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

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#include "_cxcore.h"

#ifdef HAVE_CONFIG_H
#include <cvconfig.h>
#endif

#define ICV_MATH_BLOCK_SIZE  256

#define _CV_SQRT_MAGIC     0xbe6f0000

#define _CV_SQRT_MAGIC_DBL CV_BIG_UINT(0xbfcd460000000000)

#define _CV_ATAN_CF0  (-15.8131890796f)
#define _CV_ATAN_CF1  (61.0941945596f)
#define _CV_ATAN_CF2  0.f /*(-0.140500406322f)*/

static const float icvAtanTab[8] = { 0.f + _CV_ATAN_CF2, 90.f - _CV_ATAN_CF2,
    180.f - _CV_ATAN_CF2, 90.f + _CV_ATAN_CF2,
    360.f - _CV_ATAN_CF2, 270.f + _CV_ATAN_CF2,
    180.f + _CV_ATAN_CF2, 270.f - _CV_ATAN_CF2
};

static const int icvAtanSign[8] =
    { 0, 0x80000000, 0x80000000, 0, 0x80000000, 0, 0, 0x80000000 };

CV_IMPL float
cvFastArctan( float y, float x )
{
    Cv32suf _x, _y;
    int ix, iy, ygx, idx;
    double z;

    _x.f = x; _y.f = y;
    ix = _x.i; iy = _y.i;
    idx = (ix < 0) * 2 + (iy < 0) * 4;

    ix &= 0x7fffffff;
    iy &= 0x7fffffff;

    ygx = (iy <= ix) - 1;
    idx -= ygx;

    idx &= ((ix == 0) - 1) | ((iy == 0) - 1);

    /* swap ix and iy if ix < iy */
    ix ^= iy & ygx;
    iy ^= ix & ygx;
    ix ^= iy & ygx;

    _y.i = iy ^ icvAtanSign[idx];

    /* ix = ix != 0 ? ix : 1.f */
    _x.i = ((ix ^ CV_1F) & ((ix == 0) - 1)) ^ CV_1F;

    z = _y.f / _x.f;
    return (float)((_CV_ATAN_CF0*fabs(z) + _CV_ATAN_CF1)*z + icvAtanTab[idx]);
}


IPCVAPI_IMPL( CvStatus, icvFastArctan_32f,
    (const float *__y, const float *__x, float *angle, int len ), (__y, __x, angle, len) )
{
    int i = 0;
    const int *y = (const int*)__y, *x = (const int*)__x;

    if( !(y && x && angle && len >= 0) )
        return CV_BADFACTOR_ERR;

    /* unrolled by 4 loop */
    for( ; i <= len - 4; i += 4 )
    {
        int j, idx[4];
        float xf[4], yf[4];
        double d = 1.;

        /* calc numerators and denominators */
        for( j = 0; j < 4; j++ )
        {
            int ix = x[i + j], iy = y[i + j];
            int ygx, k = (ix < 0) * 2 + (iy < 0) * 4;
            Cv32suf _x, _y;

            ix &= 0x7fffffff;
            iy &= 0x7fffffff;

            ygx = (iy <= ix) - 1;
            k -= ygx;

            k &= ((ix == 0) - 1) | ((iy == 0) - 1);

            /* swap ix and iy if ix < iy */
            ix ^= iy & ygx;
            iy ^= ix & ygx;
            ix ^= iy & ygx;

            _y.i = iy ^ icvAtanSign[k];

            /* ix = ix != 0 ? ix : 1.f */
            _x.i = ((ix ^ CV_1F) & ((ix == 0) - 1)) ^ CV_1F;
            idx[j] = k;
            yf[j] = _y.f;
            d *= (xf[j] = _x.f);
        }

        d = 1. / d;

        {
            double b = xf[2] * xf[3], a = xf[0] * xf[1];

            float z0 = (float) (yf[0] * xf[1] * b * d);
            float z1 = (float) (yf[1] * xf[0] * b * d);
            float z2 = (float) (yf[2] * xf[3] * a * d);
            float z3 = (float) (yf[3] * xf[2] * a * d);

            z0 = (float)((_CV_ATAN_CF0*fabs(z0) + _CV_ATAN_CF1)*z0 + icvAtanTab[idx[0]]);
            z1 = (float)((_CV_ATAN_CF0*fabs(z1) + _CV_ATAN_CF1)*z1 + icvAtanTab[idx[1]]);
            z2 = (float)((_CV_ATAN_CF0*fabs(z2) + _CV_ATAN_CF1)*z2 + icvAtanTab[idx[2]]);
            z3 = (float)((_CV_ATAN_CF0*fabs(z3) + _CV_ATAN_CF1)*z3 + icvAtanTab[idx[3]]);

            angle[i] = z0;
            angle[i+1] = z1;
            angle[i+2] = z2;
            angle[i+3] = z3;
        }
    }

    /* process the rest */
    for( ; i < len; i++ )
        angle[i] = cvFastArctan( __y[i], __x[i] );

    return CV_OK;
}


/* ************************************************************************** *\
   Fast cube root by Ken Turkowski
   (http://www.worldserver.com/turk/computergraphics/papers.html)
\* ************************************************************************** */
CV_IMPL  float  cvCbrt( 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 const double _0_5 = 0.5, _1_5 = 1.5;

