diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 56350777..a7536455 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -21,7 +21,7 @@ jobs:
           - '1.0'
           - '1.6'
           - '1'
-          - 'nightly'
+          # - 'nightly'
         os:
           - ubuntu-latest
         arch:
diff --git a/.gitignore b/.gitignore
index 78fb62c9..69feffb1 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,5 +4,6 @@
 *.DS_Store
 /docs/build/
 /docs/site/
+/docs/Manifest.toml
 /benchmark_data/
 /Manifest.toml
diff --git a/Project.toml b/Project.toml
index f7c66517..2ee06921 100644
--- a/Project.toml
+++ b/Project.toml
@@ -21,6 +21,7 @@ CommonSubexpressions = "0.3"
 DiffResults = "0.0.1, 0.0.2, 0.0.3, 0.0.4, 1.0.1"
 DiffRules = "1.4.0"
 DiffTests = "0.0.1, 0.1"
+IrrationalConstants = "0.1, 0.2"
 LogExpFunctions = "0.3"
 NaNMath = "0.2.2, 0.3, 1"
 Preferences = "1"
@@ -35,12 +36,13 @@ ForwardDiffStaticArraysExt = "StaticArrays"
 Calculus = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
 DiffTests = "de460e47-3fe3-5279-bb4a-814414816d5d"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Calculus", "DiffTests", "SparseArrays", "Test", "InteractiveUtils", "StaticArrays"]
+test = ["Calculus", "DiffTests", "IrrationalConstants", "SparseArrays", "Test", "InteractiveUtils", "StaticArrays"]
 
 [weakdeps]
-StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
\ No newline at end of file
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
diff --git a/docs/Project.toml b/docs/Project.toml
index 050425cf..9b9a6718 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,3 +1,6 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+
+[compat]
+Documenter = "1"
diff --git a/docs/make.jl b/docs/make.jl
index e653afca..4bbc19af 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -11,7 +11,8 @@ makedocs(modules=[ForwardDiff],
                     "Upgrading from Older Versions" => "user/upgrade.md"],
                   "Developer Documentation" => [
                     "How ForwardDiff Works" => "dev/how_it_works.md",
-                    "How to Contribute" => "dev/contributing.md"]])
+                    "How to Contribute" => "dev/contributing.md"]],
+         checkdocs=:exports)
 
 deploydocs(
     repo = "github.com/JuliaDiff/ForwardDiff.jl.git"
diff --git a/ext/ForwardDiffStaticArraysExt.jl b/ext/ForwardDiffStaticArraysExt.jl
index cb9222ff..25b73fb8 100644
--- a/ext/ForwardDiffStaticArraysExt.jl
+++ b/ext/ForwardDiffStaticArraysExt.jl
@@ -7,7 +7,7 @@ using ForwardDiff: Dual, partials, GradientConfig, JacobianConfig, HessianConfig
                    gradient, hessian, jacobian, gradient!, hessian!, jacobian!,
                    extract_gradient!, extract_jacobian!, extract_value!,
                    vector_mode_gradient, vector_mode_gradient!,
-                   vector_mode_jacobian, vector_mode_jacobian!, valtype, value, _lyap_div!
+                   vector_mode_jacobian, vector_mode_jacobian!, valtype, value
 using DiffResults: DiffResult, ImmutableDiffResult, MutableDiffResult
 
 @generated function dualize(::Type{T}, x::StaticArray) where T
@@ -23,27 +23,25 @@ end
 
 @inline static_dual_eval(::Type{T}, f, x::StaticArray) where T = f(dualize(T, x))
 
+# To fix method ambiguity issues:
 function LinearAlgebra.eigvals(A::Symmetric{<:Dual{Tg,T,N}, <:StaticArrays.StaticMatrix}) where {Tg,T<:Real,N}
-    λ,Q = eigen(Symmetric(value.(parent(A))))
-    parts = ntuple(j -> diag(Q' * getindex.(partials.(A), j) * Q), N)
-    Dual{Tg}.(λ, tuple.(parts...))
+    return ForwardDiff._eigvals(A)
 end
-
 function LinearAlgebra.eigen(A::Symmetric{<:Dual{Tg,T,N}, <:StaticArrays.StaticMatrix}) where {Tg,T<:Real,N}
-    λ = eigvals(A)
-    _,Q = eigen(Symmetric(value.(parent(A))))
-    parts = ntuple(j -> Q*ForwardDiff._lyap_div!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N)
-    Eigen(λ,Dual{Tg}.(Q, tuple.(parts...)))
+    return ForwardDiff._eigen(A)
 end
 
+# For `MMatrix` we can use the in-place method
+ForwardDiff._lyap_div!!(A::StaticArrays.MMatrix, λ::AbstractVector) = ForwardDiff._lyap_div!(A, λ)
+
 # Gradient
-@inline ForwardDiff.gradient(f, x::StaticArray)                      = vector_mode_gradient(f, x)
-@inline ForwardDiff.gradient(f, x::StaticArray, cfg::GradientConfig) = gradient(f, x)
-@inline ForwardDiff.gradient(f, x::StaticArray, cfg::GradientConfig, ::Val) = gradient(f, x)
+@inline ForwardDiff.gradient(f::F, x::StaticArray) where F                      = vector_mode_gradient(f, x)
+@inline ForwardDiff.gradient(f::F, x::StaticArray, cfg::GradientConfig) where F = gradient(f, x)
+@inline ForwardDiff.gradient(f::F, x::StaticArray, cfg::GradientConfig, ::Val) where F = gradient(f, x)
 
