mathfuncs.cpp

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#include "precomp.hpp"
#include "opencl_kernels.hpp"

namespace cv
{

static const int MAX_BLOCK_SIZE = 1024;
typedef void (*MathFunc)(const void* src, void* dst, int len);

static const float atan2_p1 = 0.9997878412794807f*(float)(180/CV_PI);
static const float atan2_p3 = -0.3258083974640975f*(float)(180/CV_PI);
static const float atan2_p5 = 0.1555786518463281f*(float)(180/CV_PI);
static const float atan2_p7 = -0.04432655554792128f*(float)(180/CV_PI);


enum { OCL_OP_LOG=0, OCL_OP_EXP=1, OCL_OP_MAG=2, OCL_OP_PHASE_DEGREES=3, OCL_OP_PHASE_RADIANS=4 };

static const char* oclop2str[] = { "OP_LOG", "OP_EXP", "OP_MAG", "OP_PHASE_DEGREES", "OP_PHASE_RADIANS", 0 };

static bool ocl_math_op(InputArray _src1, InputArray _src2, OutputArray _dst, int oclop)
{
    int type1 = _src1.type(), depth1 = CV_MAT_DEPTH(type1), cn1 = CV_MAT_CN(type1);
    int type2 = _src2.type(), cn2 = CV_MAT_CN(type2);

    char opts[1024];

    bool double_support = false;
    if(ocl::Device::getDefault().doubleFPConfig() > 0)
        double_support = true;
    if(!double_support && depth1 == CV_64F)
        return false;

        sprintf(opts, "-D %s -D %s -D dstT=%s %s", _src2.empty()?"UNARY_OP":"BINARY_OP",
            oclop2str[oclop], ocl::typeToStr(CV_MAKETYPE(depth1, 1) ), double_support ? "-D DOUBLE_SUPPORT" : "" );

    ocl::Kernel k("KF", ocl::core::arithm_oclsrc, opts);
    if( k.empty() )
        return false;

    UMat src1 = _src1.getUMat();
    UMat src2 = _src2.getUMat();
    _dst.create(src1.size(), type1);
    UMat dst = _dst.getUMat();

    ocl::KernelArg src1arg = ocl::KernelArg::ReadOnlyNoSize(src1, cn1);
    ocl::KernelArg src2arg = ocl::KernelArg::ReadOnlyNoSize(src2, cn2);
    ocl::KernelArg dstarg = ocl::KernelArg::WriteOnly(dst, cn1);

    if(_src2.empty())
        k.args(src1arg, dstarg);
    else
        k.args(src1arg, src2arg, dstarg);

    size_t globalsize[] = { src1.cols*cn1, src1.rows};

    return k.run(2, globalsize, 0, false);
}

float fastAtan2( float y, float x )
{
    float ax = std::abs(x), ay = std::abs(y);
    float a, c, c2;
    if( ax >= ay )
    {
        c = ay/(ax + (float)DBL_EPSILON);
        c2 = c*c;
        a = (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
    }
    else
    {
        c = ax/(ay + (float)DBL_EPSILON);
        c2 = c*c;
        a = 90.f - (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
    }
    if( x < 0 )
        a = 180.f - a;
    if( y < 0 )
        a = 360.f - a;
    return a;
}

static void FastAtan2_32f(const float *Y, const float *X, float *angle, int len, bool angleInDegrees=true )
{
    int i = 0;
    float scale = angleInDegrees ? 1 : (float)(CV_PI/180);

#ifdef HAVE_TEGRA_OPTIMIZATION
    if (tegra::FastAtan2_32f(Y, X, angle, len, scale))
        return;
#endif

#if CV_SSE2
    if( USE_SSE2 )
    {
        Cv32suf iabsmask; iabsmask.i = 0x7fffffff;
        __m128 eps = _mm_set1_ps((float)DBL_EPSILON), absmask = _mm_set1_ps(iabsmask.f);
        __m128 _90 = _mm_set1_ps(90.f), _180 = _mm_set1_ps(180.f), _360 = _mm_set1_ps(360.f);
        __m128 z = _mm_setzero_ps(), scale4 = _mm_set1_ps(scale);
        __m128 p1 = _mm_set1_ps(atan2_p1), p3 = _mm_set1_ps(atan2_p3);
        __m128 p5 = _mm_set1_ps(atan2_p5), p7 = _mm_set1_ps(atan2_p7);

        for( ; i <= len - 4; i += 4 )
        {
            __m128 x = _mm_loadu_ps(X + i), y = _mm_loadu_ps(Y + i);
            __m128 ax = _mm_and_ps(x, absmask), ay = _mm_and_ps(y, absmask);
            __m128 mask = _mm_cmplt_ps(ax, ay);
            __m128 tmin = _mm_min_ps(ax, ay), tmax = _mm_max_ps(ax, ay);
            __m128 c = _mm_div_ps(tmin, _mm_add_ps(tmax, eps));
            __m128 c2 = _mm_mul_ps(c, c);
            __m128 a = _mm_mul_ps(c2, p7);
            a = _mm_mul_ps(_mm_add_ps(a, p5), c2);
            a = _mm_mul_ps(_mm_add_ps(a, p3), c2);
            a = _mm_mul_ps(_mm_add_ps(a, p1), c);

            __m128 b = _mm_sub_ps(_90, a);
            a = _mm_xor_ps(a, _mm_and_ps(_mm_xor_ps(a, b), mask));

            b = _mm_sub_ps(_180, a);
            mask = _mm_cmplt_ps(x, z);
            a = _mm_xor_ps(a, _mm_and_ps(_mm_xor_ps(a, b), mask));

            b = _mm_sub_ps(_360, a);
            mask = _mm_cmplt_ps(y, z);
            a = _mm_xor_ps(a, _mm_and_ps(_mm_xor_ps(a, b), mask));

            a = _mm_mul_ps(a, scale4);
            _mm_storeu_ps(angle + i, a);
        }
    }
#endif

    for( ; i < len; i++ )
    {
        float x = X[i], y = Y[i];
        float ax = std::abs(x), ay = std::abs(y);
        float a, c, c2;
        if( ax >= ay )
        {
            c = ay/(ax + (float)DBL_EPSILON);
            c2 = c*c;
            a = (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
        }
        else
        {
            c = ax/(ay + (float)DBL_EPSILON);
            c2 = c*c;
            a = 90.f - (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
        }
        if( x < 0 )
            a = 180.f - a;
        if( y < 0 )
            a = 360.f - a;
        angle[i] = (float)(a*scale);
    }
}


/* ************************************************************************** *\
   Fast cube root by Ken Turkowski
   (http://www.worldserver.com/turk/computergraphics/papers.html)
\* ************************************************************************** */
float  cubeRoot( float value )
{
    float fr;
    Cv32suf v, m;
    int ix, s;
    int ex, shx;

    v.f = value;
    ix = v.i & 0x7fffffff;
    s = v.i & 0x80000000;
    ex = (ix >> 23) - 127;
    shx = ex % 3;
    shx -= shx >= 0 ? 3 : 0;
    ex = (ex - shx) / 3; /* exponent of cube root */
    v.i = (ix & ((1<<23)-1)) | ((shx + 127)<<23);
    fr = v.f;

    /* 0.125 <= fr < 1.0 */
    /* Use quartic rational polynomial with error < 2^(-24) */
    fr = (float)(((((45.2548339756803022511987494 * fr +
    192.2798368355061050458134625) * fr +
    119.1654824285581628956914143) * fr +
    13.43250139086239872172837314) * fr +
    0.1636161226585754240958355063)/
    ((((14.80884093219134573786480845 * fr +
    151.9714051044435648658557668) * fr +
    168.5254414101568283957668343) * fr +
    33.9905941350215598754191872) * fr +
    1.0));

    /* fr *= 2^ex * sign */
    m.f = value;
    v.f = fr;
    v.i = (v.i + (ex << 23) + s) & (m.i*2 != 0 ? -1 : 0);
    return v.f;
}

static void Magnitude_32f(const float* x, const float* y, float* mag, int len)
{
    int i = 0;

#if CV_SSE
    if( USE_SSE2 )
    {
        for( ; i <= len - 8; i += 8 )
        {
            __m128 x0 = _mm_loadu_ps(x + i), x1 = _mm_loadu_ps(x + i + 4);
            __m128 y0 = _mm_loadu_ps(y + i), y1 = _mm_loadu_ps(y + i + 4);
            x0 = _mm_add_ps(_mm_mul_ps(x0, x0), _mm_mul_ps(y0, y0));
            x1 = _mm_add_ps(_mm_mul_ps(x1, x1), _mm_mul_ps(y1, y1));
            x0 = _mm_sqrt_ps(x0); x1 = _mm_sqrt_ps(x1);
            _mm_storeu_ps(mag + i, x0); _mm_storeu_ps(mag + i + 4, x1);
        }
    }
#endif

    for( ; i < len; i++ )
    {
        float x0 = x[i], y0 = y[i];
        mag[i] = std::sqrt(x0*x0 + y0*y0);
    }
}

static void Magnitude_64f(const double* x, const double* y, double* mag, int len)
{
    int i = 0;

#if CV_SSE2
    if( USE_SSE2 )
    {
        for( ; i <= len - 4; i += 4 )
        {
            __m128d x0 = _mm_loadu_pd(x + i), x1 = _mm_loadu_pd(x + i + 2);
            __m128d y0 = _mm_loadu_pd(y + i), y1 = _mm_loadu_pd(y + i + 2);
            x0 = _mm_add_pd(_mm_mul_pd(x0, x0), _mm_mul_pd(y0, y0));
            x1 = _mm_add_pd(_mm_mul_pd(x1, x1), _mm_mul_pd(y1, y1));
            x0 = _mm_sqrt_pd(x0); x1 = _mm_sqrt_pd(x1);
            _mm_storeu_pd(mag + i, x0); _mm_storeu_pd(mag + i + 2, x1);
        }
    }
#endif

    for( ; i < len; i++ )
    {
        double x0 = x[i], y0 = y[i];
        mag[i] = std::sqrt(x0*x0 + y0*y0);
    }
}


static void InvSqrt_32f(const float* src, float* dst, int len)
{
    int i = 0;

#if CV_SSE
    if( USE_SSE2 )
    {
        __m128 _0_5 = _mm_set1_ps(0.5f), _1_5 = _mm_set1_ps(1.5f);
        if( (((size_t)src|(size_t)dst) & 15) == 0 )
            for( ; i <= len - 8; i += 8 )
            {
                __m128 t0 = _mm_load_ps(src + i), t1 = _mm_load_ps(src + i + 4);
                __m128 h0 = _mm_mul_ps(t0, _0_5), h1 = _mm_mul_ps(t1, _0_5);
                t0 = _mm_rsqrt_ps(t0); t1 = _mm_rsqrt_ps(t1);
                t0 = _mm_mul_ps(t0, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t0,t0),h0)));
                t1 = _mm_mul_ps(t1, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t1,t1),h1)));
                _mm_store_ps(dst + i, t0); _mm_store_ps(dst + i + 4, t1);
            }
        else
            for( ; i <= len - 8; i += 8 )
            {
                __m128 t0 = _mm_loadu_ps(src + i), t1 = _mm_loadu_ps(src + i + 4);
                __m128 h0 = _mm_mul_ps(t0, _0_5), h1 = _mm_mul_ps(t1, _0_5);
                t0 = _mm_rsqrt_ps(t0); t1 = _mm_rsqrt_ps(t1);
                t0 = _mm_mul_ps(t0, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t0,t0),h0)));
                t1 = _mm_mul_ps(t1, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t1,t1),h1)));
                _mm_storeu_ps(dst + i, t0); _mm_storeu_ps(dst + i + 4, t1);
            }
    }
#endif

    for( ; i < len; i++ )
        dst[i] = 1/std::sqrt(src[i]);
}


static void InvSqrt_64f(const double* src, double* dst, int len)
{
    for( int i = 0; i < len; i++ )
        dst[i] = 1/std::sqrt(src[i]);
}


static void Sqrt_32f(const float* src, float* dst, int len)
{
    int i = 0;

#if CV_SSE
    if( USE_SSE2 )
    {
        if( (((size_t)src|(size_t)dst) & 15) == 0 )
            for( ; i <= len - 8; i += 8 )
            {
                __m128 t0 = _mm_load_ps(src + i), t1 = _mm_load_ps(src + i + 4);
                t0 = _mm_sqrt_ps(t0); t1 = _mm_sqrt_ps(t1);
                _mm_store_ps(dst + i, t0); _mm_store_ps(dst + i + 4, t1);
            }
        else
            for( ; i <= len - 8; i += 8 )
            {
                __m128 t0 = _mm_loadu_ps(src + i), t1 = _mm_loadu_ps(src + i + 4);
                t0 = _mm_sqrt_ps(t0); t1 = _mm_sqrt_ps(t1);
                _mm_storeu_ps(dst + i, t0); _mm_storeu_ps(dst + i + 4, t1);
            }
    }
#endif

    for( ; i < len; i++ )
        dst[i] = std::sqrt(src[i]);
}


static void Sqrt_64f(const double* src, double* dst, int len)
{
    int i = 0;