IPCVAPI_IMPL( CvStatus, icvInvSqrt_32f, (const float *src, float *dst, int len), (src, dst, len) )
{
    int i = 0;

    if( !(src && dst && len >= 0) )
        return CV_BADFACTOR_ERR;

    for( ; i < len; i++ )
        dst[i] = (float)(1.f/sqrt(src[i]));

    return CV_OK;
}


IPCVAPI_IMPL( CvStatus, icvSqrt_32f, (const float *src, float *dst, int len), (src, dst, len) )
{
    int i = 0;

    if( !(src && dst && len >= 0) )
        return CV_BADFACTOR_ERR;

    for( ; i < len; i++ )
        dst[i] = (float)sqrt(src[i]);

    return CV_OK;
}


IPCVAPI_IMPL( CvStatus, icvSqrt_64f, (const double *src, double *dst, int len), (src, dst, len) )
{
    int i = 0;

    if( !(src && dst && len >= 0) )
        return CV_BADFACTOR_ERR;

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

    return CV_OK;
}


IPCVAPI_IMPL( CvStatus, icvInvSqrt_64f, (const double *src, double *dst, int len), (src, dst, len) )
{
    int i = 0;

    if( !(src && dst && len >= 0) )
        return CV_BADFACTOR_ERR;

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

    return CV_OK;
}


#define ICV_DEF_SQR_MAGNITUDE_FUNC(flavor, arrtype, magtype)\
static CvStatus CV_STDCALL                                  \
icvSqrMagnitude_##flavor(const arrtype* x, const arrtype* y,\
                         magtype* mag, int len)             \
{                                                           \
    int i;                                                  \
                                                            \
    for( i = 0; i <= len - 4; i += 4 )                      \
    {                                                       \
        magtype x0 = (magtype)x[i], y0 = (magtype)y[i];     \
        magtype x1 = (magtype)x[i+1], y1 = (magtype)y[i+1]; \
                                                            \
        x0 = x0*x0 + y0*y0;                                 \
        x1 = x1*x1 + y1*y1;                                 \
        mag[i] = x0;                                        \
        mag[i+1] = x1;                                      \
        x0 = (magtype)x[i+2], y0 = (magtype)y[i+2];         \
        x1 = (magtype)x[i+3], y1 = (magtype)y[i+3];         \
        x0 = x0*x0 + y0*y0;                                 \
        x1 = x1*x1 + y1*y1;                                 \
        mag[i+2] = x0;                                      \
        mag[i+3] = x1;                                      \
    }                                                       \
                                                            \
    for( ; i < len; i++ )                                   \
    {                                                       \
        magtype x0 = (magtype)x[i], y0 = (magtype)y[i];     \
        mag[i] = x0*x0 + y0*y0;                             \
    }                                                       \
                                                            \
    return CV_OK;                                           \
}


ICV_DEF_SQR_MAGNITUDE_FUNC( 32f, float, float )
ICV_DEF_SQR_MAGNITUDE_FUNC( 64f, double, double )

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

CV_IMPL void
cvCartToPolar( const CvArr* xarr, const CvArr* yarr,
               CvArr* magarr, CvArr* anglearr,
               int angle_in_degrees )
{
    CV_FUNCNAME( "cvCartToPolar" );

    __BEGIN__;

    float* mag_buffer = 0;
    float* x_buffer = 0;
    float* y_buffer = 0;
    int block_size = 0;
    CvMat xstub, *xmat = (CvMat*)xarr;
    CvMat ystub, *ymat = (CvMat*)yarr;
    CvMat magstub, *mag = (CvMat*)magarr;
    CvMat anglestub, *angle = (CvMat*)anglearr;
    int coi1 = 0, coi2 = 0, coi3 = 0, coi4 = 0;
    int depth;
    CvSize size;
    int x, y;
    int cont_flag = CV_MAT_CONT_FLAG;

    if( !CV_IS_MAT(xmat))
        CV_CALL( xmat = cvGetMat( xmat, &xstub, &coi1 ));

    if( !CV_IS_MAT(ymat))
        CV_CALL( ymat = cvGetMat( ymat, &ystub, &coi2 ));

    if( !CV_ARE_TYPES_EQ( xmat, ymat ) )
        CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

    if( !CV_ARE_SIZES_EQ( xmat, ymat ) )
        CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );

    depth = CV_MAT_DEPTH( xmat->type );
    if( depth < CV_32F )
        CV_ERROR( CV_StsUnsupportedFormat, "" );

    if( mag )
    {
        CV_CALL( mag = cvGetMat( mag, &magstub, &coi3 ));

        if( !CV_ARE_TYPES_EQ( mag, xmat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

        if( !CV_ARE_SIZES_EQ( mag, xmat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );
        cont_flag = mag->type;
    }

    if( angle )
    {
        CV_CALL( angle = cvGetMat( angle, &anglestub, &coi4 ));

        if( !CV_ARE_TYPES_EQ( angle, xmat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

