mpir/mpn/generic/toom_interpolate_16pts.c

/* Interpolaton for the algorithm Toom-Cook 8.5-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 "mpir.h"
#include "gmp-impl.h"

#if GMP_NUMB_BITS < 29
#error Not implemented: Both sublsh_n(,,,28) should be corrected; r2 and r5 need one more LIMB.
#endif

#if GMP_NUMB_BITS < 28
#error Not implemented: divexact_by188513325 and _by182712915 will not work.
#endif


#if HAVE_NATIVE_mpn_sublsh_n
#define DO_mpn_sublsh_n(dst,src,n,s,ws) mpn_sublsh_n(dst,dst,src,n,s)
#else
static mp_limb_t
DO_mpn_sublsh_n(mp_ptr dst, mp_srcptr src, mp_size_t n, unsigned int s, mp_ptr ws)
{
#if USE_MUL_1 && 0
  return mpn_submul_1(dst,src,n,CNST_LIMB(1) <<(s));
#else
  mp_limb_t __cy;
  __cy = mpn_lshift(ws,src,n,s);
  return    __cy + mpn_sub_n(dst,dst,ws,n);
#endif
}
#endif

#if HAVE_NATIVE_mpn_addlsh_n
#define DO_mpn_addlsh_n(dst,src,n,s,ws) mpn_addlsh_n(dst,dst,src,n,s)
#else
static mp_limb_t
DO_mpn_addlsh_n(mp_ptr dst, mp_srcptr src, mp_size_t n, unsigned int s, mp_ptr ws)
{
#if USE_MUL_1 && 0
  return mpn_addmul_1(dst,src,n,CNST_LIMB(1) <<(s));
#else
  mp_limb_t __cy;
  __cy = mpn_lshift(ws,src,n,s);
  return    __cy + mpn_add_n(dst,dst,ws,n);
#endif
}
#endif

#if HAVE_NATIVE_mpn_subrsh
#define DO_mpn_subrsh(dst,nd,src,ns,s,ws) mpn_subrsh(dst,nd,src,ns,s)
#else
/* FIXME: This is not a correct definition, it assumes no carry */
#define DO_mpn_subrsh(dst,nd,src,ns,s,ws)				\
do {									\
  mp_limb_t __cy;							\
  MPN_DECR_U (dst, nd, src[0] >> s);					\
  __cy = DO_mpn_sublsh_n (dst, src + 1, ns - 1, GMP_NUMB_BITS - s, ws);	\
  MPN_DECR_U (dst + ns - 1, nd - ns + 1, __cy);				\
} while (0)
#endif


/* FIXME: tuneup should decide the best variant */
#ifndef AORSMUL_FASTER_AORS_AORSLSH
#define AORSMUL_FASTER_AORS_AORSLSH 1
#endif
#ifndef AORSMUL_FASTER_AORS_2AORSLSH
#define AORSMUL_FASTER_AORS_2AORSLSH 1
#endif
#ifndef AORSMUL_FASTER_2AORSLSH
#define AORSMUL_FASTER_2AORSLSH 1
#endif
#ifndef AORSMUL_FASTER_3AORSLSH
#define AORSMUL_FASTER_3AORSLSH 1
#endif

#if GMP_NUMB_BITS < 43
#define BIT_CORRECTION 1
#define CORRECTION_BITS GMP_NUMB_BITS
#else
#define BIT_CORRECTION 0
#define CORRECTION_BITS 0
#endif

#define BINVERT_9 \
  ((((GMP_NUMB_MAX / 9) << (6 - GMP_NUMB_BITS % 6)) * 8 & GMP_NUMB_MAX) | 0x39)

#define BINVERT_255 \
  (GMP_NUMB_MAX - ((GMP_NUMB_MAX / 255) << (8 - GMP_NUMB_BITS % 8)))

