mpn/generic/toom52_mul.c - gmp - Git at Google

 /* mpn_toom52_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 4/3
    times as large as bn.  Or more accurately, bn < an < 2 bn.

    Contributed to the GNU project by Marco Bodrato.

    The idea of applying toom to unbalanced multiplication is due to Marco
    Bodrato and Alberto Zanoni.

    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 either:

   * 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.

 or

   * the GNU General Public License as published by the Free Software
     Foundation; either version 2 of the License, or (at your option) any
     later version.

 or both in parallel, as here.

 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 General Public License
 for more details.

 You should have received copies of the GNU General Public License and the
 GNU Lesser General Public License along with the GNU MP Library.  If not,
 see https://www.gnu.org/licenses/.  */


 #include "gmp-impl.h"

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

   <-s-><--n--><--n--><--n--><--n-->
    ___ ______ ______ ______ ______
   |a4_|___a3_|___a2_|___a1_|___a0_|
 			|b1|___b0_|
 			<t-><--n-->

   v0  =  a0                  * b0      #   A(0)*B(0)
   v1  = (a0+ a1+ a2+ a3+  a4)*(b0+ b1) #   A(1)*B(1)      ah  <= 4   bh <= 1
   vm1 = (a0- a1+ a2- a3+  a4)*(b0- b1) #  A(-1)*B(-1)    |ah| <= 2   bh  = 0
   v2  = (a0+2a1+4a2+8a3+16a4)*(b0+2b1) #   A(2)*B(2)      ah  <= 30  bh <= 2
   vm2 = (a0-2a1+4a2-8a3+16a4)*(b0-2b1) #  A(-2)*B(-2)    |ah| <= 20 |bh|<= 1
   vinf=                   a4 *     b1  # A(inf)*B(inf)

   Some slight optimization in evaluation are taken from the paper:
   "Towards Optimal Toom-Cook Multiplication for Univariate and
   Multivariate Polynomials in Characteristic 2 and 0."
 */

 void
 mpn_toom52_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;
   enum toom6_flags flags;

 #define a0  ap
 #define a1  (ap + n)
 #define a2  (ap + 2 * n)
 #define a3  (ap + 3 * n)
 #define a4  (ap + 4 * n)
 #define b0  bp
 #define b1  (bp + n)

   n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1);

   s = an - 4 * n;
   t = bn - n;

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

   /* Ensures that 5 values of n+1 limbs each fits in the product area.
      Borderline cases are an = 32, bn = 8, n = 7, and an = 36, bn = 9,
      n = 8. */
   ASSERT (s+t >= 5);

 #define v0    pp				/* 2n */
 #define vm1   (scratch)				/* 2n+1 */
 #define v1    (pp + 2 * n)			/* 2n+1 */
 #define vm2   (scratch + 2 * n + 1)		/* 2n+1 */
 #define v2    (scratch + 4 * n + 2)		/* 2n+1 */
 #define vinf  (pp + 5 * n)			/* s+t */
 #define bs1    pp				/* n+1 */
 #define bsm1  (scratch + 2 * n + 2)		/* n   */
 #define asm1  (scratch + 3 * n + 3)		/* n+1 */
 #define asm2  (scratch + 4 * n + 4)		/* n+1 */
 #define bsm2  (pp + n + 1)			/* n+1 */
 #define bs2   (pp + 2 * n + 2)			/* n+1 */
 #define as2   (pp + 3 * n + 3)			/* n+1 */
 #define as1   (pp + 4 * n + 4)			/* n+1 */

   /* Scratch need is 6 * n + 3 + 1. We need one extra limb, because
      products will overwrite 2n+2 limbs. */

 #define a0a2  scratch
 #define a1a3  asm1

   /* Compute as2 and asm2.  */
   flags = (enum toom6_flags) (toom6_vm2_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, a1a3));

   /* Compute bs1 and bsm1.  */
   if (t == n)
     {
 #if HAVE_NATIVE_mpn_add_n_sub_n
       mp_limb_t cy;

       if (mpn_cmp (b0, b1, n) < 0)
 	{
 	  cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
 	  flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
 	}
       else
 	{
 	  cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
 	}
       bs1[n] = cy >> 1;
 #else
       bs1[n] = mpn_add_n (bs1, b0, b1, n);
       if (mpn_cmp (b0, b1, n) < 0)
 	{
 	  mpn_sub_n (bsm1, b1, b0, n);
 	  flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
 	}
       else
 	{
 	  mpn_sub_n (bsm1, b0, b1, n);
 	}
 #endif
     }
   else
     {
       bs1[n] = mpn_add (bs1, b0, n, b1, t);
       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);
 	  flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
 	}
       else
 	{
 	  mpn_sub (bsm1, b0, n, b1, t);
 	}
     }