#if CV_SSE2
    if( USE_SSE2 )
    {
        if( (((size_t)src|(size_t)dst) & 15) == 0 )
            for( ; i <= len - 4; i += 4 )
            {
                __m128d t0 = _mm_load_pd(src + i), t1 = _mm_load_pd(src + i + 2);
                t0 = _mm_sqrt_pd(t0); t1 = _mm_sqrt_pd(t1);
                _mm_store_pd(dst + i, t0); _mm_store_pd(dst + i + 2, t1);
            }
        else
            for( ; i <= len - 4; i += 4 )
            {
                __m128d t0 = _mm_loadu_pd(src + i), t1 = _mm_loadu_pd(src + i + 2);
                t0 = _mm_sqrt_pd(t0); t1 = _mm_sqrt_pd(t1);
                _mm_storeu_pd(dst + i, t0); _mm_storeu_pd(dst + i + 2, t1);
            }
    }
#endif

    for( ; i < len; i++ )
        dst[i] = std::sqrt(src[i]);
}


/****************************************************************************************\
*                                  Cartezian -> Polar                                    *
\****************************************************************************************/

void magnitude( InputArray src1, InputArray src2, OutputArray dst )
{
    int type = src1.type(), depth = src1.depth(), cn = src1.channels();
    CV_Assert( src1.size() == src2.size() && type == src2.type() && (depth == CV_32F || depth == CV_64F));

    bool use_opencl = dst.isUMat() && ocl::useOpenCL()
        && src1.dims() <= 2 && src2.dims() <= 2;

    if(use_opencl && ocl_math_op(src1, src2, dst, OCL_OP_MAG) )
        return;

    Mat X = src1.getMat(), Y = src2.getMat();
    dst.create(X.dims, X.size, X.type());
    Mat Mag = dst.getMat();

    const Mat* arrays[] = {&X, &Y, &Mag, 0};
    uchar* ptrs[3];
    NAryMatIterator it(arrays, ptrs);
    int len = (int)it.size*cn;

    for( size_t i = 0; i < it.nplanes; i++, ++it )
    {
        if( depth == CV_32F )
        {
            const float *x = (const float*)ptrs[0], *y = (const float*)ptrs[1];
            float *mag = (float*)ptrs[2];
            Magnitude_32f( x, y, mag, len );
        }
        else
        {
            const double *x = (const double*)ptrs[0], *y = (const double*)ptrs[1];
            double *mag = (double*)ptrs[2];
            Magnitude_64f( x, y, mag, len );
        }
    }
}


void phase( InputArray src1, InputArray src2, OutputArray dst, bool angleInDegrees )
{
    int type = src1.type(), depth = src1.depth(), cn = src1.channels();
    CV_Assert( src1.size() == src2.size() && type == src2.type() && (depth == CV_32F || depth == CV_64F));

    bool use_opencl = dst.isUMat() && ocl::useOpenCL()
        && src1.dims() <= 2 && src2.dims() <= 2;

    if(use_opencl && ocl_math_op(src1, src2, dst, angleInDegrees ? OCL_OP_PHASE_DEGREES : OCL_OP_PHASE_RADIANS) )
        return;

    Mat X = src1.getMat(), Y = src2.getMat();
    dst.create( X.dims, X.size, type );
    Mat Angle = dst.getMat();

    const Mat* arrays[] = {&X, &Y, &Angle, 0};
    uchar* ptrs[3];
    NAryMatIterator it(arrays, ptrs);
    cv::AutoBuffer<float> _buf;
    float* buf[2] = {0, 0};
    int j, k, total = (int)(it.size*cn), blockSize = total;
    size_t esz1 = X.elemSize1();

    if( depth == CV_64F )
    {
        blockSize = std::min(blockSize, ((BLOCK_SIZE+cn-1)/cn)*cn);
        _buf.allocate(blockSize*2);
        buf[0] = _buf;
        buf[1] = buf[0] + blockSize;
    }

    for( size_t i = 0; i < it.nplanes; i++, ++it )
    {
        for( j = 0; j < total; j += blockSize )
        {
            int len = std::min(total - j, blockSize);
            if( depth == CV_32F )
            {
                const float *x = (const float*)ptrs[0], *y = (const float*)ptrs[1];
                float *angle = (float*)ptrs[2];
                FastAtan2_32f( y, x, angle, len, angleInDegrees );
            }
            else
            {
                const double *x = (const double*)ptrs[0], *y = (const double*)ptrs[1];
                double *angle = (double*)ptrs[2];
                for( k = 0; k < len; k++ )
                {
                    buf[0][k] = (float)x[k];
                    buf[1][k] = (float)y[k];
                }

                FastAtan2_32f( buf[1], buf[0], buf[0], len, angleInDegrees );
                for( k = 0; k < len; k++ )
                    angle[k] = buf[0][k];
            }
            ptrs[0] += len*esz1;
            ptrs[1] += len*esz1;
            ptrs[2] += len*esz1;
        }
    }
}

static bool ocl_cartToPolar( InputArray _src1, InputArray _src2,
                             OutputArray _dst1, OutputArray _dst2, bool angleInDegrees )
{
    int type = _src1.type(), depth = CV_MAT_DEPTH(type), cn = CV_MAT_CN(type);
    bool doubleSupport = ocl::Device::getDefault().doubleFPConfig() > 0;

    if ( !(_src1.dims() <= 2 && _src2.dims() <= 2 &&
           (depth == CV_32F || depth == CV_64F) && type == _src2.type()) ||
         (depth == CV_64F && !doubleSupport) )
        return false;

    UMat src1 = _src1.getUMat(), src2 = _src2.getUMat();
    Size size = src1.size();
    CV_Assert( size == src2.size() );

    _dst1.create(size, type);
    _dst2.create(size, type);
    UMat dst1 = _dst1.getUMat(), dst2 = _dst2.getUMat();

    ocl::Kernel k("KF", ocl::core::arithm_oclsrc,
                  format("-D BINARY_OP -D dstT=%s -D OP_CTP_%s%s",
                         ocl::typeToStr(CV_MAKE_TYPE(depth, 1)),
                         angleInDegrees ? "AD" : "AR",
                         doubleSupport ? " -D DOUBLE_SUPPORT" : ""));

    k.args(ocl::KernelArg::ReadOnlyNoSize(src1),
           ocl::KernelArg::ReadOnlyNoSize(src2),
           ocl::KernelArg::WriteOnly(dst1, cn),
           ocl::KernelArg::WriteOnlyNoSize(dst2));

    size_t globalsize[2] = { dst1.cols * cn, dst1.rows };
    return k.run(2, globalsize, NULL, false);
}

void cartToPolar( InputArray src1, InputArray src2,
                  OutputArray dst1, OutputArray dst2, bool angleInDegrees )
{
    if (ocl::useOpenCL() && dst1.isUMat() && dst2.isUMat() &&
            ocl_cartToPolar(src1, src2, dst1, dst2, angleInDegrees))
        return;

    Mat X = src1.getMat(), Y = src2.getMat();
    int type = X.type(), depth = X.depth(), cn = X.channels();
    CV_Assert( X.size == Y.size && type == Y.type() && (depth == CV_32F || depth == CV_64F));
    dst1.create( X.dims, X.size, type );
    dst2.create( X.dims, X.size, type );
    Mat Mag = dst1.getMat(), Angle = dst2.getMat();

    const Mat* arrays[] = {&X, &Y, &Mag, &Angle, 0};
    uchar* ptrs[4];
    NAryMatIterator it(arrays, ptrs);
    cv::AutoBuffer<float> _buf;
    float* buf[2] = {0, 0};
    int j, k, total = (int)(it.size*cn), blockSize = std::min(total, ((BLOCK_SIZE+cn-1)/cn)*cn);
    size_t esz1 = X.elemSize1();

    if( depth == CV_64F )
    {
        _buf.allocate(blockSize*2);
        buf[0] = _buf;
        buf[1] = buf[0] + blockSize;
    }

    for( size_t i = 0; i < it.nplanes; i++, ++it )
    {
        for( j = 0; j < total; j += blockSize )
        {
            int len = std::min(total - j, blockSize);
            if( depth == CV_32F )
            {
                const float *x = (const float*)ptrs[0], *y = (const float*)ptrs[1];
                float *mag = (float*)ptrs[2], *angle = (float*)ptrs[3];
                Magnitude_32f( x, y, mag, len );
                FastAtan2_32f( y, x, angle, len, angleInDegrees );
            }
            else
            {
                const double *x = (const double*)ptrs[0], *y = (const double*)ptrs[1];
                double *angle = (double*)ptrs[3];

                Magnitude_64f(x, y, (double*)ptrs[2], len);
                for( k = 0; k < len; k++ )
                {
                    buf[0][k] = (float)x[k];
                    buf[1][k] = (float)y[k];
                }

                FastAtan2_32f( buf[1], buf[0], buf[0], len, angleInDegrees );
                for( k = 0; k < len; k++ )
                    angle[k] = buf[0][k];
            }
            ptrs[0] += len*esz1;
            ptrs[1] += len*esz1;
            ptrs[2] += len*esz1;
            ptrs[3] += len*esz1;
        }
    }
}


/****************************************************************************************\
*                                  Polar -> Cartezian                                    *
\****************************************************************************************/

static void SinCos_32f( const float *angle, float *sinval, float* cosval,
                        int len, int angle_in_degrees )
{
    const int N = 64;

    static const double sin_table[] =
    {
     0.00000000000000000000,     0.09801714032956060400,
     0.19509032201612825000,     0.29028467725446233000,
     0.38268343236508978000,     0.47139673682599764000,
     0.55557023301960218000,     0.63439328416364549000,
     0.70710678118654746000,     0.77301045336273699000,
     0.83146961230254524000,     0.88192126434835494000,
     0.92387953251128674000,     0.95694033573220894000,
     0.98078528040323043000,     0.99518472667219682000,
     1.00000000000000000000,     0.99518472667219693000,
     0.98078528040323043000,     0.95694033573220894000,
     0.92387953251128674000,     0.88192126434835505000,
     0.83146961230254546000,     0.77301045336273710000,
     0.70710678118654757000,     0.63439328416364549000,
     0.55557023301960218000,     0.47139673682599786000,
     0.38268343236508989000,     0.29028467725446239000,
     0.19509032201612861000,     0.09801714032956082600,
     0.00000000000000012246,    -0.09801714032956059000,
    -0.19509032201612836000,    -0.29028467725446211000,
    -0.38268343236508967000,    -0.47139673682599764000,
    -0.55557023301960196000,    -0.63439328416364527000,
    -0.70710678118654746000,    -0.77301045336273666000,
    -0.83146961230254524000,    -0.88192126434835494000,
    -0.92387953251128652000,    -0.95694033573220882000,
    -0.98078528040323032000,    -0.99518472667219693000,
    -1.00000000000000000000,    -0.99518472667219693000,
    -0.98078528040323043000,    -0.95694033573220894000,
    -0.92387953251128663000,    -0.88192126434835505000,
    -0.83146961230254546000,    -0.77301045336273688000,
    -0.70710678118654768000,    -0.63439328416364593000,
    -0.55557023301960218000,    -0.47139673682599792000,
    -0.38268343236509039000,    -0.29028467725446250000,
    -0.19509032201612872000,    -0.09801714032956050600,
    };

    static const double k2 = (2*CV_PI)/N;

    static const double sin_a0 = -0.166630293345647*k2*k2*k2;
    static const double sin_a2 = k2;

    static const double cos_a0 = -0.499818138450326*k2*k2;
    /*static const double cos_a2 =  1;*/

    double k1;
    int i;

    if( !angle_in_degrees )
        k1 = N/(2*CV_PI);
    else
        k1 = N/360.;

    for( i = 0; i < len; i++ )
    {
        double t = angle[i]*k1;
        int it = cvRound(t);
        t -= it;
        int sin_idx = it & (N - 1);
        int cos_idx = (N/4 - sin_idx) & (N - 1);

        double sin_b = (sin_a0*t*t + sin_a2)*t;
        double cos_b = cos_a0*t*t + 1;

        double sin_a = sin_table[sin_idx];
        double cos_a = sin_table[cos_idx];

        double sin_val = sin_a*cos_b + cos_a*sin_b;
        double cos_val = cos_a*cos_b - sin_a*sin_b;

        sinval[i] = (float)sin_val;
        cosval[i] = (float)cos_val;
    }
}


static bool ocl_polarToCart( InputArray _mag, InputArray _angle,
                             OutputArray _dst1, OutputArray _dst2, bool angleInDegrees )
{
    int type = _angle.type(), depth = CV_MAT_DEPTH(type), cn = CV_MAT_CN(type);
    bool doubleSupport = ocl::Device::getDefault().doubleFPConfig() > 0;

    if ( !doubleSupport && depth == CV_64F )
        return false;

