/*

 * Copyright (c) 2005 Matteo Frigo

 * Copyright (c) 2005 Massachusetts Institute of Technology

 *

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of 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.

 *

 * This program 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 a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

 *

 */

/* Do an R{E,O}DFT00 problem (of an odd length n) recursively via an

   R{E,O}DFT00 problem and an RDFT problem of half the length.

   This works by "logically" expanding the array to a real-even/odd DFT of

   length 2n-/+2 and then applying the split-radix algorithm.

   In this way, we can avoid having to pad to twice the length

   (ala redft00-r2hc-pad), saving a factor of ~2 for n=2^m+/-1,

   but don't incur the accuracy loss that the "ordinary" algorithm

   sacrifices (ala redft00-r2hc.c).

*/

#include "reodft/reodft.h"

typedef struct {

     solver super;

} S;

typedef struct {

     plan_rdft super;

     plan *clde, *cldo;

     twid *td;

     INT is, os;

     INT n;

     INT vl;

     INT ivs, ovs;

} P;

/* redft00 */

static void apply_e(const plan *ego_, R *I, R *O)

{

     const P *ego = (const P *) ego_;

     INT is = ego->is, os = ego->os;

     INT i, j, n = ego->n + 1, n2 = (n-1)/2;

     INT iv, vl = ego->vl;

     INT ivs = ego->ivs, ovs = ego->ovs;

     R *W = ego->td->W - 2;

     R *buf;

     buf = (R *) MALLOC(sizeof(R) * n2, BUFFERS);

     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {

    /* do size (n-1)/2 r2hc transform of odd-indexed elements

       with stride 4, "wrapping around" end of array with even

       boundary conditions */

    for (j = 0, i = 1; i < n; i += 4)

         buf[j++] = I[is * i];

    for (i = 2*n-2-i; i > 0; i -= 4)

         buf[j++] = I[is * i];

    {

         plan_rdft *cld = (plan_rdft *) ego->cldo;

         cld->apply((plan *) cld, buf, buf);

    }

    /* do size (n+1)/2 redft00 of the even-indexed elements,

       writing to O: */

    {

         plan_rdft *cld = (plan_rdft *) ego->clde;

         cld->apply((plan *) cld, I, O);

    }

    /* combine the results with the twiddle factors to get output */

    { /* DC element */

         E b20 = O[0], b0 = K(2.0) * buf[0];

         O[0] = b20 + b0;

         O[2*(n2*os)] = b20 - b0;

         /* O[n2*os] = O[n2*os]; */

    }

    for (i = 1; i < n2 - i; ++i) {

         E ap, am, br, bi, wr, wi, wbr, wbi;

         br = buf[i];

         bi = buf[n2 - i];

         wr = W[2*i];

         wi = W[2*i+1];

#if FFT_SIGN == -1

         wbr = K(2.0) * (wr*br + wi*bi);

         wbi = K(2.0) * (wr*bi - wi*br);

#else

         wbr = K(2.0) * (wr*br - wi*bi);

         wbi = K(2.0) * (wr*bi + wi*br);

#endif

         ap = O[i*os];

         O[i*os] = ap + wbr;

         O[(2*n2 - i)*os] = ap - wbr;

         am = O[(n2 - i)*os];

#if FFT_SIGN == -1

         O[(n2 - i)*os] = am - wbi;

         O[(n2 + i)*os] = am + wbi;

#else

         O[(n2 - i)*os] = am + wbi;

         O[(n2 + i)*os] = am - wbi;

#endif

    }

    if (i == n2 - i) { /* Nyquist element */

         E ap, wbr;

         wbr = K(2.0) * (W[2*i] * buf[i]);

         ap = O[i*os];

         O[i*os] = ap + wbr;

         O[(2*n2 - i)*os] = ap - wbr;

    }

     }

     X(ifree)(buf);

}

/* rodft00 */

static void apply_o(const plan *ego_, R *I, R *O)

{

     const P *ego = (const P *) ego_;

     INT is = ego->is, os = ego->os;

     INT i, j, n = ego->n - 1, n2 = (n+1)/2;

