core/tool/interpr3.cxx

/**************************************************************
 *
 * Licensed to the Apache Software Foundation (ASF) under one
 * or more contributor license agreements.  See the NOTICE file
 * distributed with this work for additional information
 * regarding copyright ownership.  The ASF licenses this file
 * to you under the Apache License, Version 2.0 (the
 * "License"); you may not use this file except in compliance
 * with the License.  You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.  See the License for the
 * specific language governing permissions and limitations
 * under the License.
 *
 *************************************************************/


// MARKER(update_precomp.py): autogen include statement, do not remove
#include "precompiled_sc.hxx"

// INCLUDE ---------------------------------------------------------------

#include <tools/solar.h>
#include <stdlib.h>
#include <string.h>
#include <rtl/logfile.hxx>

#include "interpre.hxx"
#include "global.hxx"
#include "compiler.hxx"
#include "cell.hxx"
#include "document.hxx"
#include "dociter.hxx"
#include "scmatrix.hxx"
#include "globstr.hrc"

#include <math.h>
#include <vector>
#include <algorithm>

#include <boost/math/special_functions/atanh.hpp>
#include <boost/math/special_functions/expm1.hpp>
#include <boost/math/special_functions/log1p.hpp>

using ::std::vector;
using namespace formula;

// STATIC DATA -----------------------------------------------------------

#define SCdEpsilon                1.0E-7
#define SC_MAX_ITERATION_COUNT    20
#define MAX_ANZ_DOUBLE_FOR_SORT 100000
// PI jetzt als F_PI aus solar.h
//#define   PI            3.1415926535897932

const double ScInterpreter::fMaxGammaArgument = 171.624376956302;  // found experimental
const double fMachEps = ::std::numeric_limits<double>::epsilon();

//-----------------------------------------------------------------------------

class ScDistFunc
{
public:
    virtual double GetValue(double x) const = 0;
};

//  iteration for inverse distributions

//template< class T > double lcl_IterateInverse( const T& rFunction, double x0, double x1, bool& rConvError )

/** u*w<0.0 fails for values near zero */
inline bool lcl_HasChangeOfSign( double u, double w )
{
    return (u < 0.0 && w > 0.0) || (u > 0.0 && w < 0.0);
}

double lcl_IterateInverse( const ScDistFunc& rFunction, double fAx, double fBx, bool& rConvError )
{
    rConvError = false;
    const double fYEps = 1.0E-307;
    const double fXEps = ::std::numeric_limits<double>::epsilon();

    DBG_ASSERT(fAx<fBx, "IterateInverse: wrong interval");

    //  find enclosing interval

    double fAy = rFunction.GetValue(fAx);
    double fBy = rFunction.GetValue(fBx);
    double fTemp;
    unsigned short nCount;
    for (nCount = 0; nCount < 1000 && !lcl_HasChangeOfSign(fAy,fBy); nCount++)
    {
        if (fabs(fAy) <= fabs(fBy))
        {
            fTemp = fAx;
            fAx += 2.0 * (fAx - fBx);
            if (fAx < 0.0)
                fAx = 0.0;
            fBx = fTemp;
            fBy = fAy;
            fAy = rFunction.GetValue(fAx);
        }
        else
        {
            fTemp = fBx;
            fBx += 2.0 * (fBx - fAx);
            fAx = fTemp;
            fAy = fBy;
            fBy = rFunction.GetValue(fBx);
        }
    }

    if (fAy == 0.0)
        return fAx;
    if (fBy == 0.0)
        return fBx;
    if (!lcl_HasChangeOfSign( fAy, fBy))
    {
        rConvError = true;
        return 0.0;
    }
    // inverse quadric interpolation with additional brackets
    // set three points
    double fPx = fAx;
    double fPy = fAy;
    double fQx = fBx;
    double fQy = fBy;
    double fRx = fAx;
    double fRy = fAy;
    double fSx = 0.5 * (fAx + fBx); // potential next point
    bool bHasToInterpolate = true;
    nCount = 0;
    while ( nCount < 500 && fabs(fRy) > fYEps &&
            (fBx-fAx) > ::std::max( fabs(fAx), fabs(fBx)) * fXEps )
    {
        if (bHasToInterpolate)
        {
            if (fPy!=fQy && fQy!=fRy && fRy!=fPy)
            {
                fSx = fPx * fRy * fQy / (fRy-fPy) / (fQy-fPy)
                    + fRx * fQy * fPy / (fQy-fRy) / (fPy-fRy)
                    + fQx * fPy * fRy / (fPy-fQy) / (fRy-fQy);
                bHasToInterpolate = (fAx < fSx) && (fSx < fBx); // inside the brackets?
            }
            else
                bHasToInterpolate = false;
        }
        if(!bHasToInterpolate)
        {
            fSx = 0.5 * (fAx + fBx);
            // reset points
            fPx = fAx; fPy = fAy;
            fQx = fBx; fQy = fBy;
            bHasToInterpolate = true;
        }
        // shift points for next interpolation
        fPx = fQx; fQx = fRx; fRx = fSx;
        fPy = fQy; fQy = fRy; fRy = rFunction.GetValue(fSx);
        // update brackets
        if (lcl_HasChangeOfSign( fAy, fRy))
        {
            fBx = fRx; fBy = fRy;
        }
        else
        {
            fAx = fRx; fAy = fRy;
        }
        // if last interration brought to small advance, then do bisection next
        // time, for safety
        bHasToInterpolate = bHasToInterpolate && (fabs(fRy) * 2.0 <= fabs(fQy));
        ++nCount;
    }
    return fRx;
}

//-----------------------------------------------------------------------------
// Allgemeine Funktionen
//-----------------------------------------------------------------------------

void ScInterpreter::ScNoName()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScNoName" );
    PushError(errNoName);
}

void ScInterpreter::ScBadName()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScBadName" );
    short nParamCount = GetByte();
    while (nParamCount-- > 0)
    {
        PopError();
    }
    PushError( errNoName);
}

double ScInterpreter::phi(double x)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::phi" );
    return  0.39894228040143268 * exp(-(x * x) / 2.0);
}

double ScInterpreter::integralPhi(double x)
{ // Using gauss(x)+0.5 has severe cancellation errors for x<-4
    return 0.5 * ::rtl::math::erfc(-x * 0.7071067811865475); // * 1/sqrt(2)
}

double ScInterpreter::taylor(double* pPolynom, sal_uInt16 nMax, double x)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::taylor" );
    double nVal = pPolynom[nMax];
    for (short i = nMax-1; i >= 0; i--)
    {
        nVal = pPolynom[i] + (nVal * x);
    }
    return nVal;
}

double ScInterpreter::gauss(double x)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::gauss" );
    double t0[] =
    { 0.39894228040143268, -0.06649038006690545,  0.00997355701003582,
     -0.00118732821548045,  0.00011543468761616, -0.00000944465625950,
      0.00000066596935163, -0.00000004122667415,  0.00000000227352982,
      0.00000000011301172,  0.00000000000511243, -0.00000000000021218 };
    double t2[] =
    { 0.47724986805182079,  0.05399096651318805, -0.05399096651318805,
      0.02699548325659403, -0.00449924720943234, -0.00224962360471617,
      0.00134977416282970, -0.00011783742691370, -0.00011515930357476,
      0.00003704737285544,  0.00000282690796889, -0.00000354513195524,
      0.00000037669563126,  0.00000019202407921, -0.00000005226908590,
     -0.00000000491799345,  0.00000000366377919, -0.00000000015981997,
     -0.00000000017381238,  0.00000000002624031,  0.00000000000560919,
     -0.00000000000172127, -0.00000000000008634,  0.00000000000007894 };
    double t4[] =
    { 0.49996832875816688,  0.00013383022576489, -0.00026766045152977,
      0.00033457556441221, -0.00028996548915725,  0.00018178605666397,
     -0.00008252863922168,  0.00002551802519049, -0.00000391665839292,
     -0.00000074018205222,  0.00000064422023359, -0.00000017370155340,
      0.00000000909595465,  0.00000000944943118, -0.00000000329957075,
      0.00000000029492075,  0.00000000011874477, -0.00000000004420396,
      0.00000000000361422,  0.00000000000143638, -0.00000000000045848 };
    double asympt[] = { -1.0, 1.0, -3.0, 15.0, -105.0 };

    double xAbs = fabs(x);
    sal_uInt16 xShort = (sal_uInt16)::rtl::math::approxFloor(xAbs);
    double nVal = 0.0;
    if (xShort == 0)
        nVal = taylor(t0, 11, (xAbs * xAbs)) * xAbs;
    else if ((xShort >= 1) && (xShort <= 2))
        nVal = taylor(t2, 23, (xAbs - 2.0));
    else if ((xShort >= 3) && (xShort <= 4))
        nVal = taylor(t4, 20, (xAbs - 4.0));
    else
        nVal = 0.5 + phi(xAbs) * taylor(asympt, 4, 1.0 / (xAbs * xAbs)) / xAbs;
    if (x < 0.0)
        return -nVal;
    else
        return nVal;
}

//
//  #i26836# new gaussinv implementation by Martin Eitzenberger <m.eitzenberger@unix.net>
//

double ScInterpreter::gaussinv(double x)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::gaussinv" );
    double q,t,z;

    q=x-0.5;

    if(fabs(q)<=.425)
    {
        t=0.180625-q*q;

        z=
        q*
        (
            (
                (
                    (
                        (
                            (
                                (
                                    t*2509.0809287301226727+33430.575583588128105
                                )
                                *t+67265.770927008700853
                            )
                            *t+45921.953931549871457
                        )
                        *t+13731.693765509461125
                    )
                    *t+1971.5909503065514427
                )
                *t+133.14166789178437745
            )
            *t+3.387132872796366608
        )
        /
        (
            (
                (
                    (
                        (
                            (
                                (
                                    t*5226.495278852854561+28729.085735721942674
                                )
                                *t+39307.89580009271061
                            )
                            *t+21213.794301586595867
                        )
                        *t+5394.1960214247511077
                    )
                    *t+687.1870074920579083
                )
                *t+42.313330701600911252
            )
            *t+1.0
        );

    }
    else
    {
        if(q>0) t=1-x;
        else        t=x;

        t=sqrt(-log(t));

        if(t<=5.0)
        {
            t+=-1.6;

            z=
            (
                (
                    (
                        (
                            (
                                (
                                    (
                                        t*7.7454501427834140764e-4+0.0227238449892691845833
                                    )
                                    *t+0.24178072517745061177
                                )
                                *t+1.27045825245236838258
                            )
                            *t+3.64784832476320460504
                        )
                        *t+5.7694972214606914055
                    )
                    *t+4.6303378461565452959
                )
                *t+1.42343711074968357734
            )
            /
            (
                (
                    (
                        (
                            (
                                (
                                    (
                                        t*1.05075007164441684324e-9+5.475938084995344946e-4
                                    )
                                    *t+0.0151986665636164571966
                                )
                                *t+0.14810397642748007459
                            )
                            *t+0.68976733498510000455
                        )
                        *t+1.6763848301838038494
                    )
                    *t+2.05319162663775882187
                )
                *t+1.0
            );

        }
        else
        {
            t+=-5.0;

            z=
            (
                (
                    (
                        (
                            (
                                (
                                    (
                                        t*2.01033439929228813265e-7+2.71155556874348757815e-5
                                    )
                                    *t+0.0012426609473880784386
                                )
                                *t+0.026532189526576123093
                            )
                            *t+0.29656057182850489123
                        )
                        *t+1.7848265399172913358
                    )
                    *t+5.4637849111641143699
                )
                *t+6.6579046435011037772
            )
            /
            (
                (
                    (
                        (
                            (
                                (
                                    (
                                        t*2.04426310338993978564e-15+1.4215117583164458887e-7
                                    )
                                    *t+1.8463183175100546818e-5
                                )
                                *t+7.868691311456132591e-4
                            )
                            *t+0.0148753612908506148525
                        )
                        *t+0.13692988092273580531
                    )
                    *t+0.59983220655588793769
                )
                *t+1.0
            );

        }

        if(q<0.0) z=-z;
    }

    return z;
}

double ScInterpreter::Fakultaet(double x)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::Fakultaet" );
    x = ::rtl::math::approxFloor(x);
    if (x < 0.0)
        return 0.0;
    else if (x == 0.0)
        return 1.0;
    else if (x <= 170.0)
    {
        double fTemp = x;
        while (fTemp > 2.0)
        {
            fTemp--;
            x *= fTemp;
        }
    }
    else
        SetError(errNoValue);
/*                                           // Stirlingsche Naeherung zu ungenau
    else
        x = pow(x/exp(1), x) * sqrt(x) * SQRT_2_PI * (1.0 + 1.0 / (12.0 * x));
*/
    return x;
}

double ScInterpreter::BinomKoeff(double n, double k)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::BinomKoeff" );
    double nVal = 0.0;
    k = ::rtl::math::approxFloor(k);
    if (n < k)
        nVal = 0.0;
    else if (k == 0.0)
        nVal = 1.0;
    else
    {
        nVal = n/k;
        n--;
        k--;
        while (k > 0.0)
        {
            nVal *= n/k;
            k--;
            n--;
        }
/*
        double f1 = n;                      // Zaehler
        double f2 = k;                      // Nenner
        n--;
        k--;
        while (k > 0.0)
        {
            f2 *= k;
            f1 *= n;
            k--;
            n--;
        }
        nVal = f1 / f2;
*/
    }
    return nVal;
}


// The algorithm is based on lanczos13m53 in lanczos.hpp
// in math library from http://www.boost.org
/** you must ensure fZ>0
    Uses a variant of the Lanczos sum with a rational function. */
double lcl_getLanczosSum(double fZ)
{
    const double fNum[13] ={
        23531376880.41075968857200767445163675473,
        42919803642.64909876895789904700198885093,
        35711959237.35566804944018545154716670596,
        17921034426.03720969991975575445893111267,
        6039542586.35202800506429164430729792107,
        1439720407.311721673663223072794912393972,
        248874557.8620541565114603864132294232163,
        31426415.58540019438061423162831820536287,
        2876370.628935372441225409051620849613599,
        186056.2653952234950402949897160456992822,
        8071.672002365816210638002902272250613822,
        210.8242777515793458725097339207133627117,
        2.506628274631000270164908177133837338626
        };
    const double fDenom[13] = {
        0,
        39916800,
        120543840,
        150917976,
        105258076,
        45995730,
        13339535,
        2637558,
        357423,
        32670,
        1925,
        66,
        1
        };
    // Horner scheme
    double fSumNum;
    double fSumDenom;
    int nI;
    double fZInv;
    if (fZ<=1.0)
    {
        fSumNum = fNum[12];
        fSumDenom = fDenom[12];
        for (nI = 11; nI >= 0; --nI)
        {
            fSumNum *= fZ;
            fSumNum += fNum[nI];
            fSumDenom *= fZ;
            fSumDenom += fDenom[nI];
        }
    }
    else
    // Cancel down with fZ^12; Horner scheme with reverse coefficients
    {
        fZInv = 1/fZ;
        fSumNum = fNum[0];
        fSumDenom = fDenom[0];
        for (nI = 1; nI <=12; ++nI)
        {
            fSumNum *= fZInv;
            fSumNum += fNum[nI];
            fSumDenom *= fZInv;
            fSumDenom += fDenom[nI];
        }
    }
    return fSumNum/fSumDenom;
}

