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}DFT11 problem of *even* size by a pair of R2HC problems
cannam@95:    of half the size, plus some pre/post-processing.  Use a trick from:
cannam@95: 
cannam@95:    Zhongde Wang, "On computing the discrete Fourier and cosine transforms,"
cannam@95:    IEEE Trans. Acoust. Speech Sig. Proc. ASSP-33 (4), 1341--1344 (1985).
cannam@95: 
cannam@95:    to re-express as a pair of half-size REDFT01 (DCT-III) problems.  Our
cannam@95:    implementation looks quite a bit different from the algorithm described
cannam@95:    in the paper because we combined the paper's pre/post-processing with
cannam@95:    the pre/post-processing used to turn REDFT01 into R2HC.  (Also, the
cannam@95:    paper uses a DCT/DST pair, but we turn the DST into a DCT via the
cannam@95:    usual reordering/sign-flip trick.  We additionally combined a couple
cannam@95:    of the matrices/transformations of the paper into a single pass.)
cannam@95: 
cannam@95:    NOTE: We originally used a simpler method by S. C. Chan and K. L. Ho
cannam@95:    that turned out to have numerical problems; see reodft11e-r2hc.c.
cannam@95: 
cannam@95:    (For odd sizes, see reodft11e-r2hc-odd.c.)
cannam@95: */
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, *td2;
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: static void apply_re11(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, n2 = n/2;
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 *W2;
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] = K(2.0) * I[0];
cannam@95: 	  buf[n2] = K(2.0) * I[is * (n - 1)];
cannam@95: 	  for (i = 1; i + i < n2; ++i) {
cannam@95: 	       INT k = i + i;
cannam@95: 	       E a, b, a2, b2;
cannam@95: 	       {
cannam@95: 		    E u, v;
cannam@95: 		    u = I[is * (k - 1)];
cannam@95: 		    v = I[is * k];
cannam@95: 		    a = u + v;
cannam@95: 		    b2 = u - v;
cannam@95: 	       }
cannam@95: 	       {
cannam@95: 		    E u, v;
cannam@95: 		    u = I[is * (n - k - 1)];
cannam@95: 		    v = I[is * (n - k)];
cannam@95: 		    b = u + v;
cannam@95: 		    a2 = u - v;
cannam@95: 	       }
cannam@95: 	       {
cannam@95: 		    E wa, wb;
cannam@95: 		    wa = W[2*i];
cannam@95: 		    wb = W[2*i + 1];
cannam@95: 		    {
cannam@95: 			 E apb, amb;
cannam@95: 			 apb = a + b;
cannam@95: 			 amb = a - b;
cannam@95: 			 buf[i] = wa * amb + wb * apb; 
cannam@95: 			 buf[n2 - i] = wa * apb - wb * amb; 
cannam@95: 		    }
cannam@95: 		    {
cannam@95: 			 E apb, amb;
cannam@95: 			 apb = a2 + b2;
cannam@95: 			 amb = a2 - b2;
cannam@95: 			 buf[n2 + i] = wa * amb + wb * apb; 
cannam@95: 			 buf[n - i] = wa * apb - wb * amb; 
cannam@95: 		    }
cannam@95: 	       }
cannam@95: 	  }
cannam@95: 	  if (i + i == n2) {
cannam@95: 	       E u, v;
cannam@95: 	       u = I[is * (n2 - 1)];
cannam@95: 	       v = I[is * n2];
cannam@95: 	       buf[i] = (u + v) * (W[2*i] * K(2.0));
cannam@95: 	       buf[n - i] = (u - v) * (W[2*i] * K(2.0));
cannam@95: 	  }
cannam@95: 
cannam@95: 
cannam@95: 	  /* child plan: two r2hc's of size n/2 */
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: 	  W2 = ego->td2->W;
cannam@95: 	  { /* i == 0 case */
cannam@95: 	       E wa, wb;
cannam@95: 	       E a, b;
