mpn/generic/hgcd2.c - gmp - Git at Google

 /* hgcd2.c

    THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
    SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
    GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

 Copyright 1996, 1998, 2000-2004, 2008, 2012, 2019 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"
 #include "longlong.h"

 #include "mpn/generic/hgcd2-div.h"

 #if GMP_NAIL_BITS != 0
 #error Nails not implemented
 #endif

 /* Reduces a,b until |a-b| (almost) fits in one limb + 1 bit. Constructs
    matrix M. Returns 1 if we make progress, i.e. can perform at least
    one subtraction. Otherwise returns zero. */

 /* FIXME: Possible optimizations:

    The div2 function starts with checking the most significant bit of
    the numerator. We can maintained normalized operands here, call
    hgcd with normalized operands only, which should make the code
    simpler and possibly faster.

    Experiment with table lookups on the most significant bits.

    This function is also a candidate for assembler implementation.
 */
 int
 mpn_hgcd2 (mp_limb_t ah, mp_limb_t al, mp_limb_t bh, mp_limb_t bl,
 	   struct hgcd_matrix1 *M)
 {
   mp_limb_t u00, u01, u10, u11;

   if (ah < 2 || bh < 2)
     return 0;

   if (ah > bh || (ah == bh && al > bl))
     {
       sub_ddmmss (ah, al, ah, al, bh, bl);
       if (ah < 2)
 	return 0;

       u00 = u01 = u11 = 1;
       u10 = 0;
     }
   else
     {
       sub_ddmmss (bh, bl, bh, bl, ah, al);
       if (bh < 2)
 	return 0;

       u00 = u10 = u11 = 1;
       u01 = 0;
     }

   if (ah < bh)
     goto subtract_a;

   for (;;)
     {
       ASSERT (ah >= bh);
       if (ah == bh)
 	goto done;

       if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
 	{
 	  ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
 	  bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

 	  break;
 	}

       /* Subtract a -= q b, and multiply M from the right by (1 q ; 0
 	 1), affecting the second column of M. */
       ASSERT (ah > bh);
       sub_ddmmss (ah, al, ah, al, bh, bl);

       if (ah < 2)
 	goto done;

       if (ah <= bh)
 	{
 	  /* Use q = 1 */
 	  u01 += u00;
 	  u11 += u10;
 	}
       else
 	{
 	  mp_limb_t r[2];
 	  mp_limb_t q = div2 (r, ah, al, bh, bl);
 	  al = r[0]; ah = r[1];
 	  if (ah < 2)
 	    {
 	      /* A is too small, but q is correct. */
 	      u01 += q * u00;
 	      u11 += q * u10;
 	      goto done;
 	    }
 	  q++;
 	  u01 += q * u00;
 	  u11 += q * u10;
 	}
     subtract_a:
       ASSERT (bh >= ah);
       if (ah == bh)
 	goto done;

       if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
 	{
 	  ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
 	  bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

 	  goto subtract_a1;
 	}

       /* Subtract b -= q a, and multiply M from the right by (1 0 ; q
 	 1), affecting the first column of M. */
       sub_ddmmss (bh, bl, bh, bl, ah, al);

       if (bh < 2)
 	goto done;

       if (bh <= ah)
 	{
 	  /* Use q = 1 */
 	  u00 += u01;
 	  u10 += u11;
 	}
       else
 	{
 	  mp_limb_t r[2];
 	  mp_limb_t q = div2 (r, bh, bl, ah, al);
 	  bl = r[0]; bh = r[1];
 	  if (bh < 2)
 	    {
 	      /* B is too small, but q is correct. */
 	      u00 += q * u01;
 	      u10 += q * u11;
 	      goto done;
 	    }
 	  q++;
 	  u00 += q * u01;
 	  u10 += q * u11;
 	}
     }

   /* NOTE: Since we discard the least significant half limb, we don't get a
      truly maximal M (corresponding to |a - b| < 2^{GMP_LIMB_BITS +1}). */
   /* Single precision loop */
   for (;;)
     {
       ASSERT (ah >= bh);

       ah -= bh;
       if (ah < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
 	break;

       if (ah <= bh)
 	{
 	  /* Use q = 1 */
 	  u01 += u00;
 	  u11 += u10;
 	}
       else
 	{
 	  mp_double_limb_t rq = div1 (ah, bh);
 	  mp_limb_t q = rq.d1;
 	  ah = rq.d0;