-@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray) = vector_mode_gradient!(result, f, x)
-@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::GradientConfig) = gradient!(result, f, x)
-@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::GradientConfig, ::Val) = gradient!(result, f, x)
+@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f::F, x::StaticArray) where F = vector_mode_gradient!(result, f, x)
+@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f::F, x::StaticArray, cfg::GradientConfig) where F = gradient!(result, f, x)
+@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f::F, x::StaticArray, cfg::GradientConfig, ::Val) where F = gradient!(result, f, x)
 
 @generated function extract_gradient(::Type{T}, y::Real, x::S) where {T,S<:StaticArray}
     result = Expr(:tuple, [:(partials(T, y, $i)) for i in 1:length(x)]...)
@@ -65,13 +63,13 @@ end
 end
 
 # Jacobian
-@inline ForwardDiff.jacobian(f, x::StaticArray) = vector_mode_jacobian(f, x)
-@inline ForwardDiff.jacobian(f, x::StaticArray, cfg::JacobianConfig) = jacobian(f, x)
-@inline ForwardDiff.jacobian(f, x::StaticArray, cfg::JacobianConfig, ::Val) = jacobian(f, x)
+@inline ForwardDiff.jacobian(f::F, x::StaticArray) where F = vector_mode_jacobian(f, x)
+@inline ForwardDiff.jacobian(f::F, x::StaticArray, cfg::JacobianConfig) where F  = jacobian(f, x)
+@inline ForwardDiff.jacobian(f::F, x::StaticArray, cfg::JacobianConfig, ::Val)  where F = jacobian(f, x)
 
-@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray) = vector_mode_jacobian!(result, f, x)
-@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::JacobianConfig) = jacobian!(result, f, x)
-@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::JacobianConfig, ::Val) = jacobian!(result, f, x)
+@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f::F, x::StaticArray)  where F = vector_mode_jacobian!(result, f, x)
+@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f::F, x::StaticArray, cfg::JacobianConfig) where F  = jacobian!(result, f, x)
+@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f::F, x::StaticArray, cfg::JacobianConfig, ::Val) where F  = jacobian!(result, f, x)
 
 @generated function extract_jacobian(::Type{T}, ydual::StaticArray, x::S) where {T,S<:StaticArray}
     M, N = length(ydual), length(x)
@@ -110,18 +108,18 @@ end
 end
 
 # Hessian
-ForwardDiff.hessian(f, x::StaticArray) = jacobian(y -> gradient(f, y), x)
-ForwardDiff.hessian(f, x::StaticArray, cfg::HessianConfig) = hessian(f, x)
-ForwardDiff.hessian(f, x::StaticArray, cfg::HessianConfig, ::Val) = hessian(f, x)
+ForwardDiff.hessian(f::F, x::StaticArray) where F = jacobian(y -> gradient(f, y), x)
+ForwardDiff.hessian(f::F, x::StaticArray, cfg::HessianConfig) where F = hessian(f, x)
+ForwardDiff.hessian(f::F, x::StaticArray, cfg::HessianConfig, ::Val) where F = hessian(f, x)
 
-ForwardDiff.hessian!(result::AbstractArray, f, x::StaticArray) = jacobian!(result, y -> gradient(f, y), x)
+ForwardDiff.hessian!(result::AbstractArray, f::F, x::StaticArray) where F = jacobian!(result, y -> gradient(f, y), x)
 
-ForwardDiff.hessian!(result::MutableDiffResult, f, x::StaticArray) = hessian!(result, f, x, HessianConfig(f, result, x))
+ForwardDiff.hessian!(result::MutableDiffResult, f::F, x::StaticArray) where F = hessian!(result, f, x, HessianConfig(f, result, x))
 
-ForwardDiff.hessian!(result::ImmutableDiffResult, f, x::StaticArray, cfg::HessianConfig) = hessian!(result, f, x)
-ForwardDiff.hessian!(result::ImmutableDiffResult, f, x::StaticArray, cfg::HessianConfig, ::Val) = hessian!(result, f, x)
+ForwardDiff.hessian!(result::ImmutableDiffResult, f::F, x::StaticArray, cfg::HessianConfig) where F = hessian!(result, f, x)
+ForwardDiff.hessian!(result::ImmutableDiffResult, f::F, x::StaticArray, cfg::HessianConfig, ::Val) where F = hessian!(result, f, x)
 
