Math

Classes
class	al::MinMeanMax< T >
class	al::Polar< T >
class	al::Complex< T >
class	al::Frustum< T >
	Rectangular frustum. More...
class	al::Interval< T >
	A closed interval [min, max]. More...
class	al::Mat< N, T >
	Fixed-size n-by-n square matrix. More...
class	al::Matrix4< T >
class	al::Plane< T >
class	al::Quat< T >
class	al::rnd::Random< RNG >
class	al::Ray< T >
class	al::SphereCoord< T >
	Spherical coordinate in terms of two complex numbers. More...
class	al::SphericalHarmonic< L_MAX >
	Spherical harmonic evaluator using cached coefficients. More...
class	al::Vec< N, T >
	Fixed-size n-vector. More...

Functions
template<class VecN , class T >
void	al::rotatePlane (VecN &v1, VecN &v2, const Complex< T > &a)
template<class Vec3 , class T >
Vec3	al::sterProj (const al::Complex< T > &c)
bool	al::aeq (float a, float b, int maxULP=10)
	Return whether two floats are almost equal. More...
template<class T >
T	al::ampTodB (const T &amp)
template<class T >
T	al::atLeast (const T &v, const T &eps)
template<class T >
T	al::atan2Fast (const T &y, const T &x)
uint32_t	al::bitsSet (uint32_t v)
	Returns number of bits set to 1. More...
template<class T >
T	al::ceil (const T &val, const T &step)
uint32_t	al::ceilPow2 (uint32_t value)
	Returns power of two ceiling of value. More...
template<class T >
T	al::clip (const T &value, const T &hi=T(1), const T &lo=T(0))
template<class T >
T	al::clip (const T &v, int &clipFlag, const T &hi, const T &lo)
	Returns value clipped to [lo, hi] and signifies clipping behavior. More...
template<class T >
T	al::clipS (const T &value, const T &hi=T(1))
template<class T >
T	al::dBToAmp (const T &db)
template<class T >
bool	al::even (const T &v)
template<class T >
T	al::erf (const T &v)
uint32_t	al::factorial (uint32_t n0to12)
double	al::factorialSqrt (int v)
template<class T >
T	al::floor (const T &val, const T &step)
uint32_t	al::floorPow2 (uint32_t value)
	Returns power of two floor of value. More...
template<class T >
T	al::fold (const T &value, const T &hi=T(1), const T &lo=T(0))
	Returns value folded into [lo, hi]. More...
template<class T >
T	al::foldOnce (const T &value, const T &hi=T(1), const T &lo=T(0))
template<class T >
T	al::gaussian (const T &v)
template<class T >
T	al::gcd (const T &x, const T &y)
template<class T >
T	al::gudermannian (const T &x)
template<class T >
T	al::laguerreL (int n, int k, T x)
	Generalized Laguerre polynomial L{n,k}. More...
template<class T >
T	al::legendreP (int l, int m, T t)
template<class T >
bool	al::lessAbs (const T &v, const T &eps=T(0.000001))
template<typename T >
T	al::max (const T &v1, const T &v2, const T &v3)
template<class T >
T	al::mean (const T &v1, const T &v2)
template<class T >
T	al::min (const T &v1, const T &v2, const T &v3)
template<class T >
T	al::nearestDiv (T of, T to)
template<class T >
T	al::nextAfter (const T &x, const T &y)
template<class T >
T	al::nextMultiple (T val, T multiple)
template<class T >
T	al::numInt (const T &v)
template<class T >
bool	al::odd (const T &v)
template<class T >
T	al::poly (const T &x, const T &a0, const T &a1, const T &a2)
template<class T >
T	al::poly (const T &x, const T &a0, const T &a1, const T &a2, const T &a3)
template<class T >
T	al::powN (T base, unsigned power)
	Returns value to a positive integer power. More...
unsigned char	al::prime (uint32_t n)
template<class T >
T	al::round (const T &v, const T &step)
template<class T >
T	al::round (const T &v, const T &step, const T &recStep)
template<class T >
T	al::roundAway (const T &v)
template<class T >
T	al::roundAway (const T &v, const T &step)
template<class T >
T	al::sgn (const T &v, const T &norm=T(1))
template<class T >
T	al::sinc (const T &radians, const T &eps=T(0.0001))
template<class T >
