kiss_fftnd.c

/*
Copyright (c) 2003-2004, Mark Borgerding

All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
    * Neither the author nor the names of any contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

#include "kiss_fftnd.h"
#include "_kiss_fft_guts.h"

struct kiss_fftnd_state{
    int dimprod; /* dimsum would be mighty tasty right now */
    int ndims; 
    int *dims;
    kiss_fft_cfg *states; /* cfg states for each dimension */
    kiss_fft_cpx * tmpbuf; /*buffer capable of hold the entire input */
};

kiss_fftnd_cfg kiss_fftnd_alloc(const int *dims,int ndims,int inverse_fft,void*mem,size_t*lenmem)
{
    kiss_fftnd_cfg st = NULL;
    int i;
    int dimprod=1;
    size_t memneeded = sizeof(struct kiss_fftnd_state);
    char * ptr;

    for (i=0;i<ndims;++i) {
        size_t sublen=0;
        kiss_fft_alloc (dims[i], inverse_fft, NULL, &sublen);
        memneeded += sublen;   /* st->states[i] */
        dimprod *= dims[i];
    }
    memneeded += sizeof(int) * ndims;/*  st->dims */
    memneeded += sizeof(void*) * ndims;/* st->states  */
    memneeded += sizeof(kiss_fft_cpx) * dimprod; /* st->tmpbuf */

    if (lenmem == NULL) {/* allocate for the caller*/
        st = (kiss_fftnd_cfg) malloc (memneeded);
    } else { /* initialize supplied buffer if big enough */
        if (*lenmem >= memneeded)
            st = (kiss_fftnd_cfg) mem;
        *lenmem = memneeded; /*tell caller how big struct is (or would be) */
    }
    if (!st)
        return NULL; /*malloc failed or buffer too small */

    st->dimprod = dimprod;
    st->ndims = ndims;
    ptr=(char*)(st+1);

    st->states = (kiss_fft_cfg *)ptr;
    ptr += sizeof(void*) * ndims;

    st->dims = (int*)ptr;
    ptr += sizeof(int) * ndims;

    st->tmpbuf = (kiss_fft_cpx*)ptr;
    ptr += sizeof(kiss_fft_cpx) * dimprod;

    for (i=0;i<ndims;++i) {
        size_t len;
        st->dims[i] = dims[i];
        kiss_fft_alloc (st->dims[i], inverse_fft, NULL, &len);
        st->states[i] = kiss_fft_alloc (st->dims[i], inverse_fft, ptr,&len);
        ptr += len;
    }
    /*
Hi there!

If you're looking at this particular code, it probably means you've got a brain-dead bounds checker 
that thinks the above code overwrites the end of the array.

It doesn't.

-- Mark 

P.S.
The below code might give you some warm fuzzies and help convince you.
       */
    if ( ptr - (char*)st != (int)memneeded ) {
        fprintf(stderr,
                "################################################################################\n"
                "Internal error! Memory allocation miscalculation\n"
                "################################################################################\n"
               );
    }
    return st;
}

/*
 This works by tackling one dimension at a time.

 In effect,
 Each stage starts out by reshaping the matrix into a DixSi 2d matrix.
 A Di-sized fft is taken of each column, transposing the matrix as it goes.

Here's a 3-d example:
Take a 2x3x4 matrix, laid out in memory as a contiguous buffer
 [ [ [ a b c d ] [ e f g h ] [ i j k l ] ]
   [ [ m n o p ] [ q r s t ] [ u v w x ] ] ]

Stage 0 ( D=2): treat the buffer as a 2x12 matrix
   [ [a b ... k l]
     [m n ... w x] ]

   FFT each column with size 2.
   Transpose the matrix at the same time using kiss_fft_stride.

   [ [ a+m a-m ]
     [ b+n b-n]
     ...
     [ k+w k-w ]
     [ l+x l-x ] ]

   Note fft([x y]) == [x+y x-y]

Stage 1 ( D=3) treats the buffer (the output of stage D=2) as an 3x8 matrix,
   [ [ a+m a-m b+n b-n c+o c-o d+p d-p ] 
     [ e+q e-q f+r f-r g+s g-s h+t h-t ]
     [ i+u i-u j+v j-v k+w k-w l+x l-x ] ]

   And perform FFTs (size=3) on each of the columns as above, transposing 
   the matrix as it goes.  The output of stage 1 is 
       (Legend: ap = [ a+m e+q i+u ]
                am = [ a-m e-q i-u ] )
   
   [ [ sum(ap) fft(ap)[0] fft(ap)[1] ]
     [ sum(am) fft(am)[0] fft(am)[1] ]
     [ sum(bp) fft(bp)[0] fft(bp)[1] ]
     [ sum(bm) fft(bm)[0] fft(bm)[1] ]
     [ sum(cp) fft(cp)[0] fft(cp)[1] ]
     [ sum(cm) fft(cm)[0] fft(cm)[1] ]
     [ sum(dp) fft(dp)[0] fft(dp)[1] ]
     [ sum(dm) fft(dm)[0] fft(dm)[1] ]  ]

Stage 2 ( D=4) treats this buffer as a 4*6 matrix,
   [ [ sum(ap) fft(ap)[0] fft(ap)[1] sum(am) fft(am)[0] fft(am)[1] ]
     [ sum(bp) fft(bp)[0] fft(bp)[1] sum(bm) fft(bm)[0] fft(bm)[1] ]
     [ sum(cp) fft(cp)[0] fft(cp)[1] sum(cm) fft(cm)[0] fft(cm)[1] ]
     [ sum(dp) fft(dp)[0] fft(dp)[1] sum(dm) fft(dm)[0] fft(dm)[1] ]  ]

   Then FFTs each column, transposing as it goes.

   The resulting matrix is the 3d FFT of the 2x3x4 input matrix.

   Note as a sanity check that the first element of the final 
   stage's output (DC term) is 
   sum( [ sum(ap) sum(bp) sum(cp) sum(dp) ] )
   , i.e. the summation of all 24 input elements. 

*/
void kiss_fftnd(kiss_fftnd_cfg st,const kiss_fft_cpx *fin,kiss_fft_cpx *fout)
{
    int i,k;
    const kiss_fft_cpx * bufin=fin;
    kiss_fft_cpx * bufout;

    /*arrange it so the last bufout == fout*/
    if ( st->ndims & 1 ) {
        bufout = fout;
        if (fin==fout) {
            memcpy( st->tmpbuf, fin, sizeof(kiss_fft_cpx) * st->dimprod );
            bufin = st->tmpbuf;
        }
    }else
        bufout = st->tmpbuf;

    for ( k=0; k < st->ndims; ++k) {
        int curdim = st->dims[k];
        int stride = st->dimprod / curdim;

        for ( i=0 ; i<stride ; ++i ) 
            kiss_fft_stride( st->states[k], bufin+i , bufout+i*curdim, stride );

        /*toggle back and forth between the two buffers*/
        if (bufout == st->tmpbuf){
            bufout = fout;
            bufin = st->tmpbuf;
        }else{
            bufout = st->tmpbuf;
            bufin = fout;
        }
    }
}