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diff --git a/src/armadillo/include/armadillo_bits/mul_gemm.hpp b/src/armadillo/include/armadillo_bits/mul_gemm.hpp
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+// SPDX-License-Identifier: Apache-2.0
+// 
+// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
+// Copyright 2008-2016 National ICT Australia (NICTA)
+// 
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+// http://www.apache.org/licenses/LICENSE-2.0
+// 
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+// ------------------------------------------------------------------------
+
+
+//! \addtogroup gemm
+//! @{
+
+
+
+//! for tiny square matrices, size <= 4x4
+template<const bool do_trans_A=false, const bool use_alpha=false, const bool use_beta=false>
+class gemm_emul_tinysq
+  {
+  public:
+  
+  
+  template<typename eT, typename TA, typename TB>
+  arma_cold
+  inline
+  static
+  void
+  apply
+    (
+          Mat<eT>& C,
+    const TA&      A,
+    const TB&      B,
+    const eT       alpha = eT(1),
+    const eT       beta  = eT(0)
+    )
+    {
+    arma_extra_debug_sigprint();
+    
+    switch(A.n_rows)
+      {
+      case  4:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(3), A, B.colptr(3), alpha, beta );
+      // fallthrough
+      case  3:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(2), A, B.colptr(2), alpha, beta );
+      // fallthrough
+      case  2:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(1), A, B.colptr(1), alpha, beta );
+      // fallthrough
+      case  1:  gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply( C.colptr(0), A, B.colptr(0), alpha, beta );
+      // fallthrough
+      default:  ;
+      }
+    }
+  
+  };
+
+
+
+//! emulation of gemm(), for non-complex matrices only, as it assumes only simple transposes (ie. doesn't do hermitian transposes)
+template<const bool do_trans_A=false, const bool do_trans_B=false, const bool use_alpha=false, const bool use_beta=false>
+class gemm_emul_large
+  {
+  public:
+  
+  template<typename eT, typename TA, typename TB>
+  arma_hot
+  inline
+  static
+  void
+  apply
+    (
+          Mat<eT>& C,
+    const TA&      A,
+    const TB&      B,
+    const eT       alpha = eT(1),
+    const eT       beta  = eT(0)
+    )
+    {
+    arma_extra_debug_sigprint();
+
+    const uword A_n_rows = A.n_rows;
+    const uword A_n_cols = A.n_cols;
+    
+    const uword B_n_rows = B.n_rows;
+    const uword B_n_cols = B.n_cols;
+    
+    if( (do_trans_A == false) && (do_trans_B == false) )
+      {
+      arma_aligned podarray<eT> tmp(A_n_cols);
+      
+      eT* A_rowdata = tmp.memptr();
+      
+      for(uword row_A=0; row_A < A_n_rows; ++row_A)
+        {
+        tmp.copy_row(A, row_A);
+        
+        for(uword col_B=0; col_B < B_n_cols; ++col_B)
+          {
+          const eT acc = op_dot::direct_dot_arma(B_n_rows, A_rowdata, B.colptr(col_B));
+          
+               if( (use_alpha == false) && (use_beta == false) )  { C.at(row_A,col_B) =       acc;                          }
+          else if( (use_alpha == true ) && (use_beta == false) )  { C.at(row_A,col_B) = alpha*acc;                          }
+          else if( (use_alpha == false) && (use_beta == true ) )  { C.at(row_A,col_B) =       acc + beta*C.at(row_A,col_B); }
+          else if( (use_alpha == true ) && (use_beta == true ) )  { C.at(row_A,col_B) = alpha*acc + beta*C.at(row_A,col_B); }
+          }
+        }
+      }
+    else
+    if( (do_trans_A == true) && (do_trans_B == false) )
+      {
+      for(uword col_A=0; col_A < A_n_cols; ++col_A)
+        {
+        // col_A is interpreted as row_A when storing the results in matrix C
+        
+        const eT* A_coldata = A.colptr(col_A);
+        
+        for(uword col_B=0; col_B < B_n_cols; ++col_B)