  /* FIXME: find some more general expressions for inverses */
#if GMP_LIMB_BITS == 32
#define BINVERT_2835  (GMP_NUMB_MASK &		CNST_LIMB(0x53E3771B))
#define BINVERT_42525 (GMP_NUMB_MASK &		CNST_LIMB(0x9F314C35))
#define BINVERT_182712915 (GMP_NUMB_MASK &	CNST_LIMB(0x550659DB))
#define BINVERT_188513325 (GMP_NUMB_MASK &	CNST_LIMB(0xFBC333A5))
#define BINVERT_255x182712915L (GMP_NUMB_MASK &	CNST_LIMB(0x6FC4CB25))
#define BINVERT_255x188513325L (GMP_NUMB_MASK &	CNST_LIMB(0x6864275B))
#if GMP_NAIL_BITS == 0
#define BINVERT_255x182712915H CNST_LIMB(0x1B649A07)
#define BINVERT_255x188513325H CNST_LIMB(0x06DB993A)
#else /* GMP_NAIL_BITS != 0 */
#define BINVERT_255x182712915H \
  (GMP_NUMB_MASK & CNST_LIMB((0x1B649A07<<GMP_NAIL_BITS) | (0x6FC4CB25>>GMP_NUMB_BITS)))
#define BINVERT_255x188513325H \
  (GMP_NUMB_MASK & CNST_LIMB((0x06DB993A<<GMP_NAIL_BITS) | (0x6864275B>>GMP_NUMB_BITS)))
#endif
#else
#if GMP_LIMB_BITS == 64
#define BINVERT_2835  (GMP_NUMB_MASK &	CNST_LIMB(0x938CC70553E3771B))
#define BINVERT_42525 (GMP_NUMB_MASK &	CNST_LIMB(0xE7B40D449F314C35))
#define BINVERT_255x182712915  (GMP_NUMB_MASK &	CNST_LIMB(0x1B649A076FC4CB25))
#define BINVERT_255x188513325  (GMP_NUMB_MASK &	CNST_LIMB(0x06DB993A6864275B))
#endif
#endif

#ifndef mpn_divexact_by255
#if GMP_NUMB_BITS % 8 == 0
#define mpn_divexact_by255(dst,src,size) \
  (255 & 1 * mpn_divexact_byfobm1(dst, src, size, 255, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 255)))
#else
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
#define mpn_divexact_by255(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(255),BINVERT_255,0)
#else
#define mpn_divexact_by255(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(255))
#endif
#endif
#endif

#ifndef mpn_divexact_by255x4
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
#define mpn_divexact_by255x4(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(255),BINVERT_255,2)
#else
#define mpn_divexact_by255x4(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(255)<<2)
#endif
#endif

#ifndef mpn_divexact_by9x16
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
#define mpn_divexact_by9x16(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(9),BINVERT_9,4)
#else
#define mpn_divexact_by9x16(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(9)<<4)
#endif
#endif

#ifndef mpn_divexact_by42525x16
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_42525)
#define mpn_divexact_by42525x16(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(42525),BINVERT_42525,4)
#else
#define mpn_divexact_by42525x16(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(42525)<<4)
#endif
#endif

#ifndef mpn_divexact_by2835x64
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_2835)
#define mpn_divexact_by2835x64(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(2835),BINVERT_2835,6)
#else
#define mpn_divexact_by2835x64(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(2835)<<6)
#endif
#endif

#ifndef  mpn_divexact_by255x182712915
#if GMP_NUMB_BITS < 36
#if HAVE_NATIVE_mpn_bdiv_q_2_pi2 && defined(BINVERT_255x182712915H)
/* FIXME: use mpn_bdiv_q_2_pi2 */
#endif
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_182712915)
#define mpn_divexact_by255x182712915(dst,src,size)				\
  do {										\
    mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(182712915),BINVERT_182712915,0);	\
    mpn_divexact_by255(dst,dst,size);						\
  } while(0)
#else
#define mpn_divexact_by255x182712915(dst,src,size)	\
  do {							\
    mpn_divexact_1(dst,src,size,CNST_LIMB(182712915));	\
    mpn_divexact_by255(dst,dst,size);			\
  } while(0)
#endif
#else /* GMP_NUMB_BITS > 35 */
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_255x182712915)
#define mpn_divexact_by255x182712915(dst,src,size) \
  mpn_pi1_bdiv_q_1(dst,src,size,255*CNST_LIMB(182712915),BINVERT_255x182712915,0)
#else
#define mpn_divexact_by255x182712915(dst,src,size) mpn_divexact_1(dst,src,size,255*CNST_LIMB(182712915))
#endif
#endif /* GMP_NUMB_BITS >?< 36 */
#endif