        if( !CV_ARE_SIZES_EQ( angle, xmat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );
        cont_flag &= angle->type;
    }

    if( coi1 != 0 || coi2 != 0 || coi3 != 0 || coi4 != 0 )
        CV_ERROR( CV_BadCOI, "" );

    size = cvGetMatSize(xmat);
    size.width *= CV_MAT_CN(xmat->type);

    if( CV_IS_MAT_CONT( xmat->type & ymat->type & cont_flag ))
    {
        size.width *= size.height;
        size.height = 1;
    }

    block_size = MIN( size.width, ICV_MATH_BLOCK_SIZE );
    if( depth == CV_64F && angle )
    {
        x_buffer = (float*)cvStackAlloc( block_size*sizeof(float));
        y_buffer = (float*)cvStackAlloc( block_size*sizeof(float));
    }
    else if( depth == CV_32F && mag )
    {
        mag_buffer = (float*)cvStackAlloc( block_size*sizeof(float));
    }

    if( depth == CV_32F )
    {
        for( y = 0; y < size.height; y++ )
        {
            float* x_data = (float*)(xmat->data.ptr + xmat->step*y);
            float* y_data = (float*)(ymat->data.ptr + ymat->step*y);
            float* mag_data = mag ? (float*)(mag->data.ptr + mag->step*y) : 0;
            float* angle_data = angle ? (float*)(angle->data.ptr + angle->step*y) : 0;

            for( x = 0; x < size.width; x += block_size )
            {
                int len = MIN( size.width - x, block_size );

                if( mag )
                    icvSqrMagnitude_32f( x_data + x, y_data + x, mag_buffer, len );

                if( angle )
                {
                    icvFastArctan_32f( y_data + x, x_data + x, angle_data + x, len );
                    if( !angle_in_degrees )
                        icvScale_32f( angle_data + x, angle_data + x,
                                      len, (float)(CV_PI/180.), 0 );
                }

                if( mag )
                    icvSqrt_32f( mag_buffer, mag_data + x, len );
            }
        }
    }
    else
    {
        for( y = 0; y < size.height; y++ )
        {
            double* x_data = (double*)(xmat->data.ptr + xmat->step*y);
            double* y_data = (double*)(ymat->data.ptr + ymat->step*y);
            double* mag_data = mag ? (double*)(mag->data.ptr + mag->step*y) : 0;
            double* angle_data = angle ? (double*)(angle->data.ptr + angle->step*y) : 0;

            for( x = 0; x < size.width; x += block_size )
            {
                int len = MIN( size.width - x, block_size );

                if( angle )
                {
                    icvCvt_64f32f( x_data + x, x_buffer, len );
                    icvCvt_64f32f( y_data + x, y_buffer, len );
                }

                if( mag )
                {
                    icvSqrMagnitude_64f( x_data + x, y_data + x, mag_data + x, len );
                    icvSqrt_64f( mag_data + x, mag_data + x, len );
                }

                if( angle )
                {
                    icvFastArctan_32f( y_buffer, x_buffer, x_buffer, len );
                    if( !angle_in_degrees )
                        icvScale_32f( x_buffer, x_buffer, len, (float)(CV_PI/180.), 0 );
                    icvCvt_32f64f( x_buffer, angle_data + x, len );
                }
            }
        }
    }

    __END__;
}


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

static CvStatus CV_STDCALL
icvSinCos_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;
    }

    return CV_OK;
}


CV_IMPL void
cvPolarToCart( const CvArr* magarr, const CvArr* anglearr,
               CvArr* xarr, CvArr* yarr, int angle_in_degrees )
{
    CV_FUNCNAME( "cvPolarToCart" );

    __BEGIN__;

    float* x_buffer = 0;
    float* y_buffer = 0;
    int block_size = 0;
    CvMat xstub, *xmat = (CvMat*)xarr;
    CvMat ystub, *ymat = (CvMat*)yarr;
    CvMat magstub, *mag = (CvMat*)magarr;
    CvMat anglestub, *angle = (CvMat*)anglearr;
    int coi1 = 0, coi2 = 0, coi3 = 0, coi4 = 0;
    int depth;
    CvSize size;
    int x, y;
    int cont_flag;

    if( !CV_IS_MAT(angle))
        CV_CALL( angle = cvGetMat( angle, &anglestub, &coi4 ));

    depth = CV_MAT_DEPTH( angle->type );
    if( depth < CV_32F )
        CV_ERROR( CV_StsUnsupportedFormat, "" );
    cont_flag = angle->type;

    if( mag )
    {
        if( !CV_IS_MAT(mag))
            CV_CALL( mag = cvGetMat( mag, &magstub, &coi3 ));

        if( !CV_ARE_TYPES_EQ( angle, mag ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

        if( !CV_ARE_SIZES_EQ( angle, mag ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );

        cont_flag &= mag->type;
    }

    if( xmat )
    {
        if( !CV_IS_MAT(xmat))
            CV_CALL( xmat = cvGetMat( xmat, &xstub, &coi1 ));

        if( !CV_ARE_TYPES_EQ( angle, xmat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

