Define precision for Dual (#580)

* Define `precision` for `Dual`

* Fix support of `base` keyword argument

* Fix typo

* Yet another typo...

src/dual.jl

@@ -262,6 +262,18 @@ Base.copy(d::Dual) = d
 Base.eps(d::Dual) = eps(value(d))
 Base.eps(::Type{D}) where {D<:Dual} = eps(valtype(D))
 
+# The `base` keyword was added in Julia 1.8:
+# https://github.com/JuliaLang/julia/pull/42428
+if VERSION < v"1.8.0-DEV.725"
+    Base.precision(d::Dual) = precision(value(d))
+    Base.precision(::Type{D}) where {D<:Dual} = precision(valtype(D))
+else
+    Base.precision(d::Dual; base::Integer=2) = precision(value(d); base=base)
+    function Base.precision(::Type{D}; base::Integer=2) where {D<:Dual}
+        precision(valtype(D); base=base)
+    end
+end
+
 function Base.nextfloat(d::ForwardDiff.Dual{T,V,N}) where {T,V,N}
     ForwardDiff.Dual{T}(nextfloat(d.value), d.partials)
 end

test/DualTest.jl

@@ -105,6 +105,17 @@ for N in (0,3), M in (0,4), V in (Int, Float32)
         @test eps(NESTED_FDNUM) === eps(PRIMAL)
         @test eps(typeof(NESTED_FDNUM)) === eps(V)
 
+        @test precision(FDNUM) === precision(PRIMAL)
+        @test precision(typeof(FDNUM)) === precision(V)
+        @test precision(NESTED_FDNUM) === precision(PRIMAL)
+        @test precision(typeof(NESTED_FDNUM)) === precision(V)
+        if VERSION >= v"1.8.0-DEV.725" # https://github.com/JuliaLang/julia/pull/42428
+            @test precision(FDNUM; base=10) === precision(PRIMAL; base=10)
+            @test precision(typeof(FDNUM); base=10) === precision(V; base=10)
+            @test precision(NESTED_FDNUM; base=10) === precision(PRIMAL; base=10)
+            @test precision(typeof(NESTED_FDNUM); base=10) === precision(V; base=10)
+        end
+
         @test floor(Int, FDNUM) === floor(Int, PRIMAL)
         @test floor(Int, FDNUM2) === floor(Int, PRIMAL2)
         @test floor(Int, NESTED_FDNUM) === floor(Int, PRIMAL)