fix: use better epsilon

Author: avik-pal

src/Compiler.jl

@@ -702,9 +702,10 @@ function optimization_passes(
     dus_to_concat::Bool=false,
     recognize_comms::Bool=true,
     lower_comms::Bool=true,
-    max_constant_threshold::Int=1024,
     backend::String="gpu",
 )
+    (; max_constant_threshold) = compile_options
+
     transform_passes_list = [
         "patterns=compare_op_canon<16>",
         "transpose_transpose<16>",

src/TestUtils.jl

@@ -20,8 +20,21 @@ function construct_test_array(::Type{T}, dims::Int...) where {T}
     return reshape(collect(T, 1:prod(dims)), dims...)
 end
 
+# https://github.com/JuliaDiff/FiniteDiff.jl/blob/3a8c3d8d87e59de78e2831787a3f54b12b7c2075/src/epsilons.jl#L133
+function default_epslion(::Val{fdtype}, ::Type{T}) where {fdtype,T}
+    if fdtype == :forward
+        return sqrt(eps(real(T)))
+    elseif fdtype == :central
+        return cbrt(eps(real(T)))
+    elseif fdtype == :hcentral
+        return eps(T)^(T(1 / 4))
+    else
+        return one(real(T))
+    end
+end
+
 function finite_difference_gradient(
-    f, x::AbstractArray{T}; epsilon=eps(T)^(T(3 / 4))
+    f, x::AbstractArray{T}; epsilon=default_epslion(Val(:central), T)
 ) where {T}
     onehot_matrix = Reactant.promote_to(
         TracedRArray{Reactant.unwrapped_eltype(T),2},

src/TracedRNumber.jl

@@ -491,6 +491,7 @@ for (jlop, hloop) in (
     (:(Base.log), :log),
     (:(Base.log1p), :log_plus_one),
     (:(Base.sqrt), :sqrt),
+    (:(Base.cbrt), :cbrt),
     (:(Base.acos), :acos),
     (:(Base.acosh), :acosh),
     (:(Base.asin), :asin),