        if( !CV_ARE_SIZES_EQ( angle, xmat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );

        cont_flag &= xmat->type;
    }

    if( ymat )
    {
        if( !CV_IS_MAT(ymat))
            CV_CALL( ymat = cvGetMat( ymat, &ystub, &coi2 ));

        if( !CV_ARE_TYPES_EQ( angle, ymat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

        if( !CV_ARE_SIZES_EQ( angle, ymat ) )
            CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );

        cont_flag &= ymat->type;
    }

    if( coi1 != 0 || coi2 != 0 || coi3 != 0 || coi4 != 0 )
        CV_ERROR( CV_BadCOI, "" );

    size = cvGetMatSize(angle);
    size.width *= CV_MAT_CN(angle->type);

    if( CV_IS_MAT_CONT( cont_flag ))
    {
        size.width *= size.height;
        size.height = 1;
    }

    block_size = MIN( size.width, ICV_MATH_BLOCK_SIZE );
    x_buffer = (float*)cvStackAlloc( block_size*sizeof(float));
    y_buffer = (float*)cvStackAlloc( block_size*sizeof(float));

    if( depth == CV_32F )
    {
        for( y = 0; y < size.height; y++ )
        {
            float* x_data = (float*)(xmat ? xmat->data.ptr + xmat->step*y : 0);
            float* y_data = (float*)(ymat ? ymat->data.ptr + ymat->step*y : 0);
            float* mag_data = (float*)(mag ? mag->data.ptr + mag->step*y : 0);
            float* angle_data = (float*)(angle->data.ptr + angle->step*y);

            for( x = 0; x < size.width; x += block_size )
            {
                int i, len = MIN( size.width - x, block_size );

                icvSinCos_32f( angle_data+x, y_buffer, x_buffer, len, angle_in_degrees );

                for( i = 0; i < len; i++ )
                {
                    float tx = x_buffer[i];
                    float ty = y_buffer[i];

                    if( mag_data )
                    {
                        float magval = mag_data[x+i];
                        tx *= magval;
                        ty *= magval;
                    }

                    if( xmat )
                        x_data[x+i] = tx;
                    if( ymat )
                        y_data[x+i] = ty;
                }
            }
        }
    }
    else
    {
        for( y = 0; y < size.height; y++ )
        {
            double* x_data = (double*)(xmat ? xmat->data.ptr + xmat->step*y : 0);
            double* y_data = (double*)(ymat ? ymat->data.ptr + ymat->step*y : 0);
            double* mag_data = (double*)(mag ? mag->data.ptr + mag->step*y : 0);
            double* angle_data = (double*)(angle->data.ptr + angle->step*y);
            double C = angle_in_degrees ? CV_PI/180. : 1;

            for( x = 0; x < size.width; x++ )
            {
                double phi = angle_data[x]*C;
                double magval = mag_data ? mag_data[x] : 1.;
                if( xmat )
                    x_data[x] = cos(phi)*magval;
                if( ymat )
                    y_data[x] = sin(phi)*magval;
            }
        }
    }

    __END__;
}

/****************************************************************************************\
*                                          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;

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

#define EXPPOLY_32F_A0 .9670371139572337719125840413672004409288e-2

static const double icvExpTab[] = {
    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,
};

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

IPCVAPI_IMPL( CvStatus, icvExp_32f, ( const float *_x, float *y, int n ), (_x, y, n) )
{
    static const double
        EXPPOLY_32F_A4 = 1.000000000000002438532970795181890933776 / EXPPOLY_32F_A0,
        EXPPOLY_32F_A3 = .6931471805521448196800669615864773144641 / EXPPOLY_32F_A0,
        EXPPOLY_32F_A2 = .2402265109513301490103372422686535526573 / EXPPOLY_32F_A0,
        EXPPOLY_32F_A1 = .5550339366753125211915322047004666939128e-1 / EXPPOLY_32F_A0;

    #undef EXPPOLY
    #define EXPPOLY(x)  \
        (((((x) + EXPPOLY_32F_A1)*(x) + EXPPOLY_32F_A2)*(x) + EXPPOLY_32F_A3)*(x) + EXPPOLY_32F_A4)

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

    if( !x || !y )
        return CV_NULLPTR_ERR;
    if( n <= 0 )
        return CV_BADSIZE_ERR;

    buf[0].i.lo = buf[1].i.lo = buf[2].i.lo = buf[3].i.lo = 0;

    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) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[0].i.hi = t << 20;

        t = (val1 >> EXPTAB_SCALE) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[1].i.hi = t << 20;

        t = (val2 >> EXPTAB_SCALE) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[2].i.hi = t << 20;

        t = (val3 >> EXPTAB_SCALE) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[3].i.hi = t << 20;

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

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

        x2 = buf[2].d * icvExpTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
        x3 = buf[3].d * icvExpTab[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) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);

        buf[0].i.hi = t << 20;
        x0 = (x0 - val0)*exp_postscale;

