diff --git a/base/bool.jl b/base/bool.jl
index c867ede02515d..98081d1693e95 100644
--- a/base/bool.jl
+++ b/base/bool.jl
@@ -64,6 +64,8 @@ cld(x::Bool, y::Bool) = div(x,y)
 rem(x::Bool, y::Bool) = y ? false : throw(DivideError())
 mod(x::Bool, y::Bool) = rem(x,y)
 
+promote_op{T}(op::Type{T}, ::Type{Bool}) = T # to fix ambiguity
+promote_op(op, ::Type{Bool}) = typeof(op(true))
 promote_op(op, ::Type{Bool}, ::Type{Bool}) = typeof(op(true, true))
 promote_op(::typeof(^), ::Type{Bool}, ::Type{Bool}) = Bool
 promote_op{T<:Integer}(::typeof(^), ::Type{Bool}, ::Type{T}) = Bool
diff --git a/base/nullable.jl b/base/nullable.jl
index 310d0a5473731..2458129022a17 100644
--- a/base/nullable.jl
+++ b/base/nullable.jl
@@ -57,18 +57,6 @@ end
 
 isnull(x::Nullable) = x.isnull
 
-function isequal(x::Nullable, y::Nullable)
-    if x.isnull && y.isnull
-        return true
-    elseif x.isnull || y.isnull
-        return false
-    else
-        return isequal(x.value, y.value)
-    end
-end
-
-==(x::Nullable, y::Nullable) = throw(NullException())
-
 const nullablehash_seed = UInt === UInt64 ? 0x932e0143e51d0171 : 0xe51d0171
 
 function hash(x::Nullable, h::UInt)
@@ -78,3 +66,91 @@ function hash(x::Nullable, h::UInt)
         return hash(x.value, h + nullablehash_seed)
     end
 end
+
+
+## Operators
+
+"""
+    null_safe_op(f::Any, ::Type)::Bool
+    null_safe_op(f::Any, ::Type, ::Type)::Bool
+
+Returns whether an operation `f` can safely be applied to any value of the passed type(s).
+Returns `false` by default.
+
+Custom types should implement methods for some or all operations `f` when applicable:
+returning `true` means that the operation may be called on any value without
+throwing an error. In particular, this means that the operation can be applied on
+the whole domain of the type *and on uninitialized objects*. Though returning invalid or
+nonsensical results is not a problem. As a general rule, these proporties are only true for
+unchecked operations on `isbits` types.
+
+Types declared as safe can benefit from higher performance for operations on nullable: by
+always computing the result even for null values, a branch is avoided, which helps
+vectorization.
+"""
+null_safe_op(f::Any, ::Type) = false
+null_safe_op(f::Any, ::Type, ::Type) = false
+
+typealias UncheckedTypes Union{Checked.SignedInt, Checked.UnsignedInt}
+
+# Unary operators
+
+for op in (:+, :-, :~)
+    @eval begin
+        null_safe_op{T<:UncheckedTypes}(::typeof($op), ::Type{T}) = true
+    end
+end
+
+null_safe_op(::typeof(!), ::Type{Bool}) = true
+
+for op in (:+, :-, :!, :~)
+    @eval begin
+        @inline function $op{S}(x::Nullable{S})
+            R = promote_op($op, S)
+            if null_safe_op($op, S)
+                Nullable{R}($op(x.value), x.isnull)
+            else
+                x.isnull ? Nullable{R}() :
+                           Nullable{R}($op(x.value))
+            end
+        end
+    end
+end
+
+# Binary operators
+
+# Note this list does not include ^, ÷ and %
+# Operations between signed and unsigned types are not safe: promotion to unsigned
+# gives an InexactError for negative numbers
+for op in (:+, :-, :*, :/, :&, :|, :<<, :>>, :(>>>),
+           :(==), :<, :>, :<=, :>=)
+    @eval begin
+        null_safe_op{S<:Checked.SignedInt,
+                     T<:Checked.SignedInt}(::typeof($op), ::Type{S}, ::Type{T}) = true
+        null_safe_op{S<:Checked.UnsignedInt,
+                     T<:Checked.UnsignedInt}(::typeof($op), ::Type{S}, ::Type{T}) = true
+    end
+end
+
+for op in (:+, :-, :*, :/, :%, :÷, :&, :|, :^, :<<, :>>, :(>>>),
+           :(==), :<, :>, :<=, :>=)
+    @eval begin
+        @inline function $op{S,T}(x::Nullable{S}, y::Nullable{T})
+            R = promote_op($op, S, T)
+            if null_safe_op($op, S, T)
+                Nullable{R}($op(x.value, y.value), x.isnull | y.isnull)
+            else
+                (x.isnull | y.isnull) ? Nullable{R}() :
+                                        Nullable{R}($op(x.value, y.value))
+            end
+        end
+    end
+end
+
+@inline function isequal{S,T}(x::Nullable{S}, y::Nullable{T})
+    if null_safe_op(isequal, S, T)
+        (x.isnull & y.isnull) | ((!x.isnull & !y.isnull) & isequal(x.value, y.value))
+    else
+        (x.isnull & y.isnull) || ((!x.isnull & !y.isnull) && isequal(x.value, y.value))
+    end
+end
diff --git a/test/nullable.jl b/test/nullable.jl
index 3d4d0b3a11ac2..7371936924e9f 100644
--- a/test/nullable.jl
+++ b/test/nullable.jl
@@ -243,6 +243,160 @@ for T in types
     @test hash(x3) != hash(x4)
 end
 
