interval.hh File Reference

The implementation of the class Interval and related functions. More...

#include <cmath>
#include "zone.hh"

Include dependency graph for interval.hh:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Classes
struct	Interval
	Class for an interval. More...

Functions
static Interval	operator&& (const Interval &left, const Interval &right)
	The intersection of two intervals.
static void	land (std::vector< std::shared_ptr< Interval >> &left, const Interval &right)
	The intersection of a set of intervals and an interval. More...
static void	land (std::vector< std::shared_ptr< Interval >> &left, const std::vector< std::shared_ptr< Interval >> &right)
	The intersection of two sets of intervals. More...
static Interval	operator+ (Interval left, const Interval &right)
	The sum of two intervals. The formal definition is as follows. More...
static void	operator+= (std::vector< std::shared_ptr< Interval >> &left, const std::vector< std::shared_ptr< Interval >> &right)
	The sum of two sets of intervals. More...
void	plus (std::vector< std::shared_ptr< Interval >> &intervals)
static std::ostream &	operator<< (std::ostream &stream, const Interval &interval)

Detailed Description

The implementation of the class Interval and related functions.

Author

Masaki Waga

Function Documentation

land() [1/2]

static void land ( std::vector< std::shared_ptr< Interval >> &  left, const Interval &  right  )

inlinestatic

The intersection of a set of intervals and an interval.

Note

This function is destructive.

Parameters

[in,out]	left	The set of intervals. We take intersection for each element of left and overwrite.
[in]	right	The interval.

We have the following relation between the input and the overwritten value of \(\texttt{left}\).

\[t \in \bigcup_{I \in \texttt{left}_{\mathrm{post}}} I \iff t \in \bigcup_{I \in \texttt{left}_{\mathrm{pre}}} (I \cap \texttt{right})\]

land() [2/2]

static void land ( std::vector< std::shared_ptr< Interval >> &  left, const std::vector< std::shared_ptr< Interval >> &  right  )

inlinestatic

The intersection of two sets of intervals.

Note

This function is destructive.

Parameters

[in,out]	left	The set of intervals. We take intersection for each element of left and overwrite.
[in]	right	A set of interval. This is not overwritten.

We have the following relation between the input and the overwritten value of \(\texttt{left}\).

\[t \in \bigcup_{I \in \texttt{left}_{\mathrm{post}}} I \iff t \in \bigcup_{I \in \texttt{left}_{\mathrm{pre}}, I' \in \texttt{right}} (I \cap I')\]

operator+()

static Interval operator+ ( Interval  left, const Interval &  right  )

inlinestatic

The sum of two intervals. The formal definition is as follows.

\[I + I' = \{t + t' \mid \exists t \in I, t' \in I'\}\]

operator+=()

static void operator+= ( std::vector< std::shared_ptr< Interval >> &  left, const std::vector< std::shared_ptr< Interval >> &  right  )

inlinestatic

The sum of two sets of intervals.

Note

This function is destructive.

Parameters

[in,out]	left	The set of intervals. We take sum for each element of left and overwrite.
[in]	right	A set of interval. This is not overwritten.

We have the following for any \(t \in \mathbb{R}\).

\[t \in \bigcup_{I \in \texttt{left}_{\mathrm{post}}} I \iff \exists t' \in \bigcup_{I \in \texttt{left}_{\mathrm{pre}}}, \exists t'' \in \bigcup_{I' \in \texttt{right}}. t = t' + t'' \]

plus()

void plus ( std::vector< std::shared_ptr< Interval >> &  intervals )

inline

Todo:

Optimization: We can use * - 0 instead of cup of +