Chris@42: /*
Chris@42:  * Copyright (c) 2003, 2007-14 Matteo Frigo
Chris@42:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
Chris@42:  *
Chris@42:  * This program is free software; you can redistribute it and/or modify
Chris@42:  * it under the terms of the GNU General Public License as published by
Chris@42:  * the Free Software Foundation; either version 2 of the License, or
Chris@42:  * (at your option) any later version.
Chris@42:  *
Chris@42:  * This program is distributed in the hope that it will be useful,
Chris@42:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@42:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@42:  * GNU General Public License for more details.
Chris@42:  *
Chris@42:  * You should have received a copy of the GNU General Public License
Chris@42:  * along with this program; if not, write to the Free Software
Chris@42:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@42:  *
Chris@42:  */
Chris@42: 
Chris@42: #include "rdft.h"
Chris@42: 
Chris@42: /*
Chris@42:  * Compute DHTs of prime sizes using Rader's trick: turn them
Chris@42:  * into convolutions of size n - 1, which we then perform via a pair
Chris@42:  * of FFTs.   (We can then do prime real FFTs via rdft-dht.c.)
Chris@42:  *
Chris@42:  * Optionally (determined by the "pad" field of the solver), we can
Chris@42:  * perform the (cyclic) convolution by zero-padding to a size
Chris@42:  * >= 2*(n-1) - 1.  This is advantageous if n-1 has large prime factors.
Chris@42:  *
Chris@42:  */
Chris@42: 
Chris@42: typedef struct {
Chris@42:      solver super;
Chris@42:      int pad;
Chris@42: } S;
Chris@42: 
Chris@42: typedef struct {
Chris@42:      plan_rdft super;
Chris@42: 
Chris@42:      plan *cld1, *cld2;
Chris@42:      R *omega;
Chris@42:      INT n, npad, g, ginv;
Chris@42:      INT is, os;
Chris@42:      plan *cld_omega;
Chris@42: } P;
Chris@42: 
Chris@42: static rader_tl *omegas = 0;
Chris@42: 
Chris@42: /***************************************************************************/
Chris@42: 
Chris@42: /* If R2HC_ONLY_CONV is 1, we use a trick to perform the convolution
Chris@42:    purely in terms of R2HC transforms, as opposed to R2HC followed by H2RC.
Chris@42:    This requires a few more operations, but allows us to share the same
Chris@42:    plan/codelets for both Rader children. */
Chris@42: #define R2HC_ONLY_CONV 1
Chris@42: 
Chris@42: static void apply(const plan *ego_, R *I, R *O)
Chris@42: {
Chris@42:      const P *ego = (const P *) ego_;
Chris@42:      INT n = ego->n; /* prime */
Chris@42:      INT npad = ego->npad; /* == n - 1 for unpadded Rader; always even */
Chris@42:      INT is = ego->is, os;
Chris@42:      INT k, gpower, g;
Chris@42:      R *buf, *omega;
Chris@42:      R r0;
Chris@42: 
Chris@42:      buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
Chris@42: 
Chris@42:      /* First, permute the input, storing in buf: */
Chris@42:      g = ego->g; 
Chris@42:      for (gpower = 1, k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
Chris@42: 	  buf[k] = I[gpower * is];
Chris@42:      }
Chris@42:      /* gpower == g^(n-1) mod n == 1 */;
Chris@42: 
Chris@42:      A(n - 1 <= npad);
Chris@42:      for (k = n - 1; k < npad; ++k) /* optionally, zero-pad convolution */
Chris@42: 	  buf[k] = 0;
Chris@42: 
Chris@42:      os = ego->os;
Chris@42: 
Chris@42:      /* compute RDFT of buf, storing in buf (i.e., in-place): */
Chris@42:      {
Chris@42: 	    plan_rdft *cld = (plan_rdft *) ego->cld1;
Chris@42: 	    cld->apply((plan *) cld, buf, buf);
Chris@42:      }
Chris@42: 
