xref: /external/opencv/cxcore/src/cxdxt.cpp

/*M///////////////////////////////////////////////////////////////////////////////////////
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//  If you do not agree to this license, do not download, install,
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//
//                        Intel License Agreement
//                For Open Source Computer Vision Library
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//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
//   * Redistribution's of source code must retain the above copyright notice,
//     this list of conditions and the following disclaimer.
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// loss of use, data, or profits; or business interruption) however caused
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#include "_cxcore.h"

// On Win64 (IA64) optimized versions of DFT and DCT fail the tests
#if defined WIN64 && !defined EM64T
#pragma optimize("", off)
#endif

icvDFTInitAlloc_C_32fc_t icvDFTInitAlloc_C_32fc_p = 0;
icvDFTFree_C_32fc_t icvDFTFree_C_32fc_p = 0;
icvDFTGetBufSize_C_32fc_t icvDFTGetBufSize_C_32fc_p = 0;
icvDFTFwd_CToC_32fc_t icvDFTFwd_CToC_32fc_p = 0;
icvDFTInv_CToC_32fc_t icvDFTInv_CToC_32fc_p = 0;

icvDFTInitAlloc_C_64fc_t icvDFTInitAlloc_C_64fc_p = 0;
icvDFTFree_C_64fc_t icvDFTFree_C_64fc_p = 0;
icvDFTGetBufSize_C_64fc_t icvDFTGetBufSize_C_64fc_p = 0;
icvDFTFwd_CToC_64fc_t icvDFTFwd_CToC_64fc_p = 0;
icvDFTInv_CToC_64fc_t icvDFTInv_CToC_64fc_p = 0;

icvDFTInitAlloc_R_32f_t icvDFTInitAlloc_R_32f_p = 0;
icvDFTFree_R_32f_t icvDFTFree_R_32f_p = 0;
icvDFTGetBufSize_R_32f_t icvDFTGetBufSize_R_32f_p = 0;
icvDFTFwd_RToPack_32f_t icvDFTFwd_RToPack_32f_p = 0;
icvDFTInv_PackToR_32f_t icvDFTInv_PackToR_32f_p = 0;

icvDFTInitAlloc_R_64f_t icvDFTInitAlloc_R_64f_p = 0;
icvDFTFree_R_64f_t icvDFTFree_R_64f_p = 0;
icvDFTGetBufSize_R_64f_t icvDFTGetBufSize_R_64f_p = 0;
icvDFTFwd_RToPack_64f_t icvDFTFwd_RToPack_64f_p = 0;
icvDFTInv_PackToR_64f_t icvDFTInv_PackToR_64f_p = 0;

/*icvDCTFwdInitAlloc_32f_t icvDCTFwdInitAlloc_32f_p = 0;
icvDCTFwdFree_32f_t icvDCTFwdFree_32f_p = 0;
icvDCTFwdGetBufSize_32f_t icvDCTFwdGetBufSize_32f_p = 0;
icvDCTFwd_32f_t icvDCTFwd_32f_p = 0;

icvDCTInvInitAlloc_32f_t icvDCTInvInitAlloc_32f_p = 0;
icvDCTInvFree_32f_t icvDCTInvFree_32f_p = 0;
icvDCTInvGetBufSize_32f_t icvDCTInvGetBufSize_32f_p = 0;
icvDCTInv_32f_t icvDCTInv_32f_p = 0;

icvDCTFwdInitAlloc_64f_t icvDCTFwdInitAlloc_64f_p = 0;
icvDCTFwdFree_64f_t icvDCTFwdFree_64f_p = 0;
icvDCTFwdGetBufSize_64f_t icvDCTFwdGetBufSize_64f_p = 0;
icvDCTFwd_64f_t icvDCTFwd_64f_p = 0;

icvDCTInvInitAlloc_64f_t icvDCTInvInitAlloc_64f_p = 0;
icvDCTInvFree_64f_t icvDCTInvFree_64f_p = 0;
icvDCTInvGetBufSize_64f_t icvDCTInvGetBufSize_64f_p = 0;
icvDCTInv_64f_t icvDCTInv_64f_p = 0;*/

/****************************************************************************************\
                               Discrete Fourier Transform
\****************************************************************************************/

#define CV_MAX_LOCAL_DFT_SIZE  (1 << 15)

static const uchar log2tab[] = { 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0 };
static int icvlog2( int n )
{
    int m = 0;
    int f = (n >= (1 << 16))*16;
    n >>= f;
    m += f;
    f = (n >= (1 << 8))*8;
    n >>= f;
    m += f;
    f = (n >= (1 << 4))*4;
    n >>= f;
    return m + f + log2tab[n];
}

static unsigned char icvRevTable[] =
{
  0x00,0x80,0x40,0xc0,0x20,0xa0,0x60,0xe0,0x10,0x90,0x50,0xd0,0x30,0xb0,0x70,0xf0,
  0x08,0x88,0x48,0xc8,0x28,0xa8,0x68,0xe8,0x18,0x98,0x58,0xd8,0x38,0xb8,0x78,0xf8,
  0x04,0x84,0x44,0xc4,0x24,0xa4,0x64,0xe4,0x14,0x94,0x54,0xd4,0x34,0xb4,0x74,0xf4,
  0x0c,0x8c,0x4c,0xcc,0x2c,0xac,0x6c,0xec,0x1c,0x9c,0x5c,0xdc,0x3c,0xbc,0x7c,0xfc,
  0x02,0x82,0x42,0xc2,0x22,0xa2,0x62,0xe2,0x12,0x92,0x52,0xd2,0x32,0xb2,0x72,0xf2,
  0x0a,0x8a,0x4a,0xca,0x2a,0xaa,0x6a,0xea,0x1a,0x9a,0x5a,0xda,0x3a,0xba,0x7a,0xfa,
  0x06,0x86,0x46,0xc6,0x26,0xa6,0x66,0xe6,0x16,0x96,0x56,0xd6,0x36,0xb6,0x76,0xf6,
  0x0e,0x8e,0x4e,0xce,0x2e,0xae,0x6e,0xee,0x1e,0x9e,0x5e,0xde,0x3e,0xbe,0x7e,0xfe,
  0x01,0x81,0x41,0xc1,0x21,0xa1,0x61,0xe1,0x11,0x91,0x51,0xd1,0x31,0xb1,0x71,0xf1,
  0x09,0x89,0x49,0xc9,0x29,0xa9,0x69,0xe9,0x19,0x99,0x59,0xd9,0x39,0xb9,0x79,0xf9,
  0x05,0x85,0x45,0xc5,0x25,0xa5,0x65,0xe5,0x15,0x95,0x55,0xd5,0x35,0xb5,0x75,0xf5,
  0x0d,0x8d,0x4d,0xcd,0x2d,0xad,0x6d,0xed,0x1d,0x9d,0x5d,0xdd,0x3d,0xbd,0x7d,0xfd,
  0x03,0x83,0x43,0xc3,0x23,0xa3,0x63,0xe3,0x13,0x93,0x53,0xd3,0x33,0xb3,0x73,0xf3,
  0x0b,0x8b,0x4b,0xcb,0x2b,0xab,0x6b,0xeb,0x1b,0x9b,0x5b,0xdb,0x3b,0xbb,0x7b,0xfb,
  0x07,0x87,0x47,0xc7,0x27,0xa7,0x67,0xe7,0x17,0x97,0x57,0xd7,0x37,0xb7,0x77,0xf7,
  0x0f,0x8f,0x4f,0xcf,0x2f,0xaf,0x6f,0xef,0x1f,0x9f,0x5f,0xdf,0x3f,0xbf,0x7f,0xff
};

static const double icvDxtTab[][2] =
{
{ 1.00000000000000000, 0.00000000000000000 },
{-1.00000000000000000, 0.00000000000000000 },
{ 0.00000000000000000, 1.00000000000000000 },
{ 0.70710678118654757, 0.70710678118654746 },
{ 0.92387953251128674, 0.38268343236508978 },
{ 0.98078528040323043, 0.19509032201612825 },
{ 0.99518472667219693, 0.09801714032956060 },
{ 0.99879545620517241, 0.04906767432741802 },
{ 0.99969881869620425, 0.02454122852291229 },
{ 0.99992470183914450, 0.01227153828571993 },
{ 0.99998117528260111, 0.00613588464915448 },
{ 0.99999529380957619, 0.00306795676296598 },
{ 0.99999882345170188, 0.00153398018628477 },
{ 0.99999970586288223, 0.00076699031874270 },
{ 0.99999992646571789, 0.00038349518757140 },
{ 0.99999998161642933, 0.00019174759731070 },
{ 0.99999999540410733, 0.00009587379909598 },
{ 0.99999999885102686, 0.00004793689960307 },
{ 0.99999999971275666, 0.00002396844980842 },
{ 0.99999999992818922, 0.00001198422490507 },
{ 0.99999999998204725, 0.00000599211245264 },
{ 0.99999999999551181, 0.00000299605622633 },
{ 0.99999999999887801, 0.00000149802811317 },
{ 0.99999999999971945, 0.00000074901405658 },
{ 0.99999999999992983, 0.00000037450702829 },
{ 0.99999999999998246, 0.00000018725351415 },
{ 0.99999999999999567, 0.00000009362675707 },
{ 0.99999999999999889, 0.00000004681337854 },
{ 0.99999999999999978, 0.00000002340668927 },
{ 0.99999999999999989, 0.00000001170334463 },
{ 1.00000000000000000, 0.00000000585167232 },
{ 1.00000000000000000, 0.00000000292583616 }
};

#define icvBitRev(i,shift) \
   ((int)((((unsigned)icvRevTable[(i)&255] << 24)+ \
           ((unsigned)icvRevTable[((i)>> 8)&255] << 16)+ \
           ((unsigned)icvRevTable[((i)>>16)&255] <<  8)+ \
           ((unsigned)icvRevTable[((i)>>24)])) >> (shift)))

static int
icvDFTFactorize( int n, int* factors )
{
    int nf = 0, f, i, j;

    if( n <= 5 )
    {
        factors[0] = n;
        return 1;
    }

    f = (((n - 1)^n)+1) >> 1;
    if( f > 1 )
    {
        factors[nf++] = f;
        n = f == n ? 1 : n/f;
    }

    for( f = 3; n > 1; )
    {
        int d = n/f;
        if( d*f == n )
        {
            factors[nf++] = f;
            n = d;
        }
        else
        {
            f += 2;
            if( f*f > n )
                break;
        }
    }

    if( n > 1 )
        factors[nf++] = n;

    f = (factors[0] & 1) == 0;
    for( i = f; i < (nf+f)/2; i++ )
        CV_SWAP( factors[i], factors[nf-i-1+f], j );

    return nf;
}

static void
icvDFTInit( int n0, int nf, int* factors, int* itab, int elem_size, void* _wave, int inv_itab )
{
    int digits[34], radix[34];
    int n = factors[0], m = 0;
    int* itab0 = itab;
    int i, j, k;
    CvComplex64f w, w1;
    double t;

    if( n0 <= 5 )
    {
        itab[0] = 0;
        itab[n0-1] = n0-1;

        if( n0 != 4 )
        {
            for( i = 1; i < n0-1; i++ )
                itab[i] = i;
        }
        else
        {
            itab[1] = 2;
            itab[2] = 1;
        }
        if( n0 == 5 )
        {
            if( elem_size == sizeof(CvComplex64f) )
                ((CvComplex64f*)_wave)[0] = CvComplex64f(1.,0.);
            else
                ((CvComplex32f*)_wave)[0] = CvComplex32f(1.f,0.f);
        }
        if( n0 != 4 )
            return;
        m = 2;
    }
    else
    {
	// radix[] is initialized from index 'nf' down to zero
        assert (nf < 34);
        radix[nf] = 1;
        digits[nf] = 0;
        for( i = 0; i < nf; i++ )
        {
            digits[i] = 0;
            radix[nf-i-1] = radix[nf-i]*factors[nf-i-1];
        }

        if( inv_itab && factors[0] != factors[nf-1] )
            itab = (int*)_wave;

        if( (n & 1) == 0 )
        {
            int a = radix[1], na2 = n*a>>1, na4 = na2 >> 1;
            m = icvlog2(n);

            if( n <= 2  )
            {
                itab[0] = 0;
                itab[1] = na2;
            }
            else if( n <= 256 )
            {
                int shift = 10 - m;
                for( i = 0; i <= n - 4; i += 4 )
                {
                    j = (icvRevTable[i>>2]>>shift)*a;
                    itab[i] = j;
                    itab[i+1] = j + na2;
                    itab[i+2] = j + na4;
                    itab[i+3] = j + na2 + na4;
                }
            }
            else
            {
                int shift = 34 - m;
                for( i = 0; i < n; i += 4 )
                {
                    int i4 = i >> 2;
                    j = icvBitRev(i4,shift)*a;
                    itab[i] = j;
                    itab[i+1] = j + na2;
                    itab[i+2] = j + na4;
                    itab[i+3] = j + na2 + na4;
                }
            }

            digits[1]++;

            if( nf >= 2 )
            {
                for( i = n, j = radix[2]; i < n0; )
                {
                    for( k = 0; k < n; k++ )
                        itab[i+k] = itab[k] + j;
                    if( (i += n) >= n0 )
                        break;
                    j += radix[2];
                    for( k = 1; ++digits[k] >= factors[k]; k++ )
                    {
                        digits[k] = 0;
                        j += radix[k+2] - radix[k];
                    }
                }
            }
        }
        else
        {
            for( i = 0, j = 0;; )
            {
                itab[i] = j;
                if( ++i >= n0 )
                    break;
                j += radix[1];
                for( k = 0; ++digits[k] >= factors[k]; k++ )
                {
                    digits[k] = 0;
                    j += radix[k+2] - radix[k];
                }
            }
        }

        if( itab != itab0 )
        {
            itab0[0] = 0;
            for( i = n0 & 1; i < n0; i += 2 )
            {
                int k0 = itab[i];
                int k1 = itab[i+1];
                itab0[k0] = i;
                itab0[k1] = i+1;
            }
        }
    }

    if( (n0 & (n0-1)) == 0 )
    {
        w.re = w1.re = icvDxtTab[m][0];
        w.im = w1.im = -icvDxtTab[m][1];
    }
    else
    {
        t = -CV_PI*2/n0;
        w.im = w1.im = sin(t);
        w.re = w1.re = sqrt(1. - w1.im*w1.im);
    }
    n = (n0+1)/2;

    if( elem_size == sizeof(CvComplex64f) )
    {
        CvComplex64f* wave = (CvComplex64f*)_wave;

        wave[0].re = 1.;
        wave[0].im = 0.;

        if( (n0 & 1) == 0 )
        {
            wave[n].re = -1.;
            wave[n].im = 0;
        }

        for( i = 1; i < n; i++ )
        {
            wave[i] = w;
            wave[n0-i].re = w.re;
            wave[n0-i].im = -w.im;

            t = w.re*w1.re - w.im*w1.im;
            w.im = w.re*w1.im + w.im*w1.re;
            w.re = t;
        }
    }
    else
    {
        CvComplex32f* wave = (CvComplex32f*)_wave;
        assert( elem_size == sizeof(CvComplex32f) );

        wave[0].re = 1.f;
        wave[0].im = 0.f;

        if( (n0 & 1) == 0 )
        {
            wave[n].re = -1.f;
            wave[n].im = 0.f;
        }

        for( i = 1; i < n; i++ )
        {
            wave[i].re = (float)w.re;
            wave[i].im = (float)w.im;
            wave[n0-i].re = (float)w.re;
            wave[n0-i].im = (float)-w.im;

            t = w.re*w1.re - w.im*w1.im;
            w.im = w.re*w1.im + w.im*w1.re;
            w.re = t;
        }
    }
}


static const double icv_sin_120 = 0.86602540378443864676372317075294;
static const double icv_sin_45 = 0.70710678118654752440084436210485;
static const double icv_fft5_2 = 0.559016994374947424102293417182819;
static const double icv_fft5_3 = -0.951056516295153572116439333379382;
static const double icv_fft5_4 = -1.538841768587626701285145288018455;
static const double icv_fft5_5 = 0.363271264002680442947733378740309;

