Override SpecialFunctions

REQUIRE

@@ -2,3 +2,4 @@ julia 0.6
 Compat 0.49.0
 Calculus
 NaNMath
+SpecialFunctions 0.7

src/DualNumbers.jl

@@ -2,7 +2,7 @@ __precompile__()
 
 module DualNumbers
 
-using Compat
+using Compat, SpecialFunctions
 import NaNMath
 import Calculus
 

src/dual.jl

@@ -212,6 +212,10 @@ function Base.angle(z::Dual{Complex{T}}) where T<:Real
     end
 end
 
+Base.flipsign(x::Dual,y::Dual) = y == 0 ? flipsign(x, epsilon(y)) : flipsign(x, value(y))
+Base.flipsign(x, y::Dual) = y == 0 ? flipsign(x, epsilon(y)) : flipsign(x, value(y))
+Base.flipsign(x::Dual, y) = dual(flipsign(value(x), y), flipsign(epsilon(x), y))
+
 # algebraic definitions
 conjdual(z::Dual) = Dual(value(z),-epsilon(z))
 absdual(z::Dual) = abs(value(z))
@@ -264,6 +268,8 @@ Base.:^(z::Dual, n::Number) = Dual(value(z)^n, epsilon(z)*n*value(z)^(n-1))
 NaNMath.pow(z::Dual, n::Number) = Dual(NaNMath.pow(value(z),n), epsilon(z)*n*NaNMath.pow(value(z),n-1))
 NaNMath.pow(z::Number, w::Dual) = Dual(NaNMath.pow(z,value(w)), epsilon(w)*NaNMath.pow(z,value(w))*log(z))
 
+inv(z::Dual) = dual(inv(value(z)),-epsilon(z)/value(z)^2)
+
 # force use of NaNMath functions in derivative calculations
 function to_nanmath(x::Expr)
     if x.head == :call
@@ -275,14 +281,25 @@ function to_nanmath(x::Expr)
 end
 to_nanmath(x) = x
 
+
+
+
 for (funsym, exp) in Calculus.symbolic_derivatives_1arg()
     funsym == :exp && continue
     funsym == :abs2 && continue
-    isdefined(Base, funsym) || continue
-    @eval function Base.$(funsym)(z::Dual)
-        x = value(z)
-        xp = epsilon(z)
-        Dual($(funsym)(x),xp*$exp)
+    funsym == :inv && continue
+    if isdefined(SpecialFunctions, funsym)
+        @eval function SpecialFunctions.$(funsym)(z::Dual)
+            x = value(z)
+            xp = epsilon(z)
+            Dual($(funsym)(x),xp*$exp)
+        end
+    elseif isdefined(Base, funsym)
+        @eval function Base.$(funsym)(z::Dual)
+            x = value(z)
+            xp = epsilon(z)
+            Dual($(funsym)(x),xp*$exp)
+        end
     end
     # extend corresponding NaNMath methods
     if funsym in (:sin, :cos, :tan, :asin, :acos, :acosh, :atanh, :log, :log2, :log10,

test/automatic_differentiation_test.jl

@@ -1,4 +1,4 @@
-using DualNumbers
+using DualNumbers, SpecialFunctions
 using Compat
 using Compat.Test
 using Compat.LinearAlgebra
@@ -106,6 +106,10 @@ a = angle(z)
 
 @test angle(Dual(0.0+im,0.0+im)) == π/2
 
+
+# check bug in inv
+@test inv(dual(1.0+1.0im,1.0)) == 1/dual(1.0+1.0im,1.0) == dual(1.0+1.0im,1.0)^(-1)
+
 #
 # Tests limit definition. Let z = a + b ɛ, where a and b ∈ C.
 #
@@ -145,3 +149,16 @@ test(x, y) = x^2 + y
 
 @test epsilon(Dual(-2.0,1.0)^2.0) == -4
 @test epsilon(Dual(-2.0,1.0)^Dual(2.0,0.0)) == -4
+
+
+# test for flipsign
+flipsign(Dual(1.0,1.0),2.0) == Dual(1.0,1.0)
+flipsign(Dual(1.0,1.0),-2.0) == Dual(-1.0,-1.0)
+flipsign(Dual(1.0,1.0),Dual(1.0,1.0)) == Dual(1.0,1.0)
+flipsign(Dual(1.0,1.0),Dual(0.0,-1.0)) == Dual(-1.0,-1.0)
+flipsign(-1.0,Dual(1.0,1.0)) == -1.0
+
+
+# test SpecialFunctions
+@test erf(dual(1.0,1.0)) == dual(erf(1.0), 2exp(-1.0^2)/sqrt(π))
+@test gamma(dual(1.,1)) == dual(gamma(1.0),polygamma(0,1.0))