778 lines
		
	
	
		
			22 KiB
		
	
	
	
		
			C
		
	
	
	
	
	
			
		
		
	
	
			778 lines
		
	
	
		
			22 KiB
		
	
	
	
		
			C
		
	
	
	
	
	
/*
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 * Copyright (c) 2003, 2007-14 Matteo Frigo
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 * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
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 *
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 * This program is free software; you can redistribute it and/or modify
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 * it under the terms of the GNU General Public License as published by
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 * the Free Software Foundation; either version 2 of the License, or
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 * (at your option) any later version.
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 *
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 * This program is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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 * GNU General Public License for more details.
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 *
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 * You should have received a copy of the GNU General Public License
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 * along with this program; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
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 *
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 */
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/* rank-0, vector-rank-3, non-square in-place transposition
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   (see rank0.c for square transposition)  */
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#include "rdft/rdft.h"
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#ifdef HAVE_STRING_H
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#include <string.h>		/* for memcpy() */
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#endif
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struct P_s;
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typedef struct {
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     rdftapply apply;
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     int (*applicable)(const problem_rdft *p, planner *plnr,
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		       int dim0, int dim1, int dim2, INT *nbuf);
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     int (*mkcldrn)(const problem_rdft *p, planner *plnr, struct P_s *ego);
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     const char *nam;
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} transpose_adt;
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typedef struct {
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     solver super;
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     const transpose_adt *adt;
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} S;
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typedef struct P_s {
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     plan_rdft super;
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     INT n, m, vl; /* transpose n x m matrix of vl-tuples */
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     INT nbuf; /* buffer size */
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     INT nd, md, d; /* transpose-gcd params */
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     INT nc, mc; /* transpose-cut params */
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     plan *cld1, *cld2, *cld3; /* children, null if unused */
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     const S *slv;
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} P;
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/*************************************************************************/
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/* some utilities for the solvers */
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static INT gcd(INT a, INT b)
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{
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     INT r;
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     do {
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	  r = a % b;
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	  a = b;
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	  b = r;
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     } while (r != 0);
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     return a;
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}
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/* whether we can transpose with one of our routines expecting
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   contiguous Ntuples */
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static int Ntuple_transposable(const iodim *a, const iodim *b, INT vl, INT vs)
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{
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     return (vs == 1 && b->is == vl && a->os == vl &&
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	     ((a->n == b->n && a->is == b->os
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	       && a->is >= b->n && a->is % vl == 0)
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	      || (a->is == b->n * vl && b->os == a->n * vl)));
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}
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/* check whether a and b correspond to the first and second dimensions
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   of a transpose of tuples with vector length = vl, stride = vs. */
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static int transposable(const iodim *a, const iodim *b, INT vl, INT vs)
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{
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     return ((a->n == b->n && a->os == b->is && a->is == b->os)
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             || Ntuple_transposable(a, b, vl, vs));
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}
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static int pickdim(const tensor *s, int *pdim0, int *pdim1, int *pdim2)
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{
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     int dim0, dim1;
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     for (dim0 = 0; dim0 < s->rnk; ++dim0)
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          for (dim1 = 0; dim1 < s->rnk; ++dim1) {
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	       int dim2 = 3 - dim0 - dim1;
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	       if (dim0 == dim1) continue;