-function ForwardDiff.hessian!(result::ImmutableDiffResult, f, x::StaticArray)
+function ForwardDiff.hessian!(result::ImmutableDiffResult, f::F, x::StaticArray) where F
     T = typeof(Tag(f, eltype(x)))
     d1 = dualize(T, x)
     d2 = dualize(T, d1)
diff --git a/src/ForwardDiff.jl b/src/ForwardDiff.jl
index a27d6dba..b2670451 100644
--- a/src/ForwardDiff.jl
+++ b/src/ForwardDiff.jl
@@ -7,7 +7,12 @@ if VERSION >= v"1.6"
 end
 using Random
 using LinearAlgebra
-
+if VERSION < v"1.2.0-DEV.125" # 1da48c2e4028c1514ed45688be727efbef1db884
+    require_one_based_indexing(A...) = !Base.has_offset_axes(A...) || throw(ArgumentError(
+        "offset arrays are not supported but got an array with index other than 1"))
+else
+    using Base: require_one_based_indexing
+end
 import Printf
 import NaNMath
 import SpecialFunctions
diff --git a/src/derivative.jl b/src/derivative.jl
index 5d7e5dab..b39e2a48 100644
--- a/src/derivative.jl
+++ b/src/derivative.jl
@@ -22,8 +22,9 @@ stored in `y`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-@inline function derivative(f!, y::AbstractArray, x::Real,
-                            cfg::DerivativeConfig{T} = DerivativeConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {T, CHK}
+@inline function derivative(f!::F, y::AbstractArray, x::Real,
+                            cfg::DerivativeConfig{T} = DerivativeConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {F, T, CHK}
+    require_one_based_indexing(y)
     CHK && checktag(T, f!, x)
     ydual = cfg.duals
     seed!(ydual, y)
@@ -42,6 +43,7 @@ This method assumes that `isa(f(x), Union{Real,AbstractArray})`.
 """
 @inline function derivative!(result::Union{AbstractArray,DiffResult},
                              f::F, x::R) where {F,R<:Real}
+    result isa DiffResult || require_one_based_indexing(result)
     T = typeof(Tag(f, R))
     ydual = f(Dual{T}(x, one(x)))
     result = extract_value!(T, result, ydual)
@@ -58,8 +60,9 @@ called as `f!(y, x)` where the result is stored in `y`.
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
 @inline function derivative!(result::Union{AbstractArray,DiffResult},
-                             f!, y::AbstractArray, x::Real,
-                             cfg::DerivativeConfig{T} = DerivativeConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {T, CHK}
+                             f!::F, y::AbstractArray, x::Real,
+                             cfg::DerivativeConfig{T} = DerivativeConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {F, T, CHK}
+    result isa DiffResult ? require_one_based_indexing(y) : require_one_based_indexing(result, y)
     CHK && checktag(T, f!, x)
     ydual = cfg.duals
     seed!(ydual, y)
diff --git a/src/dual.jl b/src/dual.jl
index 5afb2144..cc78b59b 100644
--- a/src/dual.jl
+++ b/src/dual.jl
@@ -78,6 +78,10 @@ end
 @inline Dual{T,V,N}(x::Number) where {T,V,N} = convert(Dual{T,V,N}, x)
 @inline Dual{T,V}(x) where {T,V} = convert(Dual{T,V}, x)
 
+# Fix method ambiguity issue by adapting the definition in Base to `Dual`s
+Dual{T,V,N}(x::Base.TwicePrecision) where {T,V,N} =
+    (Dual{T,V,N}(x.hi) + Dual{T,V,N}(x.lo))::Dual{T,V,N}
+
 ##############################
 # Utility/Accessor Functions #
 ##############################
@@ -340,7 +344,6 @@ else
     Base.div(x::Dual, y::Dual) = div(value(x), value(y))
 end
 
-Base.hash(d::Dual) = hash(value(d))
 Base.hash(d::Dual, hsh::UInt) = hash(value(d), hsh)
 
 function Base.read(io::IO, ::Type{Dual{T,V,N}}) where {T,V,N}
@@ -416,7 +419,7 @@ function Base.promote_rule(::Type{Dual{T,A,N}},
     return Dual{T,promote_type(A, B),N}
 end
 
-for R in (Irrational, Real, BigFloat, Bool)
+for R in (AbstractIrrational, Real, BigFloat, Bool)
     if isconcretetype(R) # issue #322
         @eval begin
             Base.promote_rule(::Type{$R}, ::Type{Dual{T,V,N}}) where {T,V,N} = Dual{T,promote_type($R, V),N}
@@ -703,7 +706,11 @@ end
 # Symmetric eigvals #
 #-------------------#
 
-function LinearAlgebra.eigvals(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N}
+# To be able to reuse this default definition in the StaticArrays extension
+# (has to be re-defined to avoid method ambiguity issues)
+# we forward the call to an internal method that can be shared and reused
+LinearAlgebra.eigvals(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N} = _eigvals(A)
+function _eigvals(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N}
     λ,Q = eigen(Symmetric(value.(parent(A))))
     parts = ntuple(j -> diag(Q' * getindex.(partials.(A), j) * Q), N)
     Dual{Tg}.(λ, tuple.(parts...))
@@ -721,8 +728,19 @@ function LinearAlgebra.eigvals(A::SymTridiagonal{<:Dual{Tg,T,N}}) where {Tg,T<:R
     Dual{Tg}.(λ, tuple.(parts...))
 end
 
-# A ./ (λ - λ') but with diag special cased
-function _lyap_div!(A, λ)
+# A ./ (λ' .- λ) but with diag special cased
+# Default out-of-place method
+function _lyap_div!!(A::AbstractMatrix, λ::AbstractVector)
+    return map(
+        (a, b, idx) -> a / (idx[1] == idx[2] ? oneunit(b) : b),
+        A,
+        λ' .- λ,
+        CartesianIndices(A),
+    )
+end
+# For `Matrix` (and e.g. `StaticArrays.MMatrix`) we can use an in-place method
+_lyap_div!!(A::Matrix, λ::AbstractVector) = _lyap_div!(A, λ)
+function _lyap_div!(A::AbstractMatrix, λ::AbstractVector)
     for (j,μ) in enumerate(λ), (k,λ) in enumerate(λ)
         if k ≠ j
             A[k,j] /= μ - λ
@@ -731,17 +749,21 @@ function _lyap_div!(A, λ)
     A
 end
 
