cannam@127: /*
cannam@127:  * Copyright (c) 2003, 2007-14 Matteo Frigo
cannam@127:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
cannam@127:  *
cannam@127:  * This program is free software; you can redistribute it and/or modify
cannam@127:  * it under the terms of the GNU General Public License as published by
cannam@127:  * the Free Software Foundation; either version 2 of the License, or
cannam@127:  * (at your option) any later version.
cannam@127:  *
cannam@127:  * This program is distributed in the hope that it will be useful,
cannam@127:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
cannam@127:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
cannam@127:  * GNU General Public License for more details.
cannam@127:  *
cannam@127:  * You should have received a copy of the GNU General Public License
cannam@127:  * along with this program; if not, write to the Free Software
cannam@127:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
cannam@127:  *
cannam@127:  */
cannam@127: 
cannam@127: 
cannam@127: /* Do an R{E,O}DFT11 problem via an R2HC problem, with some
cannam@127:    pre/post-processing ala FFTPACK.  Use a trick from: 
cannam@127: 
cannam@127:      S. C. Chan and K. L. Ho, "Direct methods for computing discrete
cannam@127:      sinusoidal transforms," IEE Proceedings F 137 (6), 433--442 (1990).
cannam@127: 
cannam@127:    to re-express as an REDFT01 (DCT-III) problem.
cannam@127: 
cannam@127:    NOTE: We no longer use this algorithm, because it turns out to suffer
cannam@127:    a catastrophic loss of accuracy for certain inputs, apparently because
cannam@127:    its post-processing multiplies the output by a cosine.  Near the zero
cannam@127:    of the cosine, the REDFT01 must produce a near-singular output.
cannam@127: */
cannam@127: 
cannam@127: #include "reodft.h"
cannam@127: 
cannam@127: typedef struct {
cannam@127:      solver super;
cannam@127: } S;
cannam@127: 
cannam@127: typedef struct {
cannam@127:      plan_rdft super;
cannam@127:      plan *cld;
cannam@127:      twid *td, *td2;
cannam@127:      INT is, os;
cannam@127:      INT n;
cannam@127:      INT vl;
cannam@127:      INT ivs, ovs;
cannam@127:      rdft_kind kind;
cannam@127: } P;
cannam@127: 
cannam@127: static void apply_re11(const plan *ego_, R *I, R *O)
cannam@127: {
cannam@127:      const P *ego = (const P *) ego_;
cannam@127:      INT is = ego->is, os = ego->os;
cannam@127:      INT i, n = ego->n;
cannam@127:      INT iv, vl = ego->vl;
cannam@127:      INT ivs = ego->ivs, ovs = ego->ovs;
cannam@127:      R *W;
cannam@127:      R *buf;
cannam@127:      E cur;
cannam@127: 
cannam@127:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@127: 
cannam@127:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
cannam@127: 	  /* I wish that this didn't require an extra pass. */
cannam@127: 	  /* FIXME: use recursive/cascade summation for better stability? */
cannam@127: 	  buf[n - 1] = cur = K(2.0) * I[is * (n - 1)];
cannam@127: 	  for (i = n - 1; i > 0; --i) {
cannam@127: 	       E curnew;
cannam@127: 	       buf[(i - 1)] = curnew = K(2.0) * I[is * (i - 1)] - cur;
cannam@127: 	       cur = curnew;
cannam@127: 	  }
cannam@127: 	  
cannam@127: 	  W = ego->td->W;
cannam@127: 	  for (i = 1; i < n - i; ++i) {
cannam@127: 	       E a, b, apb, amb, wa, wb;
cannam@127: 	       a = buf[i];
cannam@127: 	       b = buf[n - i];
cannam@127: 	       apb = a + b;
cannam@127: 	       amb = a - b;
cannam@127: 	       wa = W[2*i];
cannam@127: 	       wb = W[2*i + 1];
cannam@127: 	       buf[i] = wa * amb + wb * apb; 
cannam@127: 	       buf[n - i] = wa * apb - wb * amb; 
cannam@127: 	  }
cannam@127: 	  if (i == n - i) {
cannam@127: 	       buf[i] = K(2.0) * buf[i] * W[2*i];
cannam@127: 	  }
cannam@127: 	  
