Added `[BackwardDifferentiable]` tags for intrinsic + builtin methods (#2732)

* Added higher-order differentiability decorators for built-ins + preliminary tests

* Update diff.meta.slang

5 files changed, 157 insertions, 5 deletions

diff --git a/source/slang/diff.meta.slang b/source/slang/diff.meta.slang
index 26a673512..bbe94dbc2 100644
--- a/source/slang/diff.meta.slang
+++ b/source/slang/diff.meta.slang
@@ -292,6 +292,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
 
 #define VECTOR_MATRIX_BINARY_DIFF_IMPL(NAME)                                                 \
     __generic<T : __BuiltinFloatingPointType, let N : int>                                   \
+    [BackwardDifferentiable]                                                                 \
     [ForwardDerivativeOf(NAME)]                                                              \
     DifferentialPair<vector<T, N>> __d_##NAME##_vector(                                      \
         DifferentialPair<vector<T, N>> dpx, DifferentialPair<vector<T, N>> dpy)              \
@@ -309,6 +310,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         return DifferentialPair<vector<T, N>>(result, d_result);                             \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let M : int, let N : int>                      \
+    [BackwardDifferentiable]                                                                 \
     [ForwardDerivativeOf(NAME)]                                                              \
     DifferentialPair<matrix<T, M, N>> __d_##NAME##_matrix(                                   \
         DifferentialPair<matrix<T, M, N>> dpx, DifferentialPair<matrix<T, M, N>> dpy)        \
@@ -327,6 +329,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         return DifferentialPair<matrix<T, M, N>>(result, d_result);                          \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let N : int>                                   \
+    [BackwardDifferentiable]                                                                 \
     [BackwardDerivativeOf(NAME)]                                                             \
     void __d_##NAME##_vector(                                                                \
             inout DifferentialPair<vector<T, N>> dpx,                                        \
@@ -346,6 +349,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         dpy = diffPair(dpy.p, right_d_result);                                               \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let M : int, let N : int>                      \
+    [BackwardDifferentiable]                                                                 \
     [BackwardDerivativeOf(NAME)]                                                             \
     void __d_##NAME##_matrix(                                                                \
             inout DifferentialPair<matrix<T, M, N>> dpx,                                     \
@@ -368,6 +372,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
 
 #define VECTOR_MATRIX_TERNARY_DIFF_IMPL(NAME)                                                \
     __generic<T : __BuiltinFloatingPointType, let N : int>                                   \
+    [BackwardDifferentiable]                                                                 \
     [ForwardDerivativeOf(NAME)]                                                              \
     DifferentialPair<vector<T, N>> __d_##NAME##_vector(                                      \
         DifferentialPair<vector<T, N>> dpx,                                                  \
@@ -388,8 +393,9 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         return DifferentialPair<vector<T, N>>(result, d_result);                             \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let M : int, let N : int>                      \
+    [BackwardDifferentiable]                                                                 \
     [ForwardDerivativeOf(NAME)]                                                              \
-    DifferentialPair<matrix<T, M, N>> __d_##NAME##_matrix(                                  \
+    DifferentialPair<matrix<T, M, N>> __d_##NAME##_matrix(                                   \
         DifferentialPair<matrix<T, M, N>> dpx,                                               \
         DifferentialPair<matrix<T, M, N>> dpy,                                               \
         DifferentialPair<matrix<T, M, N>> dpz)                                               \
@@ -409,6 +415,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         return DifferentialPair<matrix<T, M, N>>(result, d_result);                          \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let N : int>                                   \
+    [BackwardDifferentiable]                                                                 \
     [BackwardDerivativeOf(NAME)]                                                             \
     void __d_##NAME##_vector(                                                                \
             inout DifferentialPair<vector<T, N>> dpx,                                        \
@@ -433,6 +440,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         dpz = diffPair(dpz.p, right_d_result);                                               \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let M : int, let N : int>                      \
+    [BackwardDifferentiable]                                                                 \
     [BackwardDerivativeOf(NAME)]                                                             \
     void __d_##NAME##_matrix(                                                                \
             inout DifferentialPair<matrix<T, M, N>> dpx,                                     \
@@ -460,12 +468,14 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
 
