Improve type-inference in evaluate (#276)

* improve type-inference in evaluate

* Test for BigInt

* Bump ApproxFunBase version

* Call clenshaw in each branch in evaluate

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.6.37"
+version = "0.6.38"
 
 [deps]
 ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
@@ -28,13 +28,14 @@ Static = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
 ApproxFunOrthogonalPolynomialsStaticExt = "Static"
 
 [compat]
-ApproxFunBase = "0.8.30"
+ApproxFunBase = "0.8.39"
 ApproxFunBaseTest = "0.1"
 Aqua = "0.6"
 BandedMatrices = "0.16, 0.17"
 BlockArrays = "0.14, 0.15, 0.16"
 BlockBandedMatrices = "0.10, 0.11, 0.12"
 DomainSets = "0.5, 0.6"
+DualNumbers = "0.6.2"
 FastGaussQuadrature = "0.4, 0.5"
 FastTransforms = "0.12, 0.13, 0.14, 0.15.1"
 FillArrays = "0.11, 0.12, 0.13, 1"
@@ -51,10 +52,11 @@ julia = "1.6"
 [extras]
 ApproxFunBaseTest = "a931bfaf-0cfd-4a5c-b69c-bf2eed002b43"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
 LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
 Static = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["ApproxFunBaseTest", "Aqua", "Test", "Static", "StaticArrays", "LazyArrays"]
+test = ["ApproxFunBaseTest", "Aqua", "DualNumbers", "Test", "Static", "StaticArrays", "LazyArrays"]

src/Spaces/PolynomialSpace.jl

@@ -17,16 +17,20 @@ rangespace(M::ConcreteMultiplication{U,V}) where {U<:PolynomialSpace,V<:Polynomi
 ## Evaluation
 
 function evaluate(f::AbstractVector,S::PolynomialSpace,x)
+    # We call clenshaw in each branch to obtain type-stability
+    y = tocanonical(S,x)
     if x in domain(S)
-        clenshaw(S,f,tocanonical(S,x))
+        clenshaw(S,f,y)
     elseif isambiguous(domain(S))
-        length(f) == 0 && return zero(eltype(f))
+        length(f) == 0 && return clenshaw(S, SVector{0,eltype(f)}(),y)
         for k = 2:length(f)
             iszero(f[k]) || throw(ArgumentError("Ambiguous domains only work with constants"))
         end
-        return first(f)
+        # type-stable way to evaluate the first element of the series
+        return clenshaw(S, SVector{1}(f[1]),y)
     else
-        zero(eltype(f))
+        # type-stable way to obtain the zero element
+        clenshaw(S, SVector{0,eltype(f)}(),y)
     end
 end
 

test/ChebyshevTest.jl

@@ -2,6 +2,7 @@ module ChebyshevTest
 
 using ApproxFunOrthogonalPolynomials
 using ApproxFunBase
+using DualNumbers
 using LinearAlgebra
 using Test
 using ApproxFunBase: transform!, itransform!
@@ -24,6 +25,12 @@ include("testutils.jl")
         @test Fun(x->4).coefficients == [4.0]
         @test @inferred(Fun(4)).coefficients == [4.0]
 
+        @test @inferred(Fun(Chebyshev(), [1])(1)) == 1.0
+        @test @inferred(Fun(Chebyshev(), Int[])(Dual(1,1))) == Dual(0,0)
+        @test @inferred(Fun(Chebyshev(), Int[1,2])(Dual(1,1))) == Dual(3,2)
+
+        @test @inferred(Fun(Chebyshev(), BigInt[1])(1)) == 1
+
         f = @inferred Fun(ChebyshevInterval(), [1])
         @test f(0.1) == 1
 

test/MultivariateTest.jl

@@ -2,6 +2,7 @@ module MultivariateTest
 
 using ApproxFunBase
 using ApproxFunOrthogonalPolynomials
+using DualNumbers
 using LinearAlgebra
 using SpecialFunctions
 using BlockBandedMatrices
@@ -235,6 +236,8 @@ include("testutils.jl")
         f=Fun(xy->exp(-xy[1]-2cos(xy[2])),d)
         @test f(0.5,0.5) ≈ exp(-0.5-2cos(0.5))
         @test f(SVector(0.5,0.5)) ≈ exp(-0.5-2cos(0.5))
+        @test @inferred(first(f)) ≈ f(0,0)
+        @test @inferred(last(f)) ≈ f(1,1)
 
         f=Fun(xy->exp(-xy[1]-2cos(xy[2])),d,20)
         @test f(0.5,0.5) ≈ exp(-0.5-2cos(0.5))
@@ -405,8 +408,9 @@ include("testutils.jl")
 
     @testset "off domain evaluate" begin
         g = Fun(1, Segment(SVector(0,-1) , SVector(π,-1)))
-        @test g(0.1,-1) ≈ 1
-        @test g(0.1,1) ≈ 0
+        @test @inferred(g(0.1,-1)) ≈ 1
+        @test @inferred(g(Dual(1,1),-1)) == Dual(1,0)
+        @test @inferred(g(0.1,1)) ≈ 0
     end
 
     @testset "Dirichlet" begin