Remove norm field, normalize, and normalizea

src/Octonions.jl

@@ -4,14 +4,13 @@ import Base: +, -, *, /, ^, ==
 import Base: abs, abs2, conj, exp, inv, isreal, isfinite, isinf, iszero, isnan, log, real, sqrt
 import Base: promote_rule, float
 import Base: rand, randn
-import LinearAlgebra: normalize
 using Random
 
 Base.@irrational INV_SQRT_EIGHT 0.3535533905932737622004 sqrt(big(0.125))
 
 include("octonion.jl")
 
 export Octonion, OctonionF16, OctonionF32, OctonionF64
-export imag_part, normalize, normalizea, octo, octorand
+export imag_part, octo, octorand
 
 end # module

src/octonion.jl

@@ -7,16 +7,15 @@ struct Octonion{T<:Real} <: Number
   v5::T
   v6::T
   v7::T
-  norm::Bool
 end
 
 Octonion{T}(x::Real) where {T<:Real} = Octonion(convert(T, x))
 Octonion{T}(o::Octonion) where {T<:Real} =
-  Octonion{T}(o.s, o.v1, o.v2, o.v3, o.v4, o.v5, o.v6, o.v7, o.norm)
+  Octonion{T}(o.s, o.v1, o.v2, o.v3, o.v4, o.v5, o.v6, o.v7)
 
-Octonion(s::Real, v1::Real, v2::Real, v3::Real, v4::Real, v5::Real, v6::Real, v7::Real, n::Bool = false) =
-  Octonion(promote(s, v1, v2, v3, v4, v5, v6, v7)..., n)
-Octonion(x::Real) = Octonion(x, zero(x), zero(x), zero(x), zero(x), zero(x), zero(x), zero(x), abs(x) == one(x))
+Octonion(s::Real, v1::Real, v2::Real, v3::Real, v4::Real, v5::Real, v6::Real, v7::Real) =
+  Octonion(promote(s, v1, v2, v3, v4, v5, v6, v7)...)
+Octonion(x::Real) = Octonion(x, zero(x), zero(x), zero(x), zero(x), zero(x), zero(x), zero(x))
 Octonion(s::Real, a::Vector) = Octonion(s, a[1], a[2], a[3], a[4], a[5], a[6], a[7])
 Octonion(a::Vector) = Octonion(0, a[1], a[2], a[3], a[4], a[5], a[6], a[7])
 
@@ -28,7 +27,6 @@ promote_rule(::Type{Octonion{T}}, ::Type{S}) where {T <: Real, S <: Real} = Octo
 promote_rule(::Type{Octonion{T}}, ::Type{Octonion{S}}) where {T <: Real, S <: Real} = Octonion{promote_type(T, S)}
 
 octo(p, v1, v2, v3, v4, v5, v6, v7) = Octonion(p, v1, v2, v3, v4, v5, v6, v7)
-octo(p, v1, v2, v3, v4, v5, v6, v7, n) = Octonion(p, v1, v2, v3, v4, v5, v6, v7, n)
 octo(x) = Octonion(x)
 octo(s, a) = Octonion(s, a)
 
@@ -40,37 +38,20 @@ imag_part(o::Octonion) = (o.v1, o.v2, o.v3, o.v4, o.v5, o.v6, o.v7)
 (*)(o::Octonion, x::Real) = Octonion(o.s * x, o.v1 * x, o.v2 * x, o.v3 * x, o.v4 * x, o.v5 * x, o.v6 * x, o.v7 * x)
 (*)(x::Real, o::Octonion) = o * x
 
