expint: add another condition for gamma CF use (#275)

* Add another condition for gamma CF

* Test

Author: augustt198

src/expint.jl

@@ -249,14 +249,15 @@ end
 # En_cf_nogamma and En_cf_gamma
 # returns (evaluated result, # iterations used, whether En_cf_gamma was chosen)
 function En_cf(ν::Number, z::Number, niter::Int=1000)
-    gammapart, cfpart, iters = En_cf_gamma(ν, z, niter)
-    gammaabs, cfabs = abs(gammapart), abs(cfpart)
-    if gammaabs != Inf && gammaabs > 1.0 && gammaabs > cfabs
-        # significant gamma part, use this
-        return gammapart + cfpart, iters, true
-    else
-        return En_cf_nogamma(ν, z, niter)..., false
+    if real(1-ν) > 0
+        gammapart, cfpart, iters = En_cf_gamma(ν, z, niter)
+        gammaabs, cfabs = abs(gammapart), abs(cfpart)
+        if gammaabs != Inf && gammaabs > 1.0 && gammaabs > cfabs
+            # significant gamma part, use this
+            return gammapart + cfpart, iters, true
+        end
     end
+    return En_cf_nogamma(ν, z, niter)..., false
 end
 
 # Compute expint(ν, z₀+Δ) given start = expint(ν, z₀), as described by [Amos 1980].

test/expint.jl

@@ -75,6 +75,8 @@ using Base.MathConstants
         @test expint(-2, 3.3) isa Real
         @test expint(-2, -3.3) ≅ -4.745485121488663825992363318400378114254141655964565963
         @test expint(-2, -3.3) isa Real
+        @test expint(2.2, 3.3) ≅ 0.0071305694486185747267607978483436184475047798769491326205
+        @test expint(1.2, 3.3) ≅ 0.0085837830493629441737850749465161073231031009810293477318
 
         @test expint(-2.1+3im, 4.2 +0im) ⩭ 0.003387565626497080536855067510744646235748203589175196673362104 - 0.003355838600814825542988272289126728631565803782052141768321840im
         @test expint(-4.3, -10+0.0im) ⩭ -1505.2167858114105916067190408869152177781925766866637213104 + 0.00015439438628349460776476190593323691084185406009267711345841im