/// \file
/// \brief NeuroNet.cl
/// Library consist OpenCL kernels
/// \author <A HREF="https://www.mql5.com/en/users/dng"> DNG </A>
/// \copyright Copyright 2019, DNG
//---
//--- by default some GPU doesn't support floats
//--- cl_khr_fp64 directive is used to enable work with floats
// #pragma OPENCL EXTENSION cl_khr_fp64 : enable
#define l1 1.0e-3f
#define l2 1.0e-3f
#define MAX_WEIGHT 1.0f
#define MAX_GRAD 1.0e-2f
#define LOCAL_ARRAY_SIZE 64
#define MIN_VALUE -3.4e37f
//--- Activation Functions
#define ActFunc_None         -1
#define ActFunc_TANH          0
#define ActFunc_SIGMOID       1
#define ActFunc_LReLU         2
#define ActFunc_SoftPlus      3
#define ActFunc_GELU          4
#define ActFunc_MinusSoftPlus 5
#define ActFunc_ELU           6
//---
#define BarrierLoc      barrier(CLK_LOCAL_MEM_FENCE)
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float IsNaNOrInf(const float value, const float def_value)
  {
   if(isnan(value) || isinf(value))
      return def_value;
   return value;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float2 IsNaNOrInf2(const float2 value, const float2 def_value)
  {
   if(isnan(value.x) || isinf(value.x) ||
      isnan(value.y) || isinf(value.y))
      return def_value;
   return value;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float4 IsNaNOrInf4(const float4 value, const float def_value)
  {
   float4 result;
   result.s0 = IsNaNOrInf(value.s0, def_value);
   result.s1 = IsNaNOrInf(value.s1, def_value);
   result.s2 = IsNaNOrInf(value.s2, def_value);
   result.s3 = IsNaNOrInf(value.s3, def_value);
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float fActivation(const float value, const int function)
  {
   float result = IsNaNOrInf(value, 0);
   switch(function)
     {
      case ActFunc_TANH:
         result = tanh(clamp(result, -20.0f, 20.0f));
         break;
      case ActFunc_SIGMOID:  //Sigmoid
         result = 1 / (1 + exp(clamp(-result, -20.0f, 20.0f)));
         break;
      case ActFunc_LReLU:  //LReLU
         if(result < 0)
            result *= 0.01f;
         break;
      case ActFunc_SoftPlus:  //SoftPlus
         result = (result >= 20.0f ? result : IsNaNOrInf(log(1 + exp(result)), 0));
         break;
      case ActFunc_GELU:  //GELU
         result = result / (1 + exp(clamp(-1.702f * result, -20.0f, 20.0f)));
         break;
      case ActFunc_MinusSoftPlus:  // -SoftPlus
         result = -fActivation(result, 3);
         break;
      case ActFunc_ELU:  //ELU
         if(result < 0)
            result = IsNaNOrInf(exp(result), 0) - 1;
         break;
      default:
         break;
     }
//---
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float Deactivation(const float grad, const float inp_value, const int function)
  {
   float result = IsNaNOrInf(grad, 0);
//---
   if(isnan(inp_value) || isinf(inp_value))
      result = 0;
   else
      switch(function)
        {
         case ActFunc_TANH: //TANH
            result = clamp(grad + inp_value, -1.0f, 1.0f) - inp_value;
            result *= 1.0f - pow(inp_value, 2.0f);
            break;
         case ActFunc_SIGMOID:  //Sigmoid
            result = clamp(grad + inp_value, 0.0f, 1.0f) - inp_value;
            result *= inp_value * (1.0f - inp_value);
            break;
         case ActFunc_LReLU: //LReLU
            if(inp_value < 0)
               result *= 0.01f;
            break;
         case ActFunc_SoftPlus:  //SoftPlus
            result *= fActivation(log(exp(inp_value) - 1.0f), 1);
            break;
         case ActFunc_GELU:  //GELU
            if(inp_value < 0.9f)
               result *= fActivation(5 * inp_value, 1);
            break;
         case ActFunc_MinusSoftPlus:  // -SoftPlus
            result = Deactivation(-result, -inp_value, ActFunc_SoftPlus);
            break;
         case ActFunc_ELU: //ELU
            if(inp_value < 0)
               result *= inp_value + 1;
            break;
         default:
            break;
        }
//---
   return clamp(IsNaNOrInf(result, 0), -MAX_GRAD, MAX_GRAD);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
int RCtoFlat(const int row,
             const int col,
             const int total_rows,
             const int total_cols,
             const int variable)
  {
   return (variable * total_rows + row) * total_cols + col;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float LocalMax(const float value, const int loc, __local float* Temp)
  {
   const size_t id = get_local_id(loc);
   const size_t total = get_local_size(loc);
//---
   const uint ls = min((uint)total, (uint)LOCAL_ARRAY_SIZE);
   float val = IsNaNOrInf(value, MIN_VALUE);
//--- Look Max
   for(int d = 0; d < total; d += ls)
     {
      if(id >= d && id < (d + ls) &&
         (d == 0 || Temp[id - d] < val))
         Temp[id - d] = val;
      BarrierLoc;
     }
//---
   int count = ls;
   do
     {
      count = (count + 1) / 2;
      if(id < count && (id + count) < ls && Temp[id] < Temp[id + count])
         Temp[id] = Temp[id + count];
      BarrierLoc;
     }
   while(count > 1);
//---
   return IsNaNOrInf(Temp[0], MIN_VALUE);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float LocalSum(const float value, const int loc, __local float* Temp)
  {
   const size_t id = get_local_id(loc);
   const size_t total = get_local_size(loc);
//---
   const uint ls = min((uint)total, (uint)LOCAL_ARRAY_SIZE);
//--- Sum
   float result = IsNaNOrInf(value, 0);
   for(int d = 0; d < total; d += ls)
     {
      if(id >= d && id < (d + ls))
         Temp[id - d] = (d == 0 ? result : Temp[id - d] + result);
      BarrierLoc;
     }
//---
   int count = ls;
   do
     {
      count = (count + 1) / 2;
      if(id < count && (id + count) < ls)
         Temp[id] += Temp[id + count];
      BarrierLoc;
     }
   while(count > 1);
   result = IsNaNOrInf(Temp[0], 0);
//---
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float LocalSoftMax(const float value, const int loc, __local float* Temp)
  {
//--- Look Max
   float max = LocalMax(value, loc, Temp);
   if(max == MIN_VALUE)
      max = 0;
   BarrierLoc;
//--- SoftMax
   float result = IsNaNOrInf(exp(value - max), 0);
   const float sum = LocalSum(result, loc, Temp);
   result = IsNaNOrInf(result / (sum == 0 ? 1 : sum), 0);
//---
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float LocalSoftMaxGrad(const float value, const float grad, const int loc, __local float* Temp)
  {
   const size_t id = get_local_id(loc);
   const size_t total = get_local_size(loc);
//---
   const uint ls = min((uint)total, (uint)LOCAL_ARRAY_SIZE);
//---
   float result = 0;
   float val = IsNaNOrInf(value, 0);
   for(uint d = 0; d < total; d += ls)
     {
      if(id >= d && id < (d + ls))
         Temp[id - d] = IsNaNOrInf(val * grad, 0);
      BarrierLoc;
      for(uint l = 0; l < min(ls, (uint)(total - d)); l++)
         result += Temp[l] * ((float)((d + l) == id) - val);
      BarrierLoc;
     }
//---
   return result;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_base_ff Feed forward process kernel
/// Describes the forward path process for the Neuron Base (#CNeuronBaseOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8435#para41">the link.</A>
//+------------------------------------------------------------------+
__kernel void FeedForward(__global float *matrix_w, ///<[in] Weights matrix (m+1)*n, where m - number
                          ///< of neurons in layer and n - number of outputs
                          ///< (neurons in next layer)
                          __global float *matrix_i, ///<[in] Inputs tensor
                          __global float *matrix_o, ///<[out] Output tensor
                          int inputs,               ///< Number of inputs
                          int activation            ///< Activation type (#ENUM_ACTIVATION)
                         )
  {
   int i = get_global_id(0);
   float sum = 0;
   float4 inp, weight;
   int shift = (inputs + 1) * i;
   for(int k = 0; k <= inputs; k = k + 4)
     {
      switch(inputs - k)
        {
         case 0:
            inp = (float4)(1, 0, 0, 0);
            weight = (float4)(matrix_w[shift + k], 0, 0, 0);
            break;
         case 1:
            inp = (float4)(matrix_i[k], 1, 0, 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1], 0, 0);
            break;
         case 2:
            inp = (float4)(matrix_i[k], matrix_i[k + 1], 1, 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], 0);
            break;
         case 3:
            inp = (float4)(matrix_i[k], matrix_i[k + 1], matrix_i[k + 2], 1);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], matrix_w[shift + k + 3]);
            break;
         default:
            inp = (float4)(matrix_i[k], matrix_i[k + 1], matrix_i[k + 2],
                           matrix_i[k + 3]);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], matrix_w[shift + k + 3]);
            break;
        }
      float d = dot(IsNaNOrInf4(inp, 0), IsNaNOrInf4(weight, 0));
      sum = IsNaNOrInf(sum + d, sum);
     }
//---
   matrix_o[i] = fActivation(sum, activation);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_base_gr  Neuron Base Output Gradients Calculation kernel
/// Describes the process of output gradients calculation for the Neuron Base
/// (#CNeuronBaseOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8435#para42">the link.</A>
//+------------------------------------------------------------------+
__kernel void CalcOutputGradient(__global float *matrix_t,  ///<[in] Target tensor
                                 __global float *matrix_o,  ///<[in] Output tensor
                                 __global float *matrix_ig, ///<[out] Tensor of gradients
                                 int activation, ///< Activation type (#ENUM_ACTIVATION)
                                 float error)
  {
   int i = get_global_id(0);
   float out = matrix_o[i];
   float temp = 0;
   if(!isnan(out) && !isinf(out))
      temp = Deactivation(matrix_t[i] - out, out, activation);
   matrix_ig[i] = temp;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_base_gr  Neuron Base Hidden Gradients Calculation kernel
/// Describes the process of hidden gradients calculation for the Neuron Base
/// (#CNeuronBaseOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8435#para42">the link.</A>
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradient(__global float *matrix_w,  ///<[in] Weights matrix (m+1)*n, where m - number
                                 ///< of neurons in previous layer and n - number
                                 ///< of neurons in current layer
                                 __global float *matrix_g,  ///<[in] Tensor of gradients at current layer
                                 __global float *matrix_o,  ///<[in] Previous layer Output tensor
                                 __global float *matrix_ig, ///<[out] Tensor of gradients at previous layer
                                 int outputs,               ///< Number of outputs
                                 int activation             ///< Activation type (#ENUM_ACTIVATION)
                                )
  {
   int i = get_global_id(0);
   int inputs = get_global_size(0);
   float sum = 0;
   float out = matrix_o[i];
   float4 grad, weight;
   for(int k = 0; k < outputs; k += 4)
     {
      switch(outputs - k)
        {
         case 1:
            weight = (float4)(matrix_w[k * (inputs + 1) + i], 0, 0, 0);
            grad = (float4)(matrix_g[k], 0, 0, 0);
            break;
         case 2:
            grad = (float4)(matrix_g[k], matrix_g[k + 1], 0, 0);
            weight = (float4)(matrix_w[k * (inputs + 1) + i],
                              matrix_w[(k + 1) * (inputs + 1) + i], 0, 0);
            break;
         case 3:
            grad = (float4)(matrix_g[k], matrix_g[k + 1], matrix_g[k + 2], 0);
            weight = (float4)(matrix_w[k * (inputs + 1) + i],
                              matrix_w[(k + 1) * (inputs + 1) + i],
                              matrix_w[(k + 2) * (inputs + 1) + i], 0);
            break;
         default:
            grad = (float4)(matrix_g[k], matrix_g[k + 1], matrix_g[k + 2],
                            matrix_g[k + 3]);
            weight = (float4)(matrix_w[k * (inputs + 1) + i],
                              matrix_w[(k + 1) * (inputs + 1) + i],
                              matrix_w[(k + 2) * (inputs + 1) + i],
                              matrix_w[(k + 3) * (inputs + 1) + i]);
            break;
        }
      //---
      weight = IsNaNOrInf4(weight, 0);
      grad = IsNaNOrInf4(grad, 0);
      //---
      sum += dot(grad, weight);
     }
//---
   matrix_ig[i] = Deactivation(sum, out, activation);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_base_opt  Neuron Base SGD Updating Weights Calculation kernel
/// Describes the process of SGD optimization weights for the Neuron Base
/// (#CNeuronBaseOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8435#para43">the link.</A>
//+------------------------------------------------------------------+
__kernel void UpdateWeightsMomentum(__global float *matrix_w, ///<[in,out] Weights matrix (m+1)*n, where m -
                                    ///< number of neurons in previous layer and n -
                                    ///< number of neurons in current layer
                                    __global float *matrix_g, ///<[in] Tensor of gradients at current layer
                                    __global float *matrix_i, ///<[in] Inputs tensor
                                    __global float *matrix_dw, ///<[in,out] Matrix of delta weights in last correction
                                    int inputs,     ///< Number of inputs
                                    float learning_rates, ///< Learning rates
                                    float momentum        ///< Momentum multiplier
                                   )
  {
   int i = get_global_id(0);
   int j = get_global_id(1);
   int wi = i * (inputs + 1) + j;
   float delta = learning_rates * matrix_g[i] * (j < inputs ? matrix_i[j] : 1) +
                 momentum * matrix_dw[wi];
   if(!isnan(delta) && !isinf(delta))
     {
      matrix_dw[wi] = delta;
      if(fabs(delta) > 0)
         matrix_w[wi] = clamp(matrix_w[wi] + delta, -MAX_WEIGHT, MAX_WEIGHT);
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_base_opt  Neuron Base Adam Updating Weights Calculation
/// kernel
/// Describes the process of Adam optimization weights for the Neuron Base
/// (#CNeuronBaseOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8598#para31">the link.</A>
//+------------------------------------------------------------------+
__kernel void UpdateWeightsAdam(__global float *matrix_w, ///<[in,out] Weights matrix (m+1)*n, where m -
                                ///< number of neurons in previous layer and n -
                                ///< number of neurons in current layer
                                __global const float
                                *matrix_g, ///<[in] Tensor of gradients at current layer
                                __global const float *matrix_i, ///<[in] Inputs tensor
                                __global float *matrix_m,       ///<[in,out] Matrix of first momentum
                                __global float *matrix_v,       ///<[in,out] Matrix of seconfd momentum
                                const int inputs,               ///< Number of inputs
                                const float l,                  ///< Learning rates
                                const float b1,                 ///< First momentum multiplier
                                const float b2                  ///< Second momentum multiplier
                               )
  {
   const int i = get_global_id(0);
   const int j = get_global_id(1);
   const int wi = i * (inputs + 1) + j;
   float m, v, weight, inp;
   inp = IsNaNOrInf((j == inputs ? 1.0f : matrix_i[j]), 0);
   weight = IsNaNOrInf(matrix_w[wi], 0);
   m = IsNaNOrInf(matrix_m[wi], 0);
   v = IsNaNOrInf(matrix_v[wi], 0);
//---
   float g = clamp(IsNaNOrInf(matrix_g[i] * inp, 0), -MAX_GRAD, MAX_GRAD);
   float mt = IsNaNOrInf(b1 * m + (1 - b1) * g, 0);
   float vt = IsNaNOrInf(b2 * v + (1 - b2) * pow(g, 2), 0);
   float delta =
      IsNaNOrInf(l * (mt / (sqrt(vt) + 1.0e-37f) - (l1 * sign(weight) + l2 * weight)), 0);
   if(fabs(delta) > 0)
      matrix_w[wi] = clamp(matrix_w[wi] + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[wi] = mt;
   matrix_v[wi] = vt;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_base_opt  Neuron Base Least Squares Updating Weights
/// Calculation kernel
/// Describes the process of Least Squares optimization weights for the Neuron
/// Base (#CNeuronBaseOCL).
//\details Detailed description on <A
// HREF="https://www.mql5.com/ru/articles/8598#para31">the link.</A>
//+------------------------------------------------------------------+
__kernel void UpdateWeightsLS(__global float *matrix_w, ///<[in,out] Weights matrix (m+1)*n, where m -
                              ///< number of neurons in previous layer and n -
                              ///< number of neurons in current layer
                              __global const float
                              *matrix_g, ///<[in] Tensor of gradients at current layer
                              __global const float *matrix_i, ///<[in] Inputs tensor
                              __global float *matrix_xg,      ///<[in,out] Matrix of summ x*g
                              __global float *matrix_xx,      ///<[in,out] Matrix of summ x*x
                              const int inputs,               ///< Number of inputs
                              const float l,                  ///< Learning rates
                              const int update                ///< Update flag
                             )
  {
   const int i = get_global_id(0);
   const int j = get_global_id(1);
   const int wi = i * (inputs + 1) + j * 4;
   float4 xg, xx, weight, inp;
   switch(inputs + 1 - j * 4)
     {
      case 0:
         inp = (float4)(1, 0, 0, 0);
         weight = (float4)(matrix_w[wi], 0, 0, 0);
         break;
      case 1:
         inp = (float4)(matrix_i[j * 4], 1, 0, 0);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], 0, 0);
         break;
      case 2:
         inp = (float4)(matrix_i[j * 4], matrix_i[j * 4 + 1], 1, 0);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], matrix_w[wi + 2], 0);
         break;
      case 3:
         inp =
            (float4)(matrix_i[j * 4], matrix_i[j * 4 + 1], matrix_i[j * 4 + 2], 1);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], matrix_w[wi + 2],
                           matrix_w[wi + 3]);
         break;
      default:
         inp = (float4)(matrix_i[j * 4], matrix_i[j * 4 + 1], matrix_i[j * 4 + 2],
                        matrix_i[j * 4 + 3]);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], matrix_w[wi + 2],
                           matrix_w[wi + 3]);
         break;
     }
   xg = (float4)(matrix_g[i]) * inp;
   xx = pow(inp, 2.0f);
   switch(min(inputs + 1 - j * 4, 3))
     {
      case 3:
         if(update)
           {
            matrix_w[wi + 3] =
               matrix_w[wi + 3] + l * (matrix_xg[wi + 3] + xg.s3) /
               (matrix_xx[wi + 3] + xx.s3 + 1.0e-37f);
            matrix_xg[wi + 3] = 0;
            matrix_xx[wi + 3] = 0;
           }
         else
           {
            matrix_xg[wi + 3] += xg.s3;
            matrix_xx[wi + 3] += xx.s3;
           }
      case 2:
         if(update)
           {
            matrix_w[wi + 2] =
               matrix_w[wi + 2] + l * (matrix_xg[wi + 2] + xg.s2) /
               (matrix_xx[wi + 2] + xx.s2 + 1.0e-37f);
            matrix_xg[wi + 2] = 0;
            matrix_xx[wi + 2] = 0;
           }
         else
           {
            matrix_xg[wi + 2] += xg.s2;
            matrix_xx[wi + 2] += xx.s2;
           }
      case 1:
         if(update)
           {
            matrix_w[wi + 1] =
               matrix_w[wi + 1] + l * (matrix_xg[wi + 1] + xg.s1) /
               (matrix_xx[wi + 1] + xx.s1 + 1.0e-37f);
            matrix_xg[wi + 1] = 0;
            matrix_xx[wi + 1] = 0;
           }
         else
           {
            matrix_xg[wi + 1] += xg.s1;
            matrix_xx[wi + 1] += xx.s1;
           }
      case 0:
         if(update)
           {
            matrix_w[wi] = matrix_w[wi] + l * (matrix_xg[wi] + xg.s0) /
                           (matrix_xx[wi] + xx.s0 + 1.0e-37f);
            matrix_xg[wi] = 0;
            matrix_xx[wi] = 0;
           }
         else
           {
            matrix_xg[wi] += xg.s0;
            matrix_xx[wi] += xx.s0;
           }
         break;
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_proof_ff
/// Kernel of the Pooling neuron for Feed forward process (#CNeuronProofOCL)
//+------------------------------------------------------------------+
__kernel void FeedForwardProof(__global float *matrix_i, ///<[in] Inputs tensor
                               __global float *matrix_o, ///<[out] Output tensor
                               int inputs,               ///< Number of inputs
                               int window, ///< Size of input window
                               int step    ///< Step size
                              )
  {
   int i = get_global_id(0);
   int pos = i * step;
   float result = matrix_i[pos];
//---
   for(int k = 1; k < window; k++)
     {
      int shift = k + pos;
      if(shift >= inputs)
         break;
      result = max(result, matrix_i[shift]);
     }
   matrix_o[i] = result;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_proof_gr
/// Kernel of the Pooling neuron to transfer gradient to previous layer
/// (#CNeuronProofOCL)
//+------------------------------------------------------------------+
__kernel void CalcInputGradientProof(__global float *matrix_i,  ///<[in] Inputs tensor
                                     __global float *matrix_g,  ///<[in] Tensor of gradients at current layer
                                     __global float *matrix_o,  ///<[in] Output tensor
                                     __global float *matrix_ig, ///<[out] Tensor of gradients at previous layer
                                     int outputs,               ///< Number of outputs
                                     int window,                ///< Size of input window
                                     int step                   ///< Step size
                                    )
  {
   int i = get_global_id(0);
   float prev_gradient = 0;
   float value = matrix_i[i];
   int start = i - window + step;
   start = (start - start % step) / step;
   int stop = (i - i % step) / step + 1;
   for(int out = max(0, start); out < min(outputs, stop); out++)
     {
      if(value == matrix_o[out])
         prev_gradient += matrix_g[out];
     }
   matrix_ig[i] = prev_gradient;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_ff
/// Kernel of the Convolution neuron for Feed forward process (#CNeuronConvOCL)
//+------------------------------------------------------------------+
__kernel void FeedForwardConv(__global const float *matrix_w, ///<[in] Weights matrix (m+1)*n, where m - input
                              ///< window and n - output window
                              __global const float *matrix_i, ///<[in] Inputs tensor
                              __global float *matrix_o, ///<[out] Output tensor
                              const int inputs,         ///< Number of inputs
                              const int step,           ///< Step size
                              const int window_in,      ///< Size of input window
                              const int window_out,     ///< Size of output window
                              const int activation      ///< Activation type (#ENUM_ACTIVATION)
                             )
  {
   const size_t i = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t outputs = get_global_size(0);
//---
   const int shift_out = window_out * i;
   const int shift_in = step * i;
//---
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * window_out * outputs;
   const int shift_var_w = v * window_out * (window_in + 1);
//---
   float sum = 0;
   float4 inp, weight;
//---
   for(int out = 0; out < window_out; out++)
     {
      int shift = (window_in + 1) * out;
      int stop = (window_in <= (inputs - shift_in) ? window_in : (inputs - shift_in));
      for(int k = 0; k <= stop; k += 4)
        {
         switch(stop - k)
           {
            case 0:
               inp = (float4)(1, 0, 0, 0);
               weight = (float4)(matrix_w[shift_var_w + shift + window_in], 0, 0, 0);
               break;
            case 1:
               inp = (float4)(matrix_i[shift_var_in + shift_in + k], 1, 0, 0);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + window_in], 0, 0);
               break;
            case 2:
               inp =
                  (float4)(matrix_i[shift_var_in + shift_in + k], matrix_i[shift_var_in + shift_in + k + 1], 1, 0);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + k + 1],
                                 matrix_w[shift_var_w + shift + window_in], 0);
               break;
            case 3:
               inp = (float4)(matrix_i[shift_var_in + shift_in + k], matrix_i[shift_var_in + shift_in + k + 1],
                              matrix_i[shift_var_in + shift_in + k + 2], 1);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + k + 1],
                                 matrix_w[shift_var_w + shift + k + 2], matrix_w[shift_var_w + shift + window_in]);
               break;
            default:
               inp = (float4)(matrix_i[shift_var_in + shift_in + k], matrix_i[shift_var_in + shift_in + k + 1],
                              matrix_i[shift_var_in + shift_in + k + 2], matrix_i[shift_var_in + shift_in + k + 3]);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + k + 1],
                                 matrix_w[shift_var_w + shift + k + 2], matrix_w[shift_var_w + shift + k + 3]);
               break;
           }
         sum += IsNaNOrInf(dot(IsNaNOrInf4(inp, 0), IsNaNOrInf4(weight, 0)), 0);
        }
      sum = IsNaNOrInf(sum, 0);
      //---
      matrix_o[shift_var_out + out + shift_out] = fActivation(sum, activation);;
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_gr
/// Kernel of the Convolution neuron to transfer gradient
/// to previous layer (#CNeuronConvOCL)
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientConv(__global float *matrix_w,       ///<[in] Weights matrix (m+1)*n, where m - input
                                     ///<     window and n - output window
                                     __global float *matrix_g,       ///<[in] Tensor of gradients at current layer
                                     __global float *matrix_o,       ///<[in] Output tensor
                                     __global float *matrix_ig,      ///<[out] Tensor of gradients at previous layer
                                     const int outputs,              ///< Number of outputs
                                     const int step,                 ///< Step size
                                     const int window_in,            ///< Size of input window
                                     const int window_out,           ///< Size of output window
                                     const int activation,           ///< Activation type (#ENUM_ACTIVATION)
                                     const int shift_out             ///< Shift in output and gradient buffer
                                    )
  {
   const size_t i = get_global_id(0);
   const size_t inputs = get_global_size(0);
   const size_t v = get_global_id(1);
//---
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * outputs;
   const int shift_var_w = v * window_out * (window_in + 1);
//---
   float sum = 0;
   float out = matrix_o[shift_var_in + i];
   const int w_start = i % step;
   const int start = max((int)((i - window_in + step) / step), 0);
   int stop = (w_start + step - 1) / step;
   stop = min((int)((i + step - 1) / step + 1), stop) + start;
   if(stop > (outputs / window_out))
      stop = outputs / window_out;
   for(int h = 0; h < window_out; h ++)
     {
      for(int k = start; k < stop; k++)
        {
         int shift_g = k * window_out + h;
         int shift_w = (stop - k - 1) * step + i % step + h * (window_in + 1);
         if(shift_g >= outputs || shift_w >= (window_in + 1) * window_out)
            break;
         float grad = matrix_g[shift_out + shift_g + shift_var_out];
         sum += grad * matrix_w[shift_w + shift_var_w];
        }
     }
//---
   matrix_ig[shift_var_in + i] = Deactivation(sum, out, activation);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_opt Convolution Neuron SGD optimization Updating Weights
/// Calculation kernel
/// Describes the process of SGD optimization weights for the Convolution Neuron
/// (#CNeuronConvOCL).
