g_zero_bits = MIN (u_zero_bits, v_zero_bits);				\
    }										\
										\
  /*  Call mpn_gcd.  The 2nd argument must not have more bits than the 1st.  */	\
  vsize = (usize < vsize || (usize == vsize && up[usize-1] < vp[vsize-1]))	\
    ? MPN_GCD (vp, vp, vsize, up, usize)					\
    : MPN_GCD (vp, up, usize, vp, vsize);					\
										\
  /*  Here G <-- V << (g_zero_limbs*BITS_PER_MP_LIMB + g_zero_bits).  */	\
  gsize = vsize + g_zero_limbs;							\
  if (g_zero_bits != 0)								\
    {										\
      mp_limb_t cy_limb;							\
      gsize += (vp[vsize - 1] >> (GMP_NUMB_BITS - g_zero_bits)) != 0;		\
      if (g->_mp_alloc < gsize)							\
	_mpz_realloc (g, gsize);						\
      MPN_ZERO (g->_mp_d, g_zero_limbs);					\
										\
      tp = g->_mp_d + g_zero_limbs;						\
      cy_limb = mpn_lshift (tp, vp, vsize, g_zero_bits);			\
      if (cy_limb != 0)								\
	tp[vsize] = cy_limb;							\
    }										\
  else										\
    {										\
      if (g->_mp_alloc < gsize)							\
	_mpz_realloc (g, gsize);						\
      MPN_ZERO (g->_mp_d, g_zero_limbs);					\
      MPN_COPY (g->_mp_d + g_zero_limbs, vp, vsize);				\
    }										\
										\
  g->_mp_size = gsize;								\
  TMP_FREE;      								\
}

void
mpz_gcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
  GCD_BODY(mpn_gcd)

void
mpz_rgcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
  GCD_BODY(mpn_rgcd)

void
mpz_bgcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
  GCD_BODY(mpn_bgcd)

void
mpz_sgcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
  GCD_BODY(mpn_sgcd)

void
mpz_ngcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
  GCD_BODY(mpn_ngcd)

void
mpz_lgcd (mpz_ptr g, mpz_srcptr u, mpz_srcptr v)
  GCD_BODY(mpn_lgcd)

#if 0

#define ODD(x) ((x) & 1)

/* Returns the number of zero limbs at the least significant end of x,
   and the number of zero bits of the first non-zero limb. If x == 0,
   returns n and sets *bits = 0. */
static mp_size_t
power_of_2 (unsigned *bits, mp_srcptr xp, mp_size_t n)
{
  mp_size_t zlimbs;

  for (zlimbs = 0; zlimbs < n && xp[zlimbs] == 0; zlimbs++)
    ;

  if (zlimbs == n || ODD (xp[zlimbs]))
    *bits = 0;
  else
    {
      int count;

      count_trailing_zeros (count, xp[zlimbs]);
      *bits = count;
    }

  return zlimbs;
}

void
mpz_bgcd (mpz_t g, mpz_t a, mpz_t b)
{  
  mp_size_t an = ABSIZ (a);
  mp_size_t bn = ABSIZ (b);
  mp_srcptr ap = PTR (a);
  mp_srcptr bp = PTR (b);
  mp_size_t bz;
  mp_size_t az;
  
  mp_ptr tp;
  
  unsigned abits;
  unsigned bbits;
  unsigned power;
  TMP_DECL (marker);
  
  az = power_of_2(&abits, ap, an);
  if (az == an)
    {
      mpz_abs (g, b);
      return;
    }

  bz = power_of_2(&bbits, bp, bn);
  if (bz == bn)
    {
      mpz_abs (g, a);
      return;
    }

  if (az < bz)
    power = az * GMP_NUMB_BITS + abits;
  else if (az > bz)
    power = bz * GMP_NUMB_BITS + bbits;
  else
    power = az + MIN (abits, bbits);

  an -= az; ap += az;
  bn -= bz; bp += bz;

  if (an < bn)
    {
      unsigned t = abits;
      abits = bbits;
      bbits = t;
      
      MPN_SRCPTR_SWAP (ap, an, bp, bn);
    }

  TMP_MARK (marker);
  tp = TMP_ALLOC_LIMBS (an + bn);

  if (abits > 0)
    mpn_rshift (tp, ap, an, abits);
  else
    MPN_COPY (tp, ap, an);

  if (bbits > 0)
    mpn_rshift (tp + an, bp, bn, bbits);
  else
    MPN_COPY (tp + an, bp, bn);

  mpz_realloc (g, bn);
  SIZ(g) = mpn_bgcd (PTR(g), tp, an, tp + an, bn);

  TMP_FREE (marker);
}
#endif