xref: /dflybsd-src/contrib/gmp/mpn/generic/toom22_mul.c (revision 86d7f5d305c6adaa56ff4582ece9859d73106103)

/* mpn_toom22_mul -- Multiply {ap,an} and {bp,bn} where an >= bn.  Or more
   accurately, bn <= an < 2bn.

   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, 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, 0, +inf

  <-s--><--n-->
   ____ ______
  |_a1_|___a0_|
   |b1_|___b0_|
   <-t-><--n-->

  v0  =  a0     * b0       #   A(0)*B(0)
  vm1 = (a0- a1)*(b0- b1)  #  A(-1)*B(-1)
  vinf=      a1 *     b1   # A(inf)*B(inf)
*/

#if TUNE_PROGRAM_BUILD
#define MAYBE_mul_toom22   1
#else
#define MAYBE_mul_toom22						\
  (MUL_TOOM33_THRESHOLD >= 2 * MUL_TOOM22_THRESHOLD)
#endif

#define TOOM22_MUL_N_REC(p, a, b, n, ws)				\
  do {									\
    if (! MAYBE_mul_toom22						\
	|| BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD))			\
      mpn_mul_basecase (p, a, n, b, n);					\
    else								\
      mpn_toom22_mul (p, a, n, b, n, ws);				\
  } while (0)

/* Normally, this calls mul_basecase or toom22_mul.  But when when the fraction
   MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD is large, an initially small
   relative unbalance will become a larger and larger relative unbalance with
   each recursion (the difference s-t will be invariant over recursive calls).
   Therefore, we need to call toom32_mul.  FIXME: Suppress depending on
   MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD and on MUL_TOOM22_THRESHOLD.  */
#define TOOM22_MUL_REC(p, a, an, b, bn, ws)				\
  do {									\
    if (! MAYBE_mul_toom22						\
	|| BELOW_THRESHOLD (bn, MUL_TOOM22_THRESHOLD))			\
      mpn_mul_basecase (p, a, an, b, bn);				\
    else if (4 * an < 5 * bn)						\
      mpn_toom22_mul (p, a, an, b, bn, ws);				\
    else								\
      mpn_toom32_mul (p, a, an, b, bn, ws);				\
  } while (0)

void
mpn_toom22_mul (mp_ptr pp,
		mp_srcptr ap, mp_size_t an,
		mp_srcptr bp, mp_size_t bn,
		mp_ptr scratch)
{
  mp_size_t n, s, t;
  int vm1_neg;
  mp_limb_t cy, cy2;
  mp_ptr asm1;
  mp_ptr bsm1;

#define a0  ap
#define a1  (ap + n)
#define b0  bp
#define b1  (bp + n)

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

  ASSERT (an >= bn);

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

  asm1 = pp;
  bsm1 = pp + n;

  vm1_neg = 0;

  /* Compute asm1.  */
  if (s == n)
    {
      if (mpn_cmp (a0, a1, n) < 0)
	{
	  mpn_sub_n (asm1, a1, a0, n);
	  vm1_neg = 1;
	}
      else
	{
	  mpn_sub_n (asm1, a0, a1, n);
	}
    }
  else
    {
      if (mpn_zero_p (a0 + s, n - s) && mpn_cmp (a0, a1, s) < 0)
	{
	  mpn_sub_n (asm1, a1, a0, s);
	  MPN_ZERO (asm1 + s, n - s);
	  vm1_neg = 1;
	}
      else
	{
	  mpn_sub (asm1, a0, n, a1, s);
	}
    }

  /* Compute bsm1.  */
  if (t == n)
    {
      if (mpn_cmp (b0, b1, n) < 0)
	{
	  mpn_sub_n (bsm1, b1, b0, n);
	  vm1_neg ^= 1;
	}
      else
	{
	  mpn_sub_n (bsm1, b0, b1, n);
	}
    }
  else
    {
      if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
	{
	  mpn_sub_n (bsm1, b1, b0, t);
	  MPN_ZERO (bsm1 + t, n - t);
	  vm1_neg ^= 1;
	}
      else
	{
	  mpn_sub (bsm1, b0, n, b1, t);
	}
    }

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

  /* vm1, 2n limbs */
  TOOM22_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);

  if (s > t)  TOOM22_MUL_REC (vinf, a1, s, b1, t, scratch_out);
  else        TOOM22_MUL_N_REC (vinf, a1, b1, s, scratch_out);

  /* v0, 2n limbs */
  TOOM22_MUL_N_REC (v0, ap, bp, 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 + t - n);

  if (vm1_neg)
    cy += mpn_add_n (pp + n, pp + n, vm1, 2 * n);
  else
    cy -= mpn_sub_n (pp + n, pp + n, vm1, 2 * n);

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

  mpn_incr_u (pp + 2 * n, cy2);
  if (LIKELY (cy <= 2))
    mpn_incr_u (pp + 3 * n, cy);
  else
    mpn_decr_u (pp + 3 * n, 1);
}