cannam@95: 	       wa = W2[0]; /* cos */
cannam@95: 	       wb = W2[1]; /* sin */
cannam@95: 	       a = buf[0];
cannam@95: 	       b = buf[n2];
cannam@95: 	       O[0] = wa * a + wb * b;
cannam@95: 	       O[os * (n - 1)] = wb * a - wa * b;
cannam@95: 	  }
cannam@95: 	  W2 += 2;
cannam@95: 	  for (i = 1; i + i < n2; ++i, W2 += 2) {
cannam@95: 	       INT k;
cannam@95: 	       E u, v, u2, v2;
cannam@95: 	       u = buf[i];
cannam@95: 	       v = buf[n2 - i];
cannam@95: 	       u2 = buf[n2 + i];
cannam@95: 	       v2 = buf[n - i];
cannam@95: 	       k = (i + i) - 1;
cannam@95: 	       {
cannam@95:                     E wa, wb;
cannam@95:                     E a, b;
cannam@95:                     wa = W2[0]; /* cos */
cannam@95:                     wb = W2[1]; /* sin */
cannam@95:                     a = u - v;
cannam@95:                     b = v2 - u2;
cannam@95:                     O[os * k] = wa * a + wb * b;
cannam@95:                     O[os * (n - 1 - k)] = wb * a - wa * b;
cannam@95:                }
cannam@95: 	       ++k;
cannam@95: 	       W2 += 2;
cannam@95: 	       {
cannam@95: 		    E wa, wb;
cannam@95: 		    E a, b;
cannam@95: 		    wa = W2[0]; /* cos */
cannam@95: 		    wb = W2[1]; /* sin */
cannam@95: 		    a = u + v;
cannam@95: 		    b = u2 + v2;
cannam@95: 		    O[os * k] = wa * a + wb * b;
cannam@95: 		    O[os * (n - 1 - k)] = wb * a - wa * b;
cannam@95: 	       }
cannam@95: 	  }
cannam@95: 	  if (i + i == n2) {
cannam@95: 	       INT k = (i + i) - 1;
cannam@95: 	       E wa, wb;
cannam@95: 	       E a, b;
cannam@95: 	       wa = W2[0]; /* cos */
cannam@95: 	       wb = W2[1]; /* sin */
cannam@95: 	       a = buf[i];
cannam@95: 	       b = buf[n2 + i];
cannam@95: 	       O[os * k] = wa * a - wb * b;
cannam@95: 	       O[os * (n - 1 - k)] = wb * a + wa * b;
cannam@95: 	  }
cannam@95:      }
cannam@95: 
cannam@95:      X(ifree)(buf);
cannam@95: }
cannam@95: 
cannam@95: #if 0
cannam@95: 
cannam@95: /* This version of apply_re11 uses REDFT01 child plans, more similar
cannam@95:    to the original paper by Z. Wang.  We keep it around for reference
cannam@95:    (it is simpler) and because it may become more efficient if we
cannam@95:    ever implement REDFT01 codelets. */
cannam@95: 
cannam@95: static void apply_re11(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;
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] = K(2.0) * I[0];
cannam@95: 	  buf[n/2] = K(2.0) * I[is * (n - 1)];
cannam@95: 	  for (i = 1; i + i < n; ++i) {
cannam@95: 	       INT k = i + i;
cannam@95: 	       E a, b;
cannam@95: 	       a = I[is * (k - 1)];
cannam@95: 	       b = I[is * k];
cannam@95: 	       buf[i] = a + b;
cannam@95: 	       buf[n - i] = a - b;
cannam@95: 	  }
cannam@95: 
cannam@95: 	  /* child plan: two redft01's (DCT-III) */
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: 	  W = ego->td2->W;
cannam@95: 	  for (i = 0; i + 1 < n/2; ++i, W += 2) {
cannam@95: 	       {
cannam@95: 		    E wa, wb;
cannam@95: 		    E a, b;
cannam@95: 		    wa = W[0]; /* cos */
cannam@95: 		    wb = W[1]; /* sin */
cannam@95: 		    a = buf[i];
cannam@95: 		    b = buf[n/2 + i];
cannam@95: 		    O[os * i] = wa * a + wb * b;
cannam@95: 		    O[os * (n - 1 - i)] = wb * a - wa * b;