#define ICV_DFT_NO_PERMUTE 2
#define ICV_DFT_COMPLEX_INPUT_OR_OUTPUT 4

// mixed-radix complex discrete Fourier transform: double-precision version
static CvStatus CV_STDCALL
icvDFT_64fc( const CvComplex64f* src, CvComplex64f* dst, int n,
             int nf, int* factors, const int* itab,
             const CvComplex64f* wave, int tab_size,
             const void* spec, CvComplex64f* buf,
             int flags, double scale )
{
    int n0 = n, f_idx, nx;
    int inv = flags & CV_DXT_INVERSE;
    int dw0 = tab_size, dw;
    int i, j, k;
    CvComplex64f t;
    int tab_step;

    if( spec )
    {
        assert( icvDFTFwd_CToC_64fc_p != 0 && icvDFTInv_CToC_64fc_p != 0 );
        return !inv ?
            icvDFTFwd_CToC_64fc_p( src, dst, spec, buf ):
            icvDFTInv_CToC_64fc_p( src, dst, spec, buf );
    }

    tab_step = tab_size == n ? 1 : tab_size == n*2 ? 2 : tab_size/n;

    // 0. shuffle data
    if( dst != src )
    {
        assert( (flags & ICV_DFT_NO_PERMUTE) == 0 );
        if( !inv )
        {
            for( i = 0; i <= n - 2; i += 2, itab += 2*tab_step )
            {
                int k0 = itab[0], k1 = itab[tab_step];
                assert( (unsigned)k0 < (unsigned)n && (unsigned)k1 < (unsigned)n );
                dst[i] = src[k0]; dst[i+1] = src[k1];
            }

            if( i < n )
                dst[n-1] = src[n-1];
        }
        else
        {
            for( i = 0; i <= n - 2; i += 2, itab += 2*tab_step )
            {
                int k0 = itab[0], k1 = itab[tab_step];
                assert( (unsigned)k0 < (unsigned)n && (unsigned)k1 < (unsigned)n );
                t.re = src[k0].re; t.im = -src[k0].im;
                dst[i] = t;
                t.re = src[k1].re; t.im = -src[k1].im;
                dst[i+1] = t;
            }

            if( i < n )
            {
                t.re = src[n-1].re; t.im = -src[n-1].im;
                dst[i] = t;
            }
        }
    }
    else
    {
        if( (flags & ICV_DFT_NO_PERMUTE) == 0 )
        {
            if( factors[0] != factors[nf-1] )
                return CV_INPLACE_NOT_SUPPORTED_ERR;
            if( nf == 1 )
            {
                if( (n & 3) == 0 )
                {
                    int n2 = n/2;
                    CvComplex64f* dsth = dst + n2;

                    for( i = 0; i < n2; i += 2, itab += tab_step*2 )
                    {
                        j = itab[0];
                        assert( (unsigned)j < (unsigned)n2 );

                        CV_SWAP(dst[i+1], dsth[j], t);
                        if( j > i )
                        {
                            CV_SWAP(dst[i], dst[j], t);
                            CV_SWAP(dsth[i+1], dsth[j+1], t);
                        }
                    }
                }
                // else do nothing
            }
            else
            {
                for( i = 0; i < n; i++, itab += tab_step )
                {
                    j = itab[0];
                    assert( (unsigned)j < (unsigned)n );
                    if( j > i )
                        CV_SWAP(dst[i], dst[j], t);
                }
            }
        }

        if( inv )
        {
            for( i = 0; i <= n - 2; i += 2 )
            {
                double t0 = -dst[i].im;
                double t1 = -dst[i+1].im;
                dst[i].im = t0; dst[i+1].im = t1;
            }

            if( i < n )
                dst[n-1].im = -dst[n-1].im;
        }
    }

    n = 1;
    // 1. power-2 transforms
    if( (factors[0] & 1) == 0 )
    {
        // radix-4 transform
        for( ; n*4 <= factors[0]; )
        {
            nx = n;
            n *= 4;
            dw0 /= 4;

            for( i = 0; i < n0; i += n )
            {
                CvComplex64f* v0;
                CvComplex64f* v1;
                double r0, i0, r1, i1, r2, i2, r3, i3, r4, i4;

                v0 = dst + i;
                v1 = v0 + nx*2;

                r2 = v0[0].re; i2 = v0[0].im;
                r1 = v0[nx].re; i1 = v0[nx].im;

                r0 = r1 + r2; i0 = i1 + i2;
                r2 -= r1; i2 -= i1;

                i3 = v1[nx].re; r3 = v1[nx].im;
                i4 = v1[0].re; r4 = v1[0].im;

                r1 = i4 + i3; i1 = r4 + r3;
                r3 = r4 - r3; i3 = i3 - i4;

                v0[0].re = r0 + r1; v0[0].im = i0 + i1;
                v1[0].re = r0 - r1; v1[0].im = i0 - i1;
                v0[nx].re = r2 + r3; v0[nx].im = i2 + i3;
                v1[nx].re = r2 - r3; v1[nx].im = i2 - i3;

                for( j = 1, dw = dw0; j < nx; j++, dw += dw0 )
                {
                    v0 = dst + i + j;
                    v1 = v0 + nx*2;

                    r2 = v0[nx].re*wave[dw*2].re - v0[nx].im*wave[dw*2].im;
                    i2 = v0[nx].re*wave[dw*2].im + v0[nx].im*wave[dw*2].re;
                    r0 = v1[0].re*wave[dw].im + v1[0].im*wave[dw].re;
                    i0 = v1[0].re*wave[dw].re - v1[0].im*wave[dw].im;
                    r3 = v1[nx].re*wave[dw*3].im + v1[nx].im*wave[dw*3].re;
                    i3 = v1[nx].re*wave[dw*3].re - v1[nx].im*wave[dw*3].im;

                    r1 = i0 + i3; i1 = r0 + r3;
                    r3 = r0 - r3; i3 = i3 - i0;
                    r4 = v0[0].re; i4 = v0[0].im;

                    r0 = r4 + r2; i0 = i4 + i2;
                    r2 = r4 - r2; i2 = i4 - i2;

                    v0[0].re = r0 + r1; v0[0].im = i0 + i1;
                    v1[0].re = r0 - r1; v1[0].im = i0 - i1;
                    v0[nx].re = r2 + r3; v0[nx].im = i2 + i3;
                    v1[nx].re = r2 - r3; v1[nx].im = i2 - i3;
                }
            }
        }

        for( ; n < factors[0]; )
        {
            // do the remaining radix-2 transform
            nx = n;
            n *= 2;
            dw0 /= 2;

            for( i = 0; i < n0; i += n )
            {
                CvComplex64f* v = dst + i;
                double r0 = v[0].re + v[nx].re;
                double i0 = v[0].im + v[nx].im;
                double r1 = v[0].re - v[nx].re;
                double i1 = v[0].im - v[nx].im;
                v[0].re = r0; v[0].im = i0;
                v[nx].re = r1; v[nx].im = i1;

                for( j = 1, dw = dw0; j < nx; j++, dw += dw0 )
                {
                    v = dst + i + j;
                    r1 = v[nx].re*wave[dw].re - v[nx].im*wave[dw].im;
                    i1 = v[nx].im*wave[dw].re + v[nx].re*wave[dw].im;
                    r0 = v[0].re; i0 = v[0].im;

                    v[0].re = r0 + r1; v[0].im = i0 + i1;
                    v[nx].re = r0 - r1; v[nx].im = i0 - i1;
                }
            }
        }
    }

    // 2. all the other transforms
    for( f_idx = (factors[0]&1) ? 0 : 1; f_idx < nf; f_idx++ )
    {
        int factor = factors[f_idx];
        nx = n;
        n *= factor;
        dw0 /= factor;

        if( factor == 3 )
        {
            // radix-3
            for( i = 0; i < n0; i += n )
            {
                CvComplex64f* v = dst + i;

                double r1 = v[nx].re + v[nx*2].re;
                double i1 = v[nx].im + v[nx*2].im;
                double r0 = v[0].re;
                double i0 = v[0].im;
                double r2 = icv_sin_120*(v[nx].im - v[nx*2].im);
                double i2 = icv_sin_120*(v[nx*2].re - v[nx].re);
                v[0].re = r0 + r1; v[0].im = i0 + i1;
                r0 -= 0.5*r1; i0 -= 0.5*i1;
                v[nx].re = r0 + r2; v[nx].im = i0 + i2;
                v[nx*2].re = r0 - r2; v[nx*2].im = i0 - i2;

                for( j = 1, dw = dw0; j < nx; j++, dw += dw0 )
                {
                    v = dst + i + j;
                    r0 = v[nx].re*wave[dw].re - v[nx].im*wave[dw].im;
                    i0 = v[nx].re*wave[dw].im + v[nx].im*wave[dw].re;
                    i2 = v[nx*2].re*wave[dw*2].re - v[nx*2].im*wave[dw*2].im;
                    r2 = v[nx*2].re*wave[dw*2].im + v[nx*2].im*wave[dw*2].re;
                    r1 = r0 + i2; i1 = i0 + r2;

                    r2 = icv_sin_120*(i0 - r2); i2 = icv_sin_120*(i2 - r0);
                    r0 = v[0].re; i0 = v[0].im;
                    v[0].re = r0 + r1; v[0].im = i0 + i1;
                    r0 -= 0.5*r1; i0 -= 0.5*i1;
                    v[nx].re = r0 + r2; v[nx].im = i0 + i2;
                    v[nx*2].re = r0 - r2; v[nx*2].im = i0 - i2;
                }
            }
        }
        else if( factor == 5 )
        {
            // radix-5
            for( i = 0; i < n0; i += n )
            {
                for( j = 0, dw = 0; j < nx; j++, dw += dw0 )
                {
                    CvComplex64f* v0 = dst + i + j;
                    CvComplex64f* v1 = v0 + nx*2;
                    CvComplex64f* v2 = v1 + nx*2;

                    double r0, i0, r1, i1, r2, i2, r3, i3, r4, i4, r5, i5;

                    r3 = v0[nx].re*wave[dw].re - v0[nx].im*wave[dw].im;
                    i3 = v0[nx].re*wave[dw].im + v0[nx].im*wave[dw].re;
                    r2 = v2[0].re*wave[dw*4].re - v2[0].im*wave[dw*4].im;
                    i2 = v2[0].re*wave[dw*4].im + v2[0].im*wave[dw*4].re;

                    r1 = r3 + r2; i1 = i3 + i2;
                    r3 -= r2; i3 -= i2;

                    r4 = v1[nx].re*wave[dw*3].re - v1[nx].im*wave[dw*3].im;
                    i4 = v1[nx].re*wave[dw*3].im + v1[nx].im*wave[dw*3].re;
                    r0 = v1[0].re*wave[dw*2].re - v1[0].im*wave[dw*2].im;
                    i0 = v1[0].re*wave[dw*2].im + v1[0].im*wave[dw*2].re;

                    r2 = r4 + r0; i2 = i4 + i0;
                    r4 -= r0; i4 -= i0;

                    r0 = v0[0].re; i0 = v0[0].im;
                    r5 = r1 + r2; i5 = i1 + i2;

                    v0[0].re = r0 + r5; v0[0].im = i0 + i5;

                    r0 -= 0.25*r5; i0 -= 0.25*i5;
                    r1 = icv_fft5_2*(r1 - r2); i1 = icv_fft5_2*(i1 - i2);
                    r2 = -icv_fft5_3*(i3 + i4); i2 = icv_fft5_3*(r3 + r4);

                    i3 *= -icv_fft5_5; r3 *= icv_fft5_5;
                    i4 *= -icv_fft5_4; r4 *= icv_fft5_4;

                    r5 = r2 + i3; i5 = i2 + r3;
                    r2 -= i4; i2 -= r4;

                    r3 = r0 + r1; i3 = i0 + i1;
                    r0 -= r1; i0 -= i1;

                    v0[nx].re = r3 + r2; v0[nx].im = i3 + i2;
                    v2[0].re = r3 - r2; v2[0].im = i3 - i2;

                    v1[0].re = r0 + r5; v1[0].im = i0 + i5;
                    v1[nx].re = r0 - r5; v1[nx].im = i0 - i5;
                }
            }
        }
        else
        {
            // radix-"factor" - an odd number
            int p, q, factor2 = (factor - 1)/2;
            int d, dd, dw_f = tab_size/factor;
            CvComplex64f* a = buf;
            CvComplex64f* b = buf + factor2;

            for( i = 0; i < n0; i += n )
            {
                for( j = 0, dw = 0; j < nx; j++, dw += dw0 )
                {
                    CvComplex64f* v = dst + i + j;
                    CvComplex64f v_0 = v[0];
                    CvComplex64f vn_0 = v_0;

                    if( j == 0 )
                    {
                        for( p = 1, k = nx; p <= factor2; p++, k += nx )
                        {
                            double r0 = v[k].re + v[n-k].re;
                            double i0 = v[k].im - v[n-k].im;
                            double r1 = v[k].re - v[n-k].re;
                            double i1 = v[k].im + v[n-k].im;

                            vn_0.re += r0; vn_0.im += i1;
                            a[p-1].re = r0; a[p-1].im = i0;
                            b[p-1].re = r1; b[p-1].im = i1;
                        }
                    }
                    else
                    {
                        const CvComplex64f* wave_ = wave + dw*factor;
                        d = dw;

                        for( p = 1, k = nx; p <= factor2; p++, k += nx, d += dw )
                        {
                            double r2 = v[k].re*wave[d].re - v[k].im*wave[d].im;
                            double i2 = v[k].re*wave[d].im + v[k].im*wave[d].re;

                            double r1 = v[n-k].re*wave_[-d].re - v[n-k].im*wave_[-d].im;
                            double i1 = v[n-k].re*wave_[-d].im + v[n-k].im*wave_[-d].re;

                            double r0 = r2 + r1;
                            double i0 = i2 - i1;
                            r1 = r2 - r1;
                            i1 = i2 + i1;

                            vn_0.re += r0; vn_0.im += i1;
                            a[p-1].re = r0; a[p-1].im = i0;
                            b[p-1].re = r1; b[p-1].im = i1;
                        }
                    }

                    v[0] = vn_0;

                    for( p = 1, k = nx; p <= factor2; p++, k += nx )
                    {
                        CvComplex64f s0 = v_0, s1 = v_0;
                        d = dd = dw_f*p;

                        for( q = 0; q < factor2; q++ )
                        {
                            double r0 = wave[d].re * a[q].re;
                            double i0 = wave[d].im * a[q].im;
                            double r1 = wave[d].re * b[q].im;
                            double i1 = wave[d].im * b[q].re;

                            s1.re += r0 + i0; s0.re += r0 - i0;
                            s1.im += r1 - i1; s0.im += r1 + i1;

                            d += dd;
                            d -= -(d >= tab_size) & tab_size;
                        }

