Scalar.h File Reference

This is a user-includable header which includes everything needed to make use of SimMatrix Scalar code. More...

Go to the source code of this file.

Namespaces
	SimTK
	This is the top-level SimTK namespace into which all SimTK names are placed to avoid collision with other symbols.

Typedefs
typedef conjugate< Real >	SimTK::Conjugate

Functions
bool	SimTK::atMostOneBitIsSet (unsigned char v)
bool	SimTK::atMostOneBitIsSet (unsigned short v)
bool	SimTK::atMostOneBitIsSet (unsigned int v)
bool	SimTK::atMostOneBitIsSet (unsigned long v)
bool	SimTK::atMostOneBitIsSet (unsigned long long v)
bool	SimTK::atMostOneBitIsSet (signed char v)
bool	SimTK::atMostOneBitIsSet (char v)
bool	SimTK::atMostOneBitIsSet (short v)
bool	SimTK::atMostOneBitIsSet (int v)
bool	SimTK::atMostOneBitIsSet (long v)
bool	SimTK::atMostOneBitIsSet (long long v)
bool	SimTK::exactlyOneBitIsSet (unsigned char v)
bool	SimTK::exactlyOneBitIsSet (unsigned short v)
bool	SimTK::exactlyOneBitIsSet (unsigned int v)
bool	SimTK::exactlyOneBitIsSet (unsigned long v)
bool	SimTK::exactlyOneBitIsSet (unsigned long long v)
bool	SimTK::exactlyOneBitIsSet (signed char v)
bool	SimTK::exactlyOneBitIsSet (char v)
bool	SimTK::exactlyOneBitIsSet (short v)
bool	SimTK::exactlyOneBitIsSet (int v)
bool	SimTK::exactlyOneBitIsSet (long v)
bool	SimTK::exactlyOneBitIsSet (long long v)
bool	SimTK::signBit (unsigned char u)
bool	SimTK::signBit (unsigned short u)
bool	SimTK::signBit (unsigned int u)
bool	SimTK::signBit (unsigned long u)
bool	SimTK::signBit (unsigned long long u)
bool	SimTK::signBit (signed char i)
bool	SimTK::signBit (short i)
bool	SimTK::signBit (int i)
bool	SimTK::signBit (long long i)
bool	SimTK::signBit (long i)
bool	SimTK::signBit (const float &f)
bool	SimTK::signBit (const double &d)
bool	SimTK::signBit (const negator< float > &nf)
bool	SimTK::signBit (const negator< double > &nd)
unsigned int	SimTK::sign (unsigned char u)
unsigned int	SimTK::sign (unsigned short u)
unsigned int	SimTK::sign (unsigned int u)
unsigned int	SimTK::sign (unsigned long u)
unsigned int	SimTK::sign (unsigned long long u)
int	SimTK::sign (signed char i)
int	SimTK::sign (short i)
int	SimTK::sign (int i)
int	SimTK::sign (long i)
int	SimTK::sign (long long i)
int	SimTK::sign (const float &x)
int	SimTK::sign (const double &x)
int	SimTK::sign (const negator< float > &x)
int	SimTK::sign (const negator< double > &x)
unsigned char	SimTK::square (unsigned char u)
unsigned short	SimTK::square (unsigned short u)
unsigned int	SimTK::square (unsigned int u)
unsigned long	SimTK::square (unsigned long u)
unsigned long long	SimTK::square (unsigned long long u)
char	SimTK::square (char c)
signed char	SimTK::square (signed char i)
short	SimTK::square (short i)
int	SimTK::square (int i)
long	SimTK::square (long i)
long long	SimTK::square (long long i)
float	SimTK::square (const float &x)
double	SimTK::square (const double &x)
float	SimTK::square (const negator< float > &x)
double	SimTK::square (const negator< double > &x)
template<class P >
std::complex< P >	SimTK::square (const std::complex< P > &x)
template<class P >
std::complex< P >	SimTK::square (const conjugate< P > &x)
template<class P >
std::complex< P >	SimTK::square (const negator< std::complex< P > > &x)
template<class P >
std::complex< P >	SimTK::square (const negator< conjugate< P > > &x)
unsigned char	SimTK::cube (unsigned char u)
unsigned short	SimTK::cube (unsigned short u)
unsigned int	SimTK::cube (unsigned int u)
unsigned long	SimTK::cube (unsigned long u)
unsigned long long	SimTK::cube (unsigned long long u)
char	SimTK::cube (char c)
signed char	SimTK::cube (signed char i)
short	SimTK::cube (short i)
int	SimTK::cube (int i)
long	SimTK::cube (long i)
long long	SimTK::cube (long long i)
float	SimTK::cube (const float &x)
double	SimTK::cube (const double &x)
negator< float >	SimTK::cube (const negator< float > &x)
negator< double >	SimTK::cube (const negator< double > &x)
template<class P >
std::complex< P >	SimTK::cube (const std::complex< P > &x)
template<class P >
std::complex< P >	SimTK::cube (const negator< std::complex< P > > &x)
template<class P >
std::complex< P >	SimTK::cube (const conjugate< P > &x)
template<class P >
std::complex< P >	SimTK::cube (const negator< conjugate< P > > &x)
double &	SimTK::clampInPlace (double low, double &v, double high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
float &	SimTK::clampInPlace (float low, float &v, float high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
double &	SimTK::clampInPlace (int low, double &v, int high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
float &	SimTK::clampInPlace (int low, float &v, int high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
double &	SimTK::clampInPlace (int low, double &v, double high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
float &	SimTK::clampInPlace (int low, float &v, float high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
