uniform points in a 3-ball, Julia

## Julia 0.6
## https://news.ycombinator.com/item?id=17688599
## https://karthikkaranth.me/blog/generating-random-points-in-a-sphere/

function vec4(n)
    out = Matrix{Float64}(3,n)
    @inbounds for i=1:n
        θ = 2π*rand()
        cϕ = 2*rand()-1  ## don't write ϕ = acos(cϕ)...
        sϕ = sqrt(1-cϕ^2)
        r = cbrt(rand())
        out[1,i] = r * sϕ * cos(θ)
        out[2,i] = r * sϕ * sin(θ)
        out[3,i] = r * cϕ
    end
    out
end

function vec1(n)
    out = Matrix{Float64}(3,n)
    rr = ones(3)
    i=0
    @inbounds while i<n
        rand!(rr)
        scale!(rr,2)
        rr .-= 1
        if sum(abs2,rr)<=1
            i+=1
            out[:,i] .= rr
        end
    end
    out
end

using BenchmarkTools

@btime vec1(10^7) ## 1.470 s
@btime vec4(10^7) ## 967.866 ms