    UMat mag = _mag.getUMat(), angle = _angle.getUMat();
    Size size = angle.size();
    CV_Assert(mag.size() == size);

    _dst1.create(size, type);
    _dst2.create(size, type);
    UMat dst1 = _dst1.getUMat(), dst2 = _dst2.getUMat();

    ocl::Kernel k("KF", ocl::core::arithm_oclsrc,
                  format("-D dstT=%s -D BINARY_OP -D OP_PTC_%s%s",
                         ocl::typeToStr(CV_MAKE_TYPE(depth, 1)),
                         angleInDegrees ? "AD" : "AR",
                         doubleSupport ? " -D DOUBLE_SUPPORT" : ""));

    k.args(ocl::KernelArg::ReadOnlyNoSize(mag), ocl::KernelArg::ReadOnlyNoSize(angle),
           ocl::KernelArg::WriteOnly(dst1, cn), ocl::KernelArg::WriteOnlyNoSize(dst2));

    size_t globalsize[2] = { dst1.cols * cn, dst1.rows };
    return k.run(2, globalsize, NULL, false);
}

void polarToCart( InputArray src1, InputArray src2,
                  OutputArray dst1, OutputArray dst2, bool angleInDegrees )
{
    int type = src2.type(), depth = CV_MAT_DEPTH(type), cn = CV_MAT_CN(type);
    CV_Assert((depth == CV_32F || depth == CV_64F) && (src1.empty() || src1.type() == type));

    if (ocl::useOpenCL() && !src1.empty() && src2.dims() <= 2 && dst1.isUMat() && dst2.isUMat() &&
            ocl_polarToCart(src1, src2, dst1, dst2, angleInDegrees))
        return;

    Mat Mag = src1.getMat(), Angle = src2.getMat();
    CV_Assert( Mag.empty() || Angle.size == Mag.size);
    dst1.create( Angle.dims, Angle.size, type );
    dst2.create( Angle.dims, Angle.size, type );
    Mat X = dst1.getMat(), Y = dst2.getMat();

    const Mat* arrays[] = {&Mag, &Angle, &X, &Y, 0};
    uchar* ptrs[4];
    NAryMatIterator it(arrays, ptrs);
    cv::AutoBuffer<float> _buf;
    float* buf[2] = {0, 0};
    int j, k, total = (int)(it.size*cn), blockSize = std::min(total, ((BLOCK_SIZE+cn-1)/cn)*cn);
    size_t esz1 = Angle.elemSize1();

    if( depth == CV_64F )
    {
        _buf.allocate(blockSize*2);
        buf[0] = _buf;
        buf[1] = buf[0] + blockSize;
    }

    for( size_t i = 0; i < it.nplanes; i++, ++it )
    {
        for( j = 0; j < total; j += blockSize )
        {
            int len = std::min(total - j, blockSize);
            if( depth == CV_32F )
            {
                const float *mag = (const float*)ptrs[0], *angle = (const float*)ptrs[1];
                float *x = (float*)ptrs[2], *y = (float*)ptrs[3];

                SinCos_32f( angle, y, x, len, angleInDegrees );
                if( mag )
                    for( k = 0; k < len; k++ )
                    {
                        float m = mag[k];
                        x[k] *= m; y[k] *= m;
                    }
            }
            else
            {
                const double *mag = (const double*)ptrs[0], *angle = (const double*)ptrs[1];
                double *x = (double*)ptrs[2], *y = (double*)ptrs[3];

                for( k = 0; k < len; k++ )
                    buf[0][k] = (float)angle[k];

                SinCos_32f( buf[0], buf[1], buf[0], len, angleInDegrees );
                if( mag )
                    for( k = 0; k < len; k++ )
                    {
                        double m = mag[k];
                        x[k] = buf[0][k]*m; y[k] = buf[1][k]*m;
                    }
                else
                    for( k = 0; k < len; k++ )
                    {
                        x[k] = buf[0][k]; y[k] = buf[1][k];
                    }
            }

            if( ptrs[0] )
                ptrs[0] += len*esz1;
            ptrs[1] += len*esz1;
            ptrs[2] += len*esz1;
            ptrs[3] += len*esz1;
        }
    }
}

/****************************************************************************************\
*                                          E X P                                         *
\****************************************************************************************/

typedef union
{
    struct {
#if ( defined( WORDS_BIGENDIAN ) && !defined( OPENCV_UNIVERSAL_BUILD ) ) || defined( __BIG_ENDIAN__ )
        int hi;
        int lo;
#else
        int lo;
        int hi;
#endif
    } i;
    double d;
}
DBLINT;

#ifndef HAVE_IPP

#define EXPTAB_SCALE 6
#define EXPTAB_MASK  ((1 << EXPTAB_SCALE) - 1)

#define EXPPOLY_32F_A0 .9670371139572337719125840413672004409288e-2

static const double expTab[] = {
    1.0 * EXPPOLY_32F_A0,
    1.0108892860517004600204097905619 * EXPPOLY_32F_A0,
    1.0218971486541166782344801347833 * EXPPOLY_32F_A0,
    1.0330248790212284225001082839705 * EXPPOLY_32F_A0,
    1.0442737824274138403219664787399 * EXPPOLY_32F_A0,
    1.0556451783605571588083413251529 * EXPPOLY_32F_A0,
    1.0671404006768236181695211209928 * EXPPOLY_32F_A0,
    1.0787607977571197937406800374385 * EXPPOLY_32F_A0,
    1.0905077326652576592070106557607 * EXPPOLY_32F_A0,
    1.1023825833078409435564142094256 * EXPPOLY_32F_A0,
    1.1143867425958925363088129569196 * EXPPOLY_32F_A0,
    1.126521618608241899794798643787 * EXPPOLY_32F_A0,
    1.1387886347566916537038302838415 * EXPPOLY_32F_A0,
    1.151189229952982705817759635202 * EXPPOLY_32F_A0,
    1.1637248587775775138135735990922 * EXPPOLY_32F_A0,
    1.1763969916502812762846457284838 * EXPPOLY_32F_A0,
    1.1892071150027210667174999705605 * EXPPOLY_32F_A0,
    1.2021567314527031420963969574978 * EXPPOLY_32F_A0,
    1.2152473599804688781165202513388 * EXPPOLY_32F_A0,
    1.2284805361068700056940089577928 * EXPPOLY_32F_A0,
    1.2418578120734840485936774687266 * EXPPOLY_32F_A0,
    1.2553807570246910895793906574423 * EXPPOLY_32F_A0,
    1.2690509571917332225544190810323 * EXPPOLY_32F_A0,
    1.2828700160787782807266697810215 * EXPPOLY_32F_A0,
    1.2968395546510096659337541177925 * EXPPOLY_32F_A0,
    1.3109612115247643419229917863308 * EXPPOLY_32F_A0,
    1.3252366431597412946295370954987 * EXPPOLY_32F_A0,
    1.3396675240533030053600306697244 * EXPPOLY_32F_A0,
    1.3542555469368927282980147401407 * EXPPOLY_32F_A0,
    1.3690024229745906119296011329822 * EXPPOLY_32F_A0,
    1.3839098819638319548726595272652 * EXPPOLY_32F_A0,
    1.3989796725383111402095281367152 * EXPPOLY_32F_A0,
    1.4142135623730950488016887242097 * EXPPOLY_32F_A0,
    1.4296133383919700112350657782751 * EXPPOLY_32F_A0,
    1.4451808069770466200370062414717 * EXPPOLY_32F_A0,
    1.4609177941806469886513028903106 * EXPPOLY_32F_A0,
    1.476826145939499311386907480374 * EXPPOLY_32F_A0,
    1.4929077282912648492006435314867 * EXPPOLY_32F_A0,
    1.5091644275934227397660195510332 * EXPPOLY_32F_A0,
    1.5255981507445383068512536895169 * EXPPOLY_32F_A0,
    1.5422108254079408236122918620907 * EXPPOLY_32F_A0,
    1.5590044002378369670337280894749 * EXPPOLY_32F_A0,
    1.5759808451078864864552701601819 * EXPPOLY_32F_A0,
    1.5931421513422668979372486431191 * EXPPOLY_32F_A0,
    1.6104903319492543081795206673574 * EXPPOLY_32F_A0,
    1.628027421857347766848218522014 * EXPPOLY_32F_A0,
    1.6457554781539648445187567247258 * EXPPOLY_32F_A0,
    1.6636765803267364350463364569764 * EXPPOLY_32F_A0,
    1.6817928305074290860622509524664 * EXPPOLY_32F_A0,
    1.7001063537185234695013625734975 * EXPPOLY_32F_A0,
    1.7186192981224779156293443764563 * EXPPOLY_32F_A0,
    1.7373338352737062489942020818722 * EXPPOLY_32F_A0,
    1.7562521603732994831121606193753 * EXPPOLY_32F_A0,
    1.7753764925265212525505592001993 * EXPPOLY_32F_A0,
    1.7947090750031071864277032421278 * EXPPOLY_32F_A0,
    1.8142521755003987562498346003623 * EXPPOLY_32F_A0,
    1.8340080864093424634870831895883 * EXPPOLY_32F_A0,
    1.8539791250833855683924530703377 * EXPPOLY_32F_A0,
    1.8741676341102999013299989499544 * EXPPOLY_32F_A0,
    1.8945759815869656413402186534269 * EXPPOLY_32F_A0,
    1.9152065613971472938726112702958 * EXPPOLY_32F_A0,
    1.9360617934922944505980559045667 * EXPPOLY_32F_A0,
    1.9571441241754002690183222516269 * EXPPOLY_32F_A0,
    1.9784560263879509682582499181312 * EXPPOLY_32F_A0,
};


// the code below uses _mm_cast* intrinsics, which are not avialable on VS2005
#if (defined _MSC_VER && _MSC_VER < 1500) || \
    (!defined __APPLE__ && defined __GNUC__ && __GNUC__*100 + __GNUC_MINOR__ < 402)
#undef CV_SSE2
#define CV_SSE2 0
#endif

static const double exp_prescale = 1.4426950408889634073599246810019 * (1 << EXPTAB_SCALE);
static const double exp_postscale = 1./(1 << EXPTAB_SCALE);
static const double exp_max_val = 3000.*(1 << EXPTAB_SCALE); // log10(DBL_MAX) < 3000

static void Exp_32f( const float *_x, float *y, int n )
{
    static const float
        A4 = (float)(1.000000000000002438532970795181890933776 / EXPPOLY_32F_A0),
        A3 = (float)(.6931471805521448196800669615864773144641 / EXPPOLY_32F_A0),
        A2 = (float)(.2402265109513301490103372422686535526573 / EXPPOLY_32F_A0),
        A1 = (float)(.5550339366753125211915322047004666939128e-1 / EXPPOLY_32F_A0);

#undef EXPPOLY
#define EXPPOLY(x)  \
    (((((x) + A1)*(x) + A2)*(x) + A3)*(x) + A4)

    int i = 0;
    const Cv32suf* x = (const Cv32suf*)_x;
    Cv32suf buf[4];

#if CV_SSE2
    if( n >= 8 && USE_SSE2 )
    {
        static const __m128d prescale2 = _mm_set1_pd(exp_prescale);
        static const __m128 postscale4 = _mm_set1_ps((float)exp_postscale);
        static const __m128 maxval4 = _mm_set1_ps((float)(exp_max_val/exp_prescale));
        static const __m128 minval4 = _mm_set1_ps((float)(-exp_max_val/exp_prescale));

        static const __m128 mA1 = _mm_set1_ps(A1);
        static const __m128 mA2 = _mm_set1_ps(A2);
        static const __m128 mA3 = _mm_set1_ps(A3);
        static const __m128 mA4 = _mm_set1_ps(A4);
        bool y_aligned = (size_t)(void*)y % 16 == 0;

        ushort CV_DECL_ALIGNED(16) tab_idx[8];

        for( ; i <= n - 8; i += 8 )
        {
            __m128 xf0, xf1;
            xf0 = _mm_loadu_ps(&x[i].f);
            xf1 = _mm_loadu_ps(&x[i+4].f);
            __m128i xi0, xi1, xi2, xi3;

            xf0 = _mm_min_ps(_mm_max_ps(xf0, minval4), maxval4);
            xf1 = _mm_min_ps(_mm_max_ps(xf1, minval4), maxval4);