T	al::slope (const T &x1, const T &y1, const T &x2, const T &y2)
template<class T >
void	al::sort (T &value1, T &value2)
template<class T >
T	al::sumOfSquares (T n)
uint32_t	al::trailingZeroes (uint32_t v)
	Returns number of trailing zeros in 32-bit int. More...
template<class T >
T	al::trunc (const T &v, const T &step)
template<class T >
T	al::trunc (const T &v, const T &step, const T &recStep)
template<class T >
bool	al::within (const T &v, const T &lo, const T &hi)
template<class T >
bool	al::within3 (const T &v1, const T &v2, const T &v3, const T &lo, const T &hi)
template<class T >
bool	al::withinIE (const T &v, const T &lo, const T &hi)
template<class T >
T	al::wrap (const T &value, const T &hi=T(1), const T &lo=T(0))
template<class T >
T	al::wrap (const T &value, long &numWraps, const T &hi=T(1), const T &lo=T(0))
	Returns value wrapped in [lo, hi). More...
template<class T >
T	al::wrapAdd1 (const T &v, const T &max)
template<class T >
T	al::wrapOnce (const T &value, const T &hi=T(1))
template<class T >
T	al::wrapPhase (const T &radians)
template<class T >
T	al::wrapPhaseOnce (const T &radians)
template<class Tf , class Tv >
Tv	al::ipl::bezier (Tf frac, const Tv &x2, const Tv &x1, const Tv &x0)
	Bezier curve, 3-point quadratic. More...
template<class Tf , class Tv >
Tv	al::ipl::bezier (Tf frac, const Tv &x3, const Tv &x2, const Tv &x1, const Tv &x0)
	Bezier curve, 4-point cubic. More...
template<class Tf , class Tv >
Tv	al::ipl::casteljau (const Tf &frac, const Tv &a, const Tv &b, const Tv &c, const Tv &d)
	de Casteljau algorithm for four point interpolation More...
template<class Tp , class Tv >
Tv	al::ipl::hermite (Tp f, const Tv &w, const Tv &x, const Tv &y, const Tv &z, Tp tension, Tp bias)
template<class T >
void	al::ipl::lagrange (T *h, T delay, int order)
	Computes FIR coefficients for Waring-Lagrange interpolation. More...
template<class T >
void	al::ipl::lagrange1 (T *h, T delay)
template<class T >
void	al::ipl::lagrange2 (T *h, T delay)
template<class T >
void	al::ipl::lagrange3 (T *h, T delay)
template<class Tf , class Tv >
void	al::ipl::cardinalSpline (Tv *w, const Tv *x, const Tf &f, double b)
	Compute weights for cubic cardinal spline. More...
template<class Tf , class Tv >
Tv	al::ipl::cubic (Tf frac, const Tv &w, const Tv &x, const Tv &y, const Tv &z)
	Cubic interpolation. More...
template<class Tf , class Tv >
Tv	al::ipl::cubic2 (Tf frac, const Tv &w, const Tv &x, const Tv &y, const Tv &z)
	Cubic interpolation. More...
template<class Tf , class Tv >
Tv	al::ipl::linear (Tf frac, const Tv &x, const Tv &y)
template<class Tf , class Tv >
Tv	al::ipl::linear (Tf frac, const Tv &x, const Tv &y, const Tv &z)
template<class Tf , class Tv >
Tv	al::ipl::linearCyclic (Tf frac, const Tv &x, const Tv &y, const Tv &z)
template<class Tf , class Tv >
void	al::ipl::linear (Tv *dst, const Tv *xs, const Tv *xp1s, int len, const Tf &frac)
template<class Tf , class Tv >
Tv	al::ipl::nearest (Tf frac, const Tv &x, const Tv &y)
template<class Tf , class Tv >
Tv	al::ipl::bilinear (const Tf &fracX, const Tf &fracY, const Tv &xy, const Tv &Xy, const Tv &xY, const Tv &XY)
template<class Tf2 , class Tv >
Tv	al::ipl::bilinear (const Tf2 &f, const Tv &xy, const Tv &Xy, const Tv &xY, const Tv &XY)
template<class Tf , class Tv >
Tv	al::ipl::trilinear (const Tf &fracX, const Tf &fracY, const Tf &fracZ, const Tv &xyz, const Tv &Xyz, const Tv &xYz, const Tv &XYz, const Tv &xyZ, const Tv &XyZ, const Tv &xYZ, const Tv &XYZ)
template<class Tf3 , class Tv >
Tv	al::ipl::trilinear (const Tf3 &f, const Tv &xyz, const Tv &Xyz, const Tv &xYz, const Tv &XYz, const Tv &xyZ, const Tv &XyZ, const Tv &xYZ, const Tv &XYZ)
	Trilinear interpolation between values on corners of a hexahedron. More...

