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transpose.c

/*
 * Copyright (c) 2003 Matteo Frigo
 * Copyright (c) 2003 Massachusetts Institute of Technology
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 */

/* transposes of unit-stride arrays, including arrays of N-tuples and
   non-square matrices, using cache-oblivious recursive algorithms */

#include "ifftw.h"
#include <string.h> /* memcpy */

#define CUTOFF 8 /* size below which we do a naive transpose */

/*************************************************************************/
/* some utilities for the solvers */

static int Ntuple_transposable(const iodim *a, const iodim *b,
                         int vl, int s, R *ri, R *ii)
{
     return(2 == s && (ii == ri + 1 || ri == ii + 1)
          &&
          ((a->is == b->os && a->is == (vl*2)
            && a->os == b->n * (vl*2) && b->is == a->n * (vl*2))
           ||
           (a->os == b->is && a->os == (vl*2)
            && a->is == b->n * (vl*2) && b->os == a->n * (vl*2))));
}


/* our solvers' transpose routines work for square matrices of arbitrary
   stride, or for non-square matrices of a given vl*vl2 corresponding
   to the N of the Ntuple with vl2 == s. */
int X(transposable)(const iodim *a, const iodim *b,
                int vl, int s, R *ri, R *ii)
{
     return ((a->n == b->n && a->os == b->is && a->is == b->os)
           || Ntuple_transposable(a, b, vl, s, ri, ii));
}

static int gcd(int a, int b)
{
     int r;
     do {
        r = a % b;
        a = b;
        b = r;
     } while (r != 0);
     
     return a;
}

/* all of the solvers need to extract n, m, d, n/d, and m/d from the
   two iodims, so we put it here to save code space */
void X(transpose_dims)(const iodim *a, const iodim *b,
                   int *n, int *m, int *d, int *nd, int *md)
{
     int n0, m0, d0;
     /* matrix should be n x m, row-major */
     if (a->is < b->is) {
        *n = n0 = b->n;
        *m = m0 = a->n;
     }
     else {
        *n = n0 = a->n;
        *m = m0 = b->n;
     }
     *d = d0 = gcd(n0, m0);
     *nd = n0 / d0;
     *md = m0 / d0;
}

/* use the simple square transpose in the solver for square matrices
   that aren't too big or which have the wrong stride */
int X(transpose_simplep)(const iodim *a, const iodim *b, int vl, int s,
                   R *ri, R *ii)
{
     return (a->n == b->n &&
           (a->n*(vl*2) < CUTOFF 
            ||  !Ntuple_transposable(a, b, vl, s, ri, ii)));
}

/* use the slow general transpose if the buffer would be more than 1/8
   the whole transpose and the transpose is fairly big.
   (FIXME: use the CONSERVE_MEMORY flag?) */
int X(transpose_slowp)(const iodim *a, const iodim *b, int N)
{
     int d = gcd(a->n, b->n);
     return (d < 8 && (a->n * b->n * N) / d > 65536);
}

/*************************************************************************/
/* Out-of-place transposes: */

/* Transpose A (n x m) to B (m x n), where A and B are stored
   as n x fda and m x fda arrays, respectively, operating on N-tuples: */
static void rec_transpose_Ntuple(R *A, R *B, int n, int m, int fda, int fdb,
                    int N)
{
     if (n == 1 || m == 1 || (n + m) * N < CUTOFF*2) {
        int i, j, k;
        for (i = 0; i < n; ++i) {
             for (j = 0; j < m; ++j) {
                for (k = 0; k < N; ++k) { /* FIXME: unroll */
                   B[(j*fdb + i) * N + k] = A[(i*fda + j) * N + k];
                }
             }
        }
     }
     else if (n > m) {
        int n2 = n / 2;
        rec_transpose_Ntuple(A, B, n2, m, fda, fdb, N);
        rec_transpose_Ntuple(A + n2*N*fda, B + n2*N, n - n2, m, fda, fdb, N);
     }
     else {
        int m2 = m / 2;
        rec_transpose_Ntuple(A, B, n, m2, fda, fdb, N);
        rec_transpose_Ntuple(A + m2*N, B + m2*N*fdb, n, m - m2, fda, fdb, N);
     }
}

