#include <Alge.h>

Inheritance diagram for honey::Alge_< Real >:

Collaboration diagram for honey::Alge_< Real >:

Static Public Member Functions
static Int	abs (Int x)
	Get absolute value of signed integer. More...

static UInt	abs (UInt x)
	Get absolute value of unsigned integer. More...

static Real	abs (Real x)
	Get absolute value of real number. More...

static Int	sign (Int x)
	Get sign of number {-1,0,1}. More...

static UInt	sign (UInt x)

static Real	sign (Real x)

static Real	ceil (Real x)
	Round up to the nearest whole number towards +inf. More...

static Real	floor (Real x)
	Round down to the nearest whole number towards -inf. More...

static Real	round (Real x)
	Round to the nearest whole number. More...

static Real	trunc (Real x)
	Remove fractional part, leaving just the whole number. More...

static Real	frac (Real x)
	Remove the whole part, leaving just the fraction. More...

static Real	mod (Real x, Real y)
	Modulo, same as x % y. Returns remainder of division: x/y. More...

static Real	modNormalize (Real mod, Real val)
	Get an equivalent value in the normalized modular interval [-mod, mod]. More...

static Real	modDistSigned (Real mod, Real x, Real y)
	Calc smallest signed distance between two normalized values in a modular field. More...

template<class Num >
static Num	sqr (Num x)
	Square. More...

static Real	sqrt (Real x)
	Square Root. More...

static Real	sqrtInv (Real x)
	Inverse Square Root. More...

static Real	exp (Real x)
	Euler's number e raised to exponent x (e^x) More...

static Real	expm1 (Real x)
	exp(x) - 1, more accurate than exp() for small values of x. More...

static Real	pow (Real x, Real y)
	x raised to exponent y More...

static Real	log (Real x)
	Natural logarithm. ie. ln(x) More...

static Real	log (Real x, Real base)
	Logarithm with base number. More...

static Real	log1p (Real x)
	log(1 + x), more accurate than log() for small values of x. More...

template<class Num , class Num2 >
static std::common_type< Num, Num2 >::type	min (Num a, Num2 b)
	Get the minimum of two numbers. More...

template<class Num , class Num2 >
static std::common_type< Num, Num2 >::type	max (Num a, Num2 b)
	Get the maximum of two numbers. More...

template<class Num , class Num2 , class Num3 >
static std::common_type< Num, Num2, Num3 >::type	clamp (Num val, Num2 min, Num3 max)
	Ensure that a number is within a range. More...

static bool	isNan (Real x)
	Returns true if real is not a number. More...

static bool	isNear (Int a, Int b, Int tol)
	Check whether two numbers are near each other, given a tolerance. More...

static bool	isNear (Real a, Real b, Real tol=Real_::zeroTol)

static bool	isNearZero (Real val, Real tol=Real_::zeroTol)
	Check whether a number is close to zero. More...

template<class Num , class Num2 , class Num3 >
static bool	isInRange (Num val, Num2 min, Num3 max)
	Check if value is within min/max inclusive range. More...

static Real	hypot (Real a, Real b)
	Get the hypotenuse of a right angle triangle with side lengths `a` and `b`. This method is more numerically stable than the direct approach: sqrt(aa + bb) More...

static tuple< bool, Real, Real >	solve (Real a, Real b, Real c, Real d, Real u, Real v)
	Solve an equation pair using Gauss-Jordan elimination. More...

Static Public Attributes
static const Real	logMin = log(numeral<Real>().smallest())
	The lowest negative value x for which exp(x) can be calucated without underflow. More...

static const Real	logMax = log(numeral<Real>().max())
	The highest value x for which exp(x) can be calucated without overflow. More...

Detailed Description

template<class Real>
class honey::Alge_< Real >

Algebra.

Member Function Documentation

template<class Real >

static Int honey::Alge_< Real >::abs ( Int x )

inlinestatic

Get absolute value of signed integer.

template<class Real >

static UInt honey::Alge_< Real >::abs ( UInt x )

inlinestatic

Get absolute value of unsigned integer.

template<class Real >

static Real honey::Alge_< Real >::abs ( Real x )

inlinestatic

Get absolute value of real number.

template<class Real >

static Real honey::Alge_< Real >::ceil ( Real x )

inlinestatic

Round up to the nearest whole number towards +inf.

template<class Real >

template<class Num , class Num2 , class Num3 >

static std::common_type<Num, Num2, Num3>::type honey::Alge_< Real >::clamp	(	Num	val,
		Num2	min,
		Num3	max
	)

inlinestatic

Ensure that a number is within a range.

template<class Real >

static Real honey::Alge_< Real >::exp ( Real x )

inlinestatic

Euler's number e raised to exponent x (e^x)

template<class Real >

Real honey::Alge_< Real >::expm1 ( Real x )

static

exp(x) - 1, more accurate than exp() for small values of x.

template<class Real >

static Real honey::Alge_< Real >::floor ( Real x )

inlinestatic

Round down to the nearest whole number towards -inf.

