diff --git a/src/ForwardDiffNumber.jl b/src/ForwardDiffNumber.jl
index 29d8af9c..b7166c60 100644
--- a/src/ForwardDiffNumber.jl
+++ b/src/ForwardDiffNumber.jl
@@ -78,6 +78,9 @@ conj(n::ForwardDiffNumber) = n
 transpose(n::ForwardDiffNumber) = n
 ctranspose(n::ForwardDiffNumber) = n
 
+@inline abs(n::ForwardDiffNumber) = signbit(value(n)) ? -n : n
+@inline abs2(n::ForwardDiffNumber) = n*n
+
 # NaNMath Helper Functions # 
 #--------------------------#
 function to_nanmath(x::Expr)
diff --git a/src/GradientNumber.jl b/src/GradientNumber.jl
index 11dc5eeb..5aa7e082 100644
--- a/src/GradientNumber.jl
+++ b/src/GradientNumber.jl
@@ -210,9 +210,6 @@ end
 
 # Other Functions #
 #-----------------#
-@inline abs(g::GradientNumber) = (value(g) >= 0) ? g : -g
-@inline abs2(g::GradientNumber) = g*g
-
 @inline calc_atan2(y::GradientNumber, x::GradientNumber) = atan2(value(y), value(x))
 @inline calc_atan2(y::Real, x::GradientNumber) = atan2(y, value(x))
 @inline calc_atan2(y::GradientNumber, x::Real) = atan2(value(y), x)
diff --git a/test/test_gradients.jl b/test/test_gradients.jl
index aac1521b..a55719aa 100644
--- a/test/test_gradients.jl
+++ b/test/test_gradients.jl
@@ -175,8 +175,8 @@ for (test_partials, Grad) in ((test_partialstup, ForwardDiff.GradNumTup), (test_
     grad_approx_eq(test_grad^rand_val, exp(rand_val * log(test_grad)))
     grad_approx_eq(rand_val^test_grad, exp(test_grad * log(rand_val)))
 
-    # Univariate functions #
-    #----------------------#
+    # Unary functions #
+    #-----------------#
     for (fsym, expr) in Calculus.symbolic_derivatives_1arg()
         @eval begin
             func = $fsym
diff --git a/test/test_hessians.jl b/test/test_hessians.jl
index 10c81677..9de7cf29 100644
--- a/test/test_hessians.jl
+++ b/test/test_hessians.jl
@@ -203,6 +203,10 @@ hess_approx_eq(rand_val^test_hess, exp(test_hess * log(rand_val)))
 
 # Special Cases #
 #---------------#
+@test abs(test_hess) == test_hess
+@test abs(-test_hess) == test_hess
+hess_approx_eq(abs2(test_hess), test_hess*test_hess)
+
 atan2_hess = atan2(test_hess, rand_hess)
 atanyx_hess = atan(test_hess/rand_hess)
 
@@ -210,8 +214,8 @@ atanyx_hess = atan(test_hess/rand_hess)
 @test_approx_eq collect(grad(atan2_hess)) collect(grad(atanyx_hess))
 @test_approx_eq hess(atan2_hess) hess(atanyx_hess)
 
-# Univariate functions/API usage testing #
-#----------------------------------------#
+# Unary functions/API usage testing #
+#-----------------------------------#
 N = 6
 testout = Array(Float64, N, N)
 
diff --git a/test/test_tensors.jl b/test/test_tensors.jl
index 4ecdb530..cfcd20ba 100644
--- a/test/test_tensors.jl
+++ b/test/test_tensors.jl
@@ -221,6 +221,10 @@ tens_approx_eq(rand_val^test_tens, exp(test_tens * log(rand_val)))
 
 # Special Cases #
 #---------------#
+@test abs(test_tens) == test_tens
+@test abs(-test_tens) == test_tens
+tens_approx_eq(abs2(test_tens), test_tens*test_tens)
+
 atan2_tens = atan2(test_tens, rand_tens)
 atanyx_tens = atan(test_tens/rand_tens)
 
@@ -229,8 +233,8 @@ atanyx_tens = atan(test_tens/rand_tens)
 @test_approx_eq hess(atan2_tens) hess(atanyx_tens)
 @test_approx_eq tens(atan2_tens) tens(atanyx_tens)
 
-# Univariate functions/API usage testing #
-#----------------------------------------#
+# Unary functions/API usage testing #
+#-----------------------------------#
 testout = Array(Float64, N, N, N)
 
 function tens_deriv_ijk(f_expr, x::Vector, i, j, k)