+          {
+          const eT acc = op_dot::direct_dot_arma(B_n_rows, A_coldata, B.colptr(col_B));
+          
+               if( (use_alpha == false) && (use_beta == false) )  { C.at(col_A,col_B) =       acc;                          }
+          else if( (use_alpha == true ) && (use_beta == false) )  { C.at(col_A,col_B) = alpha*acc;                          }
+          else if( (use_alpha == false) && (use_beta == true ) )  { C.at(col_A,col_B) =       acc + beta*C.at(col_A,col_B); }
+          else if( (use_alpha == true ) && (use_beta == true ) )  { C.at(col_A,col_B) = alpha*acc + beta*C.at(col_A,col_B); }
+          }
+        }
+      }
+    else
+    if( (do_trans_A == false) && (do_trans_B == true) )
+      {
+      Mat<eT> BB;
+      op_strans::apply_mat_noalias(BB, B);
+      
+      gemm_emul_large<false, false, use_alpha, use_beta>::apply(C, A, BB, alpha, beta);
+      }
+    else
+    if( (do_trans_A == true) && (do_trans_B == true) )
+      {
+      // mat B_tmp = trans(B);
+      // dgemm_arma<true, false,  use_alpha, use_beta>::apply(C, A, B_tmp, alpha, beta);
+      
+      
+      // By using the trans(A)*trans(B) = trans(B*A) equivalency,
+      // transpose operations are not needed
+      
+      arma_aligned podarray<eT> tmp(B.n_cols);
+      eT* B_rowdata = tmp.memptr();
+      
+      for(uword row_B=0; row_B < B_n_rows; ++row_B)
+        {
+        tmp.copy_row(B, row_B);
+        
+        for(uword col_A=0; col_A < A_n_cols; ++col_A)
+          {
+          const eT acc = op_dot::direct_dot_arma(A_n_rows, B_rowdata, A.colptr(col_A));
+          
+               if( (use_alpha == false) && (use_beta == false) )  { C.at(col_A,row_B) =       acc;                          }
+          else if( (use_alpha == true ) && (use_beta == false) )  { C.at(col_A,row_B) = alpha*acc;                          }
+          else if( (use_alpha == false) && (use_beta == true ) )  { C.at(col_A,row_B) =       acc + beta*C.at(col_A,row_B); }
+          else if( (use_alpha == true ) && (use_beta == true ) )  { C.at(col_A,row_B) = alpha*acc + beta*C.at(col_A,row_B); }
+          }
+        }
+      }
+    }
+  
+  };
+  
+
+
+template<const bool do_trans_A=false, const bool do_trans_B=false, const bool use_alpha=false, const bool use_beta=false>
+class gemm_emul
+  {
+  public:
+  
+  
+  template<typename eT, typename TA, typename TB>
+  arma_hot
+  inline
+  static
+  void
+  apply
+    (
+          Mat<eT>& C,
+    const TA&      A,
+    const TB&      B,
+    const eT       alpha = eT(1),
+    const eT       beta  = eT(0),
+    const typename arma_not_cx<eT>::result* junk = nullptr
+    )
+    {
+    arma_extra_debug_sigprint();
+    arma_ignore(junk);
+    
+    gemm_emul_large<do_trans_A, do_trans_B, use_alpha, use_beta>::apply(C, A, B, alpha, beta);
+    }
+  
+  
+  
+  template<typename eT>
+  arma_hot
+  inline
+  static
+  void
+  apply
+    (
+          Mat<eT>& C,
+    const Mat<eT>& A,
+    const Mat<eT>& B,
+    const eT       alpha = eT(1),
+    const eT       beta  = eT(0),
+    const typename arma_cx_only<eT>::result* junk = nullptr
+    )
+    {
+    arma_extra_debug_sigprint();
+    arma_ignore(junk);
+    
+    // "better than nothing" handling of hermitian transposes for complex number matrices
+    
+    Mat<eT> tmp_A;
+    Mat<eT> tmp_B;
+    
+    if(do_trans_A)  { op_htrans::apply_mat_noalias(tmp_A, A); }
+    if(do_trans_B)  { op_htrans::apply_mat_noalias(tmp_B, B); }
+    
+    const Mat<eT>& AA = (do_trans_A == false) ? A : tmp_A;
+    const Mat<eT>& BB = (do_trans_B == false) ? B : tmp_B;
+    
+    gemm_emul_large<false, false, use_alpha, use_beta>::apply(C, AA, BB, alpha, beta);
+    }
+
+  };
+
+
+
+//! \brief
+//! Wrapper for BLAS dgemm function, using template arguments to control the arguments passed to dgemm.