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

    return CV_OK;
}


IPCVAPI_IMPL( CvStatus, icvExp_64f, ( const double *_x, double *y, int n ), (_x, y, 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;
    DBLINT buf[4];
    const Cv64suf* x = (const Cv64suf*)_x;

    if( !x || !y )
        return CV_NULLPTR_ERR;
    if( n <= 0 )
        return CV_BADSIZE_ERR;

    buf[0].i.lo = buf[1].i.lo = buf[2].i.lo = buf[3].i.lo = 0;

    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 | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[0].i.hi = t << 20;

        t = (val1 >> EXPTAB_SCALE) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[1].i.hi = t << 20;

        t = (val2 >> EXPTAB_SCALE) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[2].i.hi = t << 20;

        t = (val3 >> EXPTAB_SCALE) + 1023;
        t = (t | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);
        buf[3].i.hi = t << 20;

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

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

        y2 = buf[2].d * icvExpTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
        y3 = buf[3].d * icvExpTab[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 | ((t < 2047) - 1)) & (((t < 0) - 1) & 2047);

        buf[0].i.hi = t << 20;
        x0 = (x0 - val0)*exp_postscale;

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

    return CV_OK;
}

#undef EXPTAB_SCALE
#undef EXPTAB_MASK
#undef EXPPOLY_32F_A0

CV_IMPL void cvExp( const CvArr* srcarr, CvArr* dstarr )
{
    CV_FUNCNAME( "cvExp" );

    __BEGIN__;

    CvMat srcstub, *src = (CvMat*)srcarr;
    CvMat dststub, *dst = (CvMat*)dstarr;
    int coi1 = 0, coi2 = 0, src_depth, dst_depth;
    double* buffer = 0;
    CvSize size;
    int x, y, dx = 0;

    if( !CV_IS_MAT(src))
        CV_CALL( src = cvGetMat( src, &srcstub, &coi1 ));

    if( !CV_IS_MAT(dst))
        CV_CALL( dst = cvGetMat( dst, &dststub, &coi2 ));

    if( coi1 != 0 || coi2 != 0 )
        CV_ERROR( CV_BadCOI, "" );

    src_depth = CV_MAT_DEPTH(src->type);
    dst_depth = CV_MAT_DEPTH(dst->type);

    if( !CV_ARE_CNS_EQ( src, dst ) || src_depth < CV_32F || dst_depth < src_depth )
        CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

    if( !CV_ARE_SIZES_EQ( src, dst ) )
        CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );

    size = cvGetMatSize(src);
    size.width *= CV_MAT_CN(src->type);

    if( CV_IS_MAT_CONT( src->type & dst->type ))
    {
        size.width *= size.height;
        size.height = 1;
    }

    if( !CV_ARE_DEPTHS_EQ( src, dst ))
    {
        dx = MIN( 1024, size.width );
        buffer = (double*)cvStackAlloc( dx*sizeof(buffer[0]) );
    }

    for( y = 0; y < size.height; y++ )
    {
        uchar* src_data = src->data.ptr + src->step*y;
        uchar* dst_data = dst->data.ptr + dst->step*y;

        if( src_depth == CV_64F )
        {
            icvExp_64f( (double*)src_data, (double*)dst_data, size.width );
        }
        else if( src_depth == dst_depth )
        {
            icvExp_32f( (float*)src_data, (float*)dst_data, size.width );
        }
        else
        {
            for( x = 0; x < size.width; x += dx )
            {
                int len = dx;
                if( x + len > size.width )
                    len = size.width - x;
                icvCvt_32f64f( (float*)src_data + x, buffer, len );
                icvExp_64f( buffer, (double*)dst_data + x, len );
            }
        }
    }

    __END__;
}


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

#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 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,
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.62652315293135274476554741340805776417250,    .5344467640918580375782881002087682672234,
.62860865942237409420556559780379757285100,    .5333333333333333333333333333333333333333,
.63068982562619868570408243613201193511500,    .5322245322245322245322245322245322245322,
.63276666957103777644277897707070223987100,    .5311203319502074688796680497925311203320,
.63483920917301017716738442686619237065300,    .5300207039337474120082815734989648033126,
.63690746223706917739093569252872839570050,    .5289256198347107438016528925619834710744,
.63897144645792069983514238629140891134750,    .5278350515463917525773195876288659793814,
.64103117942093124081992527862894348800200,    .5267489711934156378600823045267489711934,
.64308667860302726193566513757104985415950,    .5256673511293634496919917864476386036961,
.64513796137358470073053240412264131009600,    .5245901639344262295081967213114754098361,
.64718504499530948859131740391603671014300,    .5235173824130879345603271983640081799591,
.64922794662510974195157587018911726772800,    .5224489795918367346938775510204081632653,
.65126668331495807251485530287027359008800,    .5213849287169042769857433808553971486762,
.65330127201274557080523663898929953575150,    .5203252032520325203252032520325203252033,
.65533172956312757406749369692988693714150,    .5192697768762677484787018255578093306288,
.65735807270835999727154330685152672231200,    .5182186234817813765182186234817813765182,
.65938031808912778153342060249997302889800,    .5171717171717171717171717171717171717172,
.66139848224536490484126716182800009846700,    .5161290322580645161290322580645161290323,
.66341258161706617713093692145776003599150,    .5150905432595573440643863179074446680080,
.66542263254509037562201001492212526500250,    .5140562248995983935742971887550200803213,
.66742865127195616370414654738851822912700,    .5130260521042084168336673346693386773547,
.66943065394262923906154583164607174694550,    .5120000000000000000000000000000000000000,
.67142865660530226534774556057527661323550,    .5109780439121756487025948103792415169661,
.67342267521216669923234121597488410770900,    .5099601593625498007968127490039840637450,
.67541272562017662384192817626171745359900,    .5089463220675944333996023856858846918489,
.67739882359180603188519853574689477682100,    .5079365079365079365079365079365079365079,
.67938098479579733801614338517538271844400,    .5069306930693069306930693069306930693069,
.68135922480790300781450241629499942064300,    .5059288537549407114624505928853754940711,
.68333355911162063645036823800182901322850,    .5049309664694280078895463510848126232742,
.68530400309891936760919861626462079584600,    .5039370078740157480314960629921259842520,
.68727057207096020619019327568821609020250,    .5029469548133595284872298624754420432220,
.68923328123880889251040571252815425395950,    .5019607843137254901960784313725490196078,
.69314718055994530941723212145818, 5.0e-01,
};