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               if ((s->rnk == 2 || s->dims[dim2].is == s->dims[dim2].os)
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		   && transposable(s->dims + dim0, s->dims + dim1, 
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				   s->rnk == 2 ? (INT)1 : s->dims[dim2].n,
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				   s->rnk == 2 ? (INT)1 : s->dims[dim2].is)) {
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                    *pdim0 = dim0;
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                    *pdim1 = dim1;
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		    *pdim2 = dim2;
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                    return 1;
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               }
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	  }
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     return 0;
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}
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#define MINBUFDIV 9 /* min factor by which buffer is smaller than data */
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#define MAXBUF 65536 /* maximum non-ugly buffer */
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/* generic applicability function */
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static int applicable(const solver *ego_, const problem *p_, planner *plnr,
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		      int *dim0, int *dim1, int *dim2, INT *nbuf)
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{
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     const S *ego = (const S *) ego_;
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     const problem_rdft *p = (const problem_rdft *) p_;
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     return (1
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	     && p->I == p->O
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	     && p->sz->rnk == 0
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	     && (p->vecsz->rnk == 2 || p->vecsz->rnk == 3)
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	     && pickdim(p->vecsz, dim0, dim1, dim2)
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	     /* UGLY if vecloop in wrong order for locality */
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	     && (!NO_UGLYP(plnr) ||
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		 p->vecsz->rnk == 2 ||
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		 X(iabs)(p->vecsz->dims[*dim2].is)
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		 < X(imax)(X(iabs)(p->vecsz->dims[*dim0].is),
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			   X(iabs)(p->vecsz->dims[*dim0].os)))
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	     /* SLOW if non-square */
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	     && (!NO_SLOWP(plnr)
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		 || p->vecsz->dims[*dim0].n == p->vecsz->dims[*dim1].n)
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	     && ego->adt->applicable(p, plnr, *dim0,*dim1,*dim2,nbuf)
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	     /* buffers too big are UGLY */
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	     && ((!NO_UGLYP(plnr) && !CONSERVE_MEMORYP(plnr))
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		 || *nbuf <= MAXBUF
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		 || *nbuf * MINBUFDIV <= X(tensor_sz)(p->vecsz))
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	  );
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}
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static void get_transpose_vec(const problem_rdft *p, int dim2, INT *vl,INT *vs)
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{
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     if (p->vecsz->rnk == 2) {
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	  *vl = 1; *vs = 1;
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     }
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     else {
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	  *vl = p->vecsz->dims[dim2].n;
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	  *vs = p->vecsz->dims[dim2].is; /* == os */
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     }  
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}
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/*************************************************************************/
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/* Cache-oblivious in-place transpose of non-square matrices, based 
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   on transposes of blocks given by the gcd of the dimensions.
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   This algorithm is related to algorithm V5 from Murray Dow,
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   "Transposing a matrix on a vector computer," Parallel Computing 21
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   (12), 1997-2005 (1995), with the modification that we use
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   cache-oblivious recursive transpose subroutines (and we derived
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   it independently).
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   For a p x q matrix, this requires scratch space equal to the size
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   of the matrix divided by gcd(p,q).  Alternatively, see also the
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   "cut" algorithm below, if |p-q| * gcd(p,q) < max(p,q). */
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static void apply_gcd(const plan *ego_, R *I, R *O)
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{
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     const P *ego = (const P *) ego_;
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     INT n = ego->nd, m = ego->md, d = ego->d;
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     INT vl = ego->vl;
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     R *buf = (R *)MALLOC(sizeof(R) * ego->nbuf, BUFFERS);
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     INT i, num_el = n*m*d*vl;
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     A(ego->n == n * d && ego->m == m * d);
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     UNUSED(O);
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     /* Transpose the matrix I in-place, where I is an (n*d) x (m*d) matrix
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	of vl-tuples and buf contains n*m*d*vl elements.  
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	In general, to transpose a p x q matrix, you should call this
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	routine with d = gcd(p, q), n = p/d, and m = q/d.  */
