// 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 op_dot
//! @{



//! for two arrays, generic version for non-complex values
template<typename eT>
arma_inline
typename arma_not_cx<eT>::result
op_dot::direct_dot_arma(const uword n_elem, const eT* const A, const eT* const B)
  {
  arma_debug_sigprint();
  
  #if defined(__FAST_MATH__)
    {
    eT val = eT(0);
    
    for(uword i=0; i<n_elem; ++i)
      {
      val += A[i] * B[i];
      }
    
    return val;
    }
  #else
    {
    eT val1 = eT(0);
    eT val2 = eT(0);
    
    uword i, j;
    
    for(i=0, j=1; j<n_elem; i+=2, j+=2)
      {
      val1 += A[i] * B[i];
      val2 += A[j] * B[j];
      }
    
    if(i < n_elem)
      {
      val1 += A[i] * B[i];
      }
    
    return val1 + val2;
    }
  #endif
  }



//! for two arrays, generic version for complex values
template<typename eT>
inline
typename arma_cx_only<eT>::result
op_dot::direct_dot_arma(const uword n_elem, const eT* const A, const eT* const B)
  {
  arma_debug_sigprint();
  
  typedef typename get_pod_type<eT>::result T;
  
  T val_real = T(0);
  T val_imag = T(0);
  
  for(uword i=0; i<n_elem; ++i)
    {
    const std::complex<T>& X = A[i];
    const std::complex<T>& Y = B[i];
    
    const T a = X.real();
    const T b = X.imag();
    
    const T c = Y.real();
    const T d = Y.imag();
    
    val_real += (a*c) - (b*d);
    val_imag += (a*d) + (b*c);
    }
  
  return std::complex<T>(val_real, val_imag);
  }



//! for two arrays, float and double version
template<typename eT>
inline
typename arma_real_only<eT>::result
op_dot::direct_dot(const uword n_elem, const eT* const A, const eT* const B)
  {
  arma_debug_sigprint();
  
  if( n_elem <= 32u )
    {
    return op_dot::direct_dot_arma(n_elem, A, B);
    }
  else
    {
    #if defined(ARMA_USE_ATLAS)
      {
      arma_debug_print("atlas::cblas_dot()");
      
      return atlas::cblas_dot(n_elem, A, B);
      }
    #elif defined(ARMA_USE_BLAS)
      {
      arma_debug_print("blas::dot()");
      
      return blas::dot(n_elem, A, B);
      }
    #else
      {
      return op_dot::direct_dot_arma(n_elem, A, B);
      }
    #endif
    }
  }



//! for two arrays, complex version
template<typename eT>
inline
typename arma_cx_only<eT>::result
op_dot::direct_dot(const uword n_elem, const eT* const A, const eT* const B)
  {
  if( n_elem <= 16u )
    {
    return op_dot::direct_dot_arma(n_elem, A, B);
    }
  else
    {
    #if defined(ARMA_USE_ATLAS)
      {
      arma_debug_print("atlas::cblas_cx_dot()");
      
      return atlas::cblas_cx_dot(n_elem, A, B);
      }
    #elif defined(ARMA_USE_BLAS)
      {
      arma_debug_print("blas::dot()");
      
      return blas::dot(n_elem, A, B);
      }
    #else
      {
      return op_dot::direct_dot_arma(n_elem, A, B);
      }
    #endif
    }
  }



//! for two arrays, integral version
template<typename eT>
inline
typename arma_integral_only<eT>::result
op_dot::direct_dot(const uword n_elem, const eT* const A, const eT* const B)
  {
  return op_dot::direct_dot_arma(n_elem, A, B);
  }