-function LinearAlgebra.eigen(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N}
+# To be able to reuse this default definition in the StaticArrays extension
+# (has to be re-defined to avoid method ambiguity issues)
+# we forward the call to an internal method that can be shared and reused
+LinearAlgebra.eigen(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N} = _eigen(A)
+function _eigen(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N}
     λ = eigvals(A)
     _,Q = eigen(Symmetric(value.(parent(A))))
-    parts = ntuple(j -> Q*_lyap_div!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N)
+    parts = ntuple(j -> Q*_lyap_div!!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N)
     Eigen(λ,Dual{Tg}.(Q, tuple.(parts...)))
 end
 
 function LinearAlgebra.eigen(A::SymTridiagonal{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N}
     λ = eigvals(A)
     _,Q = eigen(SymTridiagonal(value.(parent(A))))
-    parts = ntuple(j -> Q*_lyap_div!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N)
+    parts = ntuple(j -> Q*_lyap_div!!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N)
     Eigen(λ,Dual{Tg}.(Q, tuple.(parts...)))
 end
 
diff --git a/src/gradient.jl b/src/gradient.jl
index 614bea67..6d4cc791 100644
--- a/src/gradient.jl
+++ b/src/gradient.jl
@@ -13,7 +13,8 @@ This method assumes that `isa(f(x), Real)`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function gradient(f, x::AbstractArray, cfg::GradientConfig{T} = GradientConfig(f, x), ::Val{CHK}=Val{true}()) where {T, CHK}
+function gradient(f::F, x::AbstractArray, cfg::GradientConfig{T} = GradientConfig(f, x), ::Val{CHK}=Val{true}()) where {F, T, CHK}
+    require_one_based_indexing(x)
     CHK && checktag(T, f, x)
     if chunksize(cfg) == length(x)
         return vector_mode_gradient(f, x, cfg)
@@ -32,6 +33,7 @@ This method assumes that `isa(f(x), Real)`.
 
 """
 function gradient!(result::Union{AbstractArray,DiffResult}, f::F, x::AbstractArray, cfg::GradientConfig{T} = GradientConfig(f, x), ::Val{CHK}=Val{true}()) where {T, CHK, F}
+    result isa DiffResult ? require_one_based_indexing(x) : require_one_based_indexing(result, x)
     CHK && checktag(T, f, x)
     if chunksize(cfg) == length(x)
         vector_mode_gradient!(result, f, x, cfg)
diff --git a/src/hessian.jl b/src/hessian.jl
index 9a9c4f77..9c755c9a 100644
--- a/src/hessian.jl
+++ b/src/hessian.jl
@@ -11,7 +11,8 @@ This method assumes that `isa(f(x), Real)`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function hessian(f, x::AbstractArray, cfg::HessianConfig{T} = HessianConfig(f, x), ::Val{CHK}=Val{true}()) where {T,CHK}
+function hessian(f::F, x::AbstractArray, cfg::HessianConfig{T} = HessianConfig(f, x), ::Val{CHK}=Val{true}()) where {F, T,CHK}
+    require_one_based_indexing(x)
     CHK && checktag(T, f, x)
     ∇f = y -> gradient(f, y, cfg.gradient_config, Val{false}())
     return jacobian(∇f, x, cfg.jacobian_config, Val{false}())
@@ -27,7 +28,8 @@ This method assumes that `isa(f(x), Real)`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function hessian!(result::AbstractArray, f, x::AbstractArray, cfg::HessianConfig{T} = HessianConfig(f, x), ::Val{CHK}=Val{true}()) where {T,CHK}
+function hessian!(result::AbstractArray, f::F, x::AbstractArray, cfg::HessianConfig{T} = HessianConfig(f, x), ::Val{CHK}=Val{true}()) where {F,T,CHK}
+    require_one_based_indexing(result, x)
     CHK && checktag(T, f, x)
     ∇f = y -> gradient(f, y, cfg.gradient_config, Val{false}())
     jacobian!(result, ∇f, x, cfg.jacobian_config, Val{false}())
@@ -61,7 +63,7 @@ because `isa(result, DiffResult)`, `cfg` is constructed as `HessianConfig(f, res
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function hessian!(result::DiffResult, f, x::AbstractArray, cfg::HessianConfig{T} = HessianConfig(f, result, x), ::Val{CHK}=Val{true}()) where {T,CHK}
+function hessian!(result::DiffResult, f::F, x::AbstractArray, cfg::HessianConfig{T} = HessianConfig(f, result, x), ::Val{CHK}=Val{true}()) where {F,T,CHK}
     CHK && checktag(T, f, x)
     ∇f! = InnerGradientForHess(result, cfg, f)
     jacobian!(DiffResults.hessian(result), ∇f!, DiffResults.gradient(result), x, cfg.jacobian_config, Val{false}())
diff --git a/src/jacobian.jl b/src/jacobian.jl
index cd417a79..e7ca96f5 100644
--- a/src/jacobian.jl
+++ b/src/jacobian.jl
@@ -15,7 +15,8 @@ This method assumes that `isa(f(x), AbstractArray)`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function jacobian(f, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f, x), ::Val{CHK}=Val{true}()) where {T,CHK}
+function jacobian(f::F, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f, x), ::Val{CHK}=Val{true}()) where {F,T,CHK}
+    require_one_based_indexing(x)
     CHK && checktag(T, f, x)
     if chunksize(cfg) == length(x)
         return vector_mode_jacobian(f, x, cfg)
@@ -32,7 +33,8 @@ stored in `y`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function jacobian(f!, y::AbstractArray, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {T, CHK}
+function jacobian(f!::F, y::AbstractArray, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {F,T, CHK}
+    require_one_based_indexing(y, x)
     CHK && checktag(T, f!, x)
     if chunksize(cfg) == length(x)
         return vector_mode_jacobian(f!, y, x, cfg)
@@ -52,7 +54,8 @@ This method assumes that `isa(f(x), AbstractArray)`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function jacobian!(result::Union{AbstractArray,DiffResult}, f, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f, x), ::Val{CHK}=Val{true}()) where {T, CHK}
+function jacobian!(result::Union{AbstractArray,DiffResult}, f::F, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f, x), ::Val{CHK}=Val{true}()) where {F,T, CHK}
+    result isa DiffResult ? require_one_based_indexing(x) : require_one_based_indexing(result, x)
     CHK && checktag(T, f, x)
     if chunksize(cfg) == length(x)
         vector_mode_jacobian!(result, f, x, cfg)
@@ -72,7 +75,8 @@ This method assumes that `isa(f(x), AbstractArray)`.
 