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     A(n > 0 && m > 0 && vl > 0);
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     A(d > 1);
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     /* treat as (d x n) x (d' x m) matrix.  (d' = d) */
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     /* First, transpose d x (n x d') x m to d x (d' x n) x m,
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	using the buf matrix.  This consists of d transposes
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	of contiguous n x d' matrices of m-tuples. */
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     if (n > 1) {
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	  rdftapply cldapply = ((plan_rdft *) ego->cld1)->apply;
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	  for (i = 0; i < d; ++i) {
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	       cldapply(ego->cld1, I + i*num_el, buf);
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	       memcpy(I + i*num_el, buf, num_el*sizeof(R));
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	  }
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     }
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     /* Now, transpose (d x d') x (n x m) to (d' x d) x (n x m), which
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	is a square in-place transpose of n*m-tuples: */
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     {
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	  rdftapply cldapply = ((plan_rdft *) ego->cld2)->apply;
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	  cldapply(ego->cld2, I, I);
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     }
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     /* Finally, transpose d' x ((d x n) x m) to d' x (m x (d x n)),
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	using the buf matrix.  This consists of d' transposes
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	of contiguous d*n x m matrices. */
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     if (m > 1) {
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	  rdftapply cldapply = ((plan_rdft *) ego->cld3)->apply;
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	  for (i = 0; i < d; ++i) {
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	       cldapply(ego->cld3, I + i*num_el, buf);
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	       memcpy(I + i*num_el, buf, num_el*sizeof(R));
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	  }
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     }
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     X(ifree)(buf);
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}
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static int applicable_gcd(const problem_rdft *p, planner *plnr,
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			  int dim0, int dim1, int dim2, INT *nbuf)
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{
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     INT n = p->vecsz->dims[dim0].n;
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     INT m = p->vecsz->dims[dim1].n;
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     INT d, vl, vs;
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     get_transpose_vec(p, dim2, &vl, &vs);
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     d = gcd(n, m);
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     *nbuf = n * (m / d) * vl;
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     return (!NO_SLOWP(plnr) /* FIXME: not really SLOW for large 1d ffts */
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	     && n != m
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	     && d > 1
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	     && Ntuple_transposable(p->vecsz->dims + dim0,
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				    p->vecsz->dims + dim1,
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				    vl, vs));
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}
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static int mkcldrn_gcd(const problem_rdft *p, planner *plnr, P *ego)
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{
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     INT n = ego->nd, m = ego->md, d = ego->d;
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     INT vl = ego->vl;
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     R *buf = (R *)MALLOC(sizeof(R) * ego->nbuf, BUFFERS);
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     INT num_el = n*m*d*vl;
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     if (n > 1) {
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	  ego->cld1 = X(mkplan_d)(plnr,
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				  X(mkproblem_rdft_0_d)(
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				       X(mktensor_3d)(n, d*m*vl, m*vl,
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						      d, m*vl, n*m*vl,
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						      m*vl, 1, 1),
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				       TAINT(p->I, num_el), buf));
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	  if (!ego->cld1)
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	       goto nada;
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	  X(ops_madd)(d, &ego->cld1->ops, &ego->super.super.ops,
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		      &ego->super.super.ops);
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	  ego->super.super.ops.other += num_el * d * 2;
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     }
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     ego->cld2 = X(mkplan_d)(plnr,
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			     X(mkproblem_rdft_0_d)(
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				  X(mktensor_3d)(d, d*n*m*vl, n*m*vl,
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						 d, n*m*vl, d*n*m*vl,
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						 n*m*vl, 1, 1),
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				  p->I, p->I));
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     if (!ego->cld2)
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	  goto nada;
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     X(ops_add2)(&ego->cld2->ops, &ego->super.super.ops);
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     if (m > 1) {
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	  ego->cld3 = X(mkplan_d)(plnr,
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				  X(mkproblem_rdft_0_d)(
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				       X(mktensor_3d)(d*n, m*vl, vl,
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						      m, vl, d*n*vl,
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						      vl, 1, 1),