//! for three arrays
template<typename eT>
inline
eT
op_dot::direct_dot(const uword n_elem, const eT* const A, const eT* const B, const eT* C)
  {
  arma_debug_sigprint();
  
  eT val = eT(0);
  
  for(uword i=0; i<n_elem; ++i)
    {
    val += A[i] * B[i] * C[i];
    }

  return val;
  }



template<typename T1, typename T2>
inline
typename T1::elem_type
op_dot::apply(const T1& X, const T2& Y)
  {
  arma_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  if(is_subview_row<T1>::value && is_subview_row<T2>::value)
    {
    const subview_row<eT>& A = reinterpret_cast< const subview_row<eT>& >(X);
    const subview_row<eT>& B = reinterpret_cast< const subview_row<eT>& >(Y);
    
    if( (A.m.n_rows == 1) && (B.m.n_rows == 1) )
      {
      arma_debug_print("op_dot::apply(): subview_row optimisation");
      
      arma_conform_check( (A.n_elem != B.n_elem), "dot(): objects must have the same number of elements" );
      
      const eT* A_mem = A.m.memptr();
      const eT* B_mem = B.m.memptr();
      
      return op_dot::direct_dot(A.n_elem, &A_mem[A.aux_col1], &B_mem[B.aux_col1]);
      }
    }
  
  if(is_subview<T1>::value || is_subview<T2>::value)
    {
    arma_debug_print("op_dot::apply(): subview optimisation");
    
    const sv_keep_unwrap<T1>& UA(X);
    const sv_keep_unwrap<T2>& UB(Y);
    
    typedef typename sv_keep_unwrap<T1>::stored_type UA_M_type;
    typedef typename sv_keep_unwrap<T2>::stored_type UB_M_type;
    
    const UA_M_type& A = UA.M;
    const UB_M_type& B = UB.M;
    
    const uword A_n_rows = A.n_rows;
    const uword A_n_cols = A.n_cols;
    
    if( (A_n_rows == B.n_rows) && (A_n_cols == B.n_cols) )
      {
      eT acc = eT(0);
      
      for(uword c=0; c < A_n_cols; ++c)  { acc += op_dot::direct_dot(A_n_rows, A.colptr(c), B.colptr(c)); }
      
      return acc;
      }
    else
      {
      const quasi_unwrap<UA_M_type> UUA(A);
      const quasi_unwrap<UB_M_type> UUB(B);
      
      arma_conform_check( (UUA.M.n_elem != UUB.M.n_elem), "dot(): objects must have the same number of elements" );
      
      return op_dot::direct_dot(UUA.M.n_elem, UUA.M.memptr(), UUB.M.memptr());
      }
    }
  
  // if possible, bypass transposes of non-complex vectors
  
  if( (is_cx<eT>::no) && (resolves_to_vector<T1>::value) && (resolves_to_vector<T2>::value) && (partial_unwrap<T1>::is_fast) && (partial_unwrap<T2>::is_fast) )
    {
    arma_debug_print("op_dot::apply(): vector optimisation");
    
    const partial_unwrap<T1> UA(X);
    const partial_unwrap<T2> UB(Y);
    
    const typename partial_unwrap<T1>::stored_type& A = UA.M;
    const typename partial_unwrap<T2>::stored_type& B = UB.M;
    
    arma_conform_check( (A.n_elem != B.n_elem), "dot(): objects must have the same number of elements" );
    
    const eT val = op_dot::direct_dot(A.n_elem, A.memptr(), B.memptr());
    
    return (UA.do_times || UB.do_times) ? (val * UA.get_val() * UB.get_val()) : val;
    }
  
  constexpr bool proxy_is_mat = (is_Mat<typename Proxy<T1>::stored_type>::value && is_Mat<typename Proxy<T2>::stored_type>::value);
  
  constexpr bool use_at = (Proxy<T1>::use_at) || (Proxy<T2>::use_at);
  
  constexpr bool have_direct_mem = (quasi_unwrap<T1>::has_orig_mem) && (quasi_unwrap<T2>::has_orig_mem);
  
  if(proxy_is_mat || use_at || have_direct_mem)
    {
    arma_debug_print("op_dot::apply(): direct_mem optimisation");
    
    const quasi_unwrap<T1> A(X);
    const quasi_unwrap<T2> B(Y);
    
    arma_conform_check( (A.M.n_elem != B.M.n_elem), "dot(): objects must have the same number of elements" );
    
    return op_dot::direct_dot(A.M.n_elem, A.M.memptr(), B.M.memptr());
    }
  
  const Proxy<T1> PA(X);
  const Proxy<T2> PB(Y);
  
  arma_conform_check( (PA.get_n_elem() != PB.get_n_elem()), "dot(): objects must have the same number of elements" );
  
