API documentation

Half{T<:Integer} <: HalfInteger

Type for half-integers $n/2$ where $n$ is of type T.

Aliases for Half{T} are defined for all standard Signed and Unsigned integer types, so that, e.g., HalfInt can be used instead of Half{Int}:

HalfInteger <: Real

Abstract supertype for half-integers. Here, every number $n/2$ where $n\in\mathbb{Z}$ is considered a half-integer, regardless of whether $n$ is even or odd.

checked_twice(x)

Calculate 2x, checking for overflow. (not exported)

Examples

julia> x = typemax(Int64)
9223372036854775807

julia> twice(x)
-2

julia> HalfIntegers.checked_twice(x)
ERROR: OverflowError: 9223372036854775807 + 9223372036854775807 overflowed for type Int64
Stacktrace:
[...]

half([T<:Complex{<:HalfInteger},] x)

For a complex value x with integer real and imaginary parts, return x/2 as a complex number of type T. If T is not given, return an appropriate complex number type with half-integer parts. Throw an InexactError if the real or the imaginary part of x are not integer.

Examples

julia> half(3 + 2im)
3/2 + 1*im

julia> half(Complex{HalfInt32}, 1.0 + 5.0im)
1/2 + 5/2*im

half([T<:HalfInteger,] x)

For an integer value x, return x/2 as a half-integer of type T. If T is not given, return an appropriate HalfInteger type. Throw an InexactError if x is not an integer.

Examples

julia> half(3)
3/2

julia> half(-5.0)
-5/2

julia> half(HalfInt16, 8)
4

ishalfinteger(x)

Test whether x is numerically equal to some half-integer.

Examples

julia> ishalfinteger(3.5)
true

julia> ishalfinteger(2)
true

julia> ishalfinteger(1//3)
false

ishalfodd(x)

Test whether x is numerically equal to some half-odd-integer, i.e., a number $n/2$ where $n$ is an odd integer.

Examples

julia> ishalfodd(3.5)
true

julia> ishalfodd(2)
false

julia> ishalfodd(1//3)
false

onehalf(x)

Return the value 1/2 in the type of x (x can also specify the type itself).

Examples

julia> onehalf(7//3)
1//2

julia> onehalf(HalfInt)
1/2

twice(x)

Return 2x. If x is a HalfInteger, return an appropriate integer type.

Examples

julia> twice(2)
4

julia> twice(1.5)
3.0

julia> twice(HalfInt8(3/2))  # returns an Int8
3

julia> twice(HalfInt32(3.0) + HalfInt32(2.5)*im)  # returns a Complex{Int32}
6 + 5im

twice(T<:Integer, x)
twice(T<:Complex{<:Integer}, x)

Return 2x as a number of type T.

Examples

julia> twice(Int16, HalfInt(5/2))
5

julia> twice(Complex{BigInt}, HalfInt(5/2) + HalfInt(3)*im)
5 + 6im