// The algorithm is based on tgamma in gamma.hpp
// in math library from http://www.boost.org
/** You must ensure fZ>0; fZ>171.624376956302 will overflow. */
double lcl_GetGammaHelper(double fZ)
{
    double fGamma = lcl_getLanczosSum(fZ);
    const double fg = 6.024680040776729583740234375;
    double fZgHelp = fZ + fg - 0.5;
    // avoid intermediate overflow
    double fHalfpower = pow( fZgHelp, fZ / 2 - 0.25);
    fGamma *= fHalfpower;
    fGamma /= exp(fZgHelp);
    fGamma *= fHalfpower;
    if (fZ <= 20.0 && fZ == ::rtl::math::approxFloor(fZ))
        fGamma = ::rtl::math::round(fGamma);
    return fGamma;
}

// The algorithm is based on tgamma in gamma.hpp
// in math library from http://www.boost.org
/** You must ensure fZ>0 */
double lcl_GetLogGammaHelper(double fZ)
{
    const double fg = 6.024680040776729583740234375;
    double fZgHelp = fZ + fg - 0.5;
    return log( lcl_getLanczosSum(fZ)) + (fZ-0.5) * log(fZgHelp) - fZgHelp;
}

/** You must ensure non integer arguments for fZ<1 */
double ScInterpreter::GetGamma(double fZ)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetGamma" );
    const double fLogPi = log(F_PI);
    const double fLogDblMax = log( ::std::numeric_limits<double>::max());

    if (fZ > fMaxGammaArgument)
    {
        SetError(errIllegalFPOperation);
        return HUGE_VAL;
    }

    if (fZ >= 1.0)
        return lcl_GetGammaHelper(fZ);

    if (fZ >= 0.5)  // shift to x>=1 using Gamma(x)=Gamma(x+1)/x
        return lcl_GetGammaHelper(fZ+1) / fZ;

    if (fZ >= -0.5) // shift to x>=1, might overflow
    {
        double fLogTest = lcl_GetLogGammaHelper(fZ+2) - log(fZ+1) - log( fabs(fZ));
        if (fLogTest >= fLogDblMax)
        {
            SetError( errIllegalFPOperation);
            return HUGE_VAL;
        }
        return lcl_GetGammaHelper(fZ+2) / (fZ+1) / fZ;
    }
    // fZ<-0.5
    // Use Euler's reflection formula: gamma(x)= pi/ ( gamma(1-x)*sin(pi*x) )
    double fLogDivisor = lcl_GetLogGammaHelper(1-fZ) + log( fabs( ::rtl::math::sin( F_PI*fZ)));
    if (fLogDivisor - fLogPi >= fLogDblMax)     // underflow
        return 0.0;

    if (fLogDivisor<0.0)
        if (fLogPi - fLogDivisor > fLogDblMax)  // overflow
        {
            SetError(errIllegalFPOperation);
            return HUGE_VAL;
        }

    return exp( fLogPi - fLogDivisor) * ((::rtl::math::sin( F_PI*fZ) < 0.0) ? -1.0 : 1.0);
}


/** You must ensure fZ>0 */
double ScInterpreter::GetLogGamma(double fZ)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetLogGamma" );
    if (fZ >= fMaxGammaArgument)
        return lcl_GetLogGammaHelper(fZ);
    if (fZ >= 1.0)
        return log(lcl_GetGammaHelper(fZ));
    if (fZ >= 0.5)
        return log( lcl_GetGammaHelper(fZ+1) / fZ);
    return lcl_GetLogGammaHelper(fZ+2) - log(fZ+1) - log(fZ);
}

double ScInterpreter::GetFDist(double x, double fF1, double fF2)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetFDist" );
    double arg = fF2/(fF2+fF1*x);
    double alpha = fF2/2.0;
    double beta = fF1/2.0;
    return (GetBetaDist(arg, alpha, beta));
/*
    double Z = (pow(fF,1.0/3.0)*(1.0-2.0/(9.0*fF2)) - (1.0-2.0/(9.0*fF1))) /
               sqrt(2.0/(9.0*fF1) + pow(fF,2.0/3.0)*2.0/(9.0*fF2));
    return (0.5-gauss(Z));
*/
}

double ScInterpreter::GetTDist(double T, double fDF)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetTDist" );
    return 0.5 * GetBetaDist(fDF/(fDF+T*T), fDF/2.0, 0.5);
/*
    sal_uInt16 DF = (sal_uInt16) fDF;
    double A = T / sqrt(DF);
    double B = 1.0 + A*A;
    double R;
    if (DF == 1)
        R = 0.5 + atan(A)/F_PI;
    else if (DF % 2 == 0)
    {
        double S0 = A/(2.0 * sqrt(B));
        double C0 = S0;
        for (sal_uInt16 i = 2; i <= DF-2; i+=2)
        {
            C0 *= (1.0 - 1.0/(double)i)/B;
            S0 += C0;
        }
        R = 0.5 + S0;
    }
    else
    {
        double S1 = A / (B * F_PI);
        double C1 = S1;
        for (sal_uInt16 i = 3; i <= DF-2; i+=2)
        {
            C1 *= (1.0 - 1.0/(double)i)/B;
            S1 += C1;
        }
        R = 0.5 + atan(A)/F_PI + S1;
    }
    return 1.0 - R;
*/
}

// for LEGACY.CHIDIST, returns right tail, fDF=degrees of freedom
/** You must ensure fDF>0.0 */
double ScInterpreter::GetChiDist(double fX, double fDF)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetChiDist" );
    if (fX <= 0.0)
        return 1.0; // see ODFF
    else
        return GetUpRegIGamma( fDF/2.0, fX/2.0);
}

// ready for ODF 1.2
// for ODF CHISQDIST; cumulative distribution function, fDF=degrees of freedom
// returns left tail
/** You must ensure fDF>0.0 */
double ScInterpreter::GetChiSqDistCDF(double fX, double fDF)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetChiSqDistCDF" );
    if (fX <= 0.0)
        return 0.0; // see ODFF
    else
        return GetLowRegIGamma( fDF/2.0, fX/2.0);
}

double ScInterpreter::GetChiSqDistPDF(double fX, double fDF)
{
    // you must ensure fDF is positive integer
    double fValue;
    double fCount;
    if (fX <= 0.0)
        return 0.0; // see ODFF
    if (fDF*fX > 1391000.0)
    {
        // intermediate invalid values, use log
        fValue = exp((0.5*fDF - 1) * log(fX*0.5) - 0.5 * fX - log(2.0) - GetLogGamma(0.5*fDF));
    }
    else // fDF is small in most cases, we can iterate
    {
        if (fmod(fDF,2.0)<0.5)
        {
            // even
            fValue = 0.5;
            fCount = 2.0;
        }
        else
        {
            fValue = 1/sqrt(fX*2*F_PI);
            fCount = 1.0;
        }
        while ( fCount < fDF)
        {
            fValue *= (fX / fCount);
            fCount += 2.0;
        }
        if (fX>=1425.0) // underflow in e^(-x/2)
            fValue = exp(log(fValue)-fX/2);
        else
            fValue *= exp(-fX/2);
    }
    return fValue;
}

void ScInterpreter::ScChiSqDist()
{
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 2, 3 ) )
        return;
    double fX;
    bool bCumulative;
    if (nParamCount == 3)
        bCumulative = GetBool();
    else
        bCumulative = true;
    double fDF = ::rtl::math::approxFloor(GetDouble());
    if (fDF < 1.0)
        PushIllegalArgument();
    else
    {
        fX = GetDouble();
        if (bCumulative)
            PushDouble(GetChiSqDistCDF(fX,fDF));
        else
            PushDouble(GetChiSqDistPDF(fX,fDF));
    }
}

void ScInterpreter::ScGamma()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScGamma" );
    double x = GetDouble();
    double fResult;
    if (x <= 0.0 && x == ::rtl::math::approxFloor(x))
        PushIllegalArgument();
    else
    {
        fResult = GetGamma(x);
        if (nGlobalError)
        {
            PushError( nGlobalError);
            return;
        }
        PushDouble(fResult);
    }
}


void ScInterpreter::ScLogGamma()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScLogGamma" );
    double x = GetDouble();
    if (x > 0.0)    // constraint from ODFF
        PushDouble( GetLogGamma(x));
    else
        PushIllegalArgument();
}

double ScInterpreter::GetBeta(double fAlpha, double fBeta)
{
    double fA;
    double fB;
    if (fAlpha > fBeta)
    {
        fA = fAlpha; fB = fBeta;
    }
    else
    {
        fA = fBeta; fB = fAlpha;
    }
    if (fA+fB < fMaxGammaArgument) // simple case
        return GetGamma(fA)/GetGamma(fA+fB)*GetGamma(fB);
    // need logarithm
    // GetLogGamma is not accurate enough, back to Lanczos for all three
    // GetGamma and arrange factors newly.
    const double fg = 6.024680040776729583740234375; //see GetGamma
    double fgm = fg - 0.5;
    double fLanczos = lcl_getLanczosSum(fA);
    fLanczos /= lcl_getLanczosSum(fA+fB);
    fLanczos *= lcl_getLanczosSum(fB);
    double fABgm = fA+fB+fgm;
    fLanczos *= sqrt((fABgm/(fA+fgm))/(fB+fgm));
    double fTempA = fB/(fA+fgm); // (fA+fgm)/fABgm = 1 / ( 1 + fB/(fA+fgm))
    double fTempB = fA/(fB+fgm);
    double fResult = exp(-fA * ::boost::math::log1p(fTempA)
                            -fB * ::boost::math::log1p(fTempB)-fgm);
    fResult *= fLanczos;
    return fResult;
}

// Same as GetBeta but with logarithm
double ScInterpreter::GetLogBeta(double fAlpha, double fBeta)
{
    double fA;
    double fB;
    if (fAlpha > fBeta)
    {
        fA = fAlpha; fB = fBeta;
    }
    else
    {
        fA = fBeta; fB = fAlpha;
    }
    const double fg = 6.024680040776729583740234375; //see GetGamma
    double fgm = fg - 0.5;
    double fLanczos = lcl_getLanczosSum(fA);
    fLanczos /= lcl_getLanczosSum(fA+fB);
    fLanczos *= lcl_getLanczosSum(fB);
    double fLogLanczos = log(fLanczos);
    double fABgm = fA+fB+fgm;
    fLogLanczos += 0.5*(log(fABgm)-log(fA+fgm)-log(fB+fgm));
    double fTempA = fB/(fA+fgm); // (fA+fgm)/fABgm = 1 / ( 1 + fB/(fA+fgm))
    double fTempB = fA/(fB+fgm);
    double fResult = -fA * ::boost::math::log1p(fTempA)
                        -fB * ::boost::math::log1p(fTempB)-fgm;
    fResult += fLogLanczos;
    return fResult;
}

// beta distribution probability density function
double ScInterpreter::GetBetaDistPDF(double fX, double fA, double fB)
{
    // special cases
    if (fA == 1.0) // result b*(1-x)^(b-1)
    {
        if (fB == 1.0)
            return 1.0;
        if (fB == 2.0)
            return -2.0*fX + 2.0;
        if (fX == 1.0 && fB < 1.0)
        {
            SetError(errIllegalArgument);
            return HUGE_VAL;
        }
        if (fX <= 0.01)
            return fB + fB * ::boost::math::expm1((fB-1.0) * ::boost::math::log1p(-fX));
        else
            return fB * pow(0.5-fX+0.5,fB-1.0);
    }
    if (fB == 1.0) // result a*x^(a-1)
    {
        if (fA == 2.0)
            return fA * fX;
        if (fX == 0.0 && fA < 1.0)
        {
            SetError(errIllegalArgument);
            return HUGE_VAL;
        }
        return fA * pow(fX,fA-1);
    }
    if (fX <= 0.0)
    {
        if (fA < 1.0 && fX == 0.0)
        {
            SetError(errIllegalArgument);
            return HUGE_VAL;
        }
        else
            return 0.0;
    }
    if (fX >= 1.0)
    {
        if (fB < 1.0 && fX == 1.0)
        {
            SetError(errIllegalArgument);
            return HUGE_VAL;
        }
        else
            return 0.0;
    }

    // normal cases; result x^(a-1)*(1-x)^(b-1)/Beta(a,b)
    const double fLogDblMax = log( ::std::numeric_limits<double>::max());
    const double fLogDblMin = log( ::std::numeric_limits<double>::min());
    double fLogY = (fX < 0.1) ? ::boost::math::log1p(-fX) : log(0.5-fX+0.5);
    double fLogX = log(fX);
    double fAm1LogX = (fA-1.0) * fLogX;
    double fBm1LogY = (fB-1.0) * fLogY;
    double fLogBeta = GetLogBeta(fA,fB);
    // check whether parts over- or underflow
    if (   fAm1LogX < fLogDblMax  && fAm1LogX > fLogDblMin
        && fBm1LogY < fLogDblMax  && fBm1LogY > fLogDblMin
        && fLogBeta < fLogDblMax  && fLogBeta > fLogDblMin
        && fAm1LogX + fBm1LogY < fLogDblMax && fAm1LogX + fBm1LogY > fLogDblMin)
        return pow(fX,fA-1.0) * pow(0.5-fX+0.5,fB-1.0) / GetBeta(fA,fB);
    else // need logarithm;
        // might overflow as a whole, but seldom, not worth to pre-detect it
        return exp( fAm1LogX + fBm1LogY - fLogBeta);
}


/*
                x^a * (1-x)^b
    I_x(a,b) = ----------------  * result of ContFrac
                a * Beta(a,b)
*/
double lcl_GetBetaHelperContFrac(double fX, double fA, double fB)
{   // like old version
    double a1, b1, a2, b2, fnorm, apl2m, d2m, d2m1, cfnew, cf;
    a1 = 1.0; b1 = 1.0;
    b2 = 1.0 - (fA+fB)/(fA+1.0)*fX;
    if (b2 == 0.0)
    {
        a2 = 0.0;
        fnorm = 1.0;
        cf = 1.0;
    }
    else
    {
        a2 = 1.0;
        fnorm = 1.0/b2;
        cf = a2*fnorm;
    }
    cfnew = 1.0;
    double rm = 1.0;

    const double fMaxIter = 50000.0;
    // loop security, normal cases converge in less than 100 iterations.
    // FIXME: You will get so much iteratons for fX near mean,
    // I do not know a better algorithm.
    bool bfinished = false;
    do
    {
        apl2m = fA + 2.0*rm;
        d2m = rm*(fB-rm)*fX/((apl2m-1.0)*apl2m);
        d2m1 = -(fA+rm)*(fA+fB+rm)*fX/(apl2m*(apl2m+1.0));
        a1 = (a2+d2m*a1)*fnorm;
        b1 = (b2+d2m*b1)*fnorm;
        a2 = a1 + d2m1*a2*fnorm;
        b2 = b1 + d2m1*b2*fnorm;
        if (b2 != 0.0)
        {
            fnorm = 1.0/b2;
            cfnew = a2*fnorm;
            bfinished = (fabs(cf-cfnew) < fabs(cf)*fMachEps);
        }
        cf = cfnew;
        rm += 1.0;
    }
    while (rm < fMaxIter && !bfinished);
    return cf;
}

