Chris@10: /*
Chris@10:  * Copyright (c) 2003, 2007-11 Matteo Frigo
Chris@10:  * Copyright (c) 2003, 2007-11 Massachusetts Institute of Technology
Chris@10:  *
Chris@10:  * This program is free software; you can redistribute it and/or modify
Chris@10:  * it under the terms of the GNU General Public License as published by
Chris@10:  * the Free Software Foundation; either version 2 of the License, or
Chris@10:  * (at your option) any later version.
Chris@10:  *
Chris@10:  * This program is distributed in the hope that it will be useful,
Chris@10:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@10:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@10:  * GNU General Public License for more details.
Chris@10:  *
Chris@10:  * You should have received a copy of the GNU General Public License
Chris@10:  * along with this program; if not, write to the Free Software
Chris@10:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@10:  *
Chris@10:  */
Chris@10: 
Chris@10: 
Chris@10: /* Do an R{E,O}DFT11 problem of *even* size by a pair of R2HC problems
Chris@10:    of half the size, plus some pre/post-processing.  Use a trick from:
Chris@10: 
Chris@10:    Zhongde Wang, "On computing the discrete Fourier and cosine transforms,"
Chris@10:    IEEE Trans. Acoust. Speech Sig. Proc. ASSP-33 (4), 1341--1344 (1985).
Chris@10: 
Chris@10:    to re-express as a pair of half-size REDFT01 (DCT-III) problems.  Our
Chris@10:    implementation looks quite a bit different from the algorithm described
Chris@10:    in the paper because we combined the paper's pre/post-processing with
Chris@10:    the pre/post-processing used to turn REDFT01 into R2HC.  (Also, the
Chris@10:    paper uses a DCT/DST pair, but we turn the DST into a DCT via the
Chris@10:    usual reordering/sign-flip trick.  We additionally combined a couple
Chris@10:    of the matrices/transformations of the paper into a single pass.)
Chris@10: 
Chris@10:    NOTE: We originally used a simpler method by S. C. Chan and K. L. Ho
Chris@10:    that turned out to have numerical problems; see reodft11e-r2hc.c.
Chris@10: 
Chris@10:    (For odd sizes, see reodft11e-r2hc-odd.c.)
Chris@10: */
Chris@10: 
Chris@10: #include "reodft.h"
Chris@10: 
Chris@10: typedef struct {
Chris@10:      solver super;
Chris@10: } S;
Chris@10: 
Chris@10: typedef struct {
Chris@10:      plan_rdft super;
Chris@10:      plan *cld;
Chris@10:      twid *td, *td2;
Chris@10:      INT is, os;
Chris@10:      INT n;
Chris@10:      INT vl;
Chris@10:      INT ivs, ovs;
Chris@10:      rdft_kind kind;
Chris@10: } P;
Chris@10: 
Chris@10: static void apply_re11(const plan *ego_, R *I, R *O)
Chris@10: {
Chris@10:      const P *ego = (const P *) ego_;
Chris@10:      INT is = ego->is, os = ego->os;
Chris@10:      INT i, n = ego->n, n2 = n/2;
Chris@10:      INT iv, vl = ego->vl;
Chris@10:      INT ivs = ego->ivs, ovs = ego->ovs;
Chris@10:      R *W = ego->td->W;
Chris@10:      R *W2;
Chris@10:      R *buf;
Chris@10: 
Chris@10:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
