Release constraint on real

Author: tansongchen

examples/integration.jl

@@ -2,6 +2,7 @@ using TaylorDiff: TaylorDiff, TaylorScalar, make_seed, flatten, get_coefficient,
                   set_coefficient, append_coefficient
 using TaylorSeries, TaylorIntegration
 using ODEProblemLibrary, OrdinaryDiffEq, BenchmarkTools, Symbolics
+SymbolicUtils.ENABLE_HASHCONSING[] = true
 
 # There are two ways to compute the Taylor coefficients of a ODE solution
 # 1. Using naive repeated differentiation
@@ -109,3 +110,11 @@ function simplify_array_test()
     fast_oop, fast_iip = build_jetcoeffs(prob.f, prob.p, Val(P), length(prob.u0))
     @btime $fast_oop($prob.u0, $t0)
 end
+
+@generated function evaluate_polynomial(t::TaylorScalar{T, P}, z) where {T, P}
+    ex = :(v[$(P + 1)])
+    for i in P:-1:1
+        ex = :(v[$i] + z * $ex)
+    end
+    return :($(Expr(:meta, :inline)); v = flatten(t); $ex)
+end

src/TaylorDiff.jl

@@ -4,9 +4,9 @@ module TaylorDiff
     TaylorDiff.can_taylorize(V::Type)
 
 Determines whether the type V is allowed as the scalar type in a
-Dual. By default, only `<:Real` types are allowed.
+Dual. By default, only `<:Number` types are allowed.
 """
-can_taylorize(::Type{<:Real}) = true
+can_taylorize(::Type{<:Number}) = true
 can_taylorize(::Type) = false
 
 @noinline function throw_cannot_taylorize(V::Type)

src/array.jl

@@ -65,7 +65,7 @@ Base.@propagate_inbounds function Base.setindex!(
 end
 
 Base.@propagate_inbounds function Base.setindex!(
-        a::TaylorArray, s::Real, i::Int...)
+        a::TaylorArray, s, i::Int...)
     value(a)[i...] = s
     return a
 end

src/chainrules.jl

@@ -57,7 +57,7 @@ function rrule(::typeof(Base.getindex), a::TaylorArray, i::Int...)
 end
 
 function rrule(::typeof(*), A::AbstractMatrix{S},
-        t::AbstractVector{TaylorScalar{T, N}}) where {N, S <: Real, T <: Real}
+        t::AbstractVector{TaylorScalar{T, N}}) where {N, S, T}
     project_A = ProjectTo(A)
     function gemv_pullback(x̄)
         x̂ = reinterpret(reshape, T, x̄)
@@ -68,7 +68,7 @@ function rrule(::typeof(*), A::AbstractMatrix{S},
 end
 
 function rrule(::typeof(*), A::AbstractMatrix{S},
-        B::AbstractMatrix{TaylorScalar{T, N}}) where {N, S <: Real, T <: Real}
+        B::AbstractMatrix{TaylorScalar{T, N}}) where {N, S, T}
     project_A = ProjectTo(A)
     project_B = ProjectTo(B)
     function gemm_pullback(x̄)

src/derivative.jl

@@ -1,7 +1,7 @@
 export derivative, derivative!, derivatives
 
 # Added to help Zygote infer types
-@inline make_seed(x::T, l::T, ::Val{P}) where {T <: Real, P} = TaylorScalar{P}(x, l)
+@inline make_seed(x::T, l::T, ::Val{P}) where {T <: Number, P} = TaylorScalar{P}(x, l)
 @inline make_seed(x::A, l::A, p) where {A <: AbstractArray} = broadcast(make_seed, x, l, p)
 
 """

src/primitive.jl

@@ -119,7 +119,7 @@ sincos(t::TaylorScalar) = (sin(t), cos(t))
 @inline *(a::TaylorScalar, b::Number) = TaylorScalar(value(a) * b, partials(a) .* b)
 @inline /(a::TaylorScalar, b::Number) = TaylorScalar(value(a) / b, partials(a) ./ b)
 
-const AMBIGUOUS_TYPES = (AbstractFloat, Irrational, Integer, Rational, Real, RoundingMode)
+const AMBIGUOUS_TYPES = (AbstractFloat, Irrational, Integer, Rational, Real, Complex, RoundingMode)
 
 for op in [:>, :<, :(==), :(>=), :(<=)]
     for R in AMBIGUOUS_TYPES
@@ -164,7 +164,7 @@ end
 @inline literal_pow(::typeof(^), x::TaylorScalar, ::Val{-1}) = inv(x)
 @inline literal_pow(::typeof(^), x::TaylorScalar, ::Val{-2}) = (i = inv(x); i * i)
 
-for R in (Integer, Real)
+for R in (Integer, Real, Complex)
     @eval @immutable function ^(t::TaylorScalar{T, P}, n::S) where {S <: $R, T, P}
         f = flatten(t)
         v[0] = f[0]^n