            __m128d xd0 = _mm_cvtps_pd(xf0);
            __m128d xd2 = _mm_cvtps_pd(_mm_movehl_ps(xf0, xf0));
            __m128d xd1 = _mm_cvtps_pd(xf1);
            __m128d xd3 = _mm_cvtps_pd(_mm_movehl_ps(xf1, xf1));

            xd0 = _mm_mul_pd(xd0, prescale2);
            xd2 = _mm_mul_pd(xd2, prescale2);
            xd1 = _mm_mul_pd(xd1, prescale2);
            xd3 = _mm_mul_pd(xd3, prescale2);

            xi0 = _mm_cvtpd_epi32(xd0);
            xi2 = _mm_cvtpd_epi32(xd2);

            xi1 = _mm_cvtpd_epi32(xd1);
            xi3 = _mm_cvtpd_epi32(xd3);

            xd0 = _mm_sub_pd(xd0, _mm_cvtepi32_pd(xi0));
            xd2 = _mm_sub_pd(xd2, _mm_cvtepi32_pd(xi2));
            xd1 = _mm_sub_pd(xd1, _mm_cvtepi32_pd(xi1));
            xd3 = _mm_sub_pd(xd3, _mm_cvtepi32_pd(xi3));

            xf0 = _mm_movelh_ps(_mm_cvtpd_ps(xd0), _mm_cvtpd_ps(xd2));
            xf1 = _mm_movelh_ps(_mm_cvtpd_ps(xd1), _mm_cvtpd_ps(xd3));

            xf0 = _mm_mul_ps(xf0, postscale4);
            xf1 = _mm_mul_ps(xf1, postscale4);

            xi0 = _mm_unpacklo_epi64(xi0, xi2);
            xi1 = _mm_unpacklo_epi64(xi1, xi3);
            xi0 = _mm_packs_epi32(xi0, xi1);

            _mm_store_si128((__m128i*)tab_idx, _mm_and_si128(xi0, _mm_set1_epi16(EXPTAB_MASK)));

            xi0 = _mm_add_epi16(_mm_srai_epi16(xi0, EXPTAB_SCALE), _mm_set1_epi16(127));
            xi0 = _mm_max_epi16(xi0, _mm_setzero_si128());
            xi0 = _mm_min_epi16(xi0, _mm_set1_epi16(255));
            xi1 = _mm_unpackhi_epi16(xi0, _mm_setzero_si128());
            xi0 = _mm_unpacklo_epi16(xi0, _mm_setzero_si128());

            __m128d yd0 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[0]), _mm_load_sd(expTab + tab_idx[1]));
            __m128d yd1 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[2]), _mm_load_sd(expTab + tab_idx[3]));
            __m128d yd2 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[4]), _mm_load_sd(expTab + tab_idx[5]));
            __m128d yd3 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[6]), _mm_load_sd(expTab + tab_idx[7]));

            __m128 yf0 = _mm_movelh_ps(_mm_cvtpd_ps(yd0), _mm_cvtpd_ps(yd1));
            __m128 yf1 = _mm_movelh_ps(_mm_cvtpd_ps(yd2), _mm_cvtpd_ps(yd3));

            yf0 = _mm_mul_ps(yf0, _mm_castsi128_ps(_mm_slli_epi32(xi0, 23)));
            yf1 = _mm_mul_ps(yf1, _mm_castsi128_ps(_mm_slli_epi32(xi1, 23)));

            __m128 zf0 = _mm_add_ps(xf0, mA1);
            __m128 zf1 = _mm_add_ps(xf1, mA1);

            zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA2);
            zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA2);

            zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA3);
            zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA3);

            zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA4);
            zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA4);

            zf0 = _mm_mul_ps(zf0, yf0);
            zf1 = _mm_mul_ps(zf1, yf1);

            if( y_aligned )
            {
                _mm_store_ps(y + i, zf0);
                _mm_store_ps(y + i + 4, zf1);
            }
            else
            {
                _mm_storeu_ps(y + i, zf0);
                _mm_storeu_ps(y + i + 4, zf1);
            }
        }
    }
    else
#endif
    for( ; i <= n - 4; i += 4 )
    {
        double x0 = x[i].f * exp_prescale;
        double x1 = x[i + 1].f * exp_prescale;
        double x2 = x[i + 2].f * exp_prescale;
        double x3 = x[i + 3].f * exp_prescale;
        int val0, val1, val2, val3, t;

        if( ((x[i].i >> 23) & 255) > 127 + 10 )
            x0 = x[i].i < 0 ? -exp_max_val : exp_max_val;

        if( ((x[i+1].i >> 23) & 255) > 127 + 10 )
            x1 = x[i+1].i < 0 ? -exp_max_val : exp_max_val;

        if( ((x[i+2].i >> 23) & 255) > 127 + 10 )
            x2 = x[i+2].i < 0 ? -exp_max_val : exp_max_val;

        if( ((x[i+3].i >> 23) & 255) > 127 + 10 )
            x3 = x[i+3].i < 0 ? -exp_max_val : exp_max_val;

        val0 = cvRound(x0);
        val1 = cvRound(x1);
        val2 = cvRound(x2);
        val3 = cvRound(x3);

        x0 = (x0 - val0)*exp_postscale;
        x1 = (x1 - val1)*exp_postscale;
        x2 = (x2 - val2)*exp_postscale;
        x3 = (x3 - val3)*exp_postscale;

        t = (val0 >> EXPTAB_SCALE) + 127;
        t = !(t & ~255) ? t : t < 0 ? 0 : 255;
        buf[0].i = t << 23;

        t = (val1 >> EXPTAB_SCALE) + 127;
        t = !(t & ~255) ? t : t < 0 ? 0 : 255;
        buf[1].i = t << 23;

        t = (val2 >> EXPTAB_SCALE) + 127;
        t = !(t & ~255) ? t : t < 0 ? 0 : 255;
        buf[2].i = t << 23;

        t = (val3 >> EXPTAB_SCALE) + 127;
        t = !(t & ~255) ? t : t < 0 ? 0 : 255;
        buf[3].i = t << 23;

        x0 = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
        x1 = buf[1].f * expTab[val1 & EXPTAB_MASK] * EXPPOLY( x1 );

        y[i] = (float)x0;
        y[i + 1] = (float)x1;

        x2 = buf[2].f * expTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
        x3 = buf[3].f * expTab[val3 & EXPTAB_MASK] * EXPPOLY( x3 );

        y[i + 2] = (float)x2;
        y[i + 3] = (float)x3;
    }

    for( ; i < n; i++ )
    {
        double x0 = x[i].f * exp_prescale;
        int val0, t;

        if( ((x[i].i >> 23) & 255) > 127 + 10 )
            x0 = x[i].i < 0 ? -exp_max_val : exp_max_val;

        val0 = cvRound(x0);
        t = (val0 >> EXPTAB_SCALE) + 127;
        t = !(t & ~255) ? t : t < 0 ? 0 : 255;

        buf[0].i = t << 23;
        x0 = (x0 - val0)*exp_postscale;

        y[i] = (float)(buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY(x0));
    }
}


static void Exp_64f( const double *_x, double *y, int n )
{
    static const double
    A5 = .99999999999999999998285227504999 / EXPPOLY_32F_A0,
    A4 = .69314718055994546743029643825322 / EXPPOLY_32F_A0,
    A3 = .24022650695886477918181338054308 / EXPPOLY_32F_A0,
    A2 = .55504108793649567998466049042729e-1 / EXPPOLY_32F_A0,
    A1 = .96180973140732918010002372686186e-2 / EXPPOLY_32F_A0,
    A0 = .13369713757180123244806654839424e-2 / EXPPOLY_32F_A0;

#undef EXPPOLY
#define EXPPOLY(x)  (((((A0*(x) + A1)*(x) + A2)*(x) + A3)*(x) + A4)*(x) + A5)

    int i = 0;
    Cv64suf buf[4];
    const Cv64suf* x = (const Cv64suf*)_x;

#if CV_SSE2
    if( USE_SSE2 )
    {
        static const __m128d prescale2 = _mm_set1_pd(exp_prescale);
        static const __m128d postscale2 = _mm_set1_pd(exp_postscale);
        static const __m128d maxval2 = _mm_set1_pd(exp_max_val);
        static const __m128d minval2 = _mm_set1_pd(-exp_max_val);

        static const __m128d mA0 = _mm_set1_pd(A0);
        static const __m128d mA1 = _mm_set1_pd(A1);
        static const __m128d mA2 = _mm_set1_pd(A2);
        static const __m128d mA3 = _mm_set1_pd(A3);
        static const __m128d mA4 = _mm_set1_pd(A4);
        static const __m128d mA5 = _mm_set1_pd(A5);

        int CV_DECL_ALIGNED(16) tab_idx[4];

        for( ; i <= n - 4; i += 4 )
        {
            __m128d xf0 = _mm_loadu_pd(&x[i].f), xf1 = _mm_loadu_pd(&x[i+2].f);
            __m128i xi0, xi1;
            xf0 = _mm_min_pd(_mm_max_pd(xf0, minval2), maxval2);
            xf1 = _mm_min_pd(_mm_max_pd(xf1, minval2), maxval2);
            xf0 = _mm_mul_pd(xf0, prescale2);
            xf1 = _mm_mul_pd(xf1, prescale2);

            xi0 = _mm_cvtpd_epi32(xf0);
            xi1 = _mm_cvtpd_epi32(xf1);
            xf0 = _mm_mul_pd(_mm_sub_pd(xf0, _mm_cvtepi32_pd(xi0)), postscale2);
            xf1 = _mm_mul_pd(_mm_sub_pd(xf1, _mm_cvtepi32_pd(xi1)), postscale2);

            xi0 = _mm_unpacklo_epi64(xi0, xi1);
            _mm_store_si128((__m128i*)tab_idx, _mm_and_si128(xi0, _mm_set1_epi32(EXPTAB_MASK)));

            xi0 = _mm_add_epi32(_mm_srai_epi32(xi0, EXPTAB_SCALE), _mm_set1_epi32(1023));
            xi0 = _mm_packs_epi32(xi0, xi0);
            xi0 = _mm_max_epi16(xi0, _mm_setzero_si128());
            xi0 = _mm_min_epi16(xi0, _mm_set1_epi16(2047));
            xi0 = _mm_unpacklo_epi16(xi0, _mm_setzero_si128());
            xi1 = _mm_unpackhi_epi32(xi0, _mm_setzero_si128());
            xi0 = _mm_unpacklo_epi32(xi0, _mm_setzero_si128());

            __m128d yf0 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[0]), _mm_load_sd(expTab + tab_idx[1]));
            __m128d yf1 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[2]), _mm_load_sd(expTab + tab_idx[3]));
            yf0 = _mm_mul_pd(yf0, _mm_castsi128_pd(_mm_slli_epi64(xi0, 52)));
            yf1 = _mm_mul_pd(yf1, _mm_castsi128_pd(_mm_slli_epi64(xi1, 52)));

            __m128d zf0 = _mm_add_pd(_mm_mul_pd(mA0, xf0), mA1);
            __m128d zf1 = _mm_add_pd(_mm_mul_pd(mA0, xf1), mA1);

            zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA2);
            zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA2);

            zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA3);
            zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA3);

            zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA4);
            zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA4);

            zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA5);
            zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA5);

            zf0 = _mm_mul_pd(zf0, yf0);
            zf1 = _mm_mul_pd(zf1, yf1);