 	  if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
 	    {
 	      /* A is too small, but q is correct. */
 	      u01 += q * u00;
 	      u11 += q * u10;
 	      break;
 	    }
 	  q++;
 	  u01 += q * u00;
 	  u11 += q * u10;
 	}
     subtract_a1:
       ASSERT (bh >= ah);

       bh -= ah;
       if (bh < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
 	break;

       if (bh <= ah)
 	{
 	  /* Use q = 1 */
 	  u00 += u01;
 	  u10 += u11;
 	}
       else
 	{
 	  mp_double_limb_t rq = div1 (bh, ah);
 	  mp_limb_t q = rq.d1;
 	  bh = rq.d0;

 	  if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
 	    {
 	      /* B is too small, but q is correct. */
 	      u00 += q * u01;
 	      u10 += q * u11;
 	      break;
 	    }
 	  q++;
 	  u00 += q * u01;
 	  u10 += q * u11;
 	}
     }

  done:
   M->u[0][0] = u00; M->u[0][1] = u01;
   M->u[1][0] = u10; M->u[1][1] = u11;

   return 1;
 }

 /* Sets (r;b) = (a;b) M, with M = (u00, u01; u10, u11). Vector must
  * have space for n + 1 limbs. Uses three buffers to avoid a copy*/
 mp_size_t
 mpn_hgcd_mul_matrix1_vector (const struct hgcd_matrix1 *M,
 			     mp_ptr rp, mp_srcptr ap, mp_ptr bp, mp_size_t n)
 {
   mp_limb_t ah, bh;

   /* Compute (r,b) <-- (u00 a + u10 b, u01 a + u11 b) as

      r  = u00 * a
      r += u10 * b
      b *= u11
      b += u01 * a
   */

 #if HAVE_NATIVE_mpn_addaddmul_1msb0
   ah = mpn_addaddmul_1msb0 (rp, ap, bp, n, M->u[0][0], M->u[1][0]);
   bh = mpn_addaddmul_1msb0 (bp, bp, ap, n, M->u[1][1], M->u[0][1]);
 #else
   ah =     mpn_mul_1 (rp, ap, n, M->u[0][0]);
   ah += mpn_addmul_1 (rp, bp, n, M->u[1][0]);

   bh =     mpn_mul_1 (bp, bp, n, M->u[1][1]);
   bh += mpn_addmul_1 (bp, ap, n, M->u[0][1]);
 #endif
   rp[n] = ah;
   bp[n] = bh;

   n += (ah | bh) > 0;
   return n;
 }
	/* hgcd2.c

	THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
	SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
	GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

	Copyright 1996, 1998, 2000-2004, 2008, 2012, 2019 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"
	#include "longlong.h"

	#include "mpn/generic/hgcd2-div.h"

	#if GMP_NAIL_BITS != 0
	#error Nails not implemented
	#endif

	/* Reduces a,b until \|a-b\| (almost) fits in one limb + 1 bit. Constructs
	matrix M. Returns 1 if we make progress, i.e. can perform at least
	one subtraction. Otherwise returns zero. */

	/* FIXME: Possible optimizations:

	The div2 function starts with checking the most significant bit of
	the numerator. We can maintained normalized operands here, call
	hgcd with normalized operands only, which should make the code
	simpler and possibly faster.

	Experiment with table lookups on the most significant bits.

	This function is also a candidate for assembler implementation.
	*/
	int
	mpn_hgcd2 (mp_limb_t ah, mp_limb_t al, mp_limb_t bh, mp_limb_t bl,
	struct hgcd_matrix1 *M)
	{
	mp_limb_t u00, u01, u10, u11;

	if (ah < 2 \|\| bh < 2)
	return 0;

	if (ah > bh \|\| (ah == bh && al > bl))
	{
	sub_ddmmss (ah, al, ah, al, bh, bl);
	if (ah < 2)
	return 0;

	u00 = u01 = u11 = 1;
	u10 = 0;
	}
	else
	{
	sub_ddmmss (bh, bl, bh, bl, ah, al);
	if (bh < 2)
	return 0;

	u00 = u10 = u11 = 1;
	u01 = 0;
	}

	if (ah < bh)
	goto subtract_a;

	for (;;)
	{
	ASSERT (ah >= bh);
	if (ah == bh)
	goto done;

	if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
	{
	ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
	bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

	break;
	}

	/* Subtract a -= q b, and multiply M from the right by (1 q ; 0
	1), affecting the second column of M. */
	ASSERT (ah > bh);
	sub_ddmmss (ah, al, ah, al, bh, bl);

