Added zero, iszero, one, isone to dual

src/DualNumbers.jl

@@ -3,6 +3,7 @@ module DualNumbers
 using SpecialFunctions
 import NaNMath
 import Calculus
+import Random
 
 include("dual.jl")
 

src/dual.jl

@@ -21,7 +21,7 @@ const DualComplex64  = Dual{ComplexF16}
 Base.convert(::Type{Dual{T}}, z::Dual{T}) where {T<:ReComp} = z
 Base.convert(::Type{Dual{T}}, z::Dual) where {T<:ReComp} = Dual{T}(convert(T, value(z)), convert(T, epsilon(z)))
 Base.convert(::Type{Dual{T}}, x::Number) where {T<:ReComp} = Dual{T}(convert(T, x), convert(T, 0))
-Base.convert(::Type{T}, z::Dual) where {T<:ReComp} = (epsilon(z)==0 ? convert(T, value(z)) : throw(InexactError()))
+Base.convert(::Type{T}, z::Dual) where {T<:ReComp} = (iszero(epsilon(z)) ? convert(T, value(z)) : throw(InexactError()))
 
 Base.promote_rule(::Type{Dual{T}}, ::Type{Dual{S}}) where {T<:ReComp,S<:ReComp} = Dual{promote_type(T, S)}
 Base.promote_rule(::Type{Dual{T}}, ::Type{S}) where {T<:ReComp,S<:ReComp} = Dual{promote_type(T, S)}
@@ -175,7 +175,7 @@ Base.isless(z::Dual{<:Real},w::Dual{<:Real}) = value(z) < value(w)
 Base.isless(z::Real,w::Dual{<:Real}) = z < value(w)
 Base.isless(z::Dual{<:Real},w::Real) = value(z) < w
 
-Base.hash(z::Dual) = (x = hash(value(z)); epsilon(z)==0 ? x : bitmix(x,hash(epsilon(z))))
+Base.hash(z::Dual) = (x = hash(value(z)); iszero(epsilon(z)) ? x : bitmix(x,hash(epsilon(z))))
 
 Base.float(z::Union{Dual{T}, Dual{Complex{T}}}) where {T<:AbstractFloat} = z
 Base.complex(z::Dual{<:Complex}) = z
@@ -189,6 +189,21 @@ Base.ceil( ::Type{T}, z::Dual) where {T<:Real} = ceil( T, value(z))
 Base.trunc(::Type{T}, z::Dual) where {T<:Real} = trunc(T, value(z))
 Base.round(::Type{T}, z::Dual) where {T<:Real} = round(T, value(z))
 
+Base.zero(::Type{Dual{T}}) where {T} = Dual(zero(T), zero(T))
+Base.zero(x::Dual{T}) where {T} = zero(typeof(x))
+Base.iszero(z::Dual{T}) where {T} = iszero(value(z))
+
+Base.one(::Type{Dual{T}}) where {T} = Dual(one(T), zero(T))
+Base.one(::Dual{T}) where {T} = one(Dual{T})
+Base.isone(z::Dual{T}) where {T} = isone(value(z))
+
+Base.rand(r::Random.AbstractRNG, ::Random.SamplerType{Dual{T}}) where {T} = Dual{T}(rand(r, T), rand(r, T))
+Base.randn(r::Random.AbstractRNG, ::Type{Dual{T}}) where {T} = Dual{T}(randn(r, T), randn(r, T))
+
+Base.rtoldefault(::Type{Dual{T}}) where {T} = Base.rtoldefault(T)
+Base.copysign(x::Dual, y::Dual) = Dual(copysign(value(x), value(y)),
+                                       copysign(epsilon(x), epsilon(y)))
+
 for op in (:real, :imag, :conj, :float, :complex)
     @eval Base.$op(z::Dual) = Dual($op(value(z)), $op(epsilon(z)))
 end
@@ -201,8 +216,8 @@ Base.abs(z::Dual{<:Real}) = z ≥ 0 ? z : -z
 
 Base.angle(z::Dual{<:Real}) = z ≥ 0 ? zero(z) : one(z)*π
 function Base.angle(z::Dual{Complex{T}}) where T<:Real
-    if z == 0
-        if imag(epsilon(z)) == 0
+    if iszero(z)
+        if iszero(imag(epsilon(z)))
             Dual(zero(T), zero(T))
         else
             Dual(zero(T), convert(T, Inf))
@@ -212,8 +227,8 @@ 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) = iszero(y) ? flipsign(x, epsilon(y)) : flipsign(x, value(y))
+Base.flipsign(x, y::Dual) = iszero(y) ? flipsign(x, epsilon(y)) : flipsign(x, value(y))
 Base.flipsign(x::Dual, y) = dual(flipsign(value(x), y), flipsign(epsilon(x), y))
 
 # algebraic definitions
@@ -233,7 +248,7 @@ Base.:-(z::Number, w::Dual) = Dual(z-value(w), -epsilon(w))
 Base.:-(z::Dual, w::Number) = Dual(value(z)-w, epsilon(z))
 
 # avoid ambiguous definition with Bool*Number
-Base.:*(x::Bool, z::Dual) = ifelse(x, z, ifelse(signbit(real(value(z)))==0, zero(z), -zero(z)))
+Base.:*(x::Bool, z::Dual) = ifelse(x, z, ifelse(iszero(signbit(real(value(z)))), zero(z), -zero(z)))
 Base.:*(x::Dual, z::Bool) = z*x
 
 Base.:*(z::Dual, w::Dual) = Dual(value(z)*value(w), epsilon(z)*value(w)+value(z)*epsilon(w))
@@ -246,7 +261,7 @@ Base.:/(z::Dual, x::Number) = Dual(value(z)/x, epsilon(z)/x)
 
 for f in [:(Base.:^), :(NaNMath.pow)]
     @eval function ($f)(z::Dual, w::Dual)
-        if epsilon(w) == 0.0
+        if iszero(epsilon(w))
             return $f(z, value(w))
         end
         val = $f(value(z), value(w))

test/automatic_differentiation_test.jl

@@ -127,6 +127,7 @@ z = Dual(1.0+1.0im,cis(π/4))
 z = Dual(1.0+1.0im,cis(π/2))
 @test abs(z) ≡ sqrt(2) + 1/sqrt(2)*ɛ
 
+
 # tests vectorized methods
 const zv = dual.(collect(1.0:10.0), ones(10))
 
@@ -173,3 +174,12 @@ end
 
 @test value(3) == 3
 @test epsilon(44.0) ≈ 0.0
+
+@test one(Dual{Float64}) == Dual(1,0)
+@test isone(Dual(1,0))
+@test isone(one(rand(Dual{Float64})))
+
+@test zero(Dual{Float64}) == Dual(0,0)
+@test iszero(Dual(0,0))
+
+@test copysign(Dual(-1,-2), Dual(2,3)) == Dual(1,2)