/*

 * Copyright (c) 2003, 2007-14 Matteo Frigo

 * Copyright (c) 2003, 2007-14 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

 *

 */

#include "rdft/rdft.h"

/*

 * Compute DHTs of prime sizes using Rader's trick: turn them

 * into convolutions of size n - 1, which we then perform via a pair

 * of FFTs.   (We can then do prime real FFTs via rdft-dht.c.)

 *

 * Optionally (determined by the "pad" field of the solver), we can

 * perform the (cyclic) convolution by zero-padding to a size

 * >= 2*(n-1) - 1.  This is advantageous if n-1 has large prime factors.

 *

 */

typedef struct {

     solver super;

     int pad;

} S;

typedef struct {

     plan_rdft super;

     plan *cld1, *cld2;

     R *omega;

     INT n, npad, g, ginv;

     INT is, os;

     plan *cld_omega;

} P;

static rader_tl *omegas = 0;

/***************************************************************************/

/* If R2HC_ONLY_CONV is 1, we use a trick to perform the convolution

   purely in terms of R2HC transforms, as opposed to R2HC followed by H2RC.

   This requires a few more operations, but allows us to share the same

   plan/codelets for both Rader children. */

#define R2HC_ONLY_CONV 1

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

{

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

     INT n = ego->n; /* prime */

     INT npad = ego->npad; /* == n - 1 for unpadded Rader; always even */

     INT is = ego->is, os;

     INT k, gpower, g;

     R *buf, *omega;

     R r0;

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

     /* First, permute the input, storing in buf: */

     g = ego->g; 

     for (gpower = 1, k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {

    buf[k] = I[gpower * is];

     }

     /* gpower == g^(n-1) mod n == 1 */;

     A(n - 1 <= npad);

     for (k = n - 1; k < npad; ++k) /* optionally, zero-pad convolution */

    buf[k] = 0;

     os = ego->os;

     /* compute RDFT of buf, storing in buf (i.e., in-place): */

     {

      plan_rdft *cld = (plan_rdft *) ego->cld1;

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

     }

     /* set output DC component: */

     O[0] = (r0 = I[0]) + buf[0];

     /* now, multiply by omega: */

     omega = ego->omega;

     buf[0] *= omega[0];

     for (k = 1; k < npad/2; ++k) {

    E rB, iB, rW, iW, a, b;

    rW = omega[k];

    iW = omega[npad - k];

    rB = buf[k];

    iB = buf[npad - k];

    a = rW * rB - iW * iB;

    b = rW * iB + iW * rB;

#if R2HC_ONLY_CONV

    buf[k] = a + b;

    buf[npad - k] = a - b;

#else

    buf[k] = a;

    buf[npad - k] = b;

#endif

     }

     /* Nyquist component: */

     A(k + k == npad); /* since npad is even */

     buf[k] *= omega[k];

     /* this will add input[0] to all of the outputs after the ifft */

     buf[0] += r0;

     /* inverse FFT: */

     {

      plan_rdft *cld = (plan_rdft *) ego->cld2;

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

     }

     /* do inverse permutation to unshuffle the output: */

     A(gpower == 1);

#if R2HC_ONLY_CONV

     O[os] = buf[0];

     gpower = g = ego->ginv;

     A(npad == n - 1 || npad/2 >= n - 1);

     if (npad == n - 1) {

    for (k = 1; k < npad/2; ++k, gpower = MULMOD(gpower, g, n)) {

         O[gpower * os] = buf[k] + buf[npad - k];

    }

    O[gpower * os] = buf[k];

    ++k, gpower = MULMOD(gpower, g, n);

    for (; k < npad; ++k, gpower = MULMOD(gpower, g, n)) {

         O[gpower * os] = buf[npad - k] - buf[k];

    }

     }

     else {

    for (k = 1; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {

         O[gpower * os] = buf[k] + buf[npad - k];

    }

     }

#else

     g = ego->ginv;

     for (k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {

    O[gpower * os] = buf[k];

     }

#endif

     A(gpower == 1);

     X(ifree)(buf);

}

static R *mkomega(enum wakefulness wakefulness,

      plan *p_, INT n, INT npad, INT ginv)

{

     plan_rdft *p = (plan_rdft *) p_;

     R *omega;

     INT i, gpower;

     trigreal scale;

     triggen *t;

     if ((omega = X(rader_tl_find)(n, npad + 1, ginv, omegas))) 

    return omega;

     omega = (R *)MALLOC(sizeof(R) * npad, TWIDDLES);

     scale = npad; /* normalization for convolution */

     t = X(mktriggen)(wakefulness, n);

     for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {

    trigreal w[2];

    t->cexpl(t, gpower, w);

    omega[i] = (w[0] + w[1]) / scale;

     }

     X(triggen_destroy)(t);

     A(gpower == 1);

     A(npad == n - 1 || npad >= 2*(n - 1) - 1);

     for (; i < npad; ++i)

    omega[i] = K(0.0);

     if (npad > n - 1)

    for (i = 1; i < n-1; ++i)

         omega[npad - i] = omega[n - 1 - i];

     p->apply(p_, omega, omega);

     X(rader_tl_insert)(n, npad + 1, ginv, omega, &omegas);

     return omega;

}

static void free_omega(R *omega)

{

     X(rader_tl_delete)(omega, &omegas);