#ifndef  mpn_divexact_by255x188513325
#if GMP_NUMB_BITS < 36
#if HAVE_NATIVE_mpn_bdiv_q_1_pi2 && defined(BINVERT_255x188513325H)
/* FIXME: use mpn_bdiv_q_1_pi2 */
#endif
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_188513325)
#define mpn_divexact_by255x188513325(dst,src,size)			\
  do {									\
    mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(188513325),BINVERT_188513325,0);	\
    mpn_divexact_by255(dst,dst,size);					\
  } while(0)
#else
#define mpn_divexact_by255x188513325(dst,src,size)	\
  do {							\
    mpn_divexact_1(dst,src,size,CNST_LIMB(188513325));	\
    mpn_divexact_by255(dst,dst,size);			\
  } while(0)
#endif
#else /* GMP_NUMB_BITS > 35 */
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_255x188513325)
#define mpn_divexact_by255x188513325(dst,src,size) \
  mpn_pi1_bdiv_q_1(dst,src,size,255*CNST_LIMB(188513325),BINVERT_255x188513325,0)
#else
#define mpn_divexact_by255x188513325(dst,src,size) mpn_divexact_1(dst,src,size,255*CNST_LIMB(188513325))
#endif
#endif /* GMP_NUMB_BITS >?< 36 */
#endif

/* Interpolation for Toom-8.5 (or Toom-8), using the evaluation
   points: infinity(8.5 only), +-8, +-4, +-2, +-1, +-1/4, +-1/2,
   +-1/8, 0. More precisely, we want to compute
   f(2^(GMP_NUMB_BITS * n)) for a polynomial f of degree 15 (or
   14), given the 16 (rsp. 15) values:

     r0 = limit at infinity of f(x) / x^7,
     r1 = f(8),f(-8),
     r2 = f(4),f(-4),
     r3 = f(2),f(-2),
     r4 = f(1),f(-1),
     r5 = f(1/4),f(-1/4),
     r6 = f(1/2),f(-1/2),
     r7 = f(1/8),f(-1/8),
     r8 = f(0).

   All couples of the form f(n),f(-n) must be already mixed with
   toom_couple_handling(f(n),...,f(-n),...)

   The result is stored in {pp, spt + 7*n (or 8*n)}.
   At entry, r8 is stored at {pp, 2n},
   r6 is stored at {pp + 3n, 3n + 1}.
   r4 is stored at {pp + 7n, 3n + 1}.
   r2 is stored at {pp +11n, 3n + 1}.
   r0 is stored at {pp +15n, spt}.

   The other values are 3n+1 limbs each (with most significant limbs small).

   Negative intermediate results are stored two-complemented.
   Inputs are destroyed.
*/

void
mpn_toom_interpolate_16pts (mp_ptr pp, mp_ptr r1, mp_ptr r3, mp_ptr r5, mp_ptr r7,
			mp_size_t n, mp_size_t spt, int half, mp_ptr wsi)
{
  mp_limb_t cy;
  mp_size_t n3;
  mp_size_t n3p1;
  n3 = 3 * n;
  n3p1 = n3 + 1;

#define   r6    (pp + n3)			/* 3n+1 */
#define   r4    (pp + 7 * n)			/* 3n+1 */
#define   r2    (pp +11 * n)			/* 3n+1 */
#define   r0    (pp +15 * n)			/* s+t <= 2*n */

  ASSERT( spt <= 2 * n );
  /******************************* interpolation *****************************/
  if( half != 0) {
    cy = mpn_sub_n (r4, r4, r0, spt);
    MPN_DECR_U (r4 + spt, n3p1 - spt, cy);

    cy = DO_mpn_sublsh_n (r3, r0, spt, 14, wsi);
    MPN_DECR_U (r3 + spt, n3p1 - spt, cy);
    DO_mpn_subrsh(r6, n3p1, r0, spt, 2, wsi);

    cy = DO_mpn_sublsh_n (r2, r0, spt, 28, wsi);
    MPN_DECR_U (r2 + spt, n3p1 - spt, cy);
    DO_mpn_subrsh(r5, n3p1, r0, spt, 4, wsi);

