diff --git a/paddle/fluid/operators/math/jit_kernel_exp.cc b/paddle/fluid/operators/math/jit_kernel_exp.cc
index 15efeba41a26ec8e419b21b927ef06170d1a777b..66e80a07e457d78477fa7eaa1e22e6a179426846 100644
--- a/paddle/fluid/operators/math/jit_kernel_exp.cc
+++ b/paddle/fluid/operators/math/jit_kernel_exp.cc
@@ -27,13 +27,6 @@ limitations under the License. */
 namespace paddle {
 namespace operators {
 namespace math {
-
-#ifdef __AVX__
-namespace detail {
-__m256 Exp(__m256 a);
-}  // namespace detail
-#endif
-
 namespace jitkernel {
 namespace jit = platform::jit;
 
@@ -205,7 +198,7 @@ __m256 ExpAVX(__m256 x) {
 #ifdef __AVX2__
 __m256 ExpAVX2(__m256 x) {
   __m256 tmp = _mm256_setzero_ps(), fx;
-  __m256 one = *reinterpret_cast<const __m256*> _ps256_one;
+  __m256 one = *reinterpret_cast<const __m256*>(_ps256_one);
   __m256i imm0;
 
   x = _mm256_min_ps(x, *reinterpret_cast<const __m256*>(_ps256_exp_hi));
@@ -335,7 +328,8 @@ class VSigmoidKernelImpl : public VSigmoidKernel<T> {
   template <>                                                                  \
   void VSigmoidKernelImpl<float, isa, kEQ8>::Compute(const float* x, float* y) \
       const {                                                                  \
-    /*use static const??*/ __m256 max = _mm256_set1_ps(SIGMOID_THRESHOLD_MAX); \
+    /* TODO(TJ): try to use static const*/                                     \
+    __m256 max = _mm256_set1_ps(SIGMOID_THRESHOLD_MAX);                        \
     __m256 min = _mm256_set1_ps(SIGMOID_THRESHOLD_MIN);                        \
     __m256 tmp = _mm256_loadu_ps(x);                                           \
     INTRI_SIGMOID(tmp, min, max, expisa);                                      \
diff --git a/paddle/fluid/operators/math/jit_kernel_lstm.cc b/paddle/fluid/operators/math/jit_kernel_lstm.cc
index 42a2b96fd945c516f8c26ca51ecb452345a9a86f..26bd26e2e171feea569fbd646a9caf03bebbaa46 100644
--- a/paddle/fluid/operators/math/jit_kernel_lstm.cc
+++ b/paddle/fluid/operators/math/jit_kernel_lstm.cc
@@ -25,13 +25,18 @@ limitations under the License. */
 namespace paddle {
 namespace operators {
 namespace math {
-#ifdef __AVX__
+namespace jitkernel {
 namespace detail {
-__m256 Exp(__m256 a);
-}  // namespace detail
+#ifdef __AVX__
+__m256 ExpAVX(__m256 x);
 #endif
 
-namespace jitkernel {
+#ifdef __AVX2__
+__m256 ExpAVX2(__m256 x);
+#endif
+
+}  // namespace detail
+
 namespace jit = platform::jit;
 
 #ifdef __AVX__
@@ -43,43 +48,72 @@ class AVXAct {
   virtual __m256 Compute(__m256 x) const = 0;
 };
 
-template <act_type type>
+template <act_type type, jit::cpu_isa_t isa>
 class AVXActImpl : public AVXAct {
  public:
   __m256 Compute(__m256 x) const override { PADDLE_THROW("Unkown type!"); }
 };
 
-template <>
-__m256 AVXActImpl<kSigmoid>::Compute(__m256 x) const {
-  __m256 ones = _mm256_set1_ps(1.0f);
-  x = _mm256_max_ps(x, _mm256_set1_ps(SIGMOID_THRESHOLD_MIN));
-  x = _mm256_min_ps(x, _mm256_set1_ps(SIGMOID_THRESHOLD_MAX));
-  x = _mm256_sub_ps(_mm256_set1_ps(0.0f), x);
-  x = detail::Exp(x);
-  x = _mm256_add_ps(ones, x);
-  return _mm256_div_ps(ones, x);
-}
+#define AVX_SIGMOID(isa, expisa)                                 \
+  template <>                                                    \
+  __m256 AVXActImpl<kSigmoid, isa>::Compute(__m256 x) const {    \
+    __m256 ones = _mm256_set1_ps(1.0f);                          \
+    x = _mm256_max_ps(x, _mm256_set1_ps(SIGMOID_THRESHOLD_MIN)); \
+    x = _mm256_min_ps(x, _mm256_set1_ps(SIGMOID_THRESHOLD_MAX)); \
+    x = _mm256_sub_ps(_mm256_set1_ps(0.0f), x);                  \
+    x = expisa(x);                                               \
+    x = _mm256_add_ps(ones, x);                                  \
+    return _mm256_div_ps(ones, x);                               \
+  }
 