Detailed Description

Function Documentation

aeq()

bool al::aeq ( float  a, float  b, int  maxULP = 10  )

inline

Return whether two floats are almost equal.

Parameters

[in]	a	first operand
[in]	b	second operand
[in]	maxULP	maximum "units in the last place"

Algorithm from Dawson, B. "Comparing floating point numbers", http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

Definition at line 544 of file al_Functions.hpp.

ampTodB()

template<class T >

T al::ampTodB ( const T &  amp )

inline

Convert amplitude to decibels

Definition at line 70 of file al_Functions.hpp.

atan2Fast()

template<class T >

TEM T al::atan2Fast	(	const T &	y,
		const T &	x
	)

Fast approximation to atan2().

Definition at line 584 of file al_Functions.hpp.

atLeast()

template<class T >

TEM T al::atLeast ( const T &  v, const T &  eps  )

inline

Returns value clipped ouside of range [-eps, eps]

Definition at line 580 of file al_Functions.hpp.

bezier() [1/2]

template<class Tf , class Tv >

Tv al::ipl::bezier ( Tf  frac, const Tv &  x2, const Tv &  x1, const Tv &  x0  )

inline

Bezier curve, 3-point quadratic.

'frac' [0, 1) is the value on the curve btw x2 and x0

Definition at line 225 of file al_Interpolation.hpp.

bezier() [2/2]

template<class Tf , class Tv >

Tv al::ipl::bezier ( Tf  frac, const Tv &  x3, const Tv &  x2, const Tv &  x1, const Tv &  x0  )

inline

Bezier curve, 4-point cubic.

'frac' [0, 1) is the value on the curve btw x3 and x0

Definition at line 242 of file al_Interpolation.hpp.

bilinear() [1/2]

template<class Tf , class Tv >

Tv al::ipl::bilinear ( const Tf &  fracX, const Tf &  fracY, const Tv &  xy, const Tv &  Xy, const Tv &  xY, const Tv &  XY  )

inline

Bilinear interpolation between values on corners of quadrilateral

Definition at line 182 of file al_Interpolation.hpp.

bilinear() [2/2]

template<class Tf2 , class Tv >

Tv al::ipl::bilinear ( const Tf2 &  f, const Tv &  xy, const Tv &  Xy, const Tv &  xY, const Tv &  XY  )

inline

Bilinear interpolation between values on corners of quadrilateral

Definition at line 191 of file al_Interpolation.hpp.

bitsSet()

uint32_t al::bitsSet ( uint32_t  v )

inline

Returns number of bits set to 1.

From "Bit Twiddling Hacks", http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel

Definition at line 600 of file al_Functions.hpp.

cardinalSpline()

template<class Tf , class Tv >

void al::ipl::cardinalSpline ( Tv *  w, const Tv *  x, const Tf &  f, double  b  )

inline

Compute weights for cubic cardinal spline.

Parameters

[out]	w	output weights
[in]	x	input domain values; spline in [x[1], x[2]]
[in]	f	fraction in [0,1]
[in]	b	smoothness parameter in [-1,1]; 1 = Catmull-Rom

Definition at line 258 of file al_Interpolation.hpp.

casteljau()

template<class Tf , class Tv >

Tv al::ipl::casteljau	(	const Tf &	frac,
		const Tv &	a,
		const Tv &	b,
		const Tv &	c,
		const Tv &	d
	)

de Casteljau algorithm for four point interpolation

Parameters

frac	Interpolation factor [0, 1]
a	First point
b	Second point
c	Third point
d	Fourth point

Definition at line 250 of file al_Interpolation.hpp.

ceil()

template<class T >

TEM T al::ceil ( const T &  val, const T &  step  )

inline

Returns floating point value rounded to next highest integer.

Definition at line 606 of file al_Functions.hpp.

ceilPow2()

uint32_t al::ceilPow2 ( uint32_t  value )

inline

Returns power of two ceiling of value.