                        v[k] = s0;
                        v[n-k] = s1;
                    }
                }
            }
        }
    }

    if( fabs(scale - 1.) > DBL_EPSILON )
    {
        double re_scale = scale, im_scale = scale;
        if( inv )
            im_scale = -im_scale;

        for( i = 0; i < n0; i++ )
        {
            double t0 = dst[i].re*re_scale;
            double t1 = dst[i].im*im_scale;
            dst[i].re = t0;
            dst[i].im = t1;
        }
    }
    else if( inv )
    {
        for( i = 0; i <= n0 - 2; i += 2 )
        {
            double t0 = -dst[i].im;
            double t1 = -dst[i+1].im;
            dst[i].im = t0;
            dst[i+1].im = t1;
        }

        if( i < n0 )
            dst[n0-1].im = -dst[n0-1].im;
    }

    return CV_OK;
}


// mixed-radix complex discrete Fourier transform: single-precision version
static CvStatus CV_STDCALL
icvDFT_32fc( const CvComplex32f* src, CvComplex32f* dst, int n,
             int nf, int* factors, const int* itab,
             const CvComplex32f* wave, int tab_size,
             const void* spec, CvComplex32f* buf,
             int flags, double scale )
{
    int n0 = n, f_idx, nx;
    int inv = flags & CV_DXT_INVERSE;
    int dw0 = tab_size, dw;
    int i, j, k;
    CvComplex32f t;
    int tab_step = tab_size == n ? 1 : tab_size == n*2 ? 2 : tab_size/n;

    if( spec )
    {
        assert( icvDFTFwd_CToC_32fc_p != 0 && icvDFTInv_CToC_32fc_p != 0 );
        return !inv ?
            icvDFTFwd_CToC_32fc_p( src, dst, spec, buf ):
            icvDFTInv_CToC_32fc_p( src, dst, spec, buf );
    }

    // 0. shuffle data
    if( dst != src )
    {
        assert( (flags & ICV_DFT_NO_PERMUTE) == 0 );
        if( !inv )
        {
            for( i = 0; i <= n - 2; i += 2, itab += 2*tab_step )
            {
                int k0 = itab[0], k1 = itab[tab_step];
                assert( (unsigned)k0 < (unsigned)n && (unsigned)k1 < (unsigned)n );
                dst[i] = src[k0]; dst[i+1] = src[k1];
            }

            if( i < n )
                dst[n-1] = src[n-1];
        }
        else
        {
            for( i = 0; i <= n - 2; i += 2, itab += 2*tab_step )
            {
                int k0 = itab[0], k1 = itab[tab_step];
                assert( (unsigned)k0 < (unsigned)n && (unsigned)k1 < (unsigned)n );
                t.re = src[k0].re; t.im = -src[k0].im;
                dst[i] = t;
                t.re = src[k1].re; t.im = -src[k1].im;
                dst[i+1] = t;
            }

            if( i < n )
            {
                t.re = src[n-1].re; t.im = -src[n-1].im;
                dst[i] = t;
            }
        }
    }
    else
    {
        if( (flags & ICV_DFT_NO_PERMUTE) == 0 )
        {
            if( factors[0] != factors[nf-1] )
                return CV_INPLACE_NOT_SUPPORTED_ERR;
            if( nf == 1 )
            {
                if( (n & 3) == 0 )
                {
                    int n2 = n/2;
                    CvComplex32f* dsth = dst + n2;

                    for( i = 0; i < n2; i += 2, itab += tab_step*2 )
                    {
                        j = itab[0];
                        assert( (unsigned)j < (unsigned)n2 );

                        CV_SWAP(dst[i+1], dsth[j], t);
                        if( j > i )
                        {
                            CV_SWAP(dst[i], dst[j], t);
                            CV_SWAP(dsth[i+1], dsth[j+1], t);
                        }
                    }
                }
                // else do nothing
            }
            else
            {
                for( i = 0;
                i < n;
                i++)
                {
                    j = itab[0];
                    assert( (unsigned)j < (unsigned)n );
                    if( j > i )
                        CV_SWAP(dst[i], dst[j], t);
                    itab += tab_step;
                }
            }
        }

        if( inv )
        {
            // conjugate the vector - i.e. invert sign of the imaginary part
            int* idst = (int*)dst;
            for( i = 0; i <= n - 2; i += 2 )
            {
                int t0 = idst[i*2+1] ^ 0x80000000;
                int t1 = idst[i*2+3] ^ 0x80000000;
                idst[i*2+1] = t0; idst[i*2+3] = t1;
            }

            if( i < n )
                idst[2*i+1] ^= 0x80000000;
        }
    }

    n = 1;
    // 1. power-2 transforms
    if( (factors[0] & 1) == 0 )
    {
        // radix-4 transform
        for( ; n*4 <= factors[0]; )
        {
            nx = n;
            n *= 4;
            dw0 /= 4;

            for( i = 0; i < n0; i += n )
            {
                CvComplex32f* v0;
                CvComplex32f* v1;
                double r0, i0, r1, i1, r2, i2, r3, i3, r4, i4;

                v0 = dst + i;
                v1 = v0 + nx*2;

                r2 = v0[0].re; i2 = v0[0].im;
                r1 = v0[nx].re; i1 = v0[nx].im;

                r0 = r1 + r2; i0 = i1 + i2;
                r2 -= r1; i2 -= i1;

                i3 = v1[nx].re; r3 = v1[nx].im;
                i4 = v1[0].re; r4 = v1[0].im;

                r1 = i4 + i3; i1 = r4 + r3;
                r3 = r4 - r3; i3 = i3 - i4;

                v0[0].re = (float)(r0 + r1); v0[0].im = (float)(i0 + i1);
                v1[0].re = (float)(r0 - r1); v1[0].im = (float)(i0 - i1);
                v0[nx].re = (float)(r2 + r3); v0[nx].im = (float)(i2 + i3);
                v1[nx].re = (float)(r2 - r3); v1[nx].im = (float)(i2 - i3);

                for( j = 1, dw = dw0; j < nx; j++, dw += dw0 )
                {
                    v0 = dst + i + j;
                    v1 = v0 + nx*2;

                    r2 = v0[nx].re*wave[dw*2].re - v0[nx].im*wave[dw*2].im;
                    i2 = v0[nx].re*wave[dw*2].im + v0[nx].im*wave[dw*2].re;
                    r0 = v1[0].re*wave[dw].im + v1[0].im*wave[dw].re;
                    i0 = v1[0].re*wave[dw].re - v1[0].im*wave[dw].im;
                    r3 = v1[nx].re*wave[dw*3].im + v1[nx].im*wave[dw*3].re;
                    i3 = v1[nx].re*wave[dw*3].re - v1[nx].im*wave[dw*3].im;

                    r1 = i0 + i3; i1 = r0 + r3;
                    r3 = r0 - r3; i3 = i3 - i0;
                    r4 = v0[0].re; i4 = v0[0].im;

                    r0 = r4 + r2; i0 = i4 + i2;
                    r2 = r4 - r2; i2 = i4 - i2;

                    v0[0].re = (float)(r0 + r1); v0[0].im = (float)(i0 + i1);
                    v1[0].re = (float)(r0 - r1); v1[0].im = (float)(i0 - i1);
                    v0[nx].re = (float)(r2 + r3); v0[nx].im = (float)(i2 + i3);
                    v1[nx].re = (float)(r2 - r3); v1[nx].im = (float)(i2 - i3);
                }
            }
        }

        for( ; n < factors[0]; )
        {
            // do the remaining radix-2 transform
            nx = n;
            n *= 2;
            dw0 /= 2;

            for( i = 0; i < n0; i += n )
            {
                CvComplex32f* v = dst + i;
                double r0 = v[0].re + v[nx].re;
                double i0 = v[0].im + v[nx].im;
                double r1 = v[0].re - v[nx].re;
                double i1 = v[0].im - v[nx].im;
                v[0].re = (float)r0; v[0].im = (float)i0;
                v[nx].re = (float)r1; v[nx].im = (float)i1;

                for( j = 1, dw = dw0; j < nx; j++, dw += dw0 )
                {
                    v = dst + i + j;
                    r1 = v[nx].re*wave[dw].re - v[nx].im*wave[dw].im;
                    i1 = v[nx].im*wave[dw].re + v[nx].re*wave[dw].im;
                    r0 = v[0].re; i0 = v[0].im;

                    v[0].re = (float)(r0 + r1); v[0].im = (float)(i0 + i1);
                    v[nx].re = (float)(r0 - r1); v[nx].im = (float)(i0 - i1);
                }
            }
        }
    }

    // 2. all the other transforms
    for( f_idx = (factors[0]&1) ? 0 : 1; f_idx < nf; f_idx++ )
    {
        int factor = factors[f_idx];
        nx = n;
        n *= factor;
        dw0 /= factor;

        if( factor == 3 )
        {
            // radix-3
            for( i = 0; i < n0; i += n )
            {
                CvComplex32f* v = dst + i;

                double r1 = v[nx].re + v[nx*2].re;
                double i1 = v[nx].im + v[nx*2].im;
                double r0 = v[0].re;
                double i0 = v[0].im;
                double r2 = icv_sin_120*(v[nx].im - v[nx*2].im);
                double i2 = icv_sin_120*(v[nx*2].re - v[nx].re);
                v[0].re = (float)(r0 + r1); v[0].im = (float)(i0 + i1);
                r0 -= 0.5*r1; i0 -= 0.5*i1;
                v[nx].re = (float)(r0 + r2); v[nx].im = (float)(i0 + i2);
                v[nx*2].re = (float)(r0 - r2); v[nx*2].im = (float)(i0 - i2);

                for( j = 1, dw = dw0; j < nx; j++, dw += dw0 )
                {
                    v = dst + i + j;
                    r0 = v[nx].re*wave[dw].re - v[nx].im*wave[dw].im;
                    i0 = v[nx].re*wave[dw].im + v[nx].im*wave[dw].re;
                    i2 = v[nx*2].re*wave[dw*2].re - v[nx*2].im*wave[dw*2].im;
                    r2 = v[nx*2].re*wave[dw*2].im + v[nx*2].im*wave[dw*2].re;
                    r1 = r0 + i2; i1 = i0 + r2;

                    r2 = icv_sin_120*(i0 - r2); i2 = icv_sin_120*(i2 - r0);
                    r0 = v[0].re; i0 = v[0].im;
                    v[0].re = (float)(r0 + r1); v[0].im = (float)(i0 + i1);
                    r0 -= 0.5*r1; i0 -= 0.5*i1;
                    v[nx].re = (float)(r0 + r2); v[nx].im = (float)(i0 + i2);
                    v[nx*2].re = (float)(r0 - r2); v[nx*2].im = (float)(i0 - i2);
                }
            }
        }
        else if( factor == 5 )
        {
            // radix-5
            for( i = 0; i < n0; i += n )
            {
                for( j = 0, dw = 0; j < nx; j++, dw += dw0 )
                {
                    CvComplex32f* v0 = dst + i + j;
                    CvComplex32f* v1 = v0 + nx*2;
                    CvComplex32f* v2 = v1 + nx*2;

                    double r0, i0, r1, i1, r2, i2, r3, i3, r4, i4, r5, i5;

                    r3 = v0[nx].re*wave[dw].re - v0[nx].im*wave[dw].im;
                    i3 = v0[nx].re*wave[dw].im + v0[nx].im*wave[dw].re;
                    r2 = v2[0].re*wave[dw*4].re - v2[0].im*wave[dw*4].im;
                    i2 = v2[0].re*wave[dw*4].im + v2[0].im*wave[dw*4].re;

                    r1 = r3 + r2; i1 = i3 + i2;
                    r3 -= r2; i3 -= i2;

                    r4 = v1[nx].re*wave[dw*3].re - v1[nx].im*wave[dw*3].im;
                    i4 = v1[nx].re*wave[dw*3].im + v1[nx].im*wave[dw*3].re;
                    r0 = v1[0].re*wave[dw*2].re - v1[0].im*wave[dw*2].im;
                    i0 = v1[0].re*wave[dw*2].im + v1[0].im*wave[dw*2].re;

                    r2 = r4 + r0; i2 = i4 + i0;
                    r4 -= r0; i4 -= i0;

                    r0 = v0[0].re; i0 = v0[0].im;
                    r5 = r1 + r2; i5 = i1 + i2;

                    v0[0].re = (float)(r0 + r5); v0[0].im = (float)(i0 + i5);

                    r0 -= 0.25*r5; i0 -= 0.25*i5;
                    r1 = icv_fft5_2*(r1 - r2); i1 = icv_fft5_2*(i1 - i2);
                    r2 = -icv_fft5_3*(i3 + i4); i2 = icv_fft5_3*(r3 + r4);

                    i3 *= -icv_fft5_5; r3 *= icv_fft5_5;
                    i4 *= -icv_fft5_4; r4 *= icv_fft5_4;

                    r5 = r2 + i3; i5 = i2 + r3;
                    r2 -= i4; i2 -= r4;

                    r3 = r0 + r1; i3 = i0 + i1;
                    r0 -= r1; i0 -= i1;

                    v0[nx].re = (float)(r3 + r2); v0[nx].im = (float)(i3 + i2);
                    v2[0].re = (float)(r3 - r2); v2[0].im = (float)(i3 - i2);

                    v1[0].re = (float)(r0 + r5); v1[0].im = (float)(i0 + i5);
                    v1[nx].re = (float)(r0 - r5); v1[nx].im = (float)(i0 - i5);
                }
            }
        }
        else
        {
            // radix-"factor" - an odd number
            int p, q, factor2 = (factor - 1)/2;
            int d, dd, dw_f = tab_size/factor;
            CvComplex32f* a = buf;
            CvComplex32f* b = buf + factor2;

            for( i = 0; i < n0; i += n )
            {
                for( j = 0, dw = 0; j < nx; j++, dw += dw0 )
                {
                    CvComplex32f* v = dst + i + j;
                    CvComplex32f v_0 = v[0];
                    CvComplex64f vn_0(v_0);

                    if( j == 0 )
                    {
                        for( p = 1, k = nx; p <= factor2; p++, k += nx )
                        {
                            double r0 = v[k].re + v[n-k].re;
                            double i0 = v[k].im - v[n-k].im;
                            double r1 = v[k].re - v[n-k].re;
                            double i1 = v[k].im + v[n-k].im;

                            vn_0.re += r0; vn_0.im += i1;
                            a[p-1].re = (float)r0; a[p-1].im = (float)i0;
                            b[p-1].re = (float)r1; b[p-1].im = (float)i1;
                        }
                    }
                    else
                    {
                        const CvComplex32f* wave_ = wave + dw*factor;
                        d = dw;

                        for( p = 1, k = nx; p <= factor2; p++, k += nx, d += dw )
                        {
                            double r2 = v[k].re*wave[d].re - v[k].im*wave[d].im;
                            double i2 = v[k].re*wave[d].im + v[k].im*wave[d].re;

                            double r1 = v[n-k].re*wave_[-d].re - v[n-k].im*wave_[-d].im;
                            double i1 = v[n-k].re*wave_[-d].im + v[n-k].im*wave_[-d].re;

                            double r0 = r2 + r1;
                            double i0 = i2 - i1;
                            r1 = r2 - r1;
                            i1 = i2 + i1;

                            vn_0.re += r0; vn_0.im += i1;
                            a[p-1].re = (float)r0; a[p-1].im = (float)i0;
                            b[p-1].re = (float)r1; b[p-1].im = (float)i1;
                        }
                    }

                    v[0].re = (float)vn_0.re;
                    v[0].im = (float)vn_0.im;

                    for( p = 1, k = nx; p <= factor2; p++, k += nx )
                    {
                        CvComplex64f s0(v_0), s1 = s0;
                        d = dd = dw_f*p;