// cumulative distribution function, normalized
double ScInterpreter::GetBetaDist(double fXin, double fAlpha, double fBeta)
{
// special cases
    if (fXin <= 0.0)  // values are valid, see spec
        return 0.0;
    if (fXin >= 1.0)  // values are valid, see spec
        return 1.0;
    if (fBeta == 1.0)
        return pow(fXin, fAlpha);
    if (fAlpha == 1.0)
    //            1.0 - pow(1.0-fX,fBeta) is not accurate enough
        return -::boost::math::expm1(fBeta * ::boost::math::log1p(-fXin));
    //FIXME: need special algorithm for fX near fP for large fA,fB
    double fResult;
    // I use always continued fraction, power series are neither
    // faster nor more accurate.
    double fY = (0.5-fXin)+0.5;
    double flnY = ::boost::math::log1p(-fXin);
    double fX = fXin;
    double flnX = log(fXin);
    double fA = fAlpha;
    double fB = fBeta;
    bool bReflect = fXin > fAlpha/(fAlpha+fBeta);
    if (bReflect)
    {
        fA = fBeta;
        fB = fAlpha;
        fX = fY;
        fY = fXin;
        flnX = flnY;
        flnY = log(fXin);
    }
    fResult = lcl_GetBetaHelperContFrac(fX,fA,fB);
    fResult = fResult/fA;
    double fP = fA/(fA+fB);
    double fQ = fB/(fA+fB);
    double fTemp;
    if (fA > 1.0 && fB > 1.0 && fP < 0.97 && fQ < 0.97) //found experimental
        fTemp = GetBetaDistPDF(fX,fA,fB)*fX*fY;
    else
        fTemp = exp(fA*flnX + fB*flnY - GetLogBeta(fA,fB));
    fResult *= fTemp;
    if (bReflect)
        fResult = 0.5 - fResult + 0.5;
    if (fResult > 1.0) // ensure valid range
        fResult = 1.0;
    if (fResult < 0.0)
        fResult = 0.0;
    return fResult;
}

  void ScInterpreter::ScBetaDist()
  {
      sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 3, 6 ) ) // expanded, see #i91547#
          return;
    double fLowerBound, fUpperBound;
    double alpha, beta, x;
    bool bIsCumulative;
    if (nParamCount == 6)
        bIsCumulative = GetBool();
      else
        bIsCumulative = true;
    if (nParamCount >= 5)
        fUpperBound = GetDouble();
    else
        fUpperBound = 1.0;
      if (nParamCount >= 4)
        fLowerBound = GetDouble();
      else
        fLowerBound = 0.0;
      beta = GetDouble();
      alpha = GetDouble();
      x = GetDouble();
    double fScale = fUpperBound - fLowerBound;
    if (fScale <= 0.0 || alpha <= 0.0 || beta <= 0.0)
      {
          PushIllegalArgument();
          return;
      }
    if (bIsCumulative) // cumulative distribution function
    {
        // special cases
        if (x < fLowerBound)
        {
            PushDouble(0.0); return; //see spec
        }
        if (x > fUpperBound)
        {
            PushDouble(1.0); return; //see spec
        }
        // normal cases
        x = (x-fLowerBound)/fScale;  // convert to standard form
        PushDouble(GetBetaDist(x, alpha, beta));
        return;
    }
    else // probability density function
    {
        if (x < fLowerBound || x > fUpperBound)
        {
            PushDouble(0.0);
            return;
        }
        x = (x-fLowerBound)/fScale;
        PushDouble(GetBetaDistPDF(x, alpha, beta)/fScale);
        return;
    }
}

void ScInterpreter::ScPhi()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScPhi" );
    PushDouble(phi(GetDouble()));
}

void ScInterpreter::ScGauss()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScGauss" );
    PushDouble(gauss(GetDouble()));
}

void ScInterpreter::ScFisher()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScFisher" );
    double fVal = GetDouble();
    if (fabs(fVal) >= 1.0)
        PushIllegalArgument();
    else
        PushDouble( ::boost::math::atanh( fVal));
}

void ScInterpreter::ScFisherInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScFisherInv" );
    PushDouble( tanh( GetDouble()));
}

void ScInterpreter::ScFact()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScFact" );
    double nVal = GetDouble();
    if (nVal < 0.0)
        PushIllegalArgument();
    else
        PushDouble(Fakultaet(nVal));
}

void ScInterpreter::ScKombin()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScKombin" );
    if ( MustHaveParamCount( GetByte(), 2 ) )
    {
        double k = ::rtl::math::approxFloor(GetDouble());
        double n = ::rtl::math::approxFloor(GetDouble());
        if (k < 0.0 || n < 0.0 || k > n)
            PushIllegalArgument();
        else
            PushDouble(BinomKoeff(n, k));
    }
}

void ScInterpreter::ScKombin2()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScKombin2" );
    if ( MustHaveParamCount( GetByte(), 2 ) )
    {
        double k = ::rtl::math::approxFloor(GetDouble());
        double n = ::rtl::math::approxFloor(GetDouble());
        if (k < 0.0 || n < 0.0 || k > n)
            PushIllegalArgument();
        else
            PushDouble(BinomKoeff(n + k - 1, k));
    }
}

void ScInterpreter::ScVariationen()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScVariationen" );
    if ( MustHaveParamCount( GetByte(), 2 ) )
    {
        double k = ::rtl::math::approxFloor(GetDouble());
        double n = ::rtl::math::approxFloor(GetDouble());
        if (n < 0.0 || k < 0.0 || k > n)
            PushIllegalArgument();
        else if (k == 0.0)
            PushInt(1);     // (n! / (n - 0)!) == 1
        else
        {
            double nVal = n;
            for (sal_uLong i = (sal_uLong)k-1; i >= 1; i--)
                nVal *= n-(double)i;
            PushDouble(nVal);
        }
    }
}

void ScInterpreter::ScVariationen2()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScVariationen2" );
    if ( MustHaveParamCount( GetByte(), 2 ) )
    {
        double k = ::rtl::math::approxFloor(GetDouble());
        double n = ::rtl::math::approxFloor(GetDouble());
        if (n < 0.0 || k < 0.0 || k > n)
            PushIllegalArgument();
        else
            PushDouble(pow(n,k));
    }
}


double ScInterpreter::GetBinomDistPMF(double x, double n, double p)
// used in ScB and ScBinomDist
// preconditions: 0.0 <= x <= n, 0.0 < p < 1.0;  x,n integral although double
        {
    double q = (0.5 - p) + 0.5;
            double fFactor = pow(q, n);
    if (fFactor <=::std::numeric_limits<double>::min())
            {
                fFactor = pow(p, n);
        if (fFactor <= ::std::numeric_limits<double>::min())
            return GetBetaDistPDF(p, x+1.0, n-x+1.0)/(n+1.0);
                else
                {
            sal_uInt32 max = static_cast<sal_uInt32>(n - x);
            for (sal_uInt32 i = 0; i < max && fFactor > 0.0; i++)
                        fFactor *= (n-i)/(i+1)*q/p;
            return fFactor;
                }
            }
            else
            {
        sal_uInt32 max = static_cast<sal_uInt32>(x);
        for (sal_uInt32 i = 0; i < max && fFactor > 0.0; i++)
                    fFactor *= (n-i)/(i+1)*p/q;
        return fFactor;
        }
    }

double lcl_GetBinomDistRange(double n, double xs,double xe,
            double fFactor /* q^n */, double p, double q)
//preconditions: 0.0 <= xs < xe <= n; xs,xe,n integral although double
                {
    sal_uInt32 i;
    double fSum;
    // skip summands index 0 to xs-1, start sum with index xs
    sal_uInt32 nXs = static_cast<sal_uInt32>( xs );
    for (i = 1; i <= nXs && fFactor > 0.0; i++)
        fFactor *= (n-i+1)/i * p/q;
    fSum = fFactor; // Summand xs
    sal_uInt32 nXe = static_cast<sal_uInt32>(xe);
    for (i = nXs+1; i <= nXe && fFactor > 0.0; i++)
                    {
        fFactor *= (n-i+1)/i * p/q;
                        fSum += fFactor;
                    }
    return (fSum>1.0) ? 1.0 : fSum;
                }

void ScInterpreter::ScB()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScB" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 3, 4 ) )
        return ;
    if (nParamCount == 3)   // mass function
    {
        double x = ::rtl::math::approxFloor(GetDouble());
        double p = GetDouble();
        double n = ::rtl::math::approxFloor(GetDouble());
        if (n < 0.0 || x < 0.0 || x > n || p < 0.0 || p > 1.0)
            PushIllegalArgument();
        else
            if (p == 0.0)
                PushDouble( (x == 0.0) ? 1.0 : 0.0 );
            else
                if ( p == 1.0)
                    PushDouble( (x == n) ? 1.0 : 0.0);
                else
                    PushDouble(GetBinomDistPMF(x,n,p));
            }
            else
    {   // nParamCount == 4
        double xe = ::rtl::math::approxFloor(GetDouble());
        double xs = ::rtl::math::approxFloor(GetDouble());
        double p = GetDouble();
        double n = ::rtl::math::approxFloor(GetDouble());
        double q = (0.5 - p) + 0.5;
        bool bIsValidX = ( 0.0 <= xs && xs <= xe && xe <= n);
        if ( bIsValidX && 0.0 < p && p < 1.0)
            {
            if (xs == xe)       // mass function
                PushDouble(GetBinomDistPMF(xs,n,p));
            else
                {
                double fFactor = pow(q, n);
                if (fFactor > ::std::numeric_limits<double>::min())
                    PushDouble(lcl_GetBinomDistRange(n,xs,xe,fFactor,p,q));
                else
                {
                    fFactor = pow(p, n);
                    if (fFactor > ::std::numeric_limits<double>::min())
                    {
                    // sum from j=xs to xe {(n choose j) * p^j * q^(n-j)}
                    // = sum from i = n-xe to n-xs { (n choose i) * q^i * p^(n-i)}
                        PushDouble(lcl_GetBinomDistRange(n,n-xe,n-xs,fFactor,q,p));
                }
                else
                        PushDouble(GetBetaDist(q,n-xe,xe+1.0)-GetBetaDist(q,n-xs+1,xs) );
                }
            }
        }
        else
        {
            if ( bIsValidX ) // not(0<p<1)
            {
                if ( p == 0.0 )
                    PushDouble( (xs == 0.0) ? 1.0 : 0.0 );
                else if ( p == 1.0 )
                    PushDouble( (xe == n) ? 1.0 : 0.0 );
                else
                    PushIllegalArgument();
            }
            else
                PushIllegalArgument();
        }
    }
}

void ScInterpreter::ScBinomDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScBinomDist" );
    if ( MustHaveParamCount( GetByte(), 4 ) )
    {
        bool bIsCum   = GetBool();     // false=mass function; true=cumulative
        double p      = GetDouble();
        double n      = ::rtl::math::approxFloor(GetDouble());
        double x      = ::rtl::math::approxFloor(GetDouble());
        double q = (0.5 - p) + 0.5;           // get one bit more for p near 1.0
        double fFactor, fSum;
        if (n < 0.0 || x < 0.0 || x > n || p < 0.0 || p > 1.0)
        {
            PushIllegalArgument();
            return;
            }
        if ( p == 0.0)
            {
            PushDouble( (x==0.0 || bIsCum) ? 1.0 : 0.0 );
            return;
            }
        if ( p == 1.0)
        {
            PushDouble( (x==n) ? 1.0 : 0.0);
            return;
        }
        if (!bIsCum)
            PushDouble( GetBinomDistPMF(x,n,p));
        else
        {
            if (x == n)
                PushDouble(1.0);
            else
            {
                fFactor = pow(q, n);
                if (x == 0.0)
                    PushDouble(fFactor);
                else
                    if (fFactor <= ::std::numeric_limits<double>::min())
                {
                    fFactor = pow(p, n);
                        if (fFactor <= ::std::numeric_limits<double>::min())
                            PushDouble(GetBetaDist(q,n-x,x+1.0));
                    else
                    {
                            if (fFactor > fMachEps)
                            {
                        fSum = 1.0 - fFactor;
                                sal_uInt32 max = static_cast<sal_uInt32> (n - x) - 1;
                                for (sal_uInt32 i = 0; i < max && fFactor > 0.0; i++)
                        {
                            fFactor *= (n-i)/(i+1)*q/p;
                            fSum -= fFactor;
                        }
                                PushDouble( (fSum < 0.0) ? 0.0 : fSum );
                }
                else
                                PushDouble(lcl_GetBinomDistRange(n,n-x,n,fFactor,q,p));
                    }
                }
                    else
                        PushDouble( lcl_GetBinomDistRange(n,0.0,x,fFactor,p,q)) ;
            }
        }
    }
}

void ScInterpreter::ScCritBinom()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScCritBinom" );
    if ( MustHaveParamCount( GetByte(), 3 ) )
    {
        double alpha  = GetDouble();                    // alpha
        double p      = GetDouble();                    // p
        double n      = ::rtl::math::approxFloor(GetDouble());
        if (n < 0.0 || alpha <= 0.0 || alpha >= 1.0 || p < 0.0 || p > 1.0)
            PushIllegalArgument();
        else
        {
            double q = 1.0 - p;
            double fFactor = pow(q,n);
            if (fFactor == 0.0)
            {
                fFactor = pow(p, n);
                if (fFactor == 0.0)
                    PushNoValue();
                else
                {
                    double fSum = 1.0 - fFactor; sal_uLong max = (sal_uLong) n;
                    sal_uLong i;

                    for ( i = 0; i < max && fSum >= alpha; i++)
                    {
                        fFactor *= (n-i)/(i+1)*q/p;
                        fSum -= fFactor;
                    }
                    PushDouble(n-i);
                }
            }
            else
            {
                double fSum = fFactor; sal_uLong max = (sal_uLong) n;
                sal_uLong i;

                for ( i = 0; i < max && fSum < alpha; i++)
                {
                    fFactor *= (n-i)/(i+1)*p/q;
                    fSum += fFactor;
                }
                PushDouble(i);
            }
        }
    }
}

void ScInterpreter::ScNegBinomDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScNegBinomDist" );
    if ( MustHaveParamCount( GetByte(), 3 ) )
    {
        double p      = GetDouble();                    // p
        double r      = GetDouble();                    // r
        double x      = GetDouble();                    // x
        if (r < 0.0 || x < 0.0 || p < 0.0 || p > 1.0)
            PushIllegalArgument();
        else
        {
            double q = 1.0 - p;
            double fFactor = pow(p,r);
            for (double i = 0.0; i < x; i++)
                fFactor *= (i+r)/(i+1.0)*q;
            PushDouble(fFactor);
        }
    }
}

void ScInterpreter::ScNormDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScNormDist" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 3, 4))
        return;
    bool bCumulative = nParamCount == 4 ? GetBool() : true;
    double sigma = GetDouble();                 // standard deviation
    double mue = GetDouble();                   // mean
    double x = GetDouble();                     // x
    if (sigma <= 0.0)
    {
        PushIllegalArgument();
        return;
    }
    if (bCumulative)
        PushDouble(integralPhi((x-mue)/sigma));
    else
        PushDouble(phi((x-mue)/sigma)/sigma);
}

void ScInterpreter::ScLogNormDist() //expanded, see #i100119#
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScLogNormDist" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 1, 4))
        return;
    bool bCumulative = nParamCount == 4 ? GetBool() : true; // cumulative
    double sigma = nParamCount >= 3 ? GetDouble() : 1.0; // standard deviation
    double mue = nParamCount >= 2 ? GetDouble() : 0.0;   // mean
    double x = GetDouble();                              // x
    if (sigma <= 0.0)
    {
        PushIllegalArgument();
        return;
    }
    if (bCumulative)
    { // cumulative
        if (x <= 0.0)
            PushDouble(0.0);
        else
            PushDouble(integralPhi((log(x)-mue)/sigma));
    }
    else
    { // density
        if (x <= 0.0)
            PushIllegalArgument();
        else
            PushDouble(phi((log(x)-mue)/sigma)/sigma/x);
    }
}

void ScInterpreter::ScStdNormDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScStdNormDist" );
    PushDouble(integralPhi(GetDouble()));
}

void ScInterpreter::ScExpDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScExpDist" );
    if ( MustHaveParamCount( GetByte(), 3 ) )
    {
        double kum    = GetDouble();                    // 0 oder 1
        double lambda = GetDouble();                    // lambda
        double x      = GetDouble();                    // x
        if (lambda <= 0.0)
            PushIllegalArgument();
        else if (kum == 0.0)                        // Dichte
        {
            if (x >= 0.0)
                PushDouble(lambda * exp(-lambda*x));
            else
                PushInt(0);
        }
        else                                        // Verteilung
        {
            if (x > 0.0)
                PushDouble(1.0 - exp(-lambda*x));
            else
                PushInt(0);
        }
    }
}