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				       TAINT(p->I, num_el), buf));
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	  if (!ego->cld3)
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	       goto nada;
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	  X(ops_madd2)(d, &ego->cld3->ops, &ego->super.super.ops);
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	  ego->super.super.ops.other += num_el * d * 2;
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     }
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     X(ifree)(buf);
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     return 1;
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 nada:
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     X(ifree)(buf);
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     return 0;
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}
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static const transpose_adt adt_gcd =
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{
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     apply_gcd, applicable_gcd, mkcldrn_gcd,
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     "rdft-transpose-gcd"
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};
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/*************************************************************************/
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/* Cache-oblivious in-place transpose of non-square n x m matrices,
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   based on transposing a sub-matrix first and then transposing the
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   remainder(s) with the help of a buffer.  See also transpose-gcd,
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   above, if gcd(n,m) is large.
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   This algorithm is related to algorithm V3 from Murray Dow,
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   "Transposing a matrix on a vector computer," Parallel Computing 21
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   (12), 1997-2005 (1995), with the modifications that we use
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   cache-oblivious recursive transpose subroutines and we have the
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   generalization for large |n-m| below.
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   The best case, and the one described by Dow, is for |n-m| small, in
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   which case we transpose a square sub-matrix of size min(n,m),
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   handling the remainder via a buffer.  This requires scratch space
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   equal to the size of the matrix times |n-m| / max(n,m).
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   As a generalization when |n-m| is not small, we also support cutting
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   *both* dimensions to an nc x mc matrix which is *not* necessarily
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   square, but has a large gcd (and can therefore use transpose-gcd).
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*/
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static void apply_cut(const plan *ego_, R *I, R *O)
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{
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     const P *ego = (const P *) ego_;
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     INT n = ego->n, m = ego->m, nc = ego->nc, mc = ego->mc, vl = ego->vl;
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     INT i;
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     R *buf1 = (R *)MALLOC(sizeof(R) * ego->nbuf, BUFFERS);
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     UNUSED(O);
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     if (m > mc) {
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	  ((plan_rdft *) ego->cld1)->apply(ego->cld1, I + mc*vl, buf1);
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	  for (i = 0; i < nc; ++i)
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	       memmove(I + (mc*vl) * i, I + (m*vl) * i, sizeof(R) * (mc*vl));
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     }
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     ((plan_rdft *) ego->cld2)->apply(ego->cld2, I, I); /* nc x mc transpose */
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     if (n > nc) {
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	  R *buf2 = buf1 + (m-mc)*(nc*vl); /* FIXME: force better alignment? */
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	  memcpy(buf2, I + nc*(m*vl), (n-nc)*(m*vl)*sizeof(R));
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	  for (i = mc-1; i >= 0; --i)
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	       memmove(I + (n*vl) * i, I + (nc*vl) * i, sizeof(R) * (n*vl));
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	  ((plan_rdft *) ego->cld3)->apply(ego->cld3, buf2, I + nc*vl);
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     }
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     if (m > mc) {
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	  if (n > nc)
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	       for (i = mc; i < m; ++i)
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		    memcpy(I + i*(n*vl), buf1 + (i-mc)*(nc*vl),
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			   (nc*vl)*sizeof(R));
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	  else
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	       memcpy(I + mc*(n*vl), buf1, (m-mc)*(n*vl)*sizeof(R));
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     }
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     X(ifree)(buf1);
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}
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/* only cut one dimension if the resulting buffer is small enough */
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static int cut1(INT n, INT m, INT vl)
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{
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     return (X(imax)(n,m) >= X(iabs)(n-m) * MINBUFDIV
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	     || X(imin)(n,m) * X(iabs)(n-m) * vl <= MAXBUF);
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}
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#define CUT_NSRCH 32 /* range of sizes to search for possible cuts */
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static int applicable_cut(const problem_rdft *p, planner *plnr,
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			  int dim0, int dim1, int dim2, INT *nbuf)
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{