//+------------------------------------------------------------------+
__kernel void UpdateWeightsConvMomentum(__global float *matrix_w,    ///<[in,out] Weights matrix (m+1)*n, where m -
                                        ///< input window and n - output window
                                        __global float *matrix_g, ///<[in] Tensor of gradients at current layer
                                        __global float *matrix_i, ///<[in] Inputs tensor
                                        __global float
                                        *matrix_dw, ///<[in,out] Matrix of delta weights in last correction
                                        int inputs,     ///< Number of inputs
                                        float learning_rates, ///< Learning rates
                                        float momentum,       ///< Momentum multiplier
                                        int window_in,        ///< Size of input window
                                        int window_out,       ///< Size of output window
                                        int step              ///< Step size
                                       )
  {
   const size_t i = get_global_id(0);
//---
   const int v = i / ((window_in + 1) * window_out);
   const int shift = i % (window_in + 1);
   const int shift_out = i / (window_in + 1) - v;
   const int total = (inputs - window_in + step - 1) / step;
//---
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * total * window_out;
//---
   float grad = 0;
//---
   for(int t = 0; t < total; t++)
     {
      if(shift != window_in && (shift + t * window_in) >= inputs)
         break;
      grad += matrix_g[t * window_out + shift_out + shift_var_out] *
              (shift == window_in ? 1 : matrix_i[shift + t * step + shift_var_in]);
     }
   float delta = IsNaNOrInf(learning_rates * grad, 0) + momentum * matrix_dw[i];
   if(!isnan(delta))
     {
      matrix_dw[i] = delta;
      if(fabs(delta) > 0)
         matrix_w[i] = clamp(matrix_w[i] + delta, -MAX_WEIGHT, MAX_WEIGHT);
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_opt Convolution Neuron Adam optimization Updating
/// Weights Calculation kernel
/// Describes the process of Adam optimization weights for the Convolution
/// Neuron (#CNeuronConvOCL).
//+------------------------------------------------------------------+
__kernel void UpdateWeightsConvAdam(__global float *matrix_w,    ///<[in,out] Weights matrix (m+1)*n, where m -
                                    ///< input window and n - output window
                                    __global const float *matrix_g, ///<[in] Tensor of gradients at current layer
                                    __global const float *matrix_i, ///<[in] Inputs tensor
                                    __global float *matrix_m,       ///<[in] Matrix of first momentum
                                    __global float *matrix_v,       ///<[in] Matrix of seconfd momentum
                                    const int inputs,               ///< Number of inputs
                                    const float l,                  ///< Learning rates
                                    const float b1,                 ///< First momentum multiplier
                                    const float b2,                 ///< Second momentum multiplier
                                    int window_in,                  ///< Size of input window
                                    int window_out,                 ///< Size of output window
                                    int step                        ///< Step size
                                   )
  {
   const size_t i = get_global_id(0);
//---
   const int v = i / ((window_in + 1) * window_out);
   const int shift = i % (window_in + 1);
   const int shift_out = i / (window_in + 1) - v * window_out;
   const int total = (inputs - (window_in - step) + (step - 1)) / step;
//---
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * total * window_out;
//---
   float grad = 0;
//---
   for(int t = 0; t < total; t++)
     {
      if(shift != window_in && (shift + t * window_in) >= inputs)
         break;
      grad += IsNaNOrInf(matrix_g[t * window_out + shift_out + shift_var_out] *
                         (shift == window_in ? 1 : matrix_i[shift + t * step + shift_var_in]), 0);
     }
   grad = clamp(IsNaNOrInf(grad, 0), -MAX_GRAD, MAX_GRAD);
   float mt = IsNaNOrInf(clamp(b1 * matrix_m[i] + (1 - b1) * grad, -1.0e5f, 1.0e5f), 0);
   float vt = IsNaNOrInf(clamp(b2 * matrix_v[i] + (1 - b2) * pow(grad, 2), 1.0e-6f, 1.0e6f), 1.0e-6f);
   float weight = matrix_w[i];
   weight = clamp(weight + clamp(IsNaNOrInf(l * mt / sqrt(vt), 0), -0.1f * fabs(weight), 0.1f * fabs(weight)), -MAX_WEIGHT, MAX_WEIGHT);
   matrix_w[i] = weight;
   matrix_m[i] = mt;
   matrix_v[i] = vt;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_opt Convolution Neuron Least Squares optimization
/// Updating Weights Calculation kernel
/// Describes the process of Least Squares optimization weights for the
/// Convolution Neuron (#CNeuronConvOCL).
//+------------------------------------------------------------------+
__kernel void UpdateWeightsConvLS(__global float *matrix_w,    ///<[in,out] Weights matrix (m+1)*n, where m -
                                  ///< input window and n - output window
                                  __global const float
                                  *matrix_g, ///<[in] Tensor of gradients at current layer
                                  __global const float *matrix_i, ///<[in] Inputs tensor
                                  __global float *matrix_xg,      ///<[in] Matrix of summ x*g
                                  __global float *matrix_xx,      ///<[in] Matrix of summ x*x
                                  const int inputs,               ///< Number of inputs
                                  const float l,                  ///< Learning rates
                                  const int update,               ///< Update flag
                                  int window_in,                  ///< Size of input window
                                  int window_out,                 ///< Size of output window
                                  int step                        ///< Step size
                                 )
  {
   const int i = get_global_id(0);
   if(i > window_in)
      return;
//---
   int total = (inputs - (window_in - step)) % step;
   total = (inputs - (window_in - step) - total) / step + (total > 0 ? 1 : 0);
//---
   for(int out = 0; out < window_out; out++)
     {
      if((window_out - out) > 4)
        {
         float4 xg = {0, 0, 0, 0};
         float x2 = 0;
         int shift_w = i + out * (window_in + 1);
         for(int t = 0; t < total; t++)
           {
            if(i != window_in && (i + t * window_in) >= inputs)
               break;
            xg += (float4)(matrix_g[t * window_out + out],
                           matrix_g[t * window_out + out + 1],
                           matrix_g[t * window_out + out + 2],
                           matrix_g[t * window_out + out + 3]) *
                  (i == window_in ? 1 : matrix_i[i + t * step]);
            x2 += (i == window_in ? 1 : pow(matrix_i[i + t * step], 2.0f));
           }
         if(update)
           {
            xg = (float4)(matrix_xg[shift_w], matrix_xg[shift_w + window_in + 1],
                          matrix_xg[shift_w + 2 * (window_in + 1)],
                          matrix_xg[shift_w + 3 * (window_in + 1)]) +
                 xg;
            float4 xx =
               (float4)(matrix_xx[shift_w], matrix_xx[shift_w + window_in + 1],
                        matrix_xx[shift_w + 2 * (window_in + 1)],
                        matrix_xx[shift_w + 3 * (window_in + 1)]) +
               x2;
            float4 delta = l * xg / (xx + 1.0e-37f);
            float4 weight =
               (float4)(matrix_w[shift_w], matrix_w[shift_w + (window_in + 1)],
                        matrix_w[shift_w + 2 * (window_in + 1)],
                        matrix_w[shift_w + 3 * (window_in + 1)]) +
               delta;
            matrix_w[shift_w] = weight.s0;
            matrix_w[shift_w + (window_in + 1)] = weight.s1;
            matrix_w[shift_w + 2 * (window_in + 1)] = weight.s2;
            matrix_w[shift_w + 3 * (window_in + 1)] = weight.s3;
            matrix_xg[shift_w] = 0;
            matrix_xg[shift_w + (window_in + 1)] = 0;
            matrix_xg[shift_w + 2 * (window_in + 1)] = 0;
            matrix_xg[shift_w + 3 * (window_in + 1)] = 0;
            matrix_xx[shift_w] = 0;
            matrix_xx[shift_w + (window_in + 1)] = 0;
            matrix_xx[shift_w + 2 * (window_in + 1)] = 0;
            matrix_xx[shift_w + 3 * (window_in + 1)] = 0;
           }
         else
           {
            matrix_xg[shift_w] += xg.s0;
            matrix_xg[shift_w + (window_in + 1)] += xg.s1;
            matrix_xg[shift_w + 2 * (window_in + 1)] += xg.s2;
            matrix_xg[shift_w + 3 * (window_in + 1)] += xg.s3;
            matrix_xx[shift_w] = matrix_xx[shift_w + (window_in + 1)] =
                                    matrix_xx[shift_w + 2 * (window_in + 1)] =
                                       matrix_xx[shift_w + 3 * (window_in + 1)] += x2;
           }
         out += 3;
        }
      else
        {
         float xg = 0;
         float xx = 0;
         int shift_w = i + out * (window_in + 1);
         for(int t = 0; t < total; t++)
           {
            if(i != window_in && (i + t * window_in) >= inputs)
               break;
            xg += matrix_g[t * window_out + out] *
                  (i == window_in ? 1 : matrix_i[i + t * step]);
            xx += (i == window_in ? 1 : pow(matrix_i[i + t * step], 2.0f));
           }
         if(update)
           {
            xg = matrix_xg[shift_w] + xg;
            xx = matrix_xx[shift_w] + xx;
            float delta = l * xg / (xx + 1.0e-37f);
            matrix_w[shift_w] = matrix_w[shift_w] + delta;
            matrix_xg[shift_w] = 0;
            matrix_xx[shift_w] = 0;
           }
         else
           {
            matrix_xg[shift_w] += xg;
            matrix_xx[shift_w] += xx;
           }
        }
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_ff Attention Neuron Score calculation kernel |
/// Describes the Score calculation process for the Neuron of attention layer
/// (#CNeuronAttentionOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8765#para43">the link.</A>
//+------------------------------------------------------------------+
__kernel void AttentionScore(__global float *querys, ///<[in] Matrix of Querys
                             __global float *keys,   ///<[in] Matrix of Keys
                             __global float *score,  ///<[out] Matrix of Scores
                             int dimension,          ///< Dimension of Key
                             int mask ///< 1 - calc only previous units, 0 - calc all
                            )
  {
   int q = get_global_id(0);
   int shift_q = q * dimension;
   int units = get_global_size(0);
   int shift_s = q * units;
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   float sum = 0;
//---
   for(int k = 0; k < units; k++)
     {
      if(mask > 0 && k > q)
        {
         score[shift_s + k] = 0;
         continue;
        }
      float result = 0;
      int shift_k = k * dimension;
      for(int i = 0; i < dimension; i++)
         result += (querys[shift_q + i] * keys[shift_k + i]);
      result = IsNaNOrInf(exp(result / koef), 0);
      score[shift_s + k] = result;
      sum += result;
     }
//---
   for(int k = 0; (k < units && sum > 0); k++)
      score[shift_s + k] /= sum;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_ff Attention Neuron Out calculation kernel
/// Describes the Attention out calculation process for the Neuron of attention
/// layer (#CNeuronAttentionOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8765#para43">the link.</A>
//+------------------------------------------------------------------+
__kernel void AttentionOut(__global float *scores, ///<[in] Matrix of Scores
                           __global float *values, ///<[in] Matrix of Values
                           __global float *inputs, ///<[in] Inputs tensor
                           __global float *out     ///<[out] Output tensor
                          )
  {
   int units = get_global_size(0);
   int u = get_global_id(0);
   int d = get_global_id(1);
   int dimension = get_global_size(1);
   int shift = u * dimension + d;
   float result = 0;
//---
   for(int i = 0; i < units; i++)
      result += IsNaNOrInf(scores[u * units + i], 0) * IsNaNOrInf(values[i * dimension + d], 0);
   out[shift] = IsNaNOrInf(result, 0) + inputs[shift];
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_ff Kernel for calculation Sum of 2 matrixs with
/// multiplyer.
/// Describes the calculation Sum of 2 matrixs.
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8765#para43">the link.</A>
//+------------------------------------------------------------------+
__kernel void SumMatrix(__global float *matrix1,    ///<[in] First matrix
                        __global float *matrix2,    ///<[in] Second matrix
                        __global float *matrix_out, ///<[out] Output matrix
                        int dimension,              ///< Dimension of matrix
                        float multiplyer,           ///< Multiplyer for output
                        int shift_in1,              ///< Shift for input 1
                        int shift_in2,              ///< Shift for input 2
                        int shift_out               ///< Shift for output
                       )
  {
   const int i = get_global_id(0);
   const int step = get_global_size(0);
//---
   for(int k = 0; k < dimension; k++)
     {
      int index = i * dimension + k;
      matrix_out[i * shift_out + index] =
         IsNaNOrInf((matrix1[i * shift_in1 + index] + matrix2[i * shift_in2 + index]) * multiplyer, 0);
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_ff Kernel for calculation Sum of 4 matrixs with
/// multiplyer.
/// Describes the calculation Sum of 4 matrixs.
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8909#para53">the link.</A>
//+------------------------------------------------------------------+
__kernel void Sum5Matrix(__global float *matrix1,    ///<[in] First matrix
                         __global float *matrix2,    ///<[in] Second matrix
                         __global float *matrix3,    ///<[in] Third matrix
                         __global float *matrix4,    ///<[in] Fourth matrix
                         __global float *matrix5,    ///<[in] Fifth matrix
                         __global float *matrix_out, ///<[out] Output matrix
                         int dimension,              ///< Dimension of matrix
                         float multiplyer            ///< Multiplyer for output
                        )
  {
   const int i = get_global_id(0) * dimension;
//---
   for(int k = 0; k < dimension; k++)
      matrix_out[i + k] = (matrix1[i + k] + matrix2[i + k] + matrix3[i + k] +
                           matrix4[i + k] + matrix5[i + k]) *
                          multiplyer;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_gr Attention layer's neuron Gradients Calculation
/// kernel
/// Describes the gradients calculation process for the Neuron of attention
/// layer (#CNeuronAttentionOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8765#para44">the link.</A>
/// @param[in] querys Matrix of Querys
/// @param[out] querys_g Matrix of Querys' Gradients
/// @param[in] keys Matrix of Keys
/// @param[out] keys_g Matrix of Keys' Gradients
/// @param[in] values Matrix of Values
/// @param[out] values_g Matrix of Values' Gradients
/// @param[in] scores Matrix of Scores
/// @param[in] gradient Matrix of Gradients from previous iteration
//+------------------------------------------------------------------+
__kernel void AttentionInsideGradients(__global float *querys, __global float *querys_g,
                                       __global float *keys, __global float *keys_g,
                                       __global float *values, __global float *values_g,
                                       __global float *scores, __global float *gradient)
  {
   int u = get_global_id(0);
   int d = get_global_id(1);
   int units = get_global_size(0);
   int dimension = get_global_size(1);
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   float vg = 0;
   float qg = 0;
   float kg = 0;
//---
   for(int iu = 0; iu < units; iu++)
     {
      float g = gradient[iu * dimension + d];
      float sc = scores[iu * units + u];
      vg += sc * g;
      //---
      float sqg = 0;
      float skg = 0;
      for(int id = 0; id < dimension; id++)
        {
         sqg += values[iu * dimension + id] * gradient[u * dimension + id];
         skg += values[u * dimension + id] * gradient[iu * dimension + id];
        }
      qg += (scores[u * units + iu] == 0 || scores[u * units + iu] == 1
             ? 0.0001f
             : scores[u * units + iu] * (1 - scores[u * units + iu])) *
            sqg * keys[iu * dimension + d] / koef;
      //---
      kg += (scores[iu * units + u] == 0 || scores[iu * units + u] == 1
             ? 0.0001f
             : scores[iu * units + u] * (1 - scores[iu * units + u])) *
            skg * querys[iu * dimension + d] / koef;
     }
   int shift = u * dimension + d;
   values_g[shift] = clamp(IsNaNOrInf(vg, 0.0f), -1.0f, 1.0f);
   querys_g[shift] = clamp(IsNaNOrInf(qg, 0.0f), -1.0f, 1.0f);
   keys_g[shift] = clamp(IsNaNOrInf(kg, 0.0f), -1.0f, 1.0f);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_norm Kernels of matrix normalization process
/// Describes the process of matrix normalization.
///\details Detailed description on <A
/// HREF="https://arxiv.org/abs/1607.06450">the link.</A>
/// @param[in,out] buffer In/Out Matrix
/// @param[in] dimension Dimension of matrix
//+------------------------------------------------------------------+
__kernel void Normalize(__global float *buffer, int dimension)
  {
   int n = get_global_id(0);
   int shift = n * dimension;
   if(dimension < 1)
      return;
//---
   float mean = 0;
   float variance = 0;
//---
   for(int i = 0; i < dimension; i++)
     {
      float val = IsNaNOrInf(buffer[shift + i], 0);
      mean += val;
      variance += val * val;
     }
   variance -= mean * mean / dimension;
   mean /= dimension;
   variance /= dimension;
//---
   for(int i = 0; i < dimension; i++)
      if(variance > 1)
         buffer[shift + i] =
            IsNaNOrInf((buffer[shift + i] - mean) / variance, 0);
      else
         buffer[shift + i] =
            IsNaNOrInf(buffer[shift + i] - mean, 0);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_norm Kernels of weights matrix normalization process
/// Describes the process of weights matrix normalization.
///\details Detailed description on <A
/// HREF="https://arxiv.org/abs/1607.06450">the link.</A>
/// @param[in,out] buffer In/Out Matrix
/// @param[in] dimension Dimension of matrix
//+------------------------------------------------------------------+
__kernel void NormalizeWeights(__global float *buffer, int dimension)
  {
   int n = get_global_id(0);
   int shift = n * dimension;
   float sum = 0;
   float k = 1;
//---
   do
     {
      for(int i = 0; (i < dimension && !(isnan(sum) || !isinf(sum))); i++)
         sum = pow(IsNaNOrInf(buffer[shift + i], 0) / k, 2) / dimension;
      if(isnan(sum) || isinf(sum))
         k *= 10;
     }
   while(isnan(sum) || isinf(sum));
   sum = sqrt(sum);
   if(k * sum > 1)
      for(int i = 0; i < dimension; i++)
         buffer[shift + i] = IsNaNOrInf(buffer[shift + i], 0) / (k * sum);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_ff
/// Describes the process of concatenate 4 matrices.
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8909#para52">the link.</A>
/// @param[in] input1, input2, input3, input4 Input buffers
/// @param[in] window1, window2, window3, window4 Windows for every buffer
/// @param[out] output Output buffer
//+------------------------------------------------------------------+
__kernel void ConcatenateBuffers(__global float *input1, int window1,
                                 __global float *input2, int window2,
                                 __global float *input3, int window3,
                                 __global float *input4, int window4,
                                 __global float *output)
  {
   int n = get_global_id(0);
   int shift = n * (window1 + window2 + window3 + window4);
   int shift_in = n * window1;
   for(int i = 0; i < window1; i++)
      output[shift + i] = IsNaNOrInf(input1[shift_in + i], 0);
//---
   shift += window1;
   shift_in = n * window2;
//---
   for(int i = 0; i < window2; i++)
      output[shift + i] = IsNaNOrInf(input2[shift_in + i], 0);
//---
   shift += window2;
   shift_in = n * window3;
//---
   for(int i = 0; i < window3; i++)
      output[shift + i] = IsNaNOrInf(input3[shift_in + i], 0);
//---
   shift += window3;
   shift_in = n * window4;
//---
   for(int i = 0; i < window4; i++)
      output[shift + i] = IsNaNOrInf(input4[shift_in + i], 0);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_gr
/// Describes the process of deconcatenate matrix.
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/8909#para53">the link.</A>
/// @param[in] output1, output2, output3, output4 Output buffers
/// @param[in] window1, window2, window3, window4 Windows for every buffer
/// @param[out] inputs Input buffer
//+------------------------------------------------------------------+
__kernel void DeconcatenateBuffers(__global float *output1, int window1,
                                   __global float *output2, int window2,
                                   __global float *output3, int window3,
                                   __global float *output4, int window4,
                                   __global float *inputs)
  {
   int n = get_global_id(0);
//--- Head 1
   int shift = n * (window1 + window2 + window3 + window4);
   int shift_out = n * window1;
//---
   for(int i = 0; i < window1; i++)
      output1[shift_out + i] = IsNaNOrInf(inputs[shift + i], 0);
//--- Head 2
   shift += window1;
   shift_out = n * window2;
//---
   for(int i = 0; i < window2; i++)
      output2[shift_out + i] = IsNaNOrInf(inputs[shift + i], 0);
//--- Head 3
   shift += window2;
   if(window3 > 0)
     {
      shift_out = n * window3;
      //---
      for(int i = 0; i < window3; i++)
         output3[shift_out + i] = IsNaNOrInf(inputs[shift + i], 0);
     }
//--- Head 4
   shift += window3;
   if(window4 > 0)
     {
      shift_out = n * window4;
      //---
      for(int i = 0; i < window4; i++)
         output4[shift_out + i] = IsNaNOrInf(inputs[shift + i], 0);
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_ff Multi-Heads Attention Neuron Score calculation
/// kernel
/// Describes the Score calculation process for the Neuron of multi-heads
/// attention layer (#CNeuronMLMHAttentionOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9025#para42">the link.</A>
//+------------------------------------------------------------------+
__kernel void MHAttentionScore(__global float *qkv,   ///<[in] Matrix of Querys, Keys, Values
                               __global float *score, ///<[out] Matrix of Scores
                               int dimension,         ///< Dimension of Key
                               int mask ///< 1 - calc only previous units, 0 - calc all
                              )
  {
   int q = get_global_id(0);
   int h = get_global_id(1);
   int units = get_global_size(0);
   int heads = get_global_size(1);
//---
   int shift_q = dimension * (h + 3 * q * heads);
   int shift_s = units * (h + q * heads);
//---
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   float sum = 0;
//---
   for(int k = 0; k < units; k++)
     {
      if(mask > 0 && k > q)
        {
         score[shift_s + k] = 0;
         continue;
        }
      float result = 0;
      int shift_k = dimension * (h + heads * (3 * k + 1));
      for(int i = 0; i < dimension; i++)
        {
         if((dimension - i) > 4)
           {
            result += dot(IsNaNOrInf4((float4)(qkv[shift_q + i], qkv[shift_q + i + 1],
                                               qkv[shift_q + i + 2], qkv[shift_q + i + 3]), 0),
                          IsNaNOrInf4((float4)(qkv[shift_k + i], qkv[shift_k + i + 1],
                                               qkv[shift_k + i + 2], qkv[shift_k + i + 3]), 0));
            i += 3;
           }
         else
            result += IsNaNOrInf(qkv[shift_q + i] * qkv[shift_k + i], 0);
        }
      result = exp(clamp(result / koef, -100.0f, 100.0f));
      if(isnan(result))
         result = 0;
      score[shift_s + k] = result;
      sum += result;
     }
//---
   for(int k = 0; (k < units && sum > 1); k++)
      score[shift_s + k] /= sum;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_ff Multi-heads Attention Neuron Out calculation kernel
/// Describes the Multi-heads Attention out calculation process for the Neuron
/// of multi-heads attention layer (#CNeuronMLMHAttentionOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9025#para42">the link.</A>
//+------------------------------------------------------------------+
__kernel void MHAttentionOut(__global float *scores, ///<[in] Matrix of Scores
                             __global float *qkv,    ///<[in] Matrix of Values
                             __global float *out,    ///<[out] Output tensor
                             int dimension           ///< Dimension of Value
                            )
  {
   int u = get_global_id(0);
   int units = get_global_size(0);
   int h = get_global_id(1);
   int heads = get_global_size(1);
//---
   int shift_s = units * (h + heads * u);
   int shift_out = dimension * (h + heads * u);
   int layer = 3 * dimension * heads;
//---
//---
   for(int d = 0; d < dimension; d++)
     {
      float result = 0;
      for(int v = 0; v < units; v++)
        {
         int shift_v = dimension * (h + heads * (3 * v + 2)) + d;
         result += scores[shift_s + v] * qkv[shift_v];
        }
      out[shift_out + d] = result;
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_atten_gr Attention layer's neuron Gradients Calculation
/// kernel
/// Describes the gradients calculation process for the Neuron of attention
/// layer (#CNeuronMLMHAttentionOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9025#para33">the link.</A>
/// @param[in] qkv Matrix of Querys, Keys and Values
/// @param[out] qkv_g Matrix of Querys', Keys' and Values' Gradients
/// @param[in] scores Matrix of Scores
/// @param[in] scores_g Matrix of Scores' Gradients
/// @param[in] gradient Matrix of Gradients from previous iteration
/// @param[in] dimension Dimension of Key vector
//+------------------------------------------------------------------+
__kernel void MHAttentionInsideGradients(__global float *qkv, __global float *qkv_g,
      __global float *scores,
      __global float *gradient)
  {
   size_t u = get_global_id(0);
   size_t h = get_global_id(1);
   size_t d = get_global_id(2);
   size_t units = get_global_size(0);
   size_t heads = get_global_size(1);
   size_t dimension = get_global_size(2);
//---
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
//--- init
   const int shift_q = dimension * (heads * 3 * u + h);
   const int shift_k = dimension * (heads * (3 * u + 1) + h);
   const int shift_v = dimension * (heads * (3 * u + 2) + h);
   const int shift_g = dimension * (heads * u + h);
   int shift_score = h * units;
   int step_score = units * heads;
//--- Calculating Value's gradients
   float sum = 0;
//---
   for(int i = 0; i < units; i++)
      sum += gradient[(h + i * heads) * dimension + d] * scores[shift_score + u + i * step_score];
   qkv_g[shift_v + d] = sum;
//--- Calculating Query's gradients
   shift_score = h * units + u * step_score;
   float grad = 0;
   float grad_out = gradient[shift_g + d];
//---
   for(int k = 0; k < units; k++)
     {
      float sc_g = 0;
      float sc = scores[shift_score + k];
      for(int v = 0; v < units; v++)
         sc_g += scores[shift_score + v] * qkv[dimension * (heads * (3 * v + 2) + h)] *
                 grad_out * ((k == v) - sc);
      grad += sc_g / koef * qkv[dimension * (heads * (3 * k + 1) + h) + d];
     }
   qkv_g[shift_q + d] = grad;
//--- Calculating Key's gradients
   grad = 0;
//---
   for(int q = 0; q < units; q++)
     {
      shift_score = h * units + q * step_score;
      float sc_g = 0;
      float sc = scores[shift_score + u];
      float grad_out = gradient[dimension * (heads * q + h) + d];
      for(int v = 0; v < units; v++)
         sc_g += scores[shift_score + v] * qkv[dimension * (heads * (3 * v + 2) + h)] *
                 grad_out * ((u == v) - sc);
      grad += sc_g / koef * qkv[dimension * (heads * 3 * q + h) + d];
     }
   qkv_g[shift_k + d] = grad;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_dropout Kernel for Dropout.