 Set `check` to `Val{false}()` to disable tag checking. This can lead to perturbation confusion, so should be used with care.
 """
-function jacobian!(result::Union{AbstractArray,DiffResult}, f!, y::AbstractArray, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {T,CHK}
+function jacobian!(result::Union{AbstractArray,DiffResult}, f!::F, y::AbstractArray, x::AbstractArray, cfg::JacobianConfig{T} = JacobianConfig(f!, y, x), ::Val{CHK}=Val{true}()) where {F,T,CHK}
+    result isa DiffResult ? require_one_based_indexing(y, x) : require_one_based_indexing(result, y, x)
     CHK && checktag(T, f!, x)
     if chunksize(cfg) == length(x)
         vector_mode_jacobian!(result, f!, y, x, cfg)
diff --git a/src/partials.jl b/src/partials.jl
index fce67b0a..a5316e3e 100644
--- a/src/partials.jl
+++ b/src/partials.jl
@@ -52,8 +52,7 @@ Base.:(==)(a::Partials{N}, b::Partials{N}) where {N} = a.values == b.values
 
 const PARTIALS_HASH = hash(Partials)
 
-Base.hash(partials::Partials) = hash(partials.values, PARTIALS_HASH)
-Base.hash(partials::Partials, hsh::UInt64) = hash(hash(partials), hsh)
+Base.hash(partials::Partials, hsh::UInt64) = hash(hash(partials.values, PARTIALS_HASH), hsh)
 
 @inline Base.copy(partials::Partials) = partials
 
diff --git a/src/prelude.jl b/src/prelude.jl
index 1a5d0cfa..5fe0a9c1 100644
--- a/src/prelude.jl
+++ b/src/prelude.jl
@@ -14,12 +14,9 @@ const BINARY_PREDICATES = Symbol[:isequal, :isless, :<, :>, :(==), :(!=), :(<=),
 
 struct Chunk{N} end
 
-const CHUNKS = [Chunk{i}() for i in 1:DEFAULT_CHUNK_THRESHOLD]
-
 function Chunk(input_length::Integer, threshold::Integer = DEFAULT_CHUNK_THRESHOLD)
     N = pickchunksize(input_length, threshold)
-    0 < N <= DEFAULT_CHUNK_THRESHOLD && return CHUNKS[N]
-    return Chunk{N}()
+    Base.@nif 12 d->(N == d) d->(Chunk{d}()) d->(Chunk{N}())
 end
 
 function Chunk(x::AbstractArray, threshold::Integer = DEFAULT_CHUNK_THRESHOLD)
diff --git a/test/AllocationsTest.jl b/test/AllocationsTest.jl
index 2a0075a7..ad1832d0 100644
--- a/test/AllocationsTest.jl
+++ b/test/AllocationsTest.jl
@@ -24,17 +24,25 @@ convert_test_574() = convert(ForwardDiff.Dual{Nothing,ForwardDiff.Dual{Nothing,F
     index = 1
     alloc = @allocated ForwardDiff.seed!(duals, x, index, seeds)
     alloc = @allocated ForwardDiff.seed!(duals, x, index, seeds)
-    @test alloc == 0
+    if VERSION < v"1.9" || VERSION >= v"1.11"
+        @test alloc == 0
+    else
+        @test_broken alloc == 0
+    end
 
     index = 1
     alloc = @allocated ForwardDiff.seed!(duals, x, index, seed)
     alloc = @allocated ForwardDiff.seed!(duals, x, index, seed)
-    @test alloc == 0
-    
+    if VERSION < v"1.9" || VERSION >= v"1.11"
+        @test alloc == 0
+    else
+        @test_broken alloc == 0
+    end
+
     alloc = @allocated convert_test_574()
     alloc = @allocated convert_test_574()
     @test alloc == 0
-  
+
 end
 
 end
diff --git a/test/DerivativeTest.jl b/test/DerivativeTest.jl
index dfdd8ed2..4b7463c8 100644
--- a/test/DerivativeTest.jl
+++ b/test/DerivativeTest.jl
@@ -17,8 +17,7 @@ Random.seed!(1)
 
 const x = 1
 
-for f in DiffTests.NUMBER_TO_NUMBER_FUNCS
-    println("  ...testing $f")
+@testset "$f" for f in DiffTests.NUMBER_TO_NUMBER_FUNCS
     v = f(x)
     d = ForwardDiff.derivative(f, x)
     @test isapprox(d, Calculus.derivative(f, x), atol=FINITEDIFF_ERROR)
@@ -29,8 +28,7 @@ for f in DiffTests.NUMBER_TO_NUMBER_FUNCS
     @test isapprox(DiffResults.derivative(out), d)
 end
 
-for f in DiffTests.NUMBER_TO_ARRAY_FUNCS
-    println("  ...testing $f")
+@testset "$f" for f in DiffTests.NUMBER_TO_ARRAY_FUNCS
     v = f(x)
     d = ForwardDiff.derivative(f, x)
 
@@ -47,8 +45,7 @@ for f in DiffTests.NUMBER_TO_ARRAY_FUNCS
     @test isapprox(DiffResults.derivative(out), d)
 end
 
-for f! in DiffTests.INPLACE_NUMBER_TO_ARRAY_FUNCS
-    println("  ...testing $f!")
+@testset "$(f!)" for f! in DiffTests.INPLACE_NUMBER_TO_ARRAY_FUNCS
     m, n = 3, 2
     y = fill(0.0, m, n)
     f = x -> (tmp = similar(y, promote_type(eltype(y), typeof(x)), m, n); f!(tmp, x); tmp)
diff --git a/test/DualTest.jl b/test/DualTest.jl
index 8d87f90b..786d3bda 100644
--- a/test/DualTest.jl
+++ b/test/DualTest.jl
@@ -30,8 +30,7 @@ ForwardDiff.:≺(::Int, ::Type{TestTag()}) = false
 ForwardDiff.:≺(::Type{TestTag}, ::Type{OuterTestTag}) = true
 ForwardDiff.:≺(::Type{OuterTestTag}, ::Type{TestTag}) = false
 