/*************************************************************************/
/* In-place transposes of square matrices of N-tuples: */

/* Transpose both A and B, where A is n x m and B is m x n, storing
   the transpose of A in B and the transpose of B in A.  A and B
   are actually stored as n x fda and m x fda arrays. */
static void rec_transpose_swap_Ntuple(R *A, R *B, int n, int m, int fda, int N)
{
     if (n == 1 || m == 1 || (n + m) * N <= CUTOFF*2) {
        switch (N) {
            case 1: {
               int i, j;
               for (i = 0; i < n; ++i) {
                  for (j = 0; j < m; ++j) {
                       R a = A[(i*fda + j)];
                       A[(i*fda + j)] = B[(j*fda + i)];
                       B[(j*fda + i)] = a;
                  }
               }
               break;
            }
            case 2: {
               int i, j;
               for (i = 0; i < n; ++i) {
                  for (j = 0; j < m; ++j) {
                       R a0 = A[(i*fda + j) * 2 + 0];
                       R a1 = A[(i*fda + j) * 2 + 1];
                       A[(i*fda + j) * 2 + 0] = B[(j*fda + i) * 2 + 0];
                       A[(i*fda + j) * 2 + 1] = B[(j*fda + i) * 2 + 1];
                       B[(j*fda + i) * 2 + 0] = a0;
                       B[(j*fda + i) * 2 + 1] = a1;
                  }
               }
               break;
            }
            default: {
               int i, j, k;
               for (i = 0; i < n; ++i) {
                  for (j = 0; j < m; ++j) {
                       for (k = 0; k < N; ++k) {
                          R a = A[(i*fda + j) * N + k];
                          A[(i*fda + j) * N + k] = 
                               B[(j*fda + i) * N + k];
                          B[(j*fda + i) * N + k] = a;
                       }
                  }
               }
            }
        }
     } else if (n > m) {
        int n2 = n / 2;
        rec_transpose_swap_Ntuple(A, B, n2, m, fda, N);
        rec_transpose_swap_Ntuple(A + n2*N*fda, B + n2*N, n - n2, m, fda, N);
     }
     else {
        int m2 = m / 2;
        rec_transpose_swap_Ntuple(A, B, n, m2, fda, N);
        rec_transpose_swap_Ntuple(A + m2*N, B + m2*N*fda, n, m - m2, fda, N);
     }
}

/* Transpose A, an n x n matrix (stored as n x fda), in-place. */
static void rec_transpose_sq_ip_Ntuple(R *A, int n, int fda, int N)
{
     if (n == 1)
        return;
     else if (n*N <= CUTOFF) {
        switch (N) {
            case 1: {
               int i, j;
               for (i = 0; i < n; ++i) {
                  for (j = i + 1; j < n; ++j) {
                       R a = A[(i*fda + j)];
                       A[(i*fda + j)] = A[(j*fda + i)];
                       A[(j*fda + i)] = a;
                  }
               }
               break;
            }
            case 2: {
               int i, j;
               for (i = 0; i < n; ++i) {
                  for (j = i + 1; j < n; ++j) {
                       R a0 = A[(i*fda + j) * 2 + 0];
                       R a1 = A[(i*fda + j) * 2 + 1];
                       A[(i*fda + j) * 2 + 0] = A[(j*fda + i) * 2 + 0];
                       A[(i*fda + j) * 2 + 1] = A[(j*fda + i) * 2 + 1];
                       A[(j*fda + i) * 2 + 0] = a0;
                       A[(j*fda + i) * 2 + 1] = a1;
                  }
               }
               break;
            }
            default: {
               int i, j, k;
               for (i = 0; i < n; ++i) {
                  for (j = i + 1; j < n; ++j) {
                       for (k = 0; k < N; ++k) {
                          R a = A[(i*fda + j) * N + k];
                          A[(i*fda + j) * N + k] = 
                               A[(j*fda + i) * N + k];
                          A[(j*fda + i) * N + k] = a;
                       }
                  }
               }
            }
        }
     } else {
        int n2 = n / 2;
        rec_transpose_sq_ip_Ntuple(A, n2, fda, N);
        rec_transpose_sq_ip_Ntuple((A + n2*N) + n2*N*fda, n - n2, fda, N);
        rec_transpose_swap_Ntuple(A + n2*N, A + n2*N*fda, n2, n - n2, fda,N);
     }
}

