Improve inference in norm (#194)

* improve inference in norm

* version bump to v0.6.20

* add abs in norm

* specialize norm for VectorFun

* extend norm only for ScalarFun

* fix default norm

* add test

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunBase"
 uuid = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
-version = "0.6.19"
+version = "0.6.20"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/Fun.jl

@@ -414,7 +414,10 @@ for (OP,SUM) in ((:(norm),:(sum)),(:linenorm,:linesum))
     @eval begin
         $OP(f::Fun) = $OP(f,2)
 
-        function $OP(f::Fun{<:Space{<:Any,<:Number}}, p::Real)
+        # Specializing norm(::ScalarFun) helps with inference
+        $OP(f::ScalarFun) = sqrt(abs($SUM(abs2(f))))
+
+        function $OP(f::ScalarFun, p::Real)
             if p < 1
                 return error("p should be 1 ≤ p ≤ ∞")
             elseif 1 ≤ p < Inf
@@ -424,11 +427,12 @@ for (OP,SUM) in ((:(norm),:(sum)),(:linenorm,:linesum))
             end
         end
 
-        function $OP(f::Fun{<:Space{<:Any,<:Number}}, p::Int)
+        function $OP(f::ScalarFun, p::Int)
             if 1 ≤ p < Inf
+                p == 2 && return $OP(f)
                 return iseven(p) ? abs($SUM(abs2(f)^(p÷2)))^(1/p) : abs($SUM(abs2(f)^(p/2)))^(1/p)
             else
-                return error("p should be 1 ≤ p ≤ ∞")
+                error("p should be 1 ≤ p ≤ ∞")
             end
         end
     end

src/Multivariate/VectorFun.jl

@@ -143,7 +143,6 @@ norm(A::VectorFun, p::Real) = norm(norm.(Array(A)),p)
 
 
 
-
 ## Vector of fun routines
 
 function coefficientmatrix(::Type{N},f::AbstractVector{F},o...) where {N,F}

test/SpacesTest.jl

@@ -252,6 +252,7 @@ using LinearAlgebra
 
     @testset "ApproxFunOrthogonalPolynomials" begin
         @test (@inferred Fun()) == Fun(x->x, Chebyshev())
+        @test (@inferred norm(Fun())) ≈ norm(Fun(), 2) ≈ √(2/3) # √∫x^2 dx over -1..1
 
         v = rand(4)
         v2 = transform(NormalizedChebyshev(), v)