 #define UNARY_DERIVATIVE_IMPL(NAME, FWD_DIFF_FUNC, BWD_DIFF_FUNC)                            \
     __generic<T : __BuiltinFloatingPointType>                                                \
+    [BackwardDifferentiable]                                                                 \
     [ForwardDerivativeOf(NAME)]                                                              \
     DifferentialPair<T> __d_##NAME(DifferentialPair<T> dpx)                                  \
     {                                                                                        \
         return DifferentialPair<T>(NAME(dpx.p), FWD_DIFF_FUNC);                              \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let N : int>                                   \
+    [BackwardDifferentiable]                                                                 \
     [ForwardDerivativeOf(NAME)]                                                              \
     DifferentialPair<vector<T, N>> __d_##NAME##_vector(DifferentialPair<vector<T, N>> dpx)   \
     {                                                                                        \
@@ -481,6 +491,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         return DifferentialPair<vector<T, N>>(result, d_result);                             \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let M : int, let N : int>                      \
+    [BackwardDifferentiable]                                                                 \
     [ForwardDerivativeOf(NAME)]                                                              \
     DifferentialPair<matrix<T, M, N>> __d_##NAME##_m(DifferentialPair<matrix<T, M, N>> dpx)  \
     {                                                                                        \
@@ -498,12 +509,14 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         return DifferentialPair<matrix<T, M, N>>(result, d_result);                          \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType>                                                \
+    [BackwardDifferentiable]                                                                 \
     [BackwardDerivativeOf(NAME)]                                                             \
     void __d_##NAME(inout DifferentialPair<T> dpx, T.Differential dOut)                      \
     {                                                                                        \
         dpx = diffPair(dpx.p, BWD_DIFF_FUNC);                                                \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let N : int>                                   \
+    [BackwardDifferentiable]                                                                 \
     [BackwardDerivativeOf(NAME)]                                                             \
     void __d_##NAME##_vector(                                                                \
             inout DifferentialPair<vector<T, N>> dpx, vector<T, N>.Differential dOut)        \
@@ -518,6 +531,7 @@ void __d_cross(inout DifferentialPair<vector<T, 3>> a, inout DifferentialPair<ve
         dpx = diffPair(dpx.p, d_result);                                                     \
     }                                                                                        \
     __generic<T : __BuiltinFloatingPointType, let M : int, let N : int>                      \
+    [BackwardDifferentiable]                                                                 \
     [BackwardDerivativeOf(NAME)]                                                             \
     void __d_##NAME##_matrix(                                                                \
             inout DifferentialPair<matrix<T, M, N>> dpx, matrix<T, M, N>.Differential dOut)  \
@@ -581,6 +595,7 @@ SIMPLE_UNARY_DERIVATIVE_IMPL(atan, T(1.0) / (T(1.0) + dpx.p * dpx.p))
 
 // Atan2
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(atan2)]
 DifferentialPair<T> __d_atan2(DifferentialPair<T> dpy, DifferentialPair<T> dpx)
 {
@@ -592,6 +607,7 @@ DifferentialPair<T> __d_atan2(DifferentialPair<T> dpy, DifferentialPair<T> dpx)
 }
 
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(atan2)]
 void __d_atan2(inout DifferentialPair<T> dpy, inout DifferentialPair<T> dpx, T.Differential dOut)
 {
@@ -603,12 +619,14 @@ VECTOR_MATRIX_BINARY_DIFF_IMPL(atan2)
 
