Add more operators (#6)

src/conversion.jl

@@ -2,6 +2,10 @@
 Base.promote_rule(::Type{Tracer}, ::Type{N}) where {N<:Number} = Tracer
 Base.promote_rule(::Type{N}, ::Type{Tracer}) where {N<:Number} = Tracer
 
+Base.big(::Type{Tracer})   = Tracer
+Base.widen(::Type{Tracer}) = Tracer
+Base.widen(t::Tracer)      = t
+
 Base.convert(::Type{Tracer}, x::Number)   = tracer()
 Base.convert(::Type{Tracer}, t::Tracer)   = t
 Base.convert(::Type{<:Number}, t::Tracer) = t

src/operators.jl

@@ -1,53 +1,91 @@
-## Extent Base operators
-for fn in (:+, :-, :*, :/)
+## Operator definitions
+
+#! format: off
+ops_2_to_1 = (
+    :+, :-, :*, :/, 
+    # division
+    :div, :fld, :cld, 
+    # modulo
+    :mod, :rem,
+    # exponentials
+    :ldexp, 
+    # sign
+    :copysign, :flipsign,
+    # other
+    :hypot,
+)
+
+ops_1_to_1 = (
+    # trigonometric functions
+    :deg2rad, :rad2deg,
+    :cos, :cosd, :cosh, :cospi, :cosc, 
+    :sin, :sind, :sinh, :sinpi, :sinc, 
+    :tan, :tand, :tanh,
+    # reciprocal trigonometric functions
+    :csc, :cscd, :csch, 
+    :sec, :secd, :sech, 
+    :cot, :cotd, :coth,
+    # inverse trigonometric functions
+    :acos, :acosd, :acosh, 
+    :asin, :asind, :asinh, 
+    :atan, :atand, :atanh, 
+    :asec, :asech, 
+    :acsc, :acsch, 
+    :acot, :acoth,
+    # exponentials
+    :exp, :exp2, :exp10, :expm1, 
+    :log, :log2, :log10, :log1p, 
+    :abs, :abs2, 
+    # roots
+    :sqrt, :cbrt,
+    # absolute values
+    :abs, :abs2,
+    # rounding
+    :floor, :ceil, :trunc,
+    # other
+    :inv, :signbit, :hypot, :sign, :mod2pi
+)
+
+ops_1_to_2 = (
+    # trigonometric
+    :sincos,
+    :sincosd,
+    :sincospi,
+    # exponentials
+    :frexp,
+)
+#! format: on
+
+for fn in ops_1_to_1
+    @eval Base.$fn(t::Tracer) = t
+end
+
+for fn in ops_1_to_2
+    @eval Base.$fn(t::Tracer) = (t, t)
+end
+
+for fn in ops_2_to_1
     @eval Base.$fn(a::Tracer, b::Tracer) = tracer(a, b)
-    for T in (:Number,)
-        @eval Base.$fn(t::Tracer, ::$T) = t
-        @eval Base.$fn(::$T, t::Tracer) = t
-    end
+    @eval Base.$fn(t::Tracer, ::Number) = t
+    @eval Base.$fn(::Number, t::Tracer) = t
 end
 
+# Extra types required for exponent
 Base.:^(a::Tracer, b::Tracer) = tracer(a, b)
-for T in (:Number, :Integer, :Rational)
+for T in (:Real, :Integer, :Rational)
     @eval Base.:^(t::Tracer, ::$T) = t
     @eval Base.:^(::$T, t::Tracer) = t
 end
 Base.:^(t::Tracer, ::Irrational{:ℯ}) = t
 Base.:^(::Irrational{:ℯ}, t::Tracer) = t
 
-## Two-argument functions
-for fn in (:div, :fld, :cld)
-    @eval Base.$fn(a::Tracer, b::Tracer) = tracer(a, b)
-    @eval Base.$fn(t::Tracer, ::Number) = t
-    @eval Base.$fn(::Number, t::Tracer) = t
+## Precision operators create empty Tracer
+for fn in (:eps, :nextfloat, :floatmin, :floatmax, :maxintfloat, :typemax)
+    @eval Base.$fn(::Tracer) = tracer()
 end
 
-## Single-argument functions 
-
-#! format: off
-scalar_operations = (
-    :exp2, :deg2rad, :rad2deg,
-    :cos,  :cosd,  :cosh, :cospi, :cosc,
-    :sin,  :sind,  :sinh, :sinpi, :sinc,
-    :tan,  :tand,  :tanh,
-    :csc,  :cscd,  :csch,
-    :sec,  :secd,  :sech,
-    :cot,  :cotd,  :coth,
-    :acos, :acosd, :acosh,
-    :asin, :asind, :asinh,
-    :atan, :atand, :atanh,
-    :asec, :asech,
-    :acsc, :acsch,
-    :acot, :acoth,
-    :exp, :expm1, :exp10,
-    :frexp, :ldexp,
-    :abs, :abs2, :sqrt
-)
-#! format: on
-
-for fn in scalar_operations
-    @eval Base.$fn(t::Tracer) = t
-end
+## Rounding
+Base.round(t::Tracer, ::RoundingMode; kwargs...) = t
 
 ## Random numbers
 rand(::AbstractRNG, ::SamplerType{Tracer}) = tracer()