xref: /dflybsd-src/contrib/gmp/mpn/generic/toom6h_mul.c (revision 86d7f5d305c6adaa56ff4582ece9859d73106103)

/* Implementation of the multiplication algorithm for Toom-Cook 6.5-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, 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"


#if GMP_NUMB_BITS < 21
#error Not implemented.
#endif

#if TUNE_PROGRAM_BUILD
#define MAYBE_mul_basecase 1
#define MAYBE_mul_toom22   1
#define MAYBE_mul_toom33   1
#define MAYBE_mul_toom6h   1
#else
#define MAYBE_mul_basecase						\
  (MUL_TOOM6H_THRESHOLD < 6 * MUL_TOOM22_THRESHOLD)
#define MAYBE_mul_toom22						\
  (MUL_TOOM6H_THRESHOLD < 6 * MUL_TOOM33_THRESHOLD)
#define MAYBE_mul_toom33						\
  (MUL_TOOM6H_THRESHOLD < 6 * MUL_TOOM44_THRESHOLD)
#define MAYBE_mul_toom6h						\
  (MUL_FFT_THRESHOLD >= 6 * MUL_TOOM6H_THRESHOLD)
#endif

#define TOOM6H_MUL_N_REC(p, a, b, n, ws)				\
  do {									\
    if (MAYBE_mul_basecase						\
	&& BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD))			\
      mpn_mul_basecase (p, a, n, b, n);					\
    else if (MAYBE_mul_toom22						\
	     && BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD))		\
      mpn_toom22_mul (p, a, n, b, n, ws);				\
    else if (MAYBE_mul_toom33						\
	     && BELOW_THRESHOLD (n, MUL_TOOM44_THRESHOLD))		\
      mpn_toom33_mul (p, a, n, b, n, ws);				\
    else if (! MAYBE_mul_toom6h						\
	     || BELOW_THRESHOLD (n, MUL_TOOM6H_THRESHOLD))		\
      mpn_toom44_mul (p, a, n, b, n, ws);				\
    else								\
      mpn_toom6h_mul (p, a, n, b, n, ws);				\
  } while (0)

#define TOOM6H_MUL_REC(p, a, na, b, nb, ws)		\
  do {	mpn_mul (p, a, na, b, nb);			\
  } while (0)

/* Toom-6.5 , compute the product {pp,an+bn} <- {ap,an} * {bp,bn}
   With: an >= bn >= 46, an*6 <  bn * 17.
   It _may_ work with bn<=46 and bn*17 < an*6 < bn*18

   Evaluate in: infinity, +4, -4, +2, -2, +1, -1, +1/2, -1/2, +1/4, -1/4, 0.
*/
/* Estimate on needed scratch:
   S(n) <= (n+5)\6*10+4+MAX(S((n+5)\6),1+2*(n+5)\6),
   since n>42; S(n) <= ceil(log(n)/log(6))*(10+4)+n*12\6 < n*2 + lg2(n)*6
 */

void
mpn_toom6h_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 p, q, half;
  int sign;

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

  ASSERT( an >= bn);
  /* Can not handle too much unbalancement */
  ASSERT( bn >= 42 );
  /* Can not handle too much unbalancement */
  ASSERT((an*3 <  bn * 8) || ( bn >= 46 && an*6 <  bn * 17 ));

  /* Limit num/den is a rational number between
     (12/11)^(log(4)/log(2*4-1)) and (12/11)^(log(6)/log(2*6-1))             */
#define LIMIT_numerator (18)
#define LIMIT_denominat (17)

  if( an * LIMIT_denominat < LIMIT_numerator * bn ) /* is 6*... < 6*... */
    { p = q = 6; }
  else if( an * 5 * LIMIT_numerator < LIMIT_denominat * 7 * bn )
    { p = 7; q = 6; }
  else if( an * 5 * LIMIT_denominat < LIMIT_numerator * 7 * bn )
    { p = 7; q = 5; }
  else if( an * LIMIT_numerator < LIMIT_denominat * 2 * bn )  /* is 4*... < 8*... */
    { p = 8; q = 5; }
  else if( an * LIMIT_denominat < LIMIT_numerator * 2 * bn )  /* is 4*... < 8*... */
    { p = 8; q = 4; }
  else
    { p = 9; q = 4; }

  half = (p ^ q) & 1;
  n = 1 + (q * an >= p * bn ? (an - 1) / (size_t) p : (bn - 1) / (size_t) q);
  p--; q--;

  s = an - p * n;
  t = bn - q * n;

  /* With LIMIT = 16/15, the following recover is needed only if bn<=73*/
  if (half) { /* Recover from badly chosen splitting */
    if (s<1) {p--; s+=n; half=0;}
    else if (t<1) {q--; t+=n; half=0;}
  }
#undef LIMIT_numerator
#undef LIMIT_denominat