-conj(o::Octonion) = Octonion(o.s, -o.v1, -o.v2, -o.v3, -o.v4, -o.v5, -o.v6, -o.v7, o.norm)
+conj(o::Octonion) = Octonion(o.s, -o.v1, -o.v2, -o.v3, -o.v4, -o.v5, -o.v6, -o.v7)
 abs(o::Octonion) = sqrt(abs2(o))
 float(q::Octonion{T}) where T = convert(Octonion{float(T)}, q)
 abs_imag(o::Octonion) = sqrt((o.v4 * o.v4 + (o.v2 * o.v2 + o.v6 * o.v6)) + ((o.v1 * o.v1 + o.v5 * o.v5) + (o.v3 * o.v3 + o.v7 * o.v7))) # ordered to match abs2
 abs2(o::Octonion) = ((o.s * o.s + o.v4 * o.v4) + (o.v2 * o.v2 + o.v6 * o.v6)) + ((o.v1 * o.v1  + o.v5 * o.v5) + (o.v3 * o.v3 + o.v7 * o.v7))
-inv(o::Octonion) = o.norm ? conj(o) : conj(o) / abs2(o)
+inv(o::Octonion) = conj(o) / abs2(o)
 
 isreal(o::Octonion) = iszero(o.v1) & iszero(o.v2) & iszero(o.v3) & iszero(o.v4) & iszero(o.v5) & iszero(o.v6) & iszero(o.v7)
-isfinite(o::Octonion) = o.norm | (isfinite(real(o)) & isfinite(o.v1) & isfinite(o.v2) & isfinite(o.v3) & isfinite(o.v4) & isfinite(o.v5) & isfinite(o.v6) & isfinite(o.v7))
-iszero(o::Octonion) = ~o.norm & iszero(real(o)) & iszero(o.v1) & iszero(o.v2) & iszero(o.v3) & iszero(o.v4) & iszero(o.v5) & iszero(o.v6) & iszero(o.v7)
+isfinite(o::Octonion) = isfinite(real(o)) & isfinite(o.v1) & isfinite(o.v2) & isfinite(o.v3) & isfinite(o.v4) & isfinite(o.v5) & isfinite(o.v6) & isfinite(o.v7)
+iszero(o::Octonion) = iszero(real(o)) & iszero(o.v1) & iszero(o.v2) & iszero(o.v3) & iszero(o.v4) & iszero(o.v5) & iszero(o.v6) & iszero(o.v7)
 isnan(o::Octonion) = isnan(real(o)) | isnan(o.v1) | isnan(o.v2) | isnan(o.v3) | isnan(o.v4) | isnan(o.v5) | isnan(o.v6) | isnan(o.v7)
-isinf(o::Octonion) = ~o.norm & (isinf(real(o)) | isinf(o.v1) | isinf(o.v2) | isinf(o.v3) | isinf(o.v4) | isinf(o.v5) | isinf(o.v6) | isinf(o.v7))
+isinf(o::Octonion) = isinf(real(o)) | isinf(o.v1) | isinf(o.v2) | isinf(o.v3) | isinf(o.v4) | isinf(o.v5) | isinf(o.v6) | isinf(o.v7)
 
-function normalize(o::Octonion)
-  if (o.norm)
-    return o
-  end
-  o = o / abs(o)
-  Octonion(o.s, o.v1, o.v2, o.v3, o.v4, o.v5, o.v6, o.v7, true)
-end
-
-function normalizea(o::Octonion)
-  if (o.norm)
-    return (o, one(o.s))
-  end
-  a = abs(o)
-  o = o / a
-  (Octonion(o.s, o.v1, o.v2, o.v3, o.v4, o.v5, o.v6, o.v7, true), a)
-end
-
-(-)(o::Octonion) = Octonion(-o.s, -o.v1, -o.v2, -o.v3, -o.v4, -o.v5, -o.v6, -o.v7, o.norm)
+(-)(o::Octonion) = Octonion(-o.s, -o.v1, -o.v2, -o.v3, -o.v4, -o.v5, -o.v6, -o.v7)
 