    cy = DO_mpn_sublsh_n (r1 + BIT_CORRECTION, r0, spt, 42 - CORRECTION_BITS, wsi);
    MPN_DECR_U (r1 + spt + BIT_CORRECTION, n3p1 - spt - BIT_CORRECTION, cy);
#if BIT_CORRECTION
    /* FIXME: assumes r7[n3p1] is writable (it is if r5 follows). */
    cy = r7[n3p1];
    r7[n3p1] = 0x80;
#endif
    DO_mpn_subrsh(r7, n3p1 + BIT_CORRECTION, r0, spt, 6, wsi);
#if BIT_CORRECTION
    /* FIXME: assumes r7[n3p1] is writable. */
    ASSERT ( BIT_CORRECTION > 0 || r7[n3p1] == 0x80 );
    r7[n3p1] = cy;
#endif
  };

  r5[n3] -= DO_mpn_sublsh_n (r5 + n, pp, 2 * n, 28, wsi);
  DO_mpn_subrsh(r2 + n, 2 * n + 1, pp, 2 * n, 4, wsi);

#if HAVE_NATIVE_mpn_sumdiff_n
  mpn_sumdiff_n (r2, r5, r5, r2, n3p1);
#else
  mpn_sub_n (wsi, r5, r2, n3p1); /* can be negative */
  ASSERT_NOCARRY(mpn_add_n (r2, r2, r5, n3p1));
  MP_PTR_SWAP(r5, wsi);
#endif

  r6[n3] -= DO_mpn_sublsh_n (r6 + n, pp, 2 * n, 14, wsi);
  DO_mpn_subrsh(r3 + n, 2 * n + 1, pp, 2 * n, 2, wsi);

#if HAVE_NATIVE_mpn_sumdiff_n
  mpn_sumdiff_n (r3, r6, r6, r3, n3p1);
#else
  ASSERT_NOCARRY(mpn_add_n (wsi, r3, r6, n3p1));
  mpn_sub_n (r6, r6, r3, n3p1); /* can be negative */
  MP_PTR_SWAP(r3, wsi);
#endif

  r7[n3] -= DO_mpn_sublsh_n (r7 + n + BIT_CORRECTION, pp, 2 * n, 42 - CORRECTION_BITS, wsi)
	    * (1-BIT_CORRECTION); /* if BIT_CORRECTION != 0, discard the carry. */
#if BIT_CORRECTION
  MPN_DECR_U (r1 + n, 2 * n + 1, pp[0] >> 6);
  cy = DO_mpn_sublsh_n (r1 + n, pp + 1, 2 * n - 1, GMP_NUMB_BITS - 6, wsi);
  cy = mpn_sub_1(r1 + 3 * n - 1, r1 + 3 * n - 1, 2, cy);
  ASSERT ( BIT_CORRECTION > 0 || cy != 0 );
#else
  DO_mpn_subrsh(r1 + n, 2 * n + 1, pp, 2 * n, 6, wsi);
#endif

#if HAVE_NATIVE_mpn_sumdiff_n
  mpn_sumdiff_n (r1, r7, r7, r1, n3p1);
#else
  mpn_sub_n (wsi, r7, r1, n3p1); /* can be negative */
  mpn_add_n (r1, r1, r7, n3p1);  /* if BIT_CORRECTION != 0, can give a carry. */
  MP_PTR_SWAP(r7, wsi);
#endif

  r4[n3] -= mpn_sub_n (r4+n, r4+n, pp, 2 * n);

#if AORSMUL_FASTER_2AORSLSH
  mpn_submul_1 (r5, r6, n3p1, 1028); /* can be negative */
#else
  DO_mpn_sublsh_n (r5, r6, n3p1, 2, wsi); /* can be negative */
  DO_mpn_sublsh_n (r5, r6, n3p1,10, wsi); /* can be negative */
#endif

  mpn_submul_1 (r7, r5, n3p1, 1300); /* can be negative */
#if AORSMUL_FASTER_3AORSLSH
  mpn_submul_1 (r7, r6, n3p1, 1052688); /* can be negative */
#else
  DO_mpn_sublsh_n (r7, r6, n3p1, 4, wsi); /* can be negative */
  DO_mpn_sublsh_n (r7, r6, n3p1,12, wsi); /* can be negative */
  DO_mpn_sublsh_n (r7, r6, n3p1,20, wsi); /* can be negative */
#endif
  mpn_divexact_by255x188513325(r7, r7, n3p1);

  mpn_submul_1 (r5, r7, n3p1, 12567555); /* can be negative */
  /* A division by 2835x64 followsi. Warning: the operand can be negative! */
  mpn_divexact_by2835x64(r5, r5, n3p1);
  if ((r5[n3] & (GMP_NUMB_MAX << (GMP_NUMB_BITS-7))) != 0)
    r5[n3] |= (GMP_NUMB_MAX << (GMP_NUMB_BITS-6));