-for N in (0,3), M in (0,4), V in (Int, Float32)
-    println("  ...testing Dual{TestTag(),$V,$N} and Dual{TestTag(),Dual{TestTag(),$V,$M},$N}")
+@testset "Dual{Z,$V,$N} and Dual{Z,Dual{Z,$V,$M},$N}" for N in (0,3), M in (0,4), V in (Int, Float32)
 
     PARTIALS = Partials{N,V}(ntuple(n -> intrand(V), N))
     PRIMAL = intrand(V)
@@ -446,13 +445,12 @@ for N in (0,3), M in (0,4), V in (Int, Float32)
     @test abs(NESTED_FDNUM) === NESTED_FDNUM
 
     if V != Int
-        for (M, f, arity) in DiffRules.diffrules(filter_modules = nothing)
+        @testset "$(M).$(f) with $arity arguments" for (M, f, arity) in DiffRules.diffrules(filter_modules = nothing)
             if f in (:/, :rem2pi)
                 continue  # Skip these rules
             elseif !(isdefined(@__MODULE__, M) && isdefined(getfield(@__MODULE__, M), f))
                 continue  # Skip rules for methods not defined in the current scope
             end
-            println("       ...auto-testing $(M).$(f) with $arity arguments")
             if arity == 1
                 deriv = DiffRules.diffrule(M, f, :x)
                 modifier = if in(f, (:asec, :acsc, :asecd, :acscd, :acosh, :acoth))
@@ -637,4 +635,8 @@ end
     @test ForwardDiff.derivative(float, 1)::Float64 === 1.0
 end
 
+@testset "TwicePrecision" begin
+    @test ForwardDiff.derivative(x -> sum(1 .+ x .* (0:0.1:1)), 1) == 5.5
+end
+
 end # module
diff --git a/test/GradientTest.jl b/test/GradientTest.jl
index 707fcd68..d806a967 100644
--- a/test/GradientTest.jl
+++ b/test/GradientTest.jl
@@ -19,8 +19,7 @@ x = [0.1, 0.2, 0.3]
 v = f(x)
 g = [-9.4, 15.6, 52.0]
 
-for c in (1, 2, 3), tag in (nothing, Tag(f, eltype(x)))
-    println("  ...running hardcoded test with chunk size = $c and tag = $(repr(tag))")
+@testset "Rosenbrock, chunk size = $c and tag = $(repr(tag))" for c in (1, 2, 3), tag in (nothing, Tag(f, eltype(x)))
     cfg = ForwardDiff.GradientConfig(f, x, ForwardDiff.Chunk{c}(), tag)
 
     @test eltype(cfg) == Dual{typeof(tag), eltype(x), c}
@@ -59,8 +58,7 @@ for f in DiffTests.VECTOR_TO_NUMBER_FUNCS
     v = f(X)
     g = ForwardDiff.gradient(f, X)
     @test isapprox(g, Calculus.gradient(f, X), atol=FINITEDIFF_ERROR)
-    for c in CHUNK_SIZES, tag in (nothing, Tag(f, eltype(x)))
-        println("  ...testing $f with chunk size = $c and tag = $(repr(tag))")
+    @testset "... with chunk size = $c and tag = $(repr(tag))" for c in CHUNK_SIZES, tag in (nothing, Tag(f, eltype(x)))
         cfg = ForwardDiff.GradientConfig(f, X, ForwardDiff.Chunk{c}(), tag)
 
         out = ForwardDiff.gradient(f, X, cfg)
@@ -81,11 +79,9 @@ end
 # test specialized StaticArray codepaths #
 ##########################################
 
-println("  ...testing specialized StaticArray codepaths")
+@testset "Specialized StaticArray codepaths: $T" for T in (StaticArrays.SArray, StaticArrays.MArray)
+    x = rand(3, 3)
 
-x = rand(3, 3)
-
-for T in (StaticArrays.SArray, StaticArrays.MArray)
     sx = T{Tuple{3,3}}(x)
 
     cfg = ForwardDiff.GradientConfig(nothing, x)
@@ -139,6 +135,9 @@ for T in (StaticArrays.SArray, StaticArrays.MArray)
     @test DiffResults.gradient(sresult1) == DiffResults.gradient(result)
     @test DiffResults.gradient(sresult2) == DiffResults.gradient(result)
     @test DiffResults.gradient(sresult3) == DiffResults.gradient(result)
+
+    # make sure this is not a source of type instability
+    @inferred ForwardDiff.GradientConfig(f, sx)
 end
 
 @testset "exponential function at base zero" begin
@@ -166,7 +165,7 @@ end
     function f(p)
         sum(collect(0.0:p[1]:p[2]))
     end
-    @test ForwardDiff.gradient(f, [0.2,25.0]) == [7875.0, 0.0]
+    @test ForwardDiff.gradient(f, [0.3, 25.0]) == [3486.0, 0.0]
 end
 
 end # module
diff --git a/test/HessianTest.jl b/test/HessianTest.jl
index 1df4232b..64c289f2 100644
--- a/test/HessianTest.jl
+++ b/test/HessianTest.jl
@@ -22,8 +22,7 @@ h = [-66.0  -40.0    0.0;
      -40.0  130.0  -80.0;
        0.0  -80.0  200.0]
 
