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: 
Chris@42: /* Do an R{E,O}DFT11 problem via an R2HC problem, with some
Chris@42:    pre/post-processing ala FFTPACK.  Use a trick from: 
Chris@42: 
Chris@42:      S. C. Chan and K. L. Ho, "Direct methods for computing discrete
Chris@42:      sinusoidal transforms," IEE Proceedings F 137 (6), 433--442 (1990).
Chris@42: 
Chris@42:    to re-express as an REDFT01 (DCT-III) problem.
Chris@42: 
Chris@42:    NOTE: We no longer use this algorithm, because it turns out to suffer
Chris@42:    a catastrophic loss of accuracy for certain inputs, apparently because
Chris@42:    its post-processing multiplies the output by a cosine.  Near the zero
Chris@42:    of the cosine, the REDFT01 must produce a near-singular output.
Chris@42: */
Chris@42: 
Chris@42: #include "reodft.h"
Chris@42: 
Chris@42: typedef struct {
Chris@42:      solver super;
Chris@42: } S;
Chris@42: 
Chris@42: typedef struct {
Chris@42:      plan_rdft super;
Chris@42:      plan *cld;
Chris@42:      twid *td, *td2;
Chris@42:      INT is, os;
Chris@42:      INT n;
Chris@42:      INT vl;
Chris@42:      INT ivs, ovs;
Chris@42:      rdft_kind kind;
Chris@42: } P;
Chris@42: 
Chris@42: static void apply_re11(const plan *ego_, R *I, R *O)
Chris@42: {
Chris@42:      const P *ego = (const P *) ego_;
Chris@42:      INT is = ego->is, os = ego->os;
Chris@42:      INT i, n = ego->n;
Chris@42:      INT iv, vl = ego->vl;
Chris@42:      INT ivs = ego->ivs, ovs = ego->ovs;
Chris@42:      R *W;
Chris@42:      R *buf;
Chris@42:      E cur;
Chris@42: 
Chris@42:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
Chris@42: 
Chris@42:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
Chris@42: 	  /* I wish that this didn't require an extra pass. */
Chris@42: 	  /* FIXME: use recursive/cascade summation for better stability? */
Chris@42: 	  buf[n - 1] = cur = K(2.0) * I[is * (n - 1)];
Chris@42: 	  for (i = n - 1; i > 0; --i) {
Chris@42: 	       E curnew;
Chris@42: 	       buf[(i - 1)] = curnew = K(2.0) * I[is * (i - 1)] - cur;
Chris@42: 	       cur = curnew;
Chris@42: 	  }
Chris@42: 	  
Chris@42: 	  W = ego->td->W;
Chris@42: 	  for (i = 1; i < n - i; ++i) {
Chris@42: 	       E a, b, apb, amb, wa, wb;
Chris@42: 	       a = buf[i];
Chris@42: 	       b = buf[n - i];
Chris@42: 	       apb = a + b;
Chris@42: 	       amb = a - b;
Chris@42: 	       wa = W[2*i];
Chris@42: 	       wb = W[2*i + 1];
Chris@42: 	       buf[i] = wa * amb + wb * apb; 
Chris@42: 	       buf[n - i] = wa * apb - wb * amb; 
Chris@42: 	  }
Chris@42: 	  if (i == n - i) {
Chris@42: 	       buf[i] = K(2.0) * buf[i] * W[2*i];
Chris@42: 	  }
Chris@42: 	  
Chris@42: 	  {
Chris@42: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
Chris@42: 	       cld->apply((plan *) cld, buf, buf);
Chris@42: 	  }
Chris@42: 	  
Chris@42: 	  W = ego->td2->W;
Chris@42: 	  O[0] = W[0] * buf[0];
Chris@42: 	  for (i = 1; i < n - i; ++i) {
Chris@42: 	       E a, b;
Chris@42: 	       INT k;
Chris@42: 	       a = buf[i];
Chris@42: 	       b = buf[n - i];
Chris@42: 	       k = i + i;
Chris@42: 	       O[os * (k - 1)] = W[k - 1] * (a - b);