                        for( q = 0; q < factor2; q++ )
                        {
                            double r0 = wave[d].re * a[q].re;
                            double i0 = wave[d].im * a[q].im;
                            double r1 = wave[d].re * b[q].im;
                            double i1 = wave[d].im * b[q].re;

                            s1.re += r0 + i0; s0.re += r0 - i0;
                            s1.im += r1 - i1; s0.im += r1 + i1;

                            d += dd;
                            d -= -(d >= tab_size) & tab_size;
                        }

                        v[k].re = (float)s0.re;
                        v[k].im = (float)s0.im;
                        v[n-k].re = (float)s1.re;
                        v[n-k].im = (float)s1.im;
                    }
                }
            }
        }
    }

    if( fabs(scale - 1.) > DBL_EPSILON )
    {
        double re_scale = scale, im_scale = scale;
        if( inv )
            im_scale = -im_scale;

        for( i = 0; i < n0; i++ )
        {
            double t0 = dst[i].re*re_scale;
            double t1 = dst[i].im*im_scale;
            dst[i].re = (float)t0;
            dst[i].im = (float)t1;
        }
    }
    else if( inv )
    {
        for( i = 0; i <= n0 - 2; i += 2 )
        {
            double t0 = -dst[i].im;
            double t1 = -dst[i+1].im;
            dst[i].im = (float)t0;
            dst[i+1].im = (float)t1;
        }

        if( i < n0 )
            dst[n0-1].im = -dst[n0-1].im;
    }

    return CV_OK;
}


/* FFT of real vector
   output vector format:
     re(0), re(1), im(1), ... , re(n/2-1), im((n+1)/2-1) [, re((n+1)/2)] OR ...
     re(0), 0, re(1), im(1), ..., re(n/2-1), im((n+1)/2-1) [, re((n+1)/2), 0] */
#define ICV_REAL_DFT( flavor, datatype )                                \
static CvStatus CV_STDCALL                                              \
icvRealDFT_##flavor( const datatype* src, datatype* dst,                \
                     int n, int nf, int* factors, const int* itab,      \
                     const CvComplex##flavor* wave, int tab_size,       \
                     const void* spec, CvComplex##flavor* buf,          \
                     int flags, double scale )                          \
{                                                                       \
    int complex_output = (flags & ICV_DFT_COMPLEX_INPUT_OR_OUTPUT) != 0;\
    int j, n2 = n >> 1;                                                 \
    dst += complex_output;                                              \
                                                                        \
    if( spec )                                                          \
    {                                                                   \
        icvDFTFwd_RToPack_##flavor##_p( src, dst, spec, buf );          \
        goto finalize;                                                  \
    }                                                                   \
                                                                        \
    assert( tab_size == n );                                            \
                                                                        \
    if( n == 1 )                                                        \
    {                                                                   \
        dst[0] = (datatype)(src[0]*scale);                              \
    }                                                                   \
    else if( n == 2 )                                                   \
    {                                                                   \
        double t = (src[0] + src[1])*scale;                             \
        dst[1] = (datatype)((src[0] - src[1])*scale);                   \
        dst[0] = (datatype)t;                                           \
    }                                                                   \
    else if( n & 1 )                                                    \
    {                                                                   \
        dst -= complex_output;                                          \
        CvComplex##flavor* _dst = (CvComplex##flavor*)dst;              \
        _dst[0].re = (datatype)(src[0]*scale);                          \
        _dst[0].im = 0;                                                 \
        for( j = 1; j < n; j += 2 )                                     \
        {                                                               \
            double t0 = src[itab[j]]*scale;                             \
            double t1 = src[itab[j+1]]*scale;                           \
            _dst[j].re = (datatype)t0;                                  \
            _dst[j].im = 0;                                             \
            _dst[j+1].re = (datatype)t1;                                \
            _dst[j+1].im = 0;                                           \
        }                                                               \
        icvDFT_##flavor##c( _dst, _dst, n, nf, factors, itab, wave,     \
                            tab_size, 0, buf, ICV_DFT_NO_PERMUTE, 1. ); \
        if( !complex_output )                                           \
            dst[1] = dst[0];                                            \
        return CV_OK;                                                   \
    }                                                                   \
    else                                                                \
    {                                                                   \
        double t0, t;                                                   \
        double h1_re, h1_im, h2_re, h2_im;                              \
        double scale2 = scale*0.5;                                      \
        factors[0] >>= 1;                                               \
                                                                        \
        icvDFT_##flavor##c( (CvComplex##flavor*)src,                    \
                            (CvComplex##flavor*)dst, n2,                \
                            nf - (factors[0] == 1),                     \
                            factors + (factors[0] == 1),                \
                            itab, wave, tab_size, 0, buf, 0, 1. );      \
        factors[0] <<= 1;                                               \
                                                                        \
        t = dst[0] - dst[1];                                            \
        dst[0] = (datatype)((dst[0] + dst[1])*scale);                   \
        dst[1] = (datatype)(t*scale);                                   \
                                                                        \
        t0 = dst[n2];                                                   \
        t = dst[n-1];                                                   \
        dst[n-1] = dst[1];                                              \
                                                                        \
        for( j = 2, wave++; j < n2; j += 2, wave++ )                    \
        {                                                               \
            /* calc odd */                                              \
            h2_re = scale2*(dst[j+1] + t);                              \
            h2_im = scale2*(dst[n-j] - dst[j]);                         \
                                                                        \
            /* calc even */                                             \
            h1_re = scale2*(dst[j] + dst[n-j]);                         \
            h1_im = scale2*(dst[j+1] - t);                              \
                                                                        \
            /* rotate */                                                \
            t = h2_re*wave->re - h2_im*wave->im;                        \
            h2_im = h2_re*wave->im + h2_im*wave->re;                    \
            h2_re = t;                                                  \
            t = dst[n-j-1];                                             \
                                                                        \
            dst[j-1] = (datatype)(h1_re + h2_re);                       \
            dst[n-j-1] = (datatype)(h1_re - h2_re);                     \
            dst[j] = (datatype)(h1_im + h2_im);                         \
            dst[n-j] = (datatype)(h2_im - h1_im);                       \
        }                                                               \
                                                                        \
        if( j <= n2 )                                                   \
        {                                                               \
            dst[n2-1] = (datatype)(t0*scale);                           \
            dst[n2] = (datatype)(-t*scale);                             \
        }                                                               \
    }                                                                   \
                                                                        \
finalize:                                                               \
    if( complex_output )                                                \
    {                                                                   \
        dst[-1] = dst[0];                                               \
        dst[0] = 0;                                                     \
        if( (n & 1) == 0 )                                              \
            dst[n] = 0;                                                 \
    }                                                                   \
                                                                        \
    return CV_OK;                                                       \
}


/* Inverse FFT of complex conjugate-symmetric vector
   input vector format:
      re[0], re[1], im[1], ... , re[n/2-1], im[n/2-1], re[n/2] OR
      re(0), 0, re(1), im(1), ..., re(n/2-1), im((n+1)/2-1) [, re((n+1)/2), 0] */
#define ICV_CCS_IDFT( flavor, datatype )                                \
static CvStatus CV_STDCALL                                              \
icvCCSIDFT_##flavor( const datatype* src, datatype* dst,                \
                     int n, int nf, int* factors, const int* itab,      \
                     const CvComplex##flavor* wave, int tab_size,       \
                     const void* spec, CvComplex##flavor* buf,          \
                     int flags, double scale )                          \
{                                                                       \
    int complex_input = (flags & ICV_DFT_COMPLEX_INPUT_OR_OUTPUT) != 0; \
    int j, k, n2 = (n+1) >> 1;                                          \
    double save_s1 = 0.;                                                \
    double t0, t1, t2, t3, t;                                           \
                                                                        \
    assert( tab_size == n );                                            \
                                                                        \
    if( complex_input )                                                 \
    {                                                                   \
        assert( src != dst );                                           \
        save_s1 = src[1];                                               \
        ((datatype*)src)[1] = src[0];                                   \
        src++;                                                          \
    }                                                                   \
                                                                        \
    if( spec )                                                          \
    {                                                                   \
        icvDFTInv_PackToR_##flavor##_p( src, dst, spec, buf );          \
        goto finalize;                                                  \
    }                                                                   \
                                                                        \
    if( n == 1 )                                                        \
    {                                                                   \
        dst[0] = (datatype)(src[0]*scale);                              \
    }                                                                   \
    else if( n == 2 )                                                   \
    {                                                                   \
        t = (src[0] + src[1])*scale;                                    \
        dst[1] = (datatype)((src[0] - src[1])*scale);                   \
        dst[0] = (datatype)t;                                           \
    }                                                                   \
    else if( n & 1 )                                                    \
    {                                                                   \
        CvComplex##flavor* _src = (CvComplex##flavor*)(src-1);          \
        CvComplex##flavor* _dst = (CvComplex##flavor*)dst;              \
                                                                        \
        _dst[0].re = src[0];                                            \
        _dst[0].im = 0;                                                 \
        for( j = 1; j < n2; j++ )                                       \
        {                                                               \
            int k0 = itab[j], k1 = itab[n-j];                           \
            t0 = _src[j].re; t1 = _src[j].im;                           \
            _dst[k0].re = (datatype)t0; _dst[k0].im = (datatype)-t1;    \
            _dst[k1].re = (datatype)t0; _dst[k1].im = (datatype)t1;     \
        }                                                               \
                                                                        \
        icvDFT_##flavor##c( _dst, _dst, n, nf, factors, itab, wave,     \
                            tab_size, 0, buf, ICV_DFT_NO_PERMUTE, 1. ); \
        dst[0] = (datatype)(dst[0]*scale);                              \
        for( j = 1; j < n; j += 2 )                                     \
        {                                                               \
            t0 = dst[j*2]*scale;                                        \
            t1 = dst[j*2+2]*scale;                                      \
            dst[j] = (datatype)t0;                                      \
            dst[j+1] = (datatype)t1;                                    \
        }                                                               \
    }                                                                   \
    else                                                                \
    {                                                                   \
        int inplace = src == dst;                                       \
        const CvComplex##flavor* w = wave;                              \
                                                                        \
        t = src[1];                                                     \
        t0 = (src[0] + src[n-1]);                                       \
        t1 = (src[n-1] - src[0]);                                       \
        dst[0] = (datatype)t0;                                          \
        dst[1] = (datatype)t1;                                          \
                                                                        \
        for( j = 2, w++; j < n2; j += 2, w++ )                          \
        {                                                               \
            double h1_re, h1_im, h2_re, h2_im;                          \
                                                                        \
            h1_re = (t + src[n-j-1]);                                   \
            h1_im = (src[j] - src[n-j]);                                \
                                                                        \
            h2_re = (t - src[n-j-1]);                                   \
            h2_im = (src[j] + src[n-j]);                                \
                                                                        \
            t = h2_re*w->re + h2_im*w->im;                              \
            h2_im = h2_im*w->re - h2_re*w->im;                          \
            h2_re = t;                                                  \
                                                                        \
            t = src[j+1];                                               \
            t0 = h1_re - h2_im;                                         \
            t1 = -h1_im - h2_re;                                        \
            t2 = h1_re + h2_im;                                         \
            t3 = h1_im - h2_re;                                         \
                                                                        \
            if( inplace )                                               \
            {                                                           \
                dst[j] = (datatype)t0;                                  \
                dst[j+1] = (datatype)t1;                                \
                dst[n-j] = (datatype)t2;                                \
                dst[n-j+1]= (datatype)t3;                               \
            }                                                           \
            else                                                        \
            {                                                           \
                int j2 = j >> 1;                                        \
                k = itab[j2];                                           \
                dst[k] = (datatype)t0;                                  \
                dst[k+1] = (datatype)t1;                                \
                k = itab[n2-j2];                                        \
                dst[k] = (datatype)t2;                                  \
                dst[k+1]= (datatype)t3;                                 \
            }                                                           \
        }                                                               \
                                                                        \
        if( j <= n2 )                                                   \
        {                                                               \
            t0 = t*2;                                                   \
            t1 = src[n2]*2;                                             \
                                                                        \
            if( inplace )                                               \
            {                                                           \
                dst[n2] = (datatype)t0;                                 \
                dst[n2+1] = (datatype)t1;                               \
            }                                                           \
            else                                                        \
            {                                                           \
                k = itab[n2];                                           \
                dst[k*2] = (datatype)t0;                                \
                dst[k*2+1] = (datatype)t1;                              \
            }                                                           \
        }                                                               \
                                                                        \
        factors[0] >>= 1;                                               \
        icvDFT_##flavor##c( (CvComplex##flavor*)dst,                    \
                            (CvComplex##flavor*)dst, n2,                \
                            nf - (factors[0] == 1),                     \
                            factors + (factors[0] == 1), itab,          \
                            wave, tab_size, 0, buf,                     \
                            inplace ? 0 : ICV_DFT_NO_PERMUTE, 1. );     \
        factors[0] <<= 1;                                               \
                                                                        \
        for( j = 0; j < n; j += 2 )                                     \
        {                                                               \
            t0 = dst[j]*scale;                                          \
            t1 = dst[j+1]*(-scale);                                     \
            dst[j] = (datatype)t0;                                      \
            dst[j+1] = (datatype)t1;                                    \
        }                                                               \
    }                                                                   \
                                                                        \
finalize:                                                               \
    if( complex_input )                                                 \
        ((datatype*)src)[0] = (datatype)save_s1;                        \
                                                                        \
    return CV_OK;                                                       \
}