 // fmod
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(fmod)]
 DifferentialPair<T> __d_fmod(DifferentialPair<T> x, DifferentialPair<T> y)
 {
     return DifferentialPair<T>(fmod(x.p, y.p), x.d);
 }
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(fmod)]
 void __d_fmod(inout DifferentialPair<T> x, inout DifferentialPair<T> y, T.Differential dOut)
 {
@@ -619,6 +637,7 @@ VECTOR_MATRIX_BINARY_DIFF_IMPL(fmod)
 
 // Raise to a power
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(pow)]
 DifferentialPair<T> __d_pow(DifferentialPair<T> dpx, DifferentialPair<T> dpy)
 {
@@ -638,6 +657,7 @@ DifferentialPair<T> __d_pow(DifferentialPair<T> dpx, DifferentialPair<T> dpy)
 }
 
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(pow)]
 void __d_pow(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpy, T.Differential dOut)
 {
@@ -663,6 +683,7 @@ VECTOR_MATRIX_BINARY_DIFF_IMPL(pow)
 
 // Maximum
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(max)]
 DifferentialPair<T> __d_max(DifferentialPair<T> dpx, DifferentialPair<T> dpy)
 {
@@ -673,6 +694,7 @@ DifferentialPair<T> __d_max(DifferentialPair<T> dpx, DifferentialPair<T> dpy)
 }
 
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(max)]
 void __d_max(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpy, T.Differential dOut)
 {
@@ -684,6 +706,7 @@ VECTOR_MATRIX_BINARY_DIFF_IMPL(max)
 
 // Minimum
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(min)]
 DifferentialPair<T> __d_min(DifferentialPair<T> dpx, DifferentialPair<T> dpy)
 {
@@ -694,6 +717,7 @@ DifferentialPair<T> __d_min(DifferentialPair<T> dpx, DifferentialPair<T> dpy)
 }
 
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(min)]
 void __d_min(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpy, T.Differential dOut)
 {
@@ -705,6 +729,7 @@ VECTOR_MATRIX_BINARY_DIFF_IMPL(min)
 
 // Lerp
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(lerp)]
 DifferentialPair<T> __d_lerp(DifferentialPair<T> dpx, DifferentialPair<T> dpy, DifferentialPair<T> dps)
 {
@@ -714,6 +739,7 @@ DifferentialPair<T> __d_lerp(DifferentialPair<T> dpx, DifferentialPair<T> dpy, D
     );
 }
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(lerp)]
 void __d_lerp(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpy, inout DifferentialPair<T> dps, T.Differential dOut)
 {
@@ -725,6 +751,7 @@ VECTOR_MATRIX_TERNARY_DIFF_IMPL(lerp)
 
 //  Clamp
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(clamp)]
 DifferentialPair<T> __d_clamp(DifferentialPair<T> dpx, DifferentialPair<T> dpMin, DifferentialPair<T> dpMax)
 {
@@ -733,6 +760,7 @@ DifferentialPair<T> __d_clamp(DifferentialPair<T> dpx, DifferentialPair<T> dpMin
         dpx.p < dpMin.p ? (dpx.p > dpMax.p ? dpMax.d : dpx.d) : dpMin.d);
 }
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(clamp)]
 void __d_clamp(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpMin, inout DifferentialPair<T> dpMax, T.Differential dOut)
 {
@@ -743,6 +771,7 @@ void __d_clamp(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpMin, i
 VECTOR_MATRIX_TERNARY_DIFF_IMPL(clamp)
 