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

IPCVAPI_IMPL( CvStatus, icvLog_32f, ( const float *_x, float *y, int n ), (_x, y, n) )
{
    static const double shift[] = { 0, -1./512 };
    static const double
        A0 = 0.3333333333333333333333333,
        A1 = -0.5,
        A2 = 1;

    #undef LOGPOLY
    #define LOGPOLY(x,k) ((x)+=shift[k],((A0*(x) + A1)*(x) + A2)*(x))

    int i = 0;
    union
    {
        int i;
        float f;
    }
    buf[4];

    const int* x = (const int*)_x;

    if( !x || !y )
        return CV_NULLPTR_ERR;
    if( n <= 0 )
        return CV_BADSIZE_ERR;

    for( i = 0; 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 );

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

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

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

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

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

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

        y[i] = (float)y0;
    }

    return CV_OK;
}


IPCVAPI_IMPL( CvStatus, icvLog_64f, ( const double *x, double *y, int n ), (x, y, n) )
{
    static const double shift[] = { 0, -1./512 };
    static const double
        A0 = -.1666666666666666666666666666666666666666,
        A1 = +0.2,
        A2 = -0.25,
        A3 = +0.3333333333333333333333333333333333333333,
        A4 = -0.5,
        A5 = +1.0;

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

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

    if( !x || !y )
        return CV_NULLPTR_ERR;
    if( n <= 0 )
        return CV_BADSIZE_ERR;

    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;
    }

    return CV_OK;
}


CV_IMPL void cvLog( const CvArr* srcarr, CvArr* dstarr )
{
    CV_FUNCNAME( "cvLog" );

    __BEGIN__;

    CvMat srcstub, *src = (CvMat*)srcarr;
    CvMat dststub, *dst = (CvMat*)dstarr;
    int coi1 = 0, coi2 = 0, src_depth, dst_depth;
    double* buffer = 0;
    CvSize size;
    int x, y, dx = 0;

    if( !CV_IS_MAT(src))
        CV_CALL( src = cvGetMat( src, &srcstub, &coi1 ));

    if( !CV_IS_MAT(dst))
        CV_CALL( dst = cvGetMat( dst, &dststub, &coi2 ));

    if( coi1 != 0 || coi2 != 0 )
        CV_ERROR( CV_BadCOI, "" );

    src_depth = CV_MAT_DEPTH(src->type);
    dst_depth = CV_MAT_DEPTH(dst->type);

    if( !CV_ARE_CNS_EQ( src, dst ) || dst_depth < CV_32F || src_depth < dst_depth )
        CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

    if( !CV_ARE_SIZES_EQ( src, dst ) )
        CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );

    size = cvGetMatSize(src);
    size.width *= CV_MAT_CN(src->type);

    if( CV_IS_MAT_CONT( src->type & dst->type ))
    {
        size.width *= size.height;
        size.height = 1;
    }

    if( !CV_ARE_DEPTHS_EQ( src, dst ))
    {
        dx = MIN( 1024, size.width );
        buffer = (double*)cvStackAlloc( dx*sizeof(buffer[0]) );
    }

    for( y = 0; y < size.height; y++ )
    {
        uchar* src_data = src->data.ptr + src->step*y;
        uchar* dst_data = dst->data.ptr + dst->step*y;

        if( dst_depth == CV_64F )
        {
            icvLog_64f( (double*)src_data, (double*)dst_data, size.width );
        }
        else if( src_depth == dst_depth )
        {
            icvLog_32f( (float*)src_data, (float*)dst_data, size.width );
        }
        else
        {
            for( x = 0; x < size.width; x += dx )
            {
                int len = dx;
                if( x + len > size.width )
                    len = size.width - x;
                icvLog_64f( (double*)src_data + x, buffer, len );
                icvCvt_64f32f( buffer, (float*)dst_data + x, len );
            }
        }
    }

    __END__;
}


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

#define ICV_DEF_IPOW_OP( flavor, arrtype, worktype, cast_macro )                    \
static CvStatus CV_STDCALL                                                          \
icvIPow_##flavor( const arrtype* src, arrtype* dst, int len, int power )            \
{                                                                                   \
    int i;                                                                          \
                                                                                    \
    for( i = 0; i < len; i++ )                                                      \
    {                                                                               \
        worktype a = 1, b = src[i];                                                 \
        int p = power;                                                              \
        while( p > 1 )                                                              \
        {                                                                           \
            if( p & 1 )                                                             \
                a *= b;                                                             \
            b *= b;                                                                 \
            p >>= 1;                                                                \
        }                                                                           \
                                                                                    \
        a *= b;                                                                     \
        dst[i] = cast_macro(a);                                                     \
    }                                                                               \
                                                                                    \
    return CV_OK;                                                                   \
}


ICV_DEF_IPOW_OP( 8u, uchar, int, CV_CAST_8U )
ICV_DEF_IPOW_OP( 16u, ushort, int, CV_CAST_16U )
ICV_DEF_IPOW_OP( 16s, short, int, CV_CAST_16S )
ICV_DEF_IPOW_OP( 32s, int, int, CV_CAST_32S )
ICV_DEF_IPOW_OP( 32f, float, double, CV_CAST_32F )
ICV_DEF_IPOW_OP( 64f, double, double, CV_CAST_64F )

#define icvIPow_8s 0

CV_DEF_INIT_FUNC_TAB_1D( IPow )

typedef CvStatus (CV_STDCALL * CvIPowFunc)( const void* src, void* dst, int len, int power );
typedef CvStatus (CV_STDCALL * CvSqrtFunc)( const void* src, void* dst, int len );

CV_IMPL void cvPow( const CvArr* srcarr, CvArr* dstarr, double power )
{
    static CvFuncTable ipow_tab;
    static int inittab = 0;

    CV_FUNCNAME( "cvPow" );

    __BEGIN__;

    void* temp_buffer = 0;
    int block_size = 0;
    CvMat srcstub, *src = (CvMat*)srcarr;
    CvMat dststub, *dst = (CvMat*)dstarr;
    int coi1 = 0, coi2 = 0;
    int depth;
    CvSize size;
    int x, y;
    int ipower = cvRound( power );
    int is_ipower = 0;

    if( !CV_IS_MAT(src))
        CV_CALL( src = cvGetMat( src, &srcstub, &coi1 ));

    if( !CV_IS_MAT(dst))
        CV_CALL( dst = cvGetMat( dst, &dststub, &coi2 ));

    if( coi1 != 0 || coi2 != 0 )
        CV_ERROR( CV_BadCOI, "" );

    if( !CV_ARE_TYPES_EQ( src, dst ))
        CV_ERROR_FROM_CODE( CV_StsUnmatchedFormats );

    if( !CV_ARE_SIZES_EQ( src, dst ) )
        CV_ERROR_FROM_CODE( CV_StsUnmatchedSizes );

    depth = CV_MAT_DEPTH( src->type );

    if( fabs(ipower - power) < DBL_EPSILON )
    {
        if( !inittab )
        {
            icvInitIPowTable( &ipow_tab );
            inittab = 1;
        }

        if( ipower < 0 )
        {
            CV_CALL( cvDiv( 0, src, dst ));

            if( ipower == -1 )
                EXIT;
            ipower = -ipower;
            src = dst;
        }

        switch( ipower )
        {
        case 0:
            cvSet( dst, cvScalarAll(1));
            EXIT;
        case 1:
            cvCopy( src, dst );
            EXIT;
        case 2:
            cvMul( src, src, dst );
            EXIT;
        default:
            is_ipower = 1;
        }
    }
    else if( depth < CV_32F )
        CV_ERROR( CV_StsUnsupportedFormat,
        "Fractional or negative integer power factor can be used "
        "with floating-point types only");

    size = cvGetMatSize(src);
    size.width *= CV_MAT_CN(src->type);

    if( CV_IS_MAT_CONT( src->type & dst->type ))
    {
        size.width *= size.height;
        size.height = 1;
    }

    if( is_ipower )
    {
        CvIPowFunc pow_func = (CvIPowFunc)ipow_tab.fn_2d[depth];
        if( !pow_func )
            CV_ERROR( CV_StsUnsupportedFormat, "The data type is not supported" );

        for( y = 0; y < size.height; y++ )
        {
            uchar* src_data = src->data.ptr + src->step*y;
            uchar* dst_data = dst->data.ptr + dst->step*y;

            pow_func( src_data, dst_data, size.width, ipower );
        }
    }
    else if( fabs(fabs(power) - 0.5) < DBL_EPSILON )
    {
        CvSqrtFunc sqrt_func = power < 0 ?
            (depth == CV_32F ? (CvSqrtFunc)icvInvSqrt_32f : (CvSqrtFunc)icvInvSqrt_64f) :
            (depth == CV_32F ? (CvSqrtFunc)icvSqrt_32f : (CvSqrtFunc)icvSqrt_64f);

        for( y = 0; y < size.height; y++ )
        {
            uchar* src_data = src->data.ptr + src->step*y;
            uchar* dst_data = dst->data.ptr + dst->step*y;

            sqrt_func( src_data, dst_data, size.width );
        }
    }
    else
    {
        block_size = MIN( size.width, ICV_MATH_BLOCK_SIZE );
        temp_buffer = cvStackAlloc( block_size*CV_ELEM_SIZE(depth) );

        for( y = 0; y < size.height; y++ )
        {
            uchar* src_data = src->data.ptr + src->step*y;
            uchar* dst_data = dst->data.ptr + dst->step*y;

            for( x = 0; x < size.width; x += block_size )
            {
                int len = MIN( size.width - x, block_size );
                if( depth == CV_32F )
                {
                    icvLog_32f( (float*)src_data + x, (float*)temp_buffer, len );
                    icvScale_32f( (float*)temp_buffer, (float*)temp_buffer, len, (float)power, 0 );
                    icvExp_32f( (float*)temp_buffer, (float*)dst_data + x, len );
                }
                else
                {
                    icvLog_64f( (double*)src_data + x, (double*)temp_buffer, len );
                    icvScale_64f( (double*)temp_buffer, (double*)temp_buffer, len, power, 0 );
                    icvExp_64f( (double*)temp_buffer, (double*)dst_data + x, len );
                }
            }
        }
    }

    __END__;
}


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

IPCVAPI_IMPL( CvStatus, icvCheckArray_32f_C1R,
    ( const float* src, int srcstep, CvSize size, int flags, double min_val, double max_val ),
     (src, srcstep, size, flags, min_val, max_val) )
{
    Cv32suf a, b;
    int ia, ib;
    const int* isrc = (const int*)src;

    if( !src )
        return CV_NULLPTR_ERR;

    if( size.width <= 0 || size.height <= 0 )
        return CV_BADSIZE_ERR;

    if( flags & CV_CHECK_RANGE )
    {
        a.f = (float)min_val;
        b.f = (float)max_val;
    }
    else
    {
        a.f = -FLT_MAX;
        b.f = FLT_MAX;
    }

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

    srcstep /= sizeof(isrc[0]);
    for( ; size.height--; isrc += srcstep )
    {
        int i;
        for( i = 0; i < size.width; i++ )
        {
            int val = isrc[i];
            val = CV_TOGGLE_FLT(val);

            if( val < ia || val >= ib )
                return CV_BADRANGE_ERR;
        }
    }

    return CV_OK;
}


IPCVAPI_IMPL( CvStatus,  icvCheckArray_64f_C1R,
    ( const double* src, int srcstep, CvSize size, int flags, double min_val, double max_val ),
    (src, srcstep, size, flags, min_val, max_val) )
{
    Cv64suf a, b;
    int64 ia, ib;
    const int64* isrc = (const int64*)src;

    if( !src )
        return CV_NULLPTR_ERR;

    if( size.width <= 0 || size.height <= 0 )
        return CV_BADSIZE_ERR;

    if( flags & CV_CHECK_RANGE )
    {
        a.f = min_val;
        b.f = max_val;
    }
    else
    {
        a.f = -DBL_MAX;
        b.f = DBL_MAX;
    }

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

    srcstep /= sizeof(isrc[0]);
    for( ; size.height--; isrc += srcstep )
    {
        int i;
        for( i = 0; i < size.width; i++ )
        {
            int64 val = isrc[i];
            val = CV_TOGGLE_DBL(val);

            if( val < ia || val >= ib )
                return CV_BADRANGE_ERR;
        }
    }

    return CV_OK;
}


CV_IMPL  int  cvCheckArr( const CvArr* arr, int flags,
                          double minVal, double maxVal )
{
    int result = 0;

    CV_FUNCNAME( "cvCheckArr" );

    __BEGIN__;

    if( arr )
    {
        CvStatus status = CV_OK;
        CvMat stub, *mat = (CvMat*)arr;
        int type;
        CvSize size;

        if( !CV_IS_MAT( mat ))
            CV_CALL( mat = cvGetMat( mat, &stub, 0, 1 ));

        type = CV_MAT_TYPE( mat->type );
        size = cvGetMatSize( mat );

        size.width *= CV_MAT_CN( type );

        if( CV_IS_MAT_CONT( mat->type ))
        {
            size.width *= size.height;
            size.height = 1;
        }

        if( CV_MAT_DEPTH(type) == CV_32F )
        {
            status = icvCheckArray_32f_C1R( mat->data.fl, mat->step, size,
                                            flags, minVal, maxVal );
        }
        else if( CV_MAT_DEPTH(type) == CV_64F )
        {
            status = icvCheckArray_64f_C1R( mat->data.db, mat->step, size,
                                            flags, minVal, maxVal );
        }
        else
        {
            CV_ERROR( CV_StsUnsupportedFormat, "" );
        }

        if( status < 0 )
        {
            if( status != CV_BADRANGE_ERR || !(flags & CV_CHECK_QUIET))
                CV_ERROR( CV_StsOutOfRange, "CheckArray failed" );
            EXIT;
        }
    }

    result = 1;

    __END__;

    return result;
}


/* End of file. */