Support high order diff pattern: `bwd_diff(fwd_diff(f))`. (#2695)

* Support high order diff pattern: `bwd_diff(fwd_diff(f))`.

* Fix.

---------

Co-authored-by: Yong He <yhe@nvidia.com>

6 files changed, 148 insertions, 0 deletions

diff --git a/tests/autodiff/high-order-backward-diff-2.slang b/tests/autodiff/high-order-backward-diff-2.slang
new file mode 100644
index 000000000..08fa5edda
--- /dev/null
+++ b/tests/autodiff/high-order-backward-diff-2.slang
@@ -0,0 +1,51 @@
+//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;
+
+struct A : IDifferentiable
+{
+    float x;
+    int nx;
+}
+
+[BackwardDifferentiable]
+float f(A x)
+{
+    return x.x * x.x;
+}
+
+[BackwardDifferentiable]
+float outerF(A x)
+{
+    A nx;
+    nx.x = x.x * x.x;
+    nx.nx = 2;//x.nx;
+    return f(nx);
+}
+
+[BackwardDifferentiable]
+float df(A x)
+{
+    A.Differential ad;
+    ad.x = 1.0;
+    return __fwd_diff(outerF)(DifferentialPair<A>(x, ad)).d; // 4*x^3
+}
+
+[numthreads(1, 1, 1)]
+void computeMain(uint3 dispatchThreadID : SV_DispatchThreadID)
+{
+    // Given f(x) = x^4,
+    // f''(x) = 12 * x^2
+    // Expect f''(4) = 192
+    A a;
+    a.x = 4.0;
+    a.nx = 54;
+    A.Differential ad;
+    ad.x = 1.0;
+    var p = diffPair(a, ad);
+    __bwd_diff(df)(p, 1.0);
+    outputBuffer[0] = p.d.x;
+}
diff --git a/tests/autodiff/high-order-backward-diff-2.slang.expected.txt b/tests/autodiff/high-order-backward-diff-2.slang.expected.txt
new file mode 100644
index 000000000..0f08247f0
--- /dev/null
+++ b/tests/autodiff/high-order-backward-diff-2.slang.expected.txt
@@ -0,0 +1,5 @@
+type: float
+192.000000
+0.000000
+0.000000
+0.000000
diff --git a/tests/autodiff/high-order-backward-diff-3.slang b/tests/autodiff/high-order-backward-diff-3.slang
new file mode 100644
index 000000000..0a52c87a6
--- /dev/null
+++ b/tests/autodiff/high-order-backward-diff-3.slang
@@ -0,0 +1,52 @@
+//DISABLED_TEST(compute):COMPARE_COMPUTE_EX:-cpu -compute -output-using-type -shaderobj
+//DISABLED_TEST(compute):COMPARE_COMPUTE_EX:-slang -compute -shaderobj -output-using-type
+//DISABLED_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;
+
+struct A : IDifferentiable
+{
+    float x;
+    int nx;
+}
+
+[BackwardDifferentiable]
+float f(A x)
+{
+    return x.x * x.x;
+}
+
+[BackwardDifferentiable]
+float outerF(A x)
+{
+    A nx;
+    nx.x = x.x * x.x;
+    nx.nx = 2;//x.nx;
+    return f(nx);
+}
+
+[BackwardDifferentiable]
+float df(A x)
+{
+    A.Differential ad;
+    ad.x = 0.0;
+    var p = diffPair(x, ad);
+    __bwd_diff(outerF)(p, 1.0);
+    return p.d.x;
+}
+
+[numthreads(1, 1, 1)]
+void computeMain(uint3 dispatchThreadID : SV_DispatchThreadID)
+{
+    // Given f(x) = x^4,
+    // f''(x) = 12 * x^2
+    // Expect f''(4) = 192
+    A a;
+    a.x = 4.0;
+    a.nx = 54;
+    A.Differential ad;
+    ad.x = 1.0;
+    var p = diffPair(a, ad);
+    outputBuffer[0] = __fwd_diff(df)(p).d;
+}
diff --git a/tests/autodiff/high-order-backward-diff-3.slang.expected.txt b/tests/autodiff/high-order-backward-diff-3.slang.expected.txt
new file mode 100644
index 000000000..e69de29bb
--- /dev/null
+++ b/tests/autodiff/high-order-backward-diff-3.slang.expected.txt
diff --git a/tests/autodiff/high-order-backward-diff.slang b/tests/autodiff/high-order-backward-diff.slang
new file mode 100644
index 000000000..1ce77e29b
--- /dev/null
+++ b/tests/autodiff/high-order-backward-diff.slang
@@ -0,0 +1,35 @@
+//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(x * x);
+}
+
+[BackwardDifferentiable]
+float df(float x)
+{
+    return __fwd_diff(outerF)(DifferentialPair<float>(x, 1.0)).d; // 4*x^3
+}
+
+[numthreads(1, 1, 1)]
+void computeMain(uint3 dispatchThreadID : SV_DispatchThreadID)
+{
+    // Given f(x) = x^4,
+    // f''(x) = 12 * x^2
+    // Expect f''(4) = 192
+    var p = diffPair(4.0, 1.0);
+    __bwd_diff(df)(p, 1.0);
+    outputBuffer[0] = p.d;
+}
diff --git a/tests/autodiff/high-order-backward-diff.slang.expected.txt b/tests/autodiff/high-order-backward-diff.slang.expected.txt
new file mode 100644
index 000000000..0f08247f0
--- /dev/null
+++ b/tests/autodiff/high-order-backward-diff.slang.expected.txt
@@ -0,0 +1,5 @@
+type: float
+192.000000
+0.000000
+0.000000
+0.000000