double &	SimTK::clampInPlace (double low, double &v, int high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
float &	SimTK::clampInPlace (float low, float &v, int high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
unsigned char &	SimTK::clampInPlace (unsigned char low, unsigned char &v, unsigned char high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
unsigned short &	SimTK::clampInPlace (unsigned short low, unsigned short &v, unsigned short high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
unsigned int &	SimTK::clampInPlace (unsigned int low, unsigned int &v, unsigned int high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
unsigned long &	SimTK::clampInPlace (unsigned long low, unsigned long &v, unsigned long high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
unsigned long long &	SimTK::clampInPlace (unsigned long long low, unsigned long long &v, unsigned long long high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
char &	SimTK::clampInPlace (char low, char &v, char high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
signed char &	SimTK::clampInPlace (signed char low, signed char &v, signed char high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
short &	SimTK::clampInPlace (short low, short &v, short high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
int &	SimTK::clampInPlace (int low, int &v, int high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
long &	SimTK::clampInPlace (long low, long &v, long high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
long long &	SimTK::clampInPlace (long long low, long long &v, long long high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
negator< float > &	SimTK::clampInPlace (float low, negator< float > &v, float high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
negator< double > &	SimTK::clampInPlace (double low, negator< double > &v, double high)
	Check that low <= v <= high and modify v in place if necessary to bring it into that range. More...
double	SimTK::clamp (double low, double v, double high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
float	SimTK::clamp (float low, float v, float high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
double	SimTK::clamp (int low, double v, int high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
float	SimTK::clamp (int low, float v, int high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
double	SimTK::clamp (int low, double v, double high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
float	SimTK::clamp (int low, float v, float high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
double	SimTK::clamp (double low, double v, int high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
float	SimTK::clamp (float low, float v, int high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
unsigned char	SimTK::clamp (unsigned char low, unsigned char v, unsigned char high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
unsigned short	SimTK::clamp (unsigned short low, unsigned short v, unsigned short high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
unsigned int	SimTK::clamp (unsigned int low, unsigned int v, unsigned int high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
unsigned long	SimTK::clamp (unsigned long low, unsigned long v, unsigned long high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
unsigned long long	SimTK::clamp (unsigned long long low, unsigned long long v, unsigned long long high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
char	SimTK::clamp (char low, char v, char high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
signed char	SimTK::clamp (signed char low, signed char v, signed char high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
short	SimTK::clamp (short low, short v, short high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
int	SimTK::clamp (int low, int v, int high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
long	SimTK::clamp (long low, long v, long high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
long long	SimTK::clamp (long long low, long long v, long long high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
float	SimTK::clamp (float low, negator< float > v, float high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
double	SimTK::clamp (double low, negator< double > v, double high)
	If v is in range low <= v <= high then return v, otherwise return the nearest bound; this function does not modify the input variable v. More...
double	SimTK::stepUp (double x)
	Interpolate smoothly from 0 up to 1 as the input argument goes from 0 to 1, with first and second derivatives zero at either end of the interval. More...
double	SimTK::stepDown (double x)
	Interpolate smoothly from 1 down to 0 as the input argument goes from 0 to 1, with first and second derivatives zero at either end of the interval. More...