   /* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1  */
   mpn_add (bs2, bs1, n+1, b1, t);
   if (flags & toom6_vm1_neg)
     {
       bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t);
       flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
     }
   else
     {
       bsm2[n] = 0;
       if (t == n)
 	{
 	  if (mpn_cmp (bsm1, b1, n) < 0)
 	    {
 	      mpn_sub_n (bsm2, b1, bsm1, n);
 	      flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
 	    }
 	  else
 	    {
 	      mpn_sub_n (bsm2, bsm1, b1, n);
 	    }
 	}
       else
 	{
 	  if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0)
 	    {
 	      mpn_sub_n (bsm2, b1, bsm1, t);
 	      MPN_ZERO (bsm2 + t, n - t);
 	      flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
 	    }
 	  else
 	    {
 	      mpn_sub (bsm2, bsm1, n, b1, t);
 	    }
 	}
     }

   /* Compute as1 and asm1.  */
   flags = (enum toom6_flags) (flags ^ (toom6_vm1_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, a0a2)));

   ASSERT (as1[n] <= 4);
   ASSERT (bs1[n] <= 1);
   ASSERT (asm1[n] <= 2);
 /*   ASSERT (bsm1[n] <= 1); */
   ASSERT (as2[n] <=30);
   ASSERT (bs2[n] <= 2);
   ASSERT (asm2[n] <= 20);
   ASSERT (bsm2[n] <= 1);

   /* vm1, 2n+1 limbs */
   mpn_mul (vm1, asm1, n+1, bsm1, n);  /* W4 */

   /* vm2, 2n+1 limbs */
   mpn_mul_n (vm2, asm2, bsm2, n+1);  /* W2 */

   /* v2, 2n+1 limbs */
   mpn_mul_n (v2, as2, bs2, n+1);  /* W1 */

   /* v1, 2n+1 limbs */
   mpn_mul_n (v1, as1, bs1, n+1);  /* W3 */

   /* vinf, s+t limbs */   /* W0 */
   if (s > t)  mpn_mul (vinf, a4, s, b1, t);
   else        mpn_mul (vinf, b1, t, a4, s);

   /* v0, 2n limbs */
   mpn_mul_n (v0, ap, bp, n);  /* W5 */

   mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s);

 #undef v0
 #undef vm1
 #undef v1
 #undef vm2
 #undef v2
 #undef vinf
 #undef bs1
 #undef bs2
 #undef bsm1
 #undef bsm2
 #undef asm1
 #undef asm2
 #undef as1
 #undef as2
 #undef a0a2
 #undef b0b2
 #undef a1a3
 #undef a0
 #undef a1
 #undef a2
 #undef a3
 #undef b0
 #undef b1
 #undef b2

 }
	/* mpn_toom52_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 4/3
	times as large as bn. Or more accurately, bn < an < 2 bn.

	Contributed to the GNU project by Marco Bodrato.

	The idea of applying toom to unbalanced multiplication is due to Marco
	Bodrato and Alberto Zanoni.

	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 either:

	* 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.

	or

	* the GNU General Public License as published by the Free Software
	Foundation; either version 2 of the License, or (at your option) any
	later version.

	or both in parallel, as here.

	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 General Public License
	for more details.

	You should have received copies of the GNU General Public License and the
	GNU Lesser General Public License along with the GNU MP Library. If not,
	see https://www.gnu.org/licenses/. */


	#include "gmp-impl.h"

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

	<-s-><--n--><--n--><--n--><--n-->
	___ ______ ______ ______ ______
	\|a4_\|___a3_\|___a2_\|___a1_\|___a0_\|
	\|b1\|___b0_\|
	<t-><--n-->

	v0 = a0 * b0 # A(0)*B(0)
	v1 = (a0+ a1+ a2+ a3+ a4)(b0+ b1) # A(1)B(1) ah <= 4 bh <= 1
	vm1 = (a0- a1+ a2- a3+ a4)(b0- b1) # A(-1)B(-1) \|ah\| <= 2 bh = 0
	v2 = (a0+2a1+4a2+8a3+16a4)(b0+2b1) # A(2)B(2) ah <= 30 bh <= 2
	vm2 = (a0-2a1+4a2-8a3+16a4)(b0-2b1) # A(-2)B(-2) \|ah\| <= 20 \|bh\|<= 1
	vinf= a4 * b1 # A(inf)*B(inf)

	Some slight optimization in evaluation are taken from the paper:
	"Towards Optimal Toom-Cook Multiplication for Univariate and
	Multivariate Polynomials in Characteristic 2 and 0."
	*/

	void
	mpn_toom52_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;
	enum toom6_flags flags;

	#define a0 ap
	#define a1 (ap + n)
	#define a2 (ap + 2 * n)
	#define a3 (ap + 3 * n)
	#define a4 (ap + 4 * n)
	#define b0 bp
	#define b1 (bp + n)

	n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1);

	s = an - 4 * n;
	t = bn - n;

