fix spurious expint domain errors (#273)

* fix spurious expint domain errors

* uncomment test

Author: stevengj

src/expint.jl

@@ -197,6 +197,7 @@ end
 
 # Calculate Γ(1 - ν) * z^(ν-1) safely
 En_safe_gamma_term(ν::Number, z::Number) = exp((ν - 1)*log(z) + loggamma(1 - oftype(z, ν)))
+En_safe_gamma_term(ν::Integer, z::Real) = (z ≥ 0 || isodd(ν) ? 1 : -1) * exp((ν - 1)*log(abs(z)) + loggamma(1 - oftype(z, ν)))
 
 # continued fraction for En(ν, z) that uses the gamma function:
 # https://functions.wolfram.com/GammaBetaErf/ExpIntegralE/10/0005/
@@ -369,7 +370,7 @@ function expint(ν::Number, z::Number, niter::Int=1000)
         return oftype(z, NaN) * z
     end
 
-    if z isa Real && (isinteger(ν) ? (z < 0 && ν > 0) : (z < 0 || ν < 0))
+    if z isa Real && (isinteger(ν) ? (z < 0 && ν > 0) : z < 0)
         throw(DomainError(z, "En will only return a complex result if called with a complex argument"))
     end
 

test/expint.jl

@@ -121,6 +121,12 @@ using Base.MathConstants
         @test expint(-4, big"5.7") ≈ big"0.0013051784816041557674219259305064008704427556690521012788554962045721241678128274" rtol=1e-76
         @test expint(+4, big"5.7") ≈ big"0.00035851619983733810063957822090566023258844652925986297947736355731994111784745604432" rtol=1e-74
     end
+
+    # issue #272: more cases with real results
+    @test expint(-2, 2.2) ≈ 0.11696351427428933590118175681379776 rtol=1e-14
+    @test expint(-2, -2.2) ≈ -2.0680909972407264331884989 rtol=1e-14
+    @test expint(-2.2, 3.2) ≈ 0.024950173497409329191241353395358 rtol=1e-14
+    #@test expint(+2.2, 3.2) ≈ 0.008044603700773423319087602010 rtol=1e-14
 end
 
 expinti_real(x) = invoke(expinti, Tuple{Real}, x)