ICV_REAL_DFT( 64f, double )
ICV_CCS_IDFT( 64f, double )
ICV_REAL_DFT( 32f, float )
ICV_CCS_IDFT( 32f, float )


static void
icvCopyColumn( const uchar* _src, int src_step,
               uchar* _dst, int dst_step,
               int len, int elem_size )
{
    int i, t0, t1;
    const int* src = (const int*)_src;
    int* dst = (int*)_dst;
    src_step /= sizeof(src[0]);
    dst_step /= sizeof(dst[0]);

    if( elem_size == sizeof(int) )
    {
        for( i = 0; i < len; i++, src += src_step, dst += dst_step )
            dst[0] = src[0];
    }
    else if( elem_size == sizeof(int)*2 )
    {
        for( i = 0; i < len; i++, src += src_step, dst += dst_step )
        {
            t0 = src[0]; t1 = src[1];
            dst[0] = t0; dst[1] = t1;
        }
    }
    else if( elem_size == sizeof(int)*4 )
    {
        for( i = 0; i < len; i++, src += src_step, dst += dst_step )
        {
            t0 = src[0]; t1 = src[1];
            dst[0] = t0; dst[1] = t1;
            t0 = src[2]; t1 = src[3];
            dst[2] = t0; dst[3] = t1;
        }
    }
}


static void
icvCopyFrom2Columns( const uchar* _src, int src_step,
                     uchar* _dst0, uchar* _dst1,
                     int len, int elem_size )
{
    int i, t0, t1;
    const int* src = (const int*)_src;
    int* dst0 = (int*)_dst0;
    int* dst1 = (int*)_dst1;
    src_step /= sizeof(src[0]);

    if( elem_size == sizeof(int) )
    {
        for( i = 0; i < len; i++, src += src_step )
        {
            t0 = src[0]; t1 = src[1];
            dst0[i] = t0; dst1[i] = t1;
        }
    }
    else if( elem_size == sizeof(int)*2 )
    {
        for( i = 0; i < len*2; i += 2, src += src_step )
        {
            t0 = src[0]; t1 = src[1];
            dst0[i] = t0; dst0[i+1] = t1;
            t0 = src[2]; t1 = src[3];
            dst1[i] = t0; dst1[i+1] = t1;
        }
    }
    else if( elem_size == sizeof(int)*4 )
    {
        for( i = 0; i < len*4; i += 4, src += src_step )
        {
            t0 = src[0]; t1 = src[1];
            dst0[i] = t0; dst0[i+1] = t1;
            t0 = src[2]; t1 = src[3];
            dst0[i+2] = t0; dst0[i+3] = t1;
            t0 = src[4]; t1 = src[5];
            dst1[i] = t0; dst1[i+1] = t1;
            t0 = src[6]; t1 = src[7];
            dst1[i+2] = t0; dst1[i+3] = t1;
        }
    }
}


static void
icvCopyTo2Columns( const uchar* _src0, const uchar* _src1,
                   uchar* _dst, int dst_step,
                   int len, int elem_size )
{
    int i, t0, t1;
    const int* src0 = (const int*)_src0;
    const int* src1 = (const int*)_src1;
    int* dst = (int*)_dst;
    dst_step /= sizeof(dst[0]);

    if( elem_size == sizeof(int) )
    {
        for( i = 0; i < len; i++, dst += dst_step )
        {
            t0 = src0[i]; t1 = src1[i];
            dst[0] = t0; dst[1] = t1;
        }
    }
    else if( elem_size == sizeof(int)*2 )
    {
        for( i = 0; i < len*2; i += 2, dst += dst_step )
        {
            t0 = src0[i]; t1 = src0[i+1];
            dst[0] = t0; dst[1] = t1;
            t0 = src1[i]; t1 = src1[i+1];
            dst[2] = t0; dst[3] = t1;
        }
    }
    else if( elem_size == sizeof(int)*4 )
    {
        for( i = 0; i < len*4; i += 4, dst += dst_step )
        {
            t0 = src0[i]; t1 = src0[i+1];
            dst[0] = t0; dst[1] = t1;
            t0 = src0[i+2]; t1 = src0[i+3];
            dst[2] = t0; dst[3] = t1;
            t0 = src1[i]; t1 = src1[i+1];
            dst[4] = t0; dst[5] = t1;
            t0 = src1[i+2]; t1 = src1[i+3];
            dst[6] = t0; dst[7] = t1;
        }
    }
}


static void
icvExpandCCS( uchar* _ptr, int len, int elem_size )
{
    int i;
    _ptr -= elem_size;
    memcpy( _ptr, _ptr + elem_size, elem_size );
    memset( _ptr + elem_size, 0, elem_size );
    if( (len & 1) == 0 )
        memset( _ptr + (len+1)*elem_size, 0, elem_size );

    if( elem_size == sizeof(float) )
    {
        CvComplex32f* ptr = (CvComplex32f*)_ptr;

        for( i = 1; i < (len+1)/2; i++ )
        {
            CvComplex32f t;
            t.re = ptr[i].re;
            t.im = -ptr[i].im;
            ptr[len-i] = t;
        }
    }
    else
    {
        CvComplex64f* ptr = (CvComplex64f*)_ptr;

        for( i = 1; i < (len+1)/2; i++ )
        {
            CvComplex64f t;
            t.re = ptr[i].re;
            t.im = -ptr[i].im;
            ptr[len-i] = t;
        }
    }
}


typedef CvStatus (CV_STDCALL *CvDFTFunc)(
     const void* src, void* dst, int n, int nf, int* factors,
     const int* itab, const void* wave, int tab_size,
     const void* spec, void* buf, int inv, double scale );

CV_IMPL void
cvDFT( const CvArr* srcarr, CvArr* dstarr, int flags, int nonzero_rows )
{
    static CvDFTFunc dft_tbl[6];
    static int inittab = 0;

    void* buffer = 0;
    int local_alloc = 1;
    int depth = -1;
    void *spec_c = 0, *spec_r = 0, *spec = 0;

    CV_FUNCNAME( "cvDFT" );

    __BEGIN__;

    int prev_len = 0, buf_size = 0, stage = 0;
    int nf = 0, inv = (flags & CV_DXT_INVERSE) != 0;
    int real_transform = 0;
    CvMat *src = (CvMat*)srcarr, *dst = (CvMat*)dstarr;
    CvMat srcstub, dststub, *src0;
    int complex_elem_size, elem_size;
    int factors[34], inplace_transform = 0;
    int ipp_norm_flag = 0;

    if( !inittab )
    {
        dft_tbl[0] = (CvDFTFunc)icvDFT_32fc;
        dft_tbl[1] = (CvDFTFunc)icvRealDFT_32f;
        dft_tbl[2] = (CvDFTFunc)icvCCSIDFT_32f;
        dft_tbl[3] = (CvDFTFunc)icvDFT_64fc;
        dft_tbl[4] = (CvDFTFunc)icvRealDFT_64f;
        dft_tbl[5] = (CvDFTFunc)icvCCSIDFT_64f;
        inittab = 1;
    }

    if( !CV_IS_MAT( src ))
    {
        int coi = 0;
        CV_CALL( src = cvGetMat( src, &srcstub, &coi ));

        if( coi != 0 )
            CV_ERROR( CV_BadCOI, "" );
    }

    if( !CV_IS_MAT( dst ))
    {
        int coi = 0;
        CV_CALL( dst = cvGetMat( dst, &dststub, &coi ));

        if( coi != 0 )
            CV_ERROR( CV_BadCOI, "" );
    }

    src0 = src;
    elem_size = CV_ELEM_SIZE1(src->type);
    complex_elem_size = elem_size*2;

    // check types and sizes
    if( !CV_ARE_DEPTHS_EQ(src, dst) )
        CV_ERROR( CV_StsUnmatchedFormats, "" );

    depth = CV_MAT_DEPTH(src->type);
    if( depth < CV_32F )
        CV_ERROR( CV_StsUnsupportedFormat,
        "Only 32fC1, 32fC2, 64fC1 and 64fC2 formats are supported" );

    if( CV_ARE_CNS_EQ(src, dst) )
    {
        if( CV_MAT_CN(src->type) > 2 )
            CV_ERROR( CV_StsUnsupportedFormat,
            "Only 32fC1, 32fC2, 64fC1 and 64fC2 formats are supported" );

        if( !CV_ARE_SIZES_EQ(src, dst) )
            CV_ERROR( CV_StsUnmatchedSizes, "" );
        real_transform = CV_MAT_CN(src->type) == 1;
        if( !real_transform )
            elem_size = complex_elem_size;
    }
    else if( !inv && CV_MAT_CN(src->type) == 1 && CV_MAT_CN(dst->type) == 2 )
    {
        if( (src->cols != 1 || dst->cols != 1 ||
            (src->rows/2+1 != dst->rows && src->rows != dst->rows)) &&
            (src->cols/2+1 != dst->cols || src->rows != dst->rows) )
            CV_ERROR( CV_StsUnmatchedSizes, "" );
        real_transform = 1;
    }
    else if( inv && CV_MAT_CN(src->type) == 2 && CV_MAT_CN(dst->type) == 1 )
    {
        if( (src->cols != 1 || dst->cols != 1 ||
            (dst->rows/2+1 != src->rows && src->rows != dst->rows)) &&
            (dst->cols/2+1 != src->cols || src->rows != dst->rows) )
            CV_ERROR( CV_StsUnmatchedSizes, "" );
        real_transform = 1;
    }
    else
        CV_ERROR( CV_StsUnmatchedFormats,
        "Incorrect or unsupported combination of input & output formats" );

    if( src->cols == 1 && nonzero_rows > 0 )
        CV_ERROR( CV_StsNotImplemented,
        "This mode (using nonzero_rows with a single-column matrix) breaks the function logic, so it is prohibited.\n"
        "For fast convolution/correlation use 2-column matrix or single-row matrix instead" );

    // determine, which transform to do first - row-wise
    // (stage 0) or column-wise (stage 1) transform
    if( !(flags & CV_DXT_ROWS) && src->rows > 1 &&
        ((src->cols == 1 && !CV_IS_MAT_CONT(src->type & dst->type)) ||
        (src->cols > 1 && inv && real_transform)) )
        stage = 1;

    ipp_norm_flag = !(flags & CV_DXT_SCALE) ? 8 : (flags & CV_DXT_INVERSE) ? 2 : 1;

    for(;;)
    {
        double scale = 1;
        uchar* wave = 0;
        int* itab = 0;
        uchar* ptr;
        int i, len, count, sz = 0;
        int use_buf = 0, odd_real = 0;
        CvDFTFunc dft_func;

        if( stage == 0 ) // row-wise transform
        {
            len = !inv ? src->cols : dst->cols;
            count = src->rows;
            if( len == 1 && !(flags & CV_DXT_ROWS) )
            {
                len = !inv ? src->rows : dst->rows;
                count = 1;
            }
            odd_real = real_transform && (len & 1);
        }
        else
        {
            len = dst->rows;
            count = !inv ? src0->cols : dst->cols;
            sz = 2*len*complex_elem_size;
        }

        spec = 0;
        if( len*count >= 64 && icvDFTInitAlloc_R_32f_p != 0 ) // use IPP DFT if available
        {
            int ipp_sz = 0;

            if( real_transform && stage == 0 )
            {
                if( depth == CV_32F )
                {
                    if( spec_r )
                        IPPI_CALL( icvDFTFree_R_32f_p( spec_r ));
                    IPPI_CALL( icvDFTInitAlloc_R_32f_p(
                        &spec_r, len, ipp_norm_flag, cvAlgHintNone ));
                    IPPI_CALL( icvDFTGetBufSize_R_32f_p( spec_r, &ipp_sz ));
                }
                else
                {
                    if( spec_r )
                        IPPI_CALL( icvDFTFree_R_64f_p( spec_r ));
                    IPPI_CALL( icvDFTInitAlloc_R_64f_p(
                        &spec_r, len, ipp_norm_flag, cvAlgHintNone ));
                    IPPI_CALL( icvDFTGetBufSize_R_64f_p( spec_r, &ipp_sz ));
                }
                spec = spec_r;
            }
            else
            {
                if( depth == CV_32F )
                {
                    if( spec_c )
                        IPPI_CALL( icvDFTFree_C_32fc_p( spec_c ));
                    IPPI_CALL( icvDFTInitAlloc_C_32fc_p(
                        &spec_c, len, ipp_norm_flag, cvAlgHintNone ));
                    IPPI_CALL( icvDFTGetBufSize_C_32fc_p( spec_c, &ipp_sz ));
                }
                else
                {
                    if( spec_c )
                        IPPI_CALL( icvDFTFree_C_64fc_p( spec_c ));
                    IPPI_CALL( icvDFTInitAlloc_C_64fc_p(
                        &spec_c, len, ipp_norm_flag, cvAlgHintNone ));
                    IPPI_CALL( icvDFTGetBufSize_C_64fc_p( spec_c, &ipp_sz ));
                }
                spec = spec_c;
            }

            sz += ipp_sz;
        }
        else
        {
            if( len != prev_len )
                nf = icvDFTFactorize( len, factors );

            inplace_transform = factors[0] == factors[nf-1];
            sz += len*(complex_elem_size + sizeof(int));
            i = nf > 1 && (factors[0] & 1) == 0;
            if( (factors[i] & 1) != 0 && factors[i] > 5 )
                sz += (factors[i]+1)*complex_elem_size;

            if( (stage == 0 && ((src->data.ptr == dst->data.ptr && !inplace_transform) || odd_real)) ||
                (stage == 1 && !inplace_transform) )
            {
                use_buf = 1;
                sz += len*complex_elem_size;
            }
        }

        if( sz > buf_size )
        {
            prev_len = 0; // because we release the buffer,
                          // force recalculation of
                          // twiddle factors and permutation table
            if( !local_alloc && buffer )
                cvFree( &buffer );
            if( sz <= CV_MAX_LOCAL_DFT_SIZE )
            {
                buf_size = sz = CV_MAX_LOCAL_DFT_SIZE;
                buffer = cvStackAlloc(sz + 32);
                local_alloc = 1;
            }
            else
            {
                CV_CALL( buffer = cvAlloc(sz + 32) );
                buf_size = sz;
                local_alloc = 0;
            }
        }

        ptr = (uchar*)buffer;
        if( !spec )
        {
            wave = ptr;
            ptr += len*complex_elem_size;
            itab = (int*)ptr;
            ptr = (uchar*)cvAlignPtr( ptr + len*sizeof(int), 16 );

            if( len != prev_len || (!inplace_transform && inv && real_transform))
                icvDFTInit( len, nf, factors, itab, complex_elem_size,
                            wave, stage == 0 && inv && real_transform );
            // otherwise reuse the tables calculated on the previous stage
        }

        if( stage == 0 )
        {
            uchar* tmp_buf = 0;
            int dptr_offset = 0;
            int dst_full_len = len*elem_size;
            int _flags = inv + (CV_MAT_CN(src->type) != CV_MAT_CN(dst->type) ?
                         ICV_DFT_COMPLEX_INPUT_OR_OUTPUT : 0);
            if( use_buf )
            {
                tmp_buf = ptr;
                ptr += len*complex_elem_size;
                if( odd_real && !inv && len > 1 &&
                    !(_flags & ICV_DFT_COMPLEX_INPUT_OR_OUTPUT))
                    dptr_offset = elem_size;
            }

            if( !inv && (_flags & ICV_DFT_COMPLEX_INPUT_OR_OUTPUT) )
                dst_full_len += (len & 1) ? elem_size : complex_elem_size;

            dft_func = dft_tbl[(!real_transform ? 0 : !inv ? 1 : 2) + (depth == CV_64F)*3];

            if( count > 1 && !(flags & CV_DXT_ROWS) && (!inv || !real_transform) )
                stage = 1;
            else if( flags & CV_DXT_SCALE )
                scale = 1./(len * (flags & CV_DXT_ROWS ? 1 : count));

            if( nonzero_rows <= 0 || nonzero_rows > count )
                nonzero_rows = count;

            for( i = 0; i < nonzero_rows; i++ )
            {
                uchar* sptr = src->data.ptr + i*src->step;
                uchar* dptr0 = dst->data.ptr + i*dst->step;
                uchar* dptr = dptr0;

                if( tmp_buf )
                    dptr = tmp_buf;

                dft_func( sptr, dptr, len, nf, factors, itab, wave, len, spec, ptr, _flags, scale );
                if( dptr != dptr0 )
                    memcpy( dptr0, dptr + dptr_offset, dst_full_len );
            }

            for( ; i < count; i++ )
            {
                uchar* dptr0 = dst->data.ptr + i*dst->step;
                memset( dptr0, 0, dst_full_len );
            }

            if( stage != 1 )
                break;
            src = dst;
        }
        else
        {
            int a = 0, b = count;
            uchar *buf0, *buf1, *dbuf0, *dbuf1;
            uchar* sptr0 = src->data.ptr;
            uchar* dptr0 = dst->data.ptr;
            buf0 = ptr;
            ptr += len*complex_elem_size;
            buf1 = ptr;
            ptr += len*complex_elem_size;
            dbuf0 = buf0, dbuf1 = buf1;

            if( use_buf )
            {
                dbuf1 = ptr;
                dbuf0 = buf1;
                ptr += len*complex_elem_size;
            }

            dft_func = dft_tbl[(depth == CV_64F)*3];

            if( real_transform && inv && src->cols > 1 )
                stage = 0;
            else if( flags & CV_DXT_SCALE )
                scale = 1./(len * count);

