Improve test for Heaviside backward

include/aidge/backend/cpu/operator/HeavisideImpl_kernels.hpp

@@ -42,14 +42,18 @@ void HeavisideImplCpuBackwardKernel(std::size_t inputLength,
                                     const void* grad_output_,
                                     void* grad_input_) {
 
+    /*
+     * Heaviside is approximated by an arctan function for backward :
+     * S ~= \frac{1}{\pi}\text{arctan}(\pi U \frac{\alpha}{2})
+     * \frac{dS}{dU} = \frac{\alpha}{2} \frac{1}{(1+(\frac{\pi U \alpha}{2})^2)}}
+     * */
+
     const O* output = static_cast<const O*>(output_);
     const GO* grad_output = static_cast<const GO*>(grad_output_);
     GI* grad_input = static_cast<GI*>(grad_input_);
 
     for (size_t i = 0; i < inputLength; ++i) {
-        // dx = dy * (1/PI) * (1 / (1 + (PI * x)^2))
-        // grad_input[i] = (1 / M_PI) * grad_output[i] * static_cast<O>(1.0 / (1.0 + (output[i] * output[i]) * (M_PI * M_PI)));
-        grad_input[i] = grad_output[i] * static_cast<O>(1.0 / (1.0 + (output[i] * output[i]) * (M_PI * M_PI)));
+        grad_input[i] = grad_output[i] * static_cast<O>(1.0 / (1.0 + (output[i] * M_PI) * (output[i] * M_PI)));
     }
 }
 

unit_tests/operator/Test_HeavisideImpl.cpp

@@ -117,13 +117,10 @@ TEST_CASE("[cpu/operator] Heaviside(backward)", "[Heaviside][CPU]") {
     op->setInput(IOIndex_t(0), std::make_shared<Tensor>(input));
     op->forward();
 
-    Log::info("Output : ");
-    op->getOutput(0)->print();
-
     op->getOutput(0)->setGrad(std::make_shared<Tensor>(grad));
     op->backward();
 
-    Log::info("Gradient : ");
-    op->getInput(0)->grad()->print();
+    auto expectedResult = Tensor(Array1D<float,3>({0.0920, 0.0920, 0.0920}));
+    REQUIRE(approxEq<float>(*(op->getInput(0)->grad()), expectedResult));
 }
 }