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     INT n = p->vecsz->dims[dim0].n;
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     INT m = p->vecsz->dims[dim1].n;
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     INT vl, vs;
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     get_transpose_vec(p, dim2, &vl, &vs);
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     *nbuf = 0; /* always small enough to be non-UGLY (?) */
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     A(MINBUFDIV <= CUT_NSRCH); /* assumed to avoid inf. loops below */
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     return (!NO_SLOWP(plnr) /* FIXME: not really SLOW for large 1d ffts? */
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	     && n != m
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	     /* Don't call transpose-cut recursively (avoid inf. loops):
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	        the non-square sub-transpose produced when !cut1
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	        should always have gcd(n,m) >= min(CUT_NSRCH,n,m),
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	        for which transpose-gcd is applicable */
 | 
						|
	     && (cut1(n, m, vl)
 | 
						|
		 || gcd(n, m) < X(imin)(MINBUFDIV, X(imin)(n,m)))
 | 
						|
 | 
						|
	     && Ntuple_transposable(p->vecsz->dims + dim0,
 | 
						|
				    p->vecsz->dims + dim1,
 | 
						|
				    vl, vs));
 | 
						|
}
 | 
						|
 | 
						|
static int mkcldrn_cut(const problem_rdft *p, planner *plnr, P *ego)
 | 
						|
{
 | 
						|
     INT n = ego->n, m = ego->m, nc, mc;
 | 
						|
     INT vl = ego->vl;
 | 
						|
     R *buf;
 | 
						|
 | 
						|
     /* pick the "best" cut */
 | 
						|
     if (cut1(n, m, vl)) {
 | 
						|
	  nc = mc = X(imin)(n,m);
 | 
						|
     }
 | 
						|
     else {
 | 
						|
	  INT dc, ns, ms;
 | 
						|
	  dc = gcd(m, n); nc = n; mc = m;
 | 
						|
	  /* search for cut with largest gcd
 | 
						|
	     (TODO: different optimality criteria? different search range?) */
 | 
						|
	  for (ms = m; ms > 0 && ms > m - CUT_NSRCH; --ms) {
 | 
						|
	       for (ns = n; ns > 0 && ns > n - CUT_NSRCH; --ns) {
 | 
						|
		    INT ds = gcd(ms, ns);
 | 
						|
		    if (ds > dc) {
 | 
						|
			 dc = ds; nc = ns; mc = ms;
 | 
						|
			 if (dc == X(imin)(ns, ms))
 | 
						|
			      break; /* cannot get larger than this */
 | 
						|
		    }
 | 
						|
	       }
 | 
						|
	       if (dc == X(imin)(n, ms))
 | 
						|
		    break; /* cannot get larger than this */
 | 
						|
	  }
 | 
						|
	  A(dc >= X(imin)(CUT_NSRCH, X(imin)(n, m)));
 | 
						|
     }
 | 
						|
     ego->nc = nc;
 | 
						|
     ego->mc = mc;
 | 
						|
     ego->nbuf = (m-mc)*(nc*vl) + (n-nc)*(m*vl);
 | 
						|
 | 
						|
     buf = (R *)MALLOC(sizeof(R) * ego->nbuf, BUFFERS);
 | 
						|
 | 
						|
     if (m > mc) {
 | 
						|
	  ego->cld1 = X(mkplan_d)(plnr,
 | 
						|
				  X(mkproblem_rdft_0_d)(
 | 
						|
				       X(mktensor_3d)(nc, m*vl, vl,
 | 
						|
						      m-mc, vl, nc*vl,
 | 
						|
						      vl, 1, 1),
 | 
						|
				       p->I + mc*vl, buf));
 | 
						|
	  if (!ego->cld1)
 | 
						|
	       goto nada;
 | 
						|
	  X(ops_add2)(&ego->cld1->ops, &ego->super.super.ops);
 | 
						|
     }
 | 
						|
 | 
						|
     ego->cld2 = X(mkplan_d)(plnr,
 | 
						|
			     X(mkproblem_rdft_0_d)(
 | 
						|
				  X(mktensor_3d)(nc, mc*vl, vl,
 | 
						|
						 mc, vl, nc*vl,
 | 
						|
						 vl, 1, 1),
 | 
						|
				  p->I, p->I));
 | 
						|
     if (!ego->cld2)
 | 
						|
	  goto nada;
 | 
						|
     X(ops_add2)(&ego->cld2->ops, &ego->super.super.ops);
 | 
						|
 | 
						|
     if (n > nc) {
 | 
						|
	  ego->cld3 = X(mkplan_d)(plnr,
 | 
						|
				  X(mkproblem_rdft_0_d)(
 | 
						|
				       X(mktensor_3d)(n-nc, m*vl, vl,
 | 
						|
						      m, vl, n*vl,
 | 
						|
						      vl, 1, 1),
 | 
						|
				       buf + (m-mc)*(nc*vl), p->I + nc*vl));
 | 
						|
	  if (!ego->cld3)
 | 
						|
	       goto nada;
 | 
						|
	  X(ops_add2)(&ego->cld3->ops, &ego->super.super.ops);
 | 
						|
     }
 | 
						|
 | 
						|
     /* memcpy/memmove operations */
 | 
						|
     ego->super.super.ops.other += 2 * vl * (nc*mc * ((m > mc) + (n > nc))
 | 
						|
					     + (n-nc)*m + (m-mc)*nc);
 | 
						|
 | 
						|
     X(ifree)(buf);
 | 
						|
     return 1;
 | 
						|
 | 
						|
 nada:
 | 
						|
     X(ifree)(buf);
 | 
						|
     return 0;
 | 
						|
}
 | 
						|
 | 
						|
static const transpose_adt adt_cut =
 | 
						|
{
 | 
						|
     apply_cut, applicable_cut, mkcldrn_cut,
 | 
						|
     "rdft-transpose-cut"
 | 
						|
};
 | 
						|
 | 
						|
/*************************************************************************/
 | 
						|
/* In-place transpose routine from TOMS, which follows the cycles of
 | 
						|
   the permutation so that it writes to each location only once.
 | 
						|
   Because of cache-line and other issues, however, this routine is
 | 
						|
   typically much slower than transpose-gcd or transpose-cut, even
 | 
						|
   though the latter do some extra writes.  On the other hand, if the
 | 
						|
   vector length is large then the TOMS routine is best.
 | 
						|
 | 
						|
   The TOMS routine also has the advantage of requiring less buffer
 | 
						|
   space for the case of gcd(nx,ny) small.  However, in this case it
 | 
						|
   has been superseded by the combination of the generalized
 | 
						|
   transpose-cut method with the transpose-gcd method, which can
 | 
						|
   always transpose with buffers a small fraction of the array size
 | 
						|
   regardless of gcd(nx,ny). */
 | 
						|
 | 
						|
/*
 | 
						|
 * TOMS Transpose.  Algorithm 513 (Revised version of algorithm 380).
 | 
						|
 * 
 | 
						|
 * These routines do in-place transposes of arrays.
 | 
						|
 * 
 | 
						|
 * [ Cate, E.G. and Twigg, D.W., ACM Transactions on Mathematical Software, 
 | 
						|
 *   vol. 3, no. 1, 104-110 (1977) ]
 | 
						|
 * 
 | 
						|
 * C version by Steven G. Johnson (February 1997).
 | 
						|
 */
 | 
						|
 | 
						|
/*
 | 
						|
 * "a" is a 1D array of length ny*nx*N which constains the nx x ny
 | 
						|
 * matrix of N-tuples to be transposed.  "a" is stored in row-major
 | 
						|
 * order (last index varies fastest).  move is a 1D array of length
 | 
						|
 * move_size used to store information to speed up the process.  The
 | 
						|
 * value move_size=(ny+nx)/2 is recommended.  buf should be an array
 | 
						|
 * of length 2*N.
 | 
						|
 * 
 | 
						|
 */
 | 
						|
 | 
						|
static void transpose_toms513(R *a, INT nx, INT ny, INT N,
 | 
						|
                              char *move, INT move_size, R *buf)
 | 
						|
{
 | 
						|
     INT i, im, mn;
 | 
						|
     R *b, *c, *d;
 | 
						|
     INT ncount;
 | 
						|
     INT k;
 | 
						|
     