/// Describes the dropout method.
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9112#para32">the link.</A>
//+------------------------------------------------------------------+
__kernel void Dropout(__global const float *inputs, ///<[in] Input matrix
                      __global const float *map,    ///<[in] Dropout map matrix
                      __global float *out,    ///<[out] Output matrix
                      const int dimension           ///< Dimension of matrix
                     )
  {
   const int i = get_global_id(0) * 4;
   if(i + 3 < dimension)
     {
      float4 k = IsNaNOrInf4(
                    (float4)(inputs[i], inputs[i + 1], inputs[i + 2], inputs[i + 3]) *
                    (float4)(map[i], map[i + 1], map[i + 2], map[i + 3]), 0);
      out[i] = k.s0;
      out[i + 1] = k.s1;
      out[i + 2] = k.s2;
      out[i + 3] = k.s3;
     }
   else
      for(int k = i; k < min(dimension, i + 4); k++)
         out[i + k] = IsNaNOrInf(inputs[i + k] * map[i + k], 0);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_norm Kernels of Batch normalization process
/// Describes the process of Batch normalization. (#CNeuronBatchNormOCL)
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9207#para42">the link.</A>
/// @param[in] inputs Input data tenzor
/// @param[in,out] options Tenzor of variables
/// @param[out] output Tenzor of output data
/// @param[in] batch Batch size
/// @param[in] optimization Optimization type
/// @param[in] activation Activation type
//+------------------------------------------------------------------+
__kernel void BatchFeedForward(__global float *inputs, __global float *options,
                               __global float *output, int batch,
                               int optimization, int activation)
  {
   if(batch <= 1)
      return;
   int n = get_global_id(0);
   int shift = n * (optimization == 0 ? 7 : 9);
//---
   float inp = IsNaNOrInf(inputs[n], 0);
   float mean = (IsNaNOrInf(options[shift], 0) * max((float)batch - 1.0f, 0.0f) + inp) / max((float)batch, 1.0f);
   float delt = inp - mean;
   float variance = (IsNaNOrInf(options[shift + 1] * max((float)batch - 1.0f, 0.0f), 0) + pow(delt, 2.0f)) / max((float)batch, 1.0f);
   if(variance <= 0)
      variance = 1;
   float nx = delt / sqrt(variance);
//---
   float gamma = IsNaNOrInf(options[shift + 3], 1);
   if(gamma == 0)
     {
      options[shift + 3] = 1;
      gamma = 1;
     }
   float betta = IsNaNOrInf(options[shift + 4], 0);
//---
   options[shift] = mean;
   options[shift + 1] = variance;
   options[shift + 2] = nx;
   output[n] = fActivation(gamma * nx + betta, activation);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_gr
/// Kernel of the Batch neuron to transfer gradient to previous layer
/// (#CNeuronBatchNormOCL)
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9207#para43">the link.</A>
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientBatch(__global float *options,      ///<[in] Options matrix m*(7 or 9), where m - Number of neurons in previous layer
                                      __global float *matrix_g,  ///<[in] Tensor of gradients at current layer
                                      __global float *matrix_i,  ///<[in] Tensor of previous layer output
                                      __global float *matrix_ig, ///<[out] Tensor of gradients at previous layer
                                      int activation,            ///< Activation type (#ENUM_ACTIVATION)
                                      int batch,                 ///< Batch size
                                      int optimization           ///< Optimization type
                                     )
  {
   if(batch <= 1)
      return;
//---
   int n = get_global_id(0);
   int shift = n * (optimization == 0 ? 7 : 9);
//---
   float variance = IsNaNOrInf(options[shift + 1], 1);
//---
   float inp = IsNaNOrInf(matrix_i[n], 0);
   float gnx = IsNaNOrInf(matrix_g[n], 0) * IsNaNOrInf(options[shift + 3], 1);
   float temp = (variance > 0 ? 1.0f / sqrt(variance) : 0);
   float gmu = (-temp) * gnx;
   float gvar =
      (variance > 0
       ? (IsNaNOrInf(options[shift], 0) * inp) / (2 * pow(variance, 3.0f / 2.0f)) * gnx
       : 0);
   float gx = temp * gnx + gmu / max(batch, 1) +
              gvar * 2 * inp / max(batch, 1) * pow(max((float)(batch - 1), 0.0f) / max((float)batch, 1.0f), 2.0f);
//---
   matrix_ig[n] = Deactivation(gx, inp, activation);;
  }
//+------------------------------------------------------------------+
///\ingroup neuron_opt Batch normalization Neuron SGD optimization Updating
/// options kernel
/// Describes the process of SGD optimization options for the Batch
/// normalization Neuron (#CNeuronBatchNormOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9207#para43">the link.</A>
//+------------------------------------------------------------------+
__kernel void UpdateBatchOptionsMomentum(__global float *options,     ///<[in,out] Options matrix m*7, where m - Number of neurons in previous layer
      __global float *matrix_g, ///<[in] Tensor of gradients at current layer
      float learning_rates,     ///< Learning rates
      float momentum            ///< Momentum multiplier
                                        )
  {
   const int n = get_global_id(0);
   const int inputs = get_global_size(0);
   const int shift = n * 7;
   float grad = clamp(IsNaNOrInf(matrix_g[n], 0), -MAX_GRAD, MAX_GRAD);
//---
   float2 delta = learning_rates * grad * (float2)(IsNaNOrInf(options[shift + 2], 0), 1) +
                  momentum * (float2)(IsNaNOrInf(options[shift + 5], 0), IsNaNOrInf(options[shift + 6], 0));
//---
   delta.s0 = IsNaNOrInf(delta.s0, 0);
   delta.s1 = IsNaNOrInf(delta.s1, 0);
   options[shift + 5] = delta.s0;
   float value = IsNaNOrInf(options[shift + 3], 1);
   options[shift + 3] = value + delta.s0 - learning_rates * (l1 * sign(value) +
                        l2 * value / inputs);
//---
   options[shift + 6] = delta.s1;
   value = IsNaNOrInf(options[shift + 4], 0);
   options[shift + 4] = value + delta.s1 - learning_rates * (l1 * sign(value) +
                        l2 * value / inputs);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_opt Batch normalization Neuron Adam optimization Updating
/// options kernel
/// Describes the process of Adam optimization options for the Batch
/// normalization  Neuron (#CNeuronBatchNormOCL).
///\details Detailed description on <A
/// HREF="https://www.mql5.com/ru/articles/9207#para43">the link.</A>
//+------------------------------------------------------------------+
__kernel void UpdateBatchOptionsAdam(__global float *options,     ///<[in,out] Options matrix m*9, where m - Number of neurons in previous layer
                                     __global float *matrix_g, ///<[in] Tensor of gradients at current layer
                                     const float l,            ///< Learning rates
                                     const float b1,           ///< First momentum multiplier
                                     const float b2            ///< Second momentum multiplier
                                    )
  {
   const int n = get_global_id(0);
   int inputs = get_global_size(0);
   const int shift = n * 9;
   float grad = clamp(IsNaNOrInf(matrix_g[n], 0), -MAX_GRAD, MAX_GRAD);
//---
   float nx = IsNaNOrInf(options[shift + 2], 0);
   float gamma = IsNaNOrInf(options[shift + 3], 1);
   if(gamma == 0)
      gamma = 1;
   float betta = IsNaNOrInf(options[shift + 4], 0);
//---
   float gamma_m1 = IsNaNOrInf(options[shift + 5], 0);
   float betta_m1 = IsNaNOrInf(options[shift + 6], 0);
   float gamma_m2 = IsNaNOrInf(options[shift + 7], 0);
   float betta_m2 = IsNaNOrInf(options[shift + 8], 0);
//---
   float2 mt = b1 * (float2)(gamma_m1, betta_m1) +
               (1 - b1) * (float2)(grad * nx, grad);
   float2 vt = b2 * (float2)(gamma_m2, betta_m2) +
               (1 - b2) * pow((float2)(grad * nx, grad), 2);
   vt.s0 = IsNaNOrInf(vt.s0, 1);
   vt.s1 = IsNaNOrInf(vt.s1, 1);
   float2 delta = l * mt / sqrt(vt);
   delta.s0 = IsNaNOrInf(delta.s0, 0);
   delta.s1 = IsNaNOrInf(delta.s0, 0);
   float2 weight = delta -
                   (l1 * sign((float2)(gamma, betta)) +
                    l2 * (float2)(gamma, betta) / inputs);
//---
   options[shift + 3] = IsNaNOrInf(gamma + weight.s0, 1);
   options[shift + 4] = IsNaNOrInf(betta + weight.s1, 0);
   options[shift + 5] = IsNaNOrInf(mt.s0, 0);
   options[shift + 6] = IsNaNOrInf(mt.s1, 0);
   options[shift + 7] = vt.s0;
   options[shift + 8] = vt.s1;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void VAE_FeedForward(__global float *inputs, __global float *random,
                              __global float *outputs)
  {
   uint i = (uint)get_global_id(0);
   uint total = (uint)get_global_size(0);
   outputs[i] = IsNaNOrInf(inputs[i], 0) + IsNaNOrInf(exp(0.5f * inputs[i + total]), 0) * random[i];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void VAE_CalcHiddenGradient(__global float *inputs,
                                     __global float *inp_grad,
                                     __global float *random,
                                     __global float *gradient,
                                     const float kld_mult)
  {
   uint i = (uint)get_global_id(0);
   uint total = (uint)get_global_size(0);
   float log_var = IsNaNOrInf(inputs[i + total], 0);
   float mean = IsNaNOrInf(inputs[i], 0);
   float kld =
      kld_mult * 0.5f * (log_var - exp(log_var) - pow(mean, 2.0f) + 1);
   float grad = clamp(IsNaNOrInf(gradient[i], 0), -MAX_GRAD, MAX_GRAD);
   inp_grad[i] = IsNaNOrInf(grad / exp(0.5f * log_var) + kld * mean, 0);
   inp_grad[i + total] = IsNaNOrInf(0.5f * (grad * random[i] - kld * (1 - exp(log_var))), 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void LSTM_FeedForward(__global const float *inputs, int inputs_size,
                               __global const float *weights,
                               __global float *concatenated,
                               __global float *memory, __global float *output)
  {
   uint id = (uint)get_global_id(0);
   uint total = (uint)get_global_size(0);
   uint id2 = (uint)get_local_id(1);
   uint idv = (uint)get_global_id(2);
   uint total_v = (uint)get_global_size(2);
//---
   __local float Temp[4];
//---
   float sum = 0;
   uint shift_in = idv * inputs_size;
   uint shift_out = idv * total;
   uint shift = (inputs_size + total + 1) * (id2 + id);
//---
   for(uint i = 0; i < total; i += 4)
     {
      if(total - i > 4)
         sum += IsNaNOrInf(
                   dot((float4)(output[shift_out + i], output[shift_out + i + 1], output[shift_out + i + 2], output[shift_out + i + 3]),
                       (float4)(weights[shift + i], weights[shift + i + 1],
                                weights[shift + i + 2], weights[shift + i + 3])), 0);
      else
         for(uint k = i; k < total; k++)
            sum += IsNaNOrInf(output[shift_out + k] * weights[shift + k], 0);
     }
//---
   shift += total;
//---
   for(uint i = 0; i < inputs_size; i += 4)
     {
      if(total - i > 4)
         sum += IsNaNOrInf(
                   dot((float4)(inputs[shift_in + i], inputs[shift_in + i + 1], inputs[shift_in + i + 2], inputs[shift_in + i + 3]),
                       (float4)(weights[shift + i], weights[shift + i + 1],
                                weights[shift + i + 2], weights[shift + i + 3])), 0);
      else
         for(uint k = i; k < total; k++)
            sum += IsNaNOrInf(inputs[shift_in + k] * weights[shift + k], 0);
     }
   sum += IsNaNOrInf(weights[shift + inputs_size], 0);
   if(id2 < 3)
      sum = fActivation(sum, 1);
   else
      sum = fActivation(sum, 0);
   Temp[id2] = sum;
   concatenated[4 * shift_out + id2 * total + id] = sum;
//---
   BarrierLoc;
   if(id2 == 0)
     {
      float mem = memory[shift_out + id + total_v * total] = memory[shift_out + id];
      float fg = Temp[0];
      float ig = Temp[1];
      float og = Temp[2];
      float nc = Temp[3];
      //---
      memory[shift_out + id] = mem = IsNaNOrInf(mem * fg + ig * nc, 0);
      output[shift_out + id] = IsNaNOrInf(og * fActivation(mem, 0), 0);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void LSTM_ConcatenatedGradient(__global float *gradient,
                                        __global float *concatenated_gradient,
                                        __global float *memory,
                                        __global float *concatenated)
  {
   uint id = (uint)get_global_id(0);
   uint total = (uint)get_global_size(0);
   uint idv = (uint)get_global_id(1);
   uint total_v = (uint)get_global_size(1);
//---
   uint shift_out = idv * total;
   float t = tanh(memory[shift_out + id]);
//---
   concatenated_gradient[4 * shift_out + id + 2 * total] = gradient[shift_out + id] * t; // output gate
//---
   float memory_gradient = gradient[shift_out + id] * concatenated[4 * shift_out + id + 2 * total];
   memory_gradient *= 1 - pow(t, 2.0f);
//---
   concatenated_gradient[4 * shift_out + id + 3 * total] =
      memory_gradient * concatenated[4 * shift_out + id + total]; // new content
//---
   concatenated_gradient[4 * shift_out + id + total] =
      memory_gradient * concatenated[4 * shift_out + id + 3 * total]; // input gate
//---
   concatenated_gradient[4 * shift_out + id] =
      memory_gradient * memory[shift_out + id + total_v * total]; // forgat gate
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void LSTM_HiddenGradient(__global float *concatenated_gradient, __global float *inputs_gradient,
                                  __global float *weights_gradient, __global float *hidden_state,
                                  __global float *inputs, __global float *weights, __global float *output,
                                  const int hidden_size, const int inputs_size)
  {
   uint id = get_global_id(0);
   uint total = get_global_size(0);
   uint idv = (uint)get_global_id(1);
   uint total_v = (uint)get_global_size(1);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   uint ls = min(total_v, (uint)LOCAL_ARRAY_SIZE);
//---
   uint shift_in = idv * inputs_size;
   uint shift_out = idv * total;
   uint weights_step = hidden_size + inputs_size + 1;
//---
//---
   for(int i = id; i < (hidden_size + inputs_size); i += total)
     {
      float inp = 0;
      if(i < hidden_size)
        {
         inp = hidden_state[shift_out + i];
         hidden_state[shift_out + i] = output[shift_out + i];
        }
      else
        {
         inp = inputs[shift_in + i - hidden_size];
         float grad = 0;
         for(uint g = 0; g < 3 * hidden_size; g++)
           {
            float temp = concatenated_gradient[4 * shift_out + g];
            grad += temp * (1 - temp) * weights[i + g * weights_step];
           }
         for(uint g = 3 * hidden_size; g < 4 * hidden_size; g++)
           {
            float temp = concatenated_gradient[4 * shift_out + g];
            grad += temp * (1 - pow(temp, 2.0f)) * weights[i + g * weights_step];
           }
         inputs_gradient[shift_in + i - hidden_size] = grad;
        }
      //---
      for(uint g = 0; g < 3 * hidden_size; g++)
        {
         float temp = concatenated_gradient[4 * shift_out + g];
         if(idv < ls)
            Temp[idv % ls] = 0;
         BarrierLoc;
         for(uint v = 0; v < total_v; v += ls)
           {
            if(idv >= v && idv < v + ls)
               Temp[idv % ls] += temp * (1 - temp) * inp;
            BarrierLoc;
           }
         if(idv == 0)
           {
            temp = Temp[0];
            for(int v = 1; v < ls; v++)
               temp += Temp[v];
            weights_gradient[i + g * weights_step] = temp;
           }
         BarrierLoc;
        }
      for(uint g = 3 * hidden_size; g < 4 * hidden_size; g++)
        {
         float temp = concatenated_gradient[4 * shift_out + g];
         if(idv < ls)
            Temp[idv % ls] = 0;
         BarrierLoc;
         for(uint v = 0; v < total_v; v += ls)
           {
            if(idv >= v && idv < v + ls)
               Temp[idv % ls] += temp * (1 - pow(temp, 2.0f)) * inp;
            BarrierLoc;
           }
         if(idv == 0)
           {
            temp = Temp[0];
            for(int v = 1; v < ls; v++)
               temp += Temp[v];
            weights_gradient[i + g * weights_step] = temp;
           }
         BarrierLoc;
        }
     }
//---
   for(int i = id; i < 4 * hidden_size; i += total)
     {
      if(idv < ls)
         Temp[idv % ls] = 0;
      BarrierLoc;
      float temp = concatenated_gradient[4 * shift_out + i];
      if(i < 3 * hidden_size)
        {
         for(uint v = 0; v < total_v; v += ls)
           {
            if(idv >= v && idv < v + ls)
               Temp[idv % ls] += temp * (1 - temp);
            BarrierLoc;
           }
        }
      else
        {
         for(uint v = 0; v < total_v; v += ls)
           {
            if(idv >= v && idv < v + ls)
               Temp[idv % ls] += 1 - pow(temp, 2.0f);
            BarrierLoc;
           }
        }
      if(idv == 0)
        {
         temp = Temp[0];
         for(int v = 1; v < ls; v++)
            temp += Temp[v];
         weights_gradient[(i + 1) * weights_step] = temp;
        }
      BarrierLoc;
     }
  }
//+------------------------------------------------------------------+
///\ingroup LSTM_opt  LSTM Adam Updating Weights Calculation kernel
/// Describes the process of Adam optimization weights for the Neuron LSTM
/// (#CNeuronLSTMOCL).
//+------------------------------------------------------------------+
__kernel void LSTM_UpdateWeightsAdam(__global float *weights,   ///<[in,out] Weights matrix (m+1)*n, where m -
                                     ///< number of neurons in previous layer and n -
                                     ///< number of neurons in current layer
                                     __global float
                                     *weights_gradient,    ///<[in] Tensor of gradients at current layer
                                     __global float *matrix_m, ///<[in,out] Matrix of first momentum
                                     __global float *matrix_v, ///<[in,out] Matrix of seconfd momentum
                                     const float l,            ///< Learning rates
                                     const float b1,           ///< First momentum multiplier
                                     const float b2            ///< Second momentum multiplier
                                    )
  {
   const uint id = get_global_id(0);
   const uint total = get_global_size(0);
   const uint id1 = get_global_id(1);
   const uint wi = id1 * total + id;
   float g = weights_gradient[wi];
   float mt = b1 * matrix_m[wi] + (1 - b1) * g;
   float vt = b2 * matrix_v[wi] + (1 - b2) * pow(g, 2);
   float delta = l * (mt / (sqrt(vt) + 1.0e-37f) -
                      (l1 * sign(weights[wi]) + l2 * weights[wi] / total));
   weights[wi] = clamp(weights[wi] + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[wi] = mt;
   matrix_v[wi] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SoftMax_FeedForward(__global float *inputs,
                                  __global float *outputs)
  {
   const uint total = (uint)get_local_size(0);
   const uint l = (uint)get_local_id(0);
   const uint h = (uint)get_global_id(1);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   uint shift_head = h * total;
//---
   outputs[shift_head + l] = LocalSoftMax(IsNaNOrInf(inputs[shift_head + l], MIN_VALUE), 0, Temp);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SoftMax_HiddenGradient(__global float *outputs,
                                     __global float *output_gr,
                                     __global float *input_gr)
  {
   size_t i = get_local_id(0);
   size_t outputs_total = get_local_size(0);
   size_t h = get_global_id(1);
   __local float Temp[LOCAL_ARRAY_SIZE];
//---
   uint shift = h * outputs_total;
   float output = IsNaNOrInf(outputs[shift + i], 0);
   float grad = IsNaNOrInf(output_gr[shift + i], 0);
   input_gr[shift + i] = LocalSoftMaxGrad(output, grad, 0, Temp);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SoftMax_OutputGradient(__global float *outputs,
                                     __global float *targets,
                                     __global float *output_gr)
  {
   size_t i = get_global_id(0);
   output_gr[i] = (outputs[i] == 0 ? 0 : targets[i] / outputs[i]);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FQF_Cosine(__global float *softmax, __global float *output)
  {
   size_t i = get_global_id(0);
   size_t total = get_global_size(0);
   size_t action = get_global_id(1);
   int shift = action * total;
//---
   float result = 0;
//---
   for(int it = 0; it < i; it++)
      result += softmax[shift + it];
   result += softmax[shift + i] / 2.0f;
   output[shift + i] = cos(i * M_PI_F * result);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FQF_Output(__global float *quantiles, __global float *delta_taus,
                         __global float *output, int total)
  {
   size_t action = get_global_id(0);
   int shift = action * total;
//---
   float result = 0;
//---
   for(int i = 0; i < total; i++)
      result += quantiles[shift + i] * delta_taus[shift + i];
   output[action] = result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FQF_OutputGradient(__global float *quantiles,
                                 __global float *delta_taus,
                                 __global float *output_gr,
                                 __global float *quantiles_gr,
                                 __global float *taus_gr)
  {
   size_t i = get_global_id(0);
   size_t total = get_global_size(0);
   size_t action = get_global_id(1);
   int shift = action * total;
//---
   float gradient = output_gr[action];
   quantiles_gr[shift + i] = gradient * delta_taus[shift + i];
   taus_gr[shift + i] = gradient * quantiles[shift + i];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FQF_QuantileGradient(__global float *state_embeding,
                                   __global float *taus_embeding,
                                   __global float *quantiles_gr,
                                   __global float *state_gr,
                                   __global float *taus_gr)
  {
   size_t i = get_global_id(0);
   size_t total = get_global_size(0);
   size_t action = get_global_id(1);
   int shift = action * total;
//---
   float gradient = quantiles_gr[shift + i];
   state_gr[shift + i] = gradient * taus_embeding[shift + i];
   taus_gr[shift + i] = gradient * state_embeding[shift + i];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FQF_CosineGradient(__global float *softmax,
                                 __global float *output_gr,
                                 __global float *softmax_gr)
  {
   size_t i = get_global_id(0);
   size_t total = get_global_size(0);
   size_t action = get_global_id(1);
   int shift = action * total;
//---
   float cumul = 0;
//---
   for(int it = 0; it < i; it++)
      cumul += softmax[shift + it];
   float result = -M_PI_F * i *
                  sin(M_PI_F * i * (cumul + softmax[shift + i] / 2)) *
                  output_gr[shift + i];
//---
   for(int it = i + 1; it < total; it++)
     {
      cumul += softmax[shift + it - 1];
      float temp = cumul + softmax[shift + it] / 2;
      result += -M_PI_F * it * sin(M_PI_F * it * temp) * output_gr[shift + it] *
                softmax[shift + it] / temp;
     }
   softmax_gr[shift + i] += result;
  }
//+------------------------------------------------------------------+
//| Sparse Attention                                                 |
//+------------------------------------------------------------------+
__kernel void MHSparseAttentionScore(__global float *qkv,     ///<[in] Matrix of Querys, Keys, Values
                                     __global float *score, ///<[out] Matrix of Scores
                                     int dimension,         ///< Dimension of Key
                                     float sparse           ///< less than 1.0 coefficient of sparse
                                    )
  {
   int q = get_global_id(0);
   int h = get_global_id(1);
   int units = get_global_size(0);
   int heads = get_global_size(1);
//---
   int shift_q = dimension * (h + 3 * q * heads);
   int shift_s = units * (h + q * heads);
   int active_units = (int)max((float)(units * sparse), min((float)units, 3.0f));
//---
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   float sum = 0.0f;
   float min_s = 0.0f;
   float max_s = 0.0f;
//---
   for(int k = 0; k < units; k++)
     {
      float result = 0;
      int shift_k = dimension * (h + heads * (3 * k + 1));
      for(int i = 0; i < dimension; i++)
        {
         if((dimension - i) > 4)
           {
            result += dot((float4)(qkv[shift_q + i], qkv[shift_q + i + 1],
                                   qkv[shift_q + i + 2], qkv[shift_q + i + 3]),
                          (float4)(qkv[shift_k + i], qkv[shift_k + i + 1],
                                   qkv[shift_k + i + 2], qkv[shift_k + i + 3]));
            i += 3;
           }
         else
            result += (qkv[shift_q + i] * qkv[shift_k + i]);
        }
      score[shift_s + k] = result;
      if(k == 0)
         min_s = max_s = result;
      else
        {
         max_s = max(max_s, result);
         min_s = min(min_s, result);
        }
     }
//---
   int count = units;
//---
   while(count > active_units && min_s < max_s)
     {
      count = 0;
      float temp = max_s;
      for(int k = 0; k < units; k++)
        {
         float value = score[shift_s + k];
         if(value < min_s)
            continue;
         count++;
         if(value < temp && value > min_s)
            temp = value;
        }
      if(count > active_units)
         min_s = temp;
     }
//---
   if(max_s == 0.0f)
      max_s = 1.0f;
//---
   for(int k = 0; k < units; k++)
     {
      float value = score[shift_s + k];
      if(value < min_s)
        {
         score[shift_s + k] = 0.0f;
         continue;
        }
      value = exp(value / max_s / koef);
      score[shift_s + k] = value;
      sum += value;
     }
//---
   for(int k = 0; (k < units && sum > 1); k++)
     {
      float temp = score[shift_s + k];
      if(temp == 0.0f)
         continue;
      score[shift_s + k] = temp / sum;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MHSparseAttentionOut(__global float *scores, ///<[in] Matrix of Scores
                                   __global float *qkv,   ///<[in] Matrix of Values
                                   __global float *out,   ///<[out] Output tensor
                                   int dimension           ///< Dimension of Value
                                  )
  {
   int u = get_global_id(0);
   int units = get_global_size(0);
   int h = get_global_id(1);
   int heads = get_global_size(1);
//---
   int shift_s = units * (h + heads * u);
   int shift_out = dimension * (h + heads * u);
//---
   for(int d = 0; d < dimension; d++)
     {
      float result = 0;
      for(int v = 0; v < units; v++)
        {
         float cur_score = scores[shift_s + v];
         if(cur_score == 0)
            continue;
         int shift_v = dimension * (h + heads * (3 * v + 2)) + d;
         result += cur_score * qkv[shift_v];
        }
      out[shift_out + d] = result;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardMultiModels(__global float *matrix_w,   ///<[in] Weights matrix (m+1)*n, where m - number of neurons in layer and n - number of outputs (neurons in next layer)
                                     __global float *matrix_i, ///<[in] Inputs tensor
                                     __global float *matrix_o, ///<[out] Output tensor
                                     int inputs,               ///< Number of inputs
                                     int activation            ///< Activation type (#ENUM_ACTIVATION)
                                    )
  {
   int i = get_global_id(0);