 // fma
+[BackwardDifferentiable]
 [ForwardDerivativeOf(fma)]
 DifferentialPair<double> __d_fma(DifferentialPair<double> dpx, DifferentialPair<double> dpy, DifferentialPair<double> dpz)
 {
@@ -750,6 +779,7 @@ DifferentialPair<double> __d_fma(DifferentialPair<double> dpx, DifferentialPair<
         fma(dpx.p, dpy.p, dpz.p),
         dpy.p * dpx.d + dpx.p * dpy.d + dpz.d);
 }
+[BackwardDifferentiable]
 [BackwardDerivativeOf(fma)]
 void __d_fma(inout DifferentialPair<double> dpx, inout DifferentialPair<double> dpy, inout DifferentialPair<double> dpz, double dOut)
 {
@@ -758,6 +788,7 @@ void __d_fma(inout DifferentialPair<double> dpx, inout DifferentialPair<double>
     dpz = diffPair(dpz.p, dOut);
 }
 __generic<let N : int>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(fma)]
 DifferentialPair<vector<double, N>> __d_fma_vector(
     DifferentialPair<vector<double, N>> dpx,
@@ -778,6 +809,7 @@ DifferentialPair<vector<double, N>> __d_fma_vector(
     return DifferentialPair<vector<double, N>>(result, d_result);
 }
 __generic<let N : int>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(fma)]
 void __d_fma_vector(
         inout DifferentialPair<vector<double, N>> dpx,
@@ -803,6 +835,7 @@ void __d_fma_vector(
 
 // mad
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(mad)]
 DifferentialPair<T> __d_mad(DifferentialPair<T> dpx, DifferentialPair<T> dpy, DifferentialPair<T> dpz)
 {
@@ -811,6 +844,7 @@ DifferentialPair<T> __d_mad(DifferentialPair<T> dpx, DifferentialPair<T> dpy, Di
         T.dadd(T.dadd(T.dmul(dpy.p, dpx.d), T.dmul(dpx.p, dpy.d)), dpz.d));
 }
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(mad)]
 void __d_mad(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpy, inout DifferentialPair<T> dpz, T.Differential dOut)
 {
@@ -829,12 +863,14 @@ T __smoothstep_impl(T minVal, T maxVal, T x)
     return t * t * (T(3.0) - T(2.0) * t);
 }
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(smoothstep)]
 DifferentialPair<T> __d_smoothstep(DifferentialPair<T> minVal, DifferentialPair<T> maxVal, DifferentialPair<T> x)
 {
     return __fwd_diff(__smoothstep_impl)(minVal, maxVal, x);
 }
 __generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(smoothstep)]
 void __d_smoothstep(inout DifferentialPair<T> minVal, inout DifferentialPair<T> maxVal, inout DifferentialPair<T> x, T.Differential dOut)
 {
@@ -856,6 +892,7 @@ T __length_impl(vector<T, N> x)
 }
 
 __generic<T: __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(length)]
 [ForceInline]
 DifferentialPair<T> __d_length(DifferentialPair<vector<T, N>> x)
@@ -864,6 +901,7 @@ DifferentialPair<T> __d_length(DifferentialPair<vector<T, N>> x)
 }
 
 __generic<T: __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(length)]
 [ForceInline]
 void __d_length(inout DifferentialPair<vector<T, N>> x, T.Differential dOut)
@@ -872,13 +910,14 @@ void __d_length(inout DifferentialPair<vector<T, N>> x, T.Differential dOut)
 }
 
 // Vector distance
-__generic<T : __BuiltinFloatingPointType, let N : int>
+__generic<T: __BuiltinFloatingPointType, let N : int>
 [BackwardDifferentiable]
 T __distance_impl(vector<T, N> x, vector<T, N> y)
 {
     return length(y - x);
 }
 __generic<T: __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(distance)]
 [ForceInline]
 DifferentialPair<T> __d_distance(DifferentialPair<vector<T, N>> x, DifferentialPair<vector<T, N>> y)
@@ -887,6 +926,7 @@ DifferentialPair<T> __d_distance(DifferentialPair<vector<T, N>> x, DifferentialP
 }
 
