gcc/gmp/mpn/generic/hgcd2.c - native_client/nacl-toolchain - 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, 2001, 2002, 2003, 2004, 2008 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"
 #include "longlong.h"

 #if GMP_NAIL_BITS == 0

 /* Copied from the old mpn/generic/gcdext.c, and modified slightly to return
    the remainder. */

 /* Single-limb division optimized for small quotients. */
 static inline mp_limb_t
 div1 (mp_ptr rp,
       mp_limb_t n0,
       mp_limb_t d0)
 {
   mp_limb_t q = 0;

   if ((mp_limb_signed_t) n0 < 0)
     {
       int cnt;
       for (cnt = 1; (mp_limb_signed_t) d0 >= 0; cnt++)
 	{
 	  d0 = d0 << 1;
 	}

       q = 0;
       while (cnt)
 	{
 	  q <<= 1;
 	  if (n0 >= d0)
 	    {
 	      n0 = n0 - d0;
 	      q |= 1;
 	    }
 	  d0 = d0 >> 1;
 	  cnt--;
 	}
     }
   else
     {
       int cnt;
       for (cnt = 0; n0 >= d0; cnt++)
 	{
 	  d0 = d0 << 1;
 	}

       q = 0;
       while (cnt)
 	{
 	  d0 = d0 >> 1;
 	  q <<= 1;
 	  if (n0 >= d0)
 	    {
 	      n0 = n0 - d0;
 	      q |= 1;
 	    }
 	  cnt--;
 	}
     }
   *rp = n0;
   return q;
 }

 /* Two-limb division optimized for small quotients.  */
 static inline mp_limb_t
 div2 (mp_ptr rp,
       mp_limb_t nh, mp_limb_t nl,
       mp_limb_t dh, mp_limb_t dl)
 {
   mp_limb_t q = 0;

   if ((mp_limb_signed_t) nh < 0)
     {
       int cnt;
       for (cnt = 1; (mp_limb_signed_t) dh >= 0; cnt++)
 	{
 	  dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
 	  dl = dl << 1;
 	}

       while (cnt)
 	{
 	  q <<= 1;
 	  if (nh > dh || (nh == dh && nl >= dl))
 	    {
 	      sub_ddmmss (nh, nl, nh, nl, dh, dl);
 	      q |= 1;
 	    }
 	  dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
 	  dh = dh >> 1;
 	  cnt--;
 	}
     }
   else
     {
       int cnt;
       for (cnt = 0; nh > dh || (nh == dh && nl >= dl); cnt++)
 	{
 	  dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
 	  dl = dl << 1;
 	}

       while (cnt)
 	{
 	  dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
 	  dh = dh >> 1;
 	  q <<= 1;
 	  if (nh > dh || (nh == dh && nl >= dl))
 	    {
 	      sub_ddmmss (nh, nl, nh, nl, dh, dl);
 	      q |= 1;
 	    }
 	  cnt--;
 	}
     }

   rp[0] = nl;
   rp[1] = nh;

   return q;
 }

 #if 0
 /* This div2 uses less branches, but it seems to nevertheless be
    slightly slower than the above code. */
 static inline mp_limb_t
 div2 (mp_ptr rp,
       mp_limb_t nh, mp_limb_t nl,
       mp_limb_t dh, mp_limb_t dl)
 {
   mp_limb_t q = 0;
   int ncnt;
   int dcnt;

   count_leading_zeros (ncnt, nh);
   count_leading_zeros (dcnt, dh);
   dcnt -= ncnt;

   dh = (dh << dcnt) + (-(dcnt > 0) & (dl >> (GMP_LIMB_BITS - dcnt)));
   dl <<= dcnt;

   do
     {
       mp_limb_t bit;
       q <<= 1;
       if (UNLIKELY (nh == dh))
 	bit = (nl >= dl);
       else
 	bit = (nh > dh);

       q |= bit;