Chris@10: 
Chris@10:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
Chris@10: 	  buf[0] = K(2.0) * I[0];
Chris@10: 	  buf[n2] = K(2.0) * I[is * (n - 1)];
Chris@10: 	  for (i = 1; i + i < n2; ++i) {
Chris@10: 	       INT k = i + i;
Chris@10: 	       E a, b, a2, b2;
Chris@10: 	       {
Chris@10: 		    E u, v;
Chris@10: 		    u = I[is * (k - 1)];
Chris@10: 		    v = I[is * k];
Chris@10: 		    a = u + v;
Chris@10: 		    b2 = u - v;
Chris@10: 	       }
Chris@10: 	       {
Chris@10: 		    E u, v;
Chris@10: 		    u = I[is * (n - k - 1)];
Chris@10: 		    v = I[is * (n - k)];
Chris@10: 		    b = u + v;
Chris@10: 		    a2 = u - v;
Chris@10: 	       }
Chris@10: 	       {
Chris@10: 		    E wa, wb;
Chris@10: 		    wa = W[2*i];
Chris@10: 		    wb = W[2*i + 1];
Chris@10: 		    {
Chris@10: 			 E apb, amb;
Chris@10: 			 apb = a + b;
Chris@10: 			 amb = a - b;
Chris@10: 			 buf[i] = wa * amb + wb * apb; 
Chris@10: 			 buf[n2 - i] = wa * apb - wb * amb; 
Chris@10: 		    }
Chris@10: 		    {
Chris@10: 			 E apb, amb;
Chris@10: 			 apb = a2 + b2;
Chris@10: 			 amb = a2 - b2;
Chris@10: 			 buf[n2 + i] = wa * amb + wb * apb; 
Chris@10: 			 buf[n - i] = wa * apb - wb * amb; 
Chris@10: 		    }
Chris@10: 	       }
Chris@10: 	  }
Chris@10: 	  if (i + i == n2) {
Chris@10: 	       E u, v;
Chris@10: 	       u = I[is * (n2 - 1)];
Chris@10: 	       v = I[is * n2];
Chris@10: 	       buf[i] = (u + v) * (W[2*i] * K(2.0));
Chris@10: 	       buf[n - i] = (u - v) * (W[2*i] * K(2.0));
Chris@10: 	  }
Chris@10: 
Chris@10: 
Chris@10: 	  /* child plan: two r2hc's of size n/2 */
Chris@10: 	  {
Chris@10: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
Chris@10: 	       cld->apply((plan *) cld, buf, buf);
Chris@10: 	  }
Chris@10: 	  
Chris@10: 	  W2 = ego->td2->W;
Chris@10: 	  { /* i == 0 case */
Chris@10: 	       E wa, wb;
Chris@10: 	       E a, b;
Chris@10: 	       wa = W2[0]; /* cos */
Chris@10: 	       wb = W2[1]; /* sin */
Chris@10: 	       a = buf[0];
Chris@10: 	       b = buf[n2];
Chris@10: 	       O[0] = wa * a + wb * b;
Chris@10: 	       O[os * (n - 1)] = wb * a - wa * b;
Chris@10: 	  }
Chris@10: 	  W2 += 2;
Chris@10: 	  for (i = 1; i + i < n2; ++i, W2 += 2) {
Chris@10: 	       INT k;
Chris@10: 	       E u, v, u2, v2;
Chris@10: 	       u = buf[i];
Chris@10: 	       v = buf[n2 - i];
Chris@10: 	       u2 = buf[n2 + i];
Chris@10: 	       v2 = buf[n - i];
Chris@10: 	       k = (i + i) - 1;
Chris@10: 	       {
Chris@10:                     E wa, wb;
Chris@10:                     E a, b;
Chris@10:                     wa = W2[0]; /* cos */
Chris@10:                     wb = W2[1]; /* sin */
Chris@10:                     a = u - v;
Chris@10:                     b = v2 - u2;
Chris@10:                     O[os * k] = wa * a + wb * b;
Chris@10:                     O[os * (n - 1 - k)] = wb * a - wa * b;
Chris@10:                }
Chris@10: 	       ++k;
Chris@10: 	       W2 += 2;
Chris@10: 	       {
Chris@10: 		    E wa, wb;
Chris@10: 		    E a, b;
Chris@10: 		    wa = W2[0]; /* cos */
Chris@10: 		    wb = W2[1]; /* sin */
Chris@10: 		    a = u + v;
Chris@10: 		    b = u2 + v2;
Chris@10: 		    O[os * k] = wa * a + wb * b;
Chris@10: 		    O[os * (n - 1 - k)] = wb * a - wa * b;
Chris@10: 	       }
Chris@10: 	  }
Chris@10: 	  if (i + i == n2) {
Chris@10: 	       INT k = (i + i) - 1;
Chris@10: 	       E wa, wb;
Chris@10: 	       E a, b;
Chris@10: 	       wa = W2[0]; /* cos */
Chris@10: 	       wb = W2[1]; /* sin */
Chris@10: 	       a = buf[i];
Chris@10: 	       b = buf[n2 + i];
Chris@10: 	       O[os * k] = wa * a - wb * b;
Chris@10: 	       O[os * (n - 1 - k)] = wb * a + wa * b;
Chris@10: 	  }
Chris@10:      }
Chris@10: 
Chris@10:      X(ifree)(buf);
Chris@10: }
Chris@10: 
Chris@10: #if 0
Chris@10: 
Chris@10: /* This version of apply_re11 uses REDFT01 child plans, more similar
Chris@10:    to the original paper by Z. Wang.  We keep it around for reference
Chris@10:    (it is simpler) and because it may become more efficient if we
Chris@10:    ever implement REDFT01 codelets. */
Chris@10: 
Chris@10: static void apply_re11(const plan *ego_, R *I, R *O)
Chris@10: {
Chris@10:      const P *ego = (const P *) ego_;
Chris@10:      INT is = ego->is, os = ego->os;
Chris@10:      INT i, n = ego->n;
Chris@10:      INT iv, vl = ego->vl;
Chris@10:      INT ivs = ego->ivs, ovs = ego->ovs;
Chris@10:      R *W;
Chris@10:      R *buf;
Chris@10: 
Chris@10:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
Chris@10: 
Chris@10:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
Chris@10: 	  buf[0] = K(2.0) * I[0];
Chris@10: 	  buf[n/2] = K(2.0) * I[is * (n - 1)];
Chris@10: 	  for (i = 1; i + i < n; ++i) {
Chris@10: 	       INT k = i + i;
Chris@10: 	       E a, b;
Chris@10: 	       a = I[is * (k - 1)];
Chris@10: 	       b = I[is * k];
Chris@10: 	       buf[i] = a + b;
Chris@10: 	       buf[n - i] = a - b;
Chris@10: 	  }
Chris@10: 
Chris@10: 	  /* child plan: two redft01's (DCT-III) */
Chris@10: 	  {
Chris@10: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
Chris@10: 	       cld->apply((plan *) cld, buf, buf);
Chris@10: 	  }
Chris@10: 	  
Chris@10: 	  W = ego->td2->W;
Chris@10: 	  for (i = 0; i + 1 < n/2; ++i, W += 2) {
Chris@10: 	       {
Chris@10: 		    E wa, wb;
Chris@10: 		    E a, b;
Chris@10: 		    wa = W[0]; /* cos */
Chris@10: 		    wb = W[1]; /* sin */
Chris@10: 		    a = buf[i];
Chris@10: 		    b = buf[n/2 + i];
Chris@10: 		    O[os * i] = wa * a + wb * b;
Chris@10: 		    O[os * (n - 1 - i)] = wb * a - wa * b;
Chris@10: 	       }
Chris@10: 	       ++i;
Chris@10: 	       W += 2;
Chris@10: 	       {
Chris@10:                     E wa, wb;
Chris@10:                     E a, b;
Chris@10:                     wa = W[0]; /* cos */
Chris@10:                     wb = W[1]; /* sin */
Chris@10:                     a = buf[i];
Chris@10:                     b = buf[n/2 + i];
Chris@10:                     O[os * i] = wa * a - wb * b;
Chris@10:                     O[os * (n - 1 - i)] = wb * a + wa * b;
Chris@10:                }
Chris@10: 	  }
Chris@10: 	  if (i < n/2) {
Chris@10: 	       E wa, wb;
Chris@10: 	       E a, b;
Chris@10: 	       wa = W[0]; /* cos */
Chris@10: 	       wb = W[1]; /* sin */
Chris@10: 	       a = buf[i];
Chris@10: 	       b = buf[n/2 + i];
Chris@10: 	       O[os * i] = wa * a + wb * b;
Chris@10: 	       O[os * (n - 1 - i)] = wb * a - wa * b;
Chris@10: 	  }
Chris@10:      }
Chris@10: 
Chris@10:      X(ifree)(buf);
Chris@10: }
Chris@10: 
Chris@10: #endif /* 0 */
Chris@10: 
Chris@10: /* like for rodft01, rodft11 is obtained from redft11 by
Chris@10:    reversing the input and flipping the sign of every other output. */
Chris@10: static void apply_ro11(const plan *ego_, R *I, R *O)
Chris@10: {
Chris@10:      const P *ego = (const P *) ego_;
Chris@10:      INT is = ego->is, os = ego->os;
Chris@10:      INT i, n = ego->n, n2 = n/2;
Chris@10:      INT iv, vl = ego->vl;
Chris@10:      INT ivs = ego->ivs, ovs = ego->ovs;
Chris@10:      R *W = ego->td->W;
Chris@10:      R *W2;
Chris@10:      R *buf;
Chris@10: 
Chris@10:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
Chris@10: 
Chris@10:      for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
Chris@10: 	  buf[0] = K(2.0) * I[is * (n - 1)];
Chris@10: 	  buf[n2] = K(2.0) * I[0];
Chris@10: 	  for (i = 1; i + i < n2; ++i) {
Chris@10: 	       INT k = i + i;
Chris@10: 	       E a, b, a2, b2;
Chris@10: 	       {
Chris@10: 		    E u, v;
Chris@10: 		    u = I[is * (n - k)];
Chris@10: 		    v = I[is * (n - 1 - k)];
Chris@10: 		    a = u + v;
Chris@10: 		    b2 = u - v;
Chris@10: 	       }
Chris@10: 	       {
Chris@10: 		    E u, v;
Chris@10: 		    u = I[is * (k)];
Chris@10: 		    v = I[is * (k - 1)];
Chris@10: 		    b = u + v;
Chris@10: 		    a2 = u - v;
Chris@10: 	       }
Chris@10: 	       {
Chris@10: 		    E wa, wb;
Chris@10: 		    wa = W[2*i];
Chris@10: 		    wb = W[2*i + 1];
Chris@10: 		    {
Chris@10: 			 E apb, amb;
Chris@10: 			 apb = a + b;
Chris@10: 			 amb = a - b;
Chris@10: 			 buf[i] = wa * amb + wb * apb; 
Chris@10: 			 buf[n2 - i] = wa * apb - wb * amb; 
Chris@10: 		    }
Chris@10: 		    {
Chris@10: 			 E apb, amb;
Chris@10: 			 apb = a2 + b2;
Chris@10: 			 amb = a2 - b2;
Chris@10: 			 buf[n2 + i] = wa * amb + wb * apb; 
Chris@10: 			 buf[n - i] = wa * apb - wb * amb; 
Chris@10: 		    }
Chris@10: 	       }
Chris@10: 	  }
Chris@10: 	  if (i + i == n2) {
Chris@10: 	       E u, v;
Chris@10: 	       u = I[is * n2];
Chris@10: 	       v = I[is * (n2 - 1)];
Chris@10: 	       buf[i] = (u + v) * (W[2*i] * K(2.0));
Chris@10: 	       buf[n - i] = (u - v) * (W[2*i] * K(2.0));
Chris@10: 	  }
Chris@10: 
Chris@10: 
Chris@10: 	  /* child plan: two r2hc's of size n/2 */
Chris@10: 	  {
Chris@10: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
Chris@10: 	       cld->apply((plan *) cld, buf, buf);
Chris@10: 	  }
Chris@10: 	  
Chris@10: 	  W2 = ego->td2->W;
Chris@10: 	  { /* i == 0 case */
Chris@10: 	       E wa, wb;
Chris@10: 	       E a, b;
Chris@10: 	       wa = W2[0]; /* cos */
Chris@10: 	       wb = W2[1]; /* sin */
Chris@10: 	       a = buf[0];
Chris@10: 	       b = buf[n2];
Chris@10: 	       O[0] = wa * a + wb * b;
Chris@10: 	       O[os * (n - 1)] = wa * b - wb * a;
Chris@10: 	  }
Chris@10: 	  W2 += 2;
Chris@10: 	  for (i = 1; i + i < n2; ++i, W2 += 2) {
Chris@10: 	       INT k;
Chris@10: 	       E u, v, u2, v2;
Chris@10: 	       u = buf[i];
Chris@10: 	       v = buf[n2 - i];
Chris@10: 	       u2 = buf[n2 + i];
Chris@10: 	       v2 = buf[n - i];
Chris@10: 	       k = (i + i) - 1;
Chris@10: 	       {
Chris@10:                     E wa, wb;
Chris@10:                     E a, b;
Chris@10:                     wa = W2[0]; /* cos */
Chris@10:                     wb = W2[1]; /* sin */
Chris@10:                     a = v - u;
Chris@10:                     b = u2 - v2;
Chris@10:                     O[os * k] = wa * a + wb * b;
Chris@10:                     O[os * (n - 1 - k)] = wa * b - wb * a;
Chris@10:                }
Chris@10: 	       ++k;
Chris@10: 	       W2 += 2;
Chris@10: 	       {
Chris@10: 		    E wa, wb;
Chris@10: 		    E a, b;
Chris@10: 		    wa = W2[0]; /* cos */
Chris@10: 		    wb = W2[1]; /* sin */
Chris@10: 		    a = u + v;
Chris@10: 		    b = u2 + v2;
Chris@10: 		    O[os * k] = wa * a + wb * b;
Chris@10: 		    O[os * (n - 1 - k)] = wa * b - wb * a;
Chris@10: 	       }
Chris@10: 	  }
Chris@10: 	  if (i + i == n2) {
Chris@10: 	       INT k = (i + i) - 1;
Chris@10: 	       E wa, wb;
Chris@10: 	       E a, b;
Chris@10: 	       wa = W2[0]; /* cos */
Chris@10: 	       wb = W2[1]; /* sin */
Chris@10: 	       a = buf[i];
Chris@10: 	       b = buf[n2 + i];
Chris@10: 	       O[os * k] = wb * b - wa * a;
Chris@10: 	       O[os * (n - 1 - k)] = wa * b + wb * a;
Chris@10: 	  }
Chris@10:      }
Chris@10: 
Chris@10:      X(ifree)(buf);
Chris@10: }
Chris@10: 
Chris@10: static void awake(plan *ego_, enum wakefulness wakefulness)
Chris@10: {
Chris@10:      P *ego = (P *) ego_;
Chris@10:      static const tw_instr reodft010e_tw[] = {
Chris@10:           { TW_COS, 0, 1 },
Chris@10:           { TW_SIN, 0, 1 },
Chris@10:           { TW_NEXT, 1, 0 }
Chris@10:      };
Chris@10:      static const tw_instr reodft11e_tw[] = {
Chris@10:           { TW_COS, 1, 1 },
Chris@10:           { TW_SIN, 1, 1 },
Chris@10:           { TW_NEXT, 2, 0 }
Chris@10:      };
Chris@10: 
Chris@10:      X(plan_awake)(ego->cld, wakefulness);
Chris@10: 
Chris@10:      X(twiddle_awake)(wakefulness, &ego->td, reodft010e_tw, 
Chris@10: 		      2*ego->n, 1, ego->n/4+1);
Chris@10:      X(twiddle_awake)(wakefulness, &ego->td2, reodft11e_tw, 
Chris@10: 		      8*ego->n, 1, ego->n);
Chris@10: }
Chris@10: 
Chris@10: static void destroy(plan *ego_)
Chris@10: {
Chris@10:      P *ego = (P *) ego_;
Chris@10:      X(plan_destroy_internal)(ego->cld);
Chris@10: }
Chris@10: 
Chris@10: static void print(const plan *ego_, printer *p)
Chris@10: {
Chris@10:      const P *ego = (const P *) ego_;
Chris@10:      p->print(p, "(%se-radix2-r2hc-%D%v%(%p%))",
Chris@10: 	      X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
Chris@10: }
Chris@10: 
Chris@10: static int applicable0(const solver *ego_, const problem *p_)
Chris@10: {
Chris@10:      const problem_rdft *p = (const problem_rdft *) p_;
Chris@10:      UNUSED(ego_);
Chris@10: 
Chris@10:      return (1
Chris@10: 	     && p->sz->rnk == 1
Chris@10: 	     && p->vecsz->rnk <= 1
Chris@10: 	     && p->sz->dims[0].n % 2 == 0
Chris@10: 	     && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
Chris@10: 	  );
Chris@10: }
Chris@10: 
Chris@10: static int applicable(const solver *ego, const problem *p, const planner *plnr)
Chris@10: {
Chris@10:      return (!NO_SLOWP(plnr) && applicable0(ego, p));
Chris@10: }
Chris@10: 
Chris@10: static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
Chris@10: {
Chris@10:      P *pln;
Chris@10:      const problem_rdft *p;
Chris@10:      plan *cld;
Chris@10:      R *buf;
Chris@10:      INT n;
Chris@10:      opcnt ops;
Chris@10: 
Chris@10:      static const plan_adt padt = {
Chris@10: 	  X(rdft_solve), awake, print, destroy
Chris@10:      };
Chris@10: 
Chris@10:      if (!applicable(ego_, p_, plnr))
Chris@10:           return (plan *)0;
Chris@10: 
Chris@10:      p = (const problem_rdft *) p_;
Chris@10: 
Chris@10:      n = p->sz->dims[0].n;
Chris@10:      buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
Chris@10: 
Chris@10:      cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n/2, 1, 1),
Chris@10:                                                    X(mktensor_1d)(2, n/2, n/2),
Chris@10:                                                    buf, buf, R2HC));
Chris@10:      X(ifree)(buf);
Chris@10:      if (!cld)
Chris@10:           return (plan *)0;
Chris@10: 
Chris@10:      pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11);
Chris@10:      pln->n = n;
Chris@10:      pln->is = p->sz->dims[0].is;
Chris@10:      pln->os = p->sz->dims[0].os;
Chris@10:      pln->cld = cld;
Chris@10:      pln->td = pln->td2 = 0;
Chris@10:      pln->kind = p->kind[0];
Chris@10:      
Chris@10:      X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
Chris@10:      
Chris@10:      X(ops_zero)(&ops);
Chris@10:      ops.add = 2 + (n/2 - 1)/2 * 20;
Chris@10:      ops.mul = 6 + (n/2 - 1)/2 * 16;
Chris@10:      ops.other = 4*n + 2 + (n/2 - 1)/2 * 6;
Chris@10:      if ((n/2) % 2 == 0) {
Chris@10: 	  ops.add += 4;
Chris@10: 	  ops.mul += 8;
Chris@10: 	  ops.other += 4;
Chris@10:      }
Chris@10: 
Chris@10:      X(ops_zero)(&pln->super.super.ops);
Chris@10:      X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
Chris@10:      X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops);
Chris@10: 
Chris@10:      return &(pln->super.super);
Chris@10: }
Chris@10: 
Chris@10: /* constructor */
Chris@10: static solver *mksolver(void)
Chris@10: {
Chris@10:      static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
Chris@10:      S *slv = MKSOLVER(S, &sadt);
Chris@10:      return &(slv->super);
Chris@10: }
Chris@10: 
Chris@10: void X(reodft11e_radix2_r2hc_register)(planner *p)
Chris@10: {
Chris@10:      REGISTER_SOLVER(p, mksolver());
Chris@10: }