 __generic<T: __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(distance)]
 [ForceInline]
 void __d_distance(inout DifferentialPair<vector<T, N>> x, inout DifferentialPair<vector<T, N>> y, T.Differential dOut)
@@ -903,13 +943,15 @@ vector<T, N> __normalize_impl(vector<T, N> x)
     return x * r;
 }
 __generic<T: __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(normalize)]
 [ForceInline]
 DifferentialPair<vector<T, N>> __d_normalize(DifferentialPair<vector<T, N>> x)
 {
     return __fwd_diff(__normalize_impl)(x);
 }
-__generic<T: __BuiltinFloatingPointType, let N : int>
+__generic<T : __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(normalize)]
 [ForceInline]
 void __d_distance(inout DifferentialPair<vector<T, N>> x, vector<T, N>.Differential dOut)
@@ -924,14 +966,16 @@ vector<T, N> __reflect_impl(vector<T, N> i, vector<T, N> n)
 {
     return  i - n * (T(2.0) * dot(i, n));
 }
-__generic<T: __BuiltinFloatingPointType, let N : int>
+__generic<T : __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(reflect)]
 [ForceInline]
 DifferentialPair<vector<T, N>> __d_reflect(DifferentialPair<vector<T, N>> i, DifferentialPair<vector<T, N>> n)
 {
     return __fwd_diff(__reflect_impl)(i, n);
 }
-__generic<T: __BuiltinFloatingPointType, let N : int>
+__generic<T : __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(reflect)]
 [ForceInline]
 void __d_reflect(inout DifferentialPair<vector<T, N>> i, inout DifferentialPair<vector<T, N>> n, vector<T, N>.Differential dOut)
@@ -948,6 +992,7 @@ vector<T, N> __refract_impl(vector<T, N> i, vector<T, N> n, T eta)
     return (k < T(0.0)) ? vector<T, N>(T(0.0)) : eta * i - (eta * dot(n, i) + sqrt(max(T(0.0),k))) * n;
 }
 __generic<T: __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(refract)]
 [ForceInline]
 DifferentialPair<vector<T, N>> __d_refract(DifferentialPair<vector<T, N>> i, DifferentialPair<vector<T, N>> n, DifferentialPair<T> eta)
@@ -955,6 +1000,7 @@ DifferentialPair<vector<T, N>> __d_refract(DifferentialPair<vector<T, N>> i, Dif
     return __fwd_diff(__refract_impl)(i, n, eta);
 }
 __generic<T: __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(refract)]
 [ForceInline]
 void __d_refract(inout DifferentialPair<vector<T, N>> i, inout DifferentialPair<vector<T, N>> n, inout DifferentialPair<T> eta, vector<T, N>.Differential dOut)
@@ -1053,6 +1099,7 @@ T __determinant_impl(matrix<T,N,N> m)
     return result;
 }
 __generic<T : __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [ForwardDerivativeOf(determinant)]
 [ForceInline]
 DifferentialPair<T> __determinant_impl(DifferentialPair<matrix<T,N,N>> m)
@@ -1060,6 +1107,7 @@ DifferentialPair<T> __determinant_impl(DifferentialPair<matrix<T,N,N>> m)
     return __fwd_diff(__determinant_impl)(m);
 }
 __generic<T : __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
 [BackwardDerivativeOf(determinant)]
 [ForceInline]
 void __d_determinant(inout DifferentialPair<matrix<T,N,N>> m, T.Differential dOut)
diff --git a/tests/autodiff/high-order-builtins-1.slang b/tests/autodiff/high-order-builtins-1.slang
new file mode 100644
index 000000000..6b0c33ca6
--- /dev/null
+++ b/tests/autodiff/high-order-builtins-1.slang
@@ -0,0 +1,47 @@