   int outputs = get_global_size(0);
   int m = get_global_id(1);
   int models = get_global_size(1);
//---
   float sum = 0;
   float4 inp, weight;
   int shift = (inputs + 1) * (i + outputs * m);
   int shift_in = inputs * m;
   int shift_out = outputs * m;
//---
   for(int k = 0; k <= inputs; k = k + 4)
     {
      switch(inputs - k)
        {
         case 0:
            inp = (float4)(1, 0, 0, 0);
            weight = (float4)(matrix_w[shift + k], 0, 0, 0);
            break;
         case 1:
            inp = (float4)(matrix_i[shift_in + k], 1, 0, 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1], 0, 0);
            break;
         case 2:
            inp = (float4)(matrix_i[shift_in + k], matrix_i[shift_in + k + 1], 1, 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], 0);
            break;
         case 3:
            inp = (float4)(matrix_i[shift_in + k], matrix_i[shift_in + k + 1],
                           matrix_i[shift_in + k + 2], 1);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], matrix_w[shift + k + 3]);
            break;
         default:
            inp = (float4)(matrix_i[shift_in + k], matrix_i[shift_in + k + 1],
                           matrix_i[shift_in + k + 2], matrix_i[shift_in + k + 3]);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], matrix_w[shift + k + 3]);
            break;
        }
      float d = dot(inp, weight);
      if(isnan(sum + d))
         continue;
      sum += d;
     }
   if(isnan(sum))
      sum = 0;
//---
   matrix_o[shift_out + i] = fActivation(sum, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientMultiModels(__global float *matrix_w, ///<[in] Weights matrix (m+1)*n, where m - number
      ///< of neurons in previous layer and n - number
      ///< of neurons in current layer
      __global float *matrix_g, ///<[in] Tensor of gradients at current layer
      __global float *matrix_o, ///<[in] Previous layer Output tensor
      __global float *matrix_ig, ///<[out] Tensor of gradients at previous layer
      int outputs,               ///< Number of outputs
      int activation,            ///< Activation type (#ENUM_ACTIVATION),
      int model)
  {
   int i = get_global_id(0);
   int inputs = get_global_size(0);
   int m = get_global_id(1);
   int models = get_global_size(1);
//---
   int shift_in = inputs * m;
   if(model >= 0 && model != m)
     {
      matrix_ig[shift_in + i] = 0;
      return;
     }
//---
   int shift_out = outputs * m;
   int shift_w = (inputs + 1) * outputs * m;
   float sum = 0;
   float out = matrix_o[shift_in + i];
   float4 grad, weight;
//---
   for(int k = 0; k < outputs; k += 4)
     {
      switch(outputs - k)
        {
         case 1:
            weight = (float4)(matrix_w[shift_w + k * (inputs + 1) + i], 0, 0, 0);
            grad = (float4)(matrix_g[shift_out + k], 0, 0, 0);
            break;
         case 2:
            grad =
               (float4)(matrix_g[shift_out + k], matrix_g[shift_out + k + 1], 0, 0);
            weight = (float4)(matrix_w[shift_w + k * (inputs + 1) + i],
                              matrix_w[shift_w + (k + 1) * (inputs + 1) + i], 0, 0);
            break;
         case 3:
            grad = (float4)(matrix_g[shift_out + k], matrix_g[shift_out + k + 1],
                            matrix_g[shift_out + k + 2], 0);
            weight = (float4)(matrix_w[shift_w + k * (inputs + 1) + i],
                              matrix_w[shift_w + (k + 1) * (inputs + 1) + i],
                              matrix_w[shift_w + (k + 2) * (inputs + 1) + i], 0);
            break;
         default:
            grad = (float4)(matrix_g[shift_out + k], matrix_g[shift_out + k + 1],
                            matrix_g[shift_out + k + 2], matrix_g[shift_out + k + 3]);
            weight = (float4)(matrix_w[shift_w + k * (inputs + 1) + i],
                              matrix_w[shift_w + (k + 1) * (inputs + 1) + i],
                              matrix_w[shift_w + (k + 2) * (inputs + 1) + i],
                              matrix_w[shift_w + (k + 3) * (inputs + 1) + i]);
            break;
        }
      sum += dot(grad, weight);
     }
//---
   matrix_ig[shift_in + i] = Deactivation(sum, out, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsAdamMultiModels(
   __global float *matrix_w, ///<[in,out] Weights matrix (m+1)*n, where m -
   ///< number of neurons in previous layer and n -
   ///< number of neurons in current layer
   __global const float
   *matrix_g, ///<[in] Tensor of gradients at current layer
   __global const float *matrix_i, ///<[in] Inputs tensor
   __global float *matrix_m,      ///<[in,out] Matrix of first momentum
   __global float *matrix_v,      ///<[in,out] Matrix of seconfd momentum
   const int inputs,               ///< Number of inputs
   const float l,                  ///< Learning rates
   const float b1,                 ///< First momentum multiplier
   const float b2,                 ///< Second momentum multiplier
   const int model)
  {
   const int outputs = get_global_size(0);
   const int i = get_global_id(0);
   const int j = get_global_id(1);
   const int wi = (i + outputs * model) * (inputs + 1) + j * 4;
   float4 m, v, weight, inp;
   int shift_in = j * 4 + inputs * model;
   if((inputs + 1 - j * 4) < 0)
      return;
   switch(inputs + 1 - j * 4)
     {
      case 0:
         inp = (float4)(1, 0, 0, 0);
         weight = (float4)(matrix_w[wi], 0, 0, 0);
         m = (float4)(matrix_m[wi], 0, 0, 0);
         v = (float4)(matrix_v[wi], 0, 0, 0);
         break;
      case 1:
         inp = (float4)(matrix_i[shift_in], 1, 0, 0);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], 0, 0);
         m = (float4)(matrix_m[wi], matrix_m[wi + 1], 0, 0);
         v = (float4)(matrix_v[wi], matrix_v[wi + 1], 0, 0);
         break;
      case 2:
         inp = (float4)(matrix_i[shift_in], matrix_i[shift_in + 1], 1, 0);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], matrix_w[wi + 2], 0);
         m = (float4)(matrix_m[wi], matrix_m[wi + 1], matrix_m[wi + 2], 0);
         v = (float4)(matrix_v[wi], matrix_v[wi + 1], matrix_v[wi + 2], 0);
         break;
      case 3:
         inp = (float4)(matrix_i[shift_in], matrix_i[shift_in + 1],
                        matrix_i[shift_in + 2], 1);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], matrix_w[wi + 2],
                           matrix_w[wi + 3]);
         m = (float4)(matrix_m[wi], matrix_m[wi + 1], matrix_m[wi + 2],
                      matrix_m[wi + 3]);
         v = (float4)(matrix_v[wi], matrix_v[wi + 1], matrix_v[wi + 2],
                      matrix_v[wi + 3]);
         break;
      default:
         inp = (float4)(matrix_i[shift_in], matrix_i[shift_in + 1],
                        matrix_i[shift_in + 2], matrix_i[shift_in + 3]);
         weight = (float4)(matrix_w[wi], matrix_w[wi + 1], matrix_w[wi + 2],
                           matrix_w[wi + 3]);
         m = (float4)(matrix_m[wi], matrix_m[wi + 1], matrix_m[wi + 2],
                      matrix_m[wi + 3]);
         v = (float4)(matrix_v[wi], matrix_v[wi + 1], matrix_v[wi + 2],
                      matrix_v[wi + 3]);
         break;
     }
   float4 g = (float4)(matrix_g[(outputs + 1) * model + i]) * inp;
   float4 mt = b1 * m + (1 - b1) * g;
   float4 vt = b2 * v + (1 - b2) * pow(g, 2);
   float4 delta =
      l * (mt / (sqrt(vt) + 1.0e-37f) - (l1 * sign(weight) + l2 * weight));
   switch(min(inputs + 1 - j * 4, 3))
     {
      case 3:
         if(fabs(delta.s3) > 0)
            matrix_w[wi + 3] =
               clamp(matrix_w[wi + 3] + delta.s3, -MAX_WEIGHT, MAX_WEIGHT);
         matrix_m[wi + 3] = mt.s3;
         matrix_v[wi + 3] = vt.s3;
      case 2:
         if(fabs(delta.s2) > 0)
            matrix_w[wi + 2] =
               clamp(matrix_w[wi + 2] + delta.s2, -MAX_WEIGHT, MAX_WEIGHT);
         matrix_m[wi + 2] = mt.s2;
         matrix_v[wi + 2] = vt.s2;
      case 1:
         if(fabs(delta.s1) > 0)
            matrix_w[wi + 1] =
               clamp(matrix_w[wi + 1] + delta.s1, -MAX_WEIGHT, MAX_WEIGHT);
         matrix_m[wi + 1] = mt.s1;
         matrix_v[wi + 1] = vt.s1;
      case 0:
         if(fabs(delta.s0) > 0)
            matrix_w[wi] = clamp(matrix_w[wi] + delta.s0, -MAX_WEIGHT, MAX_WEIGHT);
         matrix_m[wi] = mt.s0;
         matrix_v[wi] = vt.s0;
         break;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void Concat_FeedForward(__global float *matrix_w,   ///<[in] Weights matrix (m+1)*n, where m - number
                                 ///< of neurons in layer and n - number of outputs
                                 ///< (neurons in next layer)
                                 __global float *matrix_i1, ///<[in] Inputs 1 tensor
                                 __global float *matrix_i2, ///<[in] Inputs 2 tensor
                                 __global float *matrix_o, ///<[out] Output tensor
                                 int inputs1,               ///< Number of inputs
                                 int inputs2,               ///< Number of inputs
                                 int activation             ///< Activation type (#ENUM_ACTIVATION)
                                )
  {
   int i = get_global_id(0);
   float sum = 0;
   float4 inp, weight;
   int shift = (inputs1 + inputs2 + 1) * i;
//---
//---
   for(int k = 0; k < inputs1; k += 4)
     {
      switch(inputs1 - k)
        {
         case 1:
            inp = (float4)(matrix_i1[k], 0, 0, 0);
            weight = (float4)(matrix_w[shift + k], 0, 0, 0);
            break;
         case 2:
            inp = (float4)(matrix_i1[k], matrix_i1[k + 1], 0, 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1], 0, 0);
            break;
         case 3:
            inp = (float4)(matrix_i1[k], matrix_i1[k + 1], matrix_i1[k + 2], 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], 0);
            break;
         default:
            inp = (float4)(matrix_i1[k], matrix_i1[k + 1], matrix_i1[k + 2],
                           matrix_i1[k + 3]);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], matrix_w[shift + k + 3]);
            break;
        }
      float d = dot(inp, weight);
      if(isnan(sum + d))
         continue;
      sum += d;
     }
//---
   shift += inputs1;
//---
   for(int k = 0; k < inputs2; k += 4)
     {
      switch(inputs2 - k)
        {
         case 1:
            inp = (float4)(matrix_i2[k], 0, 0, 0);
            weight = (float4)(matrix_w[shift + k], 0, 0, 0);
            break;
         case 2:
            inp = (float4)(matrix_i2[k], matrix_i2[k + 1], 0, 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1], 0, 0);
            break;
         case 3:
            inp = (float4)(matrix_i2[k], matrix_i2[k + 1], matrix_i2[k + 2], 0);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], 0);
            break;
         default:
            inp = (float4)(matrix_i2[k], matrix_i2[k + 1], matrix_i2[k + 2],
                           matrix_i2[k + 3]);
            weight = (float4)(matrix_w[shift + k], matrix_w[shift + k + 1],
                              matrix_w[shift + k + 2], matrix_w[shift + k + 3]);
            break;
        }
      float d = dot(inp, weight);
      if(isnan(sum + d))
         continue;
      sum += d;
     }
   sum += matrix_w[shift + inputs2];
//---
   if(isnan(sum))
      sum = 0;
//---
   matrix_o[i] = fActivation(sum, activation);;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void Concat_HiddenGradient(__global float *matrix_w,    ///<[in] Weights matrix (m+1)*n, where m - number of neurons in previous layer and n - number of neurons in current layer
                                    __global float *matrix_g, ///<[in] Tensor of gradients at current layer
                                    __global float *matrix_o1, ///<[in] Previous layer Output tensor
                                    __global float *matrix_o2, ///<[in] Previous layer Output tensor
                                    __global float *matrix_ig1, ///<[out] Tensor of gradients at previous layer
                                    __global float *matrix_ig2, ///<[out] Tensor of gradients at previous layer
                                    int outputs,                ///< Number of outputs
                                    int inputs1, int inputs2,
                                    int activation1, ///< Activation type (#ENUM_ACTIVATION)
                                    int activation2  ///< Activation type (#ENUM_ACTIVATION)
                                   )
  {
   int i = get_global_id(0);
   if(i >= (inputs1 + inputs2))
      return;
   int inputs = inputs1 + inputs2;
   float sum = 0;
   float out = (i < inputs1 ? matrix_o1[i] : matrix_o2[i - inputs1]);
   float4 grad, weight;
//---
   for(int k = 0; k < outputs; k += 4)
     {
      switch(outputs - k)
        {
         case 1:
            weight = (float4)(matrix_w[k * (inputs + 1) + i], 0, 0, 0);
            grad = (float4)(matrix_g[k], 0, 0, 0);
            break;
         case 2:
            grad = (float4)(matrix_g[k], matrix_g[k + 1], 0, 0);
            weight = (float4)(matrix_w[k * (inputs + 1) + i],
                              matrix_w[(k + 1) * (inputs + 1) + i], 0, 0);
            break;
         case 3:
            grad = (float4)(matrix_g[k], matrix_g[k + 1], matrix_g[k + 2], 0);
            weight = (float4)(matrix_w[k * (inputs + 1) + i],
                              matrix_w[(k + 1) * (inputs + 1) + i],
                              matrix_w[(k + 2) * (inputs + 1) + i], 0);
            break;
         default:
            grad = (float4)(matrix_g[k], matrix_g[k + 1], matrix_g[k + 2],
                            matrix_g[k + 3]);
            weight = (float4)(matrix_w[k * (inputs + 1) + i],
                              matrix_w[(k + 1) * (inputs + 1) + i],
                              matrix_w[(k + 2) * (inputs + 1) + i],
                              matrix_w[(k + 3) * (inputs + 1) + i]);
            break;
        }
      sum += dot(grad, weight);
     }
   if(isnan(sum))
      sum = 0;
   if(i < inputs1)
      matrix_ig1[i] = Deactivation(sum, out, activation1);
   else
      matrix_ig2[i - inputs1] = Deactivation(sum, out, activation2);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void Concat_UpdateWeightsMomentum(__global float *matrix_w,    ///<[in,out] Weights matrix (m+1)*n, where m - number of neurons in previous layer and n - number of neurons in current layer
      __global float *matrix_g, ///<[in] Tensor of gradients at current layer
      __global float *matrix_i1, ///<[in] Inputs tensor
      __global float *matrix_i2, ///<[in] Inputs tensor
      __global float
      *matrix_dw, ///<[in,out] Matrix of delta weights in last correction
      int inputs1,    ///< Number of inputs
      int inputs2,    ///< Number of inputs
      float learning_rates, ///< Learning rates
      float momentum        ///< Momentum multiplier
                                          )
  {
   int i = get_global_id(0);
   int j = get_global_id(1);
   if(j > (inputs1 + inputs2))
      return;
   int wi = i * (inputs1 + inputs2 + 1) + j;
   float inp = (j < inputs1 ? matrix_i1[j] : ((j - inputs1) < inputs2 ? matrix_i2[j - inputs1] : 1));
   float delta = learning_rates * matrix_g[i] * inp + momentum * matrix_dw[wi];
   if(!isnan(delta))
     {
      matrix_dw[wi] = delta;
      if(fabs(delta) > 0)
         matrix_w[wi] = clamp(matrix_w[wi] + delta, -MAX_WEIGHT, MAX_WEIGHT);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void Concat_UpdateWeightsAdam(__global float *matrix_w,   ///<[in,out] Weights matrix (m+1)*n, where m -
                                       ///< number of neurons in previous layer and n -
                                       ///< number of neurons in current layer
                                       __global const float
                                       *matrix_g, ///<[in] Tensor of gradients at current layer
                                       __global const float *matrix_i1, ///<[in] Inputs tensor
                                       __global const float *matrix_i2, ///<[in] Inputs tensor
                                       __global float *matrix_m,       ///<[in,out] Matrix of first momentum
                                       __global float *matrix_v,       ///<[in,out] Matrix of seconfd momentum
                                       const int inputs1,               ///< Number of inputs
                                       const int inputs2,               ///< Number of inputs
                                       const float l,                   ///< Learning rates
                                       const float b1,                  ///< First momentum multiplier
                                       const float b2                   ///< Second momentum multiplier
                                      )
  {
   const int i = get_global_id(0);
   const int j = get_global_id(1);
   if(j > (inputs1 + inputs2))
      return;
   const int wi = i * (inputs1 + inputs2 + 1) + j;
   float inp =
      (j < inputs1 ? matrix_i1[j]
       : ((j - inputs1) < inputs2 ? matrix_i2[j - inputs1] : 1));
   float weight = matrix_w[wi];
   float g = matrix_g[i] * inp;
   float mt = b1 * matrix_m[wi] + (1 - b1) * g;
   float vt = b2 * matrix_v[wi] + (1 - b2) * pow(g, 2);
   float delta =
      l * (mt / (sqrt(vt) + 1.0e-37f) - (l1 * sign(weight) + l2 * weight));
   if(fabs(delta) > 0)
      matrix_w[wi] = clamp(matrix_w[wi] + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[wi] = mt;
   matrix_v[wi] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SoftUpdate(__global float *target, ///<[in,out] Target matrix
                         __global const float *source, ///<[in] Source matrix
                         const float tau ///<[in] Multiplicator Tau
                        )
  {
   const int i = get_global_id(0);
   target[i] = source[i] * tau + (1.0f - tau) * target[i];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SoftUpdateAdam(__global float *target, __global const float *source,
                             __global float *matrix_m, ///<[in,out] Matrix of first momentum
                             __global float *matrix_v, ///<[in,out] Matrix of seconfd momentum
                             const float tau,          ///<[in] Multiplicator Tau
                             const float b1,           ///< First momentum multiplier
                             const float b2            ///< Second momentum multiplier
                            )
  {
   const int i = get_global_id(0);
   float m, v, weight;
   m = matrix_m[i];
   v = matrix_v[i];
   weight = target[i];
   float g = source[i] - weight;
   m = b1 * m + (1 - b1) * g;
   v = b2 * v + (1 - b2) * pow(g, 2);
   float delta = tau * m / (v != 0.0f ? sqrt(v) : 1.0f);
   if(fabs(delta) > 0)
      target[i] = clamp(weight + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[i] = m;
   matrix_v[i] = v;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SAC_AlphaLogProbs(__global float *outputs,
                                __global float *quantiles,
                                __global float *probs, __global float *alphas,
                                __global float *log_probs,
                                __global float *random, const int count_quants,
                                const int activation)
  {
   const int i = get_global_id(0);
   int shift = i * count_quants;
   float prob = 0;
   float value = 0;
   float sum = 0;
   float rnd = random[i];
//---
   for(int r = 0; r < count_quants; r++)
     {
      prob = probs[shift + r];
      sum += prob;
      if(sum >= rnd || r == (count_quants - 1))
        {
         value = quantiles[shift + r];
         break;
        }
     }
//---
   outputs[i] = fActivation(value, activation);
   log_probs[i] = -alphas[i] * log(prob);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SAC_AlphaGradients(__global float *outputs,
                                 __global float *gradient,
                                 __global float *log_probs,
                                 __global float *alphas_grad,
                                 const int activation)
  {
   const int i = get_global_id(0);
   float out = outputs[i];
//---
   float grad = -gradient[i] * log_probs[i];
//---
   alphas_grad[i] = Deactivation(grad, out, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SAC_OutputGradient(__global float *quantiles, __global float *delta_taus,
                                 __global float *output_gr, __global float *quantiles_gr,
                                 __global float *taus_gr, __global float *output,
                                 const int count_quants, const int activation)
  {
   size_t action = get_global_id(0);
   int shift = action * count_quants;
   float quant1 = -1e37f;
   float quant2 = 1e37f;
   int pos1 = -1;
   int pos2 = -1;
   float value = output[action];
//---
   for(int i = 0; i < count_quants; i++)
     {
      float quant = fActivation(quantiles[shift + i], activation);
      if(value >= quant && quant1 < quant)
        {
         quant1 = quant;
         pos1 = shift + i;
        }
      if(value < quant && quant2 > quant)
        {
         quant2 = quant;
         pos2 = shift + i;
        }
      quantiles_gr[shift + i] = 0.0f;
      taus_gr[shift + i] = 0.0f;
     }
   float gradient = output_gr[action];
   if(quant1 > -1e37f)
     {
      quantiles_gr[pos1] = gradient * delta_taus[pos1];
      taus_gr[pos1] = gradient * quant1;
     }
   if(quant2 < 1e37f)
     {
      quantiles_gr[pos2] = gradient * delta_taus[pos2];
      taus_gr[pos2] = gradient * quant2;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SAC_CalcLogProbs(__global float *outputs,
                               __global float *quantiles, __global float *probs,
                               __global float *alphas,
                               __global float *log_probs,
                               const int count_quants, const int activation)
  {
   const int i = get_global_id(0);
   int shift = i * count_quants;
   float quant1 = -1e37f;
   float quant2 = 1e37f;
   float prob1 = 0;
   float prob2 = 0;
   float value = outputs[i];
//---
   for(int q = 0; q < count_quants; q++)
     {
      float quant = fActivation(quantiles[shift + q], activation);
      if(value >= quant && quant1 < quant)
        {
         quant1 = quant;
         prob1 = probs[shift + q];
        }
      if(value < quant && quant2 > quant)
        {
         quant2 = quant;
         prob2 = probs[shift + q];
        }
     }
//---
   float prob = fabs(value - quant1) / fabs(quant2 - quant1);
   prob = clamp((1 - prob) * prob1 + prob * prob2, 1.0e-3f, 1.0f);
   log_probs[i] = -alphas[i] * log(prob);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void Embedding(__global float *inputs, __global float *outputs,
                        __global float *weights, __global int *windows,
                        __global float *std, const int stack_size)
  {
   const int window_out = get_global_size(0);
   const int pos = get_global_id(0);
   const int emb = get_global_id(1);
   const int emb_total = get_global_size(1);
   const int shift_out = emb * window_out + pos;
   const int step = emb_total * window_out;
   const uint ls = min((uint)get_local_size(0), (uint)LOCAL_ARRAY_SIZE);
//---
   for(int i = stack_size - 1; i > 0; i--)
      outputs[i * step + shift_out] = outputs[(i - 1) * step + shift_out];
   int shift_in = 0;
//---
   for(int i = 0; i < emb; i++)
      shift_in += windows[i];
   const int window_in = windows[emb];
   const int shift_weights = (shift_in + emb) * window_out + (window_in + 1) * pos;
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   if(pos < LOCAL_ARRAY_SIZE)
      temp[pos] = 0;
   BarrierLoc;
//---
   float value = weights[shift_weights + window_in];
//---
   for(int i = 0; i < window_in; i++)
      value += inputs[shift_in + i] * weights[shift_weights + i];
//---
   for(int i = 0; i < window_out; i += ls)
     {
      if(pos >= i && pos < (i + ls))
         temp[pos % ls] += value;
      BarrierLoc;
     }
//---
   int count = ls;
   do
     {
      count = (count + 1) / 2;
      if(pos + count < ls)
        {
         if(pos < count)
            temp[pos] += temp[pos + count];
         temp[pos + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//---
   value -= temp[0] / (float)window_out;
   BarrierLoc;
//---
   if(pos < LOCAL_ARRAY_SIZE)
      temp[pos] = 0;
   BarrierLoc;
//---
   for(int i = 0; i < window_out; i += ls)
     {
      if(pos >= i && pos < (i + ls))
         temp[pos % ls] += pow(value, 2.0f) / (float)window_out;
      BarrierLoc;
     }
//---
   count = ls;
   do
     {
      count = (count + 1) / 2;
      if(pos + count < ls)
        {
         if(pos < count)
            temp[pos] += temp[pos + count];
         temp[pos + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//---
   if(temp[0] > 0)
      value /= sqrt(temp[0]);
//---
   outputs[shift_out] = value;
   if(pos == 0)
      std[emb] = sqrt(temp[0]);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void EmbeddingHiddenGradient(__global float *inputs_gradient,
                                      __global float *outputs_gradient,
                                      __global float *weights,
                                      __global int *windows,
                                      __global float *std,
                                      const int window_out)
  {
   const int pos = get_global_id(0);
   int emb = -1;
   int count = 0;
   do
     {
      emb++;
      count += windows[emb];
     }
   while(count < pos);
   const int shift_out = emb * window_out;
   const int shift_weights = pos + (count - windows[emb] + emb) * window_out;
//---
   float value = 0;
//---
   for(int i = 0; i < window_out; i++)
      value += outputs_gradient[shift_out + i] * weights[shift_weights + i * window_out];
   float s = std[emb];
   if(s > 0)
      value /= s;
//---
   inputs_gradient[pos] = value;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void EmbeddingUpdateWeightsAdam(__global float *weights,   ///<[in,out] Weights matrix (m+1)*n, where m -
      ///< number of neurons in previous layer and n -
      ///< number of neurons in current layer
      __global const float
      *gradient,                ///<[in] Tensor of gradients at current layer
      __global const float *inputs, ///<[in] Inputs tensor
      __global float *matrix_m,    ///<[in,out] Matrix of first momentum
      __global float *matrix_v,    ///<[in,out] Matrix of seconfd momentum
      __global int *windows, __global float *std, const int window_out,
      const float l,  ///< Learning rates
      const float b1, ///< First momentum multiplier
      const float b2  ///< Second momentum multiplier
                                        )
  {
   const int i = get_global_id(0);
   int emb = -1;
   int count = 0;
   int shift = 0;
   int window_in = 0;
   do
     {
      emb++;
      shift = count;
      window_in = windows[emb];
      count += (window_in + 1) * window_out;
     }
   while(count <= i);
   const int shift_out = emb * window_out;
   int shift_in = shift / window_out - emb;
   shift = (i - shift) % (window_in + 1);
   float inp = 1.0f;
   if(shift < window_in)
      inp = inputs[shift_in + shift];
//---
   float weight = weights[i];
   float g = gradient[shift_out] * inp / std[emb];
   float mt = b1 * matrix_m[i] + (1 - b1) * g;
   float vt = b2 * matrix_v[i] + (1 - b2) * pow(g, 2);
   float delta =
      l * (mt / (sqrt(vt) + 1.0e-37f) - (l1 * sign(weight) + l2 * weight));
   if(fabs(delta) > 0)
      weights[i] = clamp(weights[i] + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[i] = mt;
   matrix_v[i] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void Transpose(__global float *matrix_in, ///<[in] Input matrix
                        __global float *matrix_out ///<[out] Output matrix
                       )
  {
   const int r = get_global_id(0);
   const int c = get_global_id(1);
   const int rows = get_global_size(0);
   const int cols = get_global_size(1);