Chris@42:      /* set output DC component: */
Chris@42:      O[0] = (r0 = I[0]) + buf[0];
Chris@42: 
Chris@42:      /* now, multiply by omega: */
Chris@42:      omega = ego->omega;
Chris@42:      buf[0] *= omega[0];
Chris@42:      for (k = 1; k < npad/2; ++k) {
Chris@42: 	  E rB, iB, rW, iW, a, b;
Chris@42: 	  rW = omega[k];
Chris@42: 	  iW = omega[npad - k];
Chris@42: 	  rB = buf[k];
Chris@42: 	  iB = buf[npad - k];
Chris@42: 	  a = rW * rB - iW * iB;
Chris@42: 	  b = rW * iB + iW * rB;
Chris@42: #if R2HC_ONLY_CONV
Chris@42: 	  buf[k] = a + b;
Chris@42: 	  buf[npad - k] = a - b;
Chris@42: #else
Chris@42: 	  buf[k] = a;
Chris@42: 	  buf[npad - k] = b;
Chris@42: #endif
Chris@42:      }
Chris@42:      /* Nyquist component: */
Chris@42:      A(k + k == npad); /* since npad is even */
Chris@42:      buf[k] *= omega[k];
Chris@42:      
Chris@42:      /* this will add input[0] to all of the outputs after the ifft */
Chris@42:      buf[0] += r0;
Chris@42: 
Chris@42:      /* inverse FFT: */
Chris@42:      {
Chris@42: 	    plan_rdft *cld = (plan_rdft *) ego->cld2;
Chris@42: 	    cld->apply((plan *) cld, buf, buf);
Chris@42:      }
Chris@42: 
Chris@42:      /* do inverse permutation to unshuffle the output: */
Chris@42:      A(gpower == 1);
Chris@42: #if R2HC_ONLY_CONV
Chris@42:      O[os] = buf[0];
Chris@42:      gpower = g = ego->ginv;
Chris@42:      A(npad == n - 1 || npad/2 >= n - 1);
Chris@42:      if (npad == n - 1) {
Chris@42: 	  for (k = 1; k < npad/2; ++k, gpower = MULMOD(gpower, g, n)) {
Chris@42: 	       O[gpower * os] = buf[k] + buf[npad - k];
Chris@42: 	  }
Chris@42: 	  O[gpower * os] = buf[k];
Chris@42: 	  ++k, gpower = MULMOD(gpower, g, n);
Chris@42: 	  for (; k < npad; ++k, gpower = MULMOD(gpower, g, n)) {
Chris@42: 	       O[gpower * os] = buf[npad - k] - buf[k];
Chris@42: 	  }
Chris@42:      }
Chris@42:      else {
Chris@42: 	  for (k = 1; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
Chris@42: 	       O[gpower * os] = buf[k] + buf[npad - k];
Chris@42: 	  }
Chris@42:      }
Chris@42: #else
Chris@42:      g = ego->ginv;
Chris@42:      for (k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
Chris@42: 	  O[gpower * os] = buf[k];
Chris@42:      }
Chris@42: #endif
Chris@42:      A(gpower == 1);
Chris@42: 
Chris@42:      X(ifree)(buf);
Chris@42: }
Chris@42: 
Chris@42: static R *mkomega(enum wakefulness wakefulness,
Chris@42: 		  plan *p_, INT n, INT npad, INT ginv)
Chris@42: {
Chris@42:      plan_rdft *p = (plan_rdft *) p_;
Chris@42:      R *omega;
Chris@42:      INT i, gpower;
Chris@42:      trigreal scale;
Chris@42:      triggen *t;
Chris@42: 
Chris@42:      if ((omega = X(rader_tl_find)(n, npad + 1, ginv, omegas))) 
Chris@42: 	  return omega;
Chris@42: 
Chris@42:      omega = (R *)MALLOC(sizeof(R) * npad, TWIDDLES);
Chris@42: 
Chris@42:      scale = npad; /* normalization for convolution */
Chris@42: 
Chris@42:      t = X(mktriggen)(wakefulness, n);
Chris@42:      for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
Chris@42: 	  trigreal w[2];
Chris@42: 	  t->cexpl(t, gpower, w);
Chris@42: 	  omega[i] = (w[0] + w[1]) / scale;
Chris@42:      }
Chris@42:      X(triggen_destroy)(t);
Chris@42:      A(gpower == 1);
Chris@42: 
Chris@42:      A(npad == n - 1 || npad >= 2*(n - 1) - 1);
Chris@42: 
Chris@42:      for (; i < npad; ++i)
Chris@42: 	  omega[i] = K(0.0);
Chris@42:      if (npad > n - 1)
Chris@42: 	  for (i = 1; i < n-1; ++i)
Chris@42: 	       omega[npad - i] = omega[n - 1 - i];
Chris@42: 
Chris@42:      p->apply(p_, omega, omega);
Chris@42: 
