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 a REDFT00 problem via an R2HC problem, with some pre/post-processing.
Chris@42: 
Chris@42:    This code uses the trick from FFTPACK, also documented in a similar
Chris@42:    form by Numerical Recipes.  Unfortunately, this algorithm seems to
Chris@42:    have intrinsic numerical problems (similar to those in
Chris@42:    reodft11e-r2hc.c), possibly due to the fact that it multiplies its
Chris@42:    input by a cosine, causing a loss of precision near the zero.  For
Chris@42:    transforms of 16k points, it has already lost three or four decimal
Chris@42:    places of accuracy, which we deem unacceptable.
Chris@42: 
Chris@42:    So, we have abandoned this algorithm in favor of the one in
Chris@42:    redft00-r2hc-pad.c, which unfortunately sacrifices 30-50% in speed.
Chris@42:    The only other alternative in the literature that does not have
Chris@42:    similar numerical difficulties seems to be the direct adaptation of
Chris@42:    the Cooley-Tukey decomposition for symmetric data, but this would
Chris@42:    require a whole new set of codelets and it's not clear that it's
Chris@42:    worth it at this point.  However, we did implement the latter
Chris@42:    algorithm for the specific case of odd n (logically adapting the
Chris@42:    split-radix algorithm); see reodft00e-splitradix.c. */
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;
Chris@42:      INT is, os;
Chris@42:      INT n;
Chris@42:      INT vl;
Chris@42:      INT ivs, ovs;
Chris@42: } P;
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 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 = ego->td->W;
Chris@42:      R *buf;
Chris@42:      E csum;
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: 	  buf[0] = I[0] + I[is * n];
Chris@42: 	  csum = I[0] - I[is * n];
Chris@42: 	  for (i = 1; i < n - i; ++i) {
Chris@42: 	       E a, b, apb, amb;
Chris@42: 	       a = I[is * i];
Chris@42: 	       b = I[is * (n - i)];
Chris@42: 	       csum += W[2*i] * (amb = K(2.0)*(a - b));
Chris@42: 	       amb = W[2*i+1] * amb;
Chris@42: 	       apb = (a + b);
Chris@42: 	       buf[i] = apb - amb;
Chris@42: 	       buf[n - i] = apb + amb;
Chris@42: 	  }
Chris@42: 	  if (i == n - i) {
Chris@42: 	       buf[i] = K(2.0) * I[is * 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: 	  /* FIXME: use recursive/cascade summation for better stability? */
Chris@42: 	  O[0] = buf[0];
Chris@42: 	  O[os] = csum;
Chris@42: 	  for (i = 1; i + i < n; ++i) {
Chris@42: 	       INT k = i + i;
Chris@42: 	       O[os * k] = buf[i];
Chris@42: 	       O[os * (k + 1)] = O[os * (k - 1)] - buf[n - i];
Chris@42: 	  }
Chris@42: 	  if (i + i == n) {
Chris@42: 	       O[os * n] = 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 redft00e_tw[] = {
Chris@42:           { TW_COS, 0, 1 },
Chris@42:           { TW_SIN, 0, 1 },
Chris@42:           { TW_NEXT, 1, 0 }
Chris@42:      };
Chris@42: 
Chris@42:      X(plan_awake)(ego->cld, wakefulness);
Chris@42:      X(twiddle_awake)(wakefulness,
Chris@42: 		      &ego->td, redft00e_tw, 2*ego->n, 1, (ego->n+1)/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, "(redft00e-r2hc-%D%v%(%p%))", ego->n + 1, 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:      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] == REDFT00
Chris@42: 	     && p->sz->dims[0].n > 1  /* n == 1 is not well-defined */
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 - 1;
Chris@42:      A(n > 0);
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, apply);
Chris@42: 
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 = 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 = 8 + (n-1)/2 * 11 + (1 - n % 2) * 5;
Chris@42:      ops.add = 2 + (n-1)/2 * 5;
Chris@42:      ops.mul = (n-1)/2 * 3 + (1 - n % 2) * 1;
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(redft00e_r2hc_register)(planner *p)
Chris@42: {
Chris@42:      REGISTER_SOLVER(p, mksolver());
Chris@42: }