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

	/* Ensures that 5 values of n+1 limbs each fits in the product area.
	Borderline cases are an = 32, bn = 8, n = 7, and an = 36, bn = 9,
	n = 8. */
	ASSERT (s+t >= 5);

	#define v0 pp /* 2n */
	#define vm1 (scratch) /* 2n+1 */
	#define v1 (pp + 2 * n) /* 2n+1 */
	#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
	#define v2 (scratch + 4 * n + 2) /* 2n+1 */
	#define vinf (pp + 5 * n) /* s+t */
	#define bs1 pp /* n+1 */
	#define bsm1 (scratch + 2 * n + 2) /* n */
	#define asm1 (scratch + 3 * n + 3) /* n+1 */
	#define asm2 (scratch + 4 * n + 4) /* n+1 */
	#define bsm2 (pp + n + 1) /* n+1 */
	#define bs2 (pp + 2 * n + 2) /* n+1 */
	#define as2 (pp + 3 * n + 3) /* n+1 */
	#define as1 (pp + 4 * n + 4) /* n+1 */

	/* Scratch need is 6 * n + 3 + 1. We need one extra limb, because
	products will overwrite 2n+2 limbs. */

	#define a0a2 scratch
	#define a1a3 asm1

	/* Compute as2 and asm2. */
	flags = (enum toom6_flags) (toom6_vm2_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, a1a3));

	/* Compute bs1 and bsm1. */
	if (t == n)
	{
	#if HAVE_NATIVE_mpn_add_n_sub_n
	mp_limb_t cy;

	if (mpn_cmp (b0, b1, n) < 0)
	{
	cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
	flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
	}
	else
	{
	cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
	}
	bs1[n] = cy >> 1;
	#else
	bs1[n] = mpn_add_n (bs1, b0, b1, n);
	if (mpn_cmp (b0, b1, n) < 0)
	{
	mpn_sub_n (bsm1, b1, b0, n);
	flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
	}
	else
	{
	mpn_sub_n (bsm1, b0, b1, n);
	}
	#endif
	}
	else
	{
	bs1[n] = mpn_add (bs1, b0, n, b1, t);
	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);
	flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
	}
	else
	{
	mpn_sub (bsm1, b0, n, b1, t);
	}
	}

	/* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */
	mpn_add (bs2, bs1, n+1, b1, t);
	if (flags & toom6_vm1_neg)
	{
	bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t);
	flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
	}
	else
	{
	bsm2[n] = 0;
	if (t == n)
	{
	if (mpn_cmp (bsm1, b1, n) < 0)
	{
	mpn_sub_n (bsm2, b1, bsm1, n);
	flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
	}
	else
	{
	mpn_sub_n (bsm2, bsm1, b1, n);
	}
	}
	else
	{
	if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0)
	{
	mpn_sub_n (bsm2, b1, bsm1, t);
	MPN_ZERO (bsm2 + t, n - t);
	flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
	}
	else
	{
	mpn_sub (bsm2, bsm1, n, b1, t);
	}
	}
	}

	/* Compute as1 and asm1. */
	flags = (enum toom6_flags) (flags ^ (toom6_vm1_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, a0a2)));

	ASSERT (as1[n] <= 4);
	ASSERT (bs1[n] <= 1);
	ASSERT (asm1[n] <= 2);
	/* ASSERT (bsm1[n] <= 1); */
	ASSERT (as2[n] <=30);
	ASSERT (bs2[n] <= 2);
	ASSERT (asm2[n] <= 20);
	ASSERT (bsm2[n] <= 1);

	/* vm1, 2n+1 limbs */
	mpn_mul (vm1, asm1, n+1, bsm1, n); /* W4 */

	/* vm2, 2n+1 limbs */
	mpn_mul_n (vm2, asm2, bsm2, n+1); /* W2 */

	/* v2, 2n+1 limbs */
	mpn_mul_n (v2, as2, bs2, n+1); /* W1 */

	/* v1, 2n+1 limbs */
	mpn_mul_n (v1, as1, bs1, n+1); /* W3 */

	/* vinf, s+t limbs / / W0 */
	if (s > t) mpn_mul (vinf, a4, s, b1, t);
	else mpn_mul (vinf, b1, t, a4, s);

	/* v0, 2n limbs */
	mpn_mul_n (v0, ap, bp, n); /* W5 */

	mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s);

	#undef v0
	#undef vm1
	#undef v1
	#undef vm2
	#undef v2
	#undef vinf
	#undef bs1
	#undef bs2
	#undef bsm1
	#undef bsm2
	#undef asm1
	#undef asm2
	#undef as1
	#undef as2
	#undef a0a2
	#undef b0b2
	#undef a1a3
	#undef a0
	#undef a1
	#undef a2
	#undef a3
	#undef b0
	#undef b1
	#undef b2

	}