Make SearchProperties probes robust to non-primitive Real eltypes (AD)

Project.toml

@@ -7,6 +7,7 @@ authors = ["Chris Elrod <elrodc@gmail.com> and contributors"]
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 
 [compat]
+ForwardDiff = "0.10, 1"
 PrecompileTools = "1.0.1"
 SafeTestsets = "0.1"
 SciMLTesting = "2.2"
@@ -15,10 +16,11 @@ Test = "1.10"
 julia = "1.10"
 
 [extras]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SciMLTesting = "09d9d899-5365-40a9-917a-5f67fddea283"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["SafeTestsets", "SciMLTesting", "StableRNGs", "Test"]
+test = ["ForwardDiff", "SafeTestsets", "SciMLTesting", "StableRNGs", "Test"]

src/search_properties.jl

@@ -47,7 +47,7 @@ const _AUTO_LINEAR_REL_TOLERANCE = 1.0e-3
         for k in 1:9
             kk = 1 + (k * nm1) ÷ 10
             expected = v1 + (kk - 1) / nm1 * span
-            rel_err = Float64(abs(v[kk] - expected) / abs_span)
+            rel_err = abs(v[kk] - expected) / abs_span
             rel_err > max_err && (max_err = rel_err)
         end
         return max_err
@@ -83,12 +83,12 @@ function _validated_uniform(v::AbstractVector{<:Real})
     n < 2 && return false
     @inbounds begin
         v1, vn = v[1], v[n]
-        span = Float64(vn - v1)
+        span = vn - v1
         (iszero(span) || !isfinite(span)) && return false
         nm1 = n - 1
         for i in 2:nm1
             expected = v1 + (i - 1) / nm1 * span
-            abs(Float64(v[i] - expected)) > _UNIFORM_REL_TOLERANCE * abs(span) &&
+            abs(v[i] - expected) > _UNIFORM_REL_TOLERANCE * abs(span) &&
                 return false
         end
     end
@@ -110,8 +110,8 @@ end
     @inbounds begin
         v1, vn = v[1], v[n]
         (v1 <= 0 || vn <= 0 || !isfinite(v1) || !isfinite(vn)) && return false
-        log_v1 = log(Float64(v1))
-        log_vn = log(Float64(vn))
+        log_v1 = log(v1)
+        log_vn = log(vn)
         span = log_vn - log_v1
         (iszero(span) || !isfinite(span)) && return false
         abs_span = abs(span)
@@ -121,7 +121,7 @@ end
             vk = v[kk]
             (vk <= 0 || !isfinite(vk)) && return false
             expected = log_v1 + (kk - 1) / nm1 * span
-            rel_err = abs(log(Float64(vk)) - expected) / abs_span
+            rel_err = abs(log(vk) - expected) / abs_span
             rel_err > tol && return false
         end
     end

test/core_tests.jl

@@ -645,6 +645,53 @@ end
     @test p_nonuniform.inv_step == 0.0
 end
 
+@safetestset "SearchProperties with ForwardDiff.Dual knots" begin
+    using FindFirstFunctions
+    using FindFirstFunctions: SearchProperties, Auto, searchsorted_last, searchsorted_first
+    using ForwardDiff
+
+    # `ForwardDiff.Dual <: Real`, so a Dual-valued knot vector — as produced
+    # when an interpolation is reconstructed inside `ForwardDiff` and the
+    # knots are promoted to Duals — dispatches to the `<:Real` probe. The
+    # probes must not force a `Float64(::Dual)` conversion (which errors);
+    # they must classify from the primal values and keep partials intact.
+    ForwardDiff.derivative(2.0) do p
+        t = collect(range(0.0, 1.0; length = 15)) .* p    # linear Dual knots
+        props = SearchProperties(t)
+        @test props.has_props
+        @test props.is_linear                              # linear in index
+        @test props.is_uniform                             # evenly spaced
+        # first_val / inv_step carry the derivative w.r.t. p.
+        @test ForwardDiff.value(props.first_val) == 0.0
+        # sum(t) = 7.5p, so d/dp = 7.5; exercise a value that depends on the
+        # branch chosen from the probe result.
+        props.is_linear ? sum(t) : 2 * sum(t)
+    end == 7.5
+
+    # Non-uniform Dual knots must probe without error and report not-uniform.
+    ForwardDiff.derivative(3.0) do p
+        t = (Float64[0, 1, 2, 4, 8, 16, 20, 21, 22, 40, 41, 100]) .* p
+        props = SearchProperties(t)
+        @test props.has_props
+        @test !props.is_uniform
+        sum(t)
+    end
+
+    # Full search path on uniform Dual knots exercises the closed-form
+    # UniformStep kernel (`Auto` resolves to `KIND_UNIFORM_STEP`). It must
+    # return the same index as `Base` on the primal values.
+    ForwardDiff.derivative(2.0) do p
+        t = collect(range(0.0, 10.0; length = 40)) .* p
+        tv = map(ForwardDiff.value, t)
+        auto = Auto(t)
+        for q in (t[1], t[7], t[end], 5.0 * p, -1.0 * p, 11.0 * p)
+            @test searchsorted_last(auto, t, q) == searchsortedlast(tv, ForwardDiff.value(q))
+            @test searchsorted_first(auto, t, q) == searchsortedfirst(tv, ForwardDiff.value(q))
+        end
+        sum(t)
+    end
+end
+
 @safetestset "Auto{T} parametric + props-aware UniformStep kernel" begin
     using FindFirstFunctions
     using FindFirstFunctions: