xref: /dflybsd-src/contrib/gmp/mpn/generic/toom4_sqr.c (revision 86d7f5d305c6adaa56ff4582ece9859d73106103)

/* mpn_toom4_sqr -- Square {ap,an}.

   Contributed to the GNU project by Torbjorn Granlund 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 2006, 2007, 2008, 2009, 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 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 "gmp.h"
#include "gmp-impl.h"

/* Evaluate in: -1, -1/2, 0, +1/2, +1, +2, +inf

  <-s--><--n--><--n--><--n-->
   ____ ______ ______ ______
  |_a3_|___a2_|___a1_|___a0_|

  v0  =   a0             ^2 #    A(0)^2
  v1  = ( a0+ a1+ a2+ a3)^2 #    A(1)^2   ah  <= 3
  vm1 = ( a0- a1+ a2- a3)^2 #   A(-1)^2  |ah| <= 1
  v2  = ( a0+2a1+4a2+8a3)^2 #    A(2)^2   ah  <= 14
  vh  = (8a0+4a1+2a2+ a3)^2 #  A(1/2)^2   ah  <= 14
  vmh = (8a0-4a1+2a2- a3)^2 # A(-1/2)^2  -4<=ah<=9
  vinf=               a3 ^2 #  A(inf)^2
*/

#if TUNE_PROGRAM_BUILD
#define MAYBE_sqr_basecase 1
#define MAYBE_sqr_toom2   1
#define MAYBE_sqr_toom4   1
#else
#define MAYBE_sqr_basecase						\
  (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM2_THRESHOLD)
#define MAYBE_sqr_toom2							\
  (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM3_THRESHOLD)
#define MAYBE_sqr_toom4							\
  (SQR_FFT_THRESHOLD >= 4 * SQR_TOOM4_THRESHOLD)
#endif

#define TOOM4_SQR_REC(p, a, n, ws)					\
  do {									\
    if (MAYBE_sqr_basecase						\
	&& BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))			\
      mpn_sqr_basecase (p, a, n);					\
    else if (MAYBE_sqr_toom2						\
	     && BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))		\
      mpn_toom2_sqr (p, a, n, ws);					\
    else if (! MAYBE_sqr_toom4						\
	     || BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD))		\
      mpn_toom3_sqr (p, a, n, ws);					\
    else								\
      mpn_toom4_sqr (p, a, n, ws);					\
  } while (0)

void
mpn_toom4_sqr (mp_ptr pp,
	       mp_srcptr ap, mp_size_t an,
	       mp_ptr scratch)
{
  mp_size_t n, s;
  mp_limb_t cy;

#define a0  ap
#define a1  (ap + n)
#define a2  (ap + 2*n)
#define a3  (ap + 3*n)

  n = (an + 3) >> 2;

  s = an - 3 * n;

  ASSERT (0 < s && s <= n);

  /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
   * following limb, so these must be computed in order, and we need a
   * one limb gap to tp. */
#define v0    pp				/* 2n */
#define v1    (pp + 2 * n)			/* 2n+1 */
#define vinf  (pp + 6 * n)			/* s+t */
#define v2    scratch				/* 2n+1 */
#define vm2   (scratch + 2 * n + 1)		/* 2n+1 */
#define vh    (scratch + 4 * n + 2)		/* 2n+1 */
#define vm1   (scratch + 6 * n + 3)		/* 2n+1 */
#define tp (scratch + 8*n + 5)

  /* No overlap with v1 */
#define apx   pp				/* n+1 */
#define amx   (pp + 4*n + 2)			/* n+1 */

  /* Total scratch need: 8*n + 5 + scratch for recursive calls. This
     gives roughly 32 n/3 + log term. */

  /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3.  */
  mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp);

  TOOM4_SQR_REC (v2, apx, n + 1, tp);	/* v2,  2n+1 limbs */
  TOOM4_SQR_REC (vm2, amx, n + 1, tp);	/* vm2,  2n+1 limbs */

  /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
#if HAVE_NATIVE_mpn_addlsh1_n
  cy = mpn_addlsh1_n (apx, a1, a0, n);
  cy = 2*cy + mpn_addlsh1_n (apx, a2, apx, n);
  if (s < n)
    {
      mp_limb_t cy2;
      cy2 = mpn_addlsh1_n (apx, a3, apx, s);
      apx[n] = 2*cy + mpn_lshift (apx + s, apx + s, n - s, 1);
      MPN_INCR_U (apx + s, n+1-s, cy2);
    }
  else
    apx[n] = 2*cy + mpn_addlsh1_n (apx, a3, apx, n);
#else
  cy = mpn_lshift (apx, a0, n, 1);
  cy += mpn_add_n (apx, apx, a1, n);
  cy = 2*cy + mpn_lshift (apx, apx, n, 1);
  cy += mpn_add_n (apx, apx, a2, n);
  cy = 2*cy + mpn_lshift (apx, apx, n, 1);
  apx[n] = cy + mpn_add (apx, apx, n, a3, s);
#endif

  ASSERT (apx[n] < 15);

  TOOM4_SQR_REC (vh, apx, n + 1, tp);	/* vh,  2n+1 limbs */

  /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3.  */
  mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp);

  TOOM4_SQR_REC (v1, apx, n + 1, tp);	/* v1,  2n+1 limbs */
  TOOM4_SQR_REC (vm1, amx, n + 1, tp);	/* vm1,  2n+1 limbs */

  TOOM4_SQR_REC (v0, a0, n, tp);
  TOOM4_SQR_REC (vinf, a3, s, tp);	/* vinf, 2s limbs */

  mpn_toom_interpolate_7pts (pp, n, 0, vm2, vm1, v2, vh, 2*s, tp);
}