diff --git a/test/DerivativeTest.jl b/test/DerivativeTest.jl
index 4de1a6de..206a2d68 100644
--- a/test/DerivativeTest.jl
+++ b/test/DerivativeTest.jl
@@ -8,6 +8,7 @@ using Random
 using ForwardDiff
 using DiffTests
 
+include(joinpath(dirname(@__FILE__), "Furlongs.jl"))
 include(joinpath(dirname(@__FILE__), "utils.jl"))
 
 Random.seed!(1)
@@ -113,4 +114,16 @@ end
     @test ForwardDiff.derivative(x -> (1+im)*x, 0) == (1+im)
 end
 
+@testset "non-standard numbers" begin
+    Base.exp(f::Furlongs.Furlong) = exp(f.val)
+    Base.cos(f::Furlongs.Furlong) = cos(f.val)
+    Base.sin(f::Furlongs.Furlong) = sin(f.val)
+
+    furlong = Furlongs.Furlong{2}(1.0)
+
+    f(x) = exp(x) + 4*sin(x)*oneunit(x)
+
+    @test ForwardDiff.derivative(f, furlong) == exp(furlong) + 4*cos(furlong)
+end
+
 end # module
diff --git a/test/Furlongs.jl b/test/Furlongs.jl
new file mode 100644
index 00000000..3fef6683
--- /dev/null
+++ b/test/Furlongs.jl
@@ -0,0 +1,110 @@
+module Furlongs
+
+export Furlong
+
+const TNumber = Real # ForwardDiff only supports Real numbers
+
+# Here we implement a minimal dimensionful type Furlong, which is used
+# to test dimensional correctness of various functions in Base.
+
+# represents a quantity in furlongs^p
+struct Furlong{p,T<:TNumber} <: TNumber
+    val::T
+    Furlong{p,T}(v::TNumber) where {p,T} = new(v)
+end
+Furlong(x::T) where {T<:TNumber} = Furlong{1,T}(x)
+Furlong(x::Furlong) = x
+(::Type{T})(x::Furlong{0}) where {T<:TNumber} = T(x.val)::T
+(::Type{T})(x::Furlong{0}) where {T<:Furlong{0}} = T(x.val)::T
+(::Type{T})(x::Furlong{0}) where {T<:Furlong} = typeassert(x, T)
+Furlong{p}(v::TNumber) where {p} = Furlong{p,typeof(v)}(v)
+Furlong{p}(x::Furlong{q}) where {p,q} = (typeassert(x, Furlong{p}); Furlong{p,typeof(x.val)}(x.val))
+Furlong{p,T}(x::Furlong{q}) where {T,p,q} = (typeassert(x, Furlong{p}); Furlong{p,T}(T(x.val)))
+
+Base.promote_rule(::Type{Furlong{p,T}}, ::Type{Furlong{p,S}}) where {p,T,S} =
+    Furlong{p,promote_type(T,S)}
+Base.promote_rule(::Type{Furlong{0,T}}, ::Type{S}) where {T,S<:Union{Real,Complex}} =
+    Furlong{0,promote_type(T,S)}
+# only Furlong{0} forms a ring and isa TNumber
+Base.convert(::Type{T}, y::TNumber) where {T<:Furlong{0}} = T(y)::T
+Base.convert(::Type{Furlong}, y::TNumber) = Furlong{0}(y)
+Base.convert(::Type{Furlong{<:Any,T}}, y::TNumber) where {T<:TNumber} = Furlong{0,T}(y)
+Base.convert(::Type{T}, y::TNumber) where {T<:Furlong} = typeassert(y, T) # throws, since cannot convert a Furlong{0} to a Furlong{p}
+# other Furlong{p} form a group
+Base.convert(::Type{T}, y::Furlong) where {T<:Furlong{0}} = T(y)::T
+Base.convert(::Type{Furlong}, y::Furlong) = y
+Base.convert(::Type{Furlong{<:Any,T}}, y::Furlong{p}) where {p,T<:TNumber} = Furlong{p,T}(y)
+Base.convert(::Type{T}, y::Furlong) where {T<:Furlong} = T(y)::T
+
+Base.one(::Furlong{p,T}) where {p,T} = one(T)
+Base.one(::Type{Furlong{p,T}}) where {p,T} = one(T)
+Base.oneunit(::Furlong{p,T}) where {p,T} = Furlong{p,T}(one(T))
+Base.oneunit(::Type{Furlong{p,T}}) where {p,T} = Furlong{p,T}(one(T))