  return op_dot::apply_proxy_linear(PA,PB);
  }



template<typename T1, typename T2>
inline
typename arma_not_cx<typename T1::elem_type>::result
op_dot::apply_proxy_linear(const Proxy<T1>& PA, const Proxy<T2>& PB)
  {
  arma_debug_sigprint();
  
  typedef typename T1::elem_type      eT;
  typedef typename Proxy<T1>::ea_type ea_type1;
  typedef typename Proxy<T2>::ea_type ea_type2;
  
  const uword N = PA.get_n_elem();
  
  ea_type1 A = PA.get_ea();
  ea_type2 B = PB.get_ea();
  
  eT val1 = eT(0);
  eT val2 = eT(0);
  
  uword i,j;
  
  for(i=0, j=1; j<N; i+=2, j+=2)
    {
    val1 += A[i] * B[i];
    val2 += A[j] * B[j];
    }
  
  if(i < N)
    {
    val1 += A[i] * B[i];
    }
  
  return val1 + val2;
  }



template<typename T1, typename T2>
inline
typename arma_cx_only<typename T1::elem_type>::result
op_dot::apply_proxy_linear(const Proxy<T1>& PA, const Proxy<T2>& PB)
  {
  arma_debug_sigprint();
  
  typedef typename T1::elem_type            eT;
  typedef typename get_pod_type<eT>::result  T;
  
  typedef typename Proxy<T1>::ea_type ea_type1;
  typedef typename Proxy<T2>::ea_type ea_type2;
  
  const uword N = PA.get_n_elem();
  
  ea_type1 A = PA.get_ea();
  ea_type2 B = PB.get_ea();
  
  T val_real = T(0);
  T val_imag = T(0);
  
  for(uword i=0; i<N; ++i)
    {
    const std::complex<T> xx = A[i];
    const std::complex<T> yy = B[i];
    
    const T a = xx.real();
    const T b = xx.imag();
    
    const T c = yy.real();
    const T d = yy.imag();
    
    val_real += (a*c) - (b*d);
    val_imag += (a*d) + (b*c);
    }
  
  return std::complex<T>(val_real, val_imag);
  }



//
// op_norm_dot



template<typename T1, typename T2>
inline
typename T1::elem_type
op_norm_dot::apply(const T1& X, const T2& Y)
  {
  arma_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  typedef typename T1::pod_type   T;
  
  const quasi_unwrap<T1> tmp1(X);
  const quasi_unwrap<T2> tmp2(Y);
  
  const Col<eT> A( const_cast<eT*>(tmp1.M.memptr()), tmp1.M.n_elem, false );
  const Col<eT> B( const_cast<eT*>(tmp2.M.memptr()), tmp2.M.n_elem, false );
  
  arma_conform_check( (A.n_elem != B.n_elem), "norm_dot(): objects must have the same number of elements" );
  
  const T denom = norm(A,2) * norm(B,2);
  
  return (denom != T(0)) ? ( op_dot::apply(A,B) / denom ) : eT(0);
  }



//
// op_cdot



template<typename eT>
inline
eT
op_cdot::direct_cdot_arma(const uword n_elem, const eT* const A, const eT* const B)
  {
  arma_debug_sigprint();
  
  typedef typename get_pod_type<eT>::result T;
  
  T val_real = T(0);
  T val_imag = T(0);
  
  for(uword i=0; i<n_elem; ++i)
    {
    const std::complex<T>& X = A[i];
    const std::complex<T>& Y = B[i];
    
    const T a = X.real();
    const T b = X.imag();
    
    const T c = Y.real();
    const T d = Y.imag();
    
    val_real += (a*c) + (b*d);
    val_imag += (a*d) - (b*c);
    }
  
  return std::complex<T>(val_real, val_imag);
  }



template<typename eT>
inline
eT
op_cdot::direct_cdot(const uword n_elem, const eT* const A, const eT* const B)
  {
  arma_debug_sigprint();
  
  if( n_elem <= 32u )
    {
    return op_cdot::direct_cdot_arma(n_elem, A, B);
    }
  else
    {
    #if defined(ARMA_USE_BLAS)
      {
      arma_debug_print("blas::gemv()");
      