 | 
						|
     /* check arguments and initialize: */
 | 
						|
     A(ny > 0 && nx > 0 && N > 0 && move_size > 0);
 | 
						|
     
 | 
						|
     b = buf;
 | 
						|
     
 | 
						|
     /* Cate & Twigg have a special case for nx == ny, but we don't
 | 
						|
	bother, since we already have special code for this case elsewhere. */
 | 
						|
 | 
						|
     c = buf + N;
 | 
						|
     ncount = 2;		/* always at least 2 fixed points */
 | 
						|
     k = (mn = ny * nx) - 1;
 | 
						|
     
 | 
						|
     for (i = 0; i < move_size; ++i)
 | 
						|
	  move[i] = 0;
 | 
						|
     
 | 
						|
     if (ny >= 3 && nx >= 3)
 | 
						|
	  ncount += gcd(ny - 1, nx - 1) - 1;	/* # fixed points */
 | 
						|
     
 | 
						|
     i = 1;
 | 
						|
     im = ny;
 | 
						|
     
 | 
						|
     while (1) {
 | 
						|
	  INT i1, i2, i1c, i2c;
 | 
						|
	  INT kmi;
 | 
						|
	  
 | 
						|
	  /** Rearrange the elements of a loop
 | 
						|
	      and its companion loop: **/
 | 
						|
	  
 | 
						|
	  i1 = i;
 | 
						|
	  kmi = k - i;
 | 
						|
	  i1c = kmi;
 | 
						|
	  switch (N) {
 | 
						|
	      case 1:
 | 
						|
		   b[0] = a[i1];
 | 
						|
		   c[0] = a[i1c];
 | 
						|
		   break;
 | 
						|
	      case 2:
 | 
						|
		   b[0] = a[2*i1];
 | 
						|
		   b[1] = a[2*i1+1];
 | 
						|
		   c[0] = a[2*i1c];
 | 
						|
		   c[1] = a[2*i1c+1];
 | 
						|
		   break;
 | 
						|
	      default:
 | 
						|
		   memcpy(b, &a[N * i1], N * sizeof(R));
 | 
						|
		   memcpy(c, &a[N * i1c], N * sizeof(R));
 | 
						|
	  }
 | 
						|
	  while (1) {
 | 
						|
	       i2 = ny * i1 - k * (i1 / nx);
 | 
						|
	       i2c = k - i2;
 | 
						|
	       if (i1 < move_size)
 | 
						|
		    move[i1] = 1;
 | 
						|
	       if (i1c < move_size)
 | 
						|
		    move[i1c] = 1;
 | 
						|
	       ncount += 2;
 | 
						|
	       if (i2 == i)
 | 
						|
		    break;
 | 
						|
	       if (i2 == kmi) {
 | 
						|
		    d = b;
 | 
						|
		    b = c;
 | 
						|
		    c = d;
 | 
						|
		    break;
 | 
						|
	       }
 | 
						|
	       switch (N) {
 | 
						|
		   case 1:
 | 
						|
			a[i1] = a[i2];
 | 
						|
			a[i1c] = a[i2c];
 | 
						|
			break;
 | 
						|
		   case 2:
 | 
						|
			a[2*i1] = a[2*i2];
 | 
						|
			a[2*i1+1] = a[2*i2+1];
 | 
						|
			a[2*i1c] = a[2*i2c];
 | 
						|
			a[2*i1c+1] = a[2*i2c+1];
 | 
						|
			break;
 | 
						|
		   default:
 | 
						|
			memcpy(&a[N * i1], &a[N * i2], 
 | 
						|
			       N * sizeof(R));
 | 
						|
			memcpy(&a[N * i1c], &a[N * i2c], 
 | 
						|
			       N * sizeof(R));
 | 
						|
	       }
 | 
						|
	       i1 = i2;
 | 
						|
	       i1c = i2c;
 | 
						|
	  }
 | 
						|
	  switch (N) {
 | 
						|
	      case 1:
 | 
						|
		   a[i1] = b[0];
 | 
						|
		   a[i1c] = c[0];
 | 
						|
		   break;
 | 
						|
	      case 2:
 | 
						|
		   a[2*i1] = b[0];
 | 
						|
		   a[2*i1+1] = b[1];
 | 
						|
		   a[2*i1c] = c[0];
 | 
						|
		   a[2*i1c+1] = c[1];
 | 
						|
		   break;
 | 
						|
	      default:
 | 
						|
		   memcpy(&a[N * i1], b, N * sizeof(R));
 | 
						|
		   memcpy(&a[N * i1c], c, N * sizeof(R));
 | 
						|
	  }
 | 
						|
	  if (ncount >= mn)
 | 
						|
	       break;	/* we've moved all elements */
 | 
						|
	  
