#include <hmath.h>

Static Public Member Functions
static char *	format (const HNumber &n, char format= 'g', int prec=-1)
static HNumber	e ()
static HNumber	phi ()
static HNumber	pi ()
static HNumber	nan (Error error=Success)
static HNumber	rad2deg (const HNumber &angle)
static HNumber	deg2rad (const HNumber &angle)
static HNumber	max (const HNumber &n1, const HNumber &n2)
static HNumber	min (const HNumber &n1, const HNumber &n2)
static HNumber	abs (const HNumber &n)
static HNumber	integer (const HNumber &n)
static HNumber	frac (const HNumber &n)
static HNumber	floor (const HNumber &n)
static HNumber	ceil (const HNumber &n)
static HNumber	gcd (const HNumber &n1, const HNumber &n2)
static HNumber	idiv (const HNumber &n1, const HNumber &n2)
static HNumber	round (const HNumber &n, int prec=0)
static HNumber	trunc (const HNumber &n, int prec=0)
static HNumber	sqrt (const HNumber &n)
static HNumber	cbrt (const HNumber &n)
static HNumber	raise (const HNumber &n1, int n)
static HNumber	raise (const HNumber &n1, const HNumber &n2)
static HNumber	sgn (const HNumber &x)
static HNumber	exp (const HNumber &x)
static HNumber	ln (const HNumber &x)
static HNumber	lg (const HNumber &x)
static HNumber	lb (const HNumber &x)
static HNumber	log (const HNumber &base, const HNumber &x)
static HNumber	sinh (const HNumber &x)
static HNumber	cosh (const HNumber &x)
static HNumber	tanh (const HNumber &x)
static HNumber	arsinh (const HNumber &x)
static HNumber	arcosh (const HNumber &x)
static HNumber	artanh (const HNumber &x)
static HNumber	sin (const HNumber &x)
static HNumber	cos (const HNumber &x)
static HNumber	tan (const HNumber &x)
static HNumber	cot (const HNumber &x)
static HNumber	sec (const HNumber &x)
static HNumber	csc (const HNumber &x)
static HNumber	arcsin (const HNumber &x)
static HNumber	arccos (const HNumber &x)
static HNumber	arctan (const HNumber &x)
static HNumber	factorial (const HNumber &x, const HNumber &base=HNumber(1))
static HNumber	gamma (const HNumber &x)
static HNumber	lnGamma (const HNumber &x)
static HNumber	erf (const HNumber &x)
static HNumber	erfc (const HNumber &x)
static HNumber	nCr (const HNumber &n, const HNumber &k)
static HNumber	nPr (const HNumber &n, const HNumber &r)
static HNumber	binomialPmf (const HNumber &k, const HNumber &n, const HNumber &p)
static HNumber	binomialCdf (const HNumber &k, const HNumber &n, const HNumber &p)
static HNumber	binomialMean (const HNumber &n, const HNumber &p)
static HNumber	binomialVariance (const HNumber &n, const HNumber &p)
static HNumber	hypergeometricPmf (const HNumber &k, const HNumber &N, const HNumber &M, const HNumber &n)
static HNumber	hypergeometricCdf (const HNumber &k, const HNumber &N, const HNumber &M, const HNumber &n)
static HNumber	hypergeometricMean (const HNumber &N, const HNumber &M, const HNumber &n)
static HNumber	hypergeometricVariance (const HNumber &N, const HNumber &M, const HNumber &n)
static HNumber	poissonPmf (const HNumber &k, const HNumber &l)
static HNumber	poissonCdf (const HNumber &k, const HNumber &l)
static HNumber	poissonMean (const HNumber &l)
static HNumber	poissonVariance (const HNumber &l)
static HNumber	mask (const HNumber &val, const HNumber &bits)
static HNumber	sgnext (const HNumber &val, const HNumber &bits)
static HNumber	ashr (const HNumber &val, const HNumber &bits)

Member Function Documentation

HNumber HMath::abs ( const HNumber & n ) [static]

Returns the absolute value of n.

HNumber HMath::arccos ( const HNumber & x ) [static]

Returns the arc cosine of x.

HNumber HMath::arcosh ( const HNumber & x ) [static]

Returns the area hyperbolic cosine of x.