      // using gemv() workaround due to compatibility issues with cdotc() and zdotc()
      
      const char trans   = 'C';
      
      const blas_int m   = blas_int(n_elem);
      const blas_int n   = 1;
      //const blas_int lda = (n_elem > 0) ? blas_int(n_elem) : blas_int(1);
      const blas_int inc = 1;
      
      const eT alpha     = eT(1);
      const eT beta      = eT(0);
      
      eT result[2];  // paranoia: using two elements instead of one
      
      //blas::gemv(&trans, &m, &n, &alpha, A, &lda, B, &inc, &beta, &result[0], &inc);
      blas::gemv(&trans, &m, &n, &alpha, A, &m, B, &inc, &beta, &result[0], &inc);
      
      return result[0];
      }
    #else
      {
      return op_cdot::direct_cdot_arma(n_elem, A, B);
      }
    #endif
    }
  }



template<typename T1, typename T2>
inline
typename T1::elem_type
op_cdot::apply(const T1& X, const T2& Y)
  {
  arma_debug_sigprint();
  
  if(is_Mat<T1>::value && is_Mat<T2>::value)
    {
    return op_cdot::apply_unwrap(X,Y);
    }
  else
    {
    return op_cdot::apply_proxy(X,Y);
    }
  }



template<typename T1, typename T2>
inline
typename T1::elem_type
op_cdot::apply_unwrap(const T1& X, const T2& Y)
  {
  arma_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const unwrap<T1> tmp1(X);
  const unwrap<T2> tmp2(Y);
  
  const Mat<eT>& A = tmp1.M;
  const Mat<eT>& B = tmp2.M;
  
  arma_conform_check( (A.n_elem != B.n_elem), "cdot(): objects must have the same number of elements" );
  
  return op_cdot::direct_cdot( A.n_elem, A.mem, B.mem );
  }



template<typename T1, typename T2>
inline
typename T1::elem_type
op_cdot::apply_proxy(const T1& X, const T2& Y)
  {
  arma_debug_sigprint();
  
  typedef typename T1::elem_type            eT;
  typedef typename get_pod_type<eT>::result  T;
  
  typedef typename Proxy<T1>::ea_type ea_type1;
  typedef typename Proxy<T2>::ea_type ea_type2;
  
  constexpr bool use_at = (Proxy<T1>::use_at) || (Proxy<T2>::use_at);
  
  if(use_at == false)
    {
    const Proxy<T1> PA(X);
    const Proxy<T2> PB(Y);
    
    const uword N = PA.get_n_elem();
    
    arma_conform_check( (N != PB.get_n_elem()), "cdot(): objects must have the same number of elements" );
    
    ea_type1 A = PA.get_ea();
    ea_type2 B = PB.get_ea();
    
    T val_real = T(0);
    T val_imag = T(0);
    
    for(uword i=0; i<N; ++i)
      {
      const std::complex<T> AA = A[i];
      const std::complex<T> BB = B[i];
      
      const T a = AA.real();
      const T b = AA.imag();
      
      const T c = BB.real();
      const T d = BB.imag();
      
      val_real += (a*c) + (b*d);
      val_imag += (a*d) - (b*c);
      }
    
    return std::complex<T>(val_real, val_imag);
    }
  else
    {
    return op_cdot::apply_unwrap( X, Y );
    }
  }



template<typename T1, typename T2>
inline
typename promote_type<typename T1::elem_type, typename T2::elem_type>::result
op_dot_mixed::apply(const T1& A, const T2& B)
  {
  arma_debug_sigprint();
  
  typedef typename T1::elem_type in_eT1;
  typedef typename T2::elem_type in_eT2;
  
  typedef typename promote_type<in_eT1, in_eT2>::result out_eT;
  
  const Proxy<T1> PA(A);
  const Proxy<T2> PB(B);
  
  const uword N = PA.get_n_elem();
  
  arma_conform_check( (N != PB.get_n_elem()), "dot(): objects must have the same number of elements" );
  
  out_eT acc = out_eT(0);
  
  for(uword i=0; i < N; ++i)
    {
    acc += upgrade_val<in_eT1,in_eT2>::apply(PA[i]) * upgrade_val<in_eT1,in_eT2>::apply(PB[i]);
    }
  
  return acc;
  }



//! @}