 | 
						|
	  /** Search for loops to rearrange: **/
 | 
						|
	  
 | 
						|
	  while (1) {
 | 
						|
	       INT max = k - i;
 | 
						|
	       ++i;
 | 
						|
	       A(i <= max);
 | 
						|
	       im += ny;
 | 
						|
	       if (im > k)
 | 
						|
		    im -= k;
 | 
						|
	       i2 = im;
 | 
						|
	       if (i == i2)
 | 
						|
		    continue;
 | 
						|
	       if (i >= move_size) {
 | 
						|
		    while (i2 > i && i2 < max) {
 | 
						|
			 i1 = i2;
 | 
						|
			 i2 = ny * i1 - k * (i1 / nx);
 | 
						|
		    }
 | 
						|
		    if (i2 == i)
 | 
						|
			 break;
 | 
						|
	       } else if (!move[i])
 | 
						|
		    break;
 | 
						|
	  }
 | 
						|
     }
 | 
						|
}
 | 
						|
 | 
						|
static void apply_toms513(const plan *ego_, R *I, R *O)
 | 
						|
{
 | 
						|
     const P *ego = (const P *) ego_;
 | 
						|
     INT n = ego->n, m = ego->m;
 | 
						|
     INT vl = ego->vl;
 | 
						|
     R *buf = (R *)MALLOC(sizeof(R) * ego->nbuf, BUFFERS);
 | 
						|
     UNUSED(O);
 | 
						|
     transpose_toms513(I, n, m, vl, (char *) (buf + 2*vl), (n+m)/2, buf);
 | 
						|
     X(ifree)(buf);
 | 
						|
}
 | 
						|
 | 
						|
static int applicable_toms513(const problem_rdft *p, planner *plnr,
 | 
						|
			   int dim0, int dim1, int dim2, INT *nbuf)
 | 
						|
{
 | 
						|
     INT n = p->vecsz->dims[dim0].n;
 | 
						|
     INT m = p->vecsz->dims[dim1].n;
 | 
						|
     INT vl, vs;
 | 
						|
     get_transpose_vec(p, dim2, &vl, &vs);
 | 
						|
     *nbuf = 2*vl 
 | 
						|
	  + ((n + m) / 2 * sizeof(char) + sizeof(R) - 1) / sizeof(R);
 | 
						|
     return (!NO_SLOWP(plnr)
 | 
						|
	     && (vl > 8 || !NO_UGLYP(plnr)) /* UGLY for small vl */
 | 
						|
	     && n != m
 | 
						|
	     && Ntuple_transposable(p->vecsz->dims + dim0,
 | 
						|
				    p->vecsz->dims + dim1,
 | 
						|
				    vl, vs));
 | 
						|
}
 | 
						|
 | 
						|
static int mkcldrn_toms513(const problem_rdft *p, planner *plnr, P *ego)
 | 
						|
{
 | 
						|
     UNUSED(p); UNUSED(plnr);
 | 
						|
     /* heuristic so that TOMS algorithm is last resort for small vl */
 | 
						|
     ego->super.super.ops.other += ego->n * ego->m * 2 * (ego->vl + 30);
 | 
						|
     return 1;
 | 
						|
}
 | 
						|
 | 
						|
static const transpose_adt adt_toms513 =
 | 
						|
{
 | 
						|
     apply_toms513, applicable_toms513, mkcldrn_toms513,
 | 
						|
     "rdft-transpose-toms513"
 | 
						|
};
 | 
						|
 | 
						|
/*-----------------------------------------------------------------------*/
 | 
						|
/*-----------------------------------------------------------------------*/
 | 
						|
/* generic stuff: */
 | 
						|
 | 
						|
static void awake(plan *ego_, enum wakefulness wakefulness)
 | 
						|
{
 | 
						|
     P *ego = (P *) ego_;
 | 
						|
     X(plan_awake)(ego->cld1, wakefulness);
 | 
						|
     X(plan_awake)(ego->cld2, wakefulness);
 | 
						|
