Make copysign function differentiable (#7585)

* Initial plan

* Implement copysign forward and backward derivatives

Co-authored-by: csyonghe <2652293+csyonghe@users.noreply.github.com>

* Fix copysign test format to use expected.txt file

Co-authored-by: csyonghe <2652293+csyonghe@users.noreply.github.com>

* Add wgsl support to copysign and fix y==0 derivative case

Co-authored-by: csyonghe <2652293+csyonghe@users.noreply.github.com>

* Add wgsl support to copysign helper functions

Co-authored-by: csyonghe <2652293+csyonghe@users.noreply.github.com>

* Fix copysign derivative to return 0 when either x or y is 0

Co-authored-by: csyonghe <2652293+csyonghe@users.noreply.github.com>

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: csyonghe <2652293+csyonghe@users.noreply.github.com>

2 files changed, 129 insertions, 0 deletions

diff --git a/tests/autodiff-dstdlib/dstdlib-copysign.slang b/tests/autodiff-dstdlib/dstdlib-copysign.slang
new file mode 100644
index 000000000..30140c605
--- /dev/null
+++ b/tests/autodiff-dstdlib/dstdlib-copysign.slang
@@ -0,0 +1,108 @@
+//TEST(compute, vulkan):COMPARE_COMPUTE_EX:-vk -compute -shaderobj -output-using-type
+//TEST(compute):COMPARE_COMPUTE_EX:-slang -compute -shaderobj -output-using-type
+//TEST(compute):COMPARE_COMPUTE_EX:-wgpu -compute -output-using-type
+
+//TEST_INPUT:ubuffer(data=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0], stride=4):out,name=outputBuffer
+RWStructuredBuffer<float> outputBuffer;
+
+typedef DifferentialPair<float> dpfloat;
+typedef DifferentialPair<float2> dpfloat2;
+
+[BackwardDifferentiable]
+float diffCopysign(float x, float y)
+{
+    return copysign(x, y);
+}
+
+[BackwardDifferentiable]
+float2 diffCopysign(float2 x, float2 y)
+{
+    return copysign(x, y);
+}
+
+[numthreads(1, 1, 1)]
+void computeMain(uint3 dispatchThreadID: SV_DispatchThreadID)
+{
+    // Test 1: forward diff copysign(3.0, -1.0) with dx=2.0, dy=1.0
+    {
+        dpfloat dpx = dpfloat(3.0, 2.0);
+        dpfloat dpy = dpfloat(-1.0, 1.0);
+        dpfloat res = __fwd_diff(diffCopysign)(dpx, dpy);
+        outputBuffer[0] = res.p;               
+        outputBuffer[1] = res.d;
+    }
+
+    // Test 2: forward diff copysign(-2.0, 4.0) with dx=1.5, dy=-0.5
+    {
+        dpfloat dpx = dpfloat(-2.0, 1.5);
+        dpfloat dpy = dpfloat(4.0, -0.5);
+        dpfloat res = __fwd_diff(diffCopysign)(dpx, dpy);
+        outputBuffer[2] = res.p;               
+        outputBuffer[3] = res.d;
+    }
+
+    // Test 3: forward diff copysign(0.0, -1.0) with dx=3.0, dy=2.0
+    {
+        dpfloat dpx = dpfloat(0.0, 3.0);
+        dpfloat dpy = dpfloat(-1.0, 2.0);
+        dpfloat res = __fwd_diff(diffCopysign)(dpx, dpy);
+        outputBuffer[4] = res.p;               
+        outputBuffer[5] = res.d;
+    }
+
+    // Test 4: vector forward diff
+    {
+        dpfloat2 dpx = dpfloat2(float2(5.0, -3.0), float2(1.0, 2.0));
+        dpfloat2 dpy = dpfloat2(float2(-2.0, 4.0), float2(0.5, -1.0));
+        dpfloat2 res = __fwd_diff(diffCopysign)(dpx, dpy);
+        outputBuffer[6] = res.p[0];            
+        outputBuffer[7] = res.d[0];            
+        outputBuffer[8] = res.p[1];            
+        outputBuffer[9] = res.d[1];
+    }
+
+    // Test 5: backward diff copysign(4.0, -2.0)
+    {
+        dpfloat dpx = dpfloat(4.0, 0.0);
+        dpfloat dpy = dpfloat(-2.0, 0.0);
+        __bwd_diff(diffCopysign)(dpx, dpy, 1.0);
+        outputBuffer[10] = dpx.d;              
+        outputBuffer[11] = dpy.d;
+    }
+
+    // Test 6: backward diff copysign(-3.0, 5.0)  
+    {
+        dpfloat dpx = dpfloat(-3.0, 0.0);
+        dpfloat dpy = dpfloat(5.0, 0.0);
+        __bwd_diff(diffCopysign)(dpx, dpy, 2.0);
+        outputBuffer[12] = dpx.d;              
+        outputBuffer[13] = dpy.d;
+    }
+
+    // Test 7: copysign with y=0 - derivative should be 0
+    {
+        dpfloat dpx = dpfloat(3.0, 2.0);
+        dpfloat dpy = dpfloat(0.0, 1.0);
+        dpfloat res = __fwd_diff(diffCopysign)(dpx, dpy);
+        outputBuffer[14] = res.p;               
+        outputBuffer[15] = res.d;
+    }
+
+    // Test 8: copysign with x=0 - derivative should be 0
+    {
+        dpfloat dpx = dpfloat(0.0, 2.0);
+        dpfloat dpy = dpfloat(-1.0, 1.0);
+        dpfloat res = __fwd_diff(diffCopysign)(dpx, dpy);
+        outputBuffer[16] = res.p;               
+        outputBuffer[17] = res.d;
+    }
+
+    // Test 9: vector backward diff
+    {
+        dpfloat2 dpx = dpfloat2(float2(2.0, -1.0), float2(0.0, 0.0));
+        dpfloat2 dpy = dpfloat2(float2(-3.0, 4.0), float2(0.0, 0.0));
+        __bwd_diff(diffCopysign)(dpx, dpy, float2(1.0, 3.0));
+        outputBuffer[18] = dpx.d[0];           
+        outputBuffer[19] = dpx.d[1];           
+    }
+}
\ No newline at end of file
diff --git a/tests/autodiff-dstdlib/dstdlib-copysign.slang.expected.txt b/tests/autodiff-dstdlib/dstdlib-copysign.slang.expected.txt
new file mode 100644
index 000000000..71f3de9fd
--- /dev/null
+++ b/tests/autodiff-dstdlib/dstdlib-copysign.slang.expected.txt
@@ -0,0 +1,21 @@
+type: float
+-3.000000
+-2.000000
+2.000000
+-1.500000
+0.000000
+0.000000
+-5.000000
+-1.000000
+3.000000
+-2.000000
+-1.000000
+0.000000
+-2.000000
+0.000000
+3.000000
+0.000000
+0.000000
+0.000000
+-1.000000
+-3.000000
\ No newline at end of file