            _mm_storeu_pd(y + i, zf0);
            _mm_storeu_pd(y + i + 2, zf1);
        }
    }
    else
#endif
    for( ; i <= n - 4; i += 4 )
    {
        double x0 = x[i].f * exp_prescale;
        double x1 = x[i + 1].f * exp_prescale;
        double x2 = x[i + 2].f * exp_prescale;
        double x3 = x[i + 3].f * exp_prescale;

        double y0, y1, y2, y3;
        int val0, val1, val2, val3, t;

        t = (int)(x[i].i >> 52);
        if( (t & 2047) > 1023 + 10 )
            x0 = t < 0 ? -exp_max_val : exp_max_val;

        t = (int)(x[i+1].i >> 52);
        if( (t & 2047) > 1023 + 10 )
            x1 = t < 0 ? -exp_max_val : exp_max_val;

        t = (int)(x[i+2].i >> 52);
        if( (t & 2047) > 1023 + 10 )
            x2 = t < 0 ? -exp_max_val : exp_max_val;

        t = (int)(x[i+3].i >> 52);
        if( (t & 2047) > 1023 + 10 )
            x3 = t < 0 ? -exp_max_val : exp_max_val;

        val0 = cvRound(x0);
        val1 = cvRound(x1);
        val2 = cvRound(x2);
        val3 = cvRound(x3);

        x0 = (x0 - val0)*exp_postscale;
        x1 = (x1 - val1)*exp_postscale;
        x2 = (x2 - val2)*exp_postscale;
        x3 = (x3 - val3)*exp_postscale;

        t = (val0 >> EXPTAB_SCALE) + 1023;
        t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
        buf[0].i = (int64)t << 52;

        t = (val1 >> EXPTAB_SCALE) + 1023;
        t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
        buf[1].i = (int64)t << 52;

        t = (val2 >> EXPTAB_SCALE) + 1023;
        t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
        buf[2].i = (int64)t << 52;

        t = (val3 >> EXPTAB_SCALE) + 1023;
        t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
        buf[3].i = (int64)t << 52;

        y0 = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
        y1 = buf[1].f * expTab[val1 & EXPTAB_MASK] * EXPPOLY( x1 );

        y[i] = y0;
        y[i + 1] = y1;

        y2 = buf[2].f * expTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
        y3 = buf[3].f * expTab[val3 & EXPTAB_MASK] * EXPPOLY( x3 );

        y[i + 2] = y2;
        y[i + 3] = y3;
    }

    for( ; i < n; i++ )
    {
        double x0 = x[i].f * exp_prescale;
        int val0, t;

        t = (int)(x[i].i >> 52);
        if( (t & 2047) > 1023 + 10 )
            x0 = t < 0 ? -exp_max_val : exp_max_val;

        val0 = cvRound(x0);
        t = (val0 >> EXPTAB_SCALE) + 1023;
        t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;

        buf[0].i = (int64)t << 52;
        x0 = (x0 - val0)*exp_postscale;

        y[i] = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
    }
}

#undef EXPTAB_SCALE
#undef EXPTAB_MASK
#undef EXPPOLY_32F_A0

#else

#define Exp_32f ippsExp_32f_A21
#define Exp_64f ippsExp_64f_A50

#endif

void exp( InputArray _src, OutputArray _dst )
{
    int type = _src.type(), depth = _src.depth(), cn = _src.channels();
    CV_Assert( depth == CV_32F || depth == CV_64F );

    bool use_opencl = _dst.isUMat() && ocl::useOpenCL() && _src.dims() <= 2;

    if(use_opencl && ocl_math_op(_src, noArray(), _dst, OCL_OP_EXP) )
        return;

    Mat src = _src.getMat();
    _dst.create( src.dims, src.size, type );
    Mat dst = _dst.getMat();

    const Mat* arrays[] = {&src, &dst, 0};
    uchar* ptrs[2];
    NAryMatIterator it(arrays, ptrs);
    int len = (int)(it.size*cn);

    for( size_t i = 0; i < it.nplanes; i++, ++it )
    {
        if( depth == CV_32F )
            Exp_32f( (const float*)ptrs[0], (float*)ptrs[1], len );
        else
            Exp_64f( (const double*)ptrs[0], (double*)ptrs[1], len );
    }
}


/****************************************************************************************\
*                                          L O G                                         *
\****************************************************************************************/

#ifndef HAVE_IPP

#define LOGTAB_SCALE    8
#define LOGTAB_MASK         ((1 << LOGTAB_SCALE) - 1)
#define LOGTAB_MASK2        ((1 << (20 - LOGTAB_SCALE)) - 1)
#define LOGTAB_MASK2_32F    ((1 << (23 - LOGTAB_SCALE)) - 1)

static const double CV_DECL_ALIGNED(16) icvLogTab[] = {
0.0000000000000000000000000000000000000000,    1.000000000000000000000000000000000000000,
.00389864041565732288852075271279318258166,    .9961089494163424124513618677042801556420,
.00778214044205494809292034119607706088573,    .9922480620155038759689922480620155038760,
.01165061721997527263705585198749759001657,    .9884169884169884169884169884169884169884,
.01550418653596525274396267235488267033361,    .9846153846153846153846153846153846153846,
.01934296284313093139406447562578250654042,    .9808429118773946360153256704980842911877,
.02316705928153437593630670221500622574241,    .9770992366412213740458015267175572519084,
.02697658769820207233514075539915211265906,    .9733840304182509505703422053231939163498,
.03077165866675368732785500469617545604706,    .9696969696969696969696969696969696969697,
.03455238150665972812758397481047722976656,    .9660377358490566037735849056603773584906,
.03831886430213659461285757856785494368522,    .9624060150375939849624060150375939849624,
.04207121392068705056921373852674150839447,    .9588014981273408239700374531835205992509,
.04580953603129420126371940114040626212953,    .9552238805970149253731343283582089552239,
.04953393512227662748292900118940451648088,    .9516728624535315985130111524163568773234,
.05324451451881227759255210685296333394944,    .9481481481481481481481481481481481481481,
.05694137640013842427411105973078520037234,    .9446494464944649446494464944649446494465,
.06062462181643483993820353816772694699466,    .9411764705882352941176470588235294117647,
.06429435070539725460836422143984236754475,    .9377289377289377289377289377289377289377,
.06795066190850773679699159401934593915938,    .9343065693430656934306569343065693430657,
.07159365318700880442825962290953611955044,    .9309090909090909090909090909090909090909,
.07522342123758751775142172846244648098944,    .9275362318840579710144927536231884057971,
.07884006170777602129362549021607264876369,    .9241877256317689530685920577617328519856,
.08244366921107458556772229485432035289706,    .9208633093525179856115107913669064748201,
.08603433734180314373940490213499288074675,    .9175627240143369175627240143369175627240,
.08961215868968712416897659522874164395031,    .9142857142857142857142857142857142857143,
.09317722485418328259854092721070628613231,    .9110320284697508896797153024911032028470,
.09672962645855109897752299730200320482256,    .9078014184397163120567375886524822695035,
.10026945316367513738597949668474029749630,    .9045936395759717314487632508833922261484,
.10379679368164355934833764649738441221420,    .9014084507042253521126760563380281690141,
.10731173578908805021914218968959175981580,    .8982456140350877192982456140350877192982,
.11081436634029011301105782649756292812530,    .8951048951048951048951048951048951048951,
.11430477128005862852422325204315711744130,    .8919860627177700348432055749128919860627,
.11778303565638344185817487641543266363440,    .8888888888888888888888888888888888888889,
.12124924363286967987640707633545389398930,    .8858131487889273356401384083044982698962,
.12470347850095722663787967121606925502420,    .8827586206896551724137931034482758620690,
.12814582269193003360996385708858724683530,    .8797250859106529209621993127147766323024,
.13157635778871926146571524895989568904040,    .8767123287671232876712328767123287671233,
.13499516453750481925766280255629681050780,    .8737201365187713310580204778156996587031,
.13840232285911913123754857224412262439730,    .8707482993197278911564625850340136054422,
.14179791186025733629172407290752744302150,    .8677966101694915254237288135593220338983,
.14518200984449788903951628071808954700830,    .8648648648648648648648648648648648648649,
.14855469432313711530824207329715136438610,    .8619528619528619528619528619528619528620,
.15191604202584196858794030049466527998450,    .8590604026845637583892617449664429530201,
.15526612891112392955683674244937719777230,    .8561872909698996655518394648829431438127,
.15860503017663857283636730244325008243330,    .8533333333333333333333333333333333333333,
.16193282026931324346641360989451641216880,    .8504983388704318936877076411960132890365,
.16524957289530714521497145597095368430010,    .8476821192052980132450331125827814569536,
.16855536102980664403538924034364754334090,    .8448844884488448844884488448844884488449,
.17185025692665920060697715143760433420540,    .8421052631578947368421052631578947368421,
.17513433212784912385018287750426679849630,    .8393442622950819672131147540983606557377,
.17840765747281828179637841458315961062910,    .8366013071895424836601307189542483660131,
.18167030310763465639212199675966985523700,    .8338762214983713355048859934853420195440,
.18492233849401198964024217730184318497780,    .8311688311688311688311688311688311688312,
.18816383241818296356839823602058459073300,    .8284789644012944983818770226537216828479,
.19139485299962943898322009772527962923050,    .8258064516129032258064516129032258064516,
.19461546769967164038916962454095482826240,    .8231511254019292604501607717041800643087,
.19782574332991986754137769821682013571260,    .8205128205128205128205128205128205128205,
.20102574606059073203390141770796617493040,    .8178913738019169329073482428115015974441,
.20421554142869088876999228432396193966280,    .8152866242038216560509554140127388535032,
.20739519434607056602715147164417430758480,    .8126984126984126984126984126984126984127,
.21056476910734961416338251183333341032260,    .8101265822784810126582278481012658227848,
.21372432939771812687723695489694364368910,    .8075709779179810725552050473186119873817,
.21687393830061435506806333251006435602900,    .8050314465408805031446540880503144654088,
.22001365830528207823135744547471404075630,    .8025078369905956112852664576802507836991,
.22314355131420973710199007200571941211830,    .8000000000000000000000000000000000000000,
.22626367865045338145790765338460914790630,    .7975077881619937694704049844236760124611,
.22937410106484582006380890106811420992010,    .7950310559006211180124223602484472049689,
.23247487874309405442296849741978803649550,    .7925696594427244582043343653250773993808,
.23556607131276688371634975283086532726890,    .7901234567901234567901234567901234567901,
.23864773785017498464178231643018079921600,    .7876923076923076923076923076923076923077,
.24171993688714515924331749374687206000090,    .7852760736196319018404907975460122699387,
.24478272641769091566565919038112042471760,    .7828746177370030581039755351681957186544,
.24783616390458124145723672882013488560910,    .7804878048780487804878048780487804878049,
.25088030628580937353433455427875742316250,    .7781155015197568389057750759878419452888,
.25391520998096339667426946107298135757450,    .7757575757575757575757575757575757575758,
.25694093089750041913887912414793390780680,    .7734138972809667673716012084592145015106,
.25995752443692604627401010475296061486000,    .7710843373493975903614457831325301204819,
.26296504550088134477547896494797896593800,    .7687687687687687687687687687687687687688,
.26596354849713793599974565040611196309330,    .7664670658682634730538922155688622754491,
.26895308734550393836570947314612567424780,    .7641791044776119402985074626865671641791,
.27193371548364175804834985683555714786050,    .7619047619047619047619047619047619047619,
.27490548587279922676529508862586226314300,    .7596439169139465875370919881305637982196,
.27786845100345625159121709657483734190480,    .7573964497041420118343195266272189349112,
.28082266290088775395616949026589281857030,    .7551622418879056047197640117994100294985,
.28376817313064456316240580235898960381750,    .7529411764705882352941176470588235294118,
.28670503280395426282112225635501090437180,    .7507331378299120234604105571847507331378,
.28963329258304265634293983566749375313530,    .7485380116959064327485380116959064327485,
.29255300268637740579436012922087684273730,    .7463556851311953352769679300291545189504,
.29546421289383584252163927885703742504130,    .7441860465116279069767441860465116279070,
.29836697255179722709783618483925238251680,    .7420289855072463768115942028985507246377,
.30126133057816173455023545102449133992200,    .7398843930635838150289017341040462427746,
.30414733546729666446850615102448500692850,    .7377521613832853025936599423631123919308,
.30702503529491181888388950937951449304830,    .7356321839080459770114942528735632183908,
.30989447772286465854207904158101882785550,    .7335243553008595988538681948424068767908,
.31275571000389684739317885942000430077330,    .7314285714285714285714285714285714285714,
.31560877898630329552176476681779604405180,    .7293447293447293447293447293447293447293,
.31845373111853458869546784626436419785030,    .7272727272727272727272727272727272727273,
.32129061245373424782201254856772720813750,    .7252124645892351274787535410764872521246,
.32411946865421192853773391107097268104550,    .7231638418079096045197740112994350282486,
.32694034499585328257253991068864706903700,    .7211267605633802816901408450704225352113,
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};



#define LOGTAB_TRANSLATE(x,h) (((x) - 1.)*icvLogTab[(h)+1])
static const double ln_2 = 0.69314718055994530941723212145818;

static void Log_32f( const float *_x, float *y, int n )
{
    static const float shift[] = { 0, -1.f/512 };
    static const float
        A0 = 0.3333333333333333333333333f,
        A1 = -0.5f,
        A2 = 1.f;

    #undef LOGPOLY
    #define LOGPOLY(x) (((A0*(x) + A1)*(x) + A2)*(x))

    int i = 0;
    Cv32suf buf[4];
    const int* x = (const int*)_x;

#if CV_SSE2
    if( USE_SSE2 )
    {
        static const __m128d ln2_2 = _mm_set1_pd(ln_2);
        static const __m128 _1_4 = _mm_set1_ps(1.f);
        static const __m128 shift4 = _mm_set1_ps(-1.f/512);

        static const __m128 mA0 = _mm_set1_ps(A0);
        static const __m128 mA1 = _mm_set1_ps(A1);
        static const __m128 mA2 = _mm_set1_ps(A2);

        int CV_DECL_ALIGNED(16) idx[4];

        for( ; i <= n - 4; i += 4 )
        {
            __m128i h0 = _mm_loadu_si128((const __m128i*)(x + i));
            __m128i yi0 = _mm_sub_epi32(_mm_and_si128(_mm_srli_epi32(h0, 23), _mm_set1_epi32(255)), _mm_set1_epi32(127));
            __m128d yd0 = _mm_mul_pd(_mm_cvtepi32_pd(yi0), ln2_2);
            __m128d yd1 = _mm_mul_pd(_mm_cvtepi32_pd(_mm_unpackhi_epi64(yi0,yi0)), ln2_2);

