HalfIntegers

This package provides data types for half-integer numbers. Here, any number n/2 where n is an integer is considered a half-integer – contrary to the common definition, n does not have to be odd, i.e., the integers are a subset of the half-integers.

For example, the HalfInt type provided by this package can be used to represent numbers n/2 where n is an Int. Likewise, there exist half-integer types for all of Julia’s signed and unsigned integer types, e.g., HalfInt8, HalfUInt128, and BigHalfInt for arbitrarily large half-integers. All half-integer types are subtypes of the abstract type HalfInteger.

HalfIntegers.jl is compatible with Julia ≥ 1.0. It can be installed by typing

] add HalfIntegers

in the Julia REPL or via

using Pkg; Pkg.add("HalfIntegers")

HalfIntegers can be created from any other number type by using constructors or convert:

julia> HalfInt(-2.5)
-5/2

julia> convert(HalfUInt16, 7//2)
7/2

julia> BigHalfInt(2)
2

Another way of creating an HalfInteger is the half function:

julia> half(11)
11/2

julia> half(HalfInt8, -3)
-3/2

HalfInteger types support all standard arithmetic operations. Furthermore, this package defines the function twice. For any number x, the function twice returns the number 2x. For HalfInteger types, it returns an Integer type.

julia> twice(1.5)
3.0

julia> twice(HalfInt64(1.5))
3

julia> typeof(ans)
Int64

All concrete half-integer types provided by this package are actually just aliases for Half{T} with a specific T:

julia> typeof(HalfInt64(1/2))
Half{Int64}

The type Half{T} accepts arbitrary <:Integer types as parameter. It can be used to define half-integers based on other (non-standard) integers. For example, since HalfInt etc. are based on standard integer arithmetic, they are subject to integer overflow. If you prefer checked arithmetic, you can use the SaferIntegers package and use Half{SafeInt} instead of HalfInt.

• FixedPointNumbers.jl implements numbers with a fixed number of fraction bits. Thus, the Fixed{Int,1} type from FixedPointNumbers can be considered equivalent to the HalfInt type from this package. However, the types behave differently in some ways. For example, multiplying two Fixed{T,f} numbers results in another Fixed{T,f} number, whereas multiplying two HalfIntegers results in a floating-point number.