double	SimTK::stepAny (double y0, double yRange, double x0, double oneOverXRange, double x)
	Interpolate smoothly from y0 to y1 as the input argument goes from x0 to x1, with first and second derivatives zero at either end of the interval. More...
double	SimTK::dstepUp (double x)
	First derivative of stepUp(): d/dx stepUp(x). More...
double	SimTK::dstepDown (double x)
	First derivative of stepDown(): d/dx stepDown(x). More...
double	SimTK::dstepAny (double yRange, double x0, double oneOverXRange, double x)
	First derivative of stepAny(): d/dx stepAny(x). More...
double	SimTK::d2stepUp (double x)
	Second derivative of stepUp(): d^2/dx^2 stepUp(x). More...
double	SimTK::d2stepDown (double x)
	Second derivative of stepDown(): d^2/dx^2 stepDown(x). More...
double	SimTK::d2stepAny (double yRange, double x0, double oneOverXRange, double x)
	Second derivative of stepAny(): d^2/dx^2 stepAny(x). More...
double	SimTK::d3stepUp (double x)
	Third derivative of stepUp(): d^3/dx^3 stepUp(x). More...
double	SimTK::d3stepDown (double x)
	Third derivative of stepDown(): d^3/dx^3 stepDown(x). More...
double	SimTK::d3stepAny (double yRange, double x0, double oneOverXRange, double x)
	Third derivative of stepAny(): d^3/dx^3 stepAny(x). More...
float	SimTK::stepUp (float x)
	Interpolate smoothly from 0 up to 1 as the input argument goes from 0 to 1, with first and second derivatives zero at either end of the interval. More...
float	SimTK::stepDown (float x)
	Interpolate smoothly from 1 down to 0 as the input argument goes from 0 to 1, with first and second derivatives zero at either end of the interval. More...
float	SimTK::stepAny (float y0, float yRange, float x0, float oneOverXRange, float x)
	Interpolate smoothly from y0 to y1 as the input argument goes from x0 to x1, with first and second derivatives zero at either end of the interval. More...
float	SimTK::dstepUp (float x)
	First derivative of stepUp(): d/dx stepUp(x). More...
float	SimTK::dstepDown (float x)
	First derivative of stepDown(): d/dx stepDown(x). More...
float	SimTK::dstepAny (float yRange, float x0, float oneOverXRange, float x)
	First derivative of stepAny(): d/dx stepAny(x). More...
float	SimTK::d2stepUp (float x)
	Second derivative of stepUp(): d^2/dx^2 stepUp(x). More...
float	SimTK::d2stepDown (float x)
	Second derivative of stepDown(): d^2/dx^2 stepDown(x). More...
float	SimTK::d2stepAny (float yRange, float x0, float oneOverXRange, float x)
	Second derivative of stepAny(): d^2/dx^2 stepAny(x). More...
float	SimTK::d3stepUp (float x)
	Third derivative of stepUp(): d^3/dx^3 stepUp(x). More...
float	SimTK::d3stepDown (float x)
	Third derivative of stepDown(): d^3/dx^3 stepDown(x). More...
float	SimTK::d3stepAny (float yRange, float x0, float oneOverXRange, float x)
	Third derivative of stepAny(): d^3/dx^3 stepAny(x). More...
double	SimTK::stepUp (int x)
	Interpolate smoothly from 0 up to 1 as the input argument goes from 0 to 1, with first and second derivatives zero at either end of the interval. More...
double	SimTK::stepDown (int x)
	Interpolate smoothly from 1 down to 0 as the input argument goes from 0 to 1, with first and second derivatives zero at either end of the interval. More...
std::pair< double, double >	SimTK::approxCompleteEllipticIntegralsKE (double m)
	Given 0<=m<=1, return complete elliptic integrals of the first and second kinds, K(m) and E(m), approximated but with a maximum error of 2e-8 so at least 7 digits are correct (same in float or double precision). See Elliptic integrals for a discussion. More...
std::pair< float, float >	SimTK::approxCompleteEllipticIntegralsKE (float m)
	This is the single precision (float) version of the approximate calculation of elliptic integrals, still yielding about 7 digits of accuracy even though all calculations are done in float precision. More...
std::pair< double, double >	SimTK::approxCompleteEllipticIntegralsKE (int m)
	This integer overload is present to prevent ambiguity; it converts its argument to double precision and then calls approxCompleteEllipticIntegralsKE(double). More...
std::pair< double, double >	SimTK::completeEllipticIntegralsKE (double m)
	Given 0<=m<=1, return complete elliptic integrals of the first and second kinds, K(m) and E(m), calculated to (roughly) machine precision (float or double). See Elliptic integrals for a discussion. More...
std::pair< float, float >	SimTK::completeEllipticIntegralsKE (float m)
	This is the single precision (float) version of the machine-precision calculation of elliptic integrals, providing accuracy to float precision (about 7 digits) which is no better than you'll get with the much faster approximate version, so use that instead! More...
std::pair< double, double >	SimTK::completeEllipticIntegralsKE (int m)
	This integer overload is present to prevent ambiguity; it converts its argument to double precision and then calls completeEllipticIntegralsKE(double). More...