+//! Matrix 'C' is assumed to have been set to the correct size (ie. taking into account transposes)
+
+template<const bool do_trans_A=false, const bool do_trans_B=false, const bool use_alpha=false, const bool use_beta=false>
+class gemm
+  {
+  public:
+  
+  template<typename eT, typename TA, typename TB>
+  inline
+  static
+  void
+  apply_blas_type( Mat<eT>& C, const TA& A, const TB& B, const eT alpha = eT(1), const eT beta = eT(0) )
+    {
+    arma_extra_debug_sigprint();
+    
+    if( (A.n_rows <= 4) && (A.n_rows == A.n_cols) && (A.n_rows == B.n_rows) && (B.n_rows == B.n_cols) && (is_cx<eT>::no) ) 
+      {
+      if(do_trans_B == false)
+        {
+        gemm_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply(C, A, B, alpha, beta);
+        }
+      else
+        {
+        Mat<eT> BB(B.n_rows, B.n_rows, arma_nozeros_indicator());
+        
+        op_strans::apply_mat_noalias_tinysq(BB, B);
+        
+        gemm_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply(C, A, BB, alpha, beta);
+        }
+      }
+    else
+      {
+      #if defined(ARMA_USE_ATLAS)
+        {
+        arma_extra_debug_print("atlas::cblas_gemm()");
+        
+        arma_debug_assert_atlas_size(A,B);
+        
+        atlas::cblas_gemm<eT>
+          (
+          atlas_CblasColMajor,
+          (do_trans_A) ? ( is_cx<eT>::yes ? atlas_CblasConjTrans : atlas_CblasTrans ) : atlas_CblasNoTrans,
+          (do_trans_B) ? ( is_cx<eT>::yes ? atlas_CblasConjTrans : atlas_CblasTrans ) : atlas_CblasNoTrans,
+          C.n_rows,
+          C.n_cols,
+          (do_trans_A) ? A.n_rows : A.n_cols,
+          (use_alpha) ? alpha : eT(1),
+          A.mem,
+          (do_trans_A) ? A.n_rows : C.n_rows,
+          B.mem,
+          (do_trans_B) ? C.n_cols : ( (do_trans_A) ? A.n_rows : A.n_cols ),
+          (use_beta) ? beta : eT(0),
+          C.memptr(),
+          C.n_rows
+          );
+        }
+      #elif defined(ARMA_USE_BLAS)
+        {
+        arma_extra_debug_print("blas::gemm()");
+        
+        arma_debug_assert_blas_size(A,B);
+        
+        const char trans_A = (do_trans_A) ? ( is_cx<eT>::yes ? 'C' : 'T' ) : 'N';
+        const char trans_B = (do_trans_B) ? ( is_cx<eT>::yes ? 'C' : 'T' ) : 'N';
+        
+        const blas_int m   = blas_int(C.n_rows);
+        const blas_int n   = blas_int(C.n_cols);
+        const blas_int k   = (do_trans_A) ? blas_int(A.n_rows) : blas_int(A.n_cols);
+        
+        const eT local_alpha = (use_alpha) ? alpha : eT(1);
+        
+        const blas_int lda = (do_trans_A) ? k : m;
+        const blas_int ldb = (do_trans_B) ? n : k;
+        
+        const eT local_beta  = (use_beta) ? beta : eT(0);
+        
+        arma_extra_debug_print( arma_str::format("blas::gemm(): trans_A = %c") % trans_A );
+        arma_extra_debug_print( arma_str::format("blas::gemm(): trans_B = %c") % trans_B );
+        
+        blas::gemm<eT>
+          (
+          &trans_A,
+          &trans_B,
+          &m,
+          &n,
+          &k,
+          &local_alpha,
+          A.mem,
+          &lda,
+          B.mem,
+          &ldb,
+          &local_beta,
+          C.memptr(),
+          &m
+          );
+        }
+      #else
+        {
+        gemm_emul<do_trans_A, do_trans_B, use_alpha, use_beta>::apply(C,A,B,alpha,beta);
+        }
+      #endif
+      }
+    }
+  
+  
+  
+  //! immediate multiplication of matrices A and B, storing the result in C
+  template<typename eT, typename TA, typename TB>
+  inline
+  static
+  void
+  apply( Mat<eT>& C, const TA& A, const TB& B, const eT alpha = eT(1), const eT beta = eT(0) )
+    {
+    gemm_emul<do_trans_A, do_trans_B, use_alpha, use_beta>::apply(C,A,B,alpha,beta);
+    }
+  
+  
+  
+  template<typename TA, typename TB>
+  arma_inline
+  static
+  void
+  apply
+    (
+          Mat<float>& C,
+    const TA&         A,
+    const TB&         B,
+    const float alpha = float(1),
+    const float beta  = float(0)
+    )
+    {
+    gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
+    }
+  
+  
+  
+  template<typename TA, typename TB>
+  arma_inline
+  static
+  void
+  apply
+    (
+          Mat<double>& C,
+    const TA&          A,
+    const TB&          B,
+    const double alpha = double(1),
+    const double beta  = double(0)
+    )
+    {
+    gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
+    }
+  
+  
+  
+  template<typename TA, typename TB>
+  arma_inline
+  static
+  void
+  apply
+    (
+          Mat< std::complex<float> >& C,
+    const TA&                         A,
+    const TB&                         B,
+    const std::complex<float> alpha = std::complex<float>(1),
+    const std::complex<float> beta  = std::complex<float>(0)
+    )
+    {
+    gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
+    }
+  
+  
+  
+  template<typename TA, typename TB>
+  arma_inline
+  static
+  void
+  apply
+    (
+          Mat< std::complex<double> >& C,
+    const TA&                          A,
+    const TB&                          B,
+    const std::complex<double> alpha = std::complex<double>(1),
+    const std::complex<double> beta  = std::complex<double>(0)
+    )
+    {
+    gemm<do_trans_A, do_trans_B, use_alpha, use_beta>::apply_blas_type(C,A,B,alpha,beta);
+    }
+  
+  };
+
+
+
+//! @}