cannam@95: /*
cannam@95:  * Copyright (c) 2003, 2007-11 Matteo Frigo
cannam@95:  * Copyright (c) 2003, 2007-11 Massachusetts Institute of Technology
cannam@95:  *
cannam@95:  * This program is free software; you can redistribute it and/or modify
cannam@95:  * it under the terms of the GNU General Public License as published by
cannam@95:  * the Free Software Foundation; either version 2 of the License, or
cannam@95:  * (at your option) any later version.
cannam@95:  *
cannam@95:  * This program is distributed in the hope that it will be useful,
cannam@95:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
cannam@95:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
cannam@95:  * GNU General Public License for more details.
cannam@95:  *
cannam@95:  * You should have received a copy of the GNU General Public License
cannam@95:  * along with this program; if not, write to the Free Software
cannam@95:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
cannam@95:  *
cannam@95:  */
cannam@95: 
cannam@95: 
cannam@95: /* Do an R{E,O}DFT{01,10} problem via an R2HC problem, with some
cannam@95:    pre/post-processing ala FFTPACK. */
cannam@95: 
cannam@95: #include "reodft.h"
cannam@95: 
cannam@95: typedef struct {
cannam@95:      solver super;
cannam@95: } S;
cannam@95: 
cannam@95: typedef struct {
cannam@95:      plan_rdft super;
cannam@95:      plan *cld;
cannam@95:      twid *td;
cannam@95:      INT is, os;
cannam@95:      INT n;
cannam@95:      INT vl;
cannam@95:      INT ivs, ovs;
cannam@95:      rdft_kind kind;
cannam@95: } P;
cannam@95: 
cannam@95: /* A real-even-01 DFT operates logically on a size-4N array:
cannam@95:                    I 0 -r(I*) -I 0 r(I*),
cannam@95:    where r denotes reversal and * denotes deletion of the 0th element.
cannam@95:    To compute the transform of this, we imagine performing a radix-4
cannam@95:    (real-input) DIF step, which turns the size-4N DFT into 4 size-N
cannam@95:    (contiguous) DFTs, two of which are zero and two of which are
cannam@95:    conjugates.  The non-redundant size-N DFT has halfcomplex input, so
cannam@95:    we can do it with a size-N hc2r transform.  (In order to share
cannam@95:    plans with the re10 (inverse) transform, however, we use the DHT
cannam@95:    trick to re-express the hc2r problem as r2hc.  This has little cost
cannam@95:    since we are already pre- and post-processing the data in {i,n-i}
cannam@95:    order.)  Finally, we have to write out the data in the correct
cannam@95:    order...the two size-N redundant (conjugate) hc2r DFTs correspond
cannam@95:    to the even and odd outputs in O (i.e. the usual interleaved output
cannam@95:    of DIF transforms); since this data has even symmetry, we only
cannam@95:    write the first half of it.
cannam@95: 
cannam@95:    The real-even-10 DFT is just the reverse of these steps, i.e. a
cannam@95:    radix-4 DIT transform.  There, however, we just use the r2hc
cannam@95:    transform naturally without resorting to the DHT trick.
cannam@95: 
cannam@95:    A real-odd-01 DFT is very similar, except that the input is
cannam@95:    0 I (rI)* 0 -I -(rI)*.  This format, however, can be transformed
cannam@95:    into precisely the real-even-01 format above by sending I -> rI
cannam@95:    and shifting the array by N.  The former swap is just another
cannam@95:    transformation on the input during preprocessing; the latter
cannam@95:    multiplies the even/odd outputs by i/-i, which combines with
cannam@95:    the factor of -i (to take the imaginary part) to simply flip
cannam@95:    the sign of the odd outputs.  Vice-versa for real-odd-10.
cannam@95: 
cannam@95:    The FFTPACK source code was very helpful in working this out.
cannam@95:    (They do unnecessary passes over the array, though.)  The same
cannam@95:    algorithm is also described in:
cannam@95: 
cannam@95:       John Makhoul, "A fast cosine transform in one and two dimensions,"
cannam@95:       IEEE Trans. on Acoust. Speech and Sig. Proc., ASSP-28 (1), 27--34 (1980).
cannam@95: 
cannam@95:    Note that Numerical Recipes suggests a different algorithm that
cannam@95:    requires more operations and uses trig. functions for both the pre-
cannam@95:    and post-processing passes.