This uses an algorithm devised by Sean Anderson, Sep. 2001. From "Bit Twiddling Hacks", http://graphics.stanford.edu/~seander/bithacks.html.

Definition at line 611 of file al_Functions.hpp.

clip() [1/2]

template<class T >

TEM T al::clip ( const T &  v, int &  clipFlag, const T &  hi, const T &  lo  )

inline

Returns value clipped to [lo, hi] and signifies clipping behavior.

clipFlag signifies if and where clipping occured. 0 means no clipping occured, -1 means clipping occured at the lower bound, and 1 means clipping at the upper bound.

Definition at line 629 of file al_Functions.hpp.

clip() [2/2]

template<class T >

TEM T al::clip ( const T &  value, const T &  hi = T(1), const T &  lo = T(0)  )

inline

Returns value clipped to [lo, hi]

Definition at line 621 of file al_Functions.hpp.

clipS()

template<class T >

TEM T al::clipS ( const T &  value, const T &  hi = T(1)  )

inline

Returns value clipped to [-hi, hi].

Definition at line 641 of file al_Functions.hpp.

cubic()

template<class Tf , class Tv >

Tv al::ipl::cubic ( Tf  frac, const Tv &  w, const Tv &  x, const Tv &  y, const Tv &  z  )

inline

Cubic interpolation.

This is a Cardinal spline with a tension of 0 (AKA a Catmull-Rom spline).

Definition at line 286 of file al_Interpolation.hpp.

cubic2()

template<class Tf , class Tv >

Tv al::ipl::cubic2 ( Tf  frac, const Tv &  w, const Tv &  x, const Tv &  y, const Tv &  z  )

inline

Cubic interpolation.

This is a Cardinal spline with a tension of -1.

Definition at line 321 of file al_Interpolation.hpp.

dBToAmp()

template<class T >

T al::dBToAmp ( const T &  db )

inline

Convert decibels to amplitude

Definition at line 143 of file al_Functions.hpp.

erf()

template<class T >

TEM T al::erf ( const T &  x )

inline

The Gauss error function or probability integral

See also

http://en.wikipedia.org/wiki/Error_function

http://en.wikipedia.org/wiki/Error_function

Definition at line 646 of file al_Functions.hpp.

even()

template<class T >

TEM bool al::even ( const T &  v )

inline

Returns whether or not an integer value is even.

Definition at line 643 of file al_Functions.hpp.

factorial()

uint32_t al::factorial ( uint32_t  n0to12 )

inline

Returns factorial. Argument must be less than or equal to 12.

Definition at line 654 of file al_Functions.hpp.

factorialSqrt()

double al::factorialSqrt ( int  v )

inline

Returns square root of factorial

Definition at line 656 of file al_Functions.hpp.

floor()

template<class T >

TEM T al::floor ( const T &  val, const T &  step  )

inline

Returns floor of floating point value.

Definition at line 663 of file al_Functions.hpp.

floorPow2()

uint32_t al::floorPow2 ( uint32_t  value )

inline

Returns power of two floor of value.

This uses an algorithm devised by Sean Anderson, Sep. 2001. From "Bit Twiddling Hacks", http://graphics.stanford.edu/~seander/bithacks.html.

Definition at line 668 of file al_Functions.hpp.

fold()

template<class T >

TEM T al::fold ( const T &  value, const T &  hi = T(1), const T &  lo = T(0)  )

inline

Returns value folded into [lo, hi].

For out-of-range values, the boundaries act like mirrors reflecting the value into the range. For an even number of periods out of the range this is identical to a wrap().

Definition at line 677 of file al_Functions.hpp.

foldOnce()

template<class T >

TEM T al::foldOnce ( const T &  value, const T &  hi = T(1), const T &  lo = T(0)  )

inline

Returns value folded into [lo, hi] one time.

Definition at line 684 of file al_Functions.hpp.

gaussian()

template<class T >

TEM T al::gaussian ( const T &  v )

inline

Returns e^(-v*v)

Definition at line 690 of file al_Functions.hpp.

gcd()

template<class T >

TEM T al::gcd	(	const T &	x,
		const T &	y
	)

Return greatest common divisor of two arguments

Definition at line 692 of file al_Functions.hpp.

gudermannian()

template<class T >

TEM T al::gudermannian

(

const T &

x

)

The Gudermannian function relates circular and hyperbolic functions without using complex numbers.