void ScInterpreter::ScTDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScTDist" );
    if ( !MustHaveParamCount( GetByte(), 3 ) )
        return;
    double fFlag = ::rtl::math::approxFloor(GetDouble());
    double fDF   = ::rtl::math::approxFloor(GetDouble());
    double T     = GetDouble();
    if (fDF < 1.0 || T < 0.0 || (fFlag != 1.0 && fFlag != 2.0) )
    {
        PushIllegalArgument();
        return;
    }
    double R = GetTDist(T, fDF);
    if (fFlag == 1.0)
        PushDouble(R);
    else
        PushDouble(2.0*R);
}

void ScInterpreter::ScFDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScFDist" );
    if ( !MustHaveParamCount( GetByte(), 3 ) )
        return;
    double fF2 = ::rtl::math::approxFloor(GetDouble());
    double fF1 = ::rtl::math::approxFloor(GetDouble());
    double fF  = GetDouble();
    if (fF < 0.0 || fF1 < 1.0 || fF2 < 1.0 || fF1 >= 1.0E10 || fF2 >= 1.0E10)
    {
        PushIllegalArgument();
        return;
    }
    PushDouble(GetFDist(fF, fF1, fF2));
}

void ScInterpreter::ScChiDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScChiDist" );
    double fResult;
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    double fDF  = ::rtl::math::approxFloor(GetDouble());
    double fChi = GetDouble();
    if (fDF < 1.0) // x<=0 returns 1, see ODFF 6.17.10
    {
        PushIllegalArgument();
        return;
    }
    fResult = GetChiDist( fChi, fDF);
    if (nGlobalError)
    {
        PushError( nGlobalError);
        return;
    }
    PushDouble(fResult);
}

void ScInterpreter::ScWeibull()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScWeibull" );
    if ( MustHaveParamCount( GetByte(), 4 ) )
    {
        double kum   = GetDouble();                 // 0 oder 1
        double beta  = GetDouble();                 // beta
        double alpha = GetDouble();                 // alpha
        double x     = GetDouble();                 // x
        if (alpha <= 0.0 || beta <= 0.0 || x < 0.0)
            PushIllegalArgument();
        else if (kum == 0.0)                        // Dichte
            PushDouble(alpha/pow(beta,alpha)*pow(x,alpha-1.0)*
                       exp(-pow(x/beta,alpha)));
        else                                        // Verteilung
            PushDouble(1.0 - exp(-pow(x/beta,alpha)));
    }
}

void ScInterpreter::ScPoissonDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScPoissonDist" );
    sal_uInt8 nParamCount = GetByte();
    if ( MustHaveParamCount( nParamCount, 2, 3 ) )
    {
        bool bCumulative = (nParamCount == 3 ? GetBool() : true); // default cumulative
        double lambda    = GetDouble();                           // Mean
        double x         = ::rtl::math::approxFloor(GetDouble()); // discrete distribution
        if (lambda < 0.0 || x < 0.0)
            PushIllegalArgument();
        else if (!bCumulative)                            // Probability mass function
        {
            if (lambda == 0.0)
                PushInt(0);
            else
            {
                if (lambda >712)    // underflow in exp(-lambda)
                {   // accuracy 11 Digits
                    PushDouble( exp(x*log(lambda)-lambda-GetLogGamma(x+1.0)));
                }
                else
                {
                    double fPoissonVar = 1.0;
                    for ( double f = 0.0; f < x; ++f )
                        fPoissonVar *= lambda / ( f + 1.0 );
                    PushDouble( fPoissonVar * exp( -lambda ) );
                }
            }
        }
        else                                // Cumulative distribution function
        {
            if (lambda == 0.0)
                PushInt(1);
            else
            {
                if (lambda > 712 )  // underflow in exp(-lambda)
                {   // accuracy 12 Digits
                    PushDouble(GetUpRegIGamma(x+1.0,lambda));
                }
                else
                {
                    if (x >= 936.0) // result is always undistinghable from 1
                        PushDouble (1.0);
                    else
                    {
                        double fSummand = exp(-lambda);
                        double fSum = fSummand;
                        int nEnd = sal::static_int_cast<int>( x );
                        for (int i = 1; i <= nEnd; i++)
                        {
                            fSummand = (fSummand * lambda)/(double)i;
                            fSum += fSummand;
                        }
                        PushDouble(fSum);
                    }
                }
            }
        }
    }
}

/** Local function used in the calculation of the hypergeometric distribution.
 */
void lcl_PutFactorialElements( ::std::vector< double >& cn, double fLower, double fUpper, double fBase )
{
    for ( double i = fLower; i <= fUpper; ++i )
    {
        double fVal = fBase - i;
        if ( fVal > 1.0 )
            cn.push_back( fVal );
    }
}

/** Calculates a value of the hypergeometric distribution.

    The algorithm is designed to avoid unnecessary multiplications and division
    by expanding all factorial elements (9 of them).  It is done by excluding
    those ranges that overlap in the numerator and the denominator.  This allows
    for a fast calculation for large values which would otherwise cause an overflow
    in the intermediate values.

    @author Kohei Yoshida <kohei@openoffice.org>

    @see #i47296#

 */
void ScInterpreter::ScHypGeomDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScHypGeomDist" );
    const size_t nMaxArraySize = 500000; // arbitrary max array size

    if ( !MustHaveParamCount( GetByte(), 4 ) )
        return;

    double N = ::rtl::math::approxFloor(GetDouble());
    double M = ::rtl::math::approxFloor(GetDouble());
    double n = ::rtl::math::approxFloor(GetDouble());
    double x = ::rtl::math::approxFloor(GetDouble());

    if( (x < 0.0) || (n < x) || (M < x) || (N < n) || (N < M) || (x < n - N + M) )
    {
        PushIllegalArgument();
        return;
    }

    typedef ::std::vector< double > HypContainer;
    HypContainer cnNumer, cnDenom;

    size_t nEstContainerSize = static_cast<size_t>( x + ::std::min( n, M ) );
    size_t nMaxSize = ::std::min( cnNumer.max_size(), nMaxArraySize );
    if ( nEstContainerSize > nMaxSize )
    {
        PushNoValue();
        return;
    }
    cnNumer.reserve( nEstContainerSize + 10 );
    cnDenom.reserve( nEstContainerSize + 10 );

    // Trim coefficient C first
    double fCNumVarUpper = N - n - M + x - 1.0;
    double fCDenomVarLower = 1.0;
    if ( N - n - M + x >= M - x + 1.0 )
    {
        fCNumVarUpper = M - x - 1.0;
        fCDenomVarLower = N - n - 2.0*(M - x) + 1.0;
    }

#ifdef DBG_UTIL
    double fCNumLower = N - n - fCNumVarUpper;
#endif
    double fCDenomUpper = N - n - M + x + 1.0 - fCDenomVarLower;

    double fDNumVarLower = n - M;

    if ( n >= M + 1.0 )
    {
        if ( N - M < n + 1.0 )
        {
            // Case 1

            if ( N - n < n + 1.0 )
            {
                // no overlap
                lcl_PutFactorialElements( cnNumer, 0.0, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, N - n - 1.0, N );
            }
            else
            {
                // overlap
                DBG_ASSERT( fCNumLower < n + 1.0, "ScHypGeomDist: wrong assertion" );
                lcl_PutFactorialElements( cnNumer, N - 2.0*n, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, n - 1.0, N );
            }

            DBG_ASSERT( fCDenomUpper <= N - M, "ScHypGeomDist: wrong assertion" );

            if ( fCDenomUpper < n - x + 1.0 )
                // no overlap
                lcl_PutFactorialElements( cnNumer, 1.0, N - M - n + x, N - M + 1.0 );
            else
            {
                // overlap
                lcl_PutFactorialElements( cnNumer, 1.0, N - M - fCDenomUpper, N - M + 1.0 );

                fCDenomUpper = n - x;
                fCDenomVarLower = N - M - 2.0*(n - x) + 1.0;
            }
        }
        else
        {
            // Case 2

            if ( n > M - 1.0 )
            {
                // no overlap
                lcl_PutFactorialElements( cnNumer, 0.0, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, M - 1.0, N );
            }
            else
            {
                lcl_PutFactorialElements( cnNumer, M - n, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, n - 1.0, N );
            }

            DBG_ASSERT( fCDenomUpper <= n, "ScHypGeomDist: wrong assertion" );

            if ( fCDenomUpper < n - x + 1.0 )
                // no overlap
                lcl_PutFactorialElements( cnNumer, N - M - n + 1.0, N - M - n + x, N - M + 1.0 );
            else
            {
                lcl_PutFactorialElements( cnNumer, N - M - n + 1.0, N - M - fCDenomUpper, N - M + 1.0 );
                fCDenomUpper = n - x;
                fCDenomVarLower = N - M - 2.0*(n - x) + 1.0;
            }
        }

        DBG_ASSERT( fCDenomUpper <= M, "ScHypGeomDist: wrong assertion" );
    }
    else
    {
        if ( N - M < M + 1.0 )
        {
            // Case 3

            if ( N - n < M + 1.0 )
            {
                // No overlap
                lcl_PutFactorialElements( cnNumer, 0.0, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, N - M - 1.0, N );
            }
            else
            {
                lcl_PutFactorialElements( cnNumer, N - n - M, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, n - 1.0, N );
            }

            if ( n - x + 1.0 > fCDenomUpper )
                // No overlap
                lcl_PutFactorialElements( cnNumer, 1.0, N - M - n + x, N - M + 1.0 );
            else
            {
                // Overlap
                lcl_PutFactorialElements( cnNumer, 1.0, N - M - fCDenomUpper, N - M + 1.0 );

                fCDenomVarLower = N - M - 2.0*(n - x) + 1.0;
                fCDenomUpper = n - x;
            }
        }
        else
        {
            // Case 4

            DBG_ASSERT( M >= n - x, "ScHypGeomDist: wrong assertion" );
            DBG_ASSERT( M - x <= N - M + 1.0, "ScHypGeomDist: wrong assertion" );

            if ( N - n < N - M + 1.0 )
            {
                // No overlap
                lcl_PutFactorialElements( cnNumer, 0.0, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, M - 1.0, N );
            }
            else
            {
                // Overlap
                DBG_ASSERT( fCNumLower <= N - M + 1.0, "ScHypGeomDist: wrong assertion" );

                lcl_PutFactorialElements( cnNumer, M - n, fCNumVarUpper, N - n );
                lcl_PutFactorialElements( cnDenom, 0.0, n - 1.0, N );
            }

            if ( n - x + 1.0 > fCDenomUpper )
                // No overlap
                lcl_PutFactorialElements( cnNumer, N - 2.0*M + 1.0, N - M - n + x, N - M + 1.0 );
            else if ( M >= fCDenomUpper )
            {
                lcl_PutFactorialElements( cnNumer, N - 2.0*M + 1.0, N - M - fCDenomUpper, N - M + 1.0 );

                fCDenomUpper = n - x;
                fCDenomVarLower = N - M - 2.0*(n - x) + 1.0;
            }
            else
            {
                DBG_ASSERT( M <= fCDenomUpper, "ScHypGeomDist: wrong assertion" );
                lcl_PutFactorialElements( cnDenom, fCDenomVarLower, N - n - 2.0*M + x,
                        N - n - M + x + 1.0 );

                fCDenomUpper = n - x;
                fCDenomVarLower = N - M - 2.0*(n - x) + 1.0;
            }
        }

        DBG_ASSERT( fCDenomUpper <= n, "ScHypGeomDist: wrong assertion" );

        fDNumVarLower = 0.0;
    }

    double nDNumVarUpper   = fCDenomUpper < x + 1.0 ? n - x - 1.0     : n - fCDenomUpper - 1.0;
    double nDDenomVarLower = fCDenomUpper < x + 1.0 ? fCDenomVarLower : N - n - M + 1.0;
    lcl_PutFactorialElements( cnNumer, fDNumVarLower, nDNumVarUpper, n );
    lcl_PutFactorialElements( cnDenom, nDDenomVarLower, N - n - M + x, N - n - M + x + 1.0 );

    ::std::sort( cnNumer.begin(), cnNumer.end() );
    ::std::sort( cnDenom.begin(), cnDenom.end() );
    HypContainer::reverse_iterator it1 = cnNumer.rbegin(), it1End = cnNumer.rend();
    HypContainer::reverse_iterator it2 = cnDenom.rbegin(), it2End = cnDenom.rend();

    double fFactor = 1.0;
    for ( ; it1 != it1End || it2 != it2End; )
    {
        double fEnum = 1.0, fDenom = 1.0;
        if ( it1 != it1End )
            fEnum  = *it1++;
        if ( it2 != it2End )
            fDenom = *it2++;
        fFactor *= fEnum / fDenom;
    }

    PushDouble(fFactor);
}

void ScInterpreter::ScGammaDist()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScGammaDist" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 3, 4 ) )
        return;
    double bCumulative;
    if (nParamCount == 4)
        bCumulative = GetBool();
    else
        bCumulative = true;
    double fBeta = GetDouble();                 // scale
    double fAlpha = GetDouble();                // shape
    double fX = GetDouble();                    // x
    if (fAlpha <= 0.0 || fBeta <= 0.0)
        PushIllegalArgument();
    else
    {
        if (bCumulative)                        // distribution
            PushDouble( GetGammaDist( fX, fAlpha, fBeta));
        else                                    // density
            PushDouble( GetGammaDistPDF( fX, fAlpha, fBeta));
    }
}

void ScInterpreter::ScNormInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScNormInv" );
    if ( MustHaveParamCount( GetByte(), 3 ) )
    {
        double sigma = GetDouble();
        double mue   = GetDouble();
        double x     = GetDouble();
        if (sigma <= 0.0 || x < 0.0 || x > 1.0)
            PushIllegalArgument();
        else if (x == 0.0 || x == 1.0)
            PushNoValue();
        else
            PushDouble(gaussinv(x)*sigma + mue);
    }
}

void ScInterpreter::ScSNormInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScSNormInv" );
    double x = GetDouble();
    if (x < 0.0 || x > 1.0)
        PushIllegalArgument();
    else if (x == 0.0 || x == 1.0)
        PushNoValue();
    else
        PushDouble(gaussinv(x));
}

void ScInterpreter::ScLogNormInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScLogNormInv" );
    if ( MustHaveParamCount( GetByte(), 3 ) )
    {
        double sigma = GetDouble();                 // Stdabw
        double mue = GetDouble();                   // Mittelwert
        double y = GetDouble();                     // y
        if (sigma <= 0.0 || y <= 0.0 || y >= 1.0)
            PushIllegalArgument();
        else
            PushDouble(exp(mue+sigma*gaussinv(y)));
    }
}

class ScGammaDistFunction : public ScDistFunc
{
    ScInterpreter&  rInt;
    double          fp, fAlpha, fBeta;

public:
            ScGammaDistFunction( ScInterpreter& rI, double fpVal, double fAlphaVal, double fBetaVal ) :
                rInt(rI), fp(fpVal), fAlpha(fAlphaVal), fBeta(fBetaVal) {}

    double  GetValue( double x ) const  { return fp - rInt.GetGammaDist(x, fAlpha, fBeta); }
};

void ScInterpreter::ScGammaInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScGammaInv" );
    if ( !MustHaveParamCount( GetByte(), 3 ) )
        return;
    double fBeta  = GetDouble();
    double fAlpha = GetDouble();
    double fP = GetDouble();
    if (fAlpha <= 0.0 || fBeta <= 0.0 || fP < 0.0 || fP >= 1.0 )
    {
        PushIllegalArgument();
        return;
    }
    if (fP == 0.0)
        PushInt(0);
    else
    {
        bool bConvError;
        ScGammaDistFunction aFunc( *this, fP, fAlpha, fBeta );
        double fStart = fAlpha * fBeta;
        double fVal = lcl_IterateInverse( aFunc, fStart*0.5, fStart, bConvError );
        if (bConvError)
            SetError(errNoConvergence);
        PushDouble(fVal);
    }
}

class ScBetaDistFunction : public ScDistFunc
{
    ScInterpreter&  rInt;
    double          fp, fAlpha, fBeta;

public:
            ScBetaDistFunction( ScInterpreter& rI, double fpVal, double fAlphaVal, double fBetaVal ) :
                rInt(rI), fp(fpVal), fAlpha(fAlphaVal), fBeta(fBetaVal) {}

    double  GetValue( double x ) const  { return fp - rInt.GetBetaDist(x, fAlpha, fBeta); }
};

void ScInterpreter::ScBetaInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScBetaInv" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 3, 5 ) )
        return;
    double fP, fA, fB, fAlpha, fBeta;
    if (nParamCount == 5)
        fB = GetDouble();
    else
        fB = 1.0;
    if (nParamCount >= 4)
        fA = GetDouble();
    else
        fA = 0.0;
    fBeta  = GetDouble();
    fAlpha = GetDouble();
    fP     = GetDouble();
    if (fP < 0.0 || fP >= 1.0 || fA == fB || fAlpha <= 0.0 || fBeta <= 0.0)
    {
        PushIllegalArgument();
        return;
    }
    if (fP == 0.0)
        PushInt(0);
    else
    {
        bool bConvError;
        ScBetaDistFunction aFunc( *this, fP, fAlpha, fBeta );
        // 0..1 as range for iteration so it isn't extended beyond the valid range
        double fVal = lcl_IterateInverse( aFunc, 0.0, 1.0, bConvError );
        if (bConvError)
            PushError( errNoConvergence);
        else
            PushDouble(fA + fVal*(fB-fA));                  // scale to (A,B)
    }
}