Chris@42:      X(rader_tl_insert)(n, npad + 1, ginv, omega, &omegas);
Chris@42:      return omega;
Chris@42: }
Chris@42: 
Chris@42: static void free_omega(R *omega)
Chris@42: {
Chris@42:      X(rader_tl_delete)(omega, &omegas);
Chris@42: }
Chris@42: 
Chris@42: /***************************************************************************/
Chris@42: 
Chris@42: static void awake(plan *ego_, enum wakefulness wakefulness)
Chris@42: {
Chris@42:      P *ego = (P *) ego_;
Chris@42: 
Chris@42:      X(plan_awake)(ego->cld1, wakefulness);
Chris@42:      X(plan_awake)(ego->cld2, wakefulness);
Chris@42:      X(plan_awake)(ego->cld_omega, wakefulness);
Chris@42: 
Chris@42:      switch (wakefulness) {
Chris@42: 	 case SLEEPY:
Chris@42: 	      free_omega(ego->omega);
Chris@42: 	      ego->omega = 0;
Chris@42: 	      break;
Chris@42: 	 default:
Chris@42: 	      ego->g = X(find_generator)(ego->n);
Chris@42: 	      ego->ginv = X(power_mod)(ego->g, ego->n - 2, ego->n);
Chris@42: 	      A(MULMOD(ego->g, ego->ginv, ego->n) == 1);
Chris@42: 
Chris@42: 	      A(!ego->omega);
Chris@42: 	      ego->omega = mkomega(wakefulness, 
Chris@42: 				   ego->cld_omega,ego->n,ego->npad,ego->ginv);
Chris@42: 	      break;
Chris@42:      }
Chris@42: }
Chris@42: 
Chris@42: static void destroy(plan *ego_)
Chris@42: {
Chris@42:      P *ego = (P *) ego_;
Chris@42:      X(plan_destroy_internal)(ego->cld_omega);
Chris@42:      X(plan_destroy_internal)(ego->cld2);
Chris@42:      X(plan_destroy_internal)(ego->cld1);
Chris@42: }
Chris@42: 
Chris@42: static void print(const plan *ego_, printer *p)
Chris@42: {
Chris@42:      const P *ego = (const P *) ego_;
Chris@42: 
Chris@42:      p->print(p, "(dht-rader-%D/%D%ois=%oos=%(%p%)",
Chris@42:               ego->n, ego->npad, ego->is, ego->os, ego->cld1);
Chris@42:      if (ego->cld2 != ego->cld1)
Chris@42:           p->print(p, "%(%p%)", ego->cld2);
Chris@42:      if (ego->cld_omega != ego->cld1 && ego->cld_omega != ego->cld2)
Chris@42:           p->print(p, "%(%p%)", ego->cld_omega);
Chris@42:      p->putchr(p, ')');
Chris@42: }
Chris@42: 
Chris@42: static int applicable(const solver *ego, const problem *p_, const planner *plnr)
Chris@42: {
Chris@42:      const problem_rdft *p = (const problem_rdft *) p_;
Chris@42:      UNUSED(ego);
Chris@42:      return (1
Chris@42: 	     && p->sz->rnk == 1
Chris@42: 	     && p->vecsz->rnk == 0
Chris@42: 	     && p->kind[0] == DHT
Chris@42: 	     && X(is_prime)(p->sz->dims[0].n)
Chris@42: 	     && p->sz->dims[0].n > 2
Chris@42: 	     && CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)
Chris@42: 	     /* proclaim the solver SLOW if p-1 is not easily
Chris@42: 		factorizable.  Unlike in the complex case where
Chris@42: 		Bluestein can solve the problem, in the DHT case we
Chris@42: 		may have no other choice */
Chris@42: 	     && CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))
Chris@42: 	  );
Chris@42: }
Chris@42: 
Chris@42: static INT choose_transform_size(INT minsz)
Chris@42: {
Chris@42:      static const INT primes[] = { 2, 3, 5, 0 };
Chris@42:      while (!X(factors_into)(minsz, primes) || minsz % 2)
Chris@42: 	  ++minsz;
Chris@42:      return minsz;
Chris@42: }
Chris@42: 
Chris@42: static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
Chris@42: {
Chris@42:      const S *ego = (const S *) ego_;
Chris@42:      const problem_rdft *p = (const problem_rdft *) p_;
Chris@42:      P *pln;
Chris@42:      INT n, npad;
Chris@42:      INT is, os;
Chris@42:      plan *cld1 = (plan *) 0;
Chris@42:      plan *cld2 = (plan *) 0;