  ASSERT (0 < s && s <= n);
  ASSERT (0 < t && t <= n);
  ASSERT (half || s + t > 3);
  ASSERT (n > 2);

#define   r4    (pp + 3 * n)			/* 3n+1 */
#define   r2    (pp + 7 * n)			/* 3n+1 */
#define   r0    (pp +11 * n)			/* s+t <= 2*n */
#define   r5    (scratch)			/* 3n+1 */
#define   r3    (scratch + 3 * n + 1)		/* 3n+1 */
#define   r1    (scratch + 6 * n + 2)		/* 3n+1 */
#define   v0    (pp + 7 * n)			/* n+1 */
#define   v1    (pp + 8 * n+1)			/* n+1 */
#define   v2    (pp + 9 * n+2)			/* n+1 */
#define   v3    (scratch + 9 * n + 3)		/* n+1 */
#define   wsi   (scratch + 9 * n + 3)		/* 3n+1 */
#define   wse   (scratch +10 * n + 4)		/* 2n+1 */

  /* Alloc also 3n+1 limbs for wsi... toom_interpolate_12pts may
     need all of them  */
/*   if (scratch == NULL) */
/*     scratch = TMP_SALLOC_LIMBS(mpn_toom6_sqr_itch(n * 6)); */
  ASSERT (12 * n + 6 <= mpn_toom6h_mul_itch(an,bn));
  ASSERT (12 * n + 6 <= mpn_toom6_sqr_itch(n * 6));

  /********************** evaluation and recursive calls *********************/
  /* $\pm1/2$ */
  sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 1, pp) ^
	 mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 1, pp);
  TOOM6H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-1/2)*B(-1/2)*2^. */
  TOOM6H_MUL_N_REC(r5, v2, v3, n + 1, wse); /* A(+1/2)*B(+1/2)*2^. */
  mpn_toom_couple_handling (r5, 2 * n + 1, pp, sign, n, 1+half , half);

  /* $\pm1$ */
  sign = mpn_toom_eval_pm1 (v2, v0, p, ap, n, s,    pp);
  if (q == 3)
    sign ^= mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t,    pp);
  else
    sign ^= mpn_toom_eval_pm1 (v3, v1, q, bp, n, t,    pp);
  TOOM6H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-1)*B(-1) */
  TOOM6H_MUL_N_REC(r3, v2, v3, n + 1, wse); /* A(1)*B(1) */
  mpn_toom_couple_handling (r3, 2 * n + 1, pp, sign, n, 0, 0);

  /* $\pm4$ */
  sign = mpn_toom_eval_pm2exp (v2, v0, p, ap, n, s, 2, pp) ^
	 mpn_toom_eval_pm2exp (v3, v1, q, bp, n, t, 2, pp);
  TOOM6H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-4)*B(-4) */
  TOOM6H_MUL_N_REC(r1, v2, v3, n + 1, wse); /* A(+4)*B(+4) */
  mpn_toom_couple_handling (r1, 2 * n + 1, pp, sign, n, 2, 4);

  /* $\pm1/4$ */
  sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 2, pp) ^
	 mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 2, pp);
  TOOM6H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-1/4)*B(-1/4)*4^. */
  TOOM6H_MUL_N_REC(r4, v2, v3, n + 1, wse); /* A(+1/4)*B(+1/4)*4^. */
  mpn_toom_couple_handling (r4, 2 * n + 1, pp, sign, n, 2*(1+half), 2*(half));

  /* $\pm2$ */
  sign = mpn_toom_eval_pm2 (v2, v0, p, ap, n, s, pp) ^
	 mpn_toom_eval_pm2 (v3, v1, q, bp, n, t, pp);
  TOOM6H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-2)*B(-2) */
  TOOM6H_MUL_N_REC(r2, v2, v3, n + 1, wse); /* A(+2)*B(+2) */
  mpn_toom_couple_handling (r2, 2 * n + 1, pp, sign, n, 1, 2);

#undef v0
#undef v1
#undef v2
#undef v3
#undef wse

  /* A(0)*B(0) */
  TOOM6H_MUL_N_REC(pp, ap, bp, n, wsi);

  /* Infinity */
  if( half != 0) {
    if(s>t) {
      TOOM6H_MUL_REC(r0, ap + p * n, s, bp + q * n, t, wsi);
    } else {
      TOOM6H_MUL_REC(r0, bp + q * n, t, ap + p * n, s, wsi);
    };
  };

  mpn_toom_interpolate_12pts (pp, r1, r3, r5, n, s+t, half, wsi);

#undef r0
#undef r1
#undef r2
#undef r3
#undef r4
#undef r5
#undef wsi
}

#undef TOOM6H_MUL_N_REC
#undef TOOM6H_MUL_REC
#undef MAYBE_mul_basecase
#undef MAYBE_mul_toom22
#undef MAYBE_mul_toom33
#undef MAYBE_mul_toom6h