See also

http://en.wikipedia.org/wiki/Gudermannian_function

http://en.wikipedia.org/wiki/Gudermannian_function

Definition at line 698 of file al_Functions.hpp.

hermite()

template<class Tp , class Tv >

Tv al::ipl::hermite ( Tp  f, const Tv &  w, const Tv &  x, const Tv &  y, const Tv &  z, Tp  tension, Tp  bias  )

inline

Hermite interpolation

Definition at line 336 of file al_Interpolation.hpp.

lagrange()

template<class T >

void al::ipl::lagrange	(	T *	h,
		T	delay,
		int	order
	)

Computes FIR coefficients for Waring-Lagrange interpolation.

'h' are the FIR coefficients and should be of size ('order' + 1).
'delay' is a fractional delay in samples.
As order increases, this converges to sinc interpolation.

Definition at line 367 of file al_Interpolation.hpp.

lagrange1()

template<class T >

void al::ipl::lagrange1 ( T *  h, T  delay  )

inline

Optimized lagrange() for first order.

Definition at line 382 of file al_Interpolation.hpp.

lagrange2()

template<class T >

void al::ipl::lagrange2 ( T *  h, T  delay  )

inline

Optimized lagrange() for second order

Definition at line 388 of file al_Interpolation.hpp.

lagrange3()

template<class T >

void al::ipl::lagrange3 ( T *  h, T  delay  )

inline

Optimized lagrange() for third order

Definition at line 395 of file al_Interpolation.hpp.

laguerreL()

template<class T >

TEM T al::laguerreL	(	int	n,
		int	k,
		T	x
	)

Generalized Laguerre polynomial L{n,k}.

Parameters

[in]	n	degree, a non-negative integer
[in]	k	order
[in]	x	position http://en.wikipedia.org/wiki/Laguerre_polynomials

Definition at line 700 of file al_Functions.hpp.

legendreP()

template<class T >

TEM T al::legendreP	(	int	l,
		int	m,
		T	t
	)

Associated Legendre polynomial

P_l^m(cos(t)) = (-1)^{l+m} / (2^l l!) sin^m(t) (d/d cos(t))^{l+m} sin^{2l}(t)

Parameters

[in]	l	degree where l >= 0
[in]	m	order where 0 <= m <= l
[in]	t	angle in [0, pi]

http://comp.cs.ehime-u.ac.jp/~ogata/nac/index.html

Definition at line 834 of file al_Functions.hpp.

lessAbs()

template<class T >

TEM bool al::lessAbs ( const T &  v, const T &  eps = T(0.000001)  )

inline

Returns whether the absolute value is less than an epsilon.

Definition at line 838 of file al_Functions.hpp.

linear() [1/3]

template<class Tf , class Tv >

Tv al::ipl::linear ( Tf  frac, const Tv &  x, const Tv &  y  )

inline

Linear interpolation. Identical to first order Lagrange.

Definition at line 417 of file al_Interpolation.hpp.

linear() [2/3]

template<class Tf , class Tv >

Tv al::ipl::linear ( Tf  frac, const Tv &  x, const Tv &  y, const Tv &  z  )

inline

Linear interpolation between three elements

Definition at line 422 of file al_Interpolation.hpp.

linear() [3/3]

template<class Tf , class Tv >

void al::ipl::linear	(	Tv *	dst,
		const Tv *	xs,
		const Tv *	xp1s,
		int	len,
		const Tf &	frac
	)

Element-wise linear interpolation between two arrays of values

Definition at line 429 of file al_Interpolation.hpp.

linearCyclic()

template<class Tf , class Tv >

Tv al::ipl::linearCyclic ( Tf  frac, const Tv &  x, const Tv &  y, const Tv &  z  )

inline

Cyclic linear interpolation between three elements

Definition at line 434 of file al_Interpolation.hpp.

max()

template<typename T >

TEM T al::max ( const T &  v1, const T &  v2, const T &  v3  )

inline

Returns maximum of three values

Definition at line 840 of file al_Functions.hpp.

mean()

template<class T >

TEM T al::mean ( const T &  v1, const T &  v2  )

inline

Returns mean of two values

Definition at line 843 of file al_Functions.hpp.

min()

template<class T >

TEM T al::min ( const T &  v1, const T &  v2, const T &  v3  )

inline

Returns minimum of three values

Definition at line 844 of file al_Functions.hpp.