+
+## operators
+
+srand(1)
+
+# check for fast path (null-safe combinations of types)
+for S in Union{Base.Checked.SignedInt, Base.Checked.UnsignedInt}.types,
+    T in Union{Base.Checked.SignedInt, Base.Checked.UnsignedInt}.types
+    # mixing signed and unsigned types is unsafe (slow path tested below)
+    ((S <: Signed) $ (T <: Signed)) && continue
+
+    u0 = zero(S)
+    u1 = one(S)
+    u2 = rand(S)
+
+    v0 = zero(T)
+    v1 = one(T)
+    v2 = rand(T)
+    # unary operators
+    for op in (+, -, ~)
+        @test op(Nullable(u0)) === Nullable(op(u0))
+        @test op(Nullable(u1)) === Nullable(op(u1))
+        @test op(Nullable(u2)) === Nullable(op(u2))
+        @test op(Nullable(u0, true)) === Nullable(op(u0), true)
+    end
+
+    for u in (u0, u1, u2), v in (v0, v1, v2)
+        # safe binary operators: === checks that the fast-path was taken (no branch)
+        for op in (+, -, *, /, &, |, >>, <<, >>>,
+                   <, >, <=, >=)
+            @test op(Nullable(u), Nullable(v)) === Nullable(op(u, v))
+            @test op(Nullable(u, true), Nullable(v, true)) === Nullable(op(u, v), true)
+            @test op(Nullable(u), Nullable(v, true)) === Nullable(op(u, v), true)
+            @test op(Nullable(u, true), Nullable(v)) === Nullable(op(u, v), true)
+        end
+
+        # unsafe binary operators: we cannot use === as the underlying value is undefined
+        # ^
+        if S <: Integer
+            @test_throws DomainError Nullable(u)^Nullable(-signed(one(v)))
+        end
+        @test isequal(Nullable(u)^Nullable(2*one(T)), Nullable(u^(2*one(T))))
+        R = Base.promote_op(^, S, T)
+        x = Nullable(u, true)^Nullable(-abs(v), true)
+        @test isnull(x) && eltype(x) === R
+        x = Nullable(u, false)^Nullable(-abs(v), true)
+        @test isnull(x) && eltype(x) === R
+        x = Nullable(u, true)^Nullable(-abs(v), false)
+        @test isnull(x) && eltype(x) === R
+
+        # ÷ and %
+        for op in (÷, %)
+            if T <: Integer && v == 0
+                @test_throws DivideError op(Nullable(u), Nullable(v))
+            else
+                @test isequal(op(Nullable(u), Nullable(v)), Nullable(op(u, v)))
+            end
+            R = Base.promote_op(op, S, T)
+            x = op(Nullable(u, true), Nullable(v, true))
+            @test isa(x, Nullable{R}) && isnull(x)
+            x = op(Nullable(u, false), Nullable(v, true))
+            @test isa(x, Nullable{R}) && isnull(x)
+            x = op(Nullable(u, true), Nullable(v, false))
+            @test isa(x, Nullable{R}) && isnull(x)
+        end
+    end
+end
+
+@test !Nullable(true) === Nullable(false)
+@test !Nullable(false) === Nullable(true)
+@test !(Nullable(true, true)) === Nullable(false, true)
+@test !(Nullable(false, true)) === Nullable(true, true)
+
+# test all types (including null-unsafe types and combinations of types)
+for S in Union{Base.Checked.SignedInt, Base.Checked.UnsignedInt, BigInt, BigFloat}.types,
+    T in Union{Base.Checked.SignedInt, Base.Checked.UnsignedInt, BigInt, BigFloat}.types
