diff --git a/Eigen/src/Core/arch/AltiVec/MatrixProduct.h b/Eigen/src/Core/arch/AltiVec/MatrixProduct.h
index 8feb88ea7..01b50b7c4 100644
--- a/Eigen/src/Core/arch/AltiVec/MatrixProduct.h
+++ b/Eigen/src/Core/arch/AltiVec/MatrixProduct.h
@@ -15,6 +15,21 @@
 #define EIGEN_ALTIVEC_USE_CUSTOM_PACK    1
 #endif
 
+#ifdef _AIX
+#define POWER_10       0x40000
+#define POWER_10_ANDUP (POWER_10)
+#include <sys/systemcfg.h>
+#define __power_10_andup() (_system_configuration.implementation & POWER_10_ANDUP)
+
+static bool check_mma_support()
+{
+  if(__power_10_andup() && __power_mma_version() == MMA_V31)
+    return true;
+  else
+    return false;
+}
+#endif
+
 #include "MatrixProductCommon.h"
 
 // Since LLVM doesn't support dynamic dispatching, force either always MMA or VSX
@@ -2481,12 +2496,21 @@ void gebp_kernel<float, float, Index, DataMapper, mr, nr, ConjugateLhs, Conjugat
       //generate with MMA only
       gemm_function = &Eigen::internal::gemmMMA<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
     #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-        gemm_function = &Eigen::internal::gemmMMA<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
-      }
-      else{
-        gemm_function = &Eigen::internal::gemm<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
-      }
+      #if defined(_AIX)
+        if(check_mma_support()){
+          gemm_function = &Eigen::internal::gemmMMA<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemmMMA<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+      #endif
     #else
       gemm_function = &Eigen::internal::gemm<float, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
     #endif
@@ -2520,12 +2544,21 @@ void gebp_kernel<std::complex<float>, std::complex<float>, Index, DataMapper, mr
        //generate with MMA only
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-       if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-         gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
-       }
-       else{
-         gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
-       }
+      #if defined(_AIX)
+        if (check_mma_support()){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+      #endif
      #else
        gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      #endif
@@ -2558,12 +2591,21 @@ void gebp_kernel<float, std::complex<float>, Index, DataMapper, mr, nr, Conjugat
        //generate with MMA only
        gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-       if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-         gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
-       }
-       else{
-         gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
-       }
+      #if defined(_AIX)
+        if (check_mma_support()){
+          gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+      #endif
      #else
        gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      #endif
@@ -2596,12 +2638,21 @@ void gebp_kernel<std::complex<float>, float, Index, DataMapper, mr, nr, Conjugat
        //generate with MMA only
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-       if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-         gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
-       }
-       else{
-         gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
-       }
+      #if defined(_AIX)
+        if (check_mma_support()){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }  
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }
+      #endif
      #else
        gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      #endif
@@ -2633,12 +2684,21 @@ void gebp_kernel<double, double, Index, DataMapper, mr, nr, ConjugateLhs, Conjug
       //generate with MMA only
       gemm_function = &Eigen::internal::gemmMMA<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
     #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-      if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-        gemm_function = &Eigen::internal::gemmMMA<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
-      }
-      else{
-        gemm_function = &Eigen::internal::gemm<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
-      }
+      #if defined(_AIX)
+        if (check_mma_support()){
+          gemm_function = &Eigen::internal::gemmMMA<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemmMMA<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
+        }
+      #endif
     #else
       gemm_function = &Eigen::internal::gemm<double, Index, Packet, RhsPacket, DataMapper, accRows, accCols>;
     #endif
@@ -2671,12 +2731,21 @@ void gebp_kernel<std::complex<double>, std::complex<double>, Index, DataMapper,
        //generate with MMA only
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-       if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-         gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
-       }
-       else{
-         gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
-       }
+      #if defined(_AIX)
+        if (check_mma_support()){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+        }
+      #endif
      #else
        gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
      #endif
@@ -2709,12 +2778,21 @@ void gebp_kernel<std::complex<double>, double, Index, DataMapper, mr, nr, Conjug
        //generate with MMA only
        gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-       if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-         gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
-       }
-       else{
-         gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
-       }
+      #if defined(_AIX)
+        if (check_mma_support()){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+        }
+      #endif
      #else
        gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
      #endif
@@ -2747,12 +2825,21 @@ void gebp_kernel<double, std::complex<double>, Index, DataMapper, mr, nr, Conjug
        //generate with MMA only
        gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      #elif defined(ALTIVEC_MMA_SUPPORT) && !defined(EIGEN_ALTIVEC_DISABLE_MMA)
-       if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
-         gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
-       }
-       else{
-         gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
-       }
+      #if defined(_AIX)
+        if (check_mma_support()){
+          gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+      #else
+        if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+          gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+        else{
+          gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+        }
+      #endif
      #else
        gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Index, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
      #endif