-template <>
-__m256 AVXActImpl<kTanh>::Compute(__m256 x) const {
-  __m256 ones = _mm256_set1_ps(1.0f);
-  x = _mm256_mul_ps(_mm256_set1_ps(-2.0f), x);
-  x = _mm256_min_ps(x, _mm256_set1_ps(EXP_MAX_INPUT));
-  x = detail::Exp(x);
-  x = _mm256_add_ps(ones, x);
-  x = _mm256_div_ps(_mm256_set1_ps(2.0f), x);
-  return _mm256_sub_ps(x, ones);
-}
+#define AVX_TANH(isa, expisa)                              \
+  template <>                                              \
+  __m256 AVXActImpl<kTanh, isa>::Compute(__m256 x) const { \
+    __m256 ones = _mm256_set1_ps(1.0f);                    \
+    x = _mm256_mul_ps(_mm256_set1_ps(-2.0f), x);           \
+    x = _mm256_min_ps(x, _mm256_set1_ps(EXP_MAX_INPUT));   \
+    x = expisa(x);                                         \
+    x = _mm256_add_ps(ones, x);                            \
+    x = _mm256_div_ps(_mm256_set1_ps(2.0f), x);            \
+    return _mm256_sub_ps(x, ones);                         \
+  }
 
-template <>
-__m256 AVXActImpl<kRelu>::Compute(__m256 x) const {
-  return _mm256_max_ps(x, _mm256_setzero_ps());
-}
+#define AVX_RELU(isa)                                      \
+  template <>                                              \
+  __m256 AVXActImpl<kRelu, isa>::Compute(__m256 x) const { \
+    return _mm256_max_ps(x, _mm256_setzero_ps());          \
+  }
+
+#define AVX_IDENTITY(isa)                                      \
+  template <>                                                  \
+  __m256 AVXActImpl<kIdentity, isa>::Compute(__m256 x) const { \
+    return x;                                                  \
+  }
+
+#define FOR_EACH_AVX_ISA(macro_) \
+  macro_(jit::avx);              \
+  macro_(jit::avx2);             \
+  macro_(jit::avx512f)
+
+FOR_EACH_AVX_ISA(AVX_RELU);
+FOR_EACH_AVX_ISA(AVX_IDENTITY);
+
+AVX_SIGMOID(jit::avx, detail::ExpAVX);
+AVX_TANH(jit::avx, detail::ExpAVX);
+
+#ifdef __AVX2__
+AVX_SIGMOID(jit::avx2, detail::ExpAVX2);
+AVX_SIGMOID(jit::avx512f, detail::ExpAVX2);
+AVX_TANH(jit::avx2, detail::ExpAVX2);
+AVX_TANH(jit::avx512f, detail::ExpAVX2);
+#endif
+
+#undef FOR_EACH_AVX_ISA
+#undef AVX_IDENTITY
+#undef AVX_RELU
+#undef AVX_TANH
+#undef AVX_SIGMOID
 
-template <>
-__m256 AVXActImpl<kIdentity>::Compute(__m256 x) const {
-  return x;
-}
 #endif
 
 template <typename T>
@@ -119,23 +153,6 @@ class LSTMKernelImpl : public LSTMKernel<T> {
     act_cell_d_ = GetActKernel<T>(act_cell, d);
     vmul_d_ = KernelPool::Instance().template Get<VMulKernel<T>>(d);
     vadd_d_ = KernelPool::Instance().template Get<VAddKernel<T>>(d);
-#ifdef __AVX__
-    auto GetAVXAct = [&](const std::string& type) -> std::unique_ptr<AVXAct> {
-      if (type == "sigmoid") {
-        return std::unique_ptr<AVXAct>(new AVXActImpl<kSigmoid>());
-      } else if (type == "relu") {
-        return std::unique_ptr<AVXAct>(new AVXActImpl<kRelu>());
-      } else if (type == "tanh") {
-        return std::unique_ptr<AVXAct>(new AVXActImpl<kTanh>());
-      } else if (type == "identity" || type == "") {
-        return std::unique_ptr<AVXAct>(new AVXActImpl<kIdentity>());
-      }
-      PADDLE_THROW("Not support type: %s", type);
-    };
-    avx_act_gate_ = GetAVXAct(act_gate);
-    avx_act_cand_ = GetAVXAct(act_cand);
-    avx_act_cell_ = GetAVXAct(act_cell);
-#endif
   }
 
   void ComputeCtHt(T* gates, const T* ct_1, T* ct, T* ht, const T* wp_data,
@@ -175,26 +192,61 @@ class LSTMKernelImpl : public LSTMKernel<T> {
 #endif
 };
 