 (+)(o::Octonion, w::Octonion) = Octonion(o.s + w.s,
                                             o.v1 + w.v1,
@@ -99,13 +80,13 @@ function (*)(o::Octonion, w::Octonion)
     v5 = ((o.s * w.v5 + o.v5 * w.s) + (o.v2 * w.v7 - o.v7 * w.v2)) + ((o.v1 * w.v6 - o.v6 * w.v1) + (o.v4 * w.v3 - o.v3 * w.v4))
     v6 = ((o.s * w.v6 + o.v6 * w.s) + (o.v3 * w.v7 - o.v7 * w.v3)) + ((o.v2 * w.v4 - o.v4 * w.v2) + (o.v5 * w.v1 - o.v1 * w.v5))
     v7 = ((o.s * w.v7 + o.v7 * w.s) + (o.v5 * w.v2 - o.v2 * w.v5)) + ((o.v4 * w.v1 - o.v1 * w.v4) + (o.v6 * w.v3 - o.v3 * w.v6))
-    return Octonion(s, v1, v2, v3, v4, v5, v6, v7, o.norm & w.norm)
+    return Octonion(s, v1, v2, v3, v4, v5, v6, v7)
 end
 
 (/)(o::Octonion, w::Octonion) = o * inv(w)
 
 (==)(q::Octonion, w::Octonion) = (q.s == w.s) & (q.v1 == w.v1) & (q.v2 == w.v2) & (q.v3 == w.v3) &
-                                 (q.v4 == w.v4) & (q.v5 == w.v5) & (q.v6 == w.v6) & (q.v7 == w.v7) # ignore .norm field
+                                 (q.v4 == w.v4) & (q.v5 == w.v5) & (q.v6 == w.v6) & (q.v7 == w.v7)
 
 function exp(o::Octonion)
   s = o.s
@@ -122,12 +103,12 @@ function exp(o::Octonion)
             scale * o.v4,
             scale * o.v5,
             scale * o.v6,
-            scale * o.v7,
-            abs(s) == 0)
+            scale * o.v7)
 end
 
 function log(o::Octonion)
-  o, a = normalizea(o)
+  a = abs(o)
+  o = o / a
   s = o.s
   M = abs_imag(o)
   th = atan(M, s)
@@ -157,7 +138,7 @@ octorand() = octo(randn(), randn(), randn(), randn(), randn(), randn(), randn(),
 
 function rand(rng::AbstractRNG, ::Random.SamplerType{Octonion{T}}) where {T<:Real}
   Octonion{T}(rand(rng, T), rand(rng, T), rand(rng, T), rand(rng, T),
-              rand(rng, T), rand(rng, T), rand(rng, T), rand(rng, T), false)
+              rand(rng, T), rand(rng, T), rand(rng, T), rand(rng, T))
 end
 
 function randn(rng::AbstractRNG, ::Type{Octonion{T}}) where {T<:AbstractFloat}
@@ -170,6 +151,5 @@ function randn(rng::AbstractRNG, ::Type{Octonion{T}}) where {T<:AbstractFloat}
       randn(rng, T) * INV_SQRT_EIGHT,
       randn(rng, T) * INV_SQRT_EIGHT,
       randn(rng, T) * INV_SQRT_EIGHT,
-      false,
   )
 end