cannam@95: */
cannam@95: 
cannam@95: static void apply_re01(const plan *ego_, R *I, R *O)
cannam@95: {
cannam@95:      const P *ego = (const P *) ego_;
cannam@95:      INT is = ego->is, os = ego->os;
cannam@95:      INT i, n = ego->n;
cannam@95:      INT iv, vl = ego->vl;
cannam@95:      INT ivs = ego->ivs, ovs = ego->ovs;
cannam@95:      R *W = ego->td->W;
cannam@95:      R *buf;
cannam@95: 
cannam@95:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@95: 
cannam@95:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
cannam@95: 	  buf[0] = I[0];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E a, b, apb, amb, wa, wb;
cannam@95: 	       a = I[is * i];
cannam@95: 	       b = I[is * (n - i)];
cannam@95: 	       apb = a + b;
cannam@95: 	       amb = a - b;
cannam@95: 	       wa = W[2*i];
cannam@95: 	       wb = W[2*i + 1];
cannam@95: 	       buf[i] = wa * amb + wb * apb; 
cannam@95: 	       buf[n - i] = wa * apb - wb * amb; 
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       buf[i] = K(2.0) * I[is * i] * W[2*i];
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  {
cannam@95: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
cannam@95: 	       cld->apply((plan *) cld, buf, buf);
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  O[0] = buf[0];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E a, b;
cannam@95: 	       INT k;
cannam@95: 	       a = buf[i];
cannam@95: 	       b = buf[n - i];
cannam@95: 	       k = i + i;
cannam@95: 	       O[os * (k - 1)] = a - b;
cannam@95: 	       O[os * k] = a + b;
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       O[os * (n - 1)] = buf[i];
cannam@95: 	  }
cannam@95:      }
cannam@95: 
cannam@95:      X(ifree)(buf);
cannam@95: }
cannam@95: 
cannam@95: /* ro01 is same as re01, but with i <-> n - 1 - i in the input and
cannam@95:    the sign of the odd output elements flipped. */
cannam@95: static void apply_ro01(const plan *ego_, R *I, R *O)
cannam@95: {
cannam@95:      const P *ego = (const P *) ego_;
cannam@95:      INT is = ego->is, os = ego->os;
cannam@95:      INT i, n = ego->n;
cannam@95:      INT iv, vl = ego->vl;
cannam@95:      INT ivs = ego->ivs, ovs = ego->ovs;
cannam@95:      R *W = ego->td->W;
cannam@95:      R *buf;
cannam@95: 
cannam@95:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@95: 
cannam@95:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
cannam@95: 	  buf[0] = I[is * (n - 1)];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E a, b, apb, amb, wa, wb;
cannam@95: 	       a = I[is * (n - 1 - i)];
cannam@95: 	       b = I[is * (i - 1)];
cannam@95: 	       apb = a + b;
cannam@95: 	       amb = a - b;
cannam@95: 	       wa = W[2*i];
cannam@95: 	       wb = W[2*i+1];
cannam@95: 	       buf[i] = wa * amb + wb * apb; 
cannam@95: 	       buf[n - i] = wa * apb - wb * amb; 
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       buf[i] = K(2.0) * I[is * (i - 1)] * W[2*i];
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  {
cannam@95: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
cannam@95: 	       cld->apply((plan *) cld, buf, buf);
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  O[0] = buf[0];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E a, b;
cannam@95: 	       INT k;
cannam@95: 	       a = buf[i];
cannam@95: 	       b = buf[n - i];
cannam@95: 	       k = i + i;
cannam@95: 	       O[os * (k - 1)] = b - a;
cannam@95: 	       O[os * k] = a + b;
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       O[os * (n - 1)] = -buf[i];
cannam@95: 	  }
cannam@95:      }
cannam@95: 
cannam@95:      X(ifree)(buf);
cannam@95: }
cannam@95: 
cannam@95: static void apply_re10(const plan *ego_, R *I, R *O)
cannam@95: {
cannam@95:      const P *ego = (const P *) ego_;
cannam@95:      INT is = ego->is, os = ego->os;
cannam@95:      INT i, n = ego->n;
cannam@95:      INT iv, vl = ego->vl;
