Improve type stable in function expint (#466)

* improve type stable for expint

* add infer test && improve promote

* fix promote for Float32 case

* improve inferred test

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Co-authored-by: songjhaha <songjh96@foxmail.cc>

Author: songjhaha

src/expint.jl

@@ -207,10 +207,10 @@ En_safe_gamma_term(ν::Integer, z::Real) = (z ≥ 0 || isodd(ν) ? 1 : -1) * exp
 # https://functions.wolfram.com/GammaBetaErf/ExpIntegralE/10/0005/
 # returns the two terms from the above equation separately
 function En_cf_gamma(ν::Number, z::Number, n::Int=1000)
-    A = float(1 - ν)
-    B::typeof(A) = 1
-    Bprev::typeof(A) = 0
-    Aprev::typeof(A) = 1
+    A, z = map(float, promote(1 - ν, z))
+    B = oneunit(A)
+    Bprev = zero(B)
+    Aprev = oneunit(A)
     ϵ = 10*eps(real(B))
     scale = sqrt(floatmax(real(A)))
 

test/expint.jl

@@ -158,6 +158,9 @@ using Base.MathConstants
                 Γ, cf, iter = SpecialFunctions.En_cf_gamma(1 / 2, x)
                 @test Γ + cf*exp(-x) ≈ y
             end
+            # type stability
+            @test @inferred(SpecialFunctions.En_cf_gamma(1, 1.0 + 2.1im, 1000)) isa Tuple{ComplexF64,ComplexF64,Int}
+            @test @inferred(SpecialFunctions.En_cf_gamma(1, 1.0f0, 1000)) isa Tuple{Float32,Float32,Int}
         end
         @testset "En_expand_origin" begin
             for (x, y) in zip(xs, ys)