/*************************************************************************/
/* In-place transposes of non-square matrices: */

/* Transpose the matrix A in-place, where A is an (n*d) x (m*d) matrix
   of N-tuples and buf contains at least n*m*d*N elements.  In
   general, to transpose a p x q matrix, you should call this routine
   with d = gcd(p, q), n = p/d, and m = q/d. */
void X(transpose)(R *A, int n, int m, int d, int N, R *buf)
{
     A(n > 0 && m > 0 && N > 0 && d > 0);
     if (d == 1) {
        rec_transpose_Ntuple(A, buf, n,m, m,n, N);
        memcpy(A, buf, m*n*N*sizeof(R));
     }
     else if (n*m == 1) {
        rec_transpose_sq_ip_Ntuple(A, d, d, N);
     }
     else {
        int i, num_el = n*m*d*N;

        /* treat as (d x n) x (d' x m) matrix.  (d' = d) */

        /* First, transpose d x (n x d') x m to d x (d' x n) x m,
           using the buf matrix.  This consists of d transposes
           of contiguous n x d' matrices of m-tuples. */
        if (n > 1) {
             for (i = 0; i < d; ++i) {
                rec_transpose_Ntuple(A + i*num_el, buf,
                               n,d, d,n, m*N);
                memcpy(A + i*num_el, buf, num_el*sizeof(R));
             }
        }
        
        /* Now, transpose (d x d') x (n x m) to (d' x d) x (n x m), which
           is a square in-place transpose of n*m-tuples: */
        rec_transpose_sq_ip_Ntuple(A, d, d, n*m*N);

        /* Finally, transpose d' x ((d x n) x m) to d' x (m x (d x n)),
           using the buf matrix.  This consists of d' transposes
           of contiguous d*n x m matrices. */
        if (m > 1) {
             for (i = 0; i < d; ++i) {
                rec_transpose_Ntuple(A + i*num_el, buf,
                               d*n,m, m,d*n, N);
                memcpy(A + i*num_el, buf, num_el*sizeof(R));
             }
        }
     }
}

/*************************************************************************/
/* In-place transpose routine from TOMS.  This routine is much slower
   than the cache-oblivious algorithm above, but is has the advantage
   of requiring less buffer space for the case of gcd(nx,ny) small. */

/*
 * TOMS Transpose.  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.
 * 
 */

void X(transpose_slow)(R *a, int nx, int ny, int N,
                   char *move, int move_size, R *buf)
{
     int i, j, 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;
     
     if (ny == nx) {
        /*
         * if matrix is square, exchange elements a(i,j) and a(j,i):
         */
        for (i = 0; i < nx; ++i)
             for (j = i + 1; j < nx; ++j) {
                memcpy(b, &a[N * (i + j * nx)], N * sizeof(R));
                memcpy(&a[N * (i + j * nx)], &a[N * (j + i * nx)], N * sizeof(R));
                memcpy(&a[N * (j + i * nx)], b, N * sizeof(R));
             }
        return;
     }
     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;
        memcpy(b, &a[N * i1], N * sizeof(R));
        i1c = kmi;
        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;
             }
             memcpy(&a[N * i1], &a[N * i2], 
                  N * sizeof(R));
             memcpy(&a[N * i1c], &a[N * i2c], 
                  N * sizeof(R));
             i1 = i2;
             i1c = i2c;
        }
        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;
        }
     }
}

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