Infinitable

Infinitable is a simple library for introducing the notion of "infinity" and "negative infinity" to numeric types, such as integers, that do not have infinite values.

A representation of infinity is useful for graph algorithms such as Dijkstra's algorithm, as well as for representing a graph with an adjacency matrix.

Usage

Simply copy infinitable.h and include it in your program:

#include <iostream>
#include <cassert>
#include "infinitable.h"

int main() {
	infinitable<int> finite = infinitable<int>(5);
	infinitable<int> infinity = infinitable<int>::inf();
	infinitable<int> negative_infinity = infinitable<int>::neginf();

	assert(finite < infinity);
	assert(finite > negative_infinity);
	assert(infinity == infinity - finite);
	assert(infinity == finite * infinity);

	return 0;
}

Tests

Tests are in InfinitableTest.cpp and use CppUnit. In addition, the usage example in this README also serves as a fully executable test.

On a Unix-like system with the CppUnit library installed, simply run make test to run the tests.

Arithmetic Operations

Arithmetic operations behave as described in the following tables.

Addition

LHS	RHS	Result
Finite	Finite	Finite (add values)
Finite	inf	inf
Finite	neginf	neginf
inf	Finite	inf
inf	inf	inf
inf	neginf	Undefined (std::domain_error)
neginf	Finite	neginf
neginf	inf	Undefined (std::domain_error)
neginf	neginf	neginf

Subtraction

LHS	RHS	Result
Finite	Finite	Finite (subtract values)
Finite	inf	neginf
Finite	neginf	inf
inf	Finite	inf
inf	inf	Undefined (std::domain_error)
inf	neginf	inf
neginf	Finite	neginf
neginf	inf	neginf
neginf	neginf	Undefined (std::domain_error)

Multiplication

In the following table, "0" is the result of value-initializing the underlying type (T()), which generally represents zero for numeric types. The notation "~ 0" refers to a value that is neither less than nor greater than that value.

LHS	RHS	Result
Finite	Finite	Finite (multiply values)
Finite (> 0)	inf	inf
Finite (~ 0)	inf	Undefined (std::domain_error)
Finite (< 0)	inf	neginf
Finite (> 0)	neginf	neginf
Finite (~ 0)	neginf	Undefined (std::domain_error)
Finite (< 0)	neginf	inf
inf	Finite (> 0)	inf
inf	Finite (~ 0)	Undefined (std::domain_error)
inf	Finite (< 0)	neginf
inf	inf	inf
inf	neginf	neginf
neginf	Finite (> 0)	neginf
neginf	Finite (~ 0)	Undefined (std::domain_error)
neginf	Finite (< 0)	inf
neginf	inf	neginf
neginf	neginf	inf

Division

In the following table, "0" is the result of value-initializing the underlying type (T()), which generally represents zero for numeric types. The notation "<> 0" refers to a value that is either less than or greater than that value, "~ 0" refers to a value that is neither.

LHS	RHS	Result
Finite (> 0)	Finite (~ 0)	inf
Finite (~ 0)	Finite (~ 0)	Undefined (std::domain_error)
Finite (< 0)	Finite (~ 0)	neginf
Finite	Finite (<> 0)	Finite (divide values)
Finite	inf	0
Finite	neginf	0
inf	Finite (> 0)	inf
inf	Finite (~ 0)	inf
inf	Finite (< 0)	neginf
inf	inf	Undefined (std::domain_error)
inf	neginf	Undefined (std::domain_error)
neginf	Finite (> 0)	neginf
neginf	Finite (~ 0)	neginf
neginf	Finite (< 0)	inf
neginf	inf	Undefined (std::domain_error)
neginf	neginf	Undefined (std::domain_error)

Negation

Operand	Result
Finite	Finite (negate value)
inf	neginf
neginf	inf

Note About Floating-Point Numbers

Infinitable does not account for existing infinite values in floating-point numeric types. The infinity provided by Infinitable compares greater than all existing values, and the negative infinity provided by Infinitable compares less than all existing values.

To illustrate, here are some values listed from least to greatest:

• Infinitable neginf()
• Floating-point negative infinity
• Floating-point zero
• Floating-point infinity
• Infinitable inf()

Similarly, any existing infinite values are treated as "finite" values for the purposes of arithmetic operations.

License

Infinitable is available under the 2-clause BSD license. The header file includes the license text so simply preserving the text there will suffice for source distributions. For binary (non-source) distributions, a separate license text is provided in LICENSE.txt for convenience (although either text may be used).