	if (ah < 2)
	goto done;

	if (ah <= bh)
	{
	/* Use q = 1 */
	u01 += u00;
	u11 += u10;
	}
	else
	{
	mp_limb_t r[2];
	mp_limb_t q = div2 (r, ah, al, bh, bl);
	al = r[0]; ah = r[1];
	if (ah < 2)
	{
	/* A is too small, but q is correct. */
	u01 += q * u00;
	u11 += q * u10;
	goto done;
	}
	q++;
	u01 += q * u00;
	u11 += q * u10;
	}
	subtract_a:
	ASSERT (bh >= ah);
	if (ah == bh)
	goto done;

	if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
	{
	ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
	bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

	goto subtract_a1;
	}

	/* Subtract b -= q a, and multiply M from the right by (1 0 ; q
	1), affecting the first column of M. */
	sub_ddmmss (bh, bl, bh, bl, ah, al);

	if (bh < 2)
	goto done;

	if (bh <= ah)
	{
	/* Use q = 1 */
	u00 += u01;
	u10 += u11;
	}
	else
	{
	mp_limb_t r[2];
	mp_limb_t q = div2 (r, bh, bl, ah, al);
	bl = r[0]; bh = r[1];
	if (bh < 2)
	{
	/* B is too small, but q is correct. */
	u00 += q * u01;
	u10 += q * u11;
	goto done;
	}
	q++;
	u00 += q * u01;
	u10 += q * u11;
	}
	}

	/* NOTE: Since we discard the least significant half limb, we don't get a
	truly maximal M (corresponding to \|a - b\| < 2^{GMP_LIMB_BITS +1}). */
	/* Single precision loop */
	for (;;)
	{
	ASSERT (ah >= bh);

	ah -= bh;
	if (ah < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
	break;

	if (ah <= bh)
	{
	/* Use q = 1 */
	u01 += u00;
	u11 += u10;
	}
	else
	{
	mp_double_limb_t rq = div1 (ah, bh);
	mp_limb_t q = rq.d1;
	ah = rq.d0;

	if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
	{
	/* A is too small, but q is correct. */
	u01 += q * u00;
	u11 += q * u10;
	break;
	}
	q++;
	u01 += q * u00;
	u11 += q * u10;
	}
	subtract_a1:
	ASSERT (bh >= ah);

	bh -= ah;
	if (bh < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
	break;

	if (bh <= ah)
	{
	/* Use q = 1 */
	u00 += u01;
	u10 += u11;
	}
	else
	{
	mp_double_limb_t rq = div1 (bh, ah);
	mp_limb_t q = rq.d1;
	bh = rq.d0;

	if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
	{
	/* B is too small, but q is correct. */
	u00 += q * u01;
	u10 += q * u11;
	break;
	}
	q++;
	u00 += q * u01;
	u10 += q * u11;
	}
	}

	done:
	M->u[0][0] = u00; M->u[0][1] = u01;
	M->u[1][0] = u10; M->u[1][1] = u11;

	return 1;
	}

	/* Sets (r;b) = (a;b) M, with M = (u00, u01; u10, u11). Vector must
	* have space for n + 1 limbs. Uses three buffers to avoid a copy*/
	mp_size_t
	mpn_hgcd_mul_matrix1_vector (const struct hgcd_matrix1 *M,
	mp_ptr rp, mp_srcptr ap, mp_ptr bp, mp_size_t n)
	{
	mp_limb_t ah, bh;

	/* Compute (r,b) <-- (u00 a + u10 b, u01 a + u11 b) as

	r = u00 * a
	r += u10 * b
	b *= u11
	b += u01 * a
	*/

	#if HAVE_NATIVE_mpn_addaddmul_1msb0
	ah = mpn_addaddmul_1msb0 (rp, ap, bp, n, M->u[0][0], M->u[1][0]);
	bh = mpn_addaddmul_1msb0 (bp, bp, ap, n, M->u[1][1], M->u[0][1]);
	#else
	ah = mpn_mul_1 (rp, ap, n, M->u[0][0]);
	ah += mpn_addmul_1 (rp, bp, n, M->u[1][0]);

	bh = mpn_mul_1 (bp, bp, n, M->u[1][1]);
	bh += mpn_addmul_1 (bp, ap, n, M->u[0][1]);
	#endif
	rp[n] = ah;
	bp[n] = bh;

	n += (ah \| bh) > 0;
	return n;
	}