     INT iv, vl = ego->vl;

     INT ivs = ego->ivs, ovs = ego->ovs;

     R *W = ego->td->W - 2;

     R *buf;

     buf = (R *) MALLOC(sizeof(R) * n2, BUFFERS);

     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {

    /* do size (n+1)/2 r2hc transform of even-indexed elements

       with stride 4, "wrapping around" end of array with odd

       boundary conditions */

    for (j = 0, i = 0; i < n; i += 4)

         buf[j++] = I[is * i];

    for (i = 2*n-i; i > 0; i -= 4)

         buf[j++] = -I[is * i];

    {

         plan_rdft *cld = (plan_rdft *) ego->cldo;

         cld->apply((plan *) cld, buf, buf);

    }

    /* do size (n-1)/2 rodft00 of the odd-indexed elements,

       writing to O: */

    {

         plan_rdft *cld = (plan_rdft *) ego->clde;

         if (I == O) {

        /* can't use I+is and I, subplan would lose in-placeness */

        cld->apply((plan *) cld, I + is, I + is);

        /* we could maybe avoid this copy by modifying the

           twiddle loop, but currently I can't be bothered. */

        A(is >= os);

        for (i = 0; i < n2-1; ++i)

       O[os*i] = I[is*(i+1)];

         }

         else

        cld->apply((plan *) cld, I + is, O);

    }

    /* combine the results with the twiddle factors to get output */

    O[(n2-1)*os] = K(2.0) * buf[0];

    for (i = 1; i < n2 - i; ++i) {

         E ap, am, br, bi, wr, wi, wbr, wbi;

         br = buf[i];

         bi = buf[n2 - i];

         wr = W[2*i];

         wi = W[2*i+1];

#if FFT_SIGN == -1

         wbr = K(2.0) * (wr*br + wi*bi);

         wbi = K(2.0) * (wi*br - wr*bi);

#else

         wbr = K(2.0) * (wr*br - wi*bi);

         wbi = K(2.0) * (wr*bi + wi*br);

#endif

         ap = O[(i-1)*os];

         O[(i-1)*os] = wbi + ap;

         O[(2*n2-1 - i)*os] = wbi - ap;

         am = O[(n2-1 - i)*os];

#if FFT_SIGN == -1

         O[(n2-1 - i)*os] = wbr + am;

         O[(n2-1 + i)*os] = wbr - am;

#else

         O[(n2-1 - i)*os] = wbr + am;

         O[(n2-1 + i)*os] = wbr - am;

#endif

    }

    if (i == n2 - i) { /* Nyquist element */

         E ap, wbi;

         wbi = K(2.0) * (W[2*i+1] * buf[i]);

         ap = O[(i-1)*os];

         O[(i-1)*os] = wbi + ap;

         O[(2*n2-1 - i)*os] = wbi - ap;

    }

     }

     X(ifree)(buf);

}

static void awake(plan *ego_, enum wakefulness wakefulness)

{

     P *ego = (P *) ego_;

     static const tw_instr reodft00e_tw[] = {

          { TW_COS, 1, 1 },

          { TW_SIN, 1, 1 },

          { TW_NEXT, 1, 0 }

     };

     X(plan_awake)(ego->clde, wakefulness);

     X(plan_awake)(ego->cldo, wakefulness);

     X(twiddle_awake)(wakefulness, &ego->td, reodft00e_tw, 

          2*ego->n, 1, ego->n/4);

}

static void destroy(plan *ego_)

{

     P *ego = (P *) ego_;

     X(plan_destroy_internal)(ego->cldo);

     X(plan_destroy_internal)(ego->clde);

}

static void print(const plan *ego_, printer *p)

{

     const P *ego = (const P *) ego_;

     if (ego->super.apply == apply_e)

    p->print(p, "(redft00e-splitradix-%D%v%(%p%)%(%p%))", 

       ego->n + 1, ego->vl, ego->clde, ego->cldo);

     else

    p->print(p, "(rodft00e-splitradix-%D%v%(%p%)%(%p%))", 

       ego->n - 1, ego->vl, ego->clde, ego->cldo);

