mpir/mpn/generic/toom8_sqr_n.c

/* Implementation of the squaring algorithm with Toom-Cook 8.5-way.

   Contributed to the GNU project by 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"

#if GMP_NUMB_BITS < 29
#error Not implemented.
#endif

#if GMP_NUMB_BITS < 43
#define BIT_CORRECTION 1
#define CORRECTION_BITS GMP_NUMB_BITS
#else
#define BIT_CORRECTION 0
#define CORRECTION_BITS 0
#endif

#ifndef SQR_TOOM8_THRESHOLD
#define SQR_TOOM8_THRESHOLD MUL_TOOM8H_THRESHOLD
#endif

#define TOOM8_SQR_REC(p, a, n)					\
  do {									\
    if (BELOW_THRESHOLD (n, SQR_TOOM8_THRESHOLD))		\
      mpn_sqr (p, a, n);					\
    else								\
      mpn_toom8_sqr_n (p, a, n);					\
  } while (0)

void
mpn_toom8_sqr_n  (mp_ptr pp, mp_srcptr ap, mp_size_t an)
{
  mp_size_t n, s;
  mp_ptr scratch;

  TMP_DECL;
  
  TMP_MARK;

  /***************************** decomposition *******************************/

  ASSERT ( an >= 40 );

  n = 1 + ((an - 1)>>3);

  s = an - 7 * n;

  ASSERT (0 < s && s <= n);
  ASSERT ( s + s > 3 );

  scratch = TMP_ALLOC_LIMBS (30 * n + 6);

#define   r6    (pp + 3 * n)			/* 3n+1 */
#define   r4    (pp + 7 * n)			/* 3n+1 */
#define   r2    (pp +11 * n)			/* 3n+1 */
#define   r0    (pp +15 * n)			/* s+t <= 2*n */
#define   r7    (scratch)			/* 3n+1 */
#define   r5    (scratch + 3 * n + 1)		/* 3n+1 */
#define   r3    (scratch + 6 * n + 2)		/* 3n+1 */
#define   r1    (scratch + 9 * n + 3)		/* 3n+1 */
#define   v0    (pp +11 * n)			/* n+1 */
#define   v2    (pp +13 * n+2)			/* n+1 */
#define   wse   (scratch +12 * n + 4)		/* 3n+1 */

  /* Alloc also 3n+1 limbs for ws... toom_interpolate_16pts may
     need all of them, when DO_mpn_sublsh_n use a a scratch  */

  /********************** evaluation and recursive calls *********************/
  /* $\pm1/8$ */
  mpn_toom_eval_pm2rexp (v2, v0, 7, ap, n, s, 3, pp);
  TOOM8_SQR_REC(pp, v0, n + 1); /* A(-1/8)*B(-1/8)*8^. */
  TOOM8_SQR_REC(r7, v2, n + 1); /* A(+1/8)*B(+1/8)*8^. */
  mpn_toom_couple_handling (r7, 2 * n + 1 + BIT_CORRECTION, pp, 0, n, 3, 0);

  /* $\pm1/4$ */
  mpn_toom_eval_pm2rexp (v2, v0, 7, ap, n, s, 2, pp);
  TOOM8_SQR_REC(pp, v0, n + 1); /* A(-1/4)*B(-1/4)*4^. */
  TOOM8_SQR_REC(r5, v2, n + 1); /* A(+1/4)*B(+1/4)*4^. */
  mpn_toom_couple_handling (r5, 2 * n + 1, pp, 0, n, 2, 0);

  /* $\pm2$ */
  mpn_toom_eval_pm2 (v2, v0, 7, ap, n, s, pp);
  TOOM8_SQR_REC(pp, v0, n + 1); /* A(-2)*B(-2) */
  TOOM8_SQR_REC(r3, v2, n + 1); /* A(+2)*B(+2) */
  mpn_toom_couple_handling (r3, 2 * n + 1, pp, 0, n, 1, 2);

  /* $\pm8$ */
  mpn_toom_eval_pm2exp (v2, v0, 7, ap, n, s, 3, pp);
  TOOM8_SQR_REC(pp, v0, n + 1); /* A(-8)*B(-8) */
  TOOM8_SQR_REC(r1, v2, n + 1); /* A(+8)*B(+8) */
  mpn_toom_couple_handling (r1, 2 * n + 1 + BIT_CORRECTION, pp, 0, n, 3, 6);

  /* $\pm1/2$ */
  mpn_toom_eval_pm2rexp (v2, v0, 7, ap, n, s, 1, pp);
  TOOM8_SQR_REC(pp, v0, n + 1); /* A(-1/2)*B(-1/2)*2^. */
  TOOM8_SQR_REC(r6, v2, n + 1); /* A(+1/2)*B(+1/2)*2^. */
  mpn_toom_couple_handling (r6, 2 * n + 1, pp, 0, n, 1, 0);

  /* $\pm1$ */
  mpn_toom_eval_pm1 (v2, v0, 7, ap, n, s,    pp);
  TOOM8_SQR_REC(pp, v0, n + 1); /* A(-1)*B(-1) */
  TOOM8_SQR_REC(r4, v2, n + 1); /* A(1)*B(1) */
  mpn_toom_couple_handling (r4, 2 * n + 1, pp, 0, n, 0, 0);

  /* $\pm4$ */
  mpn_toom_eval_pm2exp (v2, v0, 7, ap, n, s, 2, pp);
  TOOM8_SQR_REC(pp, v0, n + 1); /* A(-4)*B(-4) */
  TOOM8_SQR_REC(r2, v2, n + 1); /* A(+4)*B(+4) */
  mpn_toom_couple_handling (r2, 2 * n + 1, pp, 0, n, 2, 4);

#undef v0
#undef v2

  /* A(0)*B(0) */
  TOOM8_SQR_REC(pp, ap, n);

  mpn_toom_interpolate_16pts (pp, r1, r3, r5, r7, n, 2 * s, 0, wse);

  TMP_FREE;

#undef r0
#undef r1
#undef r2
#undef r3
#undef r4
#undef r5
#undef r6
#undef wse

}