diff --git a/Project.toml b/Project.toml
index 9eb2914c..2712d857 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ForwardDiff"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "1.0.1"
+version = "1.0.2"
 
 [deps]
 CommonSubexpressions = "bbf7d656-a473-5ed7-a52c-81e309532950"
diff --git a/src/apiutils.jl b/src/apiutils.jl
index 39608d6c..f401a3fc 100644
--- a/src/apiutils.jl
+++ b/src/apiutils.jl
@@ -72,16 +72,36 @@ end
 
 function seed!(duals::AbstractArray{Dual{T,V,N}}, x,
                seed::Partials{N,V} = zero(Partials{N,V})) where {T,V,N}
-    for idx in structural_eachindex(duals, x)
-        duals[idx] = Dual{T,V,N}(x[idx], seed)
+    if isbitstype(V)
+        for idx in structural_eachindex(duals, x)
+            duals[idx] = Dual{T,V,N}(x[idx], seed)
+        end
+    else
+        for idx in structural_eachindex(duals, x)
+            if isassigned(x, idx)
+                duals[idx] = Dual{T,V,N}(x[idx], seed)
+            else
+                Base._unsetindex!(duals, idx)
+            end
+        end
     end
     return duals
 end
 
 function seed!(duals::AbstractArray{Dual{T,V,N}}, x,
                seeds::NTuple{N,Partials{N,V}}) where {T,V,N}
-    for (i, idx) in zip(1:N, structural_eachindex(duals, x))
-        duals[idx] = Dual{T,V,N}(x[idx], seeds[i])
+    if isbitstype(V)
+        for (i, idx) in zip(1:N, structural_eachindex(duals, x))
+            duals[idx] = Dual{T,V,N}(x[idx], seeds[i])
+        end
+    else
+        for (i, idx) in zip(1:N, structural_eachindex(duals, x))
+            if isassigned(x, idx)
+                duals[idx] = Dual{T,V,N}(x[idx], seeds[i])
+            else
+                Base._unsetindex!(duals, idx)
+            end
+        end
     end
     return duals
 end
@@ -90,8 +110,18 @@ function seed!(duals::AbstractArray{Dual{T,V,N}}, x, index,
                seed::Partials{N,V} = zero(Partials{N,V})) where {T,V,N}
     offset = index - 1
     idxs = Iterators.drop(structural_eachindex(duals, x), offset)
-    for idx in idxs
-        duals[idx] = Dual{T,V,N}(x[idx], seed)
+    if isbitstype(V)
+        for idx in idxs
+            duals[idx] = Dual{T,V,N}(x[idx], seed)
+        end
+    else
+        for idx in idxs
+            if isassigned(x, idx)
+                duals[idx] = Dual{T,V,N}(x[idx], seed)
+            else
+                Base._unsetindex!(duals, idx)
+            end
+        end
     end
     return duals
 end
@@ -100,8 +130,18 @@ function seed!(duals::AbstractArray{Dual{T,V,N}}, x, index,
                seeds::NTuple{N,Partials{N,V}}, chunksize = N) where {T,V,N}
     offset = index - 1
     idxs = Iterators.drop(structural_eachindex(duals, x), offset)
-    for (i, idx) in zip(1:chunksize, idxs)
-        duals[idx] = Dual{T,V,N}(x[idx], seeds[i])
+    if isbitstype(V)
+        for (i, idx) in zip(1:chunksize, idxs)
+            duals[idx] = Dual{T,V,N}(x[idx], seeds[i])
+        end
+    else
+        for (i, idx) in zip(1:chunksize, idxs)
+            if isassigned(x, idx)
+                duals[idx] = Dual{T,V,N}(x[idx], seeds[i])
+            else
+                Base._unsetindex!(duals, idx)
+            end
+        end
     end
     return duals
 end
diff --git a/test/JacobianTest.jl b/test/JacobianTest.jl
index 1e52f7fa..b010078f 100644
--- a/test/JacobianTest.jl
+++ b/test/JacobianTest.jl
@@ -279,4 +279,33 @@ end
     end
 end
 
+# issues #436, #740
+@testset "BigFloat" begin
+    # Unassigned entries in the output
+    x = BigFloat.(1:9)
+    for chunksize in (1, 2, 9)
+        y = similar(x)
+        @test all(i -> !isassigned(y, i), eachindex(y))
+        cfg = ForwardDiff.JacobianConfig(copyto!, y, x, ForwardDiff.Chunk{chunksize}())
+        res = ForwardDiff.jacobian(copyto!, y, x, cfg)
+        @test y == x
+        @test res isa Matrix{BigFloat}
+        @test res == I
+    end
+
+    # Unassigned (but unused) entry in the input and unassigned entries in the output
+    resize!(x, 10)
+    f = (y, x) -> copyto!(y, 1, x, 1, 9)
+    for chunksize in (1, 2, 10)
+        y = similar(x, 9)
+        @test all(i -> !isassigned(y, i), eachindex(y))
+        cfg = ForwardDiff.JacobianConfig(f, y, x, ForwardDiff.Chunk{chunksize}())
+        res = ForwardDiff.jacobian(f, y, x, cfg)
+        @test y == x[1:(end-1)]
+        @test res isa Matrix{BigFloat}
+        @test res[:, 1:(end-1)] == I
+        @test all(iszero, res[:, end])
+    end
+end
+
 end # module