Add exponential

src/aff.jl

@@ -203,3 +203,34 @@ function Base.inv(x::Aff, X=interval(x))
 
     return affine_approx(x, α, ζ, δ)
 end
+
+
+function Base.exp(x::Aff, X=interval(x))
+
+    # min-range approximation:  de Figuereido book, pg. 69
+
+    a, b = X.lo, X.hi
+
+    # @show a, b
+
+    exp_X = exp(X)
+    exp_a, exp_b = exp_X.lo, exp_X.hi
+
+    α = exp_a
+
+    if α == 0
+        d_min = zero(x.lo)
+        d_max = exp_b
+
+    else
+        d_max = IntervalArithmetic.@round_up(exp_b - α*b)
+        d_min = IntervalArithmetic.@round_down(exp_a - α*a)
+    end
+
+    d = interval(d_min, d_max)
+
+    ζ = mid(d)
+    δ = radius(d) * (-1..1)
+
+    return affine_approx(x, α, ζ, δ)
+end

src/affine.jl

@@ -4,7 +4,7 @@ import IntervalArithmetic: interval
 
 using LinearAlgebra
 
-import Base: +, *, ^, -, sqrt, inv
+import Base: +, *, ^, -, sqrt, inv, exp
 
 """
 Affine form with center `c`, affine components `γ` and error `Δ`.
@@ -56,7 +56,7 @@ for op in (:+, :*, :-)
     end
 end
 
-for op in (:sqrt, :inv)
+for op in (:sqrt, :inv, :exp)
     @eval function $op(x::Affine)
         affine = $op(x.affine, x.range)