Bias/Profil

Classes
class	INTERVAL
	This page only reports the modifications brought to the INTERVAL class. More...
class	INTERVAL_MATRIX
	This page only reports the modifications brought to the INTERVAL_MATRIX class. More...
class	INTERVAL_VECTOR
	This page only reports the modifications brought to the INTERVAL_VECTOR class. More...
Functions
INTERVAL	Tan (CONST INTERVAL &x)
INTERVAL	ArcSin (CONST INTERVAL &x)
INTERVAL	ArcCos (CONST INTERVAL &x)
INTERVAL	ArcTan2 (const INTERVAL &x, const INTERVAL &y)
INTERVAL	Sinh (CONST INTERVAL &x)
INTERVAL	Tanh (CONST INTERVAL &x)
INTERVAL	ArCosh (CONST INTERVAL &x)
INTERVAL	ArTanh (CONST INTERVAL &x)
INTERVAL	Log (CONST INTERVAL &x)
INTERVAL	Sqrt (CONST INTERVAL &x)
INTERVAL	Root (CONST INTERVAL &x, INT n)
bool	_GT (REAL x, REAL y)
bool	_GE (REAL x, REAL y)
bool	_LT (REAL x, REAL y)
bool	_LE (REAL x, REAL y)
INTERVAL	operator & (CONST INTERVAL &x, CONST INTERVAL &y)
INTERVAL	operator* (REAL x, CONST INTERVAL &y)
INTERVAL	operator* (CONST INTERVAL &x, REAL y)
INTERVAL	operator* (CONST INTERVAL &x, CONST INTERVAL &y)
INTERVAL	operator/ (REAL x, CONST INTERVAL &y)
INTERVAL	operator/ (CONST INTERVAL &x, REAL y)
INTERVAL	operator/ (CONST INTERVAL &x, CONST INTERVAL &y)
INTERVAL	Max (const INTERVAL &x, const INTERVAL &y)
INTERVAL	Min (const INTERVAL &x, const INTERVAL &y)
INTERVAL	Sign (const INTERVAL &x)

---

Function Documentation

INTERVAL Tan

(

CONST INTERVAL &

x

)

Compute tan(x)

Note:

In original Bias/Profil bug: Tan(0,x) yields (Tan(0),Tan(x)) even if x is greater than Pi/2.

INTERVAL ArcSin

(

CONST INTERVAL &

x

)

Compute arcsin(x).

Note:

In original Bias/Profil, bounds that exceed -1 or 1 are not allowed.
In original Bias/Profil, if 1 belongs to x, Pi/2 does not belong to the result (outwarding fails).
The result of this method may be empty.

INTERVAL ArcCos

(

CONST INTERVAL &

x

)

Compute arccos(x).

Note:

In original Bias/Profil, bounds that exceed -1 or 1 are not allowed.
In original Bias/Profil, if -1 belongs to x, Pi does not belong to the result (outwarding fails).
The result of this method may be empty.

INTERVAL ArcTan2	(	const INTERVAL &	x,
		const INTERVAL &	y
	)

Author:

Firas Khemane

Date:

Feb 2010

INTERVAL Sinh

(

CONST INTERVAL &

x

)

Compute arcsin(x).

Note:

In original Bias/Profil, bounds that exceed -1 or 1 are not allowed.
In Bias/Profil, if 1 belongs to x, Pi/2 does not belong to the result (outwarding fails).
The result of this method may be empty.

INTERVAL Tanh

(

CONST INTERVAL &

x

)

Compute tanh(x)

Note:

In original Bias/Profil, Tanh([-inf,inf]) raises a division by zero exception.

INTERVAL ArCosh

(

CONST INTERVAL &

x

)

Compute arccosh(x).

Note:

In original Bias/Profil, bounds lower than 1 are not allowed.
The result of this method may be empty.

INTERVAL ArTanh

(

CONST INTERVAL &

x

)

Compute arctanh(x).

Note:

In original Bias/Profil, bounds that exceed -1 or 1 are not allowed and infinite bounds are not handled properly.
The result of this method may be empty.

INTERVAL Log

(

CONST INTERVAL &

x

)

Compute the Neperian logarithm of x.

Note:

In original Bias/Profil, negative bounds are not allowed.
The result of this method may be empty.

INTERVAL Sqrt

(

CONST INTERVAL &

x

)

Compute sqrt(x)

Note:

In original Bias/Profil, negative bounds are not allowed.
The result of this method may be empty.

INTERVAL Root	(	CONST INTERVAL &	x,
		INT	n
	)

Compute the expon-th root of x.

Note:

In original Bias/Profil, negative bounds are not allowed (which is even a bug for even root) and Root([0,0]) does not provide the expected result.
The result of this method may be empty.

bool _GT	(	REAL	x,
		REAL	y
	)			[inline]

Return true if x is greater than y.

Note:

See the infinite bound section for conventions with infinite bounds.

bool _GE	(	REAL	x,
		REAL	y
	)			[inline]

Return true if x is greater than or equals y.

bool _LT	(	REAL	x,
		REAL	y
	)			[inline]

Return true if x is lower than y.

bool _LE	(	REAL	x,
		REAL	y
	)			[inline]

Return true if x is lower than or equals y.

INTERVAL operator &	(	CONST INTERVAL &	x,
		CONST INTERVAL &	y
	)			[inline]

Return the intersection of x and y.

Returns:

INTERVAL::EMPTY if the intersection is empty.

INTERVAL operator*	(	REAL	x,
		CONST INTERVAL &	y
	)			[inline]

Multiply a real by an interval.

INTERVAL operator*	(	CONST INTERVAL &	x,
		REAL	y
	)			[inline]

Multiply an interval by a real.

INTERVAL operator*	(	CONST INTERVAL &	x,
		CONST INTERVAL &	y
	)			[inline]

Multiply two intervals.

Returns:

x * y.

Note:

Some situations where Bias/Profil may fail (underscore stands for any value):

• [0,0] * [-inf,_]
• [0,0] * [_,inf]
• [-inf,_] * [_,0]
• [_,inf] * [_,0]
• [-0,_] * [_,inf]
• [inf([0,0])*-1,1] * [1,inf]

• [inf([0,0])*-1,1] * [-inf,1]

Warning:

This modified operator is certainly not well optimized yet.

INTERVAL operator/	(	REAL	x,
		CONST INTERVAL &	y
	)			[inline]

Divide a real by an interval. See operator/(const INTERVAL &, const INTERVAL &)

INTERVAL operator/	(	CONST INTERVAL &	x,
		REAL	y
	)			[inline]

Divide an interval by a real. See operator/(const INTERVAL &, const INTERVAL &)

INTERVAL operator/	(	CONST INTERVAL &	x,
		CONST INTERVAL &	y
	)			[inline]

Divide two intervals.

Returns:

an interval enclosure of x / y.

Note:

Contrary to the cset theory, the result is empty if y=[0,0] (whatever x is).
The semantics behind infinite bounds rather conforms to the actual C++ standardization proposal. This means that an infinite bound is actually an open bound.

See also:

operator* where examples of failure cases are given.

Warning:

This modified operator is certainly not well optimized yet.

INTERVAL Max	(	const INTERVAL &	x,
		const INTERVAL &	y
	)			[inline]

Returns the maximum of two intervals, i.e.,

INTERVAL Min	(	const INTERVAL &	x,
		const INTERVAL &	y
	)			[inline]

Returns the minimum of two intervals, i.e.,

INTERVAL Sign

(

const INTERVAL &

x

)

[inline]

Returns the sign of an interval, i.e., .

Remarks:

By convention,