test/octonion.jl

@@ -24,32 +24,28 @@ end
     @testset "Constructors" begin
         @testset "from coefficients" begin
             cs = [(1, 2.0, 3.0f0, 4//1, 5, 6, 7, 8), (1//1, 2.0f0, 3.0f0, 4, 5, 6, 7, 8)]
-            @testset for coef in cs, T in (Float32, Float64, Int), norm in (true, false)
-                q = @inferred Octonion{T}(coef..., norm)
+            @testset for coef in cs, T in (Float32, Float64, Int)
+                q = @inferred Octonion{T}(coef...)
                 @test q isa Octonion{T}
-                @test q.norm === norm
-                @test q === Octonion{T}(convert.(T, coef)..., norm)
-                q2 = @inferred Octonion(convert.(T, coef)..., norm)
-                @test Octonion(convert.(T, coef)..., norm) === q
-                if !norm
-                    @test Octonion(convert.(T, coef)...) === q
-                end
+                @test q === Octonion{T}(convert.(T, coef)...)
+                q2 = @inferred Octonion(convert.(T, coef)...)
+                @test Octonion(convert.(T, coef)...) === q
             end
         end
         @testset "from real" begin
             @testset for x in (-1//1, 1.0, 2.0), T in (Float32, Float64, Int, Rational{Int})
                 coef = T.((x, zeros(7)...))
-                @test @inferred(Octonion{T}(x)) === Octonion{T}(coef..., isone(abs(x)))
-                @test @inferred(Octonion(T(x))) === Octonion{T}(coef..., isone(abs(x)))
+                @test @inferred(Octonion{T}(x)) === Octonion{T}(coef...)
+                @test @inferred(Octonion(T(x))) === Octonion{T}(coef...)
             end
         end
         @testset "from octonion" begin
             os = (
-                Octonion(1, 2, 3, 4, 5, 6, 7, 8), OctonionF64(0, 1, 0, 0, 0, 0, 0, 0, true)
+                Octonion(1, 2, 3, 4, 5, 6, 7, 8), OctonionF64(0, 1, 0, 0, 0, 0, 0, 0)
             )
             @testset for o in os, T in (Float32, Float64)
                 coef = T.((o.s, o.v1, o.v2, o.v3, o.v4, o.v5, o.v6, o.v7))
-                @test @inferred(Octonion{T}(o)) === Octonion{T}(coef..., o.norm)
+                @test @inferred(Octonion{T}(o)) === Octonion{T}(coef...)
                 @test @inferred(Octonion(o)) === o
             end
         end
@@ -64,16 +60,14 @@ end
     @testset "==" begin
         @test Octonion(1.0, 2, 3, 4, 5, 6, 7, 8) == Octonion(1, 2, 3, 4, 5, 6, 7, 8)
         @test Octonion(1.0, 2, 3, 4, 5, 6, 7, 8) != Octonion(1, 2, 3, 4, 1, 2, 3, 4)
-        @test Octonion(1, 0, 0, 0, 0, 0, 0, 0, false) ==
-            Octonion(1, 0, 0, 0, 0, 0, 0, 0, true) # test that .norm field does not affect equality
     end
 
     @testset "convert" begin
         @test convert(Octonion{Float64}, 1) === Octonion(1.0)
         @test convert(Octonion{Float64}, Octonion(1, 2, 3, 4, 5, 6, 7, 8)) ===
             Octonion(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0)
-        @test convert(Octonion{Float64}, Octonion(0, 0, 0, 0, 1, 0, 0, 0, true)) ===
-            Octonion(0.0, 0.0, 0.0, 0.0, 1, 0, 0, 0, true)
+        @test convert(Octonion{Float64}, Octonion(0, 0, 0, 0, 1, 0, 0, 0)) ===
+            Octonion(0.0, 0.0, 0.0, 0.0, 1, 0, 0, 0)
     end
 
     @testset "promote" begin
@@ -86,13 +80,9 @@ end
     end
 
     @testset "shorthands" begin
-        @test octo(1) === Octonion(1) # checking the .norm field in particular
-        @test octo(1, 0, 0, 0, 0, 0, 0, 0) === Octonion(1, 0, 0, 0, 0, 0, 0, 0) # checking the .norm field in particular
+        @test octo(1) === Octonion(1)
         @test octo(1, 2, 3, 4, 5, 6, 7, 8) === Octonion(1, 2, 3, 4, 5, 6, 7, 8)
-        @test octo(Octonion(1, 0, 0, 0, 0, 0, 0, 0)) === Octonion(1, 0, 0, 0, 0, 0, 0, 0) # checking the .norm field in particular
         @test octo(Octonion(1, 2, 3, 4, 5, 6, 7, 8)) === Octonion(1, 2, 3, 4, 5, 6, 7, 8)
-        @test octo(1, 0, 0, 0, 0, 0, 0, 0, false).norm == false # respect the .norm input (even if wrong)
-        @test octo(1, 2, 3, 4, 5, 6, 7, 8, true).norm == true # respect the .norm input (even if wrong)
         @test octo(1, collect(2:8)) === Octonion(1:8...)
         @test octo(collect(2:8)) === Octonion(0, 2:8...)
     end
@@ -101,14 +91,12 @@ end
         @testset "octorand" begin
             o = octorand()
             @test o isa Octonion
-            @test !o.norm
         end
 