HNumber HMath::arcsin ( const HNumber & x ) [static]

Returns the arc sine of x.

HNumber HMath::arctan ( const HNumber & x ) [static]

Returns the arc tangent of x.

HNumber HMath::arsinh ( const HNumber & x ) [static]

Returns the area hyperbolic sine of x.

HNumber HMath::artanh ( const HNumber & x ) [static]

Returns the area hyperbolic tangent of x.

HNumber HMath::ashr	(	const HNumber &	val,
		const HNumber &	bits
	)		`[static]`

For bits >= 0 does an arithmetic shift right, for bits < 0 a shift left.

HNumber HMath::binomialCdf	(	const HNumber &	k,
		const HNumber &	n,
		const HNumber &	p
	)		`[static]`

Calculates the binomial cumulative distribution function:

$X{\sim}B(n,p)$

$\Pr(X \leq k|n,p)=\sum_{i=0}^{k}{n\choose i}p^{i}(1-p)^{n-i}$

Parameters:

[in]	k	the maximum number of probed successes
[in]	n	the number of trials
[in]	p	the probability of success in a single trial

Returns:: the probability of up to k successes, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::binomialMean	(	const HNumber &	n,
		const HNumber &	p
	)		`[static]`

Calculates the expected value of a binomially distributed random variable:

$X{\sim}B(n,p)$

$E(X)=np$

Parameters:

[in]	n	the number of trials
[in]	p	the probability of success in a single trial

Returns:: the expected value of the variable, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::binomialPmf	(	const HNumber &	k,
		const HNumber &	n,
		const HNumber &	p
	)		`[static]`

Calculates the binomial discrete distribution probability mass function:

$X{\sim}B(n,p)$

$\Pr(X=k|n,p)={n\choose k}p^{k}(1-p)^{n-k}$

Parameters:

[in]	k	the number of probed exact successes
[in]	n	the number of trials
[in]	p	the probability of success in a single trial

Returns:: the probability of exactly k successes, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::binomialVariance	(	const HNumber &	n,
		const HNumber &	p
	)		`[static]`

Calculates the variance of a binomially distributed random variable:

$X{\sim}B(n,p)$

$Var(X)=np(1-p)$

Parameters:

[in]	n	the number of trials
[in]	p	the probability of success in a single trial

Returns:: the variance of the variable, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::cbrt ( const HNumber & n ) [static]

Returns the cube root of n.

HNumber HMath::ceil ( const HNumber & n ) [static]

Returns the ceiling of n.

HNumber HMath::cos ( const HNumber & x ) [static]

Returns the cosine of x. Note that x must be in radians.

HNumber HMath::cosh ( const HNumber & x ) [static]

Returns the hyperbolic cosine of x.

HNumber HMath::cot ( const HNumber & x ) [static]

Returns the cotangent of x. Note that x must be in radians.

HNumber HMath::csc ( const HNumber & x ) [static]

Returns the cosecant of x. Note that x must be in radians.

HNumber HMath::deg2rad ( const HNumber & angle ) [static]

Converts degrees to radians.

HNumber HMath::e ( ) [static]

Returns the constant e (Euler's number).

HNumber HMath::erf ( const HNumber & x ) [static]

Returns the erf function (related to normal distribution).

HNumber HMath::erfc ( const HNumber & x ) [static]

Returns the complementary erf function (related to normal distribution).

HNumber HMath::exp ( const HNumber & x ) [static]

Returns e raised to x.

HNumber HMath::factorial	(	const HNumber &	x,
		const HNumber &	base = `HNumber(1)`
	)		`[static]`

Returns the falling Pochhammer symbol x*(x-1)*..*base. For base == 1, this is the usual factorial x!, what this function is named after. This function has been extended using the Gamma function, so that actually Gamma(x+1)/Gamma(base) is computed, a value that equals the falling Pochhammer symbol, when x - base is an integer, but allows other differences as well.

HNumber HMath::floor ( const HNumber & n ) [static]

Returns the floor of n.

char * HMath::format	(	const HNumber &	hn,
		char	format = `'g'`,
		int	prec = `-1`
	)		`[static]`

Formats the given number as string, using specified decimal digits. Note that the returned string must be freed.