            if( real_transform )
            {
                int even;
                a = 1;
                even = (count & 1) == 0;
                b = (count+1)/2;
                if( !inv )
                {
                    memset( buf0, 0, len*complex_elem_size );
                    icvCopyColumn( sptr0, src->step, buf0, complex_elem_size, len, elem_size );
                    sptr0 += CV_MAT_CN(dst->type)*elem_size;
                    if( even )
                    {
                        memset( buf1, 0, len*complex_elem_size );
                        icvCopyColumn( sptr0 + (count-2)*elem_size, src->step,
                                       buf1, complex_elem_size, len, elem_size );
                    }
                }
                else if( CV_MAT_CN(src->type) == 1 )
                {
                    icvCopyColumn( sptr0, src->step, buf0 + elem_size, elem_size, len, elem_size );
                    icvExpandCCS( buf0 + elem_size, len, elem_size );
                    if( even )
                    {
                        icvCopyColumn( sptr0 + (count-1)*elem_size, src->step,
                                       buf1 + elem_size, elem_size, len, elem_size );
                        icvExpandCCS( buf1 + elem_size, len, elem_size );
                    }
                    sptr0 += elem_size;
                }
                else
                {
                    icvCopyColumn( sptr0, src->step, buf0, complex_elem_size, len, complex_elem_size );
                    //memcpy( buf0 + elem_size, buf0, elem_size );
                    //icvExpandCCS( buf0 + elem_size, len, elem_size );
                    if( even )
                    {
                        icvCopyColumn( sptr0 + b*complex_elem_size, src->step,
                                       buf1, complex_elem_size, len, complex_elem_size );
                        //memcpy( buf0 + elem_size, buf0, elem_size );
                        //icvExpandCCS( buf0 + elem_size, len, elem_size );
                    }
                    sptr0 += complex_elem_size;
                }

                if( even )
                    IPPI_CALL( dft_func( buf1, dbuf1, len, nf, factors, itab,
                                         wave, len, spec, ptr, inv, scale ));
                IPPI_CALL( dft_func( buf0, dbuf0, len, nf, factors, itab,
                                     wave, len, spec, ptr, inv, scale ));

                if( CV_MAT_CN(dst->type) == 1 )
                {
                    if( !inv )
                    {
                        // copy the half of output vector to the first/last column.
                        // before doing that, defgragment the vector
                        memcpy( dbuf0 + elem_size, dbuf0, elem_size );
                        icvCopyColumn( dbuf0 + elem_size, elem_size, dptr0,
                                       dst->step, len, elem_size );
                        if( even )
                        {
                            memcpy( dbuf1 + elem_size, dbuf1, elem_size );
                            icvCopyColumn( dbuf1 + elem_size, elem_size,
                                           dptr0 + (count-1)*elem_size,
                                           dst->step, len, elem_size );
                        }
                        dptr0 += elem_size;
                    }
                    else
                    {
                        // copy the real part of the complex vector to the first/last column
                        icvCopyColumn( dbuf0, complex_elem_size, dptr0, dst->step, len, elem_size );
                        if( even )
                            icvCopyColumn( dbuf1, complex_elem_size, dptr0 + (count-1)*elem_size,
                                           dst->step, len, elem_size );
                        dptr0 += elem_size;
                    }
                }
                else
                {
                    assert( !inv );
                    icvCopyColumn( dbuf0, complex_elem_size, dptr0,
                                   dst->step, len, complex_elem_size );
                    if( even )
                        icvCopyColumn( dbuf1, complex_elem_size,
                                       dptr0 + b*complex_elem_size,
                                       dst->step, len, complex_elem_size );
                    dptr0 += complex_elem_size;
                }
            }

            for( i = a; i < b; i += 2 )
            {
                if( i+1 < b )
                {
                    icvCopyFrom2Columns( sptr0, src->step, buf0, buf1, len, complex_elem_size );
                    IPPI_CALL( dft_func( buf1, dbuf1, len, nf, factors, itab,
                                         wave, len, spec, ptr, inv, scale ));
                }
                else
                    icvCopyColumn( sptr0, src->step, buf0, complex_elem_size, len, complex_elem_size );

                IPPI_CALL( dft_func( buf0, dbuf0, len, nf, factors, itab,
                                     wave, len, spec, ptr, inv, scale ));

                if( i+1 < b )
                    icvCopyTo2Columns( dbuf0, dbuf1, dptr0, dst->step, len, complex_elem_size );
                else
                    icvCopyColumn( dbuf0, complex_elem_size, dptr0, dst->step, len, complex_elem_size );
                sptr0 += 2*complex_elem_size;
                dptr0 += 2*complex_elem_size;
            }

            if( stage != 0 )
                break;
            src = dst;
        }
    }

    __END__;

    if( buffer && !local_alloc )
        cvFree( &buffer );

    if( spec_c )
    {
        if( depth == CV_32F )
            icvDFTFree_C_32fc_p( spec_c );
        else
            icvDFTFree_C_64fc_p( spec_c );
    }

    if( spec_r )
    {
        if( depth == CV_32F )
            icvDFTFree_R_32f_p( spec_r );
        else
            icvDFTFree_R_64f_p( spec_r );
    }
}


CV_IMPL void
cvMulSpectrums( const CvArr* srcAarr, const CvArr* srcBarr,
                CvArr* dstarr, int flags )
{
    CV_FUNCNAME( "cvMulSpectrums" );

    __BEGIN__;

    CvMat stubA, *srcA = (CvMat*)srcAarr;
    CvMat stubB, *srcB = (CvMat*)srcBarr;
    CvMat dststub, *dst = (CvMat*)dstarr;
    int stepA, stepB, stepC;
    int type, cn, is_1d;
    int j, j0, j1, k, rows, cols, ncols;

    if( !CV_IS_MAT(srcA))
        CV_CALL( srcA = cvGetMat( srcA, &stubA, 0 ));

    if( !CV_IS_MAT(srcB))
        CV_CALL( srcB = cvGetMat( srcB, &stubB, 0 ));

    if( !CV_IS_MAT(dst))
        CV_CALL( dst = cvGetMat( dst, &dststub, 0 ));

    if( !CV_ARE_TYPES_EQ( srcA, srcB ) || !CV_ARE_TYPES_EQ( srcA, dst ))
        CV_ERROR( CV_StsUnmatchedFormats, "" );

    if( !CV_ARE_SIZES_EQ( srcA, srcB ) || !CV_ARE_SIZES_EQ( srcA, dst ))
        CV_ERROR( CV_StsUnmatchedSizes, "" );

    type = CV_MAT_TYPE( dst->type );
    cn = CV_MAT_CN(type);
    rows = srcA->rows;
    cols = srcA->cols;
    is_1d = (flags & CV_DXT_ROWS) ||
            (rows == 1 || (cols == 1 &&
             CV_IS_MAT_CONT( srcA->type & srcB->type & dst->type )));

    if( is_1d && !(flags & CV_DXT_ROWS) )
        cols = cols + rows - 1, rows = 1;
    ncols = cols*cn;
    j0 = cn == 1;
    j1 = ncols - (cols % 2 == 0 && cn == 1);

    if( CV_MAT_DEPTH(type) == CV_32F )
    {
        float* dataA = srcA->data.fl;
        float* dataB = srcB->data.fl;
        float* dataC = dst->data.fl;

        stepA = srcA->step/sizeof(dataA[0]);
        stepB = srcB->step/sizeof(dataB[0]);
        stepC = dst->step/sizeof(dataC[0]);

        if( !is_1d && cn == 1 )
        {
            for( k = 0; k < (cols % 2 ? 1 : 2); k++ )
            {
                if( k == 1 )
                    dataA += cols - 1, dataB += cols - 1, dataC += cols - 1;
                dataC[0] = dataA[0]*dataB[0];
                if( rows % 2 == 0 )
                    dataC[(rows-1)*stepC] = dataA[(rows-1)*stepA]*dataB[(rows-1)*stepB];
                if( !(flags & CV_DXT_MUL_CONJ) )
                    for( j = 1; j <= rows - 2; j += 2 )
                    {
                        double re = (double)dataA[j*stepA]*dataB[j*stepB] -
                                    (double)dataA[(j+1)*stepA]*dataB[(j+1)*stepB];
                        double im = (double)dataA[j*stepA]*dataB[(j+1)*stepB] +
                                    (double)dataA[(j+1)*stepA]*dataB[j*stepB];
                        dataC[j*stepC] = (float)re; dataC[(j+1)*stepC] = (float)im;
                    }
                else
                    for( j = 1; j <= rows - 2; j += 2 )
                    {
                        double re = (double)dataA[j*stepA]*dataB[j*stepB] +
                                    (double)dataA[(j+1)*stepA]*dataB[(j+1)*stepB];
                        double im = (double)dataA[(j+1)*stepA]*dataB[j*stepB] -
                                    (double)dataA[j*stepA]*dataB[(j+1)*stepB];
                        dataC[j*stepC] = (float)re; dataC[(j+1)*stepC] = (float)im;
                    }
                if( k == 1 )
                    dataA -= cols - 1, dataB -= cols - 1, dataC -= cols - 1;
            }
        }

        for( ; rows--; dataA += stepA, dataB += stepB, dataC += stepC )
        {
            if( is_1d && cn == 1 )
            {
                dataC[0] = dataA[0]*dataB[0];
                if( cols % 2 == 0 )
                    dataC[j1] = dataA[j1]*dataB[j1];
            }

            if( !(flags & CV_DXT_MUL_CONJ) )
                for( j = j0; j < j1; j += 2 )
                {
                    double re = (double)dataA[j]*dataB[j] - (double)dataA[j+1]*dataB[j+1];
                    double im = (double)dataA[j+1]*dataB[j] + (double)dataA[j]*dataB[j+1];
                    dataC[j] = (float)re; dataC[j+1] = (float)im;
                }
            else
                for( j = j0; j < j1; j += 2 )
                {
                    double re = (double)dataA[j]*dataB[j] + (double)dataA[j+1]*dataB[j+1];
                    double im = (double)dataA[j+1]*dataB[j] - (double)dataA[j]*dataB[j+1];
                    dataC[j] = (float)re; dataC[j+1] = (float)im;
                }
        }
    }
    else if( CV_MAT_DEPTH(type) == CV_64F )
    {
        double* dataA = srcA->data.db;
        double* dataB = srcB->data.db;
        double* dataC = dst->data.db;

        stepA = srcA->step/sizeof(dataA[0]);
        stepB = srcB->step/sizeof(dataB[0]);
        stepC = dst->step/sizeof(dataC[0]);

        if( !is_1d && cn == 1 )
        {
            for( k = 0; k < (cols % 2 ? 1 : 2); k++ )
            {
                if( k == 1 )
                    dataA += cols - 1, dataB += cols - 1, dataC += cols - 1;
                dataC[0] = dataA[0]*dataB[0];
                if( rows % 2 == 0 )
                    dataC[(rows-1)*stepC] = dataA[(rows-1)*stepA]*dataB[(rows-1)*stepB];
                if( !(flags & CV_DXT_MUL_CONJ) )
                    for( j = 1; j <= rows - 2; j += 2 )
                    {
                        double re = dataA[j*stepA]*dataB[j*stepB] -
                                    dataA[(j+1)*stepA]*dataB[(j+1)*stepB];
                        double im = dataA[j*stepA]*dataB[(j+1)*stepB] +
                                    dataA[(j+1)*stepA]*dataB[j*stepB];
                        dataC[j*stepC] = re; dataC[(j+1)*stepC] = im;
                    }
                else
                    for( j = 1; j <= rows - 2; j += 2 )
                    {
                        double re = dataA[j*stepA]*dataB[j*stepB] +
                                    dataA[(j+1)*stepA]*dataB[(j+1)*stepB];
                        double im = dataA[(j+1)*stepA]*dataB[j*stepB] -
                                    dataA[j*stepA]*dataB[(j+1)*stepB];
                        dataC[j*stepC] = re; dataC[(j+1)*stepC] = im;
                    }
                if( k == 1 )
                    dataA -= cols - 1, dataB -= cols - 1, dataC -= cols - 1;
            }
        }

        for( ; rows--; dataA += stepA, dataB += stepB, dataC += stepC )
        {
            if( is_1d && cn == 1 )
            {
                dataC[0] = dataA[0]*dataB[0];
                if( cols % 2 == 0 )
                    dataC[j1] = dataA[j1]*dataB[j1];
            }

            if( !(flags & CV_DXT_MUL_CONJ) )
                for( j = j0; j < j1; j += 2 )
                {
                    double re = dataA[j]*dataB[j] - dataA[j+1]*dataB[j+1];
                    double im = dataA[j+1]*dataB[j] + dataA[j]*dataB[j+1];
                    dataC[j] = re; dataC[j+1] = im;
                }
            else
                for( j = j0; j < j1; j += 2 )
                {
                    double re = dataA[j]*dataB[j] + dataA[j+1]*dataB[j+1];
                    double im = dataA[j+1]*dataB[j] - dataA[j]*dataB[j+1];
                    dataC[j] = re; dataC[j+1] = im;
                }
        }
    }
    else
    {
        CV_ERROR( CV_StsUnsupportedFormat, "Only 32f and 64f types are supported" );
    }

    __END__;
}


/****************************************************************************************\
                               Discrete Cosine Transform
\****************************************************************************************/

/* DCT is calculated using DFT, as described here:
   http://www.ece.utexas.edu/~bevans/courses/ee381k/lectures/09_DCT/lecture9/:
*/
#define ICV_DCT_FWD( flavor, datatype )                                 \
static CvStatus CV_STDCALL                                              \
icvDCT_fwd_##flavor( const datatype* src, int src_step, datatype* dft_src,\
                     datatype* dft_dst, datatype* dst, int dst_step,    \
                     int n, int nf, int* factors, const int* itab,      \
                     const CvComplex##flavor* dft_wave,                 \
                     const CvComplex##flavor* dct_wave,                 \
                     const void* spec, CvComplex##flavor* buf )         \
{                                                                       \
    int j, n2 = n >> 1;                                                 \
                                                                        \
    src_step /= sizeof(src[0]);                                         \
    dst_step /= sizeof(dst[0]);                                         \
    datatype* dst1 = dst + (n-1)*dst_step;                              \
                                                                        \
    if( n == 1 )                                                        \
    {                                                                   \
        dst[0] = src[0];                                                \
        return CV_OK;                                                   \
    }                                                                   \
                                                                        \
    for( j = 0; j < n2; j++, src += src_step*2 )                        \
    {                                                                   \
        dft_src[j] = src[0];                                            \
        dft_src[n-j-1] = src[src_step];                                 \
    }                                                                   \
                                                                        \
    icvRealDFT_##flavor( dft_src, dft_dst, n, nf, factors,              \
                         itab, dft_wave, n, spec, buf, 0, 1.0 );        \
    src = dft_dst;                                                      \
                                                                        \
    dst[0] = (datatype)(src[0]*dct_wave->re*icv_sin_45);                \
    dst += dst_step;                                                    \
    for( j = 1, dct_wave++; j < n2; j++, dct_wave++,                    \
                                    dst += dst_step, dst1 -= dst_step ) \
    {                                                                   \
        double t0 = dct_wave->re*src[j*2-1] - dct_wave->im*src[j*2];    \
        double t1 = -dct_wave->im*src[j*2-1] - dct_wave->re*src[j*2];   \
        dst[0] = (datatype)t0;                                          \
        dst1[0] = (datatype)t1;                                         \
    }                                                                   \
                                                                        \
    dst[0] = (datatype)(src[n-1]*dct_wave->re);                         \
    return CV_OK;                                                       \
}


