gelu using normcdf for cudnn

Author: GuoxiaWang

paddle/fluid/operators/gelu_op.cu

@@ -41,11 +41,7 @@ struct GeluWithoutApproximateFunctor {
   inline HOSTDEVICE T operator()(T arg_x) {
     // actual gelu with approximation = false
     MPType x = static_cast<MPType>(arg_x);
-    MPType one = static_cast<MPType>(1);
-    MPType half = static_cast<MPType>(0.5);
-    MPType erf_out = erf(x * static_cast<MPType>(M_SQRT1_2));
-    MPType out = x * half * (one + erf_out);
-    return static_cast<T>(out);
+    return static_cast<T>(x * normcdf(x));
   }
 };
 
@@ -100,12 +96,10 @@ struct GeluWithoutApproximateGradFunctor {
   inline HOSTDEVICE T operator()(T arg_x, T arg_dout) {
     MPType x = static_cast<MPType>(arg_x);
     MPType dout = static_cast<MPType>(arg_dout);
-    MPType one = static_cast<MPType>(1);
-    MPType half = static_cast<MPType>(0.5);
-    MPType kAlpha = static_cast<MPType>(M_2_SQRTPI * M_SQRT1_2);
-    auto ans = half * (one + erf(x * static_cast<MPType>(M_SQRT1_2))) +
-               half * kAlpha * x * exp(-half * x * x);
-    return static_cast<T>(ans * dout);
+    constexpr MPType kBeta = M_2_SQRTPI * M_SQRT1_2 * static_cast<MPType>(0.5);
+    const MPType cdf = normcdf(x);
+    const MPType pdf = exp(static_cast<MPType>(-0.5) * x * x) * kBeta;
+    return static_cast<T>(dout * (cdf + x * pdf));
   }
 };