Chris@42:      plan *cld_omega = (plan *) 0;
Chris@42:      R *buf = (R *) 0;
Chris@42:      problem *cldp;
Chris@42: 
Chris@42:      static const plan_adt padt = {
Chris@42: 	  X(rdft_solve), awake, print, destroy
Chris@42:      };
Chris@42: 
Chris@42:      if (!applicable(ego_, p_, plnr))
Chris@42: 	  return (plan *) 0;
Chris@42: 
Chris@42:      n = p->sz->dims[0].n;
Chris@42:      is = p->sz->dims[0].is;
Chris@42:      os = p->sz->dims[0].os;
Chris@42: 
Chris@42:      if (ego->pad)
Chris@42: 	  npad = choose_transform_size(2 * (n - 1) - 1);
Chris@42:      else
Chris@42: 	  npad = n - 1;
Chris@42: 
Chris@42:      /* initial allocation for the purpose of planning */
Chris@42:      buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
Chris@42: 
Chris@42:      cld1 = X(mkplan_f_d)(plnr, 
Chris@42: 			  X(mkproblem_rdft_1_d)(X(mktensor_1d)(npad, 1, 1),
Chris@42: 						X(mktensor_1d)(1, 0, 0),
Chris@42: 						buf, buf,
Chris@42: 						R2HC),
Chris@42: 			  NO_SLOW, 0, 0);
Chris@42:      if (!cld1) goto nada;
Chris@42: 
Chris@42:      cldp =
Chris@42:           X(mkproblem_rdft_1_d)(
Chris@42:                X(mktensor_1d)(npad, 1, 1),
Chris@42:                X(mktensor_1d)(1, 0, 0),
Chris@42: 	       buf, buf, 
Chris@42: #if R2HC_ONLY_CONV
Chris@42: 	       R2HC
Chris@42: #else
Chris@42: 	       HC2R
Chris@42: #endif
Chris@42: 	       );
Chris@42:      if (!(cld2 = X(mkplan_f_d)(plnr, cldp, NO_SLOW, 0, 0)))
Chris@42: 	  goto nada;
Chris@42: 
Chris@42:      /* plan for omega */
Chris@42:      cld_omega = X(mkplan_f_d)(plnr, 
Chris@42: 			       X(mkproblem_rdft_1_d)(
Chris@42: 				    X(mktensor_1d)(npad, 1, 1),
Chris@42: 				    X(mktensor_1d)(1, 0, 0),
Chris@42: 				    buf, buf, R2HC),
Chris@42: 			       NO_SLOW, ESTIMATE, 0);
Chris@42:      if (!cld_omega) goto nada;
Chris@42: 
Chris@42:      /* deallocate buffers; let awake() or apply() allocate them for real */
Chris@42:      X(ifree)(buf);
Chris@42:      buf = 0;
Chris@42: 
Chris@42:      pln = MKPLAN_RDFT(P, &padt, apply);
Chris@42:      pln->cld1 = cld1;
Chris@42:      pln->cld2 = cld2;
Chris@42:      pln->cld_omega = cld_omega;
Chris@42:      pln->omega = 0;
Chris@42:      pln->n = n;
Chris@42:      pln->npad = npad;
Chris@42:      pln->is = is;
Chris@42:      pln->os = os;
Chris@42: 
Chris@42:      X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
Chris@42:      pln->super.super.ops.other += (npad/2-1)*6 + npad + n + (n-1) * ego->pad;
Chris@42:      pln->super.super.ops.add += (npad/2-1)*2 + 2 + (n-1) * ego->pad;
Chris@42:      pln->super.super.ops.mul += (npad/2-1)*4 + 2 + ego->pad;
Chris@42: #if R2HC_ONLY_CONV
Chris@42:      pln->super.super.ops.other += n-2 - ego->pad;
Chris@42:      pln->super.super.ops.add += (npad/2-1)*2 + (n-2) - ego->pad;
Chris@42: #endif
Chris@42: 
Chris@42:      return &(pln->super.super);
Chris@42: 
Chris@42:  nada:
Chris@42:      X(ifree0)(buf);
Chris@42:      X(plan_destroy_internal)(cld_omega);
Chris@42:      X(plan_destroy_internal)(cld2);
Chris@42:      X(plan_destroy_internal)(cld1);
Chris@42:      return 0;
Chris@42: }
Chris@42: 
Chris@42: /* constructors */
Chris@42: 
Chris@42: static solver *mksolver(int pad)
Chris@42: {
Chris@42:      static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
Chris@42:      S *slv = MKSOLVER(S, &sadt);
Chris@42:      slv->pad = pad;
Chris@42:      return &(slv->super);
Chris@42: }
Chris@42: 
Chris@42: void X(dht_rader_register)(planner *p)
Chris@42: {
Chris@42:      REGISTER_SOLVER(p, mksolver(0));
Chris@42:      REGISTER_SOLVER(p, mksolver(1));
Chris@42: }