#if AORSMUL_FASTER_AORS_AORSLSH
  mpn_submul_1 (r6, r7, n3p1, 4095); /* can be negative */
#else
  mpn_add_n (r6, r6, r7, n3p1); /* can give a carry */
  DO_mpn_sublsh_n (r6, r7, n3p1, 12, wsi); /* can be negative */
#endif
#if AORSMUL_FASTER_2AORSLSH
  mpn_addmul_1 (r6, r5, n3p1, 240); /* can be negative */
#else
  DO_mpn_addlsh_n (r6, r5, n3p1, 8, wsi); /* can give a carry */
  DO_mpn_sublsh_n (r6, r5, n3p1, 4, wsi); /* can be negative */
#endif
  /* A division by 255x4 followsi. Warning: the operand can be negative! */
  mpn_divexact_by255x4(r6, r6, n3p1);
  if ((r6[n3] & (GMP_NUMB_MAX << (GMP_NUMB_BITS-3))) != 0)
    r6[n3] |= (GMP_NUMB_MAX << (GMP_NUMB_BITS-2));

  ASSERT_NOCARRY(DO_mpn_sublsh_n (r3, r4, n3p1, 7, wsi));

  ASSERT_NOCARRY(DO_mpn_sublsh_n (r2, r4, n3p1, 13, wsi));
  ASSERT_NOCARRY(mpn_submul_1 (r2, r3, n3p1, 400));

  /* If GMP_NUMB_BITS < 42 next operations on r1 can give a carry!*/
  DO_mpn_sublsh_n (r1, r4, n3p1, 19, wsi);
  mpn_submul_1 (r1, r2, n3p1, 1428);
  mpn_submul_1 (r1, r3, n3p1, 112896);
  mpn_divexact_by255x182712915(r1, r1, n3p1);

  ASSERT_NOCARRY(mpn_submul_1 (r2, r1, n3p1, 15181425));
  mpn_divexact_by42525x16(r2, r2, n3p1);

#if AORSMUL_FASTER_AORS_2AORSLSH
  ASSERT_NOCARRY(mpn_submul_1 (r3, r1, n3p1, 3969));
#else
  ASSERT_NOCARRY(mpn_sub_n (r3, r3, r1, n3p1));
  ASSERT_NOCARRY(DO_mpn_addlsh_n (r3, r1, n3p1, 7, wsi));
  ASSERT_NOCARRY(DO_mpn_sublsh_n (r3, r1, n3p1, 12, wsi));
#endif
  ASSERT_NOCARRY(mpn_submul_1 (r3, r2, n3p1, 900));
  mpn_divexact_by9x16(r3, r3, n3p1);

  ASSERT_NOCARRY(mpn_sub_n (r4, r4, r1, n3p1));
  ASSERT_NOCARRY(mpn_sub_n (r4, r4, r3, n3p1));
  ASSERT_NOCARRY(mpn_sub_n (r4, r4, r2, n3p1));

  mpn_add_n (r6, r2, r6, n3p1);
  ASSERT_NOCARRY(mpn_rshift(r6, r6, n3p1, 1));
  ASSERT_NOCARRY(mpn_sub_n (r2, r2, r6, n3p1));

  mpn_sub_n (r5, r3, r5, n3p1);
  ASSERT_NOCARRY(mpn_rshift(r5, r5, n3p1, 1));
  ASSERT_NOCARRY(mpn_sub_n (r3, r3, r5, n3p1));

  mpn_add_n (r7, r1, r7, n3p1);
  ASSERT_NOCARRY(mpn_rshift(r7, r7, n3p1, 1));
  ASSERT_NOCARRY(mpn_sub_n (r1, r1, r7, n3p1));

  /* last interpolation steps... */
  /* ... could be mixed with recomposition
	||H-r7|M-r7|L-r7|   ||H-r5|M-r5|L-r5|
  */