            __m128i xi0 = _mm_or_si128(_mm_and_si128(h0, _mm_set1_epi32(LOGTAB_MASK2_32F)), _mm_set1_epi32(127 << 23));

            h0 = _mm_and_si128(_mm_srli_epi32(h0, 23 - LOGTAB_SCALE - 1), _mm_set1_epi32(LOGTAB_MASK*2));
            _mm_store_si128((__m128i*)idx, h0);
            h0 = _mm_cmpeq_epi32(h0, _mm_set1_epi32(510));

            __m128d t0, t1, t2, t3, t4;
            t0 = _mm_load_pd(icvLogTab + idx[0]);
            t2 = _mm_load_pd(icvLogTab + idx[1]);
            t1 = _mm_unpackhi_pd(t0, t2);
            t0 = _mm_unpacklo_pd(t0, t2);
            t2 = _mm_load_pd(icvLogTab + idx[2]);
            t4 = _mm_load_pd(icvLogTab + idx[3]);
            t3 = _mm_unpackhi_pd(t2, t4);
            t2 = _mm_unpacklo_pd(t2, t4);

            yd0 = _mm_add_pd(yd0, t0);
            yd1 = _mm_add_pd(yd1, t2);

            __m128 yf0 = _mm_movelh_ps(_mm_cvtpd_ps(yd0), _mm_cvtpd_ps(yd1));

            __m128 xf0 = _mm_sub_ps(_mm_castsi128_ps(xi0), _1_4);
            xf0 = _mm_mul_ps(xf0, _mm_movelh_ps(_mm_cvtpd_ps(t1), _mm_cvtpd_ps(t3)));
            xf0 = _mm_add_ps(xf0, _mm_and_ps(_mm_castsi128_ps(h0), shift4));

            __m128 zf0 = _mm_mul_ps(xf0, mA0);
            zf0 = _mm_mul_ps(_mm_add_ps(zf0, mA1), xf0);
            zf0 = _mm_mul_ps(_mm_add_ps(zf0, mA2), xf0);
            yf0 = _mm_add_ps(yf0, zf0);

            _mm_storeu_ps(y + i, yf0);
        }
    }
    else
#endif
    for( ; i <= n - 4; i += 4 )
    {
        double x0, x1, x2, x3;
        double y0, y1, y2, y3;
        int h0, h1, h2, h3;

        h0 = x[i];
        h1 = x[i+1];
        buf[0].i = (h0 & LOGTAB_MASK2_32F) | (127 << 23);
        buf[1].i = (h1 & LOGTAB_MASK2_32F) | (127 << 23);

        y0 = (((h0 >> 23) & 0xff) - 127) * ln_2;
        y1 = (((h1 >> 23) & 0xff) - 127) * ln_2;

        h0 = (h0 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
        h1 = (h1 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;

        y0 += icvLogTab[h0];
        y1 += icvLogTab[h1];

        h2 = x[i+2];
        h3 = x[i+3];

        x0 = LOGTAB_TRANSLATE( buf[0].f, h0 );
        x1 = LOGTAB_TRANSLATE( buf[1].f, h1 );

        buf[2].i = (h2 & LOGTAB_MASK2_32F) | (127 << 23);
        buf[3].i = (h3 & LOGTAB_MASK2_32F) | (127 << 23);

        y2 = (((h2 >> 23) & 0xff) - 127) * ln_2;
        y3 = (((h3 >> 23) & 0xff) - 127) * ln_2;

        h2 = (h2 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
        h3 = (h3 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;

        y2 += icvLogTab[h2];
        y3 += icvLogTab[h3];

        x2 = LOGTAB_TRANSLATE( buf[2].f, h2 );
        x3 = LOGTAB_TRANSLATE( buf[3].f, h3 );

        x0 += shift[h0 == 510];
        x1 += shift[h1 == 510];
        y0 += LOGPOLY( x0 );
        y1 += LOGPOLY( x1 );

        y[i] = (float) y0;
        y[i + 1] = (float) y1;

        x2 += shift[h2 == 510];
        x3 += shift[h3 == 510];
        y2 += LOGPOLY( x2 );
        y3 += LOGPOLY( x3 );

        y[i + 2] = (float) y2;
        y[i + 3] = (float) y3;
    }

    for( ; i < n; i++ )
    {
        int h0 = x[i];
        double y0;
        float x0;

        y0 = (((h0 >> 23) & 0xff) - 127) * ln_2;

        buf[0].i = (h0 & LOGTAB_MASK2_32F) | (127 << 23);
        h0 = (h0 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;

        y0 += icvLogTab[h0];
        x0 = (float)LOGTAB_TRANSLATE( buf[0].f, h0 );
        x0 += shift[h0 == 510];
        y0 += LOGPOLY( x0 );

        y[i] = (float)y0;
    }
}


static void Log_64f( const double *x, double *y, int n )
{
    static const double shift[] = { 0, -1./512 };
    static const double
        A7 = 1.0,
        A6 = -0.5,
        A5 = 0.333333333333333314829616256247390992939472198486328125,
        A4 = -0.25,
        A3 = 0.2,
        A2 = -0.1666666666666666574148081281236954964697360992431640625,
        A1 = 0.1428571428571428769682682968777953647077083587646484375,
        A0 = -0.125;

    #undef LOGPOLY
    #define LOGPOLY(x,k) ((x)+=shift[k], xq = (x)*(x),\
        (((A0*xq + A2)*xq + A4)*xq + A6)*xq + \
        (((A1*xq + A3)*xq + A5)*xq + A7)*(x))

    int i = 0;
    DBLINT buf[4];
    DBLINT *X = (DBLINT *) x;

#if CV_SSE2
    if( USE_SSE2 )
    {
        static const __m128d ln2_2 = _mm_set1_pd(ln_2);
        static const __m128d _1_2 = _mm_set1_pd(1.);
        static const __m128d shift2 = _mm_set1_pd(-1./512);

        static const __m128i log_and_mask2 = _mm_set_epi32(LOGTAB_MASK2, 0xffffffff, LOGTAB_MASK2, 0xffffffff);
        static const __m128i log_or_mask2 = _mm_set_epi32(1023 << 20, 0, 1023 << 20, 0);

        static const __m128d mA0 = _mm_set1_pd(A0);
        static const __m128d mA1 = _mm_set1_pd(A1);
        static const __m128d mA2 = _mm_set1_pd(A2);
        static const __m128d mA3 = _mm_set1_pd(A3);
        static const __m128d mA4 = _mm_set1_pd(A4);
        static const __m128d mA5 = _mm_set1_pd(A5);
        static const __m128d mA6 = _mm_set1_pd(A6);
        static const __m128d mA7 = _mm_set1_pd(A7);

        int CV_DECL_ALIGNED(16) idx[4];

        for( ; i <= n - 4; i += 4 )
        {
            __m128i h0 = _mm_loadu_si128((const __m128i*)(x + i));
            __m128i h1 = _mm_loadu_si128((const __m128i*)(x + i + 2));

            __m128d xd0 = _mm_castsi128_pd(_mm_or_si128(_mm_and_si128(h0, log_and_mask2), log_or_mask2));
            __m128d xd1 = _mm_castsi128_pd(_mm_or_si128(_mm_and_si128(h1, log_and_mask2), log_or_mask2));

            h0 = _mm_unpackhi_epi32(_mm_unpacklo_epi32(h0, h1), _mm_unpackhi_epi32(h0, h1));

            __m128i yi0 = _mm_sub_epi32(_mm_and_si128(_mm_srli_epi32(h0, 20),
                                    _mm_set1_epi32(2047)), _mm_set1_epi32(1023));
            __m128d yd0 = _mm_mul_pd(_mm_cvtepi32_pd(yi0), ln2_2);
            __m128d yd1 = _mm_mul_pd(_mm_cvtepi32_pd(_mm_unpackhi_epi64(yi0, yi0)), ln2_2);

            h0 = _mm_and_si128(_mm_srli_epi32(h0, 20 - LOGTAB_SCALE - 1), _mm_set1_epi32(LOGTAB_MASK * 2));
            _mm_store_si128((__m128i*)idx, h0);
            h0 = _mm_cmpeq_epi32(h0, _mm_set1_epi32(510));

            __m128d t0, t1, t2, t3, t4;
            t0 = _mm_load_pd(icvLogTab + idx[0]);
            t2 = _mm_load_pd(icvLogTab + idx[1]);
            t1 = _mm_unpackhi_pd(t0, t2);
            t0 = _mm_unpacklo_pd(t0, t2);
            t2 = _mm_load_pd(icvLogTab + idx[2]);
            t4 = _mm_load_pd(icvLogTab + idx[3]);
            t3 = _mm_unpackhi_pd(t2, t4);
            t2 = _mm_unpacklo_pd(t2, t4);

            yd0 = _mm_add_pd(yd0, t0);
            yd1 = _mm_add_pd(yd1, t2);

            xd0 = _mm_mul_pd(_mm_sub_pd(xd0, _1_2), t1);
            xd1 = _mm_mul_pd(_mm_sub_pd(xd1, _1_2), t3);

            xd0 = _mm_add_pd(xd0, _mm_and_pd(_mm_castsi128_pd(_mm_unpacklo_epi32(h0, h0)), shift2));
            xd1 = _mm_add_pd(xd1, _mm_and_pd(_mm_castsi128_pd(_mm_unpackhi_epi32(h0, h0)), shift2));

            __m128d zd0 = _mm_mul_pd(xd0, mA0);
            __m128d zd1 = _mm_mul_pd(xd1, mA0);
            zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA1), xd0);
            zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA1), xd1);
            zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA2), xd0);
            zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA2), xd1);
            zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA3), xd0);
            zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA3), xd1);
            zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA4), xd0);
            zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA4), xd1);
            zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA5), xd0);
            zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA5), xd1);
            zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA6), xd0);
            zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA6), xd1);
            zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA7), xd0);
            zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA7), xd1);

            yd0 = _mm_add_pd(yd0, zd0);
            yd1 = _mm_add_pd(yd1, zd1);

            _mm_storeu_pd(y + i, yd0);
            _mm_storeu_pd(y + i + 2, yd1);
        }
    }
    else
#endif
    for( ; i <= n - 4; i += 4 )
    {
        double xq;
        double x0, x1, x2, x3;
        double y0, y1, y2, y3;
        int h0, h1, h2, h3;

        h0 = X[i].i.lo;
        h1 = X[i + 1].i.lo;
        buf[0].i.lo = h0;
        buf[1].i.lo = h1;

        h0 = X[i].i.hi;
        h1 = X[i + 1].i.hi;
        buf[0].i.hi = (h0 & LOGTAB_MASK2) | (1023 << 20);
        buf[1].i.hi = (h1 & LOGTAB_MASK2) | (1023 << 20);

        y0 = (((h0 >> 20) & 0x7ff) - 1023) * ln_2;
        y1 = (((h1 >> 20) & 0x7ff) - 1023) * ln_2;

        h2 = X[i + 2].i.lo;
        h3 = X[i + 3].i.lo;
        buf[2].i.lo = h2;
        buf[3].i.lo = h3;

        h0 = (h0 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
        h1 = (h1 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;

        y0 += icvLogTab[h0];
        y1 += icvLogTab[h1];

        h2 = X[i + 2].i.hi;
        h3 = X[i + 3].i.hi;

        x0 = LOGTAB_TRANSLATE( buf[0].d, h0 );
        x1 = LOGTAB_TRANSLATE( buf[1].d, h1 );

        buf[2].i.hi = (h2 & LOGTAB_MASK2) | (1023 << 20);
        buf[3].i.hi = (h3 & LOGTAB_MASK2) | (1023 << 20);

        y2 = (((h2 >> 20) & 0x7ff) - 1023) * ln_2;
        y3 = (((h3 >> 20) & 0x7ff) - 1023) * ln_2;

        h2 = (h2 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
        h3 = (h3 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;

        y2 += icvLogTab[h2];
        y3 += icvLogTab[h3];

        x2 = LOGTAB_TRANSLATE( buf[2].d, h2 );
        x3 = LOGTAB_TRANSLATE( buf[3].d, h3 );

        y0 += LOGPOLY( x0, h0 == 510 );
        y1 += LOGPOLY( x1, h1 == 510 );

        y[i] = y0;
        y[i + 1] = y1;

        y2 += LOGPOLY( x2, h2 == 510 );
        y3 += LOGPOLY( x3, h3 == 510 );

        y[i + 2] = y2;
        y[i + 3] = y3;
    }

    for( ; i < n; i++ )
    {
        int h0 = X[i].i.hi;
        double xq;
        double x0, y0 = (((h0 >> 20) & 0x7ff) - 1023) * ln_2;

        buf[0].i.hi = (h0 & LOGTAB_MASK2) | (1023 << 20);
        buf[0].i.lo = X[i].i.lo;
        h0 = (h0 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;

        y0 += icvLogTab[h0];
        x0 = LOGTAB_TRANSLATE( buf[0].d, h0 );
        y0 += LOGPOLY( x0, h0 == 510 );
        y[i] = y0;
    }
}