HNumber HMath::frac ( const HNumber & n ) [static]

Returns the fraction part of n.

HNumber HMath::gamma ( const HNumber & x ) [static]

Returns the Gamma function.

HNumber HMath::gcd	(	const HNumber &	n1,
		const HNumber &	n2
	)		`[static]`

Returns the greatest common divisor of n1 and n2.

HNumber HMath::hypergeometricCdf	(	const HNumber &	k,
		const HNumber &	N,
		const HNumber &	M,
		const HNumber &	n
	)		`[static]`

Calculates the hypergeometric cumulative distribution function:

$X{\sim}H(N,M,n)$

$\Pr(X\leq k|N,M,n)= \sum_{i=0}^{k}\frac{{M\choose k}{N-M\choose n-k}}{{N\choose n}}$

Parameters:

[in]	k	the maximum number of probed successes
[in]	N	the number of total elements
[in]	M	the number of success elements
[in]	n	the number of selected elements

Returns:: the probability of up to k successes, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::hypergeometricMean	(	const HNumber &	N,
		const HNumber &	M,
		const HNumber &	n
	)		`[static]`

Calculates the expected value of a hypergeometrically distributed random variable:

$X{\sim}H(N,M,n)$

$E(X)=n\frac{M}{N}$

Parameters:

[in]	N	the number of total elements
[in]	M	the number of success elements
[in]	n	the number of selected elements

Returns:: the expected value of the variable, otherwise NaN if the function is not defined for the specified parameter.

HNumber HMath::hypergeometricPmf	(	const HNumber &	k,
		const HNumber &	N,
		const HNumber &	M,
		const HNumber &	n
	)		`[static]`

Calculates the hypergeometric discrete distribution probability mass function:

$X{\sim}H(N,M,n)$

$\Pr(X=k|N,M,n)=\frac{{M\choose k}{N-M\choose n-k}}{{N\choose n}}$

Parameters:

[in]	k	the number of probed exact successes
[in]	N	the number of total elements
[in]	M	the number of success elements
[in]	n	the number of selected elements

Returns:: the probability of exactly k successes, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::hypergeometricVariance	(	const HNumber &	N,
		const HNumber &	M,
		const HNumber &	n
	)		`[static]`

Calculates the variance of a hypergeometrically distributed random variable:

$X{\sim}H(N,M,n)$

$Var(X)=\frac{n\frac{M}{N}(1-\frac{M}{N})(N-n)}{N-1}$

Parameters:

[in]	N	the number of total elements
[in]	M	the number of success elements
[in]	n	the number of selected elements

Returns:: the variance of the variable, otherwise NaN if the function is not defined for the specified parameter.

HNumber HMath::idiv	(	const HNumber &	dividend,
		const HNumber &	divisor
	)		`[static]`

Performs an integer divide

HNumber HMath::integer ( const HNumber & n ) [static]

Returns the integer part of n.

HNumber HMath::lb ( const HNumber & x ) [static]

Returns the binary logarithm of x. If x is non positive, returns NaN.

HNumber HMath::lg ( const HNumber & x ) [static]

Returns the common logarithm of x. If x is non positive, returns NaN.

HNumber HMath::ln ( const HNumber & x ) [static]

Returns the natural logarithm of x. If x is non positive, returns NaN.

HNumber HMath::lnGamma ( const HNumber & x ) [static]

Returns ln(abs(Gamma(x))).

HNumber HMath::log	(	const HNumber &	base,
		const HNumber &	x
	)		`[static]`

Returns the logarithm of x to base. If x is non positive, returns NaN.

HNumber HMath::mask	(	const HNumber &	val,
		const HNumber &	bits
	)		`[static]`

Restricts a logic value to a given bit size.

HNumber HMath::max	(	const HNumber &	n1,
		const HNumber &	n2
	)		`[static]`

Returns the maximum of two numbers.

HNumber HMath::min	(	const HNumber &	n1,
		const HNumber &	n2
	)		`[static]`

Returns the minimum of two numbers.

HNumber HMath::nan ( Error error = Success ) [static]

Returns a NaN (Not a Number) with error set to passed parameter.