template<class Real >

static Real honey::Alge_< Real >::frac ( Real x )

inlinestatic

Remove the whole part, leaving just the fraction.

template<class Real >

Real honey::Alge_< Real >::hypot	(	Real	a,
		Real	b
	)

static

Get the hypotenuse of a right angle triangle with side lengths a and b. This method is more numerically stable than the direct approach: sqrt(a*a + b*b)

template<class Real >

template<class Num , class Num2 , class Num3 >

static bool honey::Alge_< Real >::isInRange	(	Num	val,
		Num2	min,
		Num3	max
	)

inlinestatic

Check if value is within min/max inclusive range.

template<class Real >

static bool honey::Alge_< Real >::isNan ( Real x )

inlinestatic

Returns true if real is not a number.

template<class Real >

static bool honey::Alge_< Real >::isNear	(	Int	a,
		Int	b,
		Int	tol
	)

inlinestatic

Check whether two numbers are near each other, given a tolerance.

template<class Real >

static bool honey::Alge_< Real >::isNear	(	Real	a,
		Real	b,
		Real	tol = `Real_::zeroTol`
	)

inlinestatic

template<class Real >

static bool honey::Alge_< Real >::isNearZero	(	Real	val,
		Real	tol = `Real_::zeroTol`
	)

inlinestatic

Check whether a number is close to zero.

template<class Real >

static Real honey::Alge_< Real >::log ( Real x )

inlinestatic

Natural logarithm. ie. ln(x)

template<class Real >

static Real honey::Alge_< Real >::log	(	Real	x,
		Real	base
	)

inlinestatic

Logarithm with base number.

template<class Real >

Real honey::Alge_< Real >::log1p ( Real x )

static

log(1 + x), more accurate than log() for small values of x.

template<class Real >

template<class Num , class Num2 >

static std::common_type<Num, Num2>::type honey::Alge_< Real >::max	(	Num	a,
		Num2	b
	)

inlinestatic

Get the maximum of two numbers.

template<class Real >

template<class Num , class Num2 >

static std::common_type<Num, Num2>::type honey::Alge_< Real >::min	(	Num	a,
		Num2	b
	)

inlinestatic

Get the minimum of two numbers.

template<class Real >

static Real honey::Alge_< Real >::mod	(	Real	x,
		Real	y
	)

inlinestatic

Modulo, same as x % y. Returns remainder of division: x/y.

template<class Real >

static Real honey::Alge_< Real >::modDistSigned	(	Real	mod,
		Real	x,
		Real	y
	)

inlinestatic

Calc smallest signed distance between two normalized values in a modular field.

template<class Real >

static Real honey::Alge_< Real >::modNormalize	(	Real	mod,
		Real	val
	)

inlinestatic

Get an equivalent value in the normalized modular interval [-mod, mod].

template<class Real >

static Real honey::Alge_< Real >::pow	(	Real	x,
		Real	y
	)

inlinestatic

x raised to exponent y

template<class Real >

static Real honey::Alge_< Real >::round ( Real x )

inlinestatic

Round to the nearest whole number.

template<class Real >

static Int honey::Alge_< Real >::sign ( Int x )

inlinestatic

Get sign of number {-1,0,1}.

template<class Real >

static UInt honey::Alge_< Real >::sign ( UInt x )

inlinestatic

template<class Real >

static Real honey::Alge_< Real >::sign ( Real x )

inlinestatic

template<class Real >

tuple< bool, Real, Real > honey::Alge_< Real >::solve	(	Real	a,
		Real	b,
		Real	c,
		Real	d,
		Real	u,
		Real	v
	)

static

Solve an equation pair using Gauss-Jordan elimination.

This method solves for x and y:
$ ax + by = u $
$ cx + dy = v $

Return values

solved	if false then there is no unique solution (determinant is 0)
x
y

template<class Real >

template<class Num >

static Num honey::Alge_< Real >::sqr ( Num x )

inlinestatic

Square.

template<class Real >

static Real honey::Alge_< Real >::sqrt ( Real x )

inlinestatic

Square Root.

template<class Real >

static Real honey::Alge_< Real >::sqrtInv ( Real x )

inlinestatic

Inverse Square Root.

template<class Real >

static Real honey::Alge_< Real >::trunc ( Real x )

inlinestatic

Remove fractional part, leaving just the whole number.

Member Data Documentation

template<class Real >

const Real honey::Alge_< Real >::logMax = log(numeral<Real>().max())

static

The highest value x for which exp(x) can be calucated without overflow.

template<class Real >

const Real honey::Alge_< Real >::logMin = log(numeral<Real>().smallest())

static

The lowest negative value x for which exp(x) can be calucated without underflow.

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

src/common/Honey/Math/Alge/Alge.h
src/common/Honey/Math/Alge/Alge.cpp

Static Public Member Functions

Static Public Attributes

Detailed Description

template<class Real> class honey::Alge_< Real >

Member Function Documentation

Member Data Documentation

template<class Real>
class honey::Alge_< Real >