cannam@127: 	  {
cannam@127: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
cannam@127: 	       cld->apply((plan *) cld, buf, buf);
cannam@127: 	  }
cannam@127: 	  
cannam@127: 	  W = ego->td2->W;
cannam@127: 	  O[0] = W[0] * buf[0];
cannam@127: 	  for (i = 1; i < n - i; ++i) {
cannam@127: 	       E a, b;
cannam@127: 	       INT k;
cannam@127: 	       a = buf[i];
cannam@127: 	       b = buf[n - i];
cannam@127: 	       k = i + i;
cannam@127: 	       O[os * (k - 1)] = W[k - 1] * (a - b);
cannam@127: 	       O[os * k] = W[k] * (a + b);
cannam@127: 	  }
cannam@127: 	  if (i == n - i) {
cannam@127: 	       O[os * (n - 1)] = W[n - 1] * buf[i];
cannam@127: 	  }
cannam@127:      }
cannam@127: 
cannam@127:      X(ifree)(buf);
cannam@127: }
cannam@127: 
cannam@127: /* like for rodft01, rodft11 is obtained from redft11 by
cannam@127:    reversing the input and flipping the sign of every other output. */
cannam@127: static void apply_ro11(const plan *ego_, R *I, R *O)
cannam@127: {
cannam@127:      const P *ego = (const P *) ego_;
cannam@127:      INT is = ego->is, os = ego->os;
cannam@127:      INT i, n = ego->n;
cannam@127:      INT iv, vl = ego->vl;
cannam@127:      INT ivs = ego->ivs, ovs = ego->ovs;
cannam@127:      R *W;
cannam@127:      R *buf;
cannam@127:      E cur;
cannam@127: 
cannam@127:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@127: 
cannam@127:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
cannam@127: 	  /* I wish that this didn't require an extra pass. */
cannam@127: 	  /* FIXME: use recursive/cascade summation for better stability? */
cannam@127: 	  buf[n - 1] = cur = K(2.0) * I[0];
cannam@127: 	  for (i = n - 1; i > 0; --i) {
cannam@127: 	       E curnew;
cannam@127: 	       buf[(i - 1)] = curnew = K(2.0) * I[is * (n - i)] - cur;
cannam@127: 	       cur = curnew;
cannam@127: 	  }
cannam@127: 	  
cannam@127: 	  W = ego->td->W;
cannam@127: 	  for (i = 1; i < n - i; ++i) {
cannam@127: 	       E a, b, apb, amb, wa, wb;
cannam@127: 	       a = buf[i];
cannam@127: 	       b = buf[n - i];
cannam@127: 	       apb = a + b;
cannam@127: 	       amb = a - b;
cannam@127: 	       wa = W[2*i];
cannam@127: 	       wb = W[2*i + 1];
cannam@127: 	       buf[i] = wa * amb + wb * apb; 
cannam@127: 	       buf[n - i] = wa * apb - wb * amb; 
cannam@127: 	  }
cannam@127: 	  if (i == n - i) {
cannam@127: 	       buf[i] = K(2.0) * buf[i] * W[2*i];
cannam@127: 	  }
cannam@127: 	  
cannam@127: 	  {
cannam@127: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
cannam@127: 	       cld->apply((plan *) cld, buf, buf);
cannam@127: 	  }
cannam@127: 	  
cannam@127: 	  W = ego->td2->W;
cannam@127: 	  O[0] = W[0] * buf[0];
cannam@127: 	  for (i = 1; i < n - i; ++i) {
cannam@127: 	       E a, b;
cannam@127: 	       INT k;
cannam@127: 	       a = buf[i];
cannam@127: 	       b = buf[n - i];
cannam@127: 	       k = i + i;
cannam@127: 	       O[os * (k - 1)] = W[k - 1] * (b - a);
cannam@127: 	       O[os * k] = W[k] * (a + b);
cannam@127: 	  }
cannam@127: 	  if (i == n - i) {
cannam@127: 	       O[os * (n - 1)] = -W[n - 1] * buf[i];
cannam@127: 	  }
cannam@127:      }
cannam@127: 
cannam@127:      X(ifree)(buf);
cannam@127: }
cannam@127: 
cannam@127: static void awake(plan *ego_, enum wakefulness wakefulness)
cannam@127: {
cannam@127:      P *ego = (P *) ego_;
cannam@127:      static const tw_instr reodft010e_tw[] = {
cannam@127:           { TW_COS, 0, 1 },
cannam@127:           { TW_SIN, 0, 1 },
cannam@127:           { TW_NEXT, 1, 0 }
cannam@127:      };
cannam@127:      static const tw_instr reodft11e_tw[] = {
cannam@127:           { TW_COS, 1, 1 },
cannam@127:           { TW_NEXT, 2, 0 }
cannam@127:      };
cannam@127: 
cannam@127:      X(plan_awake)(ego->cld, wakefulness);
cannam@127: 
