Implement more base methods (#121)

* Add methods implemented in complex.jl

* Add tests

* Add round to docs

* Increment patch version number

* Avoid line wrapping

Project.toml

@@ -1,6 +1,6 @@
 name = "Quaternions"
 uuid = "94ee1d12-ae83-5a48-8b1c-48b8ff168ae0"
-version = "0.7.1"
+version = "0.7.2"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

docs/src/api.md

@@ -18,6 +18,10 @@ real(::Type{Quaternion{T}}) where {T}
 imag_part
 ```
 
+```@docs
+round(::Quaternion)
+```
+
 ```@docs
 conj
 ```

src/Quaternion.jl

@@ -147,6 +147,7 @@ Base.isfinite(q::Quaternion) = isfinite(q.s) & isfinite(q.v1) & isfinite(q.v2) &
 Base.iszero(q::Quaternion) = iszero(real(q)) & iszero(q.v1) & iszero(q.v2) & iszero(q.v3)
 Base.isnan(q::Quaternion) = isnan(real(q)) | isnan(q.v1) | isnan(q.v2) | isnan(q.v3)
 Base.isinf(q::Quaternion) = isinf(q.s) | isinf(q.v1) | isinf(q.v2) | isinf(q.v3)
+Base.isinteger(q::Quaternion) = isinteger(real(q)) & isreal(q)
 
 # included strictly for documentation; the base implementation is sufficient
 """
@@ -384,3 +385,59 @@ LinearAlgebra.lyap(a::Quaternion, c::Quaternion) = lyap(promote(a, c)...)
 # if a commutes with c, use a simpler expression
 LinearAlgebra.lyap(a::Real, c::Quaternion) = c / -2a
 LinearAlgebra.lyap(a::Quaternion, c::Real) = c / -2real(a)
+
+Base.widen(::Type{Quaternion{T}}) where {T} = Quaternion{widen(T)}
+
+Base.flipsign(x::Quaternion, y::Real) = ifelse(signbit(y), -x, x)
+
+function Base.read(io::IO, ::Type{Quaternion{T}}) where T<:Real
+    return Quaternion{T}(ntuple(_ -> read(io, T), Val(4))...)
+end
+Base.write(io::IO, q::Quaternion) = write(io, real(q), imag_part(q)...)
+
+Base.big(::Type{Quaternion{T}}) where {T<:Real} = Quaternion{big(T)}
+Base.big(z::Quaternion{T}) where {T<:Real} = Quaternion{big(T)}(z)
+
+"""
+    round(q::Quaternion[, RoundingModeReal, [RoundingModeImaginary]]; kwargs...)
+    round(q::Quaternion, RoundingModeReal,
+          RoundingModeImaginary1, RoundingModeImaginary2, RoundingModeImaginary3; kwargs...)
+
+Return the nearest integral value of the same type as the quaternion-valued `q` to `q`,
+breaking ties using the specified `RoundingMode`s.
+
+The first `RoundingMode` is used for rounding the real part while the second is used
+for rounding the imaginary parts. Alternatively, a `RoundingMode` may be provided for each
+part.
+
+The `kwargs` are the same as those for `round(::Real[, RoundingMode]; kwargs...)`.
+
+# Example
+```jldoctest
+julia> round(quat(3.14, 4.5, 8.3, -2.8))
+QuaternionF64(3.0, 4.0, 8.0, -3.0)
+```
+"""
+function Base.round(
+    q::Quaternion,
+    rs::RoundingMode=RoundNearest,
+    rv::RoundingMode=rs;
+    kwargs...,
+)
+    return round(q, rs, rv, rv, rv; kwargs...)
+end
+function Base.round(
+    q::Quaternion,
+    rs::RoundingMode,
+    rv1::RoundingMode,
+    rv2::RoundingMode,
+    rv3::RoundingMode;
+    kwargs...,
+)
+    return Quaternion(
+        round(real(q), rs; kwargs...),
+        round(q.v1, rv1; kwargs...),
+        round(q.v2, rv2; kwargs...),
+        round(q.v3, rv3; kwargs...),
+    )
+end

test/Quaternion.jl

@@ -227,6 +227,14 @@ end
         @test isnan(Quaternion(1, 2, 3, NaN))
     end
 
+    @testset "isinteger" begin
+        @test isinteger(quat(3))
+        @test isinteger(quat(4.0))
+        @test !isinteger(quat(4.1))
+        @test !isinteger(quat(3, 1, 2, 3))
+        @test !isinteger(quat(4, 0, 1, 0))
+    end
+
     @testset "*" begin
         # verify basic correctness
         q1 = Quaternion(1,0,0,0)
@@ -571,4 +579,53 @@ end
             @test_throws DivideError lyap(null, null)
         end
     end
+
+    @testset "widen" begin
+        @test widen(Quaternion{Int}) === Quaternion{Int128}
+        @test widen(QuaternionF32) === QuaternionF64
+        @test widen(QuaternionF64) === Quaternion{BigFloat}
+        @test widen(quat(1, 2, 3, 4)) === Quaternion{Int128}(1, 2, 3, 4)
+        q = rand(QuaternionF32)
+        @test widen(q) == convert(QuaternionF64, q)
+        q = rand(QuaternionF64)
+        @test widen(q) == convert(Quaternion{BigFloat}, q)
+    end
+
+    @testset "flipsign" begin
+        q = rand(QuaternionF64)
+        @test flipsign(q, 2) == q
+        @test flipsign(q, -3) == -q
+    end
+
+    @testset "read/write" begin
+        @testset "$T" for T in (Int16, Float32, Float64)
+            io = IOBuffer(; read=true, write=true)
+            q = rand(Quaternion{T})
+            write(io, q)
+            seek(io, 0)
+            q2 = read(io, Quaternion{T})
+            @test q == q2
+        end
+    end
+
+    @testset "big" begin
+        @test big(Quaternion{Int}) === Quaternion{BigInt}
+        @test big(QuaternionF64) === Quaternion{BigFloat}
+        @test big(quat(1, 2, 3, 4)) == Quaternion{BigInt}(1, 2, 3, 4)
+        q = rand(QuaternionF64)
+        @test big(q) == convert(Quaternion{BigFloat}, q)
+    end
+
+    @testset "round" begin
+        q = quat(1.1, 2.5, -3.5, 2.3)
+        @test round(q) == quat(1.0, 2.0, -4.0, 2.0)
+        @test round(q; digits=1) == q
+        @test round(q, RoundUp) == quat(2.0, 3.0, -3.0, 3.0)
+        @test round(q, RoundUp; digits=1) == q
+        @test round(q, RoundUp, RoundToZero) == quat(2.0, 2.0, -3.0, 2.0)
+        @test round(q, RoundUp, RoundToZero; digits=1) == q
+        rmodes = (RoundUp, RoundDown, RoundNearestTiesAway, RoundToZero)
+        @test round(q, rmodes...) == quat(2.0, 2.0, -4.0, 2.0)
+        @test round(q, rmodes...; digits=1) == q
+    end
 end