         @testset "rand($H)" for H in (OctonionF32, OctonionF64)
             rng = Random.MersenneTwister(42)
             o = rand(rng, H)
             @test o isa H
-            @test !o.norm
 
             os = rand(rng, H, 1000)
             @test eltype(os) === H
@@ -126,7 +114,6 @@ end
             rng = Random.MersenneTwister(42)
             o = randn(rng, H)
             @test o isa H
-            @test !o.norm
 
             os = randn(rng, H, 10000)
             @test eltype(os) === H
@@ -143,13 +130,13 @@ end
 
     @testset "basic" begin
         q = randn(OctonionF64)
-        qnorm = normalize(q)
+        qnorm = sign(q)
         @test real(q) === q.s
         @test_throws MethodError imag(q)
         @test @test_deprecated(Octonions.imag(q)) == [q.v1, q.v2, q.v3, q.v4, q.v5, q.v6, q.v7]
         @test imag_part(q) === (q.v1, q.v2, q.v3, q.v4, q.v5, q.v6, q.v7)
         @test conj(q) ===
-            Octonion(q.s, -q.v1, -q.v2, -q.v3, -q.v4, -q.v5, -q.v6, -q.v7, q.norm)
+            Octonion(q.s, -q.v1, -q.v2, -q.v3, -q.v4, -q.v5, -q.v6, -q.v7)
         @test conj(qnorm) === Octonion(
             qnorm.s,
             -qnorm.v1,
@@ -159,7 +146,6 @@ end
             -qnorm.v5,
             -qnorm.v6,
             -qnorm.v7,
-            qnorm.norm,
         )
         @test conj(conj(q)) === q
         @test conj(conj(qnorm)) === qnorm
@@ -212,7 +198,6 @@ end
         @test !iszero(octo(0, 0, 0, 0, 0, 1, 0, 0))
         @test !iszero(octo(0, 0, 0, 0, 0, 0, 1, 0))
         @test !iszero(octo(0, 0, 0, 0, 0, 0, 0, 1))
-        @test !iszero(octo(0, 0, 0, 0, 0, 0, 0, 0, true))
     end
 
     @testset "isone" begin
@@ -239,7 +224,6 @@ end
             @test !isfinite(octo(0, 0, 0, 0, 0, val, 0, 0))
             @test !isfinite(octo(0, 0, 0, 0, 0, 0, val, 0))
             @test !isfinite(octo(0, 0, 0, 0, 0, 0, 0, val))
-            @test isfinite(octo(fill(val, 8)..., true))
         end
     end
 
@@ -255,7 +239,6 @@ end
             @test isinf(octo(0, 0, 0, 0, 0, inf, 0, 0))
             @test isinf(octo(0, 0, 0, 0, 0, 0, inf, 0))
             @test isinf(octo(0, 0, 0, 0, 0, 0, 0, inf))
-            @test !isinf(octo(fill(inf, 8)..., true))
         end
     end
 
@@ -456,29 +439,14 @@ end
         end
     end
 
-    @testset "normalize" begin
+    @testset "sign" begin
         for _ in 1:100
             q = randn(OctonionF64)
-            qnorm = @inferred normalize(q)
+            qnorm = @inferred sign(q)
             @test abs(qnorm) ≈ 1
-            @test qnorm.norm
             @test q ≈ abs(q) * qnorm
-            @test normalize(qnorm) === qnorm
+            @test sign(qnorm) ≈ qnorm
         end
-        @test_broken @inferred(normalize(octo(1:8...)))
-    end
-
-    @testset "normalizea" begin
-        for _ in 1:100
-            q = randn(OctonionF64)
-            qnorm, a = @inferred normalizea(q)
-            @test abs(qnorm) ≈ 1
-            @test qnorm.norm
-            @test a isa Real
-            @test a ≈ abs(q)
-            @test q ≈ a * qnorm
-            @test normalizea(qnorm) === (qnorm, one(real(q)))
-        end
-        @test_broken @inferred(normalizea(octo(1:8...)))
+        @inferred(sign(octo(1:8...)))
     end
 end