       sub_ddmmss (nh, nl, nh, nl, (-bit) & dh, (-bit) & dl);

       dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
       dh = dh >> 1;
     }
   while (dcnt--);

   rp[0] = nl;
   rp[1] = nh;

   return q;
 }
 #endif

 #else /* GMP_NAIL_BITS != 0 */
 /* Check all functions for nail support. */
 /* hgcd2 should be defined to take inputs including nail bits, and
    produce a matrix with elements also including nail bits. This is
    necessary, for the matrix elements to be useful with mpn_mul_1,
    mpn_addmul_1 and friends. */
 #error Not implemented
 #endif /* GMP_NAIL_BITS != 0 */

 /* 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);
       if (ah == bh)
 	break;

       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_limb_t r;
 	  mp_limb_t q = div1 (&r, ah, bh);
 	  ah = r;
 	  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);
       if (ah == bh)
 	break;

       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_limb_t r;
 	  mp_limb_t q = div1 (&r, bh, ah);
 	  bh = r;
 	  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;
 }

 /* Sets (r;b) = M^{-1}(a;b), with M^{-1} = (u11, -u01; -u10, u00) from
    the left. Uses three buffers, to avoid a copy. */
 mp_size_t
 mpn_hgcd_mul_matrix1_inverse_vector (const struct hgcd_matrix1 *M,
 				     mp_ptr rp, mp_srcptr ap, mp_ptr bp, mp_size_t n)
 {
   mp_limb_t h0, h1;

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

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

   h0 =    mpn_mul_1 (rp, ap, n, M->u[1][1]);
   h1 = mpn_submul_1 (rp, bp, n, M->u[0][1]);
   ASSERT (h0 == h1);

   h0 =    mpn_mul_1 (bp, bp, n, M->u[0][0]);
   h1 = mpn_submul_1 (bp, ap, n, M->u[1][0]);
   ASSERT (h0 == h1);

   n -= (rp[n-1] | bp[n-1]) == 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, 2001, 2002, 2003, 2004, 2008 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"
	#include "longlong.h"

	#if GMP_NAIL_BITS == 0

	/* Copied from the old mpn/generic/gcdext.c, and modified slightly to return
	the remainder. */

	/* Single-limb division optimized for small quotients. */
	static inline mp_limb_t
	div1 (mp_ptr rp,
	mp_limb_t n0,
	mp_limb_t d0)
	{
	mp_limb_t q = 0;

	if ((mp_limb_signed_t) n0 < 0)
	{
	int cnt;
	for (cnt = 1; (mp_limb_signed_t) d0 >= 0; cnt++)
	{
	d0 = d0 << 1;
	}

	q = 0;
	while (cnt)
	{
	q <<= 1;
	if (n0 >= d0)
	{
	n0 = n0 - d0;
	q \|= 1;
	}
	d0 = d0 >> 1;
	cnt--;
	}
	}
	else
	{
	int cnt;
	for (cnt = 0; n0 >= d0; cnt++)
	{
	d0 = d0 << 1;
	}

	q = 0;
	while (cnt)
	{
	d0 = d0 >> 1;
	q <<= 1;
	if (n0 >= d0)
	{
	n0 = n0 - d0;
	q \|= 1;
	}
	cnt--;
	}
	}
	*rp = n0;
	return q;
	}

	/* Two-limb division optimized for small quotients. */
	static inline mp_limb_t
	div2 (mp_ptr rp,
	mp_limb_t nh, mp_limb_t nl,
	mp_limb_t dh, mp_limb_t dl)
	{
	mp_limb_t q = 0;

	if ((mp_limb_signed_t) nh < 0)
	{
	int cnt;
	for (cnt = 1; (mp_limb_signed_t) dh >= 0; cnt++)
	{
	dh = (dh << 1) \| (dl >> (GMP_LIMB_BITS - 1));
	dl = dl << 1;
	}