#else

#define Log_32f ippsLn_32f_A21
#define Log_64f ippsLn_64f_A50

#endif

void log( InputArray _src, OutputArray _dst )
{
    int type = _src.type(), depth = _src.depth(), cn = _src.channels();
    CV_Assert( depth == CV_32F || depth == CV_64F );

    bool use_opencl = _dst.isUMat() && ocl::useOpenCL() && _src.dims() <= 2;

    if(use_opencl && ocl_math_op(_src, noArray(), _dst, OCL_OP_LOG) )
        return;

    Mat src = _src.getMat();
    _dst.create( src.dims, src.size, type );
    Mat dst = _dst.getMat();

    const Mat* arrays[] = {&src, &dst, 0};
    uchar* ptrs[2];
    NAryMatIterator it(arrays, ptrs);
    int len = (int)(it.size*cn);

    for( size_t i = 0; i < it.nplanes; i++, ++it )
    {
        if( depth == CV_32F )
            Log_32f( (const float*)ptrs[0], (float*)ptrs[1], len );
        else
            Log_64f( (const double*)ptrs[0], (double*)ptrs[1], len );
    }
}

/****************************************************************************************\
*                                    P O W E R                                           *
\****************************************************************************************/

template<typename T, typename WT>
static void
iPow_( const T* src, T* dst, int len, int power )
{
    int i;
    for( i = 0; i < len; i++ )
    {
        WT a = 1, b = src[i];
        int p = power;
        while( p > 1 )
        {
            if( p & 1 )
                a *= b;
            b *= b;
            p >>= 1;
        }

        a *= b;
        dst[i] = saturate_cast<T>(a);
    }
}


static void iPow8u(const uchar* src, uchar* dst, int len, int power)
{
    iPow_<uchar, int>(src, dst, len, power);
}

static void iPow8s(const schar* src, schar* dst, int len, int power)
{
    iPow_<schar, int>(src, dst, len, power);
}

static void iPow16u(const ushort* src, ushort* dst, int len, int power)
{
    iPow_<ushort, int>(src, dst, len, power);
}

static void iPow16s(const short* src, short* dst, int len, int power)
{
    iPow_<short, int>(src, dst, len, power);
}

static void iPow32s(const int* src, int* dst, int len, int power)
{
    iPow_<int, int>(src, dst, len, power);
}

static void iPow32f(const float* src, float* dst, int len, int power)
{
    iPow_<float, float>(src, dst, len, power);
}

static void iPow64f(const double* src, double* dst, int len, int power)
{
    iPow_<double, double>(src, dst, len, power);
}


typedef void (*IPowFunc)( const uchar* src, uchar* dst, int len, int power );

static IPowFunc ipowTab[] =
{
    (IPowFunc)iPow8u, (IPowFunc)iPow8s, (IPowFunc)iPow16u, (IPowFunc)iPow16s,
    (IPowFunc)iPow32s, (IPowFunc)iPow32f, (IPowFunc)iPow64f, 0
};

static bool ocl_pow(InputArray _src, double power, OutputArray _dst)
{
    int type = _src.type(), depth = CV_MAT_DEPTH(type), cn = CV_MAT_CN(type);
    bool doubleSupport = ocl::Device::getDefault().doubleFPConfig() > 0;

    if ( !(_src.dims() <= 2 && (depth == CV_32F || depth == CV_64F)) ||
         (depth == CV_64F && !doubleSupport) )
        return false;

    UMat src = _src.getUMat();
    _dst.create(src.size(), type);
    UMat dst = _dst.getUMat();

    ocl::Kernel k("KF", ocl::core::arithm_oclsrc,
                  format("-D dstT=%s -D OP_POW -D UNARY_OP%s", ocl::typeToStr(CV_MAKE_TYPE(depth, 1)),
                         doubleSupport ? " -D DOUBLE_SUPPORT" : ""));

    ocl::KernelArg srcarg = ocl::KernelArg::ReadOnlyNoSize(src),
            dstarg = ocl::KernelArg::WriteOnly(dst, cn);

    if (depth == CV_32F)
        k.args(srcarg, dstarg, (float)power);
    else
        k.args(srcarg, dstarg, power);

    size_t globalsize[2] = { dst.cols *  cn, dst.rows };
    return k.run(2, globalsize, NULL, false);
}

void pow( InputArray _src, double power, OutputArray _dst )
{
    if (ocl::useOpenCL() && _dst.isUMat() && ocl_pow(_src, power, _dst))
        return;

    Mat src = _src.getMat();
    int type = src.type(), depth = src.depth(), cn = src.channels();

    _dst.create( src.dims, src.size, type );
    Mat dst = _dst.getMat();

    int ipower = cvRound(power);
    bool is_ipower = false;

    if( fabs(ipower - power) < DBL_EPSILON )
    {
        if( ipower < 0 )
        {
            divide( 1., src, dst );
            if( ipower == -1 )
                return;
            ipower = -ipower;
            src = dst;
        }

        switch( ipower )
        {
        case 0:
            dst = Scalar::all(1);
            return;
        case 1:
            src.copyTo(dst);
            return;
        case 2:
            multiply(src, src, dst);
            return;
        default:
            is_ipower = true;
        }
    }
    else
        CV_Assert( depth == CV_32F || depth == CV_64F );

    const Mat* arrays[] = {&src, &dst, 0};
    uchar* ptrs[2];
    NAryMatIterator it(arrays, ptrs);
    int len = (int)(it.size*cn);

    if( is_ipower )
    {
        IPowFunc func = ipowTab[depth];
        CV_Assert( func != 0 );

        for( size_t i = 0; i < it.nplanes; i++, ++it )
            func( ptrs[0], ptrs[1], len, ipower );
    }
    else if( fabs(fabs(power) - 0.5) < DBL_EPSILON )
    {
        MathFunc func = power < 0 ?
            (depth == CV_32F ? (MathFunc)InvSqrt_32f : (MathFunc)InvSqrt_64f) :
            (depth == CV_32F ? (MathFunc)Sqrt_32f : (MathFunc)Sqrt_64f);

        for( size_t i = 0; i < it.nplanes; i++, ++it )
            func( ptrs[0], ptrs[1], len );
    }
    else
    {
        int j, k, blockSize = std::min(len, ((BLOCK_SIZE + cn-1)/cn)*cn);
        size_t esz1 = src.elemSize1();

        for( size_t i = 0; i < it.nplanes; i++, ++it )
        {
            for( j = 0; j < len; j += blockSize )
            {
                int bsz = std::min(len - j, blockSize);
                if( depth == CV_32F )
                {
                    const float* x = (const float*)ptrs[0];
                    float* y = (float*)ptrs[1];

                    Log_32f(x, y, bsz);
                    for( k = 0; k < bsz; k++ )
                        y[k] = (float)(y[k]*power);
                    Exp_32f(y, y, bsz);
                }
                else
                {
                    const double* x = (const double*)ptrs[0];
                    double* y = (double*)ptrs[1];

                    Log_64f(x, y, bsz);
                    for( k = 0; k < bsz; k++ )
                        y[k] *= power;
                    Exp_64f(y, y, bsz);
                }
                ptrs[0] += bsz*esz1;
                ptrs[1] += bsz*esz1;
            }
        }
    }
}

void sqrt(InputArray a, OutputArray b)
{
    cv::pow(a, 0.5, b);
}

/************************** CheckArray for NaN's, Inf's *********************************/

template<int cv_mat_type> struct mat_type_assotiations{};

template<> struct mat_type_assotiations<CV_8U>
{
    typedef unsigned char type;
    static const type min_allowable = 0x0;
    static const type max_allowable = 0xFF;
};

template<> struct mat_type_assotiations<CV_8S>
{
    typedef signed char type;
    static const type min_allowable = SCHAR_MIN;
    static const type max_allowable = SCHAR_MAX;
};

template<> struct mat_type_assotiations<CV_16U>
{
    typedef unsigned short type;
    static const type min_allowable = 0x0;
    static const type max_allowable = USHRT_MAX;
};
template<> struct mat_type_assotiations<CV_16S>
{
    typedef signed short type;
    static const type min_allowable = SHRT_MIN;
    static const type max_allowable = SHRT_MAX;
};

template<> struct mat_type_assotiations<CV_32S>
{
    typedef int type;
    static const type min_allowable = (-INT_MAX - 1);
    static const type max_allowable = INT_MAX;
};

// inclusive maxVal !!!
template<int depth>
bool checkIntegerRange(cv::Mat src, Point& bad_pt, int minVal, int maxVal, double& bad_value)
{
    typedef mat_type_assotiations<depth> type_ass;

    if (minVal < type_ass::min_allowable && maxVal > type_ass::max_allowable)
    {
        return true;
    }
    else if (minVal > type_ass::max_allowable || maxVal < type_ass::min_allowable || maxVal < minVal)
    {
        bad_pt = cv::Point(0,0);
        return false;
    }
    cv::Mat as_one_channel = src.reshape(1,0);

    for (int j = 0; j < as_one_channel.rows; ++j)
        for (int i = 0; i < as_one_channel.cols; ++i)
        {
            if (as_one_channel.at<typename type_ass::type>(j ,i) < minVal || as_one_channel.at<typename type_ass::type>(j ,i) > maxVal)
            {
                bad_pt.y = j ;
                bad_pt.x = i % src.channels();
                bad_value = as_one_channel.at<typename type_ass::type>(j ,i);
                return false;
            }
        }
    bad_value = 0.0;

    return true;
}

typedef bool (*check_range_function)(cv::Mat src, Point& bad_pt, int minVal, int maxVal, double& bad_value);

check_range_function check_range_functions[] =
{
    &checkIntegerRange<CV_8U>,
    &checkIntegerRange<CV_8S>,
    &checkIntegerRange<CV_16U>,
    &checkIntegerRange<CV_16S>,
    &checkIntegerRange<CV_32S>
};

bool checkRange(InputArray _src, bool quiet, Point* pt, double minVal, double maxVal)
{
    Mat src = _src.getMat();

    if ( src.dims > 2 )
    {
        const Mat* arrays[] = {&src, 0};
        Mat planes[1];
        NAryMatIterator it(arrays, planes);

        for ( size_t i = 0; i < it.nplanes; i++, ++it )
        {
            if (!checkRange( it.planes[0], quiet, pt, minVal, maxVal ))
            {
                // todo: set index properly
                return false;
            }
        }
        return true;
    }

    int depth = src.depth();
    Point badPt(-1, -1);
    double badValue = 0;

    if (depth < CV_32F)
    {
        // see "Bug #1784"
        int minVali = minVal<(-INT_MAX - 1) ? (-INT_MAX - 1) : cvFloor(minVal);
        int maxVali = maxVal>INT_MAX ? INT_MAX : cvCeil(maxVal) - 1; // checkIntegerRang() use inclusive maxVal

