wmlmath.inl

Wild Math Library数值计算库

// Magic Software, Inc.
// http://www.magic-software.com
// http://www.wild-magic.com
// Copyright (c) 2004.  All Rights Reserved
//
// The Wild Magic Library (WML) source code is supplied under the terms of
// the license agreement http://www.magic-software.com/License/WildMagic.pdf
// and may not be copied or disclosed except in accordance with the terms of
// that agreement.

//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::ACos (Real fValue)
{
    if ( -(Real)1.0 < fValue )
    {
        if ( fValue < (Real)1.0 )
            return (Real)acos((double)fValue);
        else
            return (Real)0.0;
    }
    else
    {
        return PI;
    }
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::ASin (Real fValue)
{
    if ( -(Real)1.0 < fValue )
    {
        if ( fValue < (Real)1.0 )
            return (Real)asin((double)fValue);
        else
            return HALF_PI;
    }
    else
    {
        return -HALF_PI;
    }
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::ATan (Real fValue)
{
    return (Real)atan((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::ATan2 (Real fY, Real fX)
{
    return (Real)atan2((double)fY,(double)fX);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Ceil (Real fValue)
{
    return (Real)ceil((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Cos (Real fValue)
{
    return (Real)cos((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Exp (Real fValue)
{
    return (Real)exp((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FAbs (Real fValue)
{
    return (Real)fabs((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Floor (Real fValue)
{
    return (Real)floor((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FMod (Real fX, Real fY)
{
    return (Real)fmod((double)fX,(double)fY);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::InvSqrt (Real fValue)
{
    return (Real)(1.0/sqrt((double)fValue));
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Log (Real fValue)
{
    return (Real)log((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Pow (Real fBase, Real fExponent)
{
    return (Real)pow((double)fBase,(double)fExponent);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Sin (Real fValue)
{
    return (Real)sin((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Sqr (Real fValue)
{
    return fValue*fValue;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Sqrt (Real fValue)
{
    return (Real)sqrt((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Tan (Real fValue)
{
    return (Real)tan((double)fValue);
}
//----------------------------------------------------------------------------
template <class Real>
int Math<Real>::Sign (int iValue)
{
    if ( iValue > 0 )
        return 1;

    if ( iValue < 0 )
        return -1;

    return 0;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::Sign (Real fValue)
{
    if ( fValue > (Real)0.0 )
        return (Real)1.0;

    if ( fValue < (Real)0.0 )
        return -(Real)1.0;

    return (Real)0.0;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::UnitRandom (unsigned int uiSeed )
{
    if ( uiSeed > 0 )
        srand(uiSeed);

    double dRatio = ((double)rand())/((double)(RAND_MAX));
    return (Real)dRatio;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::SymmetricRandom (unsigned int uiSeed)
{
    if ( uiSeed > 0.0 )
        srand(uiSeed);

    double dRatio = ((double)rand())/((double)(RAND_MAX));
    return (Real)(2.0*dRatio - 1.0);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::IntervalRandom (Real fMin, Real fMax, unsigned int uiSeed)
{
    if ( uiSeed > 0 )
        srand(uiSeed);

    double dRatio = ((double)rand())/((double)(RAND_MAX));
    return fMin+(fMax-fMin)*((Real)dRatio);
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastSin0 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = (Real)7.61e-03;
    fResult *= fASqr;
    fResult -= (Real)1.6605e-01;
    fResult *= fASqr;
    fResult += (Real)1.0;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastSin1 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = -(Real)2.39e-08;
    fResult *= fASqr;
    fResult += (Real)2.7526e-06;
    fResult *= fASqr;
    fResult -= (Real)1.98409e-04;
    fResult *= fASqr;
    fResult += (Real)8.3333315e-03;
    fResult *= fASqr;
    fResult -= (Real)1.666666664e-01;
    fResult *= fASqr;
    fResult += (Real)1.0;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastCos0 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = (Real)3.705e-02;
    fResult *= fASqr;
    fResult -= (Real)4.967e-01;
    fResult *= fASqr;
    fResult += (Real)1.0;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastCos1 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = -(Real)2.605e-07;
    fResult *= fASqr;
    fResult += (Real)2.47609e-05;
    fResult *= fASqr;
    fResult -= (Real)1.3888397e-03;
    fResult *= fASqr;
    fResult += (Real)4.16666418e-02;
    fResult *= fASqr;
    fResult -= (Real)4.999999963e-01;
    fResult *= fASqr;
    fResult += (Real)1.0;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastTan0 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = (Real)2.033e-01;
    fResult *= fASqr;
    fResult += (Real)3.1755e-01;
    fResult *= fASqr;
    fResult += (Real)1.0;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastTan1 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = (Real)9.5168091e-03;
    fResult *= fASqr;
    fResult += (Real)2.900525e-03;
    fResult *= fASqr;
    fResult += (Real)2.45650893e-02;
    fResult *= fASqr;
    fResult += (Real)5.33740603e-02;
    fResult *= fASqr;
    fResult += (Real)1.333923995e-01;
    fResult *= fASqr;
    fResult += (Real)3.333314036e-01;
    fResult *= fASqr;
    fResult += (Real)1.0;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastInvSin (Real fValue)
{
    Real fRoot = Math<Real>::Sqrt(((Real)1.0)-fValue);
    Real fResult = -(Real)0.0187293;
    fResult *= fValue;
    fResult += (Real)0.0742610;
    fResult *= fValue;
    fResult -= (Real)0.2121144;
    fResult *= fValue;
    fResult += (Real)1.5707288;
    fResult = HALF_PI - fRoot*fResult;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastInvCos (Real fValue)
{
    Real fRoot = Math<Real>::Sqrt(((Real)1.0)-fValue);
    Real fResult = -(Real)0.0187293;
    fResult *= fValue;
    fResult += (Real)0.0742610;
    fResult *= fValue;
    fResult -= (Real)0.2121144;
    fResult *= fValue;
    fResult += (Real)1.5707288;
    fResult *= fRoot;
    return fResult;
}
//----------------------------------------------------------------------------
template <class Real>
Real Math<Real>::FastInvTan0 (Real fValue)
{
    Real fVSqr = fValue*fValue;
    Real fResult = (Real)0.0208351;
    fResult *= fVSqr;
    fResult -= (Real)0.085133;
    fResult *= fVSqr;
    fResult += (Real)0.180141;
    fResult *= fVSqr;
    fResult -= (Real)0.3302995;
    fResult *= fVSqr;