}

static int applicable0(const solver *ego_, const problem *p_)

{

     const problem_rdft *p = (const problem_rdft *) p_;

     UNUSED(ego_);

     return (1

       && p->sz->rnk == 1

       && p->vecsz->rnk <= 1

       && (p->kind[0] == REDFT00 || p->kind[0] == RODFT00)

       && p->sz->dims[0].n > 1  /* don't create size-0 sub-plans */

       && p->sz->dims[0].n % 2  /* odd: 4 divides "logical" DFT */

       && (p->I != p->O || p->vecsz->rnk == 0

     || p->vecsz->dims[0].is == p->vecsz->dims[0].os)

       && (p->kind[0] != RODFT00 || p->I != p->O || 

     p->sz->dims[0].is >= p->sz->dims[0].os) /* laziness */

    );

}

static int applicable(const solver *ego, const problem *p, const planner *plnr)

{

     return (!NO_SLOWP(plnr) && applicable0(ego, p));

}

static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)

{

     P *pln;

     const problem_rdft *p;

     plan *clde, *cldo;

     R *buf;

     INT n, n0;

     opcnt ops;

     int inplace_odd;

     static const plan_adt padt = {

    X(rdft_solve), awake, print, destroy

     };

     if (!applicable(ego_, p_, plnr))

          return (plan *)0;

     p = (const problem_rdft *) p_;

     n = (n0 = p->sz->dims[0].n) + (p->kind[0] == REDFT00 ? (INT)-1 : (INT)1);

     A(n > 0 && n % 2 == 0);

     buf = (R *) MALLOC(sizeof(R) * (n/2), BUFFERS);

     inplace_odd = p->kind[0]==RODFT00 && p->I == p->O;

     clde = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(

           X(mktensor_1d)(n0-n/2, 2*p->sz->dims[0].is, 

              inplace_odd ? p->sz->dims[0].is

              : p->sz->dims[0].os), 

           X(mktensor_0d)(), 

           TAINT(p->I 

           + p->sz->dims[0].is * (p->kind[0]==RODFT00),

           p->vecsz->rnk ? p->vecsz->dims[0].is : 0),

           TAINT(p->O

           + p->sz->dims[0].is * inplace_odd,

           p->vecsz->rnk ? p->vecsz->dims[0].os : 0),

           p->kind[0]));

     if (!clde) {

    X(ifree)(buf);

          return (plan *)0;

     }

     cldo = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(

           X(mktensor_1d)(n/2, 1, 1), 

           X(mktensor_0d)(), 

           buf, buf, R2HC));

     X(ifree)(buf);

     if (!cldo)

          return (plan *)0;

     pln = MKPLAN_RDFT(P, &padt, p->kind[0] == REDFT00 ? apply_e : apply_o);

     pln->n = n;

     pln->is = p->sz->dims[0].is;

     pln->os = p->sz->dims[0].os;

     pln->clde = clde;

     pln->cldo = cldo;

     pln->td = 0;

     X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);

     X(ops_zero)(&ops);

     ops.other = n/2;

     ops.add = (p->kind[0]==REDFT00 ? (INT)2 : (INT)0) +

    (n/2-1)/2 * 6 + ((n/2)%2==0) * 2;

     ops.mul = 1 + (n/2-1)/2 * 6 + ((n/2)%2==0) * 2;

     /* tweak ops.other so that r2hc-pad is used for small sizes, which

  seems to be a lot faster on my machine: */

     ops.other += 256;

     X(ops_zero)(&pln->super.super.ops);

     X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);

     X(ops_madd2)(pln->vl, &clde->ops, &pln->super.super.ops);

     X(ops_madd2)(pln->vl, &cldo->ops, &pln->super.super.ops);

     return &(pln->super.super);

}

/* constructor */

static solver *mksolver(void)

{

     static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };

     S *slv = MKSOLVER(S, &sadt);

     return &(slv->super);

}

void X(reodft00e_splitradix_register)(planner *p)

{

     REGISTER_SOLVER(p, mksolver());

}