                                                            // Achtung: T, F und Chi
                                                            // sind monoton fallend,
                                                            // deshalb 1-Dist als Funktion

class ScTDistFunction : public ScDistFunc
{
    ScInterpreter&  rInt;
    double          fp, fDF;

public:
            ScTDistFunction( ScInterpreter& rI, double fpVal, double fDFVal ) :
                rInt(rI), fp(fpVal), fDF(fDFVal) {}

    double  GetValue( double x ) const  { return fp - 2 * rInt.GetTDist(x, fDF); }
};

void ScInterpreter::ScTInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScTInv" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    double fDF  = ::rtl::math::approxFloor(GetDouble());
    double fP = GetDouble();
    if (fDF < 1.0 || fDF >= 1.0E5 || fP <= 0.0 || fP > 1.0 )
    {
        PushIllegalArgument();
        return;
    }

    bool bConvError;
    ScTDistFunction aFunc( *this, fP, fDF );
    double fVal = lcl_IterateInverse( aFunc, fDF*0.5, fDF, bConvError );
    if (bConvError)
        SetError(errNoConvergence);
    PushDouble(fVal);
}

class ScFDistFunction : public ScDistFunc
{
    ScInterpreter&  rInt;
    double          fp, fF1, fF2;

public:
            ScFDistFunction( ScInterpreter& rI, double fpVal, double fF1Val, double fF2Val ) :
                rInt(rI), fp(fpVal), fF1(fF1Val), fF2(fF2Val) {}

    double  GetValue( double x ) const  { return fp - rInt.GetFDist(x, fF1, fF2); }
};

void ScInterpreter::ScFInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScFInv" );
    if ( !MustHaveParamCount( GetByte(), 3 ) )
        return;
    double fF2 = ::rtl::math::approxFloor(GetDouble());
    double fF1 = ::rtl::math::approxFloor(GetDouble());
    double fP  = GetDouble();
    if (fP <= 0.0 || fF1 < 1.0 || fF2 < 1.0 || fF1 >= 1.0E10 || fF2 >= 1.0E10 || fP > 1.0)
    {
        PushIllegalArgument();
        return;
    }

    bool bConvError;
    ScFDistFunction aFunc( *this, fP, fF1, fF2 );
    double fVal = lcl_IterateInverse( aFunc, fF1*0.5, fF1, bConvError );
    if (bConvError)
        SetError(errNoConvergence);
    PushDouble(fVal);
}

class ScChiDistFunction : public ScDistFunc
{
    ScInterpreter&  rInt;
    double          fp, fDF;

public:
            ScChiDistFunction( ScInterpreter& rI, double fpVal, double fDFVal ) :
                rInt(rI), fp(fpVal), fDF(fDFVal) {}

    double  GetValue( double x ) const  { return fp - rInt.GetChiDist(x, fDF); }
};

void ScInterpreter::ScChiInv()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScChiInv" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    double fDF  = ::rtl::math::approxFloor(GetDouble());
    double fP = GetDouble();
    if (fDF < 1.0 || fP <= 0.0 || fP > 1.0 )
    {
        PushIllegalArgument();
        return;
    }

    bool bConvError;
    ScChiDistFunction aFunc( *this, fP, fDF );
    double fVal = lcl_IterateInverse( aFunc, fDF*0.5, fDF, bConvError );
    if (bConvError)
        SetError(errNoConvergence);
    PushDouble(fVal);
}

/***********************************************/
class ScChiSqDistFunction : public ScDistFunc
{
    ScInterpreter&  rInt;
    double          fp, fDF;

public:
            ScChiSqDistFunction( ScInterpreter& rI, double fpVal, double fDFVal ) :
                rInt(rI), fp(fpVal), fDF(fDFVal) {}

    double  GetValue( double x ) const  { return fp - rInt.GetChiSqDistCDF(x, fDF); }
};


void ScInterpreter::ScChiSqInv()
{
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    double fDF  = ::rtl::math::approxFloor(GetDouble());
    double fP = GetDouble();
    if (fDF < 1.0 || fP < 0.0 || fP >= 1.0 )
    {
        PushIllegalArgument();
        return;
    }

    bool bConvError;
    ScChiSqDistFunction aFunc( *this, fP, fDF );
    double fVal = lcl_IterateInverse( aFunc, fDF*0.5, fDF, bConvError );
    if (bConvError)
        SetError(errNoConvergence);
    PushDouble(fVal);
}


void ScInterpreter::ScConfidence()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScConfidence" );
    if ( MustHaveParamCount( GetByte(), 3 ) )
    {
        double n     = ::rtl::math::approxFloor(GetDouble());
        double sigma = GetDouble();
        double alpha = GetDouble();
        if (sigma <= 0.0 || alpha <= 0.0 || alpha >= 1.0 || n < 1.0)
            PushIllegalArgument();
        else
            PushDouble( gaussinv(1.0-alpha/2.0) * sigma/sqrt(n) );
    }
}

void ScInterpreter::ScZTest()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScZTest" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 2, 3 ) )
        return;
    double sigma = 0.0, mue, x;
    if (nParamCount == 3)
    {
        sigma = GetDouble();
        if (sigma <= 0.0)
        {
            PushIllegalArgument();
            return;
        }
    }
    x = GetDouble();

    double fSum    = 0.0;
    double fSumSqr = 0.0;
    double fVal;
    double rValCount = 0.0;
    switch (GetStackType())
    {
        case formula::svDouble :
        {
            fVal = GetDouble();
            fSum    += fVal;
            fSumSqr += fVal*fVal;
            rValCount++;
        }
        break;
        case svSingleRef :
        {
            ScAddress aAdr;
            PopSingleRef( aAdr );
            ScBaseCell* pCell = GetCell( aAdr );
            if (HasCellValueData(pCell))
            {
                fVal = GetCellValue( aAdr, pCell );
                fSum += fVal;
                fSumSqr += fVal*fVal;
                rValCount++;
            }
        }
        break;
        case svRefList :
        case formula::svDoubleRef :
        {
            short nParam = 1;
            size_t nRefInList = 0;
            while (nParam-- > 0)
            {
                ScRange aRange;
                sal_uInt16 nErr = 0;
                PopDoubleRef( aRange, nParam, nRefInList);
                ScValueIterator aValIter(pDok, aRange, glSubTotal);
                if (aValIter.GetFirst(fVal, nErr))
                {
                    fSum += fVal;
                    fSumSqr += fVal*fVal;
                    rValCount++;
                    while ((nErr == 0) && aValIter.GetNext(fVal, nErr))
                    {
                        fSum += fVal;
                        fSumSqr += fVal*fVal;
                        rValCount++;
                    }
                    SetError(nErr);
                }
            }
        }
        break;
        case svMatrix :
        {
            ScMatrixRef pMat = PopMatrix();
            if (pMat)
            {
                SCSIZE nCount = pMat->GetElementCount();
                if (pMat->IsNumeric())
                {
                    for ( SCSIZE i = 0; i < nCount; i++ )
                    {
                        fVal= pMat->GetDouble(i);
                        fSum += fVal;
                        fSumSqr += fVal * fVal;
                        rValCount++;
                    }
                }
                else
                {
                    for (SCSIZE i = 0; i < nCount; i++)
                        if (!pMat->IsString(i))
                        {
                            fVal= pMat->GetDouble(i);
                            fSum += fVal;
                            fSumSqr += fVal * fVal;
                            rValCount++;
                        }
                }
            }
        }
        break;
        default : SetError(errIllegalParameter); break;
    }
    if (rValCount <= 1.0)
        PushError( errDivisionByZero);
    else
    {
        mue = fSum/rValCount;
        if (nParamCount != 3)
        {
            sigma = (fSumSqr - fSum*fSum/rValCount)/(rValCount-1.0);
            PushDouble(0.5 - gauss((mue-x)/sqrt(sigma/rValCount)));
        }
        else
            PushDouble(0.5 - gauss((mue-x)*sqrt(rValCount)/sigma));
    }
}
bool ScInterpreter::CalculateTest(sal_Bool _bTemplin
                                  ,const SCSIZE nC1, const SCSIZE nC2,const SCSIZE nR1,const SCSIZE nR2
                                  ,const ScMatrixRef& pMat1,const ScMatrixRef& pMat2
                                  ,double& fT,double& fF)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::CalculateTest" );
    double fCount1  = 0.0;
    double fCount2  = 0.0;
    double fSum1    = 0.0;
    double fSumSqr1 = 0.0;
    double fSum2    = 0.0;
    double fSumSqr2 = 0.0;
    double fVal;
    SCSIZE i,j;
    for (i = 0; i < nC1; i++)
        for (j = 0; j < nR1; j++)
        {
            if (!pMat1->IsString(i,j))
            {
                fVal = pMat1->GetDouble(i,j);
                fSum1    += fVal;
                fSumSqr1 += fVal * fVal;
                fCount1++;
            }
        }
    for (i = 0; i < nC2; i++)
        for (j = 0; j < nR2; j++)
        {
            if (!pMat2->IsString(i,j))
            {
                fVal = pMat2->GetDouble(i,j);
                fSum2    += fVal;
                fSumSqr2 += fVal * fVal;
                fCount2++;
            }
        }
    if (fCount1 < 2.0 || fCount2 < 2.0)
    {
        PushNoValue();
        return false;
    } // if (fCount1 < 2.0 || fCount2 < 2.0)
    if ( _bTemplin )
    {
        double fS1 = (fSumSqr1-fSum1*fSum1/fCount1)/(fCount1-1.0)/fCount1;
        double fS2 = (fSumSqr2-fSum2*fSum2/fCount2)/(fCount2-1.0)/fCount2;
        if (fS1 + fS2 == 0.0)
        {
            PushNoValue();
            return false;
        }
        fT = fabs(fSum1/fCount1 - fSum2/fCount2)/sqrt(fS1+fS2);
        double c = fS1/(fS1+fS2);
// s.u. fF = ::rtl::math::approxFloor(1.0/(c*c/(fCount1-1.0)+(1.0-c)*(1.0-c)/(fCount2-1.0)));
//      fF = ::rtl::math::approxFloor((fS1+fS2)*(fS1+fS2)/(fS1*fS1/(fCount1-1.0) + fS2*fS2/(fCount2-1.0)));

    //  GetTDist wird mit GetBetaDist berechnet und kommt auch mit nicht ganzzahligen
    //  Freiheitsgraden klar. Dann stimmt das Ergebnis auch mit Excel ueberein (#52406#):
        fF = 1.0/(c*c/(fCount1-1.0)+(1.0-c)*(1.0-c)/(fCount2-1.0));
    }
    else
    {
        //  laut Bronstein-Semendjajew
        double fS1 = (fSumSqr1 - fSum1*fSum1/fCount1) / (fCount1 - 1.0);    // Varianz
        double fS2 = (fSumSqr2 - fSum2*fSum2/fCount2) / (fCount2 - 1.0);
        fT = fabs( fSum1/fCount1 - fSum2/fCount2 ) /
             sqrt( (fCount1-1.0)*fS1 + (fCount2-1.0)*fS2 ) *
             sqrt( fCount1*fCount2*(fCount1+fCount2-2)/(fCount1+fCount2) );
        fF = fCount1 + fCount2 - 2;
    }
    return true;
}
void ScInterpreter::ScTTest()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScTTest" );
    if ( !MustHaveParamCount( GetByte(), 4 ) )
        return;
    double fTyp = ::rtl::math::approxFloor(GetDouble());
    double fAnz = ::rtl::math::approxFloor(GetDouble());
    if (fAnz != 1.0 && fAnz != 2.0)
    {
        PushIllegalArgument();
        return;
    }

    ScMatrixRef pMat2 = GetMatrix();
    ScMatrixRef pMat1 = GetMatrix();
    if (!pMat1 || !pMat2)
    {
        PushIllegalParameter();
        return;
    }
    double fT, fF;
    SCSIZE nC1, nC2;
    SCSIZE nR1, nR2;
    SCSIZE i, j;
    pMat1->GetDimensions(nC1, nR1);
    pMat2->GetDimensions(nC2, nR2);
    if (fTyp == 1.0)
    {
        if (nC1 != nC2 || nR1 != nR2)
        {
            PushIllegalArgument();
            return;
        }
        double fCount   = 0.0;
        double fSum1    = 0.0;
        double fSum2    = 0.0;
        double fSumSqrD = 0.0;
        double fVal1, fVal2;
        for (i = 0; i < nC1; i++)
            for (j = 0; j < nR1; j++)
            {
                if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
                {
                    fVal1 = pMat1->GetDouble(i,j);
                    fVal2 = pMat2->GetDouble(i,j);
                    fSum1    += fVal1;
                    fSum2    += fVal2;
                    fSumSqrD += (fVal1 - fVal2)*(fVal1 - fVal2);
                    fCount++;
                }
            }
        if (fCount < 1.0)
        {
            PushNoValue();
            return;
        }
        fT = sqrt(fCount-1.0) * fabs(fSum1 - fSum2) /
             sqrt(fCount * fSumSqrD - (fSum1-fSum2)*(fSum1-fSum2));
        fF = fCount - 1.0;
    }
    else if (fTyp == 2.0)
    {
        CalculateTest(sal_False,nC1, nC2,nR1, nR2,pMat1,pMat2,fT,fF);
    }
    else if (fTyp == 3.0)
    {
        CalculateTest(sal_True,nC1, nC2,nR1, nR2,pMat1,pMat2,fT,fF);
    }

    else
    {
        PushIllegalArgument();
        return;
    }
    if (fAnz == 1.0)
        PushDouble(GetTDist(fT, fF));
    else
        PushDouble(2.0*GetTDist(fT, fF));
}

void ScInterpreter::ScFTest()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScFTest" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    ScMatrixRef pMat2 = GetMatrix();
    ScMatrixRef pMat1 = GetMatrix();
    if (!pMat1 || !pMat2)
    {
        PushIllegalParameter();
        return;
    }
    SCSIZE nC1, nC2;
    SCSIZE nR1, nR2;
    SCSIZE i, j;
    pMat1->GetDimensions(nC1, nR1);
    pMat2->GetDimensions(nC2, nR2);
    double fCount1  = 0.0;
    double fCount2  = 0.0;
    double fSum1    = 0.0;
    double fSumSqr1 = 0.0;
    double fSum2    = 0.0;
    double fSumSqr2 = 0.0;
    double fVal;
    for (i = 0; i < nC1; i++)
        for (j = 0; j < nR1; j++)
        {
            if (!pMat1->IsString(i,j))
            {
                fVal = pMat1->GetDouble(i,j);
                fSum1    += fVal;
                fSumSqr1 += fVal * fVal;
                fCount1++;
            }
        }
    for (i = 0; i < nC2; i++)
        for (j = 0; j < nR2; j++)
        {
            if (!pMat2->IsString(i,j))
            {
                fVal = pMat2->GetDouble(i,j);
                fSum2    += fVal;
                fSumSqr2 += fVal * fVal;
                fCount2++;
            }
        }
    if (fCount1 < 2.0 || fCount2 < 2.0)
    {
        PushNoValue();
        return;
    }
    double fS1 = (fSumSqr1-fSum1*fSum1/fCount1)/(fCount1-1.0);
    double fS2 = (fSumSqr2-fSum2*fSum2/fCount2)/(fCount2-1.0);
    if (fS1 == 0.0 || fS2 == 0.0)
    {
        PushNoValue();
        return;
    }
    double fF, fF1, fF2;
    if (fS1 > fS2)
    {
        fF = fS1/fS2;
        fF1 = fCount1-1.0;
        fF2 = fCount2-1.0;
    }
    else
    {
        fF = fS2/fS1;
        fF1 = fCount2-1.0;
        fF2 = fCount1-1.0;
    }
    PushDouble(2.0*GetFDist(fF, fF1, fF2));
/*
    double Z = (pow(fF,1.0/3.0)*(1.0-2.0/(9.0*fF2)) - (1.0-2.0/(9.0*fF1))) /
               sqrt(2.0/(9.0*fF1) + pow(fF,2.0/3.0)*2.0/(9.0*fF2));
    PushDouble(1.0-2.0*gauss(Z));
*/
}

void ScInterpreter::ScChiTest()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScChiTest" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    ScMatrixRef pMat2 = GetMatrix();
    ScMatrixRef pMat1 = GetMatrix();
    if (!pMat1 || !pMat2)
    {
        PushIllegalParameter();
        return;
    }
    SCSIZE nC1, nC2;
    SCSIZE nR1, nR2;
    pMat1->GetDimensions(nC1, nR1);
    pMat2->GetDimensions(nC2, nR2);
    if (nR1 != nR2 || nC1 != nC2)
    {
        PushIllegalArgument();
        return;
    }
    double fChi = 0.0;
    for (SCSIZE i = 0; i < nC1; i++)
    {
        for (SCSIZE j = 0; j < nR1; j++)
        {
            if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
            {
                double fValX = pMat1->GetDouble(i,j);
                double fValE = pMat2->GetDouble(i,j);
                fChi += (fValX - fValE) * (fValX - fValE) / fValE;
            }
            else
            {
                PushIllegalArgument();
                return;
            }
        }
    }
    double fDF;
    if (nC1 == 1 || nR1 == 1)
    {
        fDF = (double)(nC1*nR1 - 1);
        if (fDF == 0.0)
        {
            PushNoValue();
            return;
        }
    }
    else
        fDF = (double)(nC1-1)*(double)(nR1-1);
    PushDouble(GetChiDist(fChi, fDF));
/*
    double fX, fS, fT, fG;
    fX = 1.0;
    for (double fi = fDF; fi >= 2.0; fi -= 2.0)
        fX *= fChi/fi;
    fX *= exp(-fChi/2.0);
    if (fmod(fDF, 2.0) != 0.0)
        fX *= sqrt(2.0*fChi/F_PI);
    fS = 1.0;
    fT = 1.0;
    fG = fDF;
    while (fT >= 1.0E-7)
    {
        fG += 2.0;
        fT *= fChi/fG;
        fS += fT;
    }
    PushDouble(1.0 - fX*fS);
*/
}

void ScInterpreter::ScKurt()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScKurt" );
    double fSum,fCount,vSum;
    std::vector<double> values;
    if ( !CalculateSkew(fSum,fCount,vSum,values) )
        return;

    if (fCount == 0.0)
    {
        PushError( errDivisionByZero);
        return;
    }

    double fMean = fSum / fCount;

    for (size_t i = 0; i < values.size(); i++)
        vSum += (values[i] - fMean) * (values[i] - fMean);

    double fStdDev = sqrt(vSum / (fCount - 1.0));
    double dx = 0.0;
    double xpower4 = 0.0;

    if (fStdDev == 0.0)
    {
        PushError( errDivisionByZero);
        return;
    }

    for (size_t i = 0; i < values.size(); i++)
    {
        dx = (values[i] - fMean) / fStdDev;
        xpower4 = xpower4 + (dx * dx * dx * dx);
    }

    double k_d = (fCount - 2.0) * (fCount - 3.0);
    double k_l = fCount * (fCount + 1.0) / ((fCount - 1.0) * k_d);
    double k_t = 3.0 * (fCount - 1.0) * (fCount - 1.0) / k_d;

    PushDouble(xpower4 * k_l - k_t);
}

void ScInterpreter::ScHarMean()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScHarMean" );
    short nParamCount = GetByte();
    double nVal = 0.0;
    double nValCount = 0.0;
    ScAddress aAdr;
    ScRange aRange;
    size_t nRefInList = 0;
    while ((nGlobalError == 0) && (nParamCount-- > 0))
    {
        switch (GetStackType())
        {
            case formula::svDouble    :
            {
                double x = GetDouble();
                if (x > 0.0)
                {
                    nVal += 1.0/x;
                    nValCount++;
                }
                else
                    SetError( errIllegalArgument);
                break;
            }
            case svSingleRef :
            {
                PopSingleRef( aAdr );
                ScBaseCell* pCell = GetCell( aAdr );
                if (HasCellValueData(pCell))
                {
                    double x = GetCellValue( aAdr, pCell );
                    if (x > 0.0)
                    {
                        nVal += 1.0/x;
                        nValCount++;
                    }
                    else
                        SetError( errIllegalArgument);
                }
                break;
            }
            case formula::svDoubleRef :
            case svRefList :
            {
                sal_uInt16 nErr = 0;
                PopDoubleRef( aRange, nParamCount, nRefInList);
                double nCellVal;
                ScValueIterator aValIter(pDok, aRange, glSubTotal);
                if (aValIter.GetFirst(nCellVal, nErr))
                {
                    if (nCellVal > 0.0)
                    {
                        nVal += 1.0/nCellVal;
                        nValCount++;
                    }
                    else
                        SetError( errIllegalArgument);
                    SetError(nErr);
                    while ((nErr == 0) && aValIter.GetNext(nCellVal, nErr))
                    {
                        if (nCellVal > 0.0)
                        {
                            nVal += 1.0/nCellVal;
                            nValCount++;
                        }
                        else
                            SetError( errIllegalArgument);
                    }
                    SetError(nErr);
                }
            }
            break;
            case svMatrix :
            {
                ScMatrixRef pMat = PopMatrix();
                if (pMat)
                {
                    SCSIZE nCount = pMat->GetElementCount();
                    if (pMat->IsNumeric())
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                        {
                            double x = pMat->GetDouble(nElem);
                            if (x > 0.0)
                            {
                                nVal += 1.0/x;
                                nValCount++;
                            }
                            else
                                SetError( errIllegalArgument);
                        }
                    }
                    else
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                            if (!pMat->IsString(nElem))
                            {
                                double x = pMat->GetDouble(nElem);
                                if (x > 0.0)
                                {
                                    nVal += 1.0/x;
                                    nValCount++;
                                }
                                else
                                    SetError( errIllegalArgument);
                            }
                    }
                }
            }
            break;
            default : SetError(errIllegalParameter); break;
        }
    }
    if (nGlobalError == 0)
        PushDouble((double)nValCount/nVal);
    else
        PushError( nGlobalError);
}

void ScInterpreter::ScGeoMean()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScGeoMean" );
    short nParamCount = GetByte();
    double nVal = 0.0;
    double nValCount = 0.0;
    ScAddress aAdr;
    ScRange aRange;

    size_t nRefInList = 0;
    while ((nGlobalError == 0) && (nParamCount-- > 0))
    {
        switch (GetStackType())
        {
            case formula::svDouble    :
            {
                double x = GetDouble();
                if (x > 0.0)
                {
                    nVal += log(x);
                    nValCount++;
                }
                else
                    SetError( errIllegalArgument);
                break;
            }
            case svSingleRef :
            {
                PopSingleRef( aAdr );
                ScBaseCell* pCell = GetCell( aAdr );
                if (HasCellValueData(pCell))
                {
                    double x = GetCellValue( aAdr, pCell );
                    if (x > 0.0)
                    {
                        nVal += log(x);
                        nValCount++;
                    }
                    else
                        SetError( errIllegalArgument);
                }
                break;
            }
            case formula::svDoubleRef :
            case svRefList :
            {
                sal_uInt16 nErr = 0;
                PopDoubleRef( aRange, nParamCount, nRefInList);
                double nCellVal;
                ScValueIterator aValIter(pDok, aRange, glSubTotal);
                if (aValIter.GetFirst(nCellVal, nErr))
                {
                    if (nCellVal > 0.0)
                    {
                        nVal += log(nCellVal);
                        nValCount++;
                    }
                    else
                        SetError( errIllegalArgument);
                    SetError(nErr);
                    while ((nErr == 0) && aValIter.GetNext(nCellVal, nErr))
                    {
                        if (nCellVal > 0.0)
                        {
                            nVal += log(nCellVal);
                            nValCount++;
                        }
                        else
                            SetError( errIllegalArgument);
                    }
                    SetError(nErr);
                }
            }
            break;
            case svMatrix :
            {
                ScMatrixRef pMat = PopMatrix();
                if (pMat)
                {
                    SCSIZE nCount = pMat->GetElementCount();
                    if (pMat->IsNumeric())
                    {
                        for (SCSIZE ui = 0; ui < nCount; ui++)
                        {
                            double x = pMat->GetDouble(ui);
                            if (x > 0.0)
                            {
                                nVal += log(x);
                                nValCount++;
                            }
                            else
                                SetError( errIllegalArgument);
                        }
                    }
                    else
                    {
                        for (SCSIZE ui = 0; ui < nCount; ui++)
                            if (!pMat->IsString(ui))
                            {
                                double x = pMat->GetDouble(ui);
                                if (x > 0.0)
                                {
                                    nVal += log(x);
                                    nValCount++;
                                }
                                else
                                    SetError( errIllegalArgument);
                            }
                    }
                }
            }
            break;
            default : SetError(errIllegalParameter); break;
        }
    }
    if (nGlobalError == 0)
        PushDouble(exp(nVal / nValCount));
    else
        PushError( nGlobalError);
}

void ScInterpreter::ScStandard()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScStandard" );
    if ( MustHaveParamCount( GetByte(), 3 ) )
    {
        double sigma = GetDouble();
        double mue   = GetDouble();
        double x     = GetDouble();
        if (sigma < 0.0)
            PushError( errIllegalArgument);
        else if (sigma == 0.0)
            PushError( errDivisionByZero);
        else
            PushDouble((x-mue)/sigma);
    }
}
bool ScInterpreter::CalculateSkew(double& fSum,double& fCount,double& vSum,std::vector<double>& values)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::CalculateSkew" );
    short nParamCount = GetByte();
    if ( !MustHaveParamCountMin( nParamCount, 1 )  )
        return false;

    fSum   = 0.0;
    fCount = 0.0;
    vSum   = 0.0;
    double fVal = 0.0;
    ScAddress aAdr;
    ScRange aRange;
    size_t nRefInList = 0;
    while (nParamCount-- > 0)
    {
        switch (GetStackType())
        {
            case formula::svDouble :
            {
                fVal = GetDouble();
                fSum += fVal;
                values.push_back(fVal);
                fCount++;
            }
                break;
            case svSingleRef :
            {
                PopSingleRef( aAdr );
                ScBaseCell* pCell = GetCell( aAdr );
                if (HasCellValueData(pCell))
                {
                    fVal = GetCellValue( aAdr, pCell );
                    fSum += fVal;
                    values.push_back(fVal);
                    fCount++;
                }
            }
            break;
            case formula::svDoubleRef :
            case svRefList :
            {
                PopDoubleRef( aRange, nParamCount, nRefInList);
                sal_uInt16 nErr = 0;
                ScValueIterator aValIter(pDok, aRange);
                if (aValIter.GetFirst(fVal, nErr))
                {
                    fSum += fVal;
                    values.push_back(fVal);
                    fCount++;
                    SetError(nErr);
                    while ((nErr == 0) && aValIter.GetNext(fVal, nErr))
                    {
                        fSum += fVal;
                        values.push_back(fVal);
                        fCount++;
                    }
                    SetError(nErr);
                }
            }
            break;
            case svMatrix :
            {
                ScMatrixRef pMat = PopMatrix();
                if (pMat)
                {
                    SCSIZE nCount = pMat->GetElementCount();
                    if (pMat->IsNumeric())
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                        {
                            fVal = pMat->GetDouble(nElem);
                            fSum += fVal;
                            values.push_back(fVal);
                            fCount++;
                        }
                    }
                    else
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                            if (!pMat->IsString(nElem))
                            {
                                fVal = pMat->GetDouble(nElem);
                                fSum += fVal;
                                values.push_back(fVal);
                                fCount++;
                            }
                    }
                }
            }
            break;
            default :
                SetError(errIllegalParameter);
            break;
        }
    }

    if (nGlobalError)
    {
        PushError( nGlobalError);
        return false;
    } // if (nGlobalError)
    return true;
}

void ScInterpreter::ScSkew()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScSkew" );
    double fSum,fCount,vSum;
    std::vector<double> values;
    if ( !CalculateSkew(fSum,fCount,vSum,values) )
        return;

    double fMean = fSum / fCount;

    for (size_t i = 0; i < values.size(); i++)
        vSum += (values[i] - fMean) * (values[i] - fMean);

    double fStdDev = sqrt(vSum / (fCount - 1.0));
    double dx = 0.0;
    double xcube = 0.0;

    if (fStdDev == 0)
    {
        PushIllegalArgument();
        return;
    }

    for (size_t i = 0; i < values.size(); i++)
    {
        dx = (values[i] - fMean) / fStdDev;
        xcube = xcube + (dx * dx * dx);
    }

    PushDouble(((xcube * fCount) / (fCount - 1.0)) / (fCount - 2.0));
}

double ScInterpreter::GetMedian( vector<double> & rArray )
{
    size_t nSize = rArray.size();
    if (rArray.empty() || nSize == 0 || nGlobalError)
    {
        SetError( errNoValue);
        return 0.0;
    }

    // Upper median.
    size_t nMid = nSize / 2;
    vector<double>::iterator iMid = rArray.begin() + nMid;
    ::std::nth_element( rArray.begin(), iMid, rArray.end());
    if (nSize & 1)
        return *iMid;   // Lower and upper median are equal.
    else
    {
        double fUp = *iMid;
        // Lower median.
        iMid = rArray.begin() + nMid - 1;
        ::std::nth_element( rArray.begin(), iMid, rArray.end());
        return (fUp + *iMid) / 2;
    }
}

void ScInterpreter::ScMedian()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScMedian" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCountMin( nParamCount, 1 )  )
        return;
    vector<double> aArray;
    GetNumberSequenceArray( nParamCount, aArray);
    PushDouble( GetMedian( aArray));
}

double ScInterpreter::GetPercentile( vector<double> & rArray, double fPercentile )
{
    size_t nSize = rArray.size();
    if (rArray.empty() || nSize == 0 || nGlobalError)
    {
        SetError( errNoValue);
        return 0.0;
    }

    if (nSize == 1)
        return rArray[0];
    else
    {
        size_t nIndex = (size_t)::rtl::math::approxFloor( fPercentile * (nSize-1));
        double fDiff = fPercentile * (nSize-1) - ::rtl::math::approxFloor( fPercentile * (nSize-1));
        DBG_ASSERT(nIndex < nSize, "GetPercentile: wrong index(1)");
        vector<double>::iterator iter = rArray.begin() + nIndex;
        ::std::nth_element( rArray.begin(), iter, rArray.end());
        if (fDiff == 0.0)
            return *iter;
        else
        {
            DBG_ASSERT(nIndex < nSize-1, "GetPercentile: wrong index(2)");
            double fVal = *iter;
            iter = rArray.begin() + nIndex+1;
            ::std::nth_element( rArray.begin(), iter, rArray.end());
            return fVal + fDiff * (*iter - fVal);
        }
    }
}

void ScInterpreter::ScPercentile()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScPercentile" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    double alpha = GetDouble();
    if (alpha < 0.0 || alpha > 1.0)
    {
        PushIllegalArgument();
        return;
    }
    vector<double> aArray;
    GetNumberSequenceArray( 1, aArray);
    PushDouble( GetPercentile( aArray, alpha));
}

void ScInterpreter::ScQuartile()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScQuartile" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    double fFlag = ::rtl::math::approxFloor(GetDouble());
    if (fFlag < 0.0 || fFlag > 4.0)
    {
        PushIllegalArgument();
        return;
    }
    vector<double> aArray;
    GetNumberSequenceArray( 1, aArray);
    PushDouble( fFlag == 2.0 ? GetMedian( aArray) : GetPercentile( aArray, 0.25 * fFlag));
}

void ScInterpreter::ScModalValue()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScModalValue" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCountMin( nParamCount, 1 ) )
        return;
    vector<double> aSortArray;
    GetSortArray(nParamCount, aSortArray);
    SCSIZE nSize = aSortArray.size();
    if (aSortArray.empty() || nSize == 0 || nGlobalError)
        PushNoValue();
    else
    {
        SCSIZE nMaxIndex = 0, nMax = 1, nCount = 1;
        double nOldVal = aSortArray[0];
        SCSIZE i;

        for ( i = 1; i < nSize; i++)
        {
            if (aSortArray[i] == nOldVal)
                nCount++;
            else
            {
                nOldVal = aSortArray[i];
                if (nCount > nMax)
                {
                    nMax = nCount;
                    nMaxIndex = i-1;
                }
                nCount = 1;
            }
        }
        if (nCount > nMax)
        {
            nMax = nCount;
            nMaxIndex = i-1;
        }
        if (nMax == 1 && nCount == 1)
            PushNoValue();
        else if (nMax == 1)
            PushDouble(nOldVal);
        else
            PushDouble(aSortArray[nMaxIndex]);
    }
}

void ScInterpreter::CalculateSmallLarge(sal_Bool bSmall)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::CalculateSmallLarge" );
    if ( !MustHaveParamCount( GetByte(), 2 )  )
        return;
    double f = ::rtl::math::approxFloor(GetDouble());
    if (f < 1.0)
    {
        PushIllegalArgument();
        return;
    }
    SCSIZE k = static_cast<SCSIZE>(f);
    vector<double> aSortArray;
    /* TODO: using nth_element() is best for one single value, but LARGE/SMALL
     * actually are defined to return an array of values if an array of
     * positions was passed, in which case, depending on the number of values,
     * we may or will need a real sorted array again, see #i32345. */
    //GetSortArray(1, aSortArray);
    GetNumberSequenceArray(1, aSortArray);
    SCSIZE nSize = aSortArray.size();
    if (aSortArray.empty() || nSize == 0 || nGlobalError || nSize < k)
        PushNoValue();
    else
    {
        // TODO: the sorted case for array: PushDouble( aSortArray[ bSmall ? k-1 : nSize-k ] );
        vector<double>::iterator iPos = aSortArray.begin() + (bSmall ? k-1 : nSize-k);
        ::std::nth_element( aSortArray.begin(), iPos, aSortArray.end());
        PushDouble( *iPos);
    }
}

void ScInterpreter::ScLarge()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScLarge" );
    CalculateSmallLarge(sal_False);
}

void ScInterpreter::ScSmall()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScSmall" );
    CalculateSmallLarge(sal_True);
}

void ScInterpreter::ScPercentrank()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScPercentrank" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 2 ) )
        return;
#if 0
/*                          wird nicht unterstuetzt
    double fPrec;
    if (nParamCount == 3)
    {
        fPrec = ::rtl::math::approxFloor(GetDouble());
        if (fPrec < 1.0)
        {
            PushIllegalArgument();
            return;
        }
    }
    else
        fPrec = 3.0;
*/
#endif
    double fNum = GetDouble();
    vector<double> aSortArray;
    GetSortArray(1, aSortArray);
    SCSIZE nSize = aSortArray.size();
    if (aSortArray.empty() || nSize == 0 || nGlobalError)
        PushNoValue();
    else
    {
        if (fNum < aSortArray[0] || fNum > aSortArray[nSize-1])
            PushNoValue();
        else if ( nSize == 1 )
            PushDouble(1.0);            // fNum == pSortArray[0], see test above
        else
        {
            double fRes;
            SCSIZE nOldCount = 0;
            double fOldVal = aSortArray[0];
            SCSIZE i;
            for (i = 1; i < nSize && aSortArray[i] < fNum; i++)
            {
                if (aSortArray[i] != fOldVal)
                {
                    nOldCount = i;
                    fOldVal = aSortArray[i];
                }
            }
            if (aSortArray[i] != fOldVal)
                nOldCount = i;
            if (fNum == aSortArray[i])
                fRes = (double)nOldCount/(double)(nSize-1);
            else
            {
                //  #75312# nOldCount is the count of smaller entries
                //  fNum is between pSortArray[nOldCount-1] and pSortArray[nOldCount]
                //  use linear interpolation to find a position between the entries

                if ( nOldCount == 0 )
                {
                    DBG_ERROR("should not happen");
                    fRes = 0.0;
                }
                else
                {
                    double fFract = ( fNum - aSortArray[nOldCount-1] ) /
                        ( aSortArray[nOldCount] - aSortArray[nOldCount-1] );
                    fRes = ( (double)(nOldCount-1)+fFract )/(double)(nSize-1);
                }
            }
            PushDouble(fRes);
        }
    }
}

void ScInterpreter::ScTrimMean()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScTrimMean" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    double alpha = GetDouble();
    if (alpha < 0.0 || alpha >= 1.0)
    {
        PushIllegalArgument();
        return;
    }
    vector<double> aSortArray;
    GetSortArray(1, aSortArray);
    SCSIZE nSize = aSortArray.size();
    if (aSortArray.empty() || nSize == 0 || nGlobalError)
        PushNoValue();
    else
    {
        sal_uLong nIndex = (sal_uLong) ::rtl::math::approxFloor(alpha*(double)nSize);
        if (nIndex % 2 != 0)
            nIndex--;
        nIndex /= 2;
        DBG_ASSERT(nIndex < nSize, "ScTrimMean: falscher Index");
        double fSum = 0.0;
        for (SCSIZE i = nIndex; i < nSize-nIndex; i++)
            fSum += aSortArray[i];
        PushDouble(fSum/(double)(nSize-2*nIndex));
    }
}

void ScInterpreter::GetNumberSequenceArray( sal_uInt8 nParamCount, vector<double>& rArray )
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetSortArray" );
    ScAddress aAdr;
    ScRange aRange;
    short nParam = nParamCount;
    size_t nRefInList = 0;
    while (nParam-- > 0)
    {
        switch (GetStackType())
        {
            case formula::svDouble :
                rArray.push_back( PopDouble());
            break;
            case svSingleRef :
            {
                PopSingleRef( aAdr );
                ScBaseCell* pCell = GetCell( aAdr );
                if (HasCellValueData(pCell))
                    rArray.push_back( GetCellValue( aAdr, pCell));
            }
            break;
            case formula::svDoubleRef :
            case svRefList :
            {
                PopDoubleRef( aRange, nParam, nRefInList);
                if (nGlobalError)
                    break;

                aRange.Justify();
                SCSIZE nCellCount = aRange.aEnd.Col() - aRange.aStart.Col() + 1;
                nCellCount *= aRange.aEnd.Row() - aRange.aStart.Row() + 1;
                rArray.reserve( rArray.size() + nCellCount);

                sal_uInt16 nErr = 0;
                double fCellVal;
                ScValueIterator aValIter(pDok, aRange);
                if (aValIter.GetFirst( fCellVal, nErr))
                {
                    rArray.push_back( fCellVal);
                    SetError(nErr);
                    while ((nErr == 0) && aValIter.GetNext( fCellVal, nErr))
                        rArray.push_back( fCellVal);
                    SetError(nErr);
                }
            }
            break;
            case svMatrix :
            {
                ScMatrixRef pMat = PopMatrix();
                if (!pMat)
                    break;

                SCSIZE nCount = pMat->GetElementCount();
                rArray.reserve( rArray.size() + nCount);
                if (pMat->IsNumeric())
                {
                    for (SCSIZE i = 0; i < nCount; ++i)
                        rArray.push_back( pMat->GetDouble(i));
                }
                else
                {
                    for (SCSIZE i = 0; i < nCount; ++i)
                        if (!pMat->IsString(i))
                            rArray.push_back( pMat->GetDouble(i));
                }
            }
            break;
            default :
                PopError();
                SetError( errIllegalParameter);
            break;
        }
        if (nGlobalError)
            break;  // while
    }
    // nParam > 0 in case of error, clean stack environment and obtain earlier
    // error if there was one.
    while (nParam-- > 0)
        PopError();
}

void ScInterpreter::GetSortArray( sal_uInt8 nParamCount, vector<double>& rSortArray, vector<long>* pIndexOrder )
{
    GetNumberSequenceArray( nParamCount, rSortArray);

    if (rSortArray.size() > MAX_ANZ_DOUBLE_FOR_SORT)
        SetError( errStackOverflow);
    else if (rSortArray.empty())
        SetError( errNoValue);

    if (nGlobalError == 0)
        QuickSort( rSortArray, pIndexOrder);
}

static void lcl_QuickSort( long nLo, long nHi, vector<double>& rSortArray, vector<long>* pIndexOrder )
{
    // If pIndexOrder is not NULL, we assume rSortArray.size() == pIndexOrder->size().

    using ::std::swap;

    if (nHi - nLo == 1)
    {
        if (rSortArray[nLo] > rSortArray[nHi])
        {
            swap(rSortArray[nLo],  rSortArray[nHi]);
            if (pIndexOrder)
                swap(pIndexOrder->at(nLo), pIndexOrder->at(nHi));
        }
        return;
    }

    long ni = nLo;
    long nj = nHi;
    do
    {
        double fLo = rSortArray[nLo];
        while (ni <= nHi && rSortArray[ni] < fLo) ni++;
        while (nj >= nLo && fLo < rSortArray[nj]) nj--;
        if (ni <= nj)
        {
            if (ni != nj)
            {
                swap(rSortArray[ni],  rSortArray[nj]);
                if (pIndexOrder)
                    swap(pIndexOrder->at(ni), pIndexOrder->at(nj));
            }

            ++ni;
            --nj;
        }
    }
    while (ni < nj);

    if ((nj - nLo) < (nHi - ni))
    {
        if (nLo < nj) lcl_QuickSort(nLo, nj, rSortArray, pIndexOrder);
        if (ni < nHi) lcl_QuickSort(ni, nHi, rSortArray, pIndexOrder);
    }
    else
    {
        if (ni < nHi) lcl_QuickSort(ni, nHi, rSortArray, pIndexOrder);
        if (nLo < nj) lcl_QuickSort(nLo, nj, rSortArray, pIndexOrder);
    }
}

void ScInterpreter::QuickSort( vector<double>& rSortArray, vector<long>* pIndexOrder )
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::QuickSort" );
    long n = static_cast<long>(rSortArray.size());

    if (pIndexOrder)
    {
        pIndexOrder->clear();
        pIndexOrder->reserve(n);
        for (long i = 0; i < n; ++i)
            pIndexOrder->push_back(i);
    }

    if (n < 2)
        return;

    size_t nValCount = rSortArray.size();
    for (size_t i = 0; (i + 4) <= nValCount-1; i += 4)
    {
        size_t nInd = rand() % (int) (nValCount-1);
        ::std::swap( rSortArray[i], rSortArray[nInd]);
        if (pIndexOrder)
            ::std::swap( pIndexOrder->at(i), pIndexOrder->at(nInd));
    }

    lcl_QuickSort(0, n-1, rSortArray, pIndexOrder);
}

void ScInterpreter::ScRank()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScRank" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 2, 3 ) )
        return;
    sal_Bool bDescending;
    if (nParamCount == 3)
        bDescending = GetBool();
    else
        bDescending = sal_False;
    double fCount = 1.0;
    sal_Bool bValid = sal_False;
    switch (GetStackType())
    {
        case formula::svDouble    :
        {
            double x = GetDouble();
            double fVal = GetDouble();
            if (x == fVal)
                bValid = sal_True;
            break;
        }
        case svSingleRef :
        {
            ScAddress aAdr;
            PopSingleRef( aAdr );
            double fVal = GetDouble();
            ScBaseCell* pCell = GetCell( aAdr );
            if (HasCellValueData(pCell))
            {
                double x = GetCellValue( aAdr, pCell );
                if (x == fVal)
                    bValid = sal_True;
            }
            break;
        }
        case formula::svDoubleRef :
        case svRefList :
        {
            ScRange aRange;
            short nParam = 1;
            size_t nRefInList = 0;
            while (nParam-- > 0)
            {
                sal_uInt16 nErr = 0;
                // Preserve stack until all RefList elements are done!
                sal_uInt16 nSaveSP = sp;
                PopDoubleRef( aRange, nParam, nRefInList);
                if (nParam)
                    --sp;   // simulate pop
                double fVal = GetDouble();
                if (nParam)
                    sp = nSaveSP;
                double nCellVal;
                ScValueIterator aValIter(pDok, aRange, glSubTotal);
                if (aValIter.GetFirst(nCellVal, nErr))
                {
                    if (nCellVal == fVal)
                        bValid = sal_True;
                    else if ((!bDescending && nCellVal > fVal) ||
                            (bDescending && nCellVal < fVal) )
                        fCount++;
                    SetError(nErr);
                    while ((nErr == 0) && aValIter.GetNext(nCellVal, nErr))
                    {
                        if (nCellVal == fVal)
                            bValid = sal_True;
                        else if ((!bDescending && nCellVal > fVal) ||
                                (bDescending && nCellVal < fVal) )
                            fCount++;
                    }
                }
                SetError(nErr);
            }
        }
        break;
        case svMatrix :
        {
            ScMatrixRef pMat = PopMatrix();
            double fVal = GetDouble();
            if (pMat)
            {
                SCSIZE nCount = pMat->GetElementCount();
                if (pMat->IsNumeric())
                {
                    for (SCSIZE i = 0; i < nCount; i++)
                    {
                        double x = pMat->GetDouble(i);
                        if (x == fVal)
                            bValid = sal_True;
                        else if ((!bDescending && x > fVal) ||
                                    (bDescending && x < fVal) )
                            fCount++;
                    }
                }
                else
                {
                    for (SCSIZE i = 0; i < nCount; i++)
                        if (!pMat->IsString(i))
                        {
                            double x = pMat->GetDouble(i);
                            if (x == fVal)
                                bValid = sal_True;
                            else if ((!bDescending && x > fVal) ||
                                        (bDescending && x < fVal) )
                                fCount++;
                        }
                }
            }
        }
        break;
        default : SetError(errIllegalParameter); break;
    }
    if (bValid)
        PushDouble(fCount);
    else
        PushNoValue();
}

void ScInterpreter::ScAveDev()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScAveDev" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCountMin( nParamCount, 1 ) )
        return;
    sal_uInt16 SaveSP = sp;
    double nMiddle = 0.0;
    double rVal = 0.0;
    double rValCount = 0.0;
    ScAddress aAdr;
    ScRange aRange;
    short nParam = nParamCount;
    size_t nRefInList = 0;
    while (nParam-- > 0)
    {
        switch (GetStackType())
        {
            case formula::svDouble :
                rVal += GetDouble();
                rValCount++;
                break;
            case svSingleRef :
            {
                PopSingleRef( aAdr );
                ScBaseCell* pCell = GetCell( aAdr );
                if (HasCellValueData(pCell))
                {
                    rVal += GetCellValue( aAdr, pCell );
                    rValCount++;
                }
            }
            break;
            case formula::svDoubleRef :
            case svRefList :
            {
                sal_uInt16 nErr = 0;
                double nCellVal;
                PopDoubleRef( aRange, nParam, nRefInList);
                ScValueIterator aValIter(pDok, aRange);
                if (aValIter.GetFirst(nCellVal, nErr))
                {
                    rVal += nCellVal;
                    rValCount++;
                    SetError(nErr);
                    while ((nErr == 0) && aValIter.GetNext(nCellVal, nErr))
                    {
                        rVal += nCellVal;
                        rValCount++;
                    }
                    SetError(nErr);
                }
            }
            break;
            case svMatrix :
            {
                ScMatrixRef pMat = PopMatrix();
                if (pMat)
                {
                    SCSIZE nCount = pMat->GetElementCount();
                    if (pMat->IsNumeric())
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                        {
                            rVal += pMat->GetDouble(nElem);
                            rValCount++;
                        }
                    }
                    else
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                            if (!pMat->IsString(nElem))
                            {
                                rVal += pMat->GetDouble(nElem);
                                rValCount++;
                            }
                    }
                }
            }
            break;
            default :
                SetError(errIllegalParameter);
            break;
        }
    }
    if (nGlobalError)
    {
        PushError( nGlobalError);
        return;
    }
    nMiddle = rVal / rValCount;
    sp = SaveSP;
    rVal = 0.0;
    nParam = nParamCount;
    nRefInList = 0;
    while (nParam-- > 0)
    {
        switch (GetStackType())
        {
            case formula::svDouble :
                rVal += fabs(GetDouble() - nMiddle);
                break;
            case svSingleRef :
            {
                PopSingleRef( aAdr );
                ScBaseCell* pCell = GetCell( aAdr );
                if (HasCellValueData(pCell))
                    rVal += fabs(GetCellValue( aAdr, pCell ) - nMiddle);
            }
            break;
            case formula::svDoubleRef :
            case svRefList :
            {
                sal_uInt16 nErr = 0;
                double nCellVal;
                PopDoubleRef( aRange, nParam, nRefInList);
                ScValueIterator aValIter(pDok, aRange);
                if (aValIter.GetFirst(nCellVal, nErr))
                {
                    rVal += (fabs(nCellVal - nMiddle));
                    while (aValIter.GetNext(nCellVal, nErr))
                         rVal += fabs(nCellVal - nMiddle);
                }
            }
            break;
            case svMatrix :
            {
                ScMatrixRef pMat = PopMatrix();
                if (pMat)
                {
                    SCSIZE nCount = pMat->GetElementCount();
                    if (pMat->IsNumeric())
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                        {
                            rVal += fabs(pMat->GetDouble(nElem) - nMiddle);
                        }
                    }
                    else
                    {
                        for (SCSIZE nElem = 0; nElem < nCount; nElem++)
                        {
                            if (!pMat->IsString(nElem))
                                rVal += fabs(pMat->GetDouble(nElem) - nMiddle);
                        }
                    }
                }
            }
            break;
            default : SetError(errIllegalParameter); break;
        }
    }
    PushDouble(rVal / rValCount);
}

void ScInterpreter::ScDevSq()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScDevSq" );
    double nVal;
    double nValCount;
    GetStVarParams(nVal, nValCount);
    PushDouble(nVal);
}

void ScInterpreter::ScProbability()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScProbability" );
    sal_uInt8 nParamCount = GetByte();
    if ( !MustHaveParamCount( nParamCount, 3, 4 ) )
        return;
    double fUp, fLo;
    fUp = GetDouble();
    if (nParamCount == 4)
        fLo = GetDouble();
    else
        fLo = fUp;
    if (fLo > fUp)
    {
        double fTemp = fLo;
        fLo = fUp;
        fUp = fTemp;
    }
    ScMatrixRef pMatP = GetMatrix();
    ScMatrixRef pMatW = GetMatrix();
    if (!pMatP || !pMatW)
        PushIllegalParameter();
    else
    {
        SCSIZE nC1, nC2;
        SCSIZE nR1, nR2;
        pMatP->GetDimensions(nC1, nR1);
        pMatW->GetDimensions(nC2, nR2);
        if (nC1 != nC2 || nR1 != nR2 || nC1 == 0 || nR1 == 0 ||
            nC2 == 0 || nR2 == 0)
            PushNA();
        else
        {
            double fSum = 0.0;
            double fRes = 0.0;
            sal_Bool bStop = sal_False;
            double fP, fW;
            SCSIZE nCount1 = nC1 * nR1;
            for ( SCSIZE i = 0; i < nCount1 && !bStop; i++ )
            {
                if (pMatP->IsValue(i) && pMatW->IsValue(i))
                {
                    fP = pMatP->GetDouble(i);
                    fW = pMatW->GetDouble(i);
                    if (fP < 0.0 || fP > 1.0)
                        bStop = sal_True;
                    else
                    {
                        fSum += fP;
                        if (fW >= fLo && fW <= fUp)
                            fRes += fP;
                    }
                }
                else
                    SetError( errIllegalArgument);
            }
            if (bStop || fabs(fSum -1.0) > 1.0E-7)
                PushNoValue();
            else
                PushDouble(fRes);
        }
    }
}

void ScInterpreter::ScCorrel()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScCorrel" );
    // This is identical to ScPearson()
    ScPearson();
}

void ScInterpreter::ScCovar()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScCovar" );
    CalculatePearsonCovar(sal_False,sal_False);
}

void ScInterpreter::ScPearson()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScPearson" );
    CalculatePearsonCovar(sal_True,sal_False);
}
void ScInterpreter::CalculatePearsonCovar(sal_Bool _bPearson,sal_Bool _bStexy)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::CalculatePearsonCovar" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    ScMatrixRef pMat1 = GetMatrix();
    ScMatrixRef pMat2 = GetMatrix();
    if (!pMat1 || !pMat2)
    {
        PushIllegalParameter();
        return;
    }
    SCSIZE nC1, nC2;
    SCSIZE nR1, nR2;
    pMat1->GetDimensions(nC1, nR1);
    pMat2->GetDimensions(nC2, nR2);
    if (nR1 != nR2 || nC1 != nC2)
    {
        PushIllegalArgument();
        return;
    }
    /* #i78250#
     * (sum((X-MeanX)(Y-MeanY)))/N equals (SumXY)/N-MeanX*MeanY mathematically,
     * but the latter produces wrong results if the absolute values are high,
     * for example above 10^8
     */
    double fCount           = 0.0;
    double fSumX            = 0.0;
    double fSumY            = 0.0;
    double fSumDeltaXDeltaY = 0.0; // sum of (ValX-MeanX)*(ValY-MeanY)
    double fSumSqrDeltaX    = 0.0; // sum of (ValX-MeanX)^2
    double fSumSqrDeltaY    = 0.0; // sum of (ValY-MeanY)^2
    for (SCSIZE i = 0; i < nC1; i++)
    {
        for (SCSIZE j = 0; j < nR1; j++)
        {
            if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
            {
                double fValX = pMat1->GetDouble(i,j);
                double fValY = pMat2->GetDouble(i,j);
                fSumX += fValX;
                fSumY += fValY;
                fCount++;
            }
        }
    }
    if (fCount < (_bStexy ? 3.0 : 1.0)) // fCount==1 is handled by checking denominator later on
        PushNoValue();
    else
    {
        const double fMeanX = fSumX / fCount;
        const double fMeanY = fSumY / fCount;
        for (SCSIZE i = 0; i < nC1; i++)
        {
            for (SCSIZE j = 0; j < nR1; j++)
            {
                if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
                {
                    const double fValX = pMat1->GetDouble(i,j);
                    const double fValY = pMat2->GetDouble(i,j);
                    fSumDeltaXDeltaY += (fValX - fMeanX) * (fValY - fMeanY);
                    if ( _bPearson )
                    {
                        fSumSqrDeltaX    += (fValX - fMeanX) * (fValX - fMeanX);
                        fSumSqrDeltaY    += (fValY - fMeanY) * (fValY - fMeanY);
                    }
                }
            }
        } // for (SCSIZE i = 0; i < nC1; i++)
        if ( _bPearson )
        {
            if (fSumSqrDeltaX == 0.0 || ( !_bStexy && fSumSqrDeltaY == 0.0) )
                PushError( errDivisionByZero);
            else if ( _bStexy )
                PushDouble( sqrt( (fSumSqrDeltaY - fSumDeltaXDeltaY *
                            fSumDeltaXDeltaY / fSumSqrDeltaX) / (fCount-2)));
            else
                PushDouble( fSumDeltaXDeltaY / sqrt( fSumSqrDeltaX * fSumSqrDeltaY));
        } // if ( _bPearson )
        else
        {
            PushDouble( fSumDeltaXDeltaY / fCount);
        }
    }
}

void ScInterpreter::ScRSQ()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScRSQ" );
    // Same as ScPearson()*ScPearson()
    ScPearson();
    if (!nGlobalError)
    {
        switch (GetStackType())
        {
            case formula::svDouble:
                {
                    double fVal = PopDouble();
                    PushDouble( fVal * fVal);
                }
                break;
            default:
                PopError();
                PushNoValue();
        }
    }
}

void ScInterpreter::ScSTEXY()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScSTEXY" );
    CalculatePearsonCovar(sal_True,sal_True);
}
void ScInterpreter::CalculateSlopeIntercept(sal_Bool bSlope)
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::CalculateSlopeIntercept" );
    if ( !MustHaveParamCount( GetByte(), 2 ) )
        return;
    ScMatrixRef pMat1 = GetMatrix();
    ScMatrixRef pMat2 = GetMatrix();
    if (!pMat1 || !pMat2)
    {
        PushIllegalParameter();
        return;
    }
    SCSIZE nC1, nC2;
    SCSIZE nR1, nR2;
    pMat1->GetDimensions(nC1, nR1);
    pMat2->GetDimensions(nC2, nR2);
    if (nR1 != nR2 || nC1 != nC2)
    {
        PushIllegalArgument();
        return;
    }
    // #i78250# numerical stability improved
    double fCount           = 0.0;
    double fSumX            = 0.0;
    double fSumY            = 0.0;
    double fSumDeltaXDeltaY = 0.0; // sum of (ValX-MeanX)*(ValY-MeanY)
    double fSumSqrDeltaX    = 0.0; // sum of (ValX-MeanX)^2
    for (SCSIZE i = 0; i < nC1; i++)
    {
        for (SCSIZE j = 0; j < nR1; j++)
        {
            if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
            {
                double fValX = pMat1->GetDouble(i,j);
                double fValY = pMat2->GetDouble(i,j);
                fSumX += fValX;
                fSumY += fValY;
                fCount++;
            }
        }
    }
    if (fCount < 1.0)
        PushNoValue();
    else
    {
        double fMeanX = fSumX / fCount;
        double fMeanY = fSumY / fCount;
        for (SCSIZE i = 0; i < nC1; i++)
        {
            for (SCSIZE j = 0; j < nR1; j++)
            {
                if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
                {
                    double fValX = pMat1->GetDouble(i,j);
                    double fValY = pMat2->GetDouble(i,j);
                    fSumDeltaXDeltaY += (fValX - fMeanX) * (fValY - fMeanY);
                    fSumSqrDeltaX    += (fValX - fMeanX) * (fValX - fMeanX);
                }
            }
        }
        if (fSumSqrDeltaX == 0.0)
            PushError( errDivisionByZero);
        else
        {
            if ( bSlope )
                PushDouble( fSumDeltaXDeltaY / fSumSqrDeltaX);
            else
                PushDouble( fMeanY - fSumDeltaXDeltaY / fSumSqrDeltaX * fMeanX);
        }
    }
}

void ScInterpreter::ScSlope()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScSlope" );
    CalculateSlopeIntercept(sal_True);
}

void ScInterpreter::ScIntercept()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScIntercept" );
    CalculateSlopeIntercept(sal_False);
}

void ScInterpreter::ScForecast()
{
    RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::ScForecast" );
    if ( !MustHaveParamCount( GetByte(), 3 ) )
        return;
    ScMatrixRef pMat1 = GetMatrix();
    ScMatrixRef pMat2 = GetMatrix();
    if (!pMat1 || !pMat2)
    {
        PushIllegalParameter();
        return;
    }
    SCSIZE nC1, nC2;
    SCSIZE nR1, nR2;
    pMat1->GetDimensions(nC1, nR1);
    pMat2->GetDimensions(nC2, nR2);
    if (nR1 != nR2 || nC1 != nC2)
    {
        PushIllegalArgument();
        return;
    }
    double fVal = GetDouble();
    // #i78250# numerical stability improved
    double fCount           = 0.0;
    double fSumX            = 0.0;
    double fSumY            = 0.0;
    double fSumDeltaXDeltaY = 0.0; // sum of (ValX-MeanX)*(ValY-MeanY)
    double fSumSqrDeltaX    = 0.0; // sum of (ValX-MeanX)^2
    for (SCSIZE i = 0; i < nC1; i++)
    {
        for (SCSIZE j = 0; j < nR1; j++)
        {
            if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
            {
                double fValX = pMat1->GetDouble(i,j);
                double fValY = pMat2->GetDouble(i,j);
                fSumX += fValX;
                fSumY += fValY;
                fCount++;
            }
        }
    }
    if (fCount < 1.0)
        PushNoValue();
    else
    {
        double fMeanX = fSumX / fCount;
        double fMeanY = fSumY / fCount;
        for (SCSIZE i = 0; i < nC1; i++)
        {
            for (SCSIZE j = 0; j < nR1; j++)
            {
                if (!pMat1->IsString(i,j) && !pMat2->IsString(i,j))
                {
                    double fValX = pMat1->GetDouble(i,j);
                    double fValY = pMat2->GetDouble(i,j);
                    fSumDeltaXDeltaY += (fValX - fMeanX) * (fValY - fMeanY);
                    fSumSqrDeltaX    += (fValX - fMeanX) * (fValX - fMeanX);
                }
            }
        }
        if (fSumSqrDeltaX == 0.0)
            PushError( errDivisionByZero);
        else
            PushDouble( fMeanY + fSumDeltaXDeltaY / fSumSqrDeltaX * (fVal - fMeanX));
    }
}