+//TEST(compute):COMPARE_COMPUTE_EX:-cpu -compute -output-using-type -shaderobj
+//TEST(compute):COMPARE_COMPUTE_EX:-slang -compute -shaderobj -output-using-type
+//TEST(compute, vulkan):COMPARE_COMPUTE_EX:-vk -compute -shaderobj -output-using-type
+
+//TEST_INPUT:ubuffer(data=[0 0 0 0], stride=4):out,name=outputBuffer
+RWStructuredBuffer<float> outputBuffer;
+
+[BackwardDifferentiable]
+float f(float x)
+{
+    return x * x;
+}
+
+[BackwardDifferentiable]
+float outerF(float x)
+{
+    return f(sin(x));
+}
+
+[BackwardDifferentiable]
+float df(float x)
+{
+    return __fwd_diff(outerF)(DifferentialPair<float>(x, 1.0)).d; // 4*sin^3(x)
+}
+
+[numthreads(1, 1, 1)]
+void computeMain(uint3 dispatchThreadID : SV_DispatchThreadID)
+{
+    // Given f(x) = sin^2(x),
+    // f'(x) = 2*sin(x)*cos(x)
+    // f''(x) = 2*cos^2(x) - 2*sin^2(x)
+    //
+
+    // Expect f''(4) = -0.291
+    {
+        var p = diffPair(4.0, 0.0);
+        __bwd_diff(df)(p, 1.0);
+        outputBuffer[0] = p.d;
+    }
+
+    // Expect f''(4) = -0.653643
+    {
+        var p = diffPair(2.0, 0.0);
+        __bwd_diff(df)(p, 0.5);
+        outputBuffer[1] = p.d;
+    }
+}
diff --git a/tests/autodiff/high-order-builtins-1.slang.expected.txt b/tests/autodiff/high-order-builtins-1.slang.expected.txt
new file mode 100644
index 000000000..4fa4ade6d
--- /dev/null
+++ b/tests/autodiff/high-order-builtins-1.slang.expected.txt
@@ -0,0 +1,5 @@
+type: float
+-0.291000
+-0.653643
+0.000000
+0.000000
diff --git a/tests/autodiff/high-order-builtins-2.slang b/tests/autodiff/high-order-builtins-2.slang
new file mode 100644
index 000000000..b15dee7c7
--- /dev/null
+++ b/tests/autodiff/high-order-builtins-2.slang
@@ -0,0 +1,47 @@
+//TEST(compute):COMPARE_COMPUTE_EX:-cpu -compute -output-using-type -shaderobj
+//TEST(compute):COMPARE_COMPUTE_EX:-slang -compute -shaderobj -output-using-type
+//TEST(compute, vulkan):COMPARE_COMPUTE_EX:-vk -compute -shaderobj -output-using-type
+
+//TEST_INPUT:ubuffer(data=[0 0 0 0], stride=4):out,name=outputBuffer
+RWStructuredBuffer<float> outputBuffer;
+
+[BackwardDifferentiable]
+float f(float x)
+{
+    return sin(x) + x * x;
+}
+
+[BackwardDifferentiable]
+float outerF(float x)
+{
+    return f(pow(x, 3));
+}
+
+[BackwardDifferentiable]
+float df(float x)
+{
+    return __fwd_diff(outerF)(DifferentialPair<float>(x, 1.0)).d; // x^3 + x^6
+}
+
+[numthreads(1, 1, 1)]
+void computeMain(uint3 dispatchThreadID : SV_DispatchThreadID)
+{
+    // Given f(x) = sin(x^3) + x^6
+    // f'(x) = cos(x^3)*(3*x^2) + 6*x^5
+    // f''(x) = 6*cos(x^3)*x - 9*sin(x^3)*(x^4) + 30*x^4
+    //
+
+    // Expect f''(4) = -0.291
+    {
+        var p = diffPair(1.0, 0.0);
+        __bwd_diff(df)(p, 1.0);
+        outputBuffer[0] = p.d;
+    }
+
+    // Expect f''(4) = -0.653643
+    {
+        var p = diffPair(2.0, 0.0);
+        __bwd_diff(df)(p, 0.5);
+        outputBuffer[1] = p.d;
+    }
+}
diff --git a/tests/autodiff/high-order-builtins-2.slang.expected.txt b/tests/autodiff/high-order-builtins-2.slang.expected.txt
new file mode 100644
index 000000000..9f5d74b29
--- /dev/null
+++ b/tests/autodiff/high-order-builtins-2.slang.expected.txt
@@ -0,0 +1,5 @@
+type: float
+25.668574
+167.893206
+0.000000
+0.000000