cannam@95: 	       }
cannam@95: 	       ++i;
cannam@95: 	       W += 2;
cannam@95: 	       {
cannam@95:                     E wa, wb;
cannam@95:                     E a, b;
cannam@95:                     wa = W[0]; /* cos */
cannam@95:                     wb = W[1]; /* sin */
cannam@95:                     a = buf[i];
cannam@95:                     b = buf[n/2 + i];
cannam@95:                     O[os * i] = wa * a - wb * b;
cannam@95:                     O[os * (n - 1 - i)] = wb * a + wa * b;
cannam@95:                }
cannam@95: 	  }
cannam@95: 	  if (i < n/2) {
cannam@95: 	       E wa, wb;
cannam@95: 	       E a, b;
cannam@95: 	       wa = W[0]; /* cos */
cannam@95: 	       wb = W[1]; /* sin */
cannam@95: 	       a = buf[i];
cannam@95: 	       b = buf[n/2 + i];
cannam@95: 	       O[os * i] = wa * a + wb * b;
cannam@95: 	       O[os * (n - 1 - i)] = wb * a - wa * b;
cannam@95: 	  }
cannam@95:      }
cannam@95: 
cannam@95:      X(ifree)(buf);
cannam@95: }
cannam@95: 
cannam@95: #endif /* 0 */
cannam@95: 
cannam@95: /* like for rodft01, rodft11 is obtained from redft11 by
cannam@95:    reversing the input and flipping the sign of every other output. */
cannam@95: static void apply_ro11(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, n2 = n/2;
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 *W2;
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] = K(2.0) * I[is * (n - 1)];
cannam@95: 	  buf[n2] = K(2.0) * I[0];
cannam@95: 	  for (i = 1; i + i < n2; ++i) {
cannam@95: 	       INT k = i + i;
cannam@95: 	       E a, b, a2, b2;
cannam@95: 	       {
cannam@95: 		    E u, v;
cannam@95: 		    u = I[is * (n - k)];
cannam@95: 		    v = I[is * (n - 1 - k)];
cannam@95: 		    a = u + v;
cannam@95: 		    b2 = u - v;
cannam@95: 	       }
cannam@95: 	       {
cannam@95: 		    E u, v;
cannam@95: 		    u = I[is * (k)];
cannam@95: 		    v = I[is * (k - 1)];
cannam@95: 		    b = u + v;
cannam@95: 		    a2 = u - v;
cannam@95: 	       }
cannam@95: 	       {
cannam@95: 		    E wa, wb;
cannam@95: 		    wa = W[2*i];
cannam@95: 		    wb = W[2*i + 1];
cannam@95: 		    {
cannam@95: 			 E apb, amb;
cannam@95: 			 apb = a + b;
cannam@95: 			 amb = a - b;
cannam@95: 			 buf[i] = wa * amb + wb * apb; 
cannam@95: 			 buf[n2 - i] = wa * apb - wb * amb; 
cannam@95: 		    }
cannam@95: 		    {
cannam@95: 			 E apb, amb;
cannam@95: 			 apb = a2 + b2;
cannam@95: 			 amb = a2 - b2;
cannam@95: 			 buf[n2 + i] = wa * amb + wb * apb; 
cannam@95: 			 buf[n - i] = wa * apb - wb * amb; 
cannam@95: 		    }
cannam@95: 	       }
cannam@95: 	  }
cannam@95: 	  if (i + i == n2) {
cannam@95: 	       E u, v;
cannam@95: 	       u = I[is * n2];
cannam@95: 	       v = I[is * (n2 - 1)];
cannam@95: 	       buf[i] = (u + v) * (W[2*i] * K(2.0));
cannam@95: 	       buf[n - i] = (u - v) * (W[2*i] * K(2.0));
cannam@95: 	  }
cannam@95: 
cannam@95: 
cannam@95: 	  /* child plan: two r2hc's of size n/2 */
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: 	  W2 = ego->td2->W;
cannam@95: 	  { /* i == 0 case */
cannam@95: 	       E wa, wb;
cannam@95: 	       E a, b;
cannam@95: 	       wa = W2[0]; /* cos */
cannam@95: 	       wb = W2[1]; /* sin */
cannam@95: 	       a = buf[0];
cannam@95: 	       b = buf[n2];
