Description of interval

interval<Tnum>		Programmers Guide
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Category:intervals,containers

Component type:type

Description

A number type which implements interval arithmetic. Evaluation of an operation performed on an interval will calculate the upper and lower bounds of a set of numbers. Within this set one can be certain that the answer lies. Interval operations round an interval "outward" (rounding the lower bound down and the upper bound up) to ensure that the exact answer will be within the interval returned.

For example:
On a machine with very limited precision, If an interval A bounded by 2.0 and 3.0 were added to an interval B bounded by 1.0 and 2.0, the sum (after outward rounding) may be an interval bounded by 3.01 and 5.01.
Or, in code:

interval A(2.0,3.0), B(1.0,2.0); cout << A+B;

may return [3.01,5.01].
When output to a character stream, intervals are expressed in the form [x,y] where x is the lower (or left) bound and y is the upper (right) bound.

Example

In construct.cc:

  interval<double> normal(1,2);
  interval<double> single(1);
  interval<double> exact(1,2,true);
  interval<double> copy_interval(normal);

Definition

interval.h

Template Parameters

Model of

Members

Member	Where defined	Description
`value_type`
`interval (const Tnum& le, const Tnum& ri,bool exact)`		Exact constructor (no outward rounding)
`interval (const Tnum& le, const Tnum& ri)`		Normal constructur
`interval (const Tnum& x = Tnum())`		Default constructor/ Single Tnum constructor
`interval (const self&)`
`template <class X> interval (const interval<X>&)`
`const Tnum& left () const`		Constant accessor for the lower bound of an interval
`const Tnum& right () const`		Constant accessor for the upper bound of an interval
`Tnum& left (void)`		Accessor for the lower bound of an interval
`Tnum& right (void)`		Accessor for the upper bound of an interval
`const Tnum& inf () const`		Alternate constant accessor for the lower bound of an interval
`const Tnum& sup () const`		Alternate constant accessor for the upper bound of an interval
`Tnum& inf (void)`		Alternate accessor for the lower bound of an interval
`Tnum& sup (void)`		Alternate accessor for the upper bound of an interval
`self& operator= (const Tnum&)`
`self& operator+= (const Tnum&)`
`self& operator-= (const Tnum&)`
`self& operator*= (const Tnum&)`
`self& operator/= (const Tnum&)`
`self& operator= (const self& x)`
`template <class X> interval<X>& operator= (const interval<X>& x)`
`template <class X> interval<X>& operator+= (const interval<X>& x)`
`template <class X> interval<X>& operator-= (const interval<X>& x)`
`template <class X> interval<X>& operator*= (const interval<X>& x)`
`template <class X> interval<X>& operator/= (const interval<X>& x)`
`self& operator ()`
`self operator (int)`
`self& operator-- ()`
`self operator-- (int)`
`static void rounddown ()`		sets the floating point rounding mode to round up
`static void roundup ()`		sets the floating point rounding mode to round down
`static void roundnear ()`		sets rounding to nearest mode
`static self pi2 ()`		Returns an interval of the number pi*2, properly rounded outward.
`static self pi ()`		Returns an interval of pi, properly rounded outward.
`static self piby2 ()`		Returns an interval of the number (1/2)*pi, properly rounded outward.
`static self pi3by2 ()`		Returns an interval of the number (3/2)*pi, properly rounded outward.
`static self pi5by2 ()`		Returns an interval of the number (5/2)*pi, properly rounded outward.
`static Tnum epsilon ()`		Utility functions equivilant to numeric_limits functions
`static Tnum eta ()`
`static Tnum pos_inf ()`
`static Tnum neg_inf ()`
`static Tnum Nan ()`		Utility function to return a non-signaling NaN
`static int rdval, ruval, rnval`

New members

Notes

See also