Add more primitives

Author: tansongchen

src/codegen.jl

@@ -8,15 +8,31 @@ using SymbolicUtils: Pow
 @scalar_rule rad2deg(x::Any) rad2deg(one(x))
 @scalar_rule asin(x::Any) inv(sqrt(1 - x^2))
 @scalar_rule acos(x::Any) inv(-sqrt(1 - x^2))
-@scalar_rule atan(x::Any) inv(1 + x^2)
+@scalar_rule atan(x::Any) inv(-(1 + x^2))
+@scalar_rule acot(x::Any) inv(-(1 + x^2))
+@scalar_rule acsc(x::Any) inv(x^2 * -sqrt(1 - x^-2))
+@scalar_rule asec(x::Any) inv(x^2 * sqrt(1 - x^-2))
 @scalar_rule log(x::Any) inv(x)
 @scalar_rule log10(x::Any) inv(log(10.0) * x)
 @scalar_rule log1p(x::Any) inv(x + 1)
 @scalar_rule log2(x::Any) inv(log(2.0) * x)
+@scalar_rule sinh(x::Any) cosh(x)
+@scalar_rule cosh(x::Any) sinh(x)
+@scalar_rule tanh(x::Any) 1-Ω^2
+@scalar_rule acosh(x::Any) inv(sqrt(x - 1) * sqrt(x + 1))
+@scalar_rule acoth(x::Any) inv(1 - x^2)
+@scalar_rule acsch(x::Any) inv(x^2 * -sqrt(1 + x^-2))
+@scalar_rule asech(x::Any) inv(x * -sqrt(1 - x^2))
+@scalar_rule asinh(x::Any) inv(sqrt(x^2 + 1))
+@scalar_rule atanh(x::Any) inv(1 - x^2)
 
 dummy = (NoTangent(), 1)
 @syms t₁
-for func in (+, -, deg2rad, rad2deg, asin, acos, atan, log, log10, log1p, log2)
+for func in (+, -, deg2rad, rad2deg,
+             sinh, cosh, tanh,
+             asin, acos, atan, asec, acsc, acot,
+             log, log10, log1p, log2,
+             asinh, acosh, atanh, asech, acsch, acoth)
     F = typeof(func)
     # base case
     @eval function (op::$F)(t::TaylorScalar{T, 2}) where {T}

src/primitive.jl

@@ -75,7 +75,7 @@ end
 
 for op in [:>, :<, :(==), :(>=), :(<=)]
     @eval @inline $op(a::Number, b::TaylorScalar) = $op(a, value(b)[1])
-    @eval @inline $op(a::TaylorScalar, b::Number) = $op(a, value(b)[1])
+    @eval @inline $op(a::TaylorScalar, b::Number) = $op(value(a)[1], b)
     @eval @inline $op(a::TaylorScalar, b::TaylorScalar) = $op(value(a)[1], value(b)[1])
 end
 
@@ -158,7 +158,7 @@ end
     end
 end
 
-raise(::T, df::S, t::TaylorScalar{T}) where {S <: Number, T <: Number} = df * t
+raise(::T, df::S, t::TaylorScalar{T, N}) where {S <: Real, T <: Number, N} = df * t
 
 @generated function raiseinv(f::T, df::TaylorScalar{T, M},
                              t::TaylorScalar{T, N}) where {T, M, N} # M + 1 == N

src/scalar.jl

@@ -54,6 +54,7 @@ end
 
 @inline value(t::TaylorScalar) = t.value
 @inline extract_derivative(t::TaylorScalar, i::Integer) = t.value[i]
+@inline extract_derivative(r, i::Integer) = false
 
 @inline zero(::Type{TaylorScalar{T, N}}) where {T, N} = TaylorScalar{T, N}(zero(T))
 @inline one(::Type{TaylorScalar{T, N}}) where {T, N} = TaylorScalar{T, N}(one(T))

test/primitive.jl

@@ -1,31 +1,34 @@
 using FiniteDifferences
 
 @testset "No derivative or linear" begin
-    some_number = 3.7
-    for f in (+, -, zero, one, adjoint, conj, deg2rad, rad2deg), order in (2, 4)
+    some_number, another_number = 1.9, 2.6
+    for f in (+, -, zero, one, adjoint, conj, deg2rad, rad2deg), order in (2,)
         @test derivative(f, some_number, order) ≈ 0.0
     end
+    for f in (+, -, <, <=, >, >=, ==), order in (2,)
+        @test derivative(x -> f(x, another_number), some_number, order) ≈ 0.0
+    end
 end
 
 @testset "Unary functions" begin
     some_number = 3.7
-    for f in (exp, expm1, exp2, exp10, sin, cos, sqrt, cbrt, inv), order in (2, 4)
+    for f in (exp, expm1, exp2, exp10, sin, cos, sqrt, cbrt, inv), order in (1, 4)
         fdm = central_fdm(12, order)
         @test derivative(f, some_number, order)≈fdm(f, some_number) rtol=1e-6
     end
 end
 
 @testset "Codegen" begin
     some_number = 0.6
-    for f in (log, ), order in (2, 4)
-        fdm = central_fdm(12, order, max_range=0.5)
+    for f in (log, sinh), order in (1, 4)
+        fdm = central_fdm(12, order, max_range = 0.5)
         @test derivative(f, some_number, order)≈fdm(f, some_number) rtol=1e-6
     end
 end
 
 @testset "Binary functions" begin
     some_number, another_number = 1.9, 2.6
-    for f in (*, /), order in (2, 4)
+    for f in (*, /), order in (1, 4)
         fdm = central_fdm(12, order)
         closure = x -> exp(f(x, another_number))
         @test derivative(closure, some_number, order)≈fdm(closure, some_number) rtol=1e-6