cannam@95:      INT ivs = ego->ivs, ovs = ego->ovs;
cannam@95:      R *W = ego->td->W;
cannam@95:      R *buf;
cannam@95: 
cannam@95:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@95: 
cannam@95:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
cannam@95: 	  buf[0] = I[0];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E u, v;
cannam@95: 	       INT k = i + i;
cannam@95: 	       u = I[is * (k - 1)];
cannam@95: 	       v = I[is * k];
cannam@95: 	       buf[n - i] = u;
cannam@95: 	       buf[i] = v;
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       buf[i] = I[is * (n - 1)];
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  {
cannam@95: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
cannam@95: 	       cld->apply((plan *) cld, buf, buf);
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  O[0] = K(2.0) * buf[0];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E a, b, wa, wb;
cannam@95: 	       a = K(2.0) * buf[i];
cannam@95: 	       b = K(2.0) * buf[n - i];
cannam@95: 	       wa = W[2*i];
cannam@95: 	       wb = W[2*i + 1];
cannam@95: 	       O[os * i] = wa * a + wb * b;
cannam@95: 	       O[os * (n - i)] = wb * a - wa * b;
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       O[os * i] = K(2.0) * buf[i] * W[2*i];
cannam@95: 	  }
cannam@95:      }
cannam@95: 
cannam@95:      X(ifree)(buf);
cannam@95: }
cannam@95: 
cannam@95: /* ro10 is same as re10, but with i <-> n - 1 - i in the output and
cannam@95:    the sign of the odd input elements flipped. */
cannam@95: static void apply_ro10(const plan *ego_, R *I, R *O)
cannam@95: {
cannam@95:      const P *ego = (const P *) ego_;
cannam@95:      INT is = ego->is, os = ego->os;
cannam@95:      INT i, n = ego->n;
cannam@95:      INT iv, vl = ego->vl;
cannam@95:      INT ivs = ego->ivs, ovs = ego->ovs;
cannam@95:      R *W = ego->td->W;
cannam@95:      R *buf;
cannam@95: 
cannam@95:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@95: 
cannam@95:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
cannam@95: 	  buf[0] = I[0];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E u, v;
cannam@95: 	       INT k = i + i;
cannam@95: 	       u = -I[is * (k - 1)];
cannam@95: 	       v = I[is * k];
cannam@95: 	       buf[n - i] = u;
cannam@95: 	       buf[i] = v;
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       buf[i] = -I[is * (n - 1)];
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  {
cannam@95: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
cannam@95: 	       cld->apply((plan *) cld, buf, buf);
cannam@95: 	  }
cannam@95: 	  
cannam@95: 	  O[os * (n - 1)] = K(2.0) * buf[0];
cannam@95: 	  for (i = 1; i < n - i; ++i) {
cannam@95: 	       E a, b, wa, wb;
cannam@95: 	       a = K(2.0) * buf[i];
cannam@95: 	       b = K(2.0) * buf[n - i];
cannam@95: 	       wa = W[2*i];
cannam@95: 	       wb = W[2*i + 1];
cannam@95: 	       O[os * (n - 1 - i)] = wa * a + wb * b;
cannam@95: 	       O[os * (i - 1)] = wb * a - wa * b;
cannam@95: 	  }
cannam@95: 	  if (i == n - i) {
cannam@95: 	       O[os * (i - 1)] = K(2.0) * buf[i] * W[2*i];
cannam@95: 	  }
cannam@95:      }
cannam@95: 
cannam@95:      X(ifree)(buf);
cannam@95: }
cannam@95: 
cannam@95: static void awake(plan *ego_, enum wakefulness wakefulness)
cannam@95: {
cannam@95:      P *ego = (P *) ego_;
cannam@95:      static const tw_instr reodft010e_tw[] = {
cannam@95:           { TW_COS, 0, 1 },
cannam@95:           { TW_SIN, 0, 1 },
cannam@95:           { TW_NEXT, 1, 0 }
cannam@95:      };
cannam@95: 
cannam@95:      X(plan_awake)(ego->cld, wakefulness);
cannam@95: 
cannam@95:      X(twiddle_awake)(wakefulness, &ego->td, reodft010e_tw, 
cannam@95: 		      4*ego->n, 1, ego->n/2+1);
cannam@95: }
cannam@95: 
cannam@95: static void destroy(plan *ego_)
cannam@95: {
cannam@95:      P *ego = (P *) ego_;
cannam@95:      X(plan_destroy_internal)(ego->cld);
