add erf(x,y) (#223)

Author: cossio

Project.toml

@@ -1,6 +1,6 @@
 name = "SpecialFunctions"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "0.11.0"
+version = "0.11.1"
 
 [deps]
 OpenSpecFun_jll = "efe28fd5-8261-553b-a9e1-b2916fc3738e"

src/erf.jl

@@ -64,6 +64,21 @@ See also: [`erfc(x)`](@ref SpecialFunctions.erfc), [`erfcx(x)`](@ref SpecialFunc
 """
 erf
 
+@doc raw"""
+    erf(x, y)
+
+Compute the difference `erf(y) - erf(x)`, in a numerically sound way (only for real arguments).
+"""
+function erf(x::Real, y::Real)
+    if 0 ≤ x && 0 ≤ y
+        erfc(x) - erfc(y)
+    elseif x ≤ 0 && y ≤ 0
+        erfc(-y) - erfc(-x)
+    else
+        erf(y) - erf(x)
+    end
+end
+
 @doc raw"""
     erfc(x)
 

test/erf.jl

@@ -131,4 +131,11 @@
         @test erfinv(one(Int))  == erfinv(1.0)
         @test erfcinv(one(Int)) == erfcinv(1.0)
     end
+
+    @testset "two args version" begin
+        @test erf(10, 11) ≈ 2.08848758232167861905709161e-45
+        @test erf(11, 10) ≈ -2.08848758232167861905709161e-45
+        @test erf(-11, -10) ≈ 2.08848758232167861905709161e-45
+        @test erf(-1, 1) ≈ 1.68540158589942973868244127017
+    end
 end