HNumber HMath::nCr	(	const HNumber &	n,
		const HNumber &	r
	)		`[static]`

Returns the binomial coefficient of n and r. Is any of n and r negative or a non-integer, 1/(n+1)*B(r+1, n-r+1)) is returned, where B(x,y) is the complete Beta function

HNumber HMath::nPr	(	const HNumber &	n,
		const HNumber &	r
	)		`[static]`

Returns the permutation of n elements chosen r elements.

HNumber HMath::phi ( ) [static]

Returns the constant Phi (golden number).

HNumber HMath::pi ( ) [static]

Returns the constant Pi.

HNumber HMath::poissonCdf	(	const HNumber &	k,
		const HNumber &	l
	)		`[static]`

Calculates the poissonian cumulative distribution function:

$X{\sim}P(\lambda)$

$\Pr(X\leq k|\lambda)=\sum_{i=0}^{k}\frac{e^{-\lambda}\lambda^k}{k!}$

Parameters:

[in]	k	the maximum number of event occurrences
[in]	l	the expected number of occurrences that occur in an interval

Returns:: the probability of up to k event occurrences, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::poissonMean ( const HNumber & l ) [static]

Calculates the expected value of a Poisson distributed random variable:

$X{\sim}P(\lambda)$

$E(X)=\lambda$

Parameters:

[in] l the expected number of occurrences that occur in an interval

Returns:: the expected value of the variable, otherwise NaN if the function is not defined for the specified parameter.

HNumber HMath::poissonPmf	(	const HNumber &	k,
		const HNumber &	l
	)		`[static]`

Calculates the poissonian discrete distribution probability mass function:

$X{\sim}P(\lambda)$

$\Pr(X=k|\lambda)=\frac{e^{-\lambda}\lambda^k}{k!}$

Parameters:

[in]	k	the number of event occurrences
[in]	l	the expected number of occurrences that occur in an interval

Returns:: the probability of exactly k event occurrences, otherwise NaN if the function is not defined for the specified parameters.

HNumber HMath::poissonVariance ( const HNumber & l ) [static]

Calculates the variance of a Poisson distributed random variable:

$X{\sim}P(\lambda)$

$Var(X)=\lambda$

Parameters:

[in] l the expected number of occurrences that occur in an interval

Returns:: the variance of the variable, otherwise NaN if the function is not defined for the specified parameter.

HNumber HMath::rad2deg ( const HNumber & angle ) [static]

Converts radians to degrees.

HNumber HMath::raise	(	const HNumber &	n1,
		int	n
	)		`[static]`

Raises n1 to an integer n.

HNumber HMath::raise	(	const HNumber &	n1,
		const HNumber &	n2
	)		`[static]`

Raises n1 to n2.

HNumber HMath::round	(	const HNumber &	n,
		int	prec = `0`
	)		`[static]`

Rounds n to the specified decimal digits.

HNumber HMath::sec ( const HNumber & x ) [static]

Returns the secant of x. Note that x must be in radians.

HNumber HMath::sgn ( const HNumber & x ) [static]

Returns signum x.

HNumber HMath::sgnext	(	const HNumber &	val,
		const HNumber &	bits
	)		`[static]`

sign-extends an unsigned value

HNumber HMath::sin ( const HNumber & x ) [static]

Returns the sine of x. Note that x must be in radians.

HNumber HMath::sinh ( const HNumber & x ) [static]

Returns the hyperbolic sine of x.

HNumber HMath::sqrt ( const HNumber & n ) [static]

Returns the square root of n. If n is negative, returns NaN.

HNumber HMath::tan ( const HNumber & x ) [static]

Returns the tangent of x. Note that x must be in radians.

HNumber HMath::tanh ( const HNumber & x ) [static]

Returns the hyperbolic tangent of x.

HNumber HMath::trunc	(	const HNumber &	n,
		int	prec = `0`
	)		`[static]`

Truncates n to the specified decimal digits.

The documentation for this class was generated from the following files:

/usr/src/RPM/BUILD/speedcrunch-0.11/src/math/hmath.h
/usr/src/RPM/BUILD/speedcrunch-0.11/src/math/hmath.cpp

Static Public Member Functions

Member Function Documentation