Julia types that represent the numbers zero and one.
Author perrutquist
5 Stars
Updated Last
1 Year Ago
Started In
March 2017


Build Status

This module provides singular datatypes named Zero and One. All instances of each datatype are identical, and represent the values zero and one, respectively. This is a light-weight alternative to StaticNumbers.jl when only these two values are needed.

Zero and One are subtypes of Integer. The most common operations, such as +, -, *, /, <, >, etc. are defined. Operations like * propagate the Zero or One type to their return values in a way that is correct for numbers, but not for IEEE 754 Inf and NaN. For example, Zero()*x reduces to Zero() at compile-time which has the effect that Zero()*Inf becomes Zero() rather than NaN. A value with this behaviour is sometimes referred to as a "strong zero".

Since the value of a Zero or One is known at compile-time, the complier might be able to make optimisations that might not be possible otherwise.

With Julia v1.3 and later, the Unicode symbols ๐ŸŽ and ๐Ÿ can be used as aliases for Zero() and One(). These can be entered from the keyboard as \bfzero or \bfone followed by a tab. (User beware: Depending on the font used, it might be hard to tell the difference between these symbols and the numbers 0 and 1.)

Trying to convert a nonzero value to Zero will throw an InexactError.

Attempting to divide by Zero() will throw a DivideError rather than returning Inf or NaN. (A compile-time zero in the denominator is usually a sign that a piece of code needs to be re-written to work optimally.)

The testzero function can be used to change the type when a variable is equal to zero. For example foo(testzero(a), b) will call foo(a,b) if a is nonzero. But if a is zero, then it will call foo(Zero(),b) instead. The function foo will then be complied specifically for input of the type Zero and this might result in speed-ups that outweigh the cost of branching.

The command

Zeros.@pirate Base

can be used to enable a few more (rarely needed) method definitions, such as +() (the sum of zero terms) and *() (the product of zero factors).

Required Packages

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