cannam@95: 	       O[0] = wa * a + wb * b;
cannam@95: 	       O[os * (n - 1)] = wa * b - wb * a;
cannam@95: 	  }
cannam@95: 	  W2 += 2;
cannam@95: 	  for (i = 1; i + i < n2; ++i, W2 += 2) {
cannam@95: 	       INT k;
cannam@95: 	       E u, v, u2, v2;
cannam@95: 	       u = buf[i];
cannam@95: 	       v = buf[n2 - i];
cannam@95: 	       u2 = buf[n2 + i];
cannam@95: 	       v2 = buf[n - i];
cannam@95: 	       k = (i + i) - 1;
cannam@95: 	       {
cannam@95:                     E wa, wb;
cannam@95:                     E a, b;
cannam@95:                     wa = W2[0]; /* cos */
cannam@95:                     wb = W2[1]; /* sin */
cannam@95:                     a = v - u;
cannam@95:                     b = u2 - v2;
cannam@95:                     O[os * k] = wa * a + wb * b;
cannam@95:                     O[os * (n - 1 - k)] = wa * b - wb * a;
cannam@95:                }
cannam@95: 	       ++k;
cannam@95: 	       W2 += 2;
cannam@95: 	       {
cannam@95: 		    E wa, wb;
cannam@95: 		    E a, b;
cannam@95: 		    wa = W2[0]; /* cos */
cannam@95: 		    wb = W2[1]; /* sin */
cannam@95: 		    a = u + v;
cannam@95: 		    b = u2 + v2;
cannam@95: 		    O[os * k] = wa * a + wb * b;
cannam@95: 		    O[os * (n - 1 - k)] = wa * b - wb * a;
cannam@95: 	       }
cannam@95: 	  }
cannam@95: 	  if (i + i == n2) {
cannam@95: 	       INT k = (i + i) - 1;
cannam@95: 	       E wa, wb;
cannam@95: 	       E a, b;
cannam@95: 	       wa = W2[0]; /* cos */
cannam@95: 	       wb = W2[1]; /* sin */
cannam@95: 	       a = buf[i];
cannam@95: 	       b = buf[n2 + i];
cannam@95: 	       O[os * k] = wb * b - wa * a;
cannam@95: 	       O[os * (n - 1 - k)] = wa * b + wb * a;
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:      static const tw_instr reodft11e_tw[] = {
cannam@95:           { TW_COS, 1, 1 },
cannam@95:           { TW_SIN, 1, 1 },
cannam@95:           { TW_NEXT, 2, 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: 		      2*ego->n, 1, ego->n/4+1);
cannam@95:      X(twiddle_awake)(wakefulness, &ego->td2, reodft11e_tw, 
cannam@95: 		      8*ego->n, 1, ego->n);
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-radix2-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->sz->dims[0].n % 2 == 0
cannam@95: 	     && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
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/2, 1, 1),
cannam@95:                                                    X(mktensor_1d)(2, n/2, n/2),
cannam@95:                                                    buf, buf, R2HC));
cannam@95:      X(ifree)(buf);
cannam@95:      if (!cld)
cannam@95:           return (plan *)0;
cannam@95: 
cannam@95:      pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11);
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 = pln->td2 = 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.add = 2 + (n/2 - 1)/2 * 20;
cannam@95:      ops.mul = 6 + (n/2 - 1)/2 * 16;
cannam@95:      ops.other = 4*n + 2 + (n/2 - 1)/2 * 6;
cannam@95:      if ((n/2) % 2 == 0) {
cannam@95: 	  ops.add += 4;
cannam@95: 	  ops.mul += 8;
cannam@95: 	  ops.other += 4;
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(reodft11e_radix2_r2hc_register)(planner *p)
cannam@95: {
cannam@95:      REGISTER_SOLVER(p, mksolver());
cannam@95: }