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 and ๐ 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).