cannam@95: }
cannam@95: 
cannam@95: static void print(const plan *ego_, printer *p)
cannam@95: {
cannam@95:      const P *ego = (const P *) ego_;
cannam@95:      p->print(p, "(%se-r2hc-%D%v%(%p%))",
cannam@95: 	      X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
cannam@95: }
cannam@95: 
cannam@95: static int applicable0(const solver *ego_, const problem *p_)
cannam@95: {
cannam@95:      const problem_rdft *p = (const problem_rdft *) p_;
cannam@95:      UNUSED(ego_);
cannam@95: 
cannam@95:      return (1
cannam@95: 	     && p->sz->rnk == 1
cannam@95: 	     && p->vecsz->rnk <= 1
cannam@95: 	     && (p->kind[0] == REDFT01 || p->kind[0] == REDFT10
cannam@95: 		 || p->kind[0] == RODFT01 || p->kind[0] == RODFT10)
cannam@95: 	  );
cannam@95: }
cannam@95: 
cannam@95: static int applicable(const solver *ego, const problem *p, const planner *plnr)
cannam@95: {
cannam@95:      return (!NO_SLOWP(plnr) && applicable0(ego, p));
cannam@95: }
cannam@95: 
cannam@95: static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
cannam@95: {
cannam@95:      P *pln;
cannam@95:      const problem_rdft *p;
cannam@95:      plan *cld;
cannam@95:      R *buf;
cannam@95:      INT n;
cannam@95:      opcnt ops;
cannam@95: 
cannam@95:      static const plan_adt padt = {
cannam@95: 	  X(rdft_solve), awake, print, destroy
cannam@95:      };
cannam@95: 
cannam@95:      if (!applicable(ego_, p_, plnr))
cannam@95:           return (plan *)0;
cannam@95: 
cannam@95:      p = (const problem_rdft *) p_;
cannam@95: 
cannam@95:      n = p->sz->dims[0].n;
cannam@95:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
cannam@95: 
cannam@95:      cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n, 1, 1),
cannam@95:                                                    X(mktensor_0d)(),
cannam@95:                                                    buf, buf, R2HC));
cannam@95:      X(ifree)(buf);
cannam@95:      if (!cld)
cannam@95:           return (plan *)0;
cannam@95: 
cannam@95:      switch (p->kind[0]) {
cannam@95: 	 case REDFT01: pln = MKPLAN_RDFT(P, &padt, apply_re01); break;
cannam@95: 	 case REDFT10: pln = MKPLAN_RDFT(P, &padt, apply_re10); break;
cannam@95: 	 case RODFT01: pln = MKPLAN_RDFT(P, &padt, apply_ro01); break;
cannam@95: 	 case RODFT10: pln = MKPLAN_RDFT(P, &padt, apply_ro10); break;
cannam@95: 	 default: A(0); return (plan*)0;
cannam@95:      }
cannam@95: 
cannam@95:      pln->n = n;
cannam@95:      pln->is = p->sz->dims[0].is;
cannam@95:      pln->os = p->sz->dims[0].os;
cannam@95:      pln->cld = cld;
cannam@95:      pln->td = 0;
cannam@95:      pln->kind = p->kind[0];
cannam@95:      
cannam@95:      X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
cannam@95:      
cannam@95:      X(ops_zero)(&ops);
cannam@95:      ops.other = 4 + (n-1)/2 * 10 + (1 - n % 2) * 5;
cannam@95:      if (p->kind[0] == REDFT01 || p->kind[0] == RODFT01) {
cannam@95: 	  ops.add = (n-1)/2 * 6;
cannam@95: 	  ops.mul = (n-1)/2 * 4 + (1 - n % 2) * 2;
cannam@95:      }
cannam@95:      else { /* 10 transforms */
cannam@95: 	  ops.add = (n-1)/2 * 2;
cannam@95: 	  ops.mul = 1 + (n-1)/2 * 6 + (1 - n % 2) * 2;
cannam@95:      }
cannam@95:      
cannam@95:      X(ops_zero)(&pln->super.super.ops);
cannam@95:      X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
cannam@95:      X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops);
cannam@95: 
cannam@95:      return &(pln->super.super);
cannam@95: }
cannam@95: 
cannam@95: /* constructor */
cannam@95: static solver *mksolver(void)
cannam@95: {
cannam@95:      static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
cannam@95:      S *slv = MKSOLVER(S, &sadt);
cannam@95:      return &(slv->super);
cannam@95: }
cannam@95: 
cannam@95: void X(reodft010e_r2hc_register)(planner *p)
cannam@95: {
cannam@95:      REGISTER_SOLVER(p, mksolver());
cannam@95: }