Geometry.jl

## Defines a plane in three dimensional Euclidean space
## given by the origin `p`, and three vectors `u,v` in the plane
## and `w` perpendicular to it.
## `u,v,w` are not independent, but filled in by the constructors.

import Base: ==, isvalid
import LinearAlgebra: dot, norm

struct Plane{T}
    p::T
    u::T
    v::T
    w::T
end

function isvalid(P::Plane)
    if norm(P.u)≉ 1.0 || norm(P.v)≉ 1.0 || norm(P.w)≉ 1.0 || dot(P.u,P.w)≉ 0 || dot(P.v,P.w)≉ 0 ||
        P.u == P.v || P.u == -P.v
        return false
    end
    return true
end
function isvalid2(P::Plane)
    if norm(P.u)≉ 1.0 || norm(P.v)≉ 1.0 || norm(P.w)≉ 1.0
        return false
    end
    return true
end
function isvalid3(P::Plane)
    if norm(P.u)≉ 1.0 || norm(P.w)≉ 1.0 || dot(P.u,P.w)≉ 0.0
        return false
    end
    return true
end

geometrytests.jl

using Test
import LinearAlgebra: cross, dot, normalize
import StaticArrays: SVector, @SVector

include("Geometry.jl")

@testset "Plane" begin
    # StaticArrays
    # isvalid, isvalid3 fail with -O2
    # but pass with -O1
    p = @SVector [0.0,0.0,0.0]
    u = normalize(@SVector [1,1,1])
    v = (@SVector [1,2,1])
    v = normalize(v - dot(u,v)*u)
    w = cross(u,v)
    
    P = Plane(p,u,v,w)

    @test isvalid(P)
    @test isvalid2(P)
    @test isvalid3(P)

    # Normal arrays
    # all tests pass
    p = [0.0,0.0,0.0]
    u = normalize([1,1,1])
    v = ([1,2,1])
    v = normalize(v - dot(u,v)*u)
    w = cross(u,v)
    
    P = Plane(p,u,v,w)    

    @test isvalid(P)
    @test isvalid2(P)
    @test isvalid3(P)
end

Manifest.toml

# This file is machine-generated - editing it directly is not advised

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runtests.sh

#!/bin/sh
if [[ -z $1 ]]
then
  JULIA="julia"
else
  JULIA=$1
fi

echo 'Running tests with -O1'
$JULIA --project=. -O1 geometrytests.jl
echo "============="
echo 'Running tests with -O2'
$JULIA --project=. -O2 geometrytests.jl

versioninfo

Julia Version 1.8.5
Commit 17cfb8e65ea (2023-01-08 06:45 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin21.4.0)
  CPU: 4 × Intel(R) Core(TM) i5-4670 CPU @ 3.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, haswell)
  Threads: 4 on 4 virtual cores
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 4