add MKL computation back to gelu's non-approximate part (#23420)

paddle/fluid/operators/gelu_op.h

@@ -41,9 +41,28 @@ struct GeluFunctor {
                       .tanh();
       out.device(d) = x * static_cast<T>(0.5) * (static_cast<T>(1) + temp);
     } else {
+#if defined(PADDLE_WITH_MKLML) && !defined(_WIN32) && !defined(__APPLE__) && \
+    !defined(__OSX__) && !defined(PADDLE_WITH_CUDA)
+      auto x_data = x.data();
+      auto out_data = out.data();
+      int n = std::min(x.size(), out.size());
+
+      std::memset(out_data, 0, n * sizeof(T));
+      math::CBlas<T>::AXPY(n, static_cast<T>(M_SQRT1_2), x_data, 1, out_data,
+                           1);
+      math::CBlas<T>::VMERF(n, out_data, out_data, VML_LA);
+      for (int i = 0; i < n; i++) {
+        out_data[i] += static_cast<T>(1);
+      }
+      math::CBlas<T>::VMUL(n, x_data, out_data, out_data);
+      for (int i = 0; i < n; i++) {
+        out_data[i] *= static_cast<T>(0.5);
+      }
+#else
       // gelu(x) = 0.5 * x *  (1 + erf(x / sqrt(2)))
       auto temp = (x * static_cast<T>(M_SQRT1_2)).erf();
       out.device(d) = x * static_cast<T>(0.5) * (static_cast<T>(1) + temp);
+#endif
     }
   }
 };
@@ -61,6 +80,41 @@ struct GeluGradFunctor {
                      (static_cast<T>(1) + y +
                       (x - x * y.square()) * (kAlpha + kBeta * x.square()));
     } else {
+#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();
+      auto dout_data = dout.data();
+      int n = std::min(x.size(), dx.size());
+
+      auto first = static_cast<T*>(std::malloc(n * sizeof(T)));
+      std::memset(first, 0, n * sizeof(T));
+      auto second = static_cast<T*>(std::malloc(n * sizeof(T)));
+      std::memset(second, 0, n * sizeof(T));
+
+      // first = (0.5 * (1 + erf(x / sqrt(2))))
+      math::CBlas<T>::AXPY(n, static_cast<T>(M_SQRT1_2), x_data, 1, first, 1);
+      math::CBlas<T>::VMERF(n, first, first, VML_LA);
+      for (int i = 0; i < n; i++) {
+        first[i] += static_cast<T>(1);
+      }
+      math::CBlas<T>::SCAL(n, static_cast<T>(0.5), first, 1);
+
+      // second = (0.5 * 2/sqrt(pi) * 1/sqrt(2) * x * exp(-0.5 * x^2))
+      math::CBlas<T>::VSQUARE(n, x_data, second);
+      math::CBlas<T>::SCAL(n, -static_cast<T>(0.5), second, 1);
+      math::CBlas<T>::VEXP(n, second, second);
+      math::CBlas<T>::VMUL(n, x_data, second, second);
+      math::CBlas<T>::SCAL(n, static_cast<T>(0.5 * M_2_SQRTPI * M_SQRT1_2),
+                           second, 1);
+
+      // dx = dout * (first + second);
+      math::CBlas<T>::VADD(n, first, second, first);
+      math::CBlas<T>::VMUL(n, dout_data, first, dx_data);
+
+      std::free(first);
+      std::free(second);
+#else
       // gelu_grad(x) = dout * 0.5 * (1 + erf(x / sqrt(2)) + x * sqrt(2 / pi) *
       // exp(- x^2 / 2)
       auto first =
@@ -70,6 +124,7 @@ struct GeluGradFunctor {
       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
     }
   }
 };