//---
   matrix_out[c * rows + r] = matrix_in[r * cols + c];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MH2AttentionOut(__global float *q,    ///<[in] Matrix of Querys
                              __global float *kv,   ///<[in] Matrix of Keys
                              __global float *score, ///<[out] Matrix of Scores
                              __global float *out, ///<[out] Matrix of attention
                              int dimension,        ///< Dimension of Key
                              int heads_kv,
                              int mask ///< 1 - calc only previous units, 0 - calc all
                             )
  {
//--- init
   const int q_id = get_global_id(0);
   const int k = get_local_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int kunits = get_local_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_k = dimension * (2 *  heads_kv * k + h_kv);
   const int shift_v = dimension * (2 *  heads_kv * k + heads_kv + h_kv);
   const int shift_s = kunits * (q_id *  heads + h) + k;
   const uint ls = min((uint)get_local_size(1), (uint)LOCAL_ARRAY_SIZE);
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   __local float temp[LOCAL_ARRAY_SIZE];
//--- Score
   float sum = MIN_VALUE;
   if(mask == 0 || q_id >= k)
     {
      sum = 0;
      for(int d = 0; d < dimension; d++)
         sum += q[shift_q + d] * kv[shift_k + d];
     }
   float sc = LocalSoftMax(IsNaNOrInf(sum / koef, MIN_VALUE), 1, temp);
   score[shift_s] = sc;
//--- out
   for(int d = 0; d < dimension; d++)
     {
      BarrierLoc;
      sum = LocalSum(IsNaNOrInf(kv[shift_v + d ] * sc, 0), 1, temp);
      //---
      if(k == 0)
         out[shift_q + d] = sum;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MH2AttentionInsideGradients(__global float *q, __global float *q_g,
      __global float *kv, __global float *kv_g,
      __global float *scores, __global float *gradient,
      int kunits, int heads_kv)
  {
//--- init
   const int q_id = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h) + d;
   const int shift_s = q_id * kunits * heads + h * kunits;
   const int shift_g = h * dimension + d;
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
//--- Calculating Value's gradients
   int step_score = kunits * heads;
   if(h < heads_kv)
     {
      //---
      for(int v = q_id; v < kunits; v += qunits)
        {
         float grad = 0;
         for(int hq = h; hq < heads; hq += heads_kv)
           {
            int shift_score = hq * kunits + v;
            for(int g = 0; g < qunits; g++)
               grad += gradient[shift_g + dimension * (hq - h + g  * heads)] *
                       scores[shift_score + g * step_score];
           }
         int shift_v = dimension * (2 *  heads_kv * v + heads_kv + h) + d;
         kv_g[shift_v] = grad;
        }
     }
//--- Calculating Query's gradients
   float grad = 0;
   float out_g = gradient[shift_g + q_id * dimension];
   int shift_val = (heads_kv + h_kv) * dimension + d;
   int shift_key = h_kv * dimension + d;
//---
   for(int k = 0; k < kunits; k++)
     {
      float sc_g = 0;
      float sc = scores[shift_s + k];
      if(sc == 0)
         continue;
      for(int v = 0; v < kunits; v++)
         sc_g += scores[shift_s + v] * out_g * kv[shift_val + 2 * v * heads_kv * dimension] *
                 ((float)(k == v) - sc);
      grad += sc_g * kv[shift_key + 2 * k * heads_kv * dimension];
     }
   q_g[shift_q] = grad / koef;
//--- Calculating Key's gradients
   if(h < heads_kv)
     {
      //---
      for(int k = q_id; k < kunits; k += qunits)
        {
         int shift_k = dimension * (2 *  heads_kv * k + h_kv) + d;
         grad = 0;
         for(int hq = h; hq < heads; hq++)
           {
            int shift_score = hq * kunits + k;
            float val = kv[shift_k + heads_kv * dimension];
            for(int scr = 0; scr < qunits; scr++)
              {
               float sc_g = 0;
               int shift_sc = scr * kunits * heads;
               float sc = scores[shift_sc + k];
               if(sc == 0)
                  continue;
               for(int v = 0; v < kunits; v++)
                  sc_g += scores[shift_sc + v] * gradient[shift_g + scr * dimension] *
                          val * ((float)(k == v) - sc);
               grad += sc_g * q[shift_q + scr * dimension];
              }
           }
         kv_g[shift_k] = grad / koef;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CGConv_HiddenGradient(__global const float *matrix_g,    ///<[in] Tensor of gradients at current layer
                                    __global const float *matrix_f, ///<[in] Previous layer Output tensor
                                    __global const float *matrix_s, ///<[in] Previous layer Output tensor
                                    __global float *matrix_fg, ///<[out] Tensor of gradients at previous layer
                                    __global float *matrix_sg, ///<[out] Tensor of gradients at previous layer
                                    const int activationf,           ///< Activation type (#ENUM_ACTIVATION)
                                    const int activations            ///< Activation type (#ENUM_ACTIVATION)
                                   )
  {
   int i = get_global_id(0);
//---
   float grad = matrix_g[i];
   float f = matrix_f[i];
   float s = matrix_s[i];
//---
   float sg = grad * f;
   float fg = grad * s;
//---
   matrix_fg[i] = Deactivation(fg, f, activationf);
   matrix_sg[i] = Deactivation(sg, s, activations);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void XCiTFeedForward(__global float *qkv, __global float *score,
                              __global float *out)
  {
   const size_t d = get_local_id(0);
   const size_t dimension = get_local_size(0);
   const size_t u = get_local_id(1);
   const size_t units = get_local_size(1);
   const size_t h = get_global_id(2);
   const size_t heads = get_global_size(2);
//---
   const uint ls_u = min((uint)units, (uint)LOCAL_ARRAY_SIZE);
   const uint ls_d = min((uint)dimension, (uint)LOCAL_ARRAY_SIZE);
   __local float q[LOCAL_ARRAY_SIZE][LOCAL_ARRAY_SIZE];
   __local float k[LOCAL_ARRAY_SIZE][LOCAL_ARRAY_SIZE];
//--- Normalize Query and Key
   for(int cur_d = 0; cur_d < dimension; cur_d += ls_d)
     {
      float q_val = 0;
      float k_val = 0;
      //---
      if(d < ls_d && (cur_d + d) < dimension && u < ls_u)
        {
         for(int count = u; count < units; count += ls_u)
           {
            int shift = count * dimension * heads * 3 + dimension * h + cur_d + d;
            q_val += pow(qkv[shift], 2.0f);
            k_val += pow(qkv[shift + dimension * heads], 2.0f);
           }
         q[u][d] = q_val;
         k[u][d] = k_val;
        }
      BarrierLoc;
      //---
      uint count = ls_u;
      do
        {
         count = (count + 1) / 2;
         if(d < ls_d)
           {
            if(u < ls_u && u < count && (u + count) < units)
              {
               float q_val = q[u][d] + q[u + count][d];
               float k_val = k[u][d] + k[u + count][d];
               q[u + count][d] = 0;
               k[u + count][d] = 0;
               q[u][d] = q_val;
               k[u][d] = k_val;
              }
           }
         BarrierLoc;
        }
      while(count > 1);
      //---
      int shift = u * dimension * heads * 3 + dimension * h + cur_d;
      qkv[shift] = qkv[shift] / sqrt(q[0][d]);
      qkv[shift + dimension * heads] =
         qkv[shift + dimension * heads] / sqrt(k[0][d]);
      BarrierLoc;
     }
//--- Score
   int step = dimension * heads * 3;
//---
   for(int cur_r = 0; cur_r < dimension; cur_r += ls_u)
     {
      for(int cur_d = 0; cur_d < dimension; cur_d += ls_d)
        {
         if(u < ls_d && d < ls_d)
            q[u][d] = 0;
         BarrierLoc;
         //---
         if((cur_r + u) < ls_d && (cur_d + d) < ls_d)
           {
            int shift_q = dimension * h + cur_d + d;
            int shift_k = dimension * (heads + h) + cur_r + u;
            float scr = 0;
            for(int i = 0; i < units; i++)
               scr += qkv[shift_q + i * step] * qkv[shift_k + i * step];
            scr = exp(scr / sqrt((float)units));
            score[(cur_r + u) * dimension * heads + dimension * h + cur_d + d] =
               scr;
            q[u][d] += scr;
           }
        }
      BarrierLoc;
      //---
      int count = ls_d;
      do
        {
         count = (count + 1) / 2;
         if(u < ls_d)
           {
            if(d < ls_d && d < count && (d + count) < dimension)
               q[u][d] += q[u][d + count];
            if(d + count < ls_d)
               q[u][d + count] = 0;
           }
         BarrierLoc;
        }
      while(count > 1);
      //---
      if((cur_r + u) < ls_d)
         score[(cur_r + u) * dimension * heads + dimension * h + d] /= q[u][0];
      BarrierLoc;
     }
//---
   int shift_out = dimension * (u * heads + h) + d;
   int shift_s = dimension * (heads * d + h);
   int shift_v = dimension * (heads * (u * 3 + 2) + h);
   float sum = 0;
//---
   for(int i = 0; i < dimension; i++)
      sum += qkv[shift_v + i] * score[shift_s + i];
   out[shift_out] = sum;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void XCiTInsideGradients(__global float *qkv, __global float *qkv_g,
                                  __global float *scores,
                                  __global float *gradient)
  {
//--- init
   const int q = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int units = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int shift_q = dimension * (heads * 3 * q + h);
   const int shift_k = dimension * (heads * (3 * q + 1) + h);
   const int shift_v = dimension * (heads * (3 * q + 2) + h);
   const int shift_g = dimension * (heads * q + h);
   int shift_score = dimension * h;
   int step_score = dimension * heads;
//--- Calculating Value's gradients
   float sum = 0;
//---
   for(int i = 0; i < dimension; i++)
      sum += gradient[shift_g + i] * scores[shift_score + d + i * step_score];
   qkv_g[shift_v + d] = sum;
//--- Calculating Query's gradients
   float grad = 0;
   float val = qkv[shift_v + d];
//---
   for(int k = 0; k < dimension; k++)
     {
      float sc_g = 0;
      float sc = scores[shift_score + k];
      for(int v = 0; v < dimension; v++)
         sc_g += scores[shift_score + v] * val *
                 gradient[shift_g + v * dimension] * ((float)(k == v) - sc);
      grad += sc_g * qkv[shift_k + k];
     }
   qkv_g[shift_q + d] = grad / sqrt((float)units);
//--- Calculating Key's gradients
   grad = 0;
   float out_g = gradient[shift_g];
//---
   for(int scr = 0; scr < dimension; scr++)
     {
      float sc_g = 0;
      int shift_sc = scr * dimension * heads;
      float sc = scores[shift_sc + d];
      for(int v = 0; v < dimension; v++)
         sc_g += scores[shift_sc + v] * out_g * qkv[shift_v + v] *
                 ((float)(d == v) - sc);
      grad += sc_g * qkv[shift_q + scr];
     }
   qkv_g[shift_k + d] = grad / sqrt((float)units);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DOTFeedForward(__global float *qkv, __global float *score,
                             __global float *rpb, __global float *out)
  {
   const size_t d = get_local_id(0);
   const size_t dimension = get_local_size(0);
   const size_t u = get_global_id(1);
   const size_t units = get_global_size(1);
   const size_t h = get_global_id(2);
   const size_t heads = get_global_size(2);
//---
   uint step = 3 * dimension * heads;
   uint start = max((int)u - 1, 0);
   uint stop = min((int)u + 1, (int)units - 1);
   uint shift_q = u * step + h * dimension;
   uint shift_k = start * step + dimension * (heads + h);
   uint shift_score = u * 3 * heads;
//---
   const uint ls_d = min((uint)dimension, (uint)LOCAL_ARRAY_SIZE);
   __local float temp[LOCAL_ARRAY_SIZE][3];
//--- Score
   if(d < ls_d)
     {
      //---
      for(uint pos = start; pos <= stop; pos++)
         temp[d][pos - start] = 0;
      //---
      for(uint dim = d; dim < dimension; dim += ls_d)
        {
         float q = qkv[shift_q + dim];
         for(uint pos = start; pos <= stop; pos++)
           {
            uint i = pos - start;
            temp[d][i] = temp[d][i] + q * qkv[shift_k + i * step + dim];
           }
        }
      BarrierLoc;
      //---
      int count = ls_d;
      //---
      do
        {
         count = (count + 1) / 2;
         if(d < count && (d + count) < dimension)
            for(uint i = 0; i <= (stop - start); i++)
              {
               temp[d][i] += temp[d + count][i];
               temp[d + count][i] = 0;
              }
         BarrierLoc;
        }
      while(count > 1);
     }
//---
   if(d == 0)
     {
      float sum = 0;
      //---
      for(uint i = 0; i <= (stop - start); i++)
        {
         temp[0][i] = exp(temp[0][i] + rpb[shift_score + i]);
         sum += temp[0][i];
        }
      //---
      for(uint i = 0; i <= (stop - start); i++)
        {
         temp[0][i] = temp[0][i] / sum;
         score[shift_score + i] = temp[0][i];
        }
     }
   BarrierLoc;
//---
   int shift_out = dimension * (u * heads + h) + d;
   int shift_v = dimension * (heads * (u * 3 + 2) + h);
   float sum = 0;
//---
   for(uint i = 0; i <= (stop - start); i++)
      sum += qkv[shift_v + i] * temp[0][i];
   out[shift_out] = sum;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DOTInsideGradients(__global float *qkv, __global float *qkv_g,
                                 __global float *scores, __global float *rpb,
                                 __global float *rpb_g,
                                 __global float *gradient)
  {
//--- init
   const uint u = get_global_id(0);
   const uint d = get_global_id(1);
   const uint h = get_global_id(2);
   const uint units = get_global_size(0);
   const uint dimension = get_global_size(1);
   const uint heads = get_global_size(2);
//---
   uint step = 3 * dimension * heads;
   uint start = max((int)u - 1, 0);
   uint stop = min((int)u + 1, (int)units - 1);
   const uint shift_q = u * step + dimension * h + d;
   const uint shift_k = u * step + dimension * (heads + h) + d;
   const uint shift_v = u * step + dimension * (2 * heads + h) + d;
//--- Calculating Value's gradients
   float sum = 0;
//---
   for(uint i = start; i <= stop; i++)
     {
      int shift_score = i * 3 * heads;
      if(u == i)
        {
         shift_score += (uint)(u > 0);
        }
      else
        {
         if(u > i)
            shift_score += (uint)(start > 0) + 1;
        }
      uint shift_g = dimension * (i * heads + h) + d;
      sum += gradient[shift_g] * scores[shift_score];
     }
   qkv_g[shift_v] = sum;
//--- Calculating Query's gradients
   float grad = 0;
   uint shift_score = u * heads * 3;
//---
   for(int k = start; k <= stop; k++)
     {
      float sc_g = 0;
      float sc = scores[shift_score + k - start];
      for(int v = start; v <= stop; v++)
         for(int dim = 0; dim < dimension; dim++)
            sc_g += scores[shift_score + v - start] *
                    qkv[v * step + dimension * (2 * heads + h) + dim] *
                    gradient[dimension * (u * heads + h) + dim] *
                    ((float)(k == v) - sc);
      grad += sc_g * qkv[k * step + dimension * (heads + h) + d];
      if(d == 0)
         rpb_g[shift_score + k - start] = sc_g;
     }
   qkv_g[shift_q] = grad;
//--- Calculating Key's gradients
   grad = 0;
//---
   for(int q = start; q <= stop; q++)
     {
      float sc_g = 0;
      shift_score = q * heads * 3;
      if(u == q)
         shift_score += (uint)(u > 0);
      else
        {
         if(u > q)
            shift_score += (uint)(start > 0) + 1;
        }
      float sc = scores[shift_score];
      for(int v = start; v <= stop; v++)
        {
         shift_score = v * heads * 3;
         if(u == v)
            shift_score += (uint)(u > 0);
         else
           {
            if(u > v)
               shift_score += (uint)(start > 0) + 1;
           }
         for(int dim = 0; dim < dimension; dim++)
            sc_g += scores[shift_score] * qkv[shift_v - d + dim] *
                    gradient[dimension * (v * heads + h) + d] *
                    ((float)(d == v) - sc);
        }
      grad += sc_g * qkv[q * step + dimension * h + d];
     }
   qkv_g[shift_k] = grad;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void RPBUpdateAdam(__global float *target, __global const float *gradient,
                            __global float *matrix_m, ///<[in,out] Matrix of first momentum
                            __global float *matrix_v, ///<[in,out] Matrix of seconfd momentum
                            const float b1,           ///< First momentum multiplier
                            const float b2            ///< Second momentum multiplier
                           )
  {
   const int i = get_global_id(0);
   float m, v, weight;
   m = matrix_m[i];
   v = matrix_v[i];
   weight = target[i];
   float g = gradient[i];
   m = b1 * m + (1 - b1) * g;
   v = b2 * v + (1 - b2) * pow(g, 2);
   float delta = m / (v != 0.0f ? sqrt(v) : 1.0f);
   target[i] = clamp(weight + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[i] = m;
   matrix_v[i] = v;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void GTEFeedForward(__global float *qkv, __global float *score,
                             __global float *out, int dimension)
  {
   const size_t cur_q = get_global_id(0);
   const size_t units_q = get_global_size(0);
   const size_t cur_k = get_local_id(1);
   const size_t units_k = get_local_size(1);
   const size_t h = get_global_id(2);
   const size_t heads = get_global_size(2);
//---
   int shift_q = dimension * (cur_q + h * units_q);
   int shift_k = (cur_k + h * units_k + heads * units_q);
   int shift_v = dimension * (h * units_k + heads * (units_q + units_k));
   int shift_score_con = units_k * (cur_q * 2 * heads + h) + cur_k;
   int shift_score_notcon = units_k * (cur_q * 2 * heads + heads + h) + cur_k;
   int shift_out_con = dimension * (cur_q + h * units_q);
   int shift_out_notcon = dimension * (cur_q + units_q * (h + heads));
//---
   const uint ls_score = min((uint)units_k, (uint)LOCAL_ARRAY_SIZE);
   __local float local_score[LOCAL_ARRAY_SIZE][2];
//--- Score
   float scr = 0;
//---
   for(int d = 0; d < dimension; d++)
      scr += qkv[shift_q + d] * qkv[shift_k + d];
   scr = exp(min(scr / sqrt((float)dimension), 30.0f));
   if(cur_q == cur_k)
     {
      score[shift_score_con] = scr;
      score[shift_score_notcon] = scr;
      if(cur_k < ls_score)
        {
         local_score[cur_k][0] = scr;
         local_score[cur_k][1] = scr;
        }
     }
   else
     {
      if(abs(cur_q - cur_k) == 1)
        {
         score[shift_score_con] = scr;
         score[shift_score_notcon] = 0;
         if(cur_k < ls_score)
           {
            local_score[cur_k][0] = scr;
            local_score[cur_k][1] = 0;
           }
        }
      else
        {
         score[shift_score_con] = 0;
         score[shift_score_notcon] = scr;
         if(cur_k < ls_score)
           {
            local_score[cur_k][0] = 0;
            local_score[cur_k][1] = scr;
           }
        }
     }
   BarrierLoc;
//---
   for(int k = ls_score; k < units_k; k += ls_score)
     {
      if((cur_k + k) < units_k)
        {
         local_score[cur_k][0] += score[shift_score_con + k];
         local_score[cur_k][1] += score[shift_score_notcon + k];
        }
     }
   BarrierLoc;
//---
   int count = ls_score;
   do
     {
      count = (count + 1) / 2;
      if(cur_k < count)
        {
         if((cur_k + count) < units_k)
           {
            local_score[cur_k][0] += local_score[cur_k + count][0];
            local_score[cur_k][1] += local_score[cur_k + count][1];
            local_score[cur_k + count][0] = 0;
            local_score[cur_k + count][1] = 0;
           }
        }
      BarrierLoc;
     }
   while(count > 1);
   BarrierLoc;
//---
   score[shift_score_con] /= local_score[0][0];
   score[shift_score_notcon] /= local_score[0][1];
   BarrierLoc;
//---
   shift_score_con -= cur_k;
   shift_score_notcon -= cur_k;
//---
   for(int d = 0; d < dimension; d += ls_score)
     {
      if((cur_k + d) < dimension)
        {
         float sum_con = 0;
         float sum_notcon = 0;
         for(int v = 0; v < units_k; v++)
           {
            sum_con += qkv[shift_v + v * dimension + cur_k + d] *
                       score[shift_score_con + v];
            sum_notcon += qkv[shift_v + v * dimension + cur_k + d] *
                          score[shift_score_notcon + v];
           }
         out[shift_out_con + cur_k + d] = sum_con;
         out[shift_out_notcon + cur_k + d] = sum_notcon;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void GTEInsideGradients(__global float *qkv, __global float *qkv_g,
                                 __global float *scores,
                                 __global float *gradient)
  {
//--- init
   const uint u = get_global_id(0);
   const uint d = get_global_id(1);
   const uint h = get_global_id(2);
   const uint units = get_global_size(0);
   const uint dimension = get_global_size(1);
   const uint heads = get_global_size(2);
//--- Calculating Value's gradients
     {
      int shift_out_con = dimension * h * units + d;
      int shift_out_notcon = dimension * units * (h + heads) + d;
      int shift_score_con = units * h + u;
      int shift_score_notcon = units * (heads + h) + u;
      int step_score = units * 2 * heads;
      int shift_v = dimension * (h * units + 2 * heads * units + u) + d;
      //---
      float sum = 0;
      //---
      for(uint i = 0; i <= units; i++)
        {
         sum += gradient[shift_out_con + i * dimension] *
                scores[shift_score_con + i * step_score];
         sum += gradient[shift_out_notcon + i * dimension] *
                scores[shift_score_notcon + i * step_score];
        }
      qkv_g[shift_v] = sum;
     }
//--- Calculating Query's gradients
     {
      int shift_q = dimension * (u + h * units) + d;
      int shift_out_con = dimension * (h * units + u) + d;
      int shift_out_notcon = dimension * (u + units * (h + heads)) + d;
      int shift_score_con = units * h;
      int shift_score_notcon = units * (heads + h);
      int shift_v = dimension * (h * units + 2 * heads * units);
      float grad = 0;
      //---
      for(int k = 0; k < units; k++)
        {
         int shift_k = (k + h * units + heads * units) + d;
         float sc_g = 0;
         float sc_con = scores[shift_score_con + k];
         float sc_notcon = scores[shift_score_notcon + k];
         for(int v = 0; v < units; v++)
            for(int dim = 0; dim < dimension; dim++)
              {
               sc_g += scores[shift_score_con + v] *
                       qkv[shift_v + v * dimension + dim] *
                       gradient[shift_out_con + dim] * ((float)(k == v) - sc_con);
               sc_g += scores[shift_score_notcon + v] *
                       qkv[shift_v + v * dimension + dim] *
                       gradient[shift_out_notcon + dim] *
                       ((float)(k == v) - sc_notcon);
              }
         grad += sc_g * qkv[shift_k];
        }
      qkv_g[shift_q] = grad;
     }
//--- Calculating Key's gradients
     {
      int shift_k = (u + (h + heads) * units) + d;
      int shift_out_con = dimension * h * units + d;
      int shift_out_notcon = dimension * units * (h + heads) + d;
      int shift_score_con = units * h + u;
      int shift_score_notcon = units * (heads + h) + u;
      int step_score = units * 2 * heads;
      int shift_v = dimension * (h * units + 2 * heads * units);
      float grad = 0;
      //---
      for(int q = 0; q < units; q++)
        {
         int shift_q = dimension * (q + h * units) + d;
         float sc_g = 0;
         float sc_con = scores[shift_score_con + u + q * step_score];
         float sc_notcon = scores[shift_score_notcon + u + q * step_score];
         for(int g = 0; g < units; g++)
           {
            for(int dim = 0; dim < dimension; dim++)
              {
               sc_g += scores[shift_score_con + g] *
                       qkv[shift_v + u * dimension + dim] *
                       gradient[shift_out_con + g * dimension + dim] *
                       ((float)(u == g) - sc_con);
               sc_g += scores[shift_score_notcon + g] *
                       qkv[shift_v + u * dimension + dim] *
                       gradient[shift_out_notcon + g * dimension + dim] *
                       ((float)(u == g) - sc_notcon);
              }
           }
         grad += sc_g * qkv[shift_q];
        }
      qkv_g[shift_k] = grad;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardNODEF(__global float *matrix_w,   ///<[in] Weights matrix (m+1)*n, where m - input
                               ///< window and n - output window
                               __global float *matrix_i, ///<[in] Inputs tensor
                               __global float *matrix_o, ///<[out] Output tensor
                               int dimension,            ///< input dimension
                               float step,               ///< h
                               int activation            ///< Activation type (#ENUM_ACTIVATION)
                              )
  {
   int d = get_global_id(0);
   int dimension_out = get_global_size(0);
   int v = get_global_id(1);
   int variables = get_global_size(1);
   int i = get_global_id(2);
   int lenth = get_global_size(2);
//---
   int shift = variables * i + v;
   int input_shift = shift * dimension;
   int output_shift = shift * dimension_out + d;
   int weight_shift = (v * dimension_out + d) * (dimension + 2);
//---
   float sum = matrix_w[dimension + 1 + weight_shift] +
               matrix_w[dimension + weight_shift] * step;
//---
   for(int w = 0; w < dimension; w++)
      sum += matrix_w[w + weight_shift] * matrix_i[input_shift + w];
//---
   if(isnan(sum))
      sum = 0;
//---
   matrix_o[output_shift] = fActivation(sum, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardNODEInpK(__global float *matrix_i,   ///<[in] Inputs tensor
                                  __global float *matrix_k1,  ///<[in] K1 tensor
                                  __global float *matrix_k2,  ///<[in] K2 tensor
                                  __global float *matrix_k3,  ///<[in] K3 tensor
                                  __global float *matrix_k4,  ///<[in] K4 tensor
                                  __global float *matrix_k5,  ///<[in] K5 tensor
                                  __global float *matrix_k6,  ///<[in] K6 tensor
                                  __global float *matrix_beta, ///<[in] beta tensor
                                  __global float *matrix_o    ///<[out] Output tensor
                                 )
  {
   int i = get_global_id(0);
//---
   float sum = matrix_i[i];
//---
   for(int b = 0; b < 6; b++)
     {
      float beta = matrix_beta[b];
      if(beta == 0.0f || isnan(beta))
         continue;
      //---
      float val = 0.0f;
      switch(b)
        {
         case 0:
            val = matrix_k1[i];
            break;
         case 1:
            val = matrix_k2[i];
            break;
         case 2:
            val = matrix_k3[i];
            break;
         case 3:
            val = matrix_k4[i];
            break;
         case 4:
            val = matrix_k5[i];
            break;
         case 5:
            val = matrix_k6[i];
            break;
        }
      if(val == 0.0f || isnan(val))
         continue;
      //---
      sum += val * beta;
     }
//---
   matrix_o[i] = sum;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void HiddenGradientNODEInpK(__global float *matrix_ig,  ///<[in] Inputs tensor
                                     __global float *matrix_k1g, ///<[in] K1 tensor
                                     __global float *matrix_k2g, ///<[in] K2 tensor
                                     __global float *matrix_k3g, ///<[in] K3 tensor
                                     __global float *matrix_k4g, ///<[in] K4 tensor
