Changing operand order causes incorrect calculation of the infinity norm

[macd]

When x = Fun() and a = abs(x) the value of norm(x - a, Inf) is incorrectly reported as 0.0, whereas norm(a - z, Inf) is correctly reported as 2.0. I found another example of this on the web. Details below.

macd@macd-NUC9:~$ julia19
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.9.2 (2023-07-05)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia @v1.9> using ApproxFun

julia @v1.9> x = Fun()
Fun(Chebyshev(), [0.0, 1.0])

julia @v1.9> a = abs(x)
Fun(ContinuousSpace{Float64, Float64, PiecewiseSegment{Float64, Vector{Float64}}}(PiecewiseSegment{Float64, Vector{Float64}}([-1.0, -0.0, 1.0])), [1.0, 5.55112e-17, 1.0])

julia @v1.9> norm(x - a, Inf)
0.0

julia @v1.9> norm(a - x, Inf)
2.0

julia @v1.9> # This behavior was noted before in:
             # https://www.cs.purdue.edu/homes/dgleich/cs514-2021/julia/Lecture-7-Approximation.html
             # (search for "why is this negative???")
             # But note that this works OK for the normal domain of [-1, 1]

             xx = Fun(Chebyshev(1..5))
Fun(Chebyshev(1 .. 5), [3.0, 2.0])

julia @v1.9> f = exp(xx);

julia @v1.9> g = exp(-xx);

julia @v1.9> norm(f - g, Inf)
148.40642115557753

julia @v1.9> norm(g - f, Inf)
-2.3504023872875983

julia @v1.9>