nearest()

template<class Tf , class Tv >

Tv al::ipl::nearest ( Tf  frac, const Tv &  x, const Tv &  y  )

inline

Nearest neighbor interpolation

Definition at line 444 of file al_Interpolation.hpp.

nearestDiv()

template<class T >

T al::nearestDiv ( T  of, T  to  )

inline

Returns nearest integer division of one value to another

Definition at line 288 of file al_Functions.hpp.

nextAfter()

template<class T >

TEM T al::nextAfter ( const T &  x, const T &  y  )

inline

Returns the next representable floating-point or integer value following x in the direction of y

Definition at line 863 of file al_Functions.hpp.

nextMultiple()

template<class T >

TEM T al::nextMultiple ( T  val, T  multiple  )

inline

Returns next largest value of 'val' that is a multiple of 'multiple'.

Definition at line 866 of file al_Functions.hpp.

numInt()

template<class T >

TEM T al::numInt ( const T &  v )

inline

Returns the number of digits in the integer portion

Definition at line 871 of file al_Functions.hpp.

odd()

template<class T >

TEM bool al::odd ( const T &  v )

inline

Returns whether or not an integer value is odd.

Definition at line 873 of file al_Functions.hpp.

poly() [1/2]

template<class T >

TEM T al::poly ( const T &  x, const T &  a0, const T &  a1, const T &  a2  )

inline

Evaluates polynomial a0 + a1 x + a2 x^2

Definition at line 875 of file al_Functions.hpp.

poly() [2/2]

template<class T >

T al::poly	(	const T &	x,
		const T &	a0,
		const T &	a1,
		const T &	a2,
		const T &	a3
	)

Evaluates polynomial a0 + a1 x + a2 x^2 + a3 x^3

powN()

template<class T >

TEM T al::powN ( T  base, unsigned  power  )

inline

Returns value to a positive integer power.

Parameters

[in]	base	the base value to exponentiate
[in]	power	the power to exponentiate by

Definition at line 893 of file al_Functions.hpp.

prime()

uint8_t al::prime ( uint32_t  n )

inline

Returns (n+1)th prime number up to n=53.

Definition at line 923 of file al_Functions.hpp.

rotatePlane()

template<class VecN , class T >

void al::rotatePlane	(	VecN &	v1,
		VecN &	v2,
		const Complex< T > &	a
	)

Rotates two vectors by angle in plane formed from bivector v1 ^ v2

Definition at line 321 of file al_Complex.hpp.

round() [1/2]

template<class T >

TEM T al::round ( const T &  v, const T &  step  )

inline

Returns value rounded to nearest integer multiple of 'step' towards zero.

Definition at line 925 of file al_Functions.hpp.

round() [2/2]

template<class T >

TEM T al::round ( const T &  v, const T &  step, const T &  recStep  )

inline

Returns value rounded to nearest integer multiple of 'step' towards zero. Faster version to avoid 1/step divide.

Definition at line 926 of file al_Functions.hpp.

roundAway() [1/2]

template<class T >

TEM T al::roundAway ( const T &  v )

inline

Returns value rounded to nearest integer away from zero.

Definition at line 929 of file al_Functions.hpp.

roundAway() [2/2]

template<class T >

TEM T al::roundAway ( const T &  v, const T &  step  )

inline

Returns value rounded to nearest to nearest integer multiple of 'step' away from zero.

Definition at line 932 of file al_Functions.hpp.

sgn()

template<class T >

TEM T al::sgn ( const T &  v, const T &  norm = T(1)  )

inline

Signum function for real numbers

Definition at line 936 of file al_Functions.hpp.

sinc()

template<class T >

TEM T al::sinc ( const T &  radians, const T &  eps = T(0.0001)  )

inline

Unnormalized sinc function

Definition at line 940 of file al_Functions.hpp.

slope()

template<class T >

TEM T al::slope ( const T &  x1, const T &  y1, const T &  x2, const T &  y2  )

inline

Returns slope of line passing through two points.

Definition at line 944 of file al_Functions.hpp.

sort()

template<class T >

TEM void al::sort ( T &  value1, T &  value2  )

inline

Sort values so that value1 <= value2.

Definition at line 948 of file al_Functions.hpp.

sterProj()

template<class Vec3 , class T >

Vec3 al::sterProj

(

const al::Complex< T > &

c

)

Stereographically project complex number onto Riemann sphere

Definition at line 331 of file al_Complex.hpp.

sumOfSquares()

template<class T >

TEM T al::sumOfSquares ( T  n )

inline

Sum of integers squared from 1 to n.