  /***************************** recomposition *******************************/
  /*
    pp[] prior to operations:
    |M r0|L r0|___||H r2|M r2|L r2|___||H r4|M r4|L r4|___||H r6|M r6|L r6|____|H_r8|L r8|pp

    summation scheme for remaining operations:
    |__16|n_15|n_14|n_13|n_12|n_11|n_10|n__9|n__8|n__7|n__6|n__5|n__4|n__3|n__2|n___|n___|pp
    |M r0|L r0|___||H r2|M r2|L r2|___||H r4|M r4|L r4|___||H r6|M r6|L r6|____|H_r8|L r8|pp
	||H r1|M r1|L r1|   ||H r3|M r3|L r3|   ||H_r5|M_r5|L_r5|   ||H r7|M r7|L r7|
  */

  cy = mpn_add_n (pp + n, pp + n, r7, n);
  cy = mpn_add_1 (pp + 2 * n, r7 + n, n, cy);
#if HAVE_NATIVE_mpn_add_nc
  cy = r7[n3] + mpn_add_nc(pp + n3, pp + n3, r7 + 2 * n, n, cy);
#else
  MPN_INCR_U (r7 + 2 * n, n + 1, cy);
  cy = r7[n3] + mpn_add_n (pp + n3, pp + n3, r7 + 2 * n, n);
#endif
  MPN_INCR_U (pp + 4 * n, 2 * n + 1, cy);

  pp[2 * n3]+= mpn_add_n (pp + 5 * n, pp + 5 * n, r5, n);
  cy = mpn_add_1 (pp + 2 * n3, r5 + n, n, pp[2 * n3]);
#if HAVE_NATIVE_mpn_add_nc
  cy = r5[n3] + mpn_add_nc(pp + 7 * n, pp + 7 * n, r5 + 2 * n, n, cy);
#else
  MPN_INCR_U (r5 + 2 * n, n + 1, cy);
  cy = r5[n3] + mpn_add_n (pp + 7 * n, pp + 7 * n, r5 + 2 * n, n);
#endif
  MPN_INCR_U (pp + 8 * n, 2 * n + 1, cy);

  pp[10 * n]+= mpn_add_n (pp + 9 * n, pp + 9 * n, r3, n);
  cy = mpn_add_1 (pp + 10 * n, r3 + n, n, pp[10 * n]);
#if HAVE_NATIVE_mpn_add_nc
  cy = r3[n3] + mpn_add_nc(pp +11 * n, pp +11 * n, r3 + 2 * n, n, cy);
#else
  MPN_INCR_U (r3 + 2 * n, n + 1, cy);
  cy = r3[n3] + mpn_add_n (pp +11 * n, pp +11 * n, r3 + 2 * n, n);
#endif
  MPN_INCR_U (pp +12 * n, 2 * n + 1, cy);

  pp[14 * n]+=mpn_add_n (pp +13 * n, pp +13 * n, r1, n);
  if ( half ) {
    cy = mpn_add_1 (pp + 14 * n, r1 + n, n, pp[14 * n]);
#if HAVE_NATIVE_mpn_add_nc
    if(LIKELY(spt > n)) {
      cy = r1[n3] + mpn_add_nc(pp + 15 * n, pp + 15 * n, r1 + 2 * n, n, cy);
      MPN_INCR_U (pp + 16 * n, spt - n, cy);
    } else {
      ASSERT_NOCARRY(mpn_add_nc(pp + 15 * n, pp + 15 * n, r1 + 2 * n, spt, cy));
    }
#else
    MPN_INCR_U (r1 + 2 * n, n + 1, cy);
    if(LIKELY(spt > n)) {
      cy = r1[n3] + mpn_add_n (pp + 15 * n, pp + 15 * n, r1 + 2 * n, n);
      MPN_INCR_U (pp + 16 * n, spt - n, cy);
    } else {
      ASSERT_NOCARRY(mpn_add_n (pp + 15 * n, pp + 15 * n, r1 + 2 * n, spt));
    }
#endif
  } else {
    ASSERT_NOCARRY(mpn_add_1 (pp + 14 * n, r1 + n, spt, pp[14 * n]));
  }

#undef   r0
#undef   r2
#undef   r4
#undef   r6
}