mpir/mpn/generic/toom_eval_pm2.c

/* mpn_toom_eval_pm2 -- Evaluate a polynomial in +2 and -2

   Contributed to the GNU project by Niels M<EFBFBD>ller and Marco Bodrato

   THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY
   SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2009 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 3 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.  If not, see http://www.gnu.org/licenses/.  */

#include "mpir.h"
#include "gmp-impl.h"

/* DO_addlsh2(d,a,b,n,cy) computes cy,{d,n} <- {a,n} + 4*(cy,{b,n}), it
   can be used as DO_addlsh2(d,a,d,n,d[n]), for accumulation on {d,n+1}. */
#if HAVE_NATIVE_mpn_addlsh2_n
#define DO_addlsh2(d, a, b, n, cy)	\
do {					\
  (cy) <<= 2;				\
  (cy) += mpn_addlsh2_n(d, a, b, n);	\
} while (0)
#else
#if HAVE_NATIVE_mpn_addlsh_n
#define DO_addlsh2(d, a, b, n, cy)	\
do {					\
  (cy) <<= 2;				\
  (cy) += mpn_addlsh_n(d, a, b, n, 2);	\
} while (0)
#else
/* The following is not a general substitute for addlsh2.
   It is correct if d == b, but it is not if d == a.	*/
#define DO_addlsh2(d, a, b, n, cy)	\
do {					\
  (cy) <<= 2;				\
  (cy) += mpn_lshift(d, b, n, 2);	\
  (cy) += mpn_add_n(d, d, a, n);	\
} while (0)
#endif
#endif

/* Evaluates a polynomial of degree 2 < k < GMP_NUMB_BITS, in the
   points +2 and -2. */
int
mpn_toom_eval_pm2 (mp_ptr xp2, mp_ptr xm2, unsigned k,
		   mp_srcptr xp, mp_size_t n, mp_size_t hn, mp_ptr tp)
{
  int i;
  int neg;
  mp_limb_t cy;

  ASSERT (k >= 3);
  ASSERT (k < GMP_NUMB_BITS);

  ASSERT (hn > 0);
  ASSERT (hn <= n);

  /* The degree k is also the number of full-size coefficients, so
   * that last coefficient, of size hn, starts at xp + k*n. */

  cy = 0;
  DO_addlsh2 (xp2, xp + (k-2) * n, xp + k * n, hn, cy);
  if (hn != n)
    cy = mpn_add_1 (xp2 + hn, xp + (k-2) * n + hn, n - hn, cy);
  for (i = k - 4; i >= 0; i -= 2)
    DO_addlsh2 (xp2, xp + i * n, xp2, n, cy);
  xp2[n] = cy;

  k--;

  cy = 0;
  DO_addlsh2 (tp, xp + (k-2) * n, xp + k * n, n, cy);
  for (i = k - 4; i >= 0; i -= 2)
    DO_addlsh2 (tp, xp + i * n, tp, n, cy);
  tp[n] = cy;

  if (k & 1)
    ASSERT_NOCARRY(mpn_lshift (tp , tp , n + 1, 1));
  else
    ASSERT_NOCARRY(mpn_lshift (xp2, xp2, n + 1, 1));

  neg = (mpn_cmp (xp2, tp, n + 1) < 0) ? ~0 : 0;

#if HAVE_NATIVE_mpn_sumdiff_n
  if (neg)
    mpn_sumdiff_n (xp2, xm2, tp, xp2, n + 1);
  else
    mpn_sumdiff_n (xp2, xm2, xp2, tp, n + 1);
#else 
  if (neg)
    mpn_sub_n (xm2, tp, xp2, n + 1);
  else
    mpn_sub_n (xm2, xp2, tp, n + 1);

  mpn_add_n (xp2, xp2, tp, n + 1);
#endif

  ASSERT (xp2[n] < (1<<(k+2))-1);
  ASSERT (xm2[n] < ((1<<(k+3))-1 - (1^k&1))/3);

  neg ^= ((k & 1) - 1);

  return neg;
}

#undef DO_addlsh2