SignType.jl

This package provides the Sign type, which represents the sign bit of a signed integer or float. While the data stored by Sign is identical to that of Bool, the arithmetic semantics are defined to match the behaviors of the real numbers +1 and -1. The logical semantics of Sign match those of the underlying Boolean representation.

Construction

A Sign can be constructed from a Real number, extracting its signbit and converting it to a Sign through reinterpretation: Sign(x::Real) = reinterpret(Sign, signbit(x)). For any custom numeric type that uses a different convention to represent sign, this method should be defined for that type.

The + and - operators are also accepted as arguments, resulting in the canonical printed representations Sign(+) or Sign(-).

Calling Sign with a Bool, Unsigned, or any other type which cannot represent negative numbers always returns Sign(+). Use reinterpret(::Type{Bool}, ::Sign) to treat a Sign as a Bool.

Zero elements

Zero elements are treated specially, since Sign cannot represent zero:

• Calling the Sign constructor on a zero element returns the Sign that would be constructed for the signbit.
• Calling convert(Sign, x) for a zero element x fails with an InexactError.
• zero(::Sign) returns false.

Arithmetic

All arithmetic operations defined on Integer are defined on Sign. Like Bool, addition or subtraction of Sign instances (or Sign and Bool instances) results in an Int.

Rational division of Sign instances returns a Sign, as Rational{Sign} can only represent the exact same range of values as Sign.

Logic

The logical operations defined on Sign treat Sign(+) and Sign(-) as their reinterpreted Boolean values false and true, respectively.

Other number systems

Sign construction will fail on elements of unordered fields, such as Complex instances. However, it may still work if the value of the input is a real number.