                                     __global float *matrix_k5g, ///<[in] K5 tensor
                                     __global float *matrix_k6g, ///<[in] K6 tensor
                                     __global float *matrix_beta, ///<[in] beta tensor
                                     __global float *matrix_og   ///<[out] Output tensor
                                    )
  {
   int i = get_global_id(0);
//---
   float grad = IsNaNOrInf(matrix_og[i], 0);
   matrix_ig[i] = grad;
//---
   for(int b = 0; b < 6; b++)
     {
      float beta = IsNaNOrInf(matrix_beta[b], 0.0f);
      //---
      float val = IsNaNOrInf(beta * grad, 0.0f);
      switch(b)
        {
         case 0:
            matrix_k1g[i] = val;
            break;
         case 1:
            matrix_k2g[i] = val;
            break;
         case 2:
            matrix_k3g[i] = val;
            break;
         case 3:
            matrix_k4g[i] = val;
            break;
         case 4:
            matrix_k5g[i] = val;
            break;
         case 5:
            matrix_k6g[i] = val;
            break;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void HiddenGradientNODEF(__global float *matrix_w,    ///<[in] Weights matrix (m+1)*n, where m - input
                                  ///< window and n - output window
                                  __global float *matrix_g, ///<[in] Gradient tensor
                                  __global float *matrix_i, ///<[in] Inputs tensor
                                  __global float *matrix_ig, ///<[out] Inputs Gradient tensor
                                  int dimension_out,         ///< output dimension
                                  int activation             ///< Input Activation type (#ENUM_ACTIVATION)
                                 )
  {
   int d = get_global_id(0);
   int dimension = get_global_size(0);
   int v = get_global_id(1);
   int variables = get_global_size(1);
   int i = get_global_id(2);
   int lenth = get_global_size(2);
//---
   int shift = variables * i + v;
   int input_shift = shift * dimension + d;
   int output_shift = shift * dimension_out;
   int weight_step = (dimension + 2);
   int weight_shift = (v * dimension_out) * weight_step + d;
//---
   float sum = 0;
//---
   for(int k = 0; k < dimension_out; k++)
      sum +=
         matrix_g[output_shift + k] * matrix_w[weight_shift + k * weight_step];
   if(isnan(sum))
      sum = 0;
//---
   float out = matrix_i[input_shift];
//---
   matrix_ig[input_shift] = Deactivation(sum, out, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void NODEF_UpdateWeightsAdam(__global float *matrix_w,   ///<[in,out] Weights matrix (m+1)*n, where m -
                                      ///< number of neurons in previous layer and n -
                                      ///< number of neurons in current layer
                                      __global const float *matrix_gk1, ///<[in] Tensor of gradients at k1
                                      __global const float *matrix_gk2, ///<[in] Tensor of gradients at k2
                                      __global const float *matrix_gk3, ///<[in] Tensor of gradients at k3
                                      __global const float *matrix_gk4, ///<[in] Tensor of gradients at k4
                                      __global const float *matrix_gk5, ///<[in] Tensor of gradients at k5
                                      __global const float *matrix_gk6, ///<[in] Tensor of gradients at k6
                                      __global const float *matrix_ik1, ///<[in] Inputs tensor
                                      __global const float *matrix_ik2, ///<[in] Inputs tensor
                                      __global const float *matrix_ik3, ///<[in] Inputs tensor
                                      __global const float *matrix_ik4, ///<[in] Inputs tensor
                                      __global const float *matrix_ik5, ///<[in] Inputs tensor
                                      __global const float *matrix_ik6, ///<[in] Inputs tensor
                                      __global float *matrix_m,        ///<[in,out] Matrix of first momentum
                                      __global float *matrix_v,        ///<[in,out] Matrix of seconfd momentum
                                      __global const float *alpha,     ///< h
                                      const int lenth,                  ///< Number of inputs
                                      const float l,                    ///< Learning rates
                                      const float b1,                   ///< First momentum multiplier
                                      const float b2                    ///< Second momentum multiplier
                                     )
  {
   const int d_in = get_global_id(0);
   const int dimension_in = get_global_size(0);
   const int d_out = get_global_id(1);
   const int dimension_out = get_global_size(1);
   const int v = get_global_id(2);
   const int variables = get_global_id(2);
//---
   const int weight_shift = (v * dimension_out + d_out) * dimension_in;
   const int input_step = variables * (dimension_in - 2);
   const int input_shift = v * (dimension_in - 2) + d_in;
   const int output_step = variables * dimension_out;
   const int output_shift = v * dimension_out + d_out;
//---
   float weight = matrix_w[weight_shift];
   float g = 0;
//---
   for(int i = 0; i < lenth; i++)
     {
      int shift_g = i * output_step + output_shift;
      int shift_i = i * input_step + input_shift;
      switch(dimension_in - d_in)
        {
         case 1:
            g += matrix_gk1[shift_g] + matrix_gk2[shift_g] + matrix_gk3[shift_g] +
                 matrix_gk4[shift_g] + matrix_gk5[shift_g] + matrix_gk6[shift_g];
            break;
         case 2:
            g += matrix_gk1[shift_g] * alpha[0] + matrix_gk2[shift_g] * alpha[1] +
                 matrix_gk3[shift_g] * alpha[2] + matrix_gk4[shift_g] * alpha[3] +
                 matrix_gk5[shift_g] * alpha[4] + matrix_gk6[shift_g] * alpha[5];
            break;
         default:
            g += matrix_gk1[shift_g] * matrix_ik1[shift_i] +
                 matrix_gk2[shift_g] * matrix_ik2[shift_i] +
                 matrix_gk3[shift_g] * matrix_ik3[shift_i] +
                 matrix_gk4[shift_g] * matrix_ik4[shift_i] +
                 matrix_gk5[shift_g] * matrix_ik5[shift_i] +
                 matrix_gk6[shift_g] * matrix_ik6[shift_i];
            break;
        }
     }
//---
   float mt = b1 * matrix_m[weight_shift] + (1 - b1) * g;
   float vt = b2 * matrix_v[weight_shift] + (1 - b2) * pow(g, 2);
   float delta =
      l * (mt / (sqrt(vt) + 1.0e-37f) - (l1 * sign(weight) + l2 * weight));
   if(fabs(delta) > 0)
      matrix_w[weight_shift] =
         clamp(matrix_w[weight_shift] + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[weight_shift] = mt;
   matrix_v[weight_shift] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void TimeDerivative(__global float *qkv, __global float *dqkv,
                             int dimension)
  {
   const size_t pos = get_global_id(0);
   const size_t variable = get_global_id(1);
   const size_t head = get_global_id(2);
   const size_t total = get_global_size(0);
   const size_t variables = get_global_size(1);
   const size_t heads = get_global_size(2);
//---
   const int shift = 3 * heads * variables * dimension;
   const int shift_query =
      pos * shift + (3 * variable * heads + head) * dimension;
   const int shift_key = shift_query + heads * dimension;
//---
//---
   for(int i = 0; i < dimension; i++)
     {
      //--- dQ/dt
        {
         int count = 0;
         float delta = 0;
         float value = qkv[shift_query + i];
         if(pos > 0)
           {
            delta = value - qkv[shift_query + i - shift];
            count++;
           }
         if(pos < (total - 1))
           {
            delta += qkv[shift_query + i + shift] - value;
            count++;
           }
         if(count > 0)
            dqkv[shift_query + i] = delta / count;
        }
      //--- dK/dt
        {
         int count = 0;
         float delta = 0;
         float value = qkv[shift_key + i];
         if(pos > 0)
           {
            delta = value - qkv[shift_key + i - shift];
            count++;
           }
         if(pos < (total - 1))
           {
            delta += qkv[shift_key + i + shift] - value;
            count++;
           }
         if(count > 0)
            dqkv[shift_key + i] = delta / count;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void HiddenGradientTimeDerivative(__global float *qkv_g,
      __global float *dqkv_g,
      int dimension)
  {
   const size_t pos = get_global_id(0);
   const size_t variable = get_global_id(1);
   const size_t head = get_global_id(2);
   const size_t total = get_global_size(0);
   const size_t variables = get_global_size(1);
   const size_t heads = get_global_size(2);
//---
   const int shift = 3 * heads * variables * dimension;
   const int shift_query =
      pos * shift + (3 * variable * heads + head) * dimension;
   const int shift_key = shift_query + heads * dimension;
//---
//---
   for(int i = 0; i < dimension; i++)
     {
      //--- dQ/dt
        {
         int count = 0;
         float grad = 0;
         float current = dqkv_g[shift_query + i];
         if(pos > 0)
           {
            grad += current - dqkv_g[shift_query + i - shift];
            count++;
           }
         if(pos < (total - 1))
           {
            grad += dqkv_g[shift_query + i + shift] - current;
            count++;
           }
         if(count > 0)
            grad /= count;
         qkv_g[shift_query + i] += grad;
        }
      //--- dK/dt
        {
         int count = 0;
         float grad = 0;
         float current = dqkv_g[shift_key + i];
         if(pos > 0)
           {
            grad += current - dqkv_g[shift_key + i - shift];
            count++;
           }
         if(pos < (total - 1))
           {
            grad += dqkv_g[shift_key + i + shift] - current;
            count++;
           }
         if(count > 0)
            grad /= count;
         qkv_g[shift_key + i] += dqkv_g[shift_key + i] + grad;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardContAtt(__global float *qkv, __global float *dqkv,
                                 __global float *score, __global float *out,
                                 int dimension,
                                 int heads)
  {
   const size_t query = get_global_id(0);
   const size_t key = get_global_id(1);
   const size_t variable = get_global_id(2);
   const size_t queris = get_global_size(0);
   const size_t keis = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const uint ls_score = min((uint)keis, (uint)LOCAL_ARRAY_SIZE);
   __local float local_score[LOCAL_ARRAY_SIZE];
//---
//---
   for(int head = 0; head < heads; head++)
     {
      const int shift = 3 * heads * variables * dimension;
      const int shift_query =
         query * shift + (3 * variable * heads + head) * dimension;
      const int shift_key =
         key * shift + (3 * variable * heads + heads + head) * dimension;
      const int shift_out =
         dimension * (heads * (query * variables + variable) + head);
      int shift_score = keis * (heads * (query * variables + variable) + head) + key;
      //--- Score
      float scr = 0;
      for(int d = 0; d < dimension; d++)
         scr += qkv[shift_query + d] * dqkv[shift_key + d] +
                qkv[shift_key + d] * dqkv[shift_query + d];
      scr = exp(min(scr / sqrt((float)dimension), 30.0f));
      score[shift_score] = scr;
      BarrierLoc;
      //---
      if(key < ls_score)
        {
         local_score[key] = scr;
         for(int k = ls_score + key; k < keis; k += ls_score)
            local_score[key] += score[shift_score + k];
        }
      BarrierLoc;
      //---
      int count = ls_score;
      do
        {
         count = (count + 1) / 2;
         if(key < count)
           {
            if((key + count) < keis)
              {
               local_score[key] += local_score[key + count];
               local_score[key + count] = 0;
              }
           }
         BarrierLoc;
        }
      while(count > 1);
      //---
      score[shift_score] /= local_score[0];
      BarrierLoc;
      //---
      shift_score -= key;
      for(int d = key; d < dimension; d += keis)
        {
         float sum = 0;
         int shift_value = (3 * variable * heads + 2 * heads + head) * dimension + d;
         for(int v = 0; v < keis; v++)
            sum += qkv[shift_value + v * shift] * score[shift_score + v];
         out[shift_out + d] = sum;
        }
      BarrierLoc;
     }
//---
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void HiddenGradientContAtt(__global float *qkv, __global float *qkv_g,
                                    __global float *dqkv,
                                    __global float *dqkv_g,
                                    __global float *score,
                                    __global float *out_g, const int dimension)
  {
   const size_t pos = get_global_id(0);
   const size_t variable = get_global_id(1);
   const size_t head = get_global_id(2);
   const size_t total = get_global_size(0);
   const size_t variables = get_global_size(1);
   const size_t heads = get_global_size(2);
//--- Value gradient
     {
      const int shift_value =
         dimension * (heads * (3 * variables * pos + 3 * variable + 2) + head);
      const int shift_out = dimension * (head + variable * heads);
      const int shift_score = total * (variable * heads + head);
      const int step_out = variables * heads * dimension;
      const int step_score = variables * heads * total;
      //---
      //---
      for(int d = 0; d < dimension; d++)
        {
         float sum = 0;
         for(int g = 0; g < total; g++)
            sum += out_g[shift_out + g * step_out + d] *
                   score[shift_score + g * step_score];
         qkv_g[shift_value + d] = sum;
        }
     }
//--- Query gradient
     {
      const int shift_out =
         dimension * (heads * (pos * variables + variable) + head);
      const int step = 3 * variables * heads * dimension;
      const int shift_query =
         dimension * (3 * heads * variable + head) + pos * step;
      const int shift_key = dimension * (heads * (3 * variable + 1) + head);
      const int shift_value = dimension * (heads * (3 * variable + 2) + head);
      const int shift_score =
         total * (heads * (pos * variables + variable) + head);
      //--- Score gradient
      //---
      for(int k = 0; k < total; k++)
        {
         float score_grad = 0;
         float scr = score[shift_score + k];
         for(int v = 0; v < total; v++)
           {
            float grad = 0;
            for(int d = 0; d < dimension; d++)
               grad += qkv[shift_value + v * step + d] * out_g[shift_out + d];
            score_grad += score[shift_score + v] * grad * ((float)(pos == v) - scr);
           }
         score_grad /= sqrt((float)dimension);
         //--- Query gradient
         for(int d = 0; d < dimension; d++)
           {
            if(k == 0)
              {
               dqkv_g[shift_query + d] = score_grad * qkv[shift_key + k * step + d];
               qkv_g[shift_query + d] = score_grad * dqkv[shift_key + k * step + d];
              }
            else
              {
               dqkv_g[shift_query + d] += score_grad * qkv[shift_key + k * step + d];
               qkv_g[shift_query + d] += score_grad * dqkv[shift_key + k * step + d];
              }
           }
        }
     }
//--- Key gradient
     {
      const int shift_key =
         dimension * (heads * (3 * variables * pos + 3 * variable + 1) + head);
      const int shift_out = dimension * (head + variable * heads);
      const int step_out = variables * heads * dimension;
      const int step = 3 * variables * heads * dimension;
      const int shift_query = dimension * (3 * heads * variable + head);
      const int shift_value =
         dimension * (heads * (3 * variable + 2) + head) + pos * step;
      const int shift_score = total * (heads * variable + head);
      const int step_score = variables * heads * total;
      //--- Score gradient
      //---
      for(int q = 0; q < total; q++)
        {
         float score_grad = 0;
         float scr = score[shift_score + q * step_score];
         for(int g = 0; g < total; g++)
           {
            float grad = 0;
            for(int d = 0; d < dimension; d++)
               grad += qkv[shift_value + d] * out_g[shift_out + d + g * step_out] / sqrt((float)dimension);
            score_grad += score[shift_score + q * step_score + g] * grad * ((float)(q == pos) - scr);
           }
         //--- Key gradient
         for(int d = 0; d < dimension; d++)
           {
            if(q == 0)
              {
               dqkv_g[shift_key + d] = qkv[shift_query + q * step + d] * score_grad;
               qkv_g[shift_key + d] = score_grad * dqkv[shift_query + q * step + d];
              }
            else
              {
               qkv_g[shift_key + d] += score_grad * dqkv[shift_query + q * step + d];
               dqkv_g[shift_key + d] += score_grad * qkv[shift_query + q * step + d];
              }
           }
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void RevInFeedForward(__global float *inputs, __global float *options,
                               __global float *output, int options_size,
                               int optimization)
  {
   int n = get_global_id(0);
   int shift = (n * (optimization == 0 ? 7 : 9)) % options_size;
//---
   float mean = options[shift];
   float variance = options[shift + 1];
   float k = options[shift + 3];
//---
   float res = 0;
   res = sqrt(variance) * (inputs[n] - options[shift + 4]) / fmax(k, 0.001f) + mean;
   if(isnan(res))
      res = 0;
//---
   output[n] = res;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void RevInHiddenGraddient(__global float *inputs, __global float *inputs_gr,
                                   __global float *options, __global float *output_gr,
                                   int options_size,
                                   int optimization,
                                   int activation)
  {
   int n = get_global_id(0);
   int shift = (n * (optimization == 0 ? 7 : 9)) % options_size;
//---
   float variance = options[shift + 1];
   float inp = inputs[n];
   float k = options[shift + 3];
//---
   float res = sqrt(variance) * output_gr[n];
   if(fabs(k) > 1)
      res /= k;
   if(isnan(res))
      res = 0;
//---
   inputs_gr[n] = Deactivation(res, inp, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void Activation(__global const float *inputs,
                         __global float *outputs,
                         const int activation)
  {
   int n = get_global_id(0);
//---
   float res = IsNaNOrInf(inputs[n], 0);
//---
   outputs[n] = fActivation(res, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DeActivation(__global const float *inputs, __global float *inputs_gr,
                           __global const float *output_gr, const int activation)
  {
   int n = get_global_id(0);
//---
   float inp = inputs[n];
   float res = IsNaNOrInf(output_gr[n], 0);
//---
   inputs_gr[n] = Deactivation(res, inp, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PatchCreate(__global float *inputs,
                          __global float *weights,
                          __global float *outputs,
                          int inputs_total,
                          int window_in,
                          int step,
                          int activation
                         )
  {
   const int i = get_global_id(0);
   const int w = get_global_id(1);
   const int v = get_global_id(2);
   const int window_out = get_global_size(1);
   const int variables = get_global_size(2);
//---
   const int shift_in = i * step * variables + v;
   const int shift_out = (i * variables + v) * window_out + w;
   const int shift_weights = (window_in + 1) * (v * window_out + w);
//---
   float res = weights[shift_weights + window_in];
//---
   for(int p = 0; p < window_in; p++)
      if((shift_in + p * variables) < inputs_total)
         res += inputs[shift_in + p * variables] * weights[shift_weights + p];
   if(isnan(res))
      res = 0;
//---
   outputs[shift_out] = fActivation(res, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PatchHiddenGradient(__global float *inputs,
                                  __global float *inputs_gr,
                                  __global float *weights,
                                  __global float *outputs_gr,
                                  int window_in,
                                  int step,
                                  int window_out,
                                  int outputs_total,
                                  int activation
                                 )
  {
   const int i = get_global_id(0);
   const int v = get_global_id(1);
   const int variables = get_global_size(1);
//---
   const int w_start = i % step;
   const int r_start = max((i - window_in + step) / step, 0);
   int total = (window_in - w_start + step - 1) / step;
   total = min((i + step) / step, total);
//---
   float grad = 0;
//---
   for(int p = 0; p < total; p ++)
     {
      int row = r_start + p;
      if(row >= outputs_total)
         break;
      for(int wo = 0; wo < window_out; wo++)
        {
         int shift_g = (row * variables + v) * window_out + wo;
         int shift_w = v * (window_in + 1) * window_out + w_start + (total - p - 1) * step + wo * (window_in + 1);
         grad += outputs_gr[shift_g] * weights[shift_w];
        }
     }
//---
   float inp = inputs[i * variables + v];
//---
   inputs_gr[i * variables + v] = Deactivation(grad, inp, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PatchUpdateWeightsAdam(__global float *weights,
                                     __global const float *outputs_gr,
                                     __global const float *inputs,
                                     __global float *weights_m,
                                     __global float *weights_v,
                                     const int inputs_total,
                                     const float l,
                                     const float b1,
                                     const float b2,
                                     int step
                                    )
  {
   const int c = get_global_id(0);
   const int r = get_global_id(1);
   const int v = get_global_id(2);
   const int window_in = get_global_size(0) - 1;
   const int window_out = get_global_size(1);
   const int variables = get_global_size(2);
//---
   const int start_input = c * variables + v;
   const int step_input = step * variables;
   const int start_out = v * window_out + r;
   const int step_out = variables * window_out;
   const int total = inputs_total / (variables * step);
//---
   float grad = 0;
//---
   for(int p = 0; p < total; p++)
     {
      int i = start_input + i * step_input;
      int o = start_out + i * step_out;
      grad += (c == window_in ? 1 : inputs[i]) * outputs_gr[0];
     }
   if(isnan(grad))
      grad = 0;
//---
   const int shift_weights = (window_in + 1) * (window_out * v + r) + c;
//---
   float weight = weights[shift_weights];
   float mt = b1 * weights_m[shift_weights] + (1 - b1) * grad;
   float vt = b2 * weights_v[shift_weights] + (1 - b2) * pow(grad, 2);
   float delta = l * (mt / (sqrt(vt) + 1.0e-37f) - (l1 * sign(weight) + l2 * weight));
   if(fabs(delta) > 0)
      weights[shift_weights] = clamp(weight + delta, -MAX_WEIGHT, MAX_WEIGHT);
   weights_m[shift_weights] = mt;
   weights_v[shift_weights] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MatMult(__global const float *matr1,
                      __global const float *matr2,
                      __global float *result,
                      int dimension,
                      int multvarsecond)
  {
   size_t row = get_global_id(0);
   size_t col = get_global_id(1);
   size_t var = get_global_id(2);
   size_t rows = get_global_size(0);
   size_t cols = get_global_size(1);
//---
   int shift1 = (row  + var * rows) * dimension;
   int shift2 = col + multvarsecond * var * dimension * cols;
   int shift_out = (row + var * rows) * cols + col;
//---
   float res = 0;
//---
   for(int i = 0; i < dimension; i++)
      res += IsNaNOrInf(matr1[shift1 + i] * matr2[shift2 + i * cols], 0);
//---
   result[shift_out] = res;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MatMultGrad(__global const float *matr1,
                          __global float *matr1_gr,
                          __global const float *matr2,
                          __global float *matr2_gr,
                          __global const float *result_gr,
                          int dimension,
                          int multvarsecond)
  {
   size_t row = get_global_id(0);
   size_t col = get_global_id(1);
   size_t var = get_global_id(2);
   size_t rows = get_global_size(0);
   size_t cols = get_global_size(1);
//---
   int shift1 = (row  + var * rows) * dimension;
   int shift2 = var * dimension * cols * multvarsecond;
   int shift_out = (row + var * rows) * cols;
//---
   for(int c = 0; c < dimension; c += cols)
     {
      if((c + col) >= dimension)
         continue;
      float grad = 0;
      for(int i = 0; i < cols; i++)
         grad += IsNaNOrInf(result_gr[shift_out + i] * matr2[shift2 + c * cols + i], 0);
      matr1_gr[shift1 + c] = IsNaNOrInf(grad, 0);
     }
//---
   shift_out = var * rows * cols + col;
//---
   for(int r = 0; r < dimension; r += rows)
     {
      if((r + row) >= dimension)
         continue;
      shift1 = var * rows * dimension + r;
      float grad = 0;
      for(int i = 0; i < rows; i++)
         grad += IsNaNOrInf(result_gr[shift_out + i * cols] * matr1[shift1 + i * dimension], 0);
      matr2_gr[shift2 + col + r * cols] = IsNaNOrInf(grad, 0);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FFT(__global float *inputs_re,
                  __global float *inputs_im,
                  __global float *outputs_re,
                  __global float *outputs_im,
                  const int input_window,
                  const int input_complex,
                  const int output_window,
                  const int reverse
                 )
  {
   size_t variable = get_global_id(0);
//---
   const ulong N = output_window;
   const ulong N2 = N / 2;
   const ulong inp_shift = input_window * variable;
   const ulong out_shift = output_window * variable;
//---
   uint target = 0;
//---
   for(uint position = 0; position < N; position++)
     {
      if(target > position)
        {
         outputs_re[out_shift + position] = (target < input_window ? inputs_re[inp_shift + target] : 0);
         outputs_im[out_shift + position] = ((target < input_window && input_complex) ? inputs_im[inp_shift + target] : 0);
         outputs_re[out_shift + target] = inputs_re[inp_shift + position];
         outputs_im[out_shift + target] = (input_complex ? inputs_im[inp_shift + position] : 0);
        }
      else
        {
         outputs_re[out_shift + position] = inputs_re[inp_shift + position];
         outputs_im[out_shift + position] = (input_complex ? inputs_im[inp_shift + position] : 0);
        }
      unsigned int mask = N;
      while(target & (mask >>= 1))
         target &= ~mask;
      target |= mask;
     }
   float real = 0, imag = 0;
//---
   for(int len = 2; len <= (int)N; len <<= 1)
     {
      float w_real = (float)cos(2 * M_PI_F / len);
      float w_imag = (float)sin(2 * M_PI_F / len);
      for(int i = 0; i < (int)N; i += len)
        {
         float cur_w_real = 1;
         float cur_w_imag = 0;
         for(int j = 0; j < len / 2; j++)
           {
            real = cur_w_real * outputs_re[out_shift + i + j + len / 2] - cur_w_imag * outputs_im[out_shift + i + j + len / 2];