#define ICV_DCT_INV( flavor, datatype )                                 \
static CvStatus CV_STDCALL                                              \
icvDCT_inv_##flavor( const datatype* src, int src_step, datatype* dft_src,\
                     datatype* dft_dst, datatype* dst, int dst_step,    \
                     int n, int nf, int* factors, const int* itab,      \
                     const CvComplex##flavor* dft_wave,                 \
                     const CvComplex##flavor* dct_wave,                 \
                     const void* spec, CvComplex##flavor* buf )         \
{                                                                       \
    int j, n2 = n >> 1;                                                 \
                                                                        \
    src_step /= sizeof(src[0]);                                         \
    dst_step /= sizeof(dst[0]);                                         \
    const datatype* src1 = src + (n-1)*src_step;                        \
                                                                        \
    if( n == 1 )                                                        \
    {                                                                   \
        dst[0] = src[0];                                                \
        return CV_OK;                                                   \
    }                                                                   \
                                                                        \
    dft_src[0] = (datatype)(src[0]*2*dct_wave->re*icv_sin_45);          \
    src += src_step;                                                    \
    for( j = 1, dct_wave++; j < n2; j++, dct_wave++,                    \
                                    src += src_step, src1 -= src_step ) \
    {                                                                   \
        double t0 = dct_wave->re*src[0] - dct_wave->im*src1[0];         \
        double t1 = -dct_wave->im*src[0] - dct_wave->re*src1[0];        \
        dft_src[j*2-1] = (datatype)t0;                                  \
        dft_src[j*2] = (datatype)t1;                                    \
    }                                                                   \
                                                                        \
    dft_src[n-1] = (datatype)(src[0]*2*dct_wave->re);                   \
    icvCCSIDFT_##flavor( dft_src, dft_dst, n, nf, factors, itab,        \
                         dft_wave, n, spec, buf, CV_DXT_INVERSE, 1.0 ); \
                                                                        \
    for( j = 0; j < n2; j++, dst += dst_step*2 )                        \
    {                                                                   \
        dst[0] = dft_dst[j];                                            \
        dst[dst_step] = dft_dst[n-j-1];                                 \
    }                                                                   \
    return CV_OK;                                                       \
}


ICV_DCT_FWD( 64f, double )
ICV_DCT_INV( 64f, double )
ICV_DCT_FWD( 32f, float )
ICV_DCT_INV( 32f, float )

static void
icvDCTInit( int n, int elem_size, void* _wave, int inv )
{
    static const double icvDctScale[] =
    {
    0.707106781186547570, 0.500000000000000000, 0.353553390593273790,
    0.250000000000000000, 0.176776695296636890, 0.125000000000000000,
    0.088388347648318447, 0.062500000000000000, 0.044194173824159223,
    0.031250000000000000, 0.022097086912079612, 0.015625000000000000,
    0.011048543456039806, 0.007812500000000000, 0.005524271728019903,
    0.003906250000000000, 0.002762135864009952, 0.001953125000000000,
    0.001381067932004976, 0.000976562500000000, 0.000690533966002488,
    0.000488281250000000, 0.000345266983001244, 0.000244140625000000,
    0.000172633491500622, 0.000122070312500000, 0.000086316745750311,
    0.000061035156250000, 0.000043158372875155, 0.000030517578125000
    };

    int i;
    CvComplex64f w, w1;
    double t, scale;

    if( n == 1 )
        return;

    assert( (n&1) == 0 );

    if( (n & (n - 1)) == 0 )
    {
        int m = icvlog2(n);
        scale = (!inv ? 2 : 1)*icvDctScale[m];
        w1.re = icvDxtTab[m+2][0];
        w1.im = -icvDxtTab[m+2][1];
    }
    else
    {
        t = 1./(2*n);
        scale = (!inv ? 2 : 1)*sqrt(t);
        w1.im = sin(-CV_PI*t);
        w1.re = sqrt(1. - w1.im*w1.im);
    }
    n >>= 1;

    if( elem_size == sizeof(CvComplex64f) )
    {
        CvComplex64f* wave = (CvComplex64f*)_wave;

        w.re = scale;
        w.im = 0.;

        for( i = 0; i <= n; i++ )
        {
            wave[i] = w;
            t = w.re*w1.re - w.im*w1.im;
            w.im = w.re*w1.im + w.im*w1.re;
            w.re = t;
        }
    }
    else
    {
        CvComplex32f* wave = (CvComplex32f*)_wave;
        assert( elem_size == sizeof(CvComplex32f) );

        w.re = (float)scale;
        w.im = 0.f;

        for( i = 0; i <= n; i++ )
        {
            wave[i].re = (float)w.re;
            wave[i].im = (float)w.im;
            t = w.re*w1.re - w.im*w1.im;
            w.im = w.re*w1.im + w.im*w1.re;
            w.re = t;
        }
    }
}


typedef CvStatus (CV_STDCALL * CvDCTFunc)(
                const void* src, int src_step, void* dft_src,
                void* dft_dst, void* dst, int dst_step, int n,
                int nf, int* factors, const int* itab, const void* dft_wave,
                const void* dct_wave, const void* spec, void* buf );

CV_IMPL void
cvDCT( const CvArr* srcarr, CvArr* dstarr, int flags )
{
    static CvDCTFunc dct_tbl[4];
    static int inittab = 0;

    void* buffer = 0;
    int local_alloc = 1;
    int inv = (flags & CV_DXT_INVERSE) != 0, depth = -1;
    void *spec_dft = 0, *spec = 0;

    CV_FUNCNAME( "cvDCT" );

    __BEGIN__;

    double scale = 1.;
    int prev_len = 0, buf_size = 0, nf = 0, stage, end_stage;
    CvMat *src = (CvMat*)srcarr, *dst = (CvMat*)dstarr;
    uchar *src_dft_buf = 0, *dst_dft_buf = 0;
    uchar *dft_wave = 0, *dct_wave = 0;
    int* itab = 0;
    uchar* ptr = 0;
    CvMat srcstub, dststub;
    int complex_elem_size, elem_size;
    int factors[34], inplace_transform;
    int i, len, count;
    CvDCTFunc dct_func;

    if( !inittab )
    {
        dct_tbl[0] = (CvDCTFunc)icvDCT_fwd_32f;
        dct_tbl[1] = (CvDCTFunc)icvDCT_inv_32f;
        dct_tbl[2] = (CvDCTFunc)icvDCT_fwd_64f;
        dct_tbl[3] = (CvDCTFunc)icvDCT_inv_64f;
        inittab = 1;
    }

    if( !CV_IS_MAT( src ))
    {
        int coi = 0;
        CV_CALL( src = cvGetMat( src, &srcstub, &coi ));

        if( coi != 0 )
            CV_ERROR( CV_BadCOI, "" );
    }

    if( !CV_IS_MAT( dst ))
    {
        int coi = 0;
        CV_CALL( dst = cvGetMat( dst, &dststub, &coi ));

        if( coi != 0 )
            CV_ERROR( CV_BadCOI, "" );
    }

    depth = CV_MAT_DEPTH(src->type);
    elem_size = CV_ELEM_SIZE1(depth);
    complex_elem_size = elem_size*2;

    // check types and sizes
    if( !CV_ARE_TYPES_EQ(src, dst) )
        CV_ERROR( CV_StsUnmatchedFormats, "" );

    if( depth < CV_32F || CV_MAT_CN(src->type) != 1 )
        CV_ERROR( CV_StsUnsupportedFormat,
        "Only 32fC1 and 64fC1 formats are supported" );

    dct_func = dct_tbl[inv + (depth == CV_64F)*2];

    if( (flags & CV_DXT_ROWS) || src->rows == 1 ||
        (src->cols == 1 && CV_IS_MAT_CONT(src->type & dst->type)))
    {
        stage = end_stage = 0;
    }
    else
    {
        stage = src->cols == 1;
        end_stage = 1;
    }

    for( ; stage <= end_stage; stage++ )
    {
        uchar *sptr = src->data.ptr, *dptr = dst->data.ptr;
        int sstep0, sstep1, dstep0, dstep1;

        if( stage == 0 )
        {
            len = src->cols;
            count = src->rows;
            if( len == 1 && !(flags & CV_DXT_ROWS) )
            {
                len = src->rows;
                count = 1;
            }
            sstep0 = src->step;
            dstep0 = dst->step;
            sstep1 = dstep1 = elem_size;
        }
        else
        {
            len = dst->rows;
            count = dst->cols;
            sstep1 = src->step;
            dstep1 = dst->step;
            sstep0 = dstep0 = elem_size;
        }

        if( len != prev_len )
        {
            int sz;

            if( len > 1 && (len & 1) )
                CV_ERROR( CV_StsNotImplemented, "Odd-size DCT\'s are not implemented" );

            sz = len*elem_size;
            sz += (len/2 + 1)*complex_elem_size;

            spec = 0;
            inplace_transform = 1;
            if( len*count >= 64 && icvDFTInitAlloc_R_32f_p )
            {
                int ipp_sz = 0;
                if( depth == CV_32F )
                {
                    if( spec_dft )
                        IPPI_CALL( icvDFTFree_R_32f_p( spec_dft ));
                    IPPI_CALL( icvDFTInitAlloc_R_32f_p( &spec_dft, len, 8, cvAlgHintNone ));
                    IPPI_CALL( icvDFTGetBufSize_R_32f_p( spec_dft, &ipp_sz ));
                }
                else
                {
                    if( spec_dft )
                        IPPI_CALL( icvDFTFree_R_64f_p( spec_dft ));
                    IPPI_CALL( icvDFTInitAlloc_R_64f_p( &spec_dft, len, 8, cvAlgHintNone ));
                    IPPI_CALL( icvDFTGetBufSize_R_64f_p( spec_dft, &ipp_sz ));
                }
                spec = spec_dft;
                sz += ipp_sz;
            }
            else
            {
                sz += len*(complex_elem_size + sizeof(int)) + complex_elem_size;

                nf = icvDFTFactorize( len, factors );
                inplace_transform = factors[0] == factors[nf-1];

                i = nf > 1 && (factors[0] & 1) == 0;
                if( (factors[i] & 1) != 0 && factors[i] > 5 )
                    sz += (factors[i]+1)*complex_elem_size;

                if( !inplace_transform )
                    sz += len*elem_size;
            }

            if( sz > buf_size )
            {
                if( !local_alloc && buffer )
                    cvFree( &buffer );
                if( sz <= CV_MAX_LOCAL_DFT_SIZE )
                {
                    buf_size = sz = CV_MAX_LOCAL_DFT_SIZE;
                    buffer = cvStackAlloc(sz + 32);
                    local_alloc = 1;
                }
                else
                {
                    CV_CALL( buffer = cvAlloc(sz + 32) );
                    buf_size = sz;
                    local_alloc = 0;
                }
            }

            ptr = (uchar*)buffer;
            if( !spec )
            {
                dft_wave = ptr;
                ptr += len*complex_elem_size;
                itab = (int*)ptr;
                ptr = (uchar*)cvAlignPtr( ptr + len*sizeof(int), 16 );
                icvDFTInit( len, nf, factors, itab, complex_elem_size, dft_wave, inv );
            }

            dct_wave = ptr;
            ptr += (len/2 + 1)*complex_elem_size;
            src_dft_buf = dst_dft_buf = ptr;
            ptr += len*elem_size;
            if( !inplace_transform )
            {
                dst_dft_buf = ptr;
                ptr += len*elem_size;
            }
            icvDCTInit( len, complex_elem_size, dct_wave, inv );
            if( !inv )
                scale += scale;
            prev_len = len;
        }
        // otherwise reuse the tables calculated on the previous stage

        for( i = 0; i < count; i++ )
        {
            dct_func( sptr + i*sstep0, sstep1, src_dft_buf, dst_dft_buf,
                      dptr + i*dstep0, dstep1, len, nf, factors,
                      itab, dft_wave, dct_wave, spec, ptr );
        }
        src = dst;
    }

    __END__;

    if( spec_dft )
    {
        if( depth == CV_32F )
            icvDFTFree_R_32f_p( spec_dft );
        else
            icvDFTFree_R_64f_p( spec_dft );
    }

