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>

4 files changed, 211 insertions, 5 deletions

diff --git a/source/slang/diff.meta.slang b/source/slang/diff.meta.slang
index 13c5d2d47..542983049 100644
--- a/source/slang/diff.meta.slang
+++ b/source/slang/diff.meta.slang
@@ -2160,6 +2160,83 @@ void __d_min(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpy, T.Dif
 
 VECTOR_MATRIX_BINARY_DIFF_IMPL(min)
 
+// copysign
+__generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
+[PreferRecompute]
+[ForwardDerivativeOf(copysign)]
+DifferentialPair<T> __d_copysign(DifferentialPair<T> dpx, DifferentialPair<T> dpy)
+{
+    // copysign(x, y) = sign(y) * abs(x)
+    // d/dx copysign(x, y) = sign(y) * sign(x) when x != 0 and y != 0, 0 when x == 0 or y == 0
+    // d/dy copysign(x, y) = 0 (sign function is not differentiable w.r.t y)
+    let sign_y = select(dpy.p >= T(0.0), T(1.0), T(-1.0));
+    let sign_x = select(dpx.p >= T(0.0), T(1.0), T(-1.0));
+    // When x == 0 or y == 0, derivative w.r.t. x should be 0
+    let dx_coeff = select((dpx.p == T(0.0)) || (dpy.p == T(0.0)), T(0.0), sign_y * sign_x);
+    return DifferentialPair<T>(
+        copysign(dpx.p, dpy.p),
+        __mul_p_d(dx_coeff, dpx.d)
+    );
+}
+
+__generic<T : __BuiltinFloatingPointType>
+[BackwardDifferentiable]
+[PreferRecompute]
+[BackwardDerivativeOf(copysign)]
+void __d_copysign(inout DifferentialPair<T> dpx, inout DifferentialPair<T> dpy, T.Differential dOut)
+{
+    let sign_y = select(dpy.p >= T(0.0), T(1.0), T(-1.0));
+    let sign_x = select(dpx.p >= T(0.0), T(1.0), T(-1.0));
+    // When x == 0 or y == 0, derivative w.r.t. x should be 0
+    let dx_coeff = select((dpx.p == T(0.0)) || (dpy.p == T(0.0)), T(0.0), sign_y * sign_x);
+    // Gradient flows only to x since d/dy copysign = 0
+    dpx = diffPair(dpx.p, __mul_p_d(dx_coeff, dOut));
+    dpy = diffPair(dpy.p, T.dzero());
+}
+
+__generic<T : __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
+[PreferRecompute]
+[ForwardDerivativeOf(copysign)]
+DifferentialPair<vector<T, N>> __d_copysign_vector(
+    DifferentialPair<vector<T, N>> dpx, DifferentialPair<vector<T, N>> dpy)
+{
+    vector<T, N> result;
+    vector<T, N>.Differential d_result;
+    [ForceUnroll] for (int i = 0; i < N; ++i)
+    {
+        DifferentialPair<T> dp_elem = __d_copysign(
+            DifferentialPair<T>(dpx.p[i], __slang_noop_cast<T.Differential>(dpx.d[i])),
+            DifferentialPair<T>(dpy.p[i], __slang_noop_cast<T.Differential>(dpy.d[i])));
+        result[i] = dp_elem.p;
+        d_result[i] = __slang_noop_cast<T>(dp_elem.d);
+    }
+    return DifferentialPair<vector<T, N>>(result, d_result);
+}
+
+__generic<T : __BuiltinFloatingPointType, let N : int>
+[BackwardDifferentiable]
+[PreferRecompute]
+[BackwardDerivativeOf(copysign)]
+void __d_copysign_vector(
+    inout DifferentialPair<vector<T, N>> dpx,
+    inout DifferentialPair<vector<T, N>> dpy,
+    vector<T, N>.Differential dOut)
+{
+    vector<T, N>.Differential x_d_result, y_d_result;
+    [ForceUnroll] for (int i = 0; i < N; ++i)
+    {
+        DifferentialPair<T> x_dp = DifferentialPair<T>(dpx.p[i], __slang_noop_cast<T.Differential>(dpx.d[i]));
+        DifferentialPair<T> y_dp = DifferentialPair<T>(dpy.p[i], __slang_noop_cast<T.Differential>(dpy.d[i]));
+        __d_copysign(x_dp, y_dp, __slang_noop_cast<T.Differential>(dOut[i]));
+        x_d_result[i] = __slang_noop_cast<T>(x_dp.d);
+        y_d_result[i] = __slang_noop_cast<T>(y_dp.d);
+    }
+    dpx = diffPair(dpx.p, x_d_result);
+    dpy = diffPair(dpy.p, y_d_result);
+}
+
 // Lerp
 __generic<T : __BuiltinFloatingPointType>
 [BackwardDifferentiable]
diff --git a/source/slang/hlsl.meta.slang b/source/slang/hlsl.meta.slang
index 38f274984..7879fc493 100644
--- a/source/slang/hlsl.meta.slang
+++ b/source/slang/hlsl.meta.slang
@@ -7685,7 +7685,7 @@ matrix<T, N, M> ceil(matrix<T, N, M> x)
 /// @category math
 __generic<let N: int>
 [__readNone]
-[require(cpp_cuda_glsl_hlsl_metal_spirv)]
+[require(cpp_cuda_glsl_hlsl_metal_spirv_wgsl)]
 vector<half,N> copysign_half(vector<half,N> x, vector<half,N> y)
 {
     let ux = reinterpret<vector<uint16_t,N>>(x);
@@ -7702,7 +7702,7 @@ vector<half,N> copysign_half(vector<half,N> x, vector<half,N> y)
 /// @category math
 __generic<let N: int>
 [__readNone]
-[require(cpp_cuda_glsl_hlsl_metal_spirv)]
+[require(cpp_cuda_glsl_hlsl_metal_spirv_wgsl)]
 vector<float,N> copysign_float(vector<float,N> x, vector<float,N> y)
 {
     let ux = reinterpret<vector<uint32_t,N>>(x);
@@ -7719,7 +7719,7 @@ vector<float,N> copysign_float(vector<float,N> x, vector<float,N> y)
 /// @category math
 __generic<let N: int>
 [__readNone]
-[require(cpp_cuda_glsl_hlsl_metal_spirv)]
+[require(cpp_cuda_glsl_hlsl_metal_spirv_wgsl)]
 vector<double,N> copysign_double(vector<double,N> x, vector<double,N> y)
 {
     let ux = reinterpret<vector<uint64_t,N>>(x);
@@ -7740,7 +7740,7 @@ vector<T,N> __real_cast(vector<U,N> val);
 /// @category math
 __generic<T : __BuiltinFloatingPointType, let N: int>
 [__readNone]
-[require(cpp_cuda_glsl_hlsl_metal_spirv)]
+[require(cpp_cuda_glsl_hlsl_metal_spirv_wgsl)]
 vector<T,N> copysign(vector<T,N> x, vector<T,N> y)
 {
     __target_switch
@@ -7766,7 +7766,7 @@ vector<T,N> copysign(vector<T,N> x, vector<T,N> y)
 
 __generic<T : __BuiltinFloatingPointType>
 [__readNone]
-[require(cpp_cuda_glsl_hlsl_metal_spirv)]
+[require(cpp_cuda_glsl_hlsl_metal_spirv_wgsl)]
 T copysign(T x, T y)
 {
     __target_switch
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