}

/***************************************************************************/

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

{

     P *ego = (P *) ego_;

     X(plan_awake)(ego->cld1, wakefulness);

     X(plan_awake)(ego->cld2, wakefulness);

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

     switch (wakefulness) {

   case SLEEPY:

        free_omega(ego->omega);

        ego->omega = 0;

        break;

   default:

        ego->g = X(find_generator)(ego->n);

        ego->ginv = X(power_mod)(ego->g, ego->n - 2, ego->n);

        A(MULMOD(ego->g, ego->ginv, ego->n) == 1);

        A(!ego->omega);

        ego->omega = mkomega(wakefulness, 

           ego->cld_omega,ego->n,ego->npad,ego->ginv);

        break;

     }

}

static void destroy(plan *ego_)

{

     P *ego = (P *) ego_;

     X(plan_destroy_internal)(ego->cld_omega);

     X(plan_destroy_internal)(ego->cld2);

     X(plan_destroy_internal)(ego->cld1);

}

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

{

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

     p->print(p, "(dht-rader-%D/%D%ois=%oos=%(%p%)",

              ego->n, ego->npad, ego->is, ego->os, ego->cld1);

     if (ego->cld2 != ego->cld1)

          p->print(p, "%(%p%)", ego->cld2);

     if (ego->cld_omega != ego->cld1 && ego->cld_omega != ego->cld2)

          p->print(p, "%(%p%)", ego->cld_omega);

     p->putchr(p, ')');

}

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

{

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

     UNUSED(ego);

     return (1

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

       && p->vecsz->rnk == 0

       && p->kind[0] == DHT

       && X(is_prime)(p->sz->dims[0].n)

       && p->sz->dims[0].n > 2

       && CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)

       /* proclaim the solver SLOW if p-1 is not easily

    factorizable.  Unlike in the complex case where

    Bluestein can solve the problem, in the DHT case we

    may have no other choice */

       && CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))

    );

}

static INT choose_transform_size(INT minsz)

{

     static const INT primes[] = { 2, 3, 5, 0 };

     while (!X(factors_into)(minsz, primes) || minsz % 2)

    ++minsz;

     return minsz;

}

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

{

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

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

     P *pln;

     INT n, npad;

     INT is, os;

     plan *cld1 = (plan *) 0;

     plan *cld2 = (plan *) 0;

     plan *cld_omega = (plan *) 0;

     R *buf = (R *) 0;

     problem *cldp;

     static const plan_adt padt = {

    X(rdft_solve), awake, print, destroy

     };

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

    return (plan *) 0;

     n = p->sz->dims[0].n;

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

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

     if (ego->pad)

    npad = choose_transform_size(2 * (n - 1) - 1);

     else

    npad = n - 1;

     /* initial allocation for the purpose of planning */

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

     cld1 = X(mkplan_f_d)(plnr, 

        X(mkproblem_rdft_1_d)(X(mktensor_1d)(npad, 1, 1),

            X(mktensor_1d)(1, 0, 0),

            buf, buf,

            R2HC),

        NO_SLOW, 0, 0);

     if (!cld1) goto nada;

     cldp =

          X(mkproblem_rdft_1_d)(

               X(mktensor_1d)(npad, 1, 1),

               X(mktensor_1d)(1, 0, 0),

         buf, buf, 

#if R2HC_ONLY_CONV

         R2HC

#else

         HC2R

#endif

         );

     if (!(cld2 = X(mkplan_f_d)(plnr, cldp, NO_SLOW, 0, 0)))

    goto nada;

     /* plan for omega */

     cld_omega = X(mkplan_f_d)(plnr, 

             X(mkproblem_rdft_1_d)(

            X(mktensor_1d)(npad, 1, 1),

            X(mktensor_1d)(1, 0, 0),

            buf, buf, R2HC),

             NO_SLOW, ESTIMATE, 0);

     if (!cld_omega) goto nada;

     /* deallocate buffers; let awake() or apply() allocate them for real */

     X(ifree)(buf);

     buf = 0;

     pln = MKPLAN_RDFT(P, &padt, apply);

     pln->cld1 = cld1;

     pln->cld2 = cld2;

     pln->cld_omega = cld_omega;

     pln->omega = 0;

     pln->n = n;

     pln->npad = npad;

     pln->is = is;

     pln->os = os;

     X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);

     pln->super.super.ops.other += (npad/2-1)*6 + npad + n + (n-1) * ego->pad;

     pln->super.super.ops.add += (npad/2-1)*2 + 2 + (n-1) * ego->pad;

     pln->super.super.ops.mul += (npad/2-1)*4 + 2 + ego->pad;

#if R2HC_ONLY_CONV

     pln->super.super.ops.other += n-2 - ego->pad;

     pln->super.super.ops.add += (npad/2-1)*2 + (n-2) - ego->pad;

#endif

     return &(pln->super.super);

 nada:

     X(ifree0)(buf);

     X(plan_destroy_internal)(cld_omega);

     X(plan_destroy_internal)(cld2);

     X(plan_destroy_internal)(cld1);

     return 0;

}

/* constructors */

static solver *mksolver(int pad)

{

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

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

     slv->pad = pad;

     return &(slv->super);

}

void X(dht_rader_register)(planner *p)

{

     REGISTER_SOLVER(p, mksolver(0));

     REGISTER_SOLVER(p, mksolver(1));

}