            imag = cur_w_imag * outputs_re[out_shift + i + j + len / 2] + cur_w_real * outputs_im[out_shift + i + j + len / 2];
            outputs_re[out_shift + i + j + len / 2] = outputs_re[out_shift + i + j] - real;
            outputs_im[out_shift + i + j + len / 2] = outputs_im[out_shift + i + j] - imag;
            outputs_re[out_shift + i + j] += real;
            outputs_im[out_shift + i + j] += imag;
            real = cur_w_real * w_real - cur_w_imag * w_imag;
            cur_w_imag = cur_w_imag * w_real + cur_w_real * w_imag;
            cur_w_real = real;
           }
        }
     }
//---
   if(reverse)
     {
      outputs_re[0] /= N;
      outputs_im[0] /= N;
      outputs_re[N2] /= N;
      outputs_im[N2] /= N;
      //---
      for(int i = 1; i < N2; i++)
        {
         real = outputs_re[i] / N;
         imag = outputs_im[i] / N;
         outputs_re[i] = outputs_re[N - i] / N;
         outputs_im[i] = outputs_im[N - i] / N;
         outputs_re[N - i] = real;
         outputs_im[N - i] = imag;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexLayer(__global float *inputs_re,
                           __global float *inputs_im,
                           __global float *outputs_re,
                           __global float *outputs_im
                          )
  {
   size_t i = get_global_id(0);
   size_t j = get_global_id(1);
   size_t total_i = get_global_size(0);
   size_t total_j = get_global_size(1);
   uint shift = i * total_j + j;
//---
   outputs_re[shift] = inputs_re[shift] - inputs_im[shift];
   outputs_im[shift] = inputs_im[shift] + inputs_re[shift];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexLayerGradient(__global float *inputs_re,
                                   __global float *inputs_im,
                                   __global float *outputs_re,
                                   __global float *outputs_im
                                  )
  {
   size_t i = get_global_id(0);
   size_t j = get_global_id(1);
   size_t total_i = get_global_size(0);
   size_t total_j = get_global_size(1);
   uint shift = i * total_j + j;
//---
   inputs_re[shift] = outputs_re[shift] + outputs_im[shift];
   inputs_im[shift] = outputs_im[shift] - outputs_re[shift];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void GradientMSA(__global float *matrix_t, ///<[in] Target tensor
                          __global float *matrix_o, ///<[in] Forecast tensor
                          __global float *matrix_g ///<[out] Tensor of gradients
                         )
  {
   int i = get_global_id(0);
   matrix_g[i] = matrix_t[i] - matrix_o[i];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CumulativeGradient(__global float *gradient1,
                                 __global float *gradient2,
                                 __global float *gradient_out,
                                 float alpha
                                )
  {
   int i = get_global_id(0);
   gradient_out[i] = alpha * gradient1[i] + (1 - alpha) * gradient2[i];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float2 ComplexMul(const float2 a, const float2 b)
  {
   float2 result = 0;
   result.x = IsNaNOrInf(a.x * b.x - a.y * b.y, 0);
   result.y = IsNaNOrInf(a.x * b.y + a.y * b.x, 0);
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float2 ComplexDiv(const float2 a, const float2 b)
  {
   float2 result = 0;
   float z = IsNaNOrInf(pow(b.x, 2) + pow(b.y, 2), 1);
   if(z > 0)
     {
      result.x = IsNaNOrInf(a.x * b.x + a.y * b.y, 0) / z;
      result.y = IsNaNOrInf(a.y * b.x - a.x * b.y, 0) / z;
     }
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float ComplexAbs(float2 a)
  {
   return sqrt(IsNaNOrInf(pow(a.x, 2) + pow(a.y, 2), 0));
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float2 ComplexSqrt(float2 a)
  {
   float2 result = 0;
   float z = ComplexAbs(a);
   result.x = sqrt((z + IsNaNOrInf(a.x, 0)) / 2);
   result.y = sqrt((z - IsNaNOrInf(a.x, 0)) / 2);
   if(a.y < 0)
      result.y *= (-1);
//---
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float2 ComplexExp(float2 a)
  {
   float2 result = exp(clamp(IsNaNOrInf(a.x, 0), -20.0f, 20.0f));
   result.x *= IsNaNOrInf(cos(a.y), 0);
   result.y *= IsNaNOrInf(sin(a.y), 0);
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float2 ComplexTanh(float2 a)
  {
   float sinh_re = sinh(a.x);
   float cosh_re = cosh(a.x);
   float sin_im = sin(a.y);
   float cos_im = cos(a.y);
//---
   float2 sinh_a = 0;
   float2 cosh_a = 0;
   sinh_a.x = sinh_re * cos_im;
   sinh_a.y = cosh_re * sin_im;
   cosh_a.x = cosh_re * cos_im;
   cosh_a.y = sinh_re * sin_im;
//---
   return ComplexDiv(sinh_a, cosh_a);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardComplexConv(__global const float2* __attribute__((aligned(8))) matrix_w, ///<[in] Weights matrix (m+1)*n, where m - input
                                     ///< window and n - output window
                                     __global const float2* __attribute__((aligned(8))) matrix_i, ///<[in] Inputs tensor
                                     __global float2* __attribute__((aligned(8))) matrix_o, ///<[out] Output tensor
                                     const int inputs,               ///< Number of inputs
                                     const int step,                 ///< Step size
                                     const int window_in,            ///< Size of input window
                                     const int activation            ///< Activation type (#ENUM_ACTIVATION)
                                    )
  {
   const size_t i = get_global_id(0);
   const size_t units = get_global_size(0);
   const size_t out = get_global_id(1);
   const size_t w_out = get_global_size(1);
   const size_t var = get_global_id(2);
   const size_t variables = get_global_size(2);
//---
   int w_in = window_in;
   int shift_out = w_out * (i + units * var);
   int shift_in = step * i;
   int shift = (w_in + 1) * (out + var * w_out);
   int stop = (w_in <= (inputs - shift_in) ? w_in : (inputs - shift_in));
   shift_in += + inputs * var;
//---
   float2 sum = ComplexMul((float2)(1, 0), matrix_w[shift + w_in]);
//---
   for(int k = 0; k < stop; k ++)
      sum += IsNaNOrInf2(ComplexMul(matrix_i[shift_in + k], matrix_w[shift + k]), (float2)0);
//---
   switch(activation)
     {
      case 0:
         sum = ComplexTanh(sum);
         break;
      case 1:
         sum = ComplexDiv((float2)(1, 0), (float2)(1, 0) + ComplexExp(-sum));
         break;
      case 2:
         if(sum.x < 0)
           {
            sum.x *= 0.01f;
            sum.y *= 0.01f;
           }
         break;
      default:
         break;
     }
   matrix_o[out + shift_out] = sum;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientComplexConv(__global const float2* __attribute__((aligned(8))) matrix_w,    ///<[in] Weights matrix (m+1)*n, where m - input
      ///< window and n - output window
      __global const float2* __attribute__((aligned(8))) matrix_g, ///<[in] Tensor of gradients at current layer
      __global const float2* __attribute__((aligned(8))) matrix_o, ///<[in] Output tensor
      __global float2* __attribute__((aligned(8))) matrix_ig, ///<[out] Tensor of gradients at previous layer
      const int outputs,               ///< Number of outputs
      const int step,                  ///< Step size
      const int window_in,             ///< Size of input window
      const int window_out,            ///< Size of output window
      const int activation,            ///< Activation type (#ENUM_ACTIVATION)
      const int shift_out              ///< Shift in output and gradient buffer
                                           )
  {
   const size_t i = get_global_id(0);
   const size_t inputs = get_global_size(0);
   const size_t var = get_global_id(1);
   const size_t variables = get_global_size(1);
//---
   float2 sum = (float2)0;
   float2 out = matrix_o[i];
   int start = i - window_in + step;
   start = max((start - start % step) / step, 0) + var * inputs;
   int stop = (i + step - 1) / step;
   if(stop > (outputs / window_out))
      stop = outputs / window_out;
   stop += var * outputs;
//---
   for(int h = 0; h < window_out; h ++)
     {
      for(int k = start; k < stop; k++)
        {
         int shift_g = k * window_out + h;
         int shift_w = (stop - k - 1) * step + i % step + h * (window_in + 1);
         if(shift_g >= outputs || shift_w >= (window_in + 1) * window_out)
            break;
         sum += ComplexMul(matrix_g[shift_out + shift_g], matrix_w[shift_w]);
        }
     }
   sum = IsNaNOrInf2(sum, (float2)0);
//---
   switch(activation)
     {
      case 0:
         sum = ComplexMul(sum, (float2)1.0f - ComplexMul(out, out));
         break;
      case 1:
         sum = ComplexMul(sum, ComplexMul(out, (float2)1.0f - out));
         break;
      case 2:
         if(out.x < 0.0f)
           {
            sum.x *= 0.01f;
            sum.y *= 0.01f;
           }
         break;
      default:
         break;
     }
   matrix_ig[i] = clamp(sum, (float2)(-MAX_GRAD), (float2)MAX_GRAD);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsComplexConvMomentum(__global float2* __attribute__((aligned(8))) matrix_w,   ///<[in,out] Weights matrix (m+1)*n, where m -
      ///< input window and n - output window
      __global float2* __attribute__((aligned(8))) matrix_g, ///<[in] Tensor of gradients at current layer
      __global float2* __attribute__((aligned(8))) matrix_i, ///<[in] Inputs tensor
      __global float2* __attribute__((aligned(8))) matrix_dw, ///<[in,out] Matrix of delta weights in last correction
      int inputs,     ///< Number of inputs
      float learning_rates, ///< Learning rates
      float momentum,       ///< Momentum multiplier
      int window_in,        ///< Size of input window
      int window_out,       ///< Size of output window
      int step              ///< Step size
                                              )
  {
   const size_t i = get_global_id(0);
   const size_t total_w = get_global_size(0);
   const size_t var = get_global_id(1);
   const size_t variables = get_global_size(1);
   const int shift = i % (window_in + 1);
   int shift_out = (i - shift) / (window_in + 1);
   int total = (inputs - window_in) % step;
   total = (inputs - window_in - total) / step + (total > 0 ? 1 : 0);
   shift_out += total * window_out * var;
   float2 grad = 0;
//---
   for(int t = 0; t < total; t++)
     {
      if(shift != window_in && (shift + t * window_in) >= inputs)
         break;
      grad += ComplexMul(matrix_g[t * window_out + shift_out],
                         (shift == window_in ? (float2)(1, 0) : matrix_i[inputs * var + shift + t * step]));
     }
   float2 delta = ComplexMul((float2)(learning_rates, 0), clamp(grad, (float2) - MAX_GRAD, (float2)MAX_GRAD)) + ComplexMul((float2)(momentum, 0), matrix_dw[i + total_w * var]);
   if(!(isnan(delta.x) || isnan(delta.y) || isinf(delta.x) || isinf(delta.y)))
     {
      matrix_dw[i + total_w * var] = delta;
      matrix_w[i + total_w * var] = clamp(matrix_w[i + total_w * var] + delta, (float2) - MAX_WEIGHT, (float2)MAX_WEIGHT);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsComplexConvAdam(__global float2* __attribute__((aligned(8))) matrix_w,   ///<[in,out] Weights matrix (m+1)*n, where m -
      ///< input window and n - output window
      __global const float2* __attribute__((aligned(8))) matrix_g, ///<[in] Tensor of gradients at current layer
      __global const float2* __attribute__((aligned(8))) matrix_i, ///<[in] Inputs tensor
      __global float2* __attribute__((aligned(8))) matrix_m,      ///<[in] Matrix of first momentum
      __global float2* __attribute__((aligned(8))) matrix_v,      ///<[in] Matrix of seconfd momentum
      const int inputs,               ///< Number of inputs
      const float l,                  ///< Learning rates
      const float b1,                 ///< First momentum multiplier
      const float b2,                 ///< Second momentum multiplier
      int window_in,                  ///< Size of input window
      int window_out,                 ///< Size of output window
      int step                        ///< Step size
                                          )
  {
   const size_t i = get_global_id(0);
   const size_t total_w = get_global_size(0);
   const size_t var = get_global_id(1);
   const size_t variables = get_global_size(1);
//---
   const int shift = i % (window_in + 1);
   int shift_out = (i - shift) / (window_in + 1);
   int total = (inputs - window_in + step - 1) / step;
   shift_out += total * window_out * var;
   const int shift_var_in = var * inputs;
   const int shift_var_out = var * total * window_out;
//---
   float2 grad = 0;
//---
   for(int t = 0; t < total; t++)
     {
      if(shift != window_in && (shift + t * window_in) >= inputs)
         break;
      grad += IsNaNOrInf2(ComplexMul(matrix_g[t * window_out + shift_out + shift_var_out],
                                     (shift == window_in ? (float2)(1, 0) : matrix_i[shift + t * step + shift_var_in])), (float2)0);
     }
   grad = clamp(grad, (float2) - MAX_GRAD, (float2)MAX_GRAD);
   float2 mt = IsNaNOrInf2(b1 * matrix_m[i + total_w * var] + (1 - b1) * grad, (float2)0);
   float2 vt = IsNaNOrInf2(b2 * matrix_v[i + total_w * var] + (1 - b2) * ComplexMul(grad, grad), (float2)(1.0e-6f, 0));
   float2 weight = matrix_w[i + total_w * var] + IsNaNOrInf2(l * ComplexDiv(mt, ComplexSqrt(vt)), (float2)0);
   matrix_w[i + total_w * var] = clamp(weight, (float2) - MAX_WEIGHT, (float2)MAX_WEIGHT);
   matrix_m[i + total_w * var] = mt;
   matrix_v[i + total_w * var] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexSoftMax_FeedForward(__global float2* __attribute__((aligned(8))) inputs,
      __global float2* __attribute__((aligned(8))) outputs, const int total)
  {
   const uint i = (uint)get_global_id(0);
   const uint l = (uint)get_local_id(0);
   const uint h = (uint)get_global_id(1);
   const uint ls = min((uint)get_local_size(0), (uint)LOCAL_ARRAY_SIZE);
   uint shift_head = h * total;
//---
   __local float2 temp[LOCAL_ARRAY_SIZE];
   uint count = 0;
   if(l < ls)
      do
        {
         uint shift = shift_head + count * ls + l;
         if(shift < ((h + 1) * total))
            temp[l].x = (count > 0 ? fmax(ComplexAbs(inputs[shift]), temp[l].x)
                         : ComplexAbs(inputs[shift]));
         count++;
        }
      while((count * ls + l) < total);
   BarrierLoc;
   float max_value = temp[0].x;
//---
   for(int i = 1; i < ls; i++)
      max_value = fmax(max_value, temp[i].x);
//---
   count = 0;
   if(l < ls)
      do
        {
         uint shift = shift_head + count * ls + l;
         temp[l] = (count > 0 ? temp[l] : (float2)0) +
                   (shift < ((h + 1) * total) ? ComplexExp(ComplexDiv(inputs[shift], (float2)(max_value, 0))) : (float2)0);
         count++;
        }
      while((count * ls + l) < total);
   BarrierLoc;
   count = min(ls, (uint)total);
   do
     {
      count = (count + 1) / 2;
      if(l < ls)
         temp[l] += (l < count && (l + count) < total ? temp[l + count] : (float2)0);
      if(l + count < ls)
         temp[l + count] = (float2)0;
      BarrierLoc;
     }
   while(count > 1);
//---
   float2 sum = temp[0];
   if(ComplexAbs(sum) > 0)
     {
      count = 0;
      while((count * ls + l) < total)
        {
         uint shift = shift_head + count * ls + l;
         if(shift < ((h + 1) * total))
            outputs[shift] = ComplexDiv(ComplexExp(ComplexDiv(inputs[shift], (float2)(max_value, 0))), sum);
         count++;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexSoftMax_HiddenGradient(__global float2* __attribute__((aligned(8))) outputs,
      __global float2* __attribute__((aligned(8))) output_gr,
      __global float2* __attribute__((aligned(8))) input_gr)
  {
   size_t i = get_global_id(0);
   size_t outputs_total = get_global_size(0);
   size_t h = get_global_id(1);
   uint shift = h * outputs_total;
   float2 output = outputs[shift + i];
   float2 result = 0;
//---
   for(int j = 0; j < outputs_total; j++)
      result += ComplexMul(ComplexMul(outputs[shift + j], output_gr[shift + j]), ((i == j ? (float2)(1, 0) : (float2)0) - output));
   input_gr[shift + i] = result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexSoftMax_OutputGradient(__global float2* __attribute__((aligned(8))) outputs,
      __global float2* __attribute__((aligned(8))) targets,
      __global float2* __attribute__((aligned(8))) output_gr)
  {
   size_t i = get_global_id(0);
   if(ComplexAbs(outputs[i]) == 0)
      output_gr[i] = (float2)0;
   else
      output_gr[i] = ComplexDiv(targets[i], outputs[i]);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexMHAttentionScore(__global float2* __attribute__((aligned(8))) qkv,  ///<[in] Matrix of Querys, Keys, Values
                                      __global float2* __attribute__((aligned(8))) score, ///<[out] Matrix of Scores
                                      int dimension,         ///< Dimension of Key
                                      int mask ///< 1 - calc only previous units, 0 - calc all
                                     )
  {
   int q = get_global_id(0);
   int h = get_global_id(1);
   int units = get_global_size(0);
   int heads = get_global_size(1);
//---
   int shift_q = dimension * (h + 3 * q * heads);
   int shift_s = units * (h + q * heads);
//---
   float2 koef = (float2)(sqrt((float)dimension), 0);
   if(koef.x < 1)
      koef.x = 1;
   float2 sum = 0;
//---
   for(int k = 0; k < units; k++)
     {
      if(mask > 0 && k > q)
        {
         score[shift_s + k] = (float2)0;
         continue;
        }
      float2 result = (float2)0;
      int shift_k = dimension * (h + heads * (3 * k + 1));
      for(int i = 0; i < dimension; i++)
         result += ComplexMul(qkv[shift_q + i], qkv[shift_k + i]);
      result = ComplexExp(ComplexDiv(result, koef));
      if(isnan(result.x) || isnan(result.y) || isinf(result.x) || isinf(result.y))
         result = (float2)0;
      score[shift_s + k] = result;
      sum += result;
     }
   if(ComplexAbs(sum) > 0)
     {
      //---
      for(int k = 0; k < units; k++)
         score[shift_s + k] = ComplexDiv(score[shift_s + k], sum);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexMHAttentionOut(__global float2* __attribute__((aligned(8))) scores, ///<[in] Matrix of Scores
                                    __global float2* __attribute__((aligned(8))) qkv,   ///<[in] Matrix of Values
                                    __global float2* __attribute__((aligned(8))) out,   ///<[out] Output tensor
                                    int dimension           ///< Dimension of Value
                                   )
  {
   int u = get_global_id(0);
   int units = get_global_size(0);
   int h = get_global_id(1);
   int heads = get_global_size(1);
//---
   int shift_s = units * (h + heads * u);
   int shift_out = dimension * (h + heads * u);
//---
//---
   for(int d = 0; d < dimension; d++)
     {
      float2 result = (float2)0;
      for(int v = 0; v < units; v++)
        {
         int shift_v = dimension * (h + heads * (3 * v + 2)) + d;
         result += ComplexMul(scores[shift_s + v], qkv[shift_v]);
        }
      out[shift_out + d] = result;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexMHAttentionGradients(__global float2* __attribute__((aligned(8))) qkv,
      __global float2* __attribute__((aligned(8))) qkv_g,
      __global float2* __attribute__((aligned(8))) scores,
      __global float2* __attribute__((aligned(8))) gradient
                                         )
  {
   size_t u = get_global_id(0);
   size_t h = get_global_id(1);
   size_t d = get_global_id(2);
   size_t units = get_global_size(0);
   size_t heads = get_global_size(1);
   size_t dimension = get_global_size(2);
//---
   float2 koef = (float2)(sqrt((float)dimension), 0);
   if(koef.x < 1)
      koef.x = 1;
//--- init
   const int shift_q = dimension * (heads * 3 * u + h);
   const int shift_k = dimension * (heads * (3 * u + 1) + h);
   const int shift_v = dimension * (heads * (3 * u + 2) + h);
   const int shift_g = dimension * (heads * u + h);
   int shift_score = h * units;
   int step_score = units * heads;
//--- Calculating Value's gradients
   float2 sum = (float2)0;
//---
   for(int i = 0; i < units; i++)
      sum += ComplexMul(gradient[(h + i * heads) * dimension + d], scores[shift_score + u + i * step_score]);
   qkv_g[shift_v + d] = sum;
//--- Calculating Query's gradients
   shift_score = h * units + u * step_score;
   float2 grad = 0;
   float2 grad_out = gradient[shift_g + d];
//---
   for(int k = 0; k < units; k++)
     {
      float2 sc_g = (float2)0;
      float2 sc = scores[shift_score + k];
      for(int v = 0; v < units; v++)
         sc_g += ComplexMul(
                    ComplexMul(scores[shift_score + v],
                               ComplexMul(qkv[dimension * (heads * (3 * v + 2) + h)],
                                          grad_out)),
                    ((float2)(k == v, 0) - sc)
                 );
      grad += ComplexMul(ComplexDiv(sc_g, koef), qkv[dimension * (heads * (3 * k + 1) + h) + d]);
     }
   qkv_g[shift_q + d] = grad;
//--- Calculating Key's gradients
   grad = 0;
//---
   for(int q = 0; q < units; q++)
     {
      shift_score = h * units + q * step_score;
      float2 sc_g = (float2)0;
      float2 sc = scores[shift_score + u];
      float2 grad_out = gradient[dimension * (heads * q + h) + d];
      for(int v = 0; v < units; v++)
         sc_g += ComplexMul(
                    ComplexMul(scores[shift_score + v],
                               ComplexMul(qkv[dimension * (heads * (3 * v + 2) + h)],
                                          grad_out)),
                    ((float2)(u == v, 0) - sc)
                 );
      grad += ComplexMul(ComplexDiv(sc_g, koef), qkv[dimension * (heads * 3 * q + h) + d]);
     }
   qkv_g[shift_k + d] = grad;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexNormalize(__global float2* __attribute__((aligned(8))) inputs,
                               __global float2* __attribute__((aligned(8))) outputs,
                               __global float2* __attribute__((aligned(8))) means,
                               __global float *vars,
                               int dimension)
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
   const float2 dim = (float2)(dimension, 0);
//---
   float2 mean = 0;
//---
   for(int i = 0; i < dimension; i++)
      mean = IsNaNOrInf2(inputs[shift + i], (float2)0);
   means[n] = mean = ComplexDiv(mean, dim);
   float variance = 0;
//---
   for(int i = 0; i < dimension; i++)
      variance += pow(ComplexAbs(inputs[shift + i] - mean), 2);
   vars[n] = variance = sqrt(IsNaNOrInf(variance / dimension, 1));
   float2 v = (float2)(variance, 0);
//---
   for(int i = 0; i < dimension; i++)
     {
      float2 val = IsNaNOrInf2(ComplexDiv((inputs[shift + i] - mean), v), (float2)0);
      outputs[shift + i] = val;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexNormalizeGradient(__global float2* __attribute__((aligned(8))) inputs_gr,
                                       __global float2* __attribute__((aligned(8))) outputs_gr,
                                       __global float *vars,
                                       int dimension)
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
//---
   float v = vars[n];
   float2 variance = (float2)((v > 0 ? v : 1.0f), 0);
//---
   for(int i = 0; i < dimension; i++)
     {
      float2 val = ComplexDiv(outputs_gr[shift + i], variance);
      if(isnan(val.x) || isinf(val.x) || isnan(val.y) || isinf(val.y))
         val = (float2)0;
      inputs_gr[shift + i] = val;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexUnNormalize(__global float2* __attribute__((aligned(8))) inputs,
                                 __global float2* __attribute__((aligned(8))) outputs,
                                 __global float2* __attribute__((aligned(8))) means,
                                 __global float *vars,
                                 int dimension)
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
//---
   float v = vars[n];
   float2 variance = (float2)((v > 0 ? v : 1.0f), 0);
   float2 mean = means[n];
//---
   for(int i = 0; i < dimension; i++)
     {
      float2 val = ComplexMul(inputs[shift + i], variance) + mean;
      if(isnan(val.x) || isinf(val.x) || isnan(val.y) || isinf(val.y))
         val = (float2)0;
      outputs[shift + i] = val;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ComplexUnNormalizeGradient(__global float2* __attribute__((aligned(8))) inputs_gr,
      __global float2* __attribute__((aligned(8))) outputs_gr,
      __global float *vars,
      int dimension
                                        )
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
//---
   float v = vars[n];
   float2 variance = (float2)((v > 0 ? v : 1.0f), 0);
//---
   for(int i = 0; i < dimension; i++)
     {
      float2 val = ComplexMul(outputs_gr[shift + i], variance);
      if(isnan(val.x) || isinf(val.x) || isnan(val.y) || isinf(val.y))
         val = (float2)0;
      inputs_gr[shift + i] = val;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MainFreqWeight(__global float2* __attribute__((aligned(8))) freq,
                             __global float *weight,
                             int dimension
                            )
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
//---
   float max_f = 0;
   float total = 0;
   float energy;
//---
   for(int i = 0; i < dimension; i++)
     {
      energy = ComplexAbs(freq[shift + i]);
      total += energy;
      max_f = fmax(max_f, energy);
     }
   weight[n] = max_f / (total > 0 ? total : 1);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void WeightedSum(__global float *inputs1,
                          __global float *inputs2,
                          __global float *outputs,
                          __global float *weight,
                          int dimension
                         )
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
//---
   float w = weight[n];
//---
   for(int i = 0; i < dimension; i++)
      outputs[shift + i] = inputs1[shift + i] * w + inputs2[shift + i] * (1 - w);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void WeightedSumGradient(__global float *inputs_gr1,
                                  __global float *inputs_gr2,
                                  __global float *outputs_gr,
                                  __global float *weight,
                                  int dimension
                                 )
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
//---
   float w = weight[n];
   float w1 = 1 - weight[n];
//---
   for(int i = 0; i < dimension; i++)
     {
      float grad = outputs_gr[shift + i];
      inputs_gr1[shift + i] = grad * w;
      inputs_gr2[shift + i] = grad * w1;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardS3(__global float *inputs,
                            __global float *probability,
                            __global float *weights,
                            __global float *outputs,
                            __global float *positions,
                            const int window,
                            const int total
                           )
  {
   int pos = get_global_id(0);
   int segments = get_global_size(0);
//---
   if((segments * window) > total)
      segments--;
//---
   int segment = 0;
   if(pos < segments)
     {
      const float prob = probability[pos];
      //---
      for(int i = 0; i < pos; i++)
        {
         if(probability[i] <= prob)
            segment++;
        }
      //---
      for(int i = pos + 1; i < segments; i++)
        {
         if(probability[i] < prob)
            segment++;
        }
     }
   else
      segment = pos;
//---
   const int shift_in = segment * window;
   const int shift_out = pos * window;
   const float w1 = weights[0];
   const float w2 = weights[1];
   positions[pos] = (float)segment;