Variables
const Real	SimTK::NaN
	This is the IEEE "not a number" constant for this implementation of the default-precision Real type; be very careful using this because it has many strange properties such as not comparing equal to itself. More...
const Real	SimTK::Infinity
	This is the IEEE positive infinity constant for this implementation of the default-precision Real type; -Infinity will produce the negative infinity constant. More...
const Real	SimTK::Eps
	Epsilon is the size of roundoff noise; it is the smallest positive number of default-precision type Real such that 1+Eps != 1. More...
const Real	SimTK::SqrtEps
	This is the square root of Eps, ~1e-8 if Real is double, ~3e-4 if Real is float. More...
const Real	SimTK::TinyReal
	TinyReal is a floating point value smaller than the floating point precision; it is defined as Eps^(5/4) which is ~1e-20 for Real==double and ~1e-9 for float. More...
const Real	SimTK::SignificantReal
	SignificantReal is the smallest value that we consider to be clearly distinct from roundoff error when it is the result of a computation; it is defined as Eps^(7/8) which is ~1e-14 when Real==double, ~1e-6 when Real==float. More...
const Real	SimTK::LeastPositiveReal
	This is the smallest positive real number that can be expressed in the type Real; it is ~1e-308 when Real==double, ~1e-38 when Real==float. More...
const Real	SimTK::MostPositiveReal
	This is the largest finite positive real number that can be expressed in the Real type; ~1e+308 when Real==double, ~1e+38 when Real==float. Note that there is also a value Infinity that will test larger than this one. More...
const Real	SimTK::LeastNegativeReal
	This is the largest negative real number (that is, closest to zero) that can be expressed in values of type Real. More...
const Real	SimTK::MostNegativeReal
	This is the smallest finite negative real number that can be expressed in values of type Real. Note that -Infinity is a value that will still test smaller than this one. More...
const int	SimTK::NumDigitsReal
	This is the number of decimal digits that can be reliably stored and retrieved in the default Real precision (typically log10(1/eps)-1), that is, about 15 digits when Real==double and 6 digits when Real==float. More...
const int	SimTK::LosslessNumDigitsReal
	This is the smallest number of decimal digits you should store in a text file if you want to be able to get exactly the same bit pattern back when you read it back in and convert the text to a Real value. More...
const Real	SimTK::Zero
	Real(0) More...
const Real	SimTK::One
	Real(1) More...
const Real	SimTK::MinusOne
	Real(-1) More...
const Real	SimTK::Two
	Real(2) More...
const Real	SimTK::Three
	Real(3) More...
const Real	SimTK::OneHalf
	Real(1)/2. More...
const Real	SimTK::OneThird
	Real(1)/3. More...
const Real	SimTK::OneFourth
	Real(1)/4. More...
const Real	SimTK::OneFifth
	Real(1)/5. More...
const Real	SimTK::OneSixth
	Real(1)/6. More...
const Real	SimTK::OneSeventh
	Real(1)/7. More...
const Real	SimTK::OneEighth
	Real(1)/8. More...
const Real	SimTK::OneNinth
	Real(1)/9. More...
const Real	SimTK::Pi
	Real(pi) More...
const Real	SimTK::OneOverPi
	1/Real(pi) More...
const Real	SimTK::E
	e = Real(exp(1)) More...
const Real	SimTK::Log2E
	Real(log2(e)) (log base 2) More...
const Real	SimTK::Log10E
	Real(log10(e)) (log base 10) More...
const Real	SimTK::Sqrt2
	Real(sqrt(2)) More...
const Real	SimTK::OneOverSqrt2
	1/sqrt(2)==sqrt(2)/2 as Real More...
const Real	SimTK::Sqrt3
	Real(sqrt(3)) More...
const Real	SimTK::OneOverSqrt3
	Real(1/sqrt(3)) More...
const Real	SimTK::CubeRoot2
	Real(2^(1/3)) (cube root of 2) More...
const Real	SimTK::CubeRoot3
	Real(3^(1/3)) (cube root of 3) More...
const Real	SimTK::Ln2
	Real(ln(2)) (natural log of 2) More...
const Real	SimTK::Ln10
	Real(ln(10)) (natural log of 10) More...
const Complex	SimTK::I
	We only need one complex constant, i = sqrt(-1). For the rest just multiply the real constant by i, or convert with Complex(the Real constant), or if you need an address you can use NTraits<Complex>::getPi(), etc. More...

Detailed Description

This is a user-includable header which includes everything needed to make use of SimMatrix Scalar code.

More commonly, this will be included from within Matrix code.