-for c in HESSIAN_CHUNK_SIZES, tag in (nothing, Tag((f,ForwardDiff.gradient), eltype(x)))
-    println("  ...running hardcoded test with chunk size = $c and tag = $(repr(tag))")
+@testset "running hardcoded test with chunk size = $c and tag = $(repr(tag))" for c in HESSIAN_CHUNK_SIZES, tag in (nothing, Tag((f,ForwardDiff.gradient), eltype(x)))
     cfg = ForwardDiff.HessianConfig(f, x, ForwardDiff.Chunk{c}(), tag)
     resultcfg = ForwardDiff.HessianConfig(f, DiffResults.HessianResult(x), x, ForwardDiff.Chunk{c}(), tag)
 
@@ -68,8 +67,7 @@ for f in DiffTests.VECTOR_TO_NUMBER_FUNCS
     h = ForwardDiff.hessian(f, X)
     # finite difference approximation error is really bad for Hessians...
     @test isapprox(h, Calculus.hessian(f, X), atol=0.02)
-    for c in HESSIAN_CHUNK_SIZES, tag in (nothing, Tag((f,ForwardDiff.gradient), eltype(x)))
-        println("  ...testing $f with chunk size = $c and tag = $(repr(tag))")
+    @testset "$f with chunk size = $c and tag = $(repr(tag))" for c in HESSIAN_CHUNK_SIZES, tag in (nothing, Tag((f,ForwardDiff.gradient), eltype(x)))
         cfg = ForwardDiff.HessianConfig(f, X, ForwardDiff.Chunk{c}(), tag)
         resultcfg = ForwardDiff.HessianConfig(f, DiffResults.HessianResult(X), X, ForwardDiff.Chunk{c}(), tag)
 
@@ -92,7 +90,7 @@ end
 # test specialized StaticArray codepaths #
 ##########################################
 
-println("  ...testing specialized StaticArray codepaths")
+@info "testing specialized StaticArray codepaths"
 
 x = rand(3, 3)
 for T in (StaticArrays.SArray, StaticArrays.MArray)
diff --git a/test/JacobianTest.jl b/test/JacobianTest.jl
index 69f9409c..0c24b018 100644
--- a/test/JacobianTest.jl
+++ b/test/JacobianTest.jl
@@ -103,11 +103,10 @@ for f in DiffTests.ARRAY_TO_ARRAY_FUNCS
     v = f(X)
     j = ForwardDiff.jacobian(f, X)
     @test isapprox(j, Calculus.jacobian(x -> vec(f(x)), X, :forward), atol=1.3FINITEDIFF_ERROR)
-    for c in CHUNK_SIZES, tag in (nothing, Tag)
+    @testset "$f with chunk size = $c and tag = $(repr(tag))" for c in CHUNK_SIZES, tag in (nothing, Tag)
         if tag == Tag
             tag = Tag(f, eltype(X))
         end
-        println("  ...testing $f with chunk size = $c and tag = $(repr(tag))")
         cfg = JacobianConfig(f, X, ForwardDiff.Chunk{c}(), tag)
 
         out = ForwardDiff.jacobian(f, X, cfg)
@@ -129,8 +128,7 @@ for f! in DiffTests.INPLACE_ARRAY_TO_ARRAY_FUNCS
     f!(v, X)
     j = ForwardDiff.jacobian(f!, fill!(similar(Y), 0.0), X)
     @test isapprox(j, Calculus.jacobian(x -> (y = fill!(similar(Y), 0.0); f!(y, x); vec(y)), X, :forward), atol=FINITEDIFF_ERROR)
-    for c in CHUNK_SIZES, tag in (nothing, Tag(f!, eltype(X)))
-        println("  ...testing $(f!) with chunk size = $c and tag = $(repr(tag))")
+    @testset "$(f!) with chunk size = $c and tag = $(repr(tag))" for c in CHUNK_SIZES, tag in (nothing, Tag(f!, eltype(X)))
         ycfg = JacobianConfig(f!, fill!(similar(Y), 0.0), X, ForwardDiff.Chunk{c}(), tag)
 
         y = fill!(similar(Y), 0.0)
@@ -164,7 +162,7 @@ end
 # test specialized StaticArray codepaths #
 ##########################################
 
-println("  ...testing specialized StaticArray codepaths")
+@info "testing specialized StaticArray codepaths"
 
 x = rand(3, 3)
 for T in (StaticArrays.SArray, StaticArrays.MArray)
@@ -224,6 +222,9 @@ for T in (StaticArrays.SArray, StaticArrays.MArray)
     @test DiffResults.jacobian(sresult1) == DiffResults.jacobian(result)
     @test DiffResults.jacobian(sresult2) == DiffResults.jacobian(result)
     @test DiffResults.jacobian(sresult3) == DiffResults.jacobian(result)
+
+    # make sure this is not a source of type instability
+    @inferred ForwardDiff.JacobianConfig(f, sx)
 end
 
 @testset "dimension errors for jacobian" begin
@@ -235,14 +236,18 @@ end
 @testset "eigen" begin
     @test ForwardDiff.jacobian(x -> eigvals(SymTridiagonal(x, x[1:end-1])), [1.,2.]) ≈ [(1 - 3/sqrt(5))/2 (1 - 1/sqrt(5))/2 ; (1 + 3/sqrt(5))/2 (1 + 1/sqrt(5))/2]
     @test ForwardDiff.jacobian(x -> eigvals(Symmetric(x*x')), [1.,2.]) ≈ [0 0; 2 4]
-    
+
     x0 = [1.0, 2.0];
     ev1(x) = eigen(Symmetric(x*x')).vectors[:,1]
     @test ForwardDiff.jacobian(ev1, x0) ≈ Calculus.finite_difference_jacobian(ev1, x0)
     ev2(x) = eigen(SymTridiagonal(x, x[1:end-1])).vectors[:,1]
     @test ForwardDiff.jacobian(ev2, x0) ≈ Calculus.finite_difference_jacobian(ev2, x0)
-    x0_static = SVector{2}(x0)
-    @test ForwardDiff.jacobian(ev1, x0_static) ≈ Calculus.finite_difference_jacobian(ev1, x0)
+
+    x0_svector = SVector{2}(x0)
+    @test ForwardDiff.jacobian(ev1, x0_svector) ≈ Calculus.finite_difference_jacobian(ev1, x0)
+
+    x0_mvector = MVector{2}(x0)
+    @test ForwardDiff.jacobian(ev1, x0_mvector) ≈ Calculus.finite_difference_jacobian(ev1, x0)
 end
 
