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 via an R2HC problem of the same *odd* size,
Chris@10:    with some permutations and post-processing, as described in:
Chris@10: 
Chris@10:      S. C. Chan and K. L. Ho, "Fast algorithms for computing the
Chris@10:      discrete cosine transform," IEEE Trans. Circuits Systems II:
Chris@10:      Analog & Digital Sig. Proc. 39 (3), 185--190 (1992).
Chris@10: 
Chris@10:    (For even sizes, see reodft11e-radix2.c.)  
Chris@10: 
Chris@10:    This algorithm is related to the 8 x n prime-factor-algorithm (PFA)
Chris@10:    decomposition of the size 8n "logical" DFT corresponding to the
Chris@10:    R{EO}DFT11.
Chris@10: 
Chris@10:    Aside from very confusing notation (several symbols are redefined
Chris@10:    from one line to the next), be aware that this paper has some
Chris@10:    errors.  In particular, the signs are wrong in Eqs. (34-35).  Also,
Chris@10:    Eqs. (36-37) should be simply C(k) = C(2k + 1 mod N), and similarly
Chris@10:    for S (or, equivalently, the second cases should have 2*N - 2*k - 1
Chris@10:    instead of N - k - 1).  Note also that in their definition of the
Chris@10:    DFT, similarly to FFTW's, the exponent's sign is -1, but they
Chris@10:    forgot to correspondingly multiply S (the sine terms) by -1.
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:      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 DK(SQRT2, +1.4142135623730950488016887242096980785696718753769);
Chris@10: 
Chris@10: #define SGN_SET(x, i) ((i) % 2 ? -(x) : (x))
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 *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: 	  {
Chris@10: 	       INT m;
Chris@10: 	       for (i = 0, m = n2; m < n; ++i, m += 4)
Chris@10: 		    buf[i] = I[is * m];
Chris@10: 	       for (; m < 2 * n; ++i, m += 4)
Chris@10: 		    buf[i] = -I[is * (2*n - m - 1)];
Chris@10: 	       for (; m < 3 * n; ++i, m += 4)
Chris@10: 		    buf[i] = -I[is * (m - 2*n)];
Chris@10: 	       for (; m < 4 * n; ++i, m += 4)
Chris@10: 		    buf[i] = I[is * (4*n - m - 1)];
Chris@10: 	       m -= 4 * n;
Chris@10: 	       for (; i < n; ++i, m += 4)
Chris@10: 		    buf[i] = I[is * m];
Chris@10: 	  }
Chris@10: 
Chris@10: 	  { /* child plan: R2HC of size n */
Chris@10: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
Chris@10: 	       cld->apply((plan *) cld, buf, buf);
Chris@10: 	  }
Chris@10: 	  
Chris@10: 	  /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
Chris@10: 	  for (i = 0; i + i + 1 < n2; ++i) {
Chris@10: 	       INT k = i + i + 1;
Chris@10: 	       E c1, s1;
Chris@10: 	       E c2, s2;
Chris@10: 	       c1 = buf[k];
Chris@10: 	       c2 = buf[k + 1];
Chris@10: 	       s2 = buf[n - (k + 1)];
Chris@10: 	       s1 = buf[n - k];
Chris@10: 	       
Chris@10: 	       O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2) +
Chris@10: 				    SGN_SET(s1, i/2));
Chris@10: 	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2) -
Chris@10: 					      SGN_SET(s1, (n-(i+1))/2));
Chris@10: 	       
Chris@10: 	       O[os * (n2 - (i+1))] = SQRT2 * (SGN_SET(c2, (n2-i)/2) -
Chris@10: 					       SGN_SET(s2, (n2-(i+1))/2));
Chris@10: 	       O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2) +
Chris@10: 					       SGN_SET(s2, (n2+(i+1))/2));
Chris@10: 	  }
Chris@10: 	  if (i + i + 1 == n2) {
Chris@10: 	       E c, s;
Chris@10: 	       c = buf[n2];
Chris@10: 	       s = buf[n - n2];
Chris@10: 	       O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2) +
Chris@10: 				    SGN_SET(s, i/2));
Chris@10: 	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2) +
Chris@10: 					      SGN_SET(s, (i+1)/2));
Chris@10: 	  }
Chris@10: 	  O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2);
Chris@10:      }
Chris@10: 
Chris@10:      X(ifree)(buf);
Chris@10: }
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 *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: 	  {
Chris@10: 	       INT m;
Chris@10: 	       for (i = 0, m = n2; m < n; ++i, m += 4)
Chris@10: 		    buf[i] = I[is * (n - 1 - m)];
Chris@10: 	       for (; m < 2 * n; ++i, m += 4)
Chris@10: 		    buf[i] = -I[is * (m - n)];
Chris@10: 	       for (; m < 3 * n; ++i, m += 4)
Chris@10: 		    buf[i] = -I[is * (3*n - 1 - m)];
Chris@10: 	       for (; m < 4 * n; ++i, m += 4)
Chris@10: 		    buf[i] = I[is * (m - 3*n)];
Chris@10: 	       m -= 4 * n;
Chris@10: 	       for (; i < n; ++i, m += 4)
Chris@10: 		    buf[i] = I[is * (n - 1 - m)];
Chris@10: 	  }
Chris@10: 
Chris@10: 	  { /* child plan: R2HC of size n */
Chris@10: 	       plan_rdft *cld = (plan_rdft *) ego->cld;
Chris@10: 	       cld->apply((plan *) cld, buf, buf);
Chris@10: 	  }
Chris@10: 	  
Chris@10: 	  /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
Chris@10: 	  for (i = 0; i + i + 1 < n2; ++i) {
Chris@10: 	       INT k = i + i + 1;
Chris@10: 	       INT j;
Chris@10: 	       E c1, s1;
Chris@10: 	       E c2, s2;
Chris@10: 	       c1 = buf[k];
Chris@10: 	       c2 = buf[k + 1];
Chris@10: 	       s2 = buf[n - (k + 1)];
Chris@10: 	       s1 = buf[n - k];
Chris@10: 	       
Chris@10: 	       O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2 + i) +
Chris@10: 				    SGN_SET(s1, i/2 + i));
Chris@10: 	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2 + i) -
Chris@10: 					      SGN_SET(s1, (n-(i+1))/2 + i));
Chris@10: 	       
Chris@10: 	       j = n2 - (i+1);
Chris@10: 	       O[os * j] = SQRT2 * (SGN_SET(c2, (n2-i)/2 + j) -
Chris@10: 				    SGN_SET(s2, (n2-(i+1))/2 + j));
Chris@10: 	       O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2 + j) +
Chris@10: 					       SGN_SET(s2, (n2+(i+1))/2 + j));
Chris@10: 	  }
Chris@10: 	  if (i + i + 1 == n2) {
Chris@10: 	       E c, s;
Chris@10: 	       c = buf[n2];
Chris@10: 	       s = buf[n - n2];
Chris@10: 	       O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2 + i) +
Chris@10: 				    SGN_SET(s, i/2 + i));
Chris@10: 	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2 + i) +
Chris@10: 					      SGN_SET(s, (i+1)/2 + i));
Chris@10: 	  }
Chris@10: 	  O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2 + n2);
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:      X(plan_awake)(ego->cld, wakefulness);
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-r2hc-odd-%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 == 1
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, 1, 1),
Chris@10:                                                    X(mktensor_0d)(),
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->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 = n - 1;
Chris@10:      ops.mul = n;
Chris@10:      ops.other = 4*n;
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_r2hc_odd_register)(planner *p)
Chris@10: {
Chris@10:      REGISTER_SOLVER(p, mksolver());
Chris@10: }