isnegative in intpow (#590)

* isnegative in intpow

* Add UInt test

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunBase"
 uuid = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
-version = "0.9.13"
+version = "0.9.14"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/Fun.jl

@@ -594,6 +594,10 @@ end
 
 \(c::Number, f::Fun) = Fun(f.space, c \ f.coefficients)
 
+# eliminate the type-unstable 1/t branch by using an unsigned integer exponent
+isnegative(x) = x < zero(x)
+isnegative(::Unsigned) = false
+
 Base.@constprop :aggressive function intpow(f, k)
     if k == 0
         ones(cfstype(f), space(f))
@@ -607,10 +611,10 @@ Base.@constprop :aggressive function intpow(f, k)
         f * f * f * f
     else
         t = foldl(*, fill(f, abs(k)-1), init=f)
-        if k > 0
-            return t
-        else
+        if isnegative(k)
             return 1/t
+        else
+            return t
         end
     end
 end

test/SpacesTest.jl

@@ -70,6 +70,7 @@ using LinearAlgebra
                 @test ApproxFunBase.intpow(f, n) == f^n == reduce(*, fill(f, n))
             end
             @test ApproxFunBase.intpow(f,-2) == f^-2 == 1/(f*f)
+            @test f^2 == f^UInt(2)
 
             if VERSION >= v"1.8"
                 @test (@inferred (x -> x^1)(sp)) == sp