+Base.zero(::Furlong{p,T}) where {p,T} = Furlong{p,T}(zero(T))
+Base.zero(::Type{Furlong{p,T}}) where {p,T} = Furlong{p,T}(zero(T))
+Base.iszero(x::Furlong) = iszero(x.val)
+Base.float(x::Furlong{p}) where {p} = Furlong{p}(float(x.val))
+Base.eps(::Type{Furlong{p,T}}) where {p,T<:AbstractFloat} = Furlong{p}(eps(T))
+Base.eps(::Furlong{p,T}) where {p,T<:AbstractFloat} = eps(Furlong{p,T})
+Base.floatmin(::Type{Furlong{p,T}}) where {p,T<:AbstractFloat} = Furlong{p}(floatmin(T))
+Base.floatmin(::Furlong{p,T}) where {p,T<:AbstractFloat} = floatmin(Furlong{p,T})
+Base.floatmax(::Type{Furlong{p,T}}) where {p,T<:AbstractFloat} = Furlong{p}(floatmax(T))
+Base.floatmax(::Furlong{p,T}) where {p,T<:AbstractFloat} = floatmax(Furlong{p,T})
+Base.conj(x::Furlong{p,T}) where {p,T} = Furlong{p,T}(conj(x.val))
+
+# convert Furlong exponent p to a canonical form
+canonical_p(p) = isinteger(p) ? Int(p) : Rational{Int}(p)
+
+Base.abs(x::Furlong{p}) where {p} = Furlong{p}(abs(x.val))
+Base.abs2(x::Furlong{p}) where {p} = Furlong{canonical_p(2p)}(abs2(x.val))
+Base.inv(x::Furlong{p}) where {p} = Furlong{canonical_p(-p)}(inv(x.val))
+
+for f in (:isfinite, :isnan, :isreal, :isinf)
+    @eval Base.$f(x::Furlong) = $f(x.val)
+end
+for f in (:real,:imag,:complex,:+,:-)
+    @eval Base.$f(x::Furlong{p}) where {p} = Furlong{p}($f(x.val))
+end
+
+import Base: +, -, ==, !=, <, <=, isless, isequal, *, /, //, div, rem, mod, ^
+for op in (:+, :-)
+    @eval function $op(x::Furlong{p}, y::Furlong{p}) where {p}
+        v = $op(x.val, y.val)
+        Furlong{p}(v)
+    end
+end
+for op in (:(==), :(!=), :<, :<=, :isless, :isequal)
+    @eval $op(x::Furlong{p}, y::Furlong{p}) where {p} = $op(x.val, y.val)::Bool
+end
+for (f,op) in ((:_plus,:+),(:_minus,:-),(:_times,:*),(:_div,://))
+    @eval function $f(v::T, ::Furlong{p}, ::Union{Furlong{q},Val{q}}) where {T,p,q}
+        s = $op(p, q)
+        Furlong{canonical_p(s),T}(v)
+    end
+end
+for (op,eop) in ((:*, :_plus), (:/, :_minus), (://, :_minus), (:div, :_minus))
+    @eval begin
+        $op(x::Furlong{p}, y::Furlong{q}) where {p,q} =
+            $eop($op(x.val, y.val),x,y)
+        $op(x::Furlong{p}, y::S) where {p,S<:TNumber} = $op(x,Furlong{0,S}(y))
+        $op(x::S, y::Furlong{p}) where {p,S<:TNumber} = $op(Furlong{0,S}(x),y)
+    end
+end
+# to fix an ambiguity
+//(x::Furlong, y::Complex) = x // Furlong{0,typeof(y)}(y)
+for op in (:rem, :mod)
+    @eval begin
+        $op(x::Furlong{p}, y::Furlong) where {p} = Furlong{p}($op(x.val, y.val))
+        $op(x::Furlong{p}, y::TNumber) where {p} = Furlong{p}($op(x.val, y))
+    end
+end
+Base.sqrt(x::Furlong) = _div(sqrt(x.val), x, Val(2))
+Base.muladd(x::Furlong, y::Furlong, z::Furlong) = x*y + z
+Base.muladd(x::Furlong, y::TNumber, z::TNumber) = x*y + z
+Base.muladd(x::Furlong, y::Furlong, z::TNumber) = x*y + z
+Base.muladd(x::TNumber, y::Furlong, z::TNumber) = x*y + z
+Base.muladd(x::TNumber, y::TNumber, z::Furlong) = x*y + z
+Base.muladd(x::TNumber, y::Furlong, z::Furlong) = x*y + z
+Base.muladd(x::Furlong, y::TNumber, z::Furlong) = x*y + z
+
+end