//---
   for(int i = 0; i < window; i++)
     {
      if((shift_in + i) >= total || (shift_out + i) >= total)
         break;
      outputs[shift_out + i] = w1 * inputs[shift_in + i] + w2 * inputs[shift_out + i];
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void InsideGradientS3(__global float *inputs,
                               __global float *inputs_gr,
                               __global float *probability,
                               __global float *probability_gr,
                               __global float *weights,
                               __global float *outputs_gr,
                               __global float *positions,
                               const int window,
                               const int total
                              )
  {
   size_t pos = get_global_id(0);
//---
   int segment = (int)positions[pos];
   float prob = probability[pos];
   const float w1 = weights[0];
   const float w2 = weights[1];
   const int shift_in = segment * window;
   const int shift_out = pos * window;
//---
   float grad = 0;
   float temp = 0;
//---
   for(int i = 0; i < window; i++)
     {
      if((shift_out + i) >= total)
         break;
      temp = outputs_gr[shift_out + i] * w1;
      grad += temp * inputs[shift_in + i];
      inputs_gr[shift_in + i] = temp + outputs_gr[shift_in + i] * w2;
     }
   probability_gr[segment] = grad / prob;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void WeightGradientS3(__global float *inputs,
                               __global float *positions,
                               __global float *outputs_gr,
                               __global float *weights_gr,
                               const int window,
                               const int total
                              )
  {
   size_t l = get_local_id(0);
   size_t w = get_global_id(1);
   size_t ls = min((uint)get_local_size(0), (uint)LOCAL_ARRAY_SIZE);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
//---
   if(l < ls)
     {
      float val = 0;
      //---
      for(int i = l; i < total; i += ls)
        {
         int shift_in = i;
         if(w == 0)
           {
            int pos = i / window;
            shift_in = positions[pos] * window + i % window;
           }
         val += outputs_gr[i] * inputs[shift_in];
        }
      temp[l] = val;
     }
   BarrierLoc;
//---
   int t = ls;
   do
     {
      t = (t + 1) / 2;
      if(l < t && (l + t) < ls)
        {
         temp[l] += temp[l + t];
         temp[l + t] = 0;
        }
      BarrierLoc;
     }
   while(t > 1);
//---
   if(l == 0)
      weights_gr[w] = temp[0];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MH2PyrAttentionOut(__global float *q,
                                 __global float *kv,
                                 __global float *score,
                                 __global float *out,
                                 const int dimension,
                                 const int heads_kv,
                                 const int window
                                )
  {
//--- init
   const int q_id = get_global_id(0);
   const int k = get_local_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int kunits = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_k = dimension * (2 *  heads_kv * k + h_kv);
   const int shift_v = dimension * (2 *  heads_kv * k + heads_kv + h_kv);
   const int shift_s = kunits * (q_id *  heads + h) + k;
   const uint ls = min((uint)get_local_size(1), (uint)LOCAL_ARRAY_SIZE);
   const int delta_win = (window + 1) / 2;
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   __local float temp[LOCAL_ARRAY_SIZE];
//--- Score
   float sum = 0;
   for(int d = 0; d < dimension; d++)
      sum = q[shift_q + d] * kv[shift_k + d];
   float sc = LocalSoftMax(IsNaNOrInf(sum / koef, MIN_VALUE), 1, temp);
   score[shift_s] = sc;
   BarrierLoc;
//--- out
   for(int d = 0; d < dimension; d++)
     {
      uint count = 0;
      if(k < ls)
         do
           {
            if((count * ls) < (kunits - k))
              {
               sum = 0;
               if(abs(count * ls + k - q_id) <= delta_win)
                 {
                  int sh_v = 2 * dimension * heads_kv * count * ls;
                  sum = kv[shift_v + d + sh_v] * (count == 0 ? sc : score[shift_s + count * ls]);
                  if(isnan(sum))
                     sum = 0;
                 }
               temp[k] = (count > 0 ? temp[k] : 0) + sum;
              }
            count++;
           }
         while((count * ls + k) < kunits);
      BarrierLoc;
      //---
      count = min(ls, (uint)kunits);
      do
        {
         count = (count + 1) / 2;
         if(k < ls)
            temp[k] += (k < count && (k + count) < kunits ? temp[k + count] : 0);
         if(k + count < ls)
            temp[k + count] = 0;
         BarrierLoc;
        }
      while(count > 1);
      //---
      if(k == 0)
         out[shift_q + d] = temp[0];
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PLR(__global const float *inputs,
                  __global float *outputs,
                  __global int *isttp,
                  const int transpose,
                  const float min_step
                 )
  {
   const size_t i = get_global_id(0);
   const size_t lenth = get_global_size(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//--- constants
   const int shift_in = ((bool)transpose ? (i * variables + v) : (v * lenth + i));
   const int step_in = ((bool)transpose ? variables : 1);
//--- look for ttp
   float value = inputs[shift_in];
   bool bttp = false;
   if(i == 0 || i == lenth - 1)
      bttp = true;
   else
     {
      float prev = value;
      int prev_pos = i;
      float max_v = value;
      float max_pos = i;
      float min_v = value;
      float min_pos = i;
      while(fmax(fabs(prev - max_v), fabs(prev - min_v)) < min_step && prev_pos > 0)
        {
         prev_pos--;
         prev = inputs[shift_in - (i - prev_pos) * step_in];
         if(prev >= max_v && (prev - min_v) < min_step)
           {
            max_v = prev;
            max_pos = prev_pos;
           }
         if(prev <= min_v && (max_v - prev) < min_step)
           {
            min_v = prev;
            min_pos = prev_pos;
           }
        }
      //---
      float next = value;
      int next_pos = i;
      while(fmax(fabs(next - max_v), fabs(next - min_v)) < min_step && next_pos < (lenth - 1))
        {
         next_pos++;
         next = inputs[shift_in + (next_pos - i) * step_in];
         if(next > max_v && (next - min_v) < min_step)
           {
            max_v = next;
            max_pos = next_pos;
           }
         if(next < min_v && (max_v - next) < min_step)
           {
            min_v = next;
            min_pos = next_pos;
           }
        }
      //---
      if(
         (value >= prev && value > next) ||
         (value > prev && value == next) ||
         (value <= prev && value < next) ||
         (value < prev && value == next)
      )
         if(max_pos == i || min_pos == i)
            bttp = true;
     }
//---
   isttp[shift_in] = (int)bttp;
   outputs[shift_in] = 0;
   BarrierLoc;
//--- calc position
   int pos = -1;
   int prev_in = 0;
   int prev_ttp = 0;
   if(bttp)
     {
      pos = 0;
      //---
      for(int p = 0; p < i; p++)
        {
         int current_in = ((bool)transpose ? (p * variables + v) : (v * lenth + p));
         if((bool)isttp[current_in])
           {
            pos++;
            prev_ttp = p;
            prev_in = current_in;
           }
        }
     }
//--- cacl tendency
   if(pos > 0 && pos < (lenth / 3))
     {
      float sum_x = 0;
      float sum_y = 0;
      float sum_xy = 0;
      float sum_xx = 0;
      int dist = i - prev_ttp;
      //---
      for(int p = 0; p < dist; p++)
        {
         float x = (float)(p);
         float y = inputs[prev_in + p * step_in];
         sum_x += x;
         sum_y += y;
         sum_xy += x * y;
         sum_xx += x * x;
        }
      float slope = (dist * sum_xy - sum_x * sum_y) / (dist > 1 ? (dist * sum_xx - sum_x * sum_x) : 1);
      float intercept = (sum_y - slope * sum_x) / dist;
      int shift_out = ((bool)transpose ? ((pos - 1) * 3 * variables + v) : (v * lenth + (pos - 1) * 3));
      outputs[shift_out] = slope;
      outputs[shift_out + step_in] = intercept;
      outputs[shift_out + 2 * step_in] = ((float)dist) / lenth;
     }
   else
     {
      if(pos == (lenth / 3))
        {
         float sum_x = 0;
         float sum_y = 0;
         float sum_xy = 0;
         float sum_xx = 0;
         int dist = lenth - prev_ttp;
         //---
         for(int p = 0; p < dist; p++)
           {
            float x = (float)(p);
            float y = inputs[prev_in + p * step_in];
            sum_x += x;
            sum_y += y;
            sum_xy += x * y;
            sum_xx += x * x;
           }
         float slope = (dist * sum_xy - sum_x * sum_y) / (dist > 1 ? (dist * sum_xx - sum_x * sum_x) : 1);
         float intercept = (sum_y - slope * sum_x) / dist;
         int shift_out = ((bool)transpose ? ((pos - 1) * 3 * variables + v) : (v * lenth + (pos - 1) * 3));
         outputs[shift_out] = slope;
         outputs[shift_out + step_in] = intercept;
         outputs[shift_out + 2 * step_in] = ((float)dist) / lenth;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PLRGradient(__global float *inputs_gr,
                          __global const float *outputs,
                          __global const float *outputs_gr,
                          const int transpose
                         )
  {
   const size_t i = get_global_id(0);
   const size_t lenth = get_global_size(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//--- constants
   const int shift_in = ((bool)transpose ? (i * variables + v) : (v * lenth + i));
   const int step_in = ((bool)transpose ? variables : 1);
   const int shift_out = ((bool)transpose ? v : (v * lenth));
   const int step_out = 3 * step_in;
//--- calc position
   int pos = -1;
   int prev_in = 0;
   int dist = 0;
   do
     {
      pos++;
      prev_in += dist;
      dist = (int)fmax(outputs[shift_out + pos * step_out + 2 * step_in] * lenth, 1);
     }
   while(!(prev_in <= i && (prev_in + dist) > i));
//--- calc constants
   float sum_x = 0;
   float sum_xx = 0;
//---
   for(int p = 0; p < dist; p++)
     {
      float x = (float)(p);
      sum_x += x;
      sum_xx += x * x;
     }
//--- get output gradient
   float grad_slope = outputs_gr[shift_out + pos * step_out];
   float grad_intercept = outputs_gr[shift_out + pos * step_out + step_in];
//--- calc gradient
   grad_slope -= sum_x / dist * grad_intercept;
   grad_slope /= fmax(dist * sum_xx - sum_x * sum_x, 1);
   float grad = grad_intercept / dist;
   grad += (dist * (i - prev_in) - sum_x) * grad_slope;
   if(isnan(grad) || isinf(grad))
      grad = 0;
//--- save result
   inputs_gr[shift_in] = grad;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsAdamMini(__global float *matrix_w, ///<[in,out] Weights matrix (m+1)*n, where m -
                                    ///< number of neurons in previous layer and n -
                                    ///< number of neurons in current layer
                                    __global const float *matrix_g, ///<[in] Tensor of gradients at current layer
                                    __global const float *matrix_i, ///<[in] Inputs tensor
                                    __global float *matrix_m,      ///<[in,out] Matrix of first momentum
                                    __global float *matrix_v,      ///<[in,out] Matrix of seconfd momentum
                                    const float l,                  ///< Learning rates
                                    const float b1,                 ///< First momentum multiplier
                                    const float b2                  ///< Second momentum multiplier
                                   )
  {
//--- inputs
   const size_t i = get_local_id(0);
   const size_t inputs = get_local_size(0) - 1;
//--- outputs
   const size_t o = get_global_id(1);
   const size_t outputs = get_global_size(1);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const int ls = min((uint)LOCAL_ARRAY_SIZE, (uint)inputs);
   const float inp = (i < inputs ? matrix_i[i] : 1.0f);
   int count = 0;
   do
     {
      if(count == (i / ls))
        {
         int shift = i % ls;
         temp[shift] = (count == 0 ? 0 : temp[shift]) + ((isnan(inp) || isinf(inp)) ? 0 : inp * inp) / inputs;
        }
      count++;
      BarrierLoc;
     }
   while(count * ls < inputs);
//--- sum
   count = (ls + 1) / 2;
   do
     {
      if(i < count && (i + count) < ls)
        {
         temp[i] += temp[i + count];
         temp[i + count] = 0;
        }
      count = (count + 1) / 2;
      BarrierLoc;
     }
   while(count > 1);
//--- calc v
   if(i == 0)
     {
      temp[1] = matrix_g[o];
      if(isnan(temp[1]) || isinf(temp[1]))
         temp[1] = 0;
      if(isnan(temp[0]) || isinf(temp[0]))
         temp[0] = 1;
      float v = matrix_v[o];
      if(isnan(v) || isinf(v))
         v = 1;
      temp[0] = b2 * v + (1 - b2) * pow(temp[1], 2) * temp[0];
      matrix_v[o] = temp[0];
     }
   BarrierLoc;
//---
   const int wi = o * (inputs + 1) + i;
   float weight = matrix_w[wi];
   if(isnan(weight) || isinf(weight))
      weight = 0;
//---
   float m = matrix_m[wi];
   if(isnan(m) || isinf(m))
      m = 0;
//--- calc m
   m = b1 * m + (1 - b1) * temp[1] * inp;
   if(isnan(m) || isinf(m))
      m = 0;
//---
   float delta = l * (m / (sqrt(temp[0]) + 1.0e-37f) - (l1 * sign(weight) + l2 * weight));
   if(isnan(delta) || isinf(delta))
      delta = 0;
   if(delta > 0)
      matrix_w[wi] = clamp(weight + delta, -MAX_WEIGHT, MAX_WEIGHT);
   matrix_m[wi] = m;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsConvAdamMini(__global float *matrix_w,   ///<[in,out] Weights matrix (m+1)*n, where m -
                                        ///< input window and n - output window
                                        __global const float *matrix_g, ///<[in] Tensor of gradients at current layer
                                        __global const float *matrix_i, ///<[in] Inputs tensor
                                        __global float *matrix_m,      ///<[in] Matrix of first momentum
                                        __global float *matrix_v,      ///<[in] Matrix of seconfd momentum
                                        const int inputs,               ///< Number of inputs
                                        const float l,                  ///< Learning rates
                                        const float b1,                 ///< First momentum multiplier
                                        const float b2,                 ///< Second momentum multiplier
                                        int step                        ///< Step size
                                       )
  {
//--- window in
   const size_t i = get_global_id(0);
   const size_t window_in = get_global_size(0) - 1;
//--- window out
   const size_t f = get_global_id(1);
   const size_t window_out = get_global_size(1);
//--- head window out
   const size_t f_h = get_local_id(1);
   const size_t window_out_h = get_local_size(1);
//--- variable
   const size_t v = get_global_id(2);
   const size_t variables = get_global_size(2);
//--- constants
   const int total = (inputs - window_in + step - 1) / step;
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * total * window_out;
   const int shift_w = (f + v * window_out) * (window_in + 1) + i;
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const int ls = min((uint)window_in, (uint)LOCAL_ARRAY_SIZE);
//--- calc gradient
   float grad = 0;
//---
   for(int t = 0; t < total; t++)
     {
      if(i != window_in && (i + t * window_in) >= inputs)
         break;
      float gt = matrix_g[t * window_out + f + shift_var_out] *
                 (i == window_in ? 1 : matrix_i[i + t * step + shift_var_in]);
      if(!(isnan(gt) || isinf(gt)))
         grad += gt;
     }
//--- calc sum grad
   int count;
//---
   for(int h = 0; h < window_out_h; h++)
     {
      count = 0;
      do
        {
         if(h == f_h)
           {
            if(count == (i / ls))
              {
               int shift = i % ls;
               temp[shift] = ((count == 0 && h == 0) ? 0 : temp[shift]) + ((isnan(grad) || isinf(grad)) ? 0 : grad * grad) / (window_in * window_out_h);
              }
           }
         count++;
         BarrierLoc;
        }
      while((count * ls) < window_in);
     }
   count = (ls + 1) / 2;
   do
     {
      if(i < count && (i + count) < ls && f_h == 0)
        {
         temp[i] += temp[i + count];
         temp[i + count] = 0;
        }
      count = (count + 1) / 2;
      BarrierLoc;
     }
   while(count > 1);
//--- calc v
   if(i == 0 && f_h == 0)
     {
      if(isnan(temp[0]) || isinf(temp[0]))
         temp[0] = 1;
      int head = f / window_out_h;
      float v = matrix_v[head];
      if(isnan(v) || isinf(v))
         v = 1;
      temp[0] = clamp(b2 * v + (1 - b2) * temp[0], 1.0e-6f, 1.0e6f);
      matrix_v[head] = temp[0];
     }
   BarrierLoc;
//--- calc m
   float mt = clamp(b1 * matrix_m[shift_w] + (1 - b1) * grad, -1.0e5f, 1.0e5f);
   if(isnan(mt) || isinf(mt))
      mt = 0;
   float weight = clamp(matrix_w[shift_w] + l * mt / sqrt(temp[0]), -MAX_WEIGHT, MAX_WEIGHT);
   if(!(isnan(weight) || isinf(weight)))
      matrix_w[shift_w] = weight;
   matrix_m[shift_w] = mt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CutTrendAndOther(__global const float *inputs,
                               __global const float *plr,
                               __global float *trend,
                               __global float *other
                              )
  {
   const size_t i = get_global_id(0);
   const size_t lenth = get_global_size(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//--- constants
   const int shift_in = i * variables + v;
   const int step_in = variables;
   const int shift_plr = v;
   const int step_plr = 3 * step_in;
//--- calc position
   int pos = -1;
   int prev_in = 0;
   int dist = 0;
   do
     {
      pos++;
      prev_in += dist;
      dist = (int)fmax(plr[shift_plr + pos * step_plr + 2 * step_in] * lenth, 1);
     }
   while(!(prev_in <= i && (prev_in + dist) > i));
//--- calc trend
   float sloat = plr[shift_plr + pos * step_plr];
   float intercept = plr[shift_plr + pos * step_plr + step_in];
   pos = i - prev_in;
   float trend_i = sloat * pos + intercept;
   float other_i = inputs[shift_in] - trend_i;
//--- save result
   trend[shift_in] = trend_i;
   other[shift_in] = other_i;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CutTrendAndOtherGradient(__global float *inputs_gr,
                                       __global const float *plr,
                                       __global float *plr_gr,
                                       __global const float *trend_gr,
                                       __global const float *other_gr
                                      )
  {
   const size_t i = get_global_id(0);
   const size_t lenth = get_global_size(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//--- constants
   const int shift_in = i * variables + v;
   const int step_in = variables;
   const int shift_plr = v;
   const int step_plr = 3 * step_in;
//--- calc position
   int pos = -1;
   int prev_in = 0;
   int dist = 0;
   do
     {
      pos++;
      prev_in += dist;
      dist = (int)fmax(plr[shift_plr + pos * step_plr + 2 * step_in] * lenth, 1);
     }
   while(!(prev_in <= i && (prev_in + dist) > i));
//--- get gradient
   float other_i_gr = other_gr[shift_in];
   float trend_i_gr = trend_gr[shift_in] - other_i_gr;
//--- calc plr gradient
   pos = i - prev_in;
   float sloat_gr = trend_i_gr * pos;
   float intercept_gr = trend_i_gr;
//--- save result
   plr_gr[shift_plr + pos * step_plr] += sloat_gr;
   plr_gr[shift_plr + pos * step_plr + step_in] += intercept_gr;
   inputs_gr[shift_in] = other_i_gr;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CutOneFromAnother(__global const float *inputs,
                                __global const float *cut,
                                __global float *other
                               )
  {
   const size_t i = get_global_id(0);
//--- save result
   other[i] = inputs[i] - cut[i];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CutOneFromAnotherGradient(__global float *inputs_gr,
                                        __global float *cut_gr,
                                        __global const float *other_gr
                                       )
  {
   const size_t i = get_global_id(0);
   float gr = other_gr[i];
//--- save result
   inputs_gr[i] = gr;
   cut_gr[i] = (-gr);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UniTrajPrepare(__global const float *history,
                             __global const float *h_mask,
                             __global const float *future,
                             __global const float *f_mask,
                             __global float *output,
                             const int h_total,
                             const int f_total
                            )
  {
   const size_t i = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//---
   const int shift_in = i * variables + v;
   const int shift_out = 3 * shift_in;
   const int shift_f_out = 3 * (h_total * variables + v);
//--- history
   if(i < h_total)
     {
      float mask = h_mask[shift_in];
      float h = history[shift_in];
      float v = (i < (h_total - 1) && mask != 0 ? (history[shift_in + variables] - h) * mask : 0);
      if(isnan(v) || isinf(v))
         v = h = mask = 0;
      output[shift_out] = h * mask;
      output[shift_out + 1] = v;
      output[shift_out + 2] = mask;
     }
//--- future
   if(i < f_total)
     {
      float mask = f_mask[shift_in];
      float f = future[shift_in];
      float v = (i < (f_total - 1) && mask != 0 ? (future[shift_in + variables] - f) * mask : 0);
      if(isnan(v) || isinf(v))
         v = f = mask = 0;
      output[shift_f_out + shift_out] = f * mask;
      output[shift_f_out + shift_out + 1] = v;
      output[shift_f_out + shift_out + 2] = mask;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UniTrajPrepareGrad(__global float *history_gr,
                                 __global float *future_gr,
                                 __global const float *output,
                                 __global const float *output_gr,
                                 const int h_total,
                                 const int f_total
                                )
  {
   const size_t i = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//---
   const int shift_in = i * variables + v;
   const int shift_out = 3 * shift_in;
   const int shift_f_out = 3 * (h_total * variables + v);
//--- history
   if(i < h_total)
     {
      float mask = output[shift_out + 2];
      float grad = 0;
      if(mask > 0)
        {
         grad = output_gr[shift_out] * mask;
         grad -= (i < (h_total - 1) && mask != 0 ? (output_gr[shift_out + 1]) * mask : 0);
         grad += (i > 0 ? output[shift_out + 1 - 3 * variables] * output[shift_out + 2 - 3 * variables] : 0);
         if(isnan(grad) || isinf(grad))
            grad = 0;
         //---
        }
      history_gr[shift_in] = grad;
     }
//--- future
   if(i < f_total)
     {
      float mask = output[shift_f_out + shift_out + 2];
      float grad = 0;
      if(mask > 0)
        {
         grad = output_gr[shift_f_out + shift_out] * mask;
         grad -= (i < (h_total - 1) && mask != 0 ? (output_gr[shift_f_out + shift_out + 1]) * mask : 0);
         grad += (i > 0 ? output[shift_f_out + shift_out + 1 - 3 * variables] * output[shift_f_out + shift_out + 2 - 3 * variables] : 0);
         if(isnan(grad) || isinf(grad))
            grad = 0;
         //---
        }
      future_gr[shift_in] = grad;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UniTrajBTS(__global const float *concat_inp,
                         __global float *d_forw,
                         __global float *d_bakw,
                         const int total
                        )
  {
   const size_t i = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//---
   if(i == 0)
     {
      const int step = variables * 3;
      const int start = v * 3 + 2;
      float last = 0;
      d_forw[v] = 0;
      //---
      for(int p = 1; p < total; p++)
        {
         float m = concat_inp[start + p * step];
         d_forw[p * variables + v] = last = 1 + (1 - m) * last;
        }
     }
   else
     {
      const int step = -(variables * 3);
      const int start = (total - 1) * variables + v * 3 + 2;
      float last = 0;
      d_bakw[(total - 1) + v] = 0;
      //---
      for(int p = 1; p < total; p++)
        {
         float m = concat_inp[start + p * step];
         d_bakw[(total - 1 - p) * variables + v] = last = 1 + (1 - m) * last;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
float2 Rotate(const float x, const float cos_theta, const float sin_theta)
  {
   float2 result = 0;
   result.s0 = cos_theta + x * sin_theta;
   result.s1 = x * cos_theta - sin_theta;
   return result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void HiVTPrepare(__global const float *data,
                          __global float2* __attribute__((aligned(8))) output
                         )
  {
   const size_t t = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t total_v = get_global_size(1);
//---
   const int shift_data = t * total_v;
   const int shift_out = shift_data * total_v;
//---
   float value = data[shift_data + v + total_v] - data[shift_data + v];
   const float theta = atan(value);
   const float cos_theta = cos(theta);
   const float sin_theta = sin(theta);
   const float2 main = Rotate(value, cos_theta, sin_theta);
//---
//---
   for(int a = 0; a < total_v; a++)
     {
      float2 o = main;
      if(a != v)
         o -= Rotate(data[shift_data + a + total_v] - data[shift_data + a], cos_theta, sin_theta);
      output[shift_out + a] = o;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void GateElementMul(__global const float *inputs1,
                             __global const float *inputs2,
                             __global const float *gate,
                             __global float *out
                            )
  {
   const int i = get_global_id(0);
//---
   const float g = IsNaNOrInf(gate[i],0.5f);
   float result = g * IsNaNOrInf(inputs1[i],0) + (1 - g) * IsNaNOrInf(inputs2[i],0);
//---
   out[i] = IsNaNOrInf(result,0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void GateElementMulGrad(__global const float *inputs1,
                                 __global float *inputs1_gr,
                                 __global const float *inputs2,
                                 __global float *inputs2_gr,
                                 __global const float *gate,
                                 __global float *gate_gr,
                                 __global const float *out_gr,
                                 const int activ1,
                                 const int activ2,
                                 const int activ_gate
                                )
  {
   const int i = get_global_id(0);
//---
   const float g = IsNaNOrInf(gate[i],0.5f);
   const float i1 = IsNaNOrInf(inputs1[i],0);
   const float i2 = IsNaNOrInf(inputs2[i],0);
   const float grad = IsNaNOrInf(out_gr[i],0);
//---
   float i1_gr = IsNaNOrInf(grad * g,0);
   float i2_gr = IsNaNOrInf(grad * (1 - g),0);
   float g_gr = IsNaNOrInf(grad * (i1 - i2),0);
//---
   inputs1_gr[i] = Deactivation(i1_gr, i1, activ1);
   inputs2_gr[i] = Deactivation(i2_gr, i2, activ2);
   gate_gr[i] = Deactivation(g_gr, g, activ_gate);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void TransposeRCD(__global const float *matrix_in, ///<[in] Input matrix
                           __global float *matrix