    if( buffer && !local_alloc )
        cvFree( &buffer );
}


static const int icvOptimalDFTSize[] = {
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48,
50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160,
162, 180, 192, 200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375,
384, 400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720,
729, 750, 768, 800, 810, 864, 900, 960, 972, 1000, 1024, 1080, 1125, 1152, 1200,
1215, 1250, 1280, 1296, 1350, 1440, 1458, 1500, 1536, 1600, 1620, 1728, 1800, 1875,
1920, 1944, 2000, 2025, 2048, 2160, 2187, 2250, 2304, 2400, 2430, 2500, 2560, 2592,
2700, 2880, 2916, 3000, 3072, 3125, 3200, 3240, 3375, 3456, 3600, 3645, 3750, 3840,
3888, 4000, 4050, 4096, 4320, 4374, 4500, 4608, 4800, 4860, 5000, 5120, 5184, 5400,
5625, 5760, 5832, 6000, 6075, 6144, 6250, 6400, 6480, 6561, 6750, 6912, 7200, 7290,
7500, 7680, 7776, 8000, 8100, 8192, 8640, 8748, 9000, 9216, 9375, 9600, 9720, 10000,
10125, 10240, 10368, 10800, 10935, 11250, 11520, 11664, 12000, 12150, 12288, 12500,
12800, 12960, 13122, 13500, 13824, 14400, 14580, 15000, 15360, 15552, 15625, 16000,
16200, 16384, 16875, 17280, 17496, 18000, 18225, 18432, 18750, 19200, 19440, 19683,
20000, 20250, 20480, 20736, 21600, 21870, 22500, 23040, 23328, 24000, 24300, 24576,
25000, 25600, 25920, 26244, 27000, 27648, 28125, 28800, 29160, 30000, 30375, 30720,
31104, 31250, 32000, 32400, 32768, 32805, 33750, 34560, 34992, 36000, 36450, 36864,
37500, 38400, 38880, 39366, 40000, 40500, 40960, 41472, 43200, 43740, 45000, 46080,
46656, 46875, 48000, 48600, 49152, 50000, 50625, 51200, 51840, 52488, 54000, 54675,
55296, 56250, 57600, 58320, 59049, 60000, 60750, 61440, 62208, 62500, 64000, 64800,
65536, 65610, 67500, 69120, 69984, 72000, 72900, 73728, 75000, 76800, 77760, 78125,
78732, 80000, 81000, 81920, 82944, 84375, 86400, 87480, 90000, 91125, 92160, 93312,
93750, 96000, 97200, 98304, 98415, 100000, 101250, 102400, 103680, 104976, 108000,
109350, 110592, 112500, 115200, 116640, 118098, 120000, 121500, 122880, 124416, 125000,
128000, 129600, 131072, 131220, 135000, 138240, 139968, 140625, 144000, 145800, 147456,
150000, 151875, 153600, 155520, 156250, 157464, 160000, 162000, 163840, 164025, 165888,
168750, 172800, 174960, 177147, 180000, 182250, 184320, 186624, 187500, 192000, 194400,
196608, 196830, 200000, 202500, 204800, 207360, 209952, 216000, 218700, 221184, 225000,
230400, 233280, 234375, 236196, 240000, 243000, 245760, 248832, 250000, 253125, 256000,
259200, 262144, 262440, 270000, 273375, 276480, 279936, 281250, 288000, 291600, 294912,
295245, 300000, 303750, 307200, 311040, 312500, 314928, 320000, 324000, 327680, 328050,
331776, 337500, 345600, 349920, 354294, 360000, 364500, 368640, 373248, 375000, 384000,
388800, 390625, 393216, 393660, 400000, 405000, 409600, 414720, 419904, 421875, 432000,
437400, 442368, 450000, 455625, 460800, 466560, 468750, 472392, 480000, 486000, 491520,
492075, 497664, 500000, 506250, 512000, 518400, 524288, 524880, 531441, 540000, 546750,
552960, 559872, 562500, 576000, 583200, 589824, 590490, 600000, 607500, 614400, 622080,
625000, 629856, 640000, 648000, 655360, 656100, 663552, 675000, 691200, 699840, 703125,
708588, 720000, 729000, 737280, 746496, 750000, 759375, 768000, 777600, 781250, 786432,
787320, 800000, 810000, 819200, 820125, 829440, 839808, 843750, 864000, 874800, 884736,
885735, 900000, 911250, 921600, 933120, 937500, 944784, 960000, 972000, 983040, 984150,
995328, 1000000, 1012500, 1024000, 1036800, 1048576, 1049760, 1062882, 1080000, 1093500,
1105920, 1119744, 1125000, 1152000, 1166400, 1171875, 1179648, 1180980, 1200000,
1215000, 1228800, 1244160, 1250000, 1259712, 1265625, 1280000, 1296000, 1310720,
1312200, 1327104, 1350000, 1366875, 1382400, 1399680, 1406250, 1417176, 1440000,
1458000, 1474560, 1476225, 1492992, 1500000, 1518750, 1536000, 1555200, 1562500,
1572864, 1574640, 1594323, 1600000, 1620000, 1638400, 1640250, 1658880, 1679616,
1687500, 1728000, 1749600, 1769472, 1771470, 1800000, 1822500, 1843200, 1866240,
1875000, 1889568, 1920000, 1944000, 1953125, 1966080, 1968300, 1990656, 2000000,
2025000, 2048000, 2073600, 2097152, 2099520, 2109375, 2125764, 2160000, 2187000,
2211840, 2239488, 2250000, 2278125, 2304000, 2332800, 2343750, 2359296, 2361960,
2400000, 2430000, 2457600, 2460375, 2488320, 2500000, 2519424, 2531250, 2560000,
2592000, 2621440, 2624400, 2654208, 2657205, 2700000, 2733750, 2764800, 2799360,
2812500, 2834352, 2880000, 2916000, 2949120, 2952450, 2985984, 3000000, 3037500,
3072000, 3110400, 3125000, 3145728, 3149280, 3188646, 3200000, 3240000, 3276800,
3280500, 3317760, 3359232, 3375000, 3456000, 3499200, 3515625, 3538944, 3542940,
3600000, 3645000, 3686400, 3732480, 3750000, 3779136, 3796875, 3840000, 3888000,
3906250, 3932160, 3936600, 3981312, 4000000, 4050000, 4096000, 4100625, 4147200,
4194304, 4199040, 4218750, 4251528, 4320000, 4374000, 4423680, 4428675, 4478976,
4500000, 4556250, 4608000, 4665600, 4687500, 4718592, 4723920, 4782969, 4800000,
4860000, 4915200, 4920750, 4976640, 5000000, 5038848, 5062500, 5120000, 5184000,
5242880, 5248800, 5308416, 5314410, 5400000, 5467500, 5529600, 5598720, 5625000,
5668704, 5760000, 5832000, 5859375, 5898240, 5904900, 5971968, 6000000, 6075000,
6144000, 6220800, 6250000, 6291456, 6298560, 6328125, 6377292, 6400000, 6480000,
6553600, 6561000, 6635520, 6718464, 6750000, 6834375, 6912000, 6998400, 7031250,
7077888, 7085880, 7200000, 7290000, 7372800, 7381125, 7464960, 7500000, 7558272,
7593750, 7680000, 7776000, 7812500, 7864320, 7873200, 7962624, 7971615, 8000000,
8100000, 8192000, 8201250, 8294400, 8388608, 8398080, 8437500, 8503056, 8640000,
8748000, 8847360, 8857350, 8957952, 9000000, 9112500, 9216000, 9331200, 9375000,
9437184, 9447840, 9565938, 9600000, 9720000, 9765625, 9830400, 9841500, 9953280,
10000000, 10077696, 10125000, 10240000, 10368000, 10485760, 10497600, 10546875, 10616832,
10628820, 10800000, 10935000, 11059200, 11197440, 11250000, 11337408, 11390625, 11520000,
11664000, 11718750, 11796480, 11809800, 11943936, 12000000, 12150000, 12288000, 12301875,
12441600, 12500000, 12582912, 12597120, 12656250, 12754584, 12800000, 12960000, 13107200,
13122000, 13271040, 13286025, 13436928, 13500000, 13668750, 13824000, 13996800, 14062500,
14155776, 14171760, 14400000, 14580000, 14745600, 14762250, 14929920, 15000000, 15116544,
15187500, 15360000, 15552000, 15625000, 15728640, 15746400, 15925248, 15943230, 16000000,
16200000, 16384000, 16402500, 16588800, 16777216, 16796160, 16875000, 17006112, 17280000,
17496000, 17578125, 17694720, 17714700, 17915904, 18000000, 18225000, 18432000, 18662400,
18750000, 18874368, 18895680, 18984375, 19131876, 19200000, 19440000, 19531250, 19660800,
19683000, 19906560, 20000000, 20155392, 20250000, 20480000, 20503125, 20736000, 20971520,
20995200, 21093750, 21233664, 21257640, 21600000, 21870000, 22118400, 22143375, 22394880,
22500000, 22674816, 22781250, 23040000, 23328000, 23437500, 23592960, 23619600, 23887872,
23914845, 24000000, 24300000, 24576000, 24603750, 24883200, 25000000, 25165824, 25194240,
25312500, 25509168, 25600000, 25920000, 26214400, 26244000, 26542080, 26572050, 26873856,
27000000, 27337500, 27648000, 27993600, 28125000, 28311552, 28343520, 28800000, 29160000,
29296875, 29491200, 29524500, 29859840, 30000000, 30233088, 30375000, 30720000, 31104000,
31250000, 31457280, 31492800, 31640625, 31850496, 31886460, 32000000, 32400000, 32768000,
32805000, 33177600, 33554432, 33592320, 33750000, 34012224, 34171875, 34560000, 34992000,
35156250, 35389440, 35429400, 35831808, 36000000, 36450000, 36864000, 36905625, 37324800,
37500000, 37748736, 37791360, 37968750, 38263752, 38400000, 38880000, 39062500, 39321600,
39366000, 39813120, 39858075, 40000000, 40310784, 40500000, 40960000, 41006250, 41472000,
41943040, 41990400, 42187500, 42467328, 42515280, 43200000, 43740000, 44236800, 44286750,
44789760, 45000000, 45349632, 45562500, 46080000, 46656000, 46875000, 47185920, 47239200,
47775744, 47829690, 48000000, 48600000, 48828125, 49152000, 49207500, 49766400, 50000000,
50331648, 50388480, 50625000, 51018336, 51200000, 51840000, 52428800, 52488000, 52734375,
53084160, 53144100, 53747712, 54000000, 54675000, 55296000, 55987200, 56250000, 56623104,
56687040, 56953125, 57600000, 58320000, 58593750, 58982400, 59049000, 59719680, 60000000,
60466176, 60750000, 61440000, 61509375, 62208000, 62500000, 62914560, 62985600, 63281250,
63700992, 63772920, 64000000, 64800000, 65536000, 65610000, 66355200, 66430125, 67108864,
67184640, 67500000, 68024448, 68343750, 69120000, 69984000, 70312500, 70778880, 70858800,
71663616, 72000000, 72900000, 73728000, 73811250, 74649600, 75000000, 75497472, 75582720,
75937500, 76527504, 76800000, 77760000, 78125000, 78643200, 78732000, 79626240, 79716150,
80000000, 80621568, 81000000, 81920000, 82012500, 82944000, 83886080, 83980800, 84375000,
84934656, 85030560, 86400000, 87480000, 87890625, 88473600, 88573500, 89579520, 90000000,
90699264, 91125000, 92160000, 93312000, 93750000, 94371840, 94478400, 94921875, 95551488,
95659380, 96000000, 97200000, 97656250, 98304000, 98415000, 99532800, 100000000,
100663296, 100776960, 101250000, 102036672, 102400000, 102515625, 103680000, 104857600,
104976000, 105468750, 106168320, 106288200, 107495424, 108000000, 109350000, 110592000,
110716875, 111974400, 112500000, 113246208, 113374080, 113906250, 115200000, 116640000,
117187500, 117964800, 118098000, 119439360, 119574225, 120000000, 120932352, 121500000,
122880000, 123018750, 124416000, 125000000, 125829120, 125971200, 126562500, 127401984,
127545840, 128000000, 129600000, 131072000, 131220000, 132710400, 132860250, 134217728,
134369280, 135000000, 136048896, 136687500, 138240000, 139968000, 140625000, 141557760,
141717600, 143327232, 144000000, 145800000, 146484375, 147456000, 147622500, 149299200,
150000000, 150994944, 151165440, 151875000, 153055008, 153600000, 155520000, 156250000,
157286400, 157464000, 158203125, 159252480, 159432300, 160000000, 161243136, 162000000,
163840000, 164025000, 165888000, 167772160, 167961600, 168750000, 169869312, 170061120,
170859375, 172800000, 174960000, 175781250, 176947200, 177147000, 179159040, 180000000,
181398528, 182250000, 184320000, 184528125, 186624000, 187500000, 188743680, 188956800,
189843750, 191102976, 191318760, 192000000, 194400000, 195312500, 196608000, 196830000,
199065600, 199290375, 200000000, 201326592, 201553920, 202500000, 204073344, 204800000,
205031250, 207360000, 209715200, 209952000, 210937500, 212336640, 212576400, 214990848,
216000000, 218700000, 221184000, 221433750, 223948800, 225000000, 226492416, 226748160,
227812500, 230400000, 233280000, 234375000, 235929600, 236196000, 238878720, 239148450,
240000000, 241864704, 243000000, 244140625, 245760000, 246037500, 248832000, 250000000,
251658240, 251942400, 253125000, 254803968, 255091680, 256000000, 259200000, 262144000,
262440000, 263671875, 265420800, 265720500, 268435456, 268738560, 270000000, 272097792,
273375000, 276480000, 279936000, 281250000, 283115520, 283435200, 284765625, 286654464,
288000000, 291600000, 292968750, 294912000, 295245000, 298598400, 300000000, 301989888,
302330880, 303750000, 306110016, 307200000, 307546875, 311040000, 312500000, 314572800,
314928000, 316406250, 318504960, 318864600, 320000000, 322486272, 324000000, 327680000,
328050000, 331776000, 332150625, 335544320, 335923200, 337500000, 339738624, 340122240,
341718750, 345600000, 349920000, 351562500, 353894400, 354294000, 358318080, 360000000,
362797056, 364500000, 368640000, 369056250, 373248000, 375000000, 377487360, 377913600,
379687500, 382205952, 382637520, 384000000, 388800000, 390625000, 393216000, 393660000,
398131200, 398580750, 400000000, 402653184, 403107840, 405000000, 408146688, 409600000,
410062500, 414720000, 419430400, 419904000, 421875000, 424673280, 425152800, 429981696,
432000000, 437400000, 439453125, 442368000, 442867500, 447897600, 450000000, 452984832,
453496320, 455625000, 460800000, 466560000, 468750000, 471859200, 472392000, 474609375,
477757440, 478296900, 480000000, 483729408, 486000000, 488281250, 491520000, 492075000,
497664000, 500000000, 503316480, 503884800, 506250000, 509607936, 510183360, 512000000,
512578125, 518400000, 524288000, 524880000, 527343750, 530841600, 531441000, 536870912,
537477120, 540000000, 544195584, 546750000, 552960000, 553584375, 559872000, 562500000,
566231040, 566870400, 569531250, 573308928, 576000000, 583200000, 585937500, 589824000,
590490000, 597196800, 597871125, 600000000, 603979776, 604661760, 607500000, 612220032,
614400000, 615093750, 622080000, 625000000, 629145600, 629856000, 632812500, 637009920,
637729200, 640000000, 644972544, 648000000, 655360000, 656100000, 663552000, 664301250,
671088640, 671846400, 675000000, 679477248, 680244480, 683437500, 691200000, 699840000,
703125000, 707788800, 708588000, 716636160, 720000000, 725594112, 729000000, 732421875,
737280000, 738112500, 746496000, 750000000, 754974720, 755827200, 759375000, 764411904,
765275040, 768000000, 777600000, 781250000, 786432000, 787320000, 791015625, 796262400,
797161500, 800000000, 805306368, 806215680, 810000000, 816293376, 819200000, 820125000,
829440000, 838860800, 839808000, 843750000, 849346560, 850305600, 854296875, 859963392,
864000000, 874800000, 878906250, 884736000, 885735000, 895795200, 900000000, 905969664,
906992640, 911250000, 921600000, 922640625, 933120000, 937500000, 943718400, 944784000,
949218750, 955514880, 956593800, 960000000, 967458816, 972000000, 976562500, 983040000,
984150000, 995328000, 996451875, 1000000000, 1006632960, 1007769600, 1012500000,
1019215872, 1020366720, 1024000000, 1025156250, 1036800000, 1048576000, 1049760000,
1054687500, 1061683200, 1062882000, 1073741824, 1074954240, 1080000000, 1088391168,
1093500000, 1105920000, 1107168750, 1119744000, 1125000000, 1132462080, 1133740800,
1139062500, 1146617856, 1152000000, 1166400000, 1171875000, 1179648000, 1180980000,
1194393600, 1195742250, 1200000000, 1207959552, 1209323520, 1215000000, 1220703125,
1224440064, 1228800000, 1230187500, 1244160000, 1250000000, 1258291200, 1259712000,
1265625000, 1274019840, 1275458400, 1280000000, 1289945088, 1296000000, 1310720000,
1312200000, 1318359375, 1327104000, 1328602500, 1342177280, 1343692800, 1350000000,
1358954496, 1360488960, 1366875000, 1382400000, 1399680000, 1406250000, 1415577600,
1417176000, 1423828125, 1433272320, 1440000000, 1451188224, 1458000000, 1464843750,
1474560000, 1476225000, 1492992000, 1500000000, 1509949440, 1511654400, 1518750000,
1528823808, 1530550080, 1536000000, 1537734375, 1555200000, 1562500000, 1572864000,
1574640000, 1582031250, 1592524800, 1594323000, 1600000000, 1610612736, 1612431360,
1620000000, 1632586752, 1638400000, 1640250000, 1658880000, 1660753125, 1677721600,
1679616000, 1687500000, 1698693120, 1700611200, 1708593750, 1719926784, 1728000000,
1749600000, 1757812500, 1769472000, 1771470000, 1791590400, 1800000000, 1811939328,
1813985280, 1822500000, 1843200000, 1845281250, 1866240000, 1875000000, 1887436800,
1889568000, 1898437500, 1911029760, 1913187600, 1920000000, 1934917632, 1944000000,
1953125000, 1966080000, 1968300000, 1990656000, 1992903750, 2000000000, 2013265920,
2015539200, 2025000000, 2038431744, 2040733440, 2048000000, 2050312500, 2073600000,
2097152000, 2099520000, 2109375000, 2123366400, 2125764000
};


CV_IMPL int
cvGetOptimalDFTSize( int size0 )
{
    int a = 0, b = sizeof(icvOptimalDFTSize)/sizeof(icvOptimalDFTSize[0]) - 1;
    if( (unsigned)size0 >= (unsigned)icvOptimalDFTSize[b] )
        return -1;

    while( a < b )
    {
        int c = (a + b) >> 1;
        if( size0 <= icvOptimalDFTSize[c] )
            b = c;
        else
            a = c+1;
    }

    return icvOptimalDFTSize[b];
}

/* End of file. */