Exemplo n.º 1
0
void
mpn_toom6_sqr  (mp_ptr pp, mp_srcptr ap, mp_size_t an, mp_ptr scratch)
{
  mp_size_t n, s;

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

  ASSERT( an >= 18 );

  n = 1 + (an - 1) / (size_t) 6;

  s = an - 5 * n;

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

#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   v2    (pp + 9 * n+2)			/* n+1 */
#define   wse   (scratch + 9 * n + 3)		/* 3n+1 */

  /* Alloc also 3n+1 limbs for ws... toom_interpolate_12pts may
     need all of them, when DO_mpn_sublsh_n usea a scratch  */
/*   if (scratch== NULL) */
/*     scratch = TMP_SALLOC_LIMBS (12 * n + 6); */

  /********************** evaluation and recursive calls *********************/
  /* $\pm1/2$ */
  mpn_toom_eval_pm2rexp (v2, v0, 5, ap, n, s, 1, pp);
  TOOM6_SQR_REC(pp, v0, n + 1, wse); /* A(-1/2)*B(-1/2)*2^. */
  TOOM6_SQR_REC(r5, v2, n + 1, wse); /* A(+1/2)*B(+1/2)*2^. */
  mpn_toom_couple_handling (r5, 2 * n + 1, pp, 0, n, 1, 0);

  /* $\pm1$ */
  mpn_toom_eval_pm1 (v2, v0, 5, ap, n, s,    pp);
  TOOM6_SQR_REC(pp, v0, n + 1, wse); /* A(-1)*B(-1) */
  TOOM6_SQR_REC(r3, v2, n + 1, wse); /* A(1)*B(1) */
  mpn_toom_couple_handling (r3, 2 * n + 1, pp, 0, n, 0, 0);

  /* $\pm4$ */
  mpn_toom_eval_pm2exp (v2, v0, 5, ap, n, s, 2, pp);
  TOOM6_SQR_REC(pp, v0, n + 1, wse); /* A(-4)*B(-4) */
  TOOM6_SQR_REC(r1, v2, n + 1, wse); /* A(+4)*B(+4) */
  mpn_toom_couple_handling (r1, 2 * n + 1, pp, 0, n, 2, 4);

  /* $\pm1/4$ */
  mpn_toom_eval_pm2rexp (v2, v0, 5, ap, n, s, 2, pp);
  TOOM6_SQR_REC(pp, v0, n + 1, wse); /* A(-1/4)*B(-1/4)*4^. */
  TOOM6_SQR_REC(r4, v2, n + 1, wse); /* A(+1/4)*B(+1/4)*4^. */
  mpn_toom_couple_handling (r4, 2 * n + 1, pp, 0, n, 2, 0);

  /* $\pm2$ */
  mpn_toom_eval_pm2 (v2, v0, 5, ap, n, s, pp);
  TOOM6_SQR_REC(pp, v0, n + 1, wse); /* A(-2)*B(-2) */
  TOOM6_SQR_REC(r2, v2, n + 1, wse); /* A(+2)*B(+2) */
  mpn_toom_couple_handling (r2, 2 * n + 1, pp, 0, n, 1, 2);

#undef v0
#undef v2

  /* A(0)*B(0) */
  TOOM6_SQR_REC(pp, ap, n, wse);

  mpn_toom_interpolate_12pts (pp, r1, r3, r5, n, 2 * s, 0, wse);

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

}
Exemplo n.º 2
0
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 (LIKELY (an * LIMIT_denominat < LIMIT_numerator * bn)) /* is 6*... < 6*... */
    {
      n = 1 + (an - 1) / (size_t) 6;
      p = q = 5;
      half = 0;

      s = an - 5 * n;
      t = bn - 5 * n;
    }
  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 (UNLIKELY (s<1)) {p--; s+=n; half=0;}
      else if (UNLIKELY (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);
  /* A(-1/2)*B(-1/2)*2^. */ /* A(+1/2)*B(+1/2)*2^. */
  TOOM6H_MUL_N_REC(pp, v0, v1, 2, r5, v2, v3, n + 1, wse);
  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 (UNLIKELY (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);
  /* A(-1)*B(-1) */ /* A(1)*B(1) */
  TOOM6H_MUL_N_REC(pp, v0, v1, 2, r3, v2, v3, n + 1, wse);
  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);
  /* A(-4)*B(-4) */
  TOOM6H_MUL_N_REC(pp, v0, v1, 2, 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);
  /* A(-1/4)*B(-1/4)*4^. */ /* A(+1/4)*B(+1/4)*4^. */
  TOOM6H_MUL_N_REC(pp, v0, v1, 2, r4, v2, v3, n + 1, wse);
  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);
  /* A(-2)*B(-2) */ /* A(+2)*B(+2) */
  TOOM6H_MUL_N_REC(pp, v0, v1, 2, r2, v2, v3, n + 1, wse);
  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, 0, pp, ap, bp, n, wsi);

  /* Infinity */
  if (UNLIKELY (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
}