	while (cnt)
	{
	q <<= 1;
	if (nh > dh \|\| (nh == dh && nl >= dl))
	{
	sub_ddmmss (nh, nl, nh, nl, dh, dl);
	q \|= 1;
	}
	dl = (dh << (GMP_LIMB_BITS - 1)) \| (dl >> 1);
	dh = dh >> 1;
	cnt--;
	}
	}
	else
	{
	int cnt;
	for (cnt = 0; nh > dh \|\| (nh == dh && nl >= dl); cnt++)
	{
	dh = (dh << 1) \| (dl >> (GMP_LIMB_BITS - 1));
	dl = dl << 1;
	}

	while (cnt)
	{
	dl = (dh << (GMP_LIMB_BITS - 1)) \| (dl >> 1);
	dh = dh >> 1;
	q <<= 1;
	if (nh > dh \|\| (nh == dh && nl >= dl))
	{
	sub_ddmmss (nh, nl, nh, nl, dh, dl);
	q \|= 1;
	}
	cnt--;
	}
	}

	rp[0] = nl;
	rp[1] = nh;

	return q;
	}

	#if 0
	/* This div2 uses less branches, but it seems to nevertheless be
	slightly slower than the above code. */
	static inline mp_limb_t
	div2 (mp_ptr rp,
	mp_limb_t nh, mp_limb_t nl,
	mp_limb_t dh, mp_limb_t dl)
	{
	mp_limb_t q = 0;
	int ncnt;
	int dcnt;

	count_leading_zeros (ncnt, nh);
	count_leading_zeros (dcnt, dh);
	dcnt -= ncnt;

	dh = (dh << dcnt) + (-(dcnt > 0) & (dl >> (GMP_LIMB_BITS - dcnt)));
	dl <<= dcnt;

	do
	{
	mp_limb_t bit;
	q <<= 1;
	if (UNLIKELY (nh == dh))
	bit = (nl >= dl);
	else
	bit = (nh > dh);

	q \|= bit;

	sub_ddmmss (nh, nl, nh, nl, (-bit) & dh, (-bit) & dl);

	dl = (dh << (GMP_LIMB_BITS - 1)) \| (dl >> 1);
	dh = dh >> 1;
	}
	while (dcnt--);

	rp[0] = nl;
	rp[1] = nh;

	return q;
	}
	#endif

	#else /* GMP_NAIL_BITS != 0 */
	/* Check all functions for nail support. */
	/* hgcd2 should be defined to take inputs including nail bits, and
	produce a matrix with elements also including nail bits. This is
	necessary, for the matrix elements to be useful with mpn_mul_1,
	mpn_addmul_1 and friends. */
	#error Not implemented
	#endif /* GMP_NAIL_BITS != 0 */

	/* 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);
	if (ah == bh)
	break;

	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_limb_t r;
	mp_limb_t q = div1 (&r, ah, bh);
	ah = r;
	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);
	if (ah == bh)
	break;

	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_limb_t r;
	mp_limb_t q = div1 (&r, bh, ah);
	bh = r;
	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;
	}

	/* Sets (r;b) = M^{-1}(a;b), with M^{-1} = (u11, -u01; -u10, u00) from
	the left. Uses three buffers, to avoid a copy. */
	mp_size_t
	mpn_hgcd_mul_matrix1_inverse_vector (const struct hgcd_matrix1 *M,
	mp_ptr rp, mp_srcptr ap, mp_ptr bp, mp_size_t n)
	{
	mp_limb_t h0, h1;

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

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

	h0 = mpn_mul_1 (rp, ap, n, M->u[1][1]);
	h1 = mpn_submul_1 (rp, bp, n, M->u[0][1]);
	ASSERT (h0 == h1);

	h0 = mpn_mul_1 (bp, bp, n, M->u[0][0]);
	h1 = mpn_submul_1 (bp, ap, n, M->u[1][0]);
	ASSERT (h0 == h1);

	n -= (rp[n-1] \| bp[n-1]) == 0;
	return n;
	}