use mkl to accelerate gelu_grad (#18099)

test=develop

paddle/fluid/operators/activation_op.h

@@ -363,17 +363,64 @@ struct GeluFunctor : public BaseActivationFunctor<T> {
   }
 };
 
+// gelu_grad(x) = dout * (0.5 * (1 + erf(x / sqrt(2))) + 0.5 * 2 / sqrt(pie) /
+// sqrt(2) * x * exp (-0.5 * sqrt(x)))
+// gelu_grad(x) = dout * (0.5 + 0.5 * erf(x * M_SQRT1_2) + (0.5 * M_2_SQRTPI *
+// M_SQRT1_2) * x * exp (-0.5 * sqrt(x)))
 template <typename T>
 struct GeluGradFunctor : BaseActivationFunctor<T> {
   template <typename Device, typename X, typename Out, typename dOut,
             typename dX>
   void operator()(Device d, X x, Out out, dOut dout, dX dx) const {
+#if defined(PADDLE_WITH_MKLML) && !defined(_WIN32) && !defined(__APPLE__) && \
+    !defined(__OSX__) && !defined(PADDLE_WITH_CUDA)
+    auto x_data = x.data();
+    auto dx_data = dx.data();
+    int n = std::min(x.size(), dx.size());
+
+    std::memset(dx_data, 0, n * sizeof(T));
+
+    // First(dx_data) = erf(x * M_SQRT1_2)
+    math::CBlas<T>::AXPY(n, static_cast<T>(M_SQRT1_2), x_data, 1, dx_data, 1);
+    math::CBlas<T>::VMERF(n, dx_data, dx_data, VML_LA);
+
+    // Second = 0.5 * M_2_SQRTPI * M_SQRT1_2 * x * exp (-0.5 * sqrt(x))
+    auto second = static_cast<T*>(std::malloc(n * sizeof(T)));
+    std::memset(second, 0, n * sizeof(T));
+
+    math::CBlas<T>::VSQUARE(n, x_data, second);
+    for (int i = 0; i < n; i++) {
+      second[i] *= static_cast<T>(-0.5);
+    }
+    math::CBlas<T>::VEXP(n, second, second);
+    math::CBlas<T>::VMUL(n, x_data, second, second);
+    T tmp = static_cast<T>(0.5) * static_cast<T>(M_SQRT1_2) *
+            static_cast<T>(M_2_SQRTPI);
+    for (int i = 0; i < n; i++) {
+      second[i] *= tmp;
+    }
+
+    // Sum = 0.5 * First + Second
+    math::CBlas<T>::AXPY(n, static_cast<T>(0.5), dx_data, 1, second, 1);
+
+    // 0.5 + Sum
+    for (int i = 0; i < n; i++) {
+      second[i] += static_cast<T>(0.5);
+    }
+
+    // * dout
+    auto dout_data = dout.data();
+    math::CBlas<T>::VMUL(n, dout_data, second, dx_data);
+
+    std::free(second);
+#else
     auto first = static_cast<T>(0.5) *
                  (static_cast<T>(1) + ((x * static_cast<T>(M_SQRT1_2)).erf()));
 
     auto second = static_cast<T>(0.5 * M_2_SQRTPI * M_SQRT1_2) * x *
                   (-static_cast<T>(0.5) * x.square()).exp();
     dx.device(d) = dout * (first + second);
+#endif
   }
 
   static constexpr ActBwdOpFwdDeps FwdDeps() { return kDepX; }