+    u0 = zero(S)
+    u1 = one(S)
+    u2 = S <: Union{BigInt, BigFloat} ? S(rand(Int128)) : rand(S)
+
+    v0 = zero(T)
+    v1 = one(T)
+    v2 = T <: Union{BigInt, BigFloat} ? T(rand(Int128)) : rand(T)
+
+    v2 > 5 && (v2 = T(5)) # Work around issue #16989
+
+    # unary operators
+    for op in (+, -, ~) # !
+        T <: BigFloat && op == (~) && continue
+        R = Base.promote_op(op, T)
+        x = op(Nullable(v0))
+        @test isa(x, Nullable{R}) && isequal(x, Nullable(op(v0)))
+        x = op(Nullable(v1))
+        @test isa(x, Nullable{R}) && isequal(x, Nullable(op(v1)))
+        x = op(Nullable(v2))
+        @test isa(x, Nullable{R}) && isequal(x, Nullable(op(v2)))
+        x = op(Nullable(v0, true))
+        @test isa(x, Nullable{R}) && isnull(x)
+        x = op(Nullable{R}())
+        @test isa(x, Nullable{R}) && isnull(x)
+    end
+
+    for u in (u0, u1, u2), v in (v0, v1, v2)
+        # safe binary operators
+        for op in (+, -, *, /, &, |, >>, <<, >>>,
+                   <, >, <=, >=)
+            (T <: BigFloat || S <: BigFloat) && op in (&, |, >>, <<, >>>) && continue
+            if S <: Unsigned || T <: Unsigned
+                @test isequal(op(Nullable(abs(u)), Nullable(abs(v))), Nullable(op(abs(u), abs(v))))
+            else
+                @test isequal(op(Nullable(u), Nullable(v)), Nullable(op(u, v)))
+            end
+            R = Base.promote_op(op, S, T)
+            x = op(Nullable(u, true), Nullable(v, true))
+            @test isa(x, Nullable{R}) && isnull(x)
+            x = op(Nullable(u), Nullable(v, true))
+            @test isa(x, Nullable{R}) && isnull(x)
+            x = op(Nullable(u, true), Nullable(v))
+            @test isa(x, Nullable{R}) && isnull(x)
+        end
+
+        # unsafe binary operators
+        # ^
+        if S <: Integer && !(T <: BigFloat)
+            @test_throws DomainError Nullable(u)^Nullable(-signed(one(v)))
+        end
+        @test isequal(Nullable(u)^Nullable(2*one(T)), Nullable(u^(2*one(T))))
+        R = Base.promote_op(^, S, T)
+        x = Nullable(u, true)^Nullable(-abs(v), true)
+        @test isnull(x) && eltype(x) === R
+        x = Nullable(u, false)^Nullable(-abs(v), true)
+        @test isnull(x) && eltype(x) === R
+        x = Nullable(u, true)^Nullable(-abs(v), false)
+        @test isnull(x) && eltype(x) === R
+
+        # ÷ and %
+        for op in (÷, %)
+            if S <: Integer && T <: Integer && v == 0
+                @test_throws DivideError op(Nullable(u), Nullable(v))
+            else
+                @test isequal(op(Nullable(u), Nullable(v)), Nullable(op(u, v)))
+            end
+            R = Base.promote_op(op, S, T)
+            x = op(Nullable(u, true), Nullable(v, true))
+            @test isnull(x) && eltype(x) === R
+            x = op(Nullable(u, false), Nullable(v, true))
+            @test isnull(x) && eltype(x) === R
+            x = op(Nullable(u, true), Nullable(v, false))
+            @test isnull(x) && eltype(x) === R
+        end
+    end
+end
+
+
 type TestNType{T}
     v::Nullable{T}
 end