     X(plan_awake)(ego->cld3, wakefulness);
 | 
						|
}
 | 
						|
 | 
						|
static void print(const plan *ego_, printer *p)
 | 
						|
{
 | 
						|
     const P *ego = (const P *) ego_;
 | 
						|
     p->print(p, "(%s-%Dx%D%v", ego->slv->adt->nam,
 | 
						|
	      ego->n, ego->m, ego->vl);
 | 
						|
     if (ego->cld1) p->print(p, "%(%p%)", ego->cld1);
 | 
						|
     if (ego->cld2) p->print(p, "%(%p%)", ego->cld2);
 | 
						|
     if (ego->cld3) p->print(p, "%(%p%)", ego->cld3);
 | 
						|
     p->print(p, ")");
 | 
						|
}
 | 
						|
 | 
						|
static void destroy(plan *ego_)
 | 
						|
{
 | 
						|
     P *ego = (P *) ego_;
 | 
						|
     X(plan_destroy_internal)(ego->cld3);
 | 
						|
     X(plan_destroy_internal)(ego->cld2);
 | 
						|
     X(plan_destroy_internal)(ego->cld1);
 | 
						|
}
 | 
						|
 | 
						|
static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
 | 
						|
{
 | 
						|
     const S *ego = (const S *) ego_;
 | 
						|
     const problem_rdft *p;
 | 
						|
     int dim0, dim1, dim2;
 | 
						|
     INT nbuf, vs;
 | 
						|
     P *pln;
 | 
						|
 | 
						|
     static const plan_adt padt = {
 | 
						|
	  X(rdft_solve), awake, print, destroy
 | 
						|
     };
 | 
						|
 | 
						|
     if (!applicable(ego_, p_, plnr, &dim0, &dim1, &dim2, &nbuf))
 | 
						|
          return (plan *) 0;
 | 
						|
 | 
						|
     p = (const problem_rdft *) p_;
 | 
						|
     pln = MKPLAN_RDFT(P, &padt, ego->adt->apply);
 | 
						|
 | 
						|
     pln->n = p->vecsz->dims[dim0].n;
 | 
						|
     pln->m = p->vecsz->dims[dim1].n;
 | 
						|
     get_transpose_vec(p, dim2, &pln->vl, &vs);
 | 
						|
     pln->nbuf = nbuf;
 | 
						|
     pln->d = gcd(pln->n, pln->m);
 | 
						|
     pln->nd = pln->n / pln->d;
 | 
						|
     pln->md = pln->m / pln->d;
 | 
						|
     pln->slv = ego;
 | 
						|
 | 
						|
     X(ops_zero)(&pln->super.super.ops); /* mkcldrn is responsible for ops */
 | 
						|
 | 
						|
     pln->cld1 = pln->cld2 = pln->cld3 = 0;
 | 
						|
     if (!ego->adt->mkcldrn(p, plnr, pln)) {
 | 
						|
	  X(plan_destroy_internal)(&(pln->super.super));
 | 
						|
	  return 0;
 | 
						|
     }
 | 
						|
 | 
						|
     return &(pln->super.super);
 | 
						|
}
 | 
						|
 | 
						|
static solver *mksolver(const transpose_adt *adt)
 | 
						|
{
 | 
						|
     static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
 | 
						|
     S *slv = MKSOLVER(S, &sadt);
 | 
						|
     slv->adt = adt;
 | 
						|
     return &(slv->super);
 | 
						|
}
 | 
						|
 | 
						|
void X(rdft_vrank3_transpose_register)(planner *p)
 | 
						|
{
 | 
						|
     unsigned i;
 | 
						|
     static const transpose_adt *const adts[] = {
 | 
						|
	  &adt_gcd, &adt_cut,
 | 
						|
	  &adt_toms513
 | 
						|
     };
 | 
						|
     for (i = 0; i < sizeof(adts) / sizeof(adts[0]); ++i)
 | 
						|
          REGISTER_SOLVER(p, mksolver(adts[i]));
 | 
						|
}
 |