Definition at line 956 of file al_Functions.hpp.

trailingZeroes()

uint32_t al::trailingZeroes ( uint32_t  v )

inline

Returns number of trailing zeros in 32-bit int.

This implements an algorithm from the paper "Using de Bruijn Sequences to Index 1 in a Computer Word" by Charles E. Leiserson, Harald Prokof, and Keith H. Randall.

Definition at line 962 of file al_Functions.hpp.

trilinear() [1/2]

template<class Tf , class Tv >

Tv al::ipl::trilinear ( const Tf &  fracX, const Tf &  fracY, const Tf &  fracZ, const Tv &  xyz, const Tv &  Xyz, const Tv &  xYz, const Tv &  XYz, const Tv &  xyZ, const Tv &  XyZ, const Tv &  xYZ, const Tv &  XYZ  )

inline

Trilinear interpolation between values on corners of a hexahedron

Definition at line 200 of file al_Interpolation.hpp.

trilinear() [2/2]

template<class Tf3 , class Tv >

Tv al::ipl::trilinear ( const Tf3 &  f, const Tv &  xyz, const Tv &  Xyz, const Tv &  xYz, const Tv &  XYz, const Tv &  xyZ, const Tv &  XyZ, const Tv &  xYZ, const Tv &  XYZ  )

inline

Trilinear interpolation between values on corners of a hexahedron.

Parameters

[in]

f

3 element array of fractions along x, y, and z

Definition at line 214 of file al_Interpolation.hpp.

trunc() [1/2]

template<class T >

TEM T al::trunc ( const T &  v, const T &  step  )

inline

Truncates floating point value to step.

Definition at line 964 of file al_Functions.hpp.

trunc() [2/2]

template<class T >

TEM T al::trunc ( const T &  v, const T &  step, const T &  recStep  )

inline

Truncates floating point value to step. Faster version to avoid 1/step divide.

Definition at line 965 of file al_Functions.hpp.

within()

template<class T >

TEM bool al::within ( const T &  v, const T &  lo, const T &  hi  )

inline

Returns whether value is in interval [lo, hi].

Definition at line 969 of file al_Functions.hpp.

within3()

template<class T >

TEM bool al::within3 ( const T &  v1, const T &  v2, const T &  v3, const T &  lo, const T &  hi  )

inline

Returns whether 3 values are in interval [lo, hi].

Definition at line 976 of file al_Functions.hpp.

withinIE()

template<class T >

TEM bool al::withinIE ( const T &  v, const T &  lo, const T &  hi  )

inline

Returns whether value is in interval [lo, hi).

Definition at line 972 of file al_Functions.hpp.

wrap() [1/2]

template<class T >

TEM T al::wrap ( const T &  value, const T &  hi = T(1), const T &  lo = T(0)  )

inline

Returns value wrapped in [lo, hi).

Definition at line 983 of file al_Functions.hpp.

wrap() [2/2]

template<class T >

TEM T al::wrap ( const T &  value, long &  numWraps, const T &  hi = T(1), const T &  lo = T(0)  )

inline

Returns value wrapped in [lo, hi).

'numWraps' reports how many wrappings occured where the sign, + or -, signifies above 'hi' or below 'lo', respectively.

Definition at line 1005 of file al_Functions.hpp.

wrapAdd1()

template<class T >

T al::wrapAdd1	(	const T &	v,
		const T &	max
	)

Returns value incremented by 1 and wrapped into interval [0, max).

Definition at line 479 of file al_Functions.hpp.

wrapOnce()

template<class T >

TEM T al::wrapOnce ( const T &  value, const T &  hi = T(1)  )

inline

Like wrap(), but only adds or subtracts 'hi' once from value.

Definition at line 1033 of file al_Functions.hpp.

wrapPhase()

template<class T >

TEM T al::wrapPhase ( const T &  radians )

inline

Returns value wrapped in [-pi, pi)

Definition at line 1049 of file al_Functions.hpp.

wrapPhaseOnce()

template<class T >

TEM T al::wrapPhaseOnce ( const T &  radians )

inline

Like wrapPhase(), but only wraps once

Definition at line 1065 of file al_Functions.hpp.