 @testset "type stability" begin
diff --git a/test/MiscTest.jl b/test/MiscTest.jl
index 2a22cb2f..96971560 100644
--- a/test/MiscTest.jl
+++ b/test/MiscTest.jl
@@ -6,6 +6,9 @@ using Test
 using ForwardDiff
 using DiffTests
 using SparseArrays: sparse
+using StaticArrays
+using IrrationalConstants
+using LinearAlgebra
 
 include(joinpath(dirname(@__FILE__), "utils.jl"))
 
@@ -141,6 +144,24 @@ let i, j
     end
 end
 
+# AbstractIrrational numbers #
+#----------------------------#
+struct TestTag end
+intrand(V) = V == Int ? rand(2:10) : rand(V)
+
+for N in (0,3), V in (Int, Float32), I in (Irrational, AbstractIrrational)
+    PARTIALS = ForwardDiff.Partials{N,V}(ntuple(n -> intrand(V), N))
+    PRIMAL = intrand(V)
+    FDNUM = ForwardDiff.Dual{TestTag()}(PRIMAL, PARTIALS)
+    
+    @test promote_rule(typeof(FDNUM), I) == promote_rule(I, typeof(FDNUM))
+    # π::Irrational, twoπ::AbstractIrrational
+    for IRR in (π, twoπ)
+        val_dual, val_irr = promote(FDNUM, IRR)
+        @test (val_irr, val_dual) == promote(IRR, FDNUM)
+    end
+end
+
 ########
 # misc #
 ########
@@ -158,4 +179,41 @@ end
 @test ForwardDiff.derivative(x -> rem2pi(x, RoundUp), rand()) == 1
 @test ForwardDiff.derivative(x -> rem2pi(x, RoundDown), rand()) == 1
 
+@testset "_lyap_div!!" begin
+    # In-place version for `Matrix`
+    A = rand(3, 3)
+    Acopy = copy(A)
+    λ = rand(3)
+    B = @inferred(ForwardDiff._lyap_div!!(A, λ))
+    @test B === A
+    @test B[diagind(B)] == Acopy[diagind(Acopy)]
+    no_diag(X) = [X[i] for i in eachindex(X) if !(i in diagind(X))]
+    @test no_diag(B) == no_diag(Acopy ./ (λ' .- λ))
+
+    # Immutable static arrays
+    A_smatrix = SMatrix{3,3}(Acopy)
+    λ_svector = SVector{3}(λ)
+    B_smatrix = @inferred(ForwardDiff._lyap_div!!(A_smatrix, λ_svector))
+    @test B_smatrix !== A_smatrix
+    @test B_smatrix isa SMatrix{3,3}
+    @test B_smatrix == B
+    λ_mvector = MVector{3}(λ)
+    B_smatrix = @inferred(ForwardDiff._lyap_div!!(A_smatrix, λ_mvector))
+    @test B_smatrix !== A_smatrix
+    @test B_smatrix isa SMatrix{3,3}
+    @test B_smatrix == B
+
+    # Mutable static arrays
+    A_mmatrix = MMatrix{3,3}(Acopy)
+    λ_svector = SVector{3}(λ)
+    B_mmatrix = @inferred(ForwardDiff._lyap_div!!(A_mmatrix, λ_svector))
+    @test B_mmatrix === A_mmatrix
+    @test B_mmatrix == B
+    A_mmatrix = MMatrix{3,3}(Acopy)
+    λ_mvector = MVector{3}(λ)
+    B_mmatrix = @inferred(ForwardDiff._lyap_div!!(A_mmatrix, λ_mvector))
+    @test B_mmatrix === A_mmatrix
+    @test B_mmatrix == B
+end
+
 end # module
diff --git a/test/PartialsTest.jl b/test/PartialsTest.jl
index 39fb05d7..8372a53e 100644
--- a/test/PartialsTest.jl
+++ b/test/PartialsTest.jl
@@ -7,8 +7,7 @@ using ForwardDiff: Partials
 
 samerng() = MersenneTwister(1)
 
-for N in (0, 3), T in (Int, Float32, Float64)
-    println("  ...testing Partials{$N,$T}")
+@testset "Partials{$N,$T}" for N in (0, 3), T in (Int, Float32, Float64)
 
     VALUES = (rand(T,N)...,)
     PARTIALS = Partials{N,T}(VALUES)
@@ -62,7 +61,6 @@ for N in (0, 3), T in (Int, Float32, Float64)
     @test isequal(PARTIALS, copy(PARTIALS))
     @test isequal(PARTIALS, PARTIALS2) == (N == 0)
 
-    @test hash(PARTIALS) == hash(VALUES, ForwardDiff.PARTIALS_HASH)
     @test hash(PARTIALS) == hash(copy(PARTIALS))
     @test hash(PARTIALS, hash(1)) == hash(copy(PARTIALS), hash(1))
     @test hash(PARTIALS, hash(1)) == hash(copy(PARTIALS), hash(1))