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)
2Another way of creating an HalfInteger is the half function:
julia> half(11)
11/2
julia> half(HalfInt8, -3)
-3/2HalfInteger 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)
Int64All 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 fromFixedPointNumberscan be considered equivalent to theHalfInttype from this package. However, the types behave differently in some ways. For example, multiplying twoFixed{T,f}numbers results in anotherFixed{T,f}number, whereas multiplying twoHalfIntegers results in a floating-point number.
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