cannam@127:      X(twiddle_awake)(wakefulness,
cannam@127: 		      &ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
cannam@127:      X(twiddle_awake)(wakefulness,
cannam@127: 		      &ego->td2, reodft11e_tw, 8*ego->n, 1, ego->n * 2);
cannam@127: }
cannam@127: 
cannam@127: static void destroy(plan *ego_)
cannam@127: {
cannam@127:      P *ego = (P *) ego_;
cannam@127:      X(plan_destroy_internal)(ego->cld);
cannam@127: }
cannam@127: 
cannam@127: static void print(const plan *ego_, printer *p)
cannam@127: {
cannam@127:      const P *ego = (const P *) ego_;
cannam@127:      p->print(p, "(%se-r2hc-%D%v%(%p%))",
cannam@127: 	      X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
cannam@127: }
cannam@127: 
cannam@127: static int applicable0(const solver *ego_, const problem *p_)
cannam@127: {
cannam@127:      const problem_rdft *p = (const problem_rdft *) p_;
cannam@127: 
cannam@127:      UNUSED(ego_);
cannam@127: 
cannam@127:      return (1
cannam@127: 	     && p->sz->rnk == 1
cannam@127: 	     && p->vecsz->rnk <= 1
cannam@127: 	     && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
cannam@127: 	  );
cannam@127: }
cannam@127: 
cannam@127: static int applicable(const solver *ego, const problem *p, const planner *plnr)
cannam@127: {
cannam@127:      return (!NO_SLOWP(plnr) && applicable0(ego, p));
cannam@127: }
cannam@127: 
cannam@127: static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
cannam@127: {
cannam@127:      P *pln;
cannam@127:      const problem_rdft *p;
cannam@127:      plan *cld;
cannam@127:      R *buf;
cannam@127:      INT n;
cannam@127:      opcnt ops;
cannam@127: 
cannam@127:      static const plan_adt padt = {
cannam@127: 	  X(rdft_solve), awake, print, destroy
cannam@127:      };
cannam@127: 
cannam@127:      if (!applicable(ego_, p_, plnr))
cannam@127:           return (plan *)0;
cannam@127: 
cannam@127:      p = (const problem_rdft *) p_;
cannam@127: 
cannam@127:      n = p->sz->dims[0].n;
cannam@127:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@127: 
cannam@127:      cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n, 1, 1),
cannam@127:                                                    X(mktensor_0d)(),
cannam@127:                                                    buf, buf, R2HC));
cannam@127:      X(ifree)(buf);
cannam@127:      if (!cld)
cannam@127:           return (plan *)0;
cannam@127: 
cannam@127:      pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11);
cannam@127:      pln->n = n;
cannam@127:      pln->is = p->sz->dims[0].is;
cannam@127:      pln->os = p->sz->dims[0].os;
cannam@127:      pln->cld = cld;
cannam@127:      pln->td = pln->td2 = 0;
cannam@127:      pln->kind = p->kind[0];
cannam@127:      
cannam@127:      X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
cannam@127:      
cannam@127:      X(ops_zero)(&ops);
cannam@127:      ops.other = 5 + (n-1) * 2 + (n-1)/2 * 12 + (1 - n % 2) * 6;
cannam@127:      ops.add = (n - 1) * 1 + (n-1)/2 * 6;
cannam@127:      ops.mul = 2 + (n-1) * 1 + (n-1)/2 * 6 + (1 - n % 2) * 3;
cannam@127: 
cannam@127:      X(ops_zero)(&pln->super.super.ops);
cannam@127:      X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
cannam@127:      X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops);
cannam@127: 
cannam@127:      return &(pln->super.super);
cannam@127: }
cannam@127: 
cannam@127: /* constructor */
cannam@127: static solver *mksolver(void)
cannam@127: {
cannam@127:      static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
cannam@127:      S *slv = MKSOLVER(S, &sadt);
cannam@127:      return &(slv->super);
cannam@127: }
cannam@127: 
cannam@127: void X(reodft11e_r2hc_register)(planner *p)
cannam@127: {
cannam@127:      REGISTER_SOLVER(p, mksolver());
cannam@127: }