-#define INTRI8_FLOAT(isa)                                                    \
-  template <>                                                                \
-  void LSTMKernelImpl<float, isa, kEQ8>::ComputeCtHt(                        \
-      float* gates, const float* ct_1, float* ct, float* ht,                 \
-      const float* wp_data, float* checked) const {                          \
-    /* gates: W_ch, W_ih, W_fh, W_oh */                                      \
-    __m256 c, i, f, o;                                                       \
-    c = _mm256_loadu_ps(gates);                                              \
-    i = _mm256_loadu_ps(gates + 8);                                          \
-    f = _mm256_loadu_ps(gates + 16);                                         \
-    o = _mm256_loadu_ps(gates + 24);                                         \
-    /* C_t = C_t-1 * fgated + cand_gated * igated*/                          \
-    c = _mm256_mul_ps(avx_act_cand_->Compute(c), avx_act_gate_->Compute(i)); \
-    i = _mm256_loadu_ps(ct_1);                                               \
-    f = _mm256_mul_ps(i, avx_act_gate_->Compute(f));                         \
-    f = _mm256_add_ps(c, f);                                                 \
-    _mm256_storeu_ps(ct, f);                                                 \
-    /* H_t = act_cell(C_t) * ogated */                                       \
-    o = _mm256_mul_ps(avx_act_cell_->Compute(f), avx_act_gate_->Compute(o)); \
-    _mm256_storeu_ps(ht, o);                                                 \
+#define INTRI8_FLOAT(isa)                                                      \
+  template <>                                                                  \
+  LSTMKernelImpl<float, isa, kEQ8>::LSTMKernelImpl(                            \
+      const std::string& act_gate, const std::string& act_cand,                \
+      const std::string& act_cell, int d)                                      \
+      : LSTMKernel<float>() {                                                  \
+    auto GetAVXAct = [&](const std::string& type) -> std::unique_ptr<AVXAct> { \
+      if (type == "sigmoid") {                                                 \
+        return std::unique_ptr<AVXAct>(new AVXActImpl<kSigmoid, isa>());       \
+      } else if (type == "relu") {                                             \
+        return std::unique_ptr<AVXAct>(new AVXActImpl<kRelu, isa>());          \
+      } else if (type == "tanh") {                                             \
+        return std::unique_ptr<AVXAct>(new AVXActImpl<kTanh, isa>());          \
+      } else if (type == "identity" || type == "") {                           \
+        return std::unique_ptr<AVXAct>(new AVXActImpl<kIdentity, isa>());      \
+      }                                                                        \
+      PADDLE_THROW("Not support type: %s", type);                              \
+    };                                                                         \
+    avx_act_gate_ = GetAVXAct(act_gate);                                       \
+    avx_act_cand_ = GetAVXAct(act_cand);                                       \
+    avx_act_cell_ = GetAVXAct(act_cell);                                       \
+  }                                                                            \
+  template <>                                                                  \
+  void LSTMKernelImpl<float, isa, kEQ8>::ComputeCtHt(                          \
+      float* gates, const float* ct_1, float* ct, float* ht,                   \
+      const float* wp_data, float* checked) const {                            \
+    /* gates: W_ch, W_ih, W_fh, W_oh */                                        \
+    __m256 c, i, f, o;                                                         \
+    c = _mm256_loadu_ps(gates);                                                \
+    i = _mm256_loadu_ps(gates + 8);                                            \
+    f = _mm256_loadu_ps(gates + 16);                                           \
+    o = _mm256_loadu_ps(gates + 24);                                           \
+    /* C_t = C_t-1 * fgated + cand_gated * igated*/                            \
+    c = _mm256_mul_ps(avx_act_cand_->Compute(c), avx_act_gate_->Compute(i));   \
+    i = _mm256_loadu_ps(ct_1);                                                 \
+    f = _mm256_mul_ps(i, avx_act_gate_->Compute(f));                           \
+    f = _mm256_add_ps(c, f);                                                   \
+    _mm256_storeu_ps(ct, f);                                                   \
+    /* H_t = act_cell(C_t) * ogated */                                         \
+    o = _mm256_mul_ps(avx_act_cell_->Compute(f), avx_act_gate_->Compute(o));   \
+    _mm256_storeu_ps(ht, o);                                                   \
+  }                                                                            \
+  template <>                                                                  \
+  void LSTMKernelImpl<float, isa, kEQ8>::ComputeC1H1(                          \
+      float* gates, float* ct, float* ht, const float* wp_data) const {        \
+    __m256 c, i, o;                                                            \
+    c = _mm256_loadu_ps(gates);                                                \
+    i = _mm256_loadu_ps(gates + 8);                                            \
+    o = _mm256_loadu_ps(gates + 24);                                           \
+    /* C_t = igated * cgated*/                                                 \
+    c = _mm256_mul_ps(avx_act_gate_->Compute(i), avx_act_cand_->Compute(c));   \
+    _mm256_storeu_ps(ct, c);                                                   \
+    /* H_t = act_cell(C_t) * ogated */                                         \
+    o = _mm256_mul_ps(avx_act_cell_->Compute(c), avx_act_gate_->Compute(o));   \
+    _mm256_storeu_ps(ht, o);                                                   \
   }
 
 // TODO(TJ): optimize keq16