        (check_range_functions[depth])(src, badPt, minVali, maxVali, badValue);
    }
    else
    {
        int i, loc = 0;
        Size size = getContinuousSize( src, src.channels() );

        if( depth == CV_32F )
        {
            Cv32suf a, b;
            int ia, ib;
            const int* isrc = (const int*)src.data;
            size_t step = src.step/sizeof(isrc[0]);

            a.f = (float)std::max(minVal, (double)-FLT_MAX);
            b.f = (float)std::min(maxVal, (double)FLT_MAX);

            ia = CV_TOGGLE_FLT(a.i);
            ib = CV_TOGGLE_FLT(b.i);

            for( ; badPt.x < 0 && size.height--; loc += size.width, isrc += step )
            {
                for( i = 0; i < size.width; i++ )
                {
                    int val = isrc[i];
                    val = CV_TOGGLE_FLT(val);

                    if( val < ia || val >= ib )
                    {
                        badPt = Point((loc + i) % src.cols, (loc + i) / src.cols);
                        badValue = ((const float*)isrc)[i];
                        break;
                    }
                }
            }
        }
        else
        {
            Cv64suf a, b;
            int64 ia, ib;
            const int64* isrc = (const int64*)src.data;
            size_t step = src.step/sizeof(isrc[0]);

            a.f = minVal;
            b.f = maxVal;

            ia = CV_TOGGLE_DBL(a.i);
            ib = CV_TOGGLE_DBL(b.i);

            for( ; badPt.x < 0 && size.height--; loc += size.width, isrc += step )
            {
                for( i = 0; i < size.width; i++ )
                {
                    int64 val = isrc[i];
                    val = CV_TOGGLE_DBL(val);

                    if( val < ia || val >= ib )
                    {
                        badPt = Point((loc + i) % src.cols, (loc + i) / src.cols);
                        badValue = ((const double*)isrc)[i];
                        break;
                    }
                }
            }
        }
    }

    if( badPt.x >= 0 )
    {
        if( pt )
            *pt = badPt;
        if( !quiet )
            CV_Error_( CV_StsOutOfRange,
            ("the value at (%d, %d)=%g is out of range", badPt.x, badPt.y, badValue));
    }
    return badPt.x < 0;
}


void patchNaNs( InputOutputArray _a, double _val )
{
    Mat a = _a.getMat();
    CV_Assert( a.depth() == CV_32F );

    const Mat* arrays[] = {&a, 0};
    int* ptrs[1];
    NAryMatIterator it(arrays, (uchar**)ptrs);
    size_t len = it.size*a.channels();
    Cv32suf val;
    val.f = (float)_val;

    for( size_t i = 0; i < it.nplanes; i++, ++it )
    {
        int* tptr = ptrs[0];
        for( size_t j = 0; j < len; j++ )
            if( (tptr[j] & 0x7fffffff) > 0x7f800000 )
                tptr[j] = val.i;
    }
}


void exp(const float* src, float* dst, int n)
{
    Exp_32f(src, dst, n);
}

void log(const float* src, float* dst, int n)
{
    Log_32f(src, dst, n);
}

void fastAtan2(const float* y, const float* x, float* dst, int n, bool angleInDegrees)
{
    FastAtan2_32f(y, x, dst, n, angleInDegrees);
}

void magnitude(const float* x, const float* y, float* dst, int n)
{
    Magnitude_32f(x, y, dst, n);
}

}

CV_IMPL float cvCbrt(float value) { return cv::cubeRoot(value); }
CV_IMPL float cvFastArctan(float y, float x) { return cv::fastAtan2(y, x); }

CV_IMPL void
cvCartToPolar( const CvArr* xarr, const CvArr* yarr,
               CvArr* magarr, CvArr* anglearr,
               int angle_in_degrees )
{
    cv::Mat X = cv::cvarrToMat(xarr), Y = cv::cvarrToMat(yarr), Mag, Angle;
    if( magarr )
    {
        Mag = cv::cvarrToMat(magarr);
        CV_Assert( Mag.size() == X.size() && Mag.type() == X.type() );
    }
    if( anglearr )
    {
        Angle = cv::cvarrToMat(anglearr);
        CV_Assert( Angle.size() == X.size() && Angle.type() == X.type() );
    }
    if( magarr )
    {
        if( anglearr )
            cv::cartToPolar( X, Y, Mag, Angle, angle_in_degrees != 0 );
        else
            cv::magnitude( X, Y, Mag );
    }
    else
        cv::phase( X, Y, Angle, angle_in_degrees != 0 );
}

CV_IMPL void
cvPolarToCart( const CvArr* magarr, const CvArr* anglearr,
               CvArr* xarr, CvArr* yarr, int angle_in_degrees )
{
    cv::Mat X, Y, Angle = cv::cvarrToMat(anglearr), Mag;
    if( magarr )
    {
        Mag = cv::cvarrToMat(magarr);
        CV_Assert( Mag.size() == Angle.size() && Mag.type() == Angle.type() );
    }
    if( xarr )
    {
        X = cv::cvarrToMat(xarr);
        CV_Assert( X.size() == Angle.size() && X.type() == Angle.type() );
    }
    if( yarr )
    {
        Y = cv::cvarrToMat(yarr);
        CV_Assert( Y.size() == Angle.size() && Y.type() == Angle.type() );
    }

    cv::polarToCart( Mag, Angle, X, Y, angle_in_degrees != 0 );
}

CV_IMPL void cvExp( const CvArr* srcarr, CvArr* dstarr )
{
    cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr);
    CV_Assert( src.type() == dst.type() && src.size == dst.size );
    cv::exp( src, dst );
}

CV_IMPL void cvLog( const CvArr* srcarr, CvArr* dstarr )
{
    cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr);
    CV_Assert( src.type() == dst.type() && src.size == dst.size );
    cv::log( src, dst );
}

CV_IMPL void cvPow( const CvArr* srcarr, CvArr* dstarr, double power )
{
    cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr);
    CV_Assert( src.type() == dst.type() && src.size == dst.size );
    cv::pow( src, power, dst );
}

CV_IMPL int cvCheckArr( const CvArr* arr, int flags,
                        double minVal, double maxVal )
{
    if( (flags & CV_CHECK_RANGE) == 0 )
        minVal = -DBL_MAX, maxVal = DBL_MAX;
    return cv::checkRange(cv::cvarrToMat(arr), (flags & CV_CHECK_QUIET) != 0, 0, minVal, maxVal );
}


/*
  Finds real roots of cubic, quadratic or linear equation.
  The original code has been taken from Ken Turkowski web page
  (http://www.worldserver.com/turk/opensource/) and adopted for OpenCV.
  Here is the copyright notice.

  -----------------------------------------------------------------------
  Copyright (C) 1978-1999 Ken Turkowski. <turk@computer.org>

    All rights reserved.

    Warranty Information
      Even though I have reviewed this software, I make no warranty
      or representation, either express or implied, with respect to this
      software, its quality, accuracy, merchantability, or fitness for a
      particular purpose.  As a result, this software is provided "as is,"
      and you, its user, are assuming the entire risk as to its quality
      and accuracy.

    This code may be used and freely distributed as long as it includes
    this copyright notice and the above warranty information.
  -----------------------------------------------------------------------
*/

int cv::solveCubic( InputArray _coeffs, OutputArray _roots )
{
    const int n0 = 3;
    Mat coeffs = _coeffs.getMat();
    int ctype = coeffs.type();

    CV_Assert( ctype == CV_32F || ctype == CV_64F );
    CV_Assert( (coeffs.size() == Size(n0, 1) ||
                coeffs.size() == Size(n0+1, 1) ||
                coeffs.size() == Size(1, n0) ||
                coeffs.size() == Size(1, n0+1)) );

    _roots.create(n0, 1, ctype, -1, true, _OutputArray::DEPTH_MASK_FLT);
    Mat roots = _roots.getMat();

    int i = -1, n = 0;
    double a0 = 1., a1, a2, a3;
    double x0 = 0., x1 = 0., x2 = 0.;
    int ncoeffs = coeffs.rows + coeffs.cols - 1;

    if( ctype == CV_32FC1 )
    {
        if( ncoeffs == 4 )
            a0 = coeffs.at<float>(++i);

        a1 = coeffs.at<float>(i+1);
        a2 = coeffs.at<float>(i+2);
        a3 = coeffs.at<float>(i+3);
    }
    else
    {
        if( ncoeffs == 4 )
            a0 = coeffs.at<double>(++i);

        a1 = coeffs.at<double>(i+1);
        a2 = coeffs.at<double>(i+2);
        a3 = coeffs.at<double>(i+3);
    }

    if( a0 == 0 )
    {
        if( a1 == 0 )
        {
            if( a2 == 0 )
                n = a3 == 0 ? -1 : 0;
            else
            {
                // linear equation
                x0 = -a3/a2;
                n = 1;
            }
        }
        else
        {
            // quadratic equation
            double d = a2*a2 - 4*a1*a3;
            if( d >= 0 )
            {
                d = std::sqrt(d);
                double q1 = (-a2 + d) * 0.5;
                double q2 = (a2 + d) * -0.5;
                if( fabs(q1) > fabs(q2) )
                {
                    x0 = q1 / a1;
                    x1 = a3 / q1;
                }
                else
                {
                    x0 = q2 / a1;
                    x1 = a3 / q2;
                }
                n = d > 0 ? 2 : 1;
            }
        }
    }
    else
    {
        a0 = 1./a0;
        a1 *= a0;
        a2 *= a0;
        a3 *= a0;

        double Q = (a1 * a1 - 3 * a2) * (1./9);
        double R = (2 * a1 * a1 * a1 - 9 * a1 * a2 + 27 * a3) * (1./54);
        double Qcubed = Q * Q * Q;
        double d = Qcubed - R * R;

        if( d >= 0 )
        {
            double theta = acos(R / std::sqrt(Qcubed));
            double sqrtQ = std::sqrt(Q);
            double t0 = -2 * sqrtQ;
            double t1 = theta * (1./3);
            double t2 = a1 * (1./3);
            x0 = t0 * cos(t1) - t2;
            x1 = t0 * cos(t1 + (2.*CV_PI/3)) - t2;
            x2 = t0 * cos(t1 + (4.*CV_PI/3)) - t2;
            n = 3;
        }
        else
        {
            double e;
            d = std::sqrt(-d);
            e = std::pow(d + fabs(R), 0.333333333333);
            if( R > 0 )
                e = -e;
            x0 = (e + Q / e) - a1 * (1./3);
            n = 1;
        }
    }

    if( roots.type() == CV_32FC1 )
    {
        roots.at<float>(0) = (float)x0;
        roots.at<float>(1) = (float)x1;
        roots.at<float>(2) = (float)x2;
    }
    else
    {
        roots.at<double>(0) = x0;
        roots.at<double>(1) = x1;
        roots.at<double>(2) = x2;
    }

    return n;
}

/* finds complex roots of a polynomial using Durand-Kerner method:
   http://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method */
double cv::solvePoly( InputArray _coeffs0, OutputArray _roots0, int maxIters )
{
    typedef Complex<double> C;

    double maxDiff = 0;
    int iter, i, j;
    Mat coeffs0 = _coeffs0.getMat();
    int ctype = _coeffs0.type();
    int cdepth = CV_MAT_DEPTH(ctype);

    CV_Assert( CV_MAT_DEPTH(ctype) >= CV_32F && CV_MAT_CN(ctype) <= 2 );
    CV_Assert( coeffs0.rows == 1 || coeffs0.cols == 1 );

    int n = coeffs0.cols + coeffs0.rows - 2;

    _roots0.create(n, 1, CV_MAKETYPE(cdepth, 2), -1, true, _OutputArray::DEPTH_MASK_FLT);
    Mat roots0 = _roots0.getMat();

    AutoBuffer<C> buf(n*2+2);
    C *coeffs = buf, *roots = coeffs + n + 1;
    Mat coeffs1(coeffs0.size(), CV_MAKETYPE(CV_64F, coeffs0.channels()), coeffs0.channels() == 2 ? coeffs : roots);
    coeffs0.convertTo(coeffs1, coeffs1.type());
    if( coeffs0.channels() == 1 )
    {
        const double* rcoeffs = (const double*)roots;
        for( i = 0; i <= n; i++ )
            coeffs[i] = C(rcoeffs[i], 0);
    }

    C p(1, 0), r(1, 1);

    for( i = 0; i < n; i++ )
    {
        roots[i] = p;
        p = p * r;
    }

    maxIters = maxIters <= 0 ? 1000 : maxIters;
    for( iter = 0; iter < maxIters; iter++ )
    {
        maxDiff = 0;
        for( i = 0; i < n; i++ )
        {
            p = roots[i];
            C num = coeffs[n], denom = coeffs[n];
            for( j = 0; j < n; j++ )
            {
                num = num*p + coeffs[n-j-1];
                if( j != i ) denom = denom * (p - roots[j]);
            }
            num /= denom;
            roots[i] = p - num;
            maxDiff = std::max(maxDiff, cv::abs(num));
        }
        if( maxDiff <= 0 )
            break;
    }

    if( coeffs0.channels() == 1 )
    {
        const double verySmallEps = 1e-100;
        for( i = 0; i < n; i++ )
            if( fabs(roots[i].im) < verySmallEps )
                roots[i].im = 0;
    }

    Mat(roots0.size(), CV_64FC2, roots).convertTo(roots0, roots0.type());
    return maxDiff;
}


CV_IMPL int
cvSolveCubic( const CvMat* coeffs, CvMat* roots )
{
    cv::Mat _coeffs = cv::cvarrToMat(coeffs), _roots = cv::cvarrToMat(roots), _roots0 = _roots;
    int nroots = cv::solveCubic(_coeffs, _roots);
    CV_Assert( _roots.data == _roots0.data ); // check that the array of roots was not reallocated
    return nroots;
}


void cvSolvePoly(const CvMat* a, CvMat *r, int maxiter, int)
{
    cv::Mat _a = cv::cvarrToMat(a);
    cv::Mat _r = cv::cvarrToMat(r);
    cv::Mat _r0 = _r;
    cv::solvePoly(_a, _r, maxiter);
    CV_Assert( _r.data == _r0.data ); // check that the array of roots was not reallocated
}


/* End of file. */