mpn/generic/toom2_sqr.c

/* mpn_toom2_sqr -- Square {ap,an}.

   Contributed to the GNU project by Torbjorn Granlund.

   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 2006-2010, 2012, 2014, 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 "gmp-impl.h"

/* Evaluate in: -1, 0, +inf

  <-s--><--n-->
   ____ ______
  |_a1_|___a0_|

  v0  =  a0     ^2  #   A(0)^2
  vm1 = (a0- a1)^2  #  A(-1)^2
  vinf=      a1 ^2  # A(inf)^2
*/

#if TUNE_PROGRAM_BUILD || WANT_FAT_BINARY
#define MAYBE_sqr_toom2   1
#else
#define MAYBE_sqr_toom2							\
  (SQR_TOOM3_THRESHOLD >= 2 * SQR_TOOM2_THRESHOLD)
#endif

#define TOOM2_SQR_REC(p, a, n, ws)					\
  do {									\
    if (! MAYBE_sqr_toom2						\
	|| BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))			\
      mpn_sqr_basecase (p, a, n);					\
    else								\
      mpn_toom2_sqr (p, a, n, ws);					\
  } while (0)

void
mpn_toom2_sqr (mp_ptr pp,
	       mp_srcptr ap, mp_size_t an,
	       mp_ptr scratch)
{
  const int __gmpn_cpuvec_initialized = 1;
  mp_size_t n, s;
  mp_limb_t cy, cy2;
  mp_ptr asm1;

#define a0  ap
#define a1  (ap + n)

  s = an >> 1;
  n = an - s;

  ASSERT (0 < s && s <= n && s >= n - 1);

  asm1 = pp;

  /* Compute asm1.  */
  if (s == n)
    {
      if (mpn_cmp (a0, a1, n) < 0)
	{
	  mpn_sub_n (asm1, a1, a0, n);
	}
      else
	{
	  mpn_sub_n (asm1, a0, a1, n);
	}
    }
  else /* n - s == 1 */
    {
      if (a0[s] == 0 && mpn_cmp (a0, a1, s) < 0)
	{
	  mpn_sub_n (asm1, a1, a0, s);
	  asm1[s] = 0;
	}
      else
	{
	  asm1[s] = a0[s] - mpn_sub_n (asm1, a0, a1, s);
	}
    }

#define v0	pp				/* 2n */
#define vinf	(pp + 2 * n)			/* s+s */
#define vm1	scratch				/* 2n */
#define scratch_out	scratch + 2 * n

  /* vm1, 2n limbs */
  TOOM2_SQR_REC (vm1, asm1, n, scratch_out);

  /* vinf, s+s limbs */
  TOOM2_SQR_REC (vinf, a1, s, scratch_out);

  /* v0, 2n limbs */
  TOOM2_SQR_REC (v0, ap, n, scratch_out);

  /* H(v0) + L(vinf) */
  cy = mpn_add_n (pp + 2 * n, v0 + n, vinf, n);

  /* L(v0) + H(v0) */
  cy2 = cy + mpn_add_n (pp + n, pp + 2 * n, v0, n);

  /* L(vinf) + H(vinf) */
  cy += mpn_add (pp + 2 * n, pp + 2 * n, n, vinf + n, s + s - n);

  cy -= mpn_sub_n (pp + n, pp + n, vm1, 2 * n);

  ASSERT (cy + 1 <= 3);
  ASSERT (cy2 <= 2);

  if (LIKELY (cy <= 2)) {
    MPN_INCR_U (pp + 2 * n, s + s, cy2);
    MPN_INCR_U (pp + 3 * n, s + s - n, cy);
  } else { /* cy is negative */
    /* The total contribution of v0+vinf-vm1 can not be negative. */
#if WANT_ASSERT
    /* The borrow in cy stops the propagation of the carry cy2, */
    ASSERT (cy2 == 1);
    cy += mpn_add_1 (pp + 2 * n, pp + 2 * n, n, cy2);
    ASSERT (cy == 0);
#else
    /* we simply fill the area with zeros. */
    MPN_FILL (pp + 2 * n, n, 0);
#endif
  }
}