fix erf(x,y) for small arguments (#227)

* fix erf(x,y) for small arguments

* bump version

* NaN tests

Author: cossio

Project.toml

@@ -1,6 +1,6 @@
 name = "SpecialFunctions"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "0.10.1"
+version = "0.10.2"
 
 [deps]
 OpenSpecFun_jll = "efe28fd5-8261-553b-a9e1-b2916fc3738e"

src/erf.jl

@@ -69,7 +69,9 @@ See also: [`erfc(x)`](@ref SpecialFunctions.erfc), [`erfcx(x)`](@ref SpecialFunc
 erf
 
 function erf(x::Real, y::Real)
-    if 0 ≤ x && 0 ≤ y
+    if abs(x) ≤ 1/√2 && abs(y) ≤ 1/√2
+        erf(y) - erf(x)
+    elseif 0 ≤ x && 0 ≤ y
         erfc(x) - erfc(y)
     elseif x ≤ 0 && y ≤ 0
         erfc(-y) - erfc(-x)

test/erf.jl

@@ -137,5 +137,9 @@
         @test erf(11, 10) ≈ -2.08848758232167861905709161e-45
         @test erf(-11, -10) ≈ 2.08848758232167861905709161e-45
         @test erf(-1, 1) ≈ 1.68540158589942973868244127017
+        @test erf(1e-30, 2e-30) ≈ 1.12837916709551257389615890312e-30
+        @test isnan(erf(NaN, 0))
+        @test isnan(erf(0, NaN))
+        @test isnan(erf(NaN, NaN))
     end
 end