Chris@42: 	       O[os * k] = W[k] * (a + b);
Chris@42: 	  }
Chris@42: 	  if (i == n - i) {
Chris@42: 	       O[os * (n - 1)] = W[n - 1] * buf[i];
Chris@42: 	  }
Chris@42:      }
Chris@42: 
Chris@42:      X(ifree)(buf);
Chris@42: }
Chris@42: 
Chris@42: /* like for rodft01, rodft11 is obtained from redft11 by
Chris@42:    reversing the input and flipping the sign of every other output. */
Chris@42: static void apply_ro11(const plan *ego_, R *I, R *O)
Chris@42: {
Chris@42:      const P *ego = (const P *) ego_;
Chris@42:      INT is = ego->is, os = ego->os;
Chris@42:      INT i, n = ego->n;
Chris@42:      INT iv, vl = ego->vl;
Chris@42:      INT ivs = ego->ivs, ovs = ego->ovs;
Chris@42:      R *W;
Chris@42:      R *buf;
Chris@42:      E cur;
Chris@42: 
Chris@42:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
Chris@42: 
Chris@42:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
Chris@42: 	  /* I wish that this didn't require an extra pass. */
Chris@42: 	  /* FIXME: use recursive/cascade summation for better stability? */
Chris@42: 	  buf[n - 1] = cur = K(2.0) * I[0];
Chris@42: 	  for (i = n - 1; i > 0; --i) {
Chris@42: 	       E curnew;
Chris@42: 	       buf[(i - 1)] = curnew = K(2.0) * I[is * (n - i)] - cur;
Chris@42: 	       cur = curnew;
Chris@42: 	  }
Chris@42: 	  
Chris@42: 	  W = ego->td->W;
Chris@42: 	  for (i = 1; i < n - i; ++i) {
Chris@42: 	       E a, b, apb, amb, wa, wb;
Chris@42: 	       a = buf[i];
Chris@42: 	       b = buf[n - i];
Chris@42: 	       apb = a + b;
Chris@42: 	       amb = a - b;
Chris@42: 	       wa = W[2*i];
Chris@42: 	       wb = W[2*i + 1];
Chris@42: 	       buf[i] = wa * amb + wb * apb; 
Chris@42: 	       buf[n - i] = wa * apb - wb * amb; 
Chris@42: 	  }
Chris@42: 	  if (i == n - i) {
Chris@42: 	       buf[i] = K(2.0) * buf[i] * W[2*i];
Chris@42: 	  }
Chris@42: 	  
Chris@42: 	  {
Chris@42: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
Chris@42: 	       cld->apply((plan *) cld, buf, buf);
Chris@42: 	  }
Chris@42: 	  
Chris@42: 	  W = ego->td2->W;
Chris@42: 	  O[0] = W[0] * buf[0];
Chris@42: 	  for (i = 1; i < n - i; ++i) {
Chris@42: 	       E a, b;
Chris@42: 	       INT k;
Chris@42: 	       a = buf[i];
Chris@42: 	       b = buf[n - i];
Chris@42: 	       k = i + i;
Chris@42: 	       O[os * (k - 1)] = W[k - 1] * (b - a);
Chris@42: 	       O[os * k] = W[k] * (a + b);
Chris@42: 	  }
Chris@42: 	  if (i == n - i) {
Chris@42: 	       O[os * (n - 1)] = -W[n - 1] * buf[i];
Chris@42: 	  }
Chris@42:      }
Chris@42: 
Chris@42:      X(ifree)(buf);
Chris@42: }
Chris@42: 
Chris@42: static void awake(plan *ego_, enum wakefulness wakefulness)
Chris@42: {
Chris@42:      P *ego = (P *) ego_;
Chris@42:      static const tw_instr reodft010e_tw[] = {
Chris@42:           { TW_COS, 0, 1 },
Chris@42:           { TW_SIN, 0, 1 },
Chris@42:           { TW_NEXT, 1, 0 }
Chris@42:      };
Chris@42:      static const tw_instr reodft11e_tw[] = {
Chris@42:           { TW_COS, 1, 1 },
Chris@42:           { TW_NEXT, 2, 0 }
Chris@42:      };
Chris@42: 
Chris@42:      X(plan_awake)(ego->cld, wakefulness);
Chris@42: 
Chris@42:      X(twiddle_awake)(wakefulness,
Chris@42: 		      &ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
Chris@42:      X(twiddle_awake)(wakefulness,
Chris@42: 		      &ego->td2, reodft11e_tw, 8*ego->n, 1, ego->n * 2);
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);
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:      p->print(p, "(%se-r2hc-%D%v%(%p%))",
Chris@42: 	      X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
Chris@42: }
Chris@42: 
Chris@42: static int applicable0(const solver *ego_, const problem *p_)
Chris@42: {
Chris@42:      const problem_rdft *p = (const problem_rdft *) p_;
Chris@42: 
Chris@42:      UNUSED(ego_);
Chris@42: 
Chris@42:      return (1
Chris@42: 	     && p->sz->rnk == 1
Chris@42: 	     && p->vecsz->rnk <= 1
Chris@42: 	     && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
Chris@42: 	  );
Chris@42: }
Chris@42: 
Chris@42: static int applicable(const solver *ego, const problem *p, const planner *plnr)
Chris@42: {
Chris@42:      return (!NO_SLOWP(plnr) && applicable0(ego, p));
Chris@42: }
Chris@42: 
Chris@42: static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
Chris@42: {
Chris@42:      P *pln;
Chris@42:      const problem_rdft *p;
Chris@42:      plan *cld;
Chris@42:      R *buf;
Chris@42:      INT n;
Chris@42:      opcnt ops;
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:      p = (const problem_rdft *) p_;
Chris@42: 
Chris@42:      n = p->sz->dims[0].n;
Chris@42:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
Chris@42: 
Chris@42:      cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n, 1, 1),
Chris@42:                                                    X(mktensor_0d)(),
Chris@42:                                                    buf, buf, R2HC));
Chris@42:      X(ifree)(buf);
Chris@42:      if (!cld)
Chris@42:           return (plan *)0;
Chris@42: 
Chris@42:      pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11);
Chris@42:      pln->n = n;
Chris@42:      pln->is = p->sz->dims[0].is;
Chris@42:      pln->os = p->sz->dims[0].os;
Chris@42:      pln->cld = cld;
Chris@42:      pln->td = pln->td2 = 0;
Chris@42:      pln->kind = p->kind[0];
Chris@42:      
Chris@42:      X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
Chris@42:      
Chris@42:      X(ops_zero)(&ops);
Chris@42:      ops.other = 5 + (n-1) * 2 + (n-1)/2 * 12 + (1 - n % 2) * 6;
Chris@42:      ops.add = (n - 1) * 1 + (n-1)/2 * 6;
Chris@42:      ops.mul = 2 + (n-1) * 1 + (n-1)/2 * 6 + (1 - n % 2) * 3;
Chris@42: 
Chris@42:      X(ops_zero)(&pln->super.super.ops);
Chris@42:      X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
Chris@42:      X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops);
Chris@42: 
Chris@42:      return &(pln->super.super);
Chris@42: }
Chris@42: 
Chris@42: /* constructor */
Chris@42: static solver *mksolver(void)
Chris@42: {
Chris@42:      static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
Chris@42:      S *slv = MKSOLVER(S, &sadt);
Chris@42:      return &(slv->super);
Chris@42: }
Chris@42: 
Chris@42: void X(reodft11e_r2hc_register)(planner *p)
Chris@42: {
Chris@42:      REGISTER_SOLVER(p, mksolver());
Chris@42: }