/* Interpolaton for the algorithm Toom-Cook 6.5-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, 2012 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"


#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


#if GMP_NUMB_BITS < 21
#error Not implemented: Both sublsh_n(,,,20) should be corrected.
#endif

#if GMP_NUMB_BITS < 16
#error Not implemented: divexact_by42525 needs splitting.
#endif

#if GMP_NUMB_BITS < 12
#error Not implemented: Hard to adapt...
#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

#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 2835^-1, 42525^-1 */
#if GMP_LIMB_BITS == 32
#define BINVERT_2835  (GMP_NUMB_MASK &		CNST_LIMB(0x53E3771B))
#define BINVERT_42525 (GMP_NUMB_MASK &		CNST_LIMB(0x9F314C35))
#else
#if GMP_LIMB_BITS == 64
#define BINVERT_2835  (GMP_NUMB_MASK &	CNST_LIMB(0x938CC70553E3771B))
#define BINVERT_42525 (GMP_NUMB_MASK &	CNST_LIMB(0xE7B40D449F314C35))
#endif
#endif

#ifndef mpn_divexact_by255
#if GMP_NUMB_BITS % 8 == 0
#define mpn_divexact_by255(dst,src,size) \
  (255 & 1 * mpn_bdiv_dbm1 (dst, src, size, __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_by9x4
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
#define mpn_divexact_by9x4(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(9),BINVERT_9,2)
#else
#define mpn_divexact_by9x4(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(9)<<2)
#endif
#endif

#ifndef mpn_divexact_by42525
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_42525)
#define mpn_divexact_by42525(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(42525),BINVERT_42525,0)
#else
#define mpn_divexact_by42525(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(42525))
#endif
#endif

#ifndef mpn_divexact_by2835x4
#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_2835)
#define mpn_divexact_by2835x4(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(2835),BINVERT_2835,2)
#else
#define mpn_divexact_by2835x4(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(2835)<<2)
#endif
#endif

/* Interpolation for Toom-6.5 (or Toom-6), using the evaluation
   points: infinity(6.5 only), +-4, +-2, +-1, +-1/4, +-1/2, 0. More precisely,
   we want to compute f(2^(GMP_NUMB_BITS * n)) for a polynomial f of
   degree 11 (or 10), given the 12 (rsp. 11) values:

     r0 = limit at infinity of f(x) / x^7,
     r1 = f(4),f(-4),
     r2 = f(2),f(-2),
     r3 = f(1),f(-1),
     r4 = f(1/4),f(-1/4),
     r5 = f(1/2),f(-1/2),
     r6 = 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 6*n)}.
   At entry, r6 is stored at {pp, 2n},
   r4 is stored at {pp + 3n, 3n + 1}.
   r2 is stored at {pp + 7n, 3n + 1}.
   r0 is stored at {pp +11n, 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_12pts (mp_ptr pp, mp_ptr r1, mp_ptr r3, mp_ptr r5,
			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   r4    (pp + n3)			/* 3n+1 */
#define   r2    (pp + 7 * n)			/* 3n+1 */
#define   r0    (pp +11 * n)			/* s+t <= 2*n */

  /******************************* interpolation *****************************/
  if (half != 0) {
    cy = mpn_sub_n (r3, r3, r0, spt);
    MPN_DECR_U (r3 + spt, n3p1 - spt, cy);

    cy = DO_mpn_sublsh_n (r2, r0, spt, 10, wsi);
    MPN_DECR_U (r2 + spt, n3p1 - spt, cy);
    DO_mpn_subrsh(r5, n3p1, r0, spt, 2, wsi);

    cy = DO_mpn_sublsh_n (r1, r0, spt, 20, wsi);
    MPN_DECR_U (r1 + spt, n3p1 - spt, cy);
    DO_mpn_subrsh(r4, n3p1, r0, spt, 4, wsi);
  };

  r4[n3] -= DO_mpn_sublsh_n (r4 + n, pp, 2 * n, 20, wsi);
  DO_mpn_subrsh(r1 + n, 2 * n + 1, pp, 2 * n, 4, wsi);

#if HAVE_NATIVE_mpn_add_n_sub_n
  mpn_add_n_sub_n (r1, r4, r4, r1, n3p1);
#else
  ASSERT_NOCARRY(mpn_add_n (wsi, r1, r4, n3p1));
  mpn_sub_n (r4, r4, r1, n3p1); /* can be negative */
  MP_PTR_SWAP(r1, wsi);
#endif

  r5[n3] -= DO_mpn_sublsh_n (r5 + n, pp, 2 * n, 10, wsi);
  DO_mpn_subrsh(r2 + n, 2 * n + 1, pp, 2 * n, 2, wsi);

#if HAVE_NATIVE_mpn_add_n_sub_n
  mpn_add_n_sub_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

  r3[n3] -= mpn_sub_n (r3+n, r3+n, pp, 2 * n);

#if AORSMUL_FASTER_AORS_AORSLSH
  mpn_submul_1 (r4, r5, n3p1, 257); /* can be negative */
#else
  mpn_sub_n (r4, r4, r5, n3p1); /* can be negative */
  DO_mpn_sublsh_n (r4, r5, n3p1, 8, wsi); /* can be negative */
#endif
  /* A division by 2835x4 follows. Warning: the operand can be negative! */
  mpn_divexact_by2835x4(r4, r4, n3p1);
  if ((r4[n3] & (GMP_NUMB_MAX << (GMP_NUMB_BITS-3))) != 0)
    r4[n3] |= (GMP_NUMB_MAX << (GMP_NUMB_BITS-2));

#if AORSMUL_FASTER_2AORSLSH
  mpn_addmul_1 (r5, r4, n3p1, 60); /* can be negative */
#else
  DO_mpn_sublsh_n (r5, r4, n3p1, 2, wsi); /* can be negative */
  DO_mpn_addlsh_n (r5, r4, n3p1, 6, wsi); /* can give a carry */
#endif
  mpn_divexact_by255(r5, r5, n3p1);

  ASSERT_NOCARRY(DO_mpn_sublsh_n (r2, r3, n3p1, 5, wsi));

#if AORSMUL_FASTER_3AORSLSH
  ASSERT_NOCARRY(mpn_submul_1 (r1, r2, n3p1, 100));
#else
  ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 6, wsi));
  ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 5, wsi));
  ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 2, wsi));
#endif
  ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r3, n3p1, 9, wsi));
  mpn_divexact_by42525(r1, r1, n3p1);

#if AORSMUL_FASTER_AORS_2AORSLSH
  ASSERT_NOCARRY(mpn_submul_1 (r2, r1, n3p1, 225));
#else
  ASSERT_NOCARRY(mpn_sub_n (r2, r2, r1, n3p1));
  ASSERT_NOCARRY(DO_mpn_addlsh_n (r2, r1, n3p1, 5, wsi));
  ASSERT_NOCARRY(DO_mpn_sublsh_n (r2, r1, n3p1, 8, wsi));
#endif
  mpn_divexact_by9x4(r2, r2, n3p1);

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

  mpn_sub_n (r4, r2, r4, n3p1);
  ASSERT_NOCARRY(mpn_rshift(r4, r4, n3p1, 1));
  ASSERT_NOCARRY(mpn_sub_n (r2, r2, r4, n3p1));

  mpn_add_n (r5, r5, r1, n3p1);
  ASSERT_NOCARRY(mpn_rshift(r5, r5, n3p1, 1));

  /* last interpolation steps... */
  ASSERT_NOCARRY(mpn_sub_n (r3, r3, r1, n3p1));
  ASSERT_NOCARRY(mpn_sub_n (r1, r1, r5, n3p1));
  /* ... could be mixed with recomposition
	||H-r5|M-r5|L-r5|   ||H-r1|M-r1|L-r1|
  */

  /***************************** recomposition *******************************/
  /*
    pp[] prior to operations:
    |M r0|L r0|___||H r2|M r2|L r2|___||H r4|M r4|L r4|____|H_r6|L r6|pp

    summation scheme for remaining operations:
    |__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|L r6|pp
	||H r1|M r1|L r1|   ||H r3|M r3|L r3|   ||H_r5|M_r5|L_r5|
  */

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

  pp[2 * n3]+= mpn_add_n (pp + 5 * n, pp + 5 * n, r3, n);
  cy = mpn_add_1 (pp + 2 * n3, r3 + n, n, pp[2 * n3]);
#if HAVE_NATIVE_mpn_add_nc
  cy = r3[n3] + mpn_add_nc(pp + 7 * n, pp + 7 * n, r3 + 2 * n, n, cy);
#else
  MPN_INCR_U (r3 + 2 * n, n + 1, cy);
  cy = r3[n3] + mpn_add_n (pp + 7 * n, pp + 7 * n, r3 + 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, r1, n);
  if (half) {
    cy = mpn_add_1 (pp + 10 * n, r1 + n, n, pp[10 * n]);
#if HAVE_NATIVE_mpn_add_nc
    if (LIKELY (spt > n)) {
      cy = r1[n3] + mpn_add_nc(pp + 11 * n, pp + 11 * n, r1 + 2 * n, n, cy);
      MPN_INCR_U (pp + 4 * n3, spt - n, cy);
    } else {
      ASSERT_NOCARRY(mpn_add_nc(pp + 11 * n, pp + 11 * 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 + 11 * n, pp + 11 * n, r1 + 2 * n, n);
      MPN_INCR_U (pp + 4 * n3, spt - n, cy);
    } else {
      ASSERT_NOCARRY(mpn_add_n (pp + 11 * n, pp + 11 * n, r1 + 2 * n, spt));
    }
#endif
  } else {
    ASSERT_NOCARRY(mpn_add_1 (pp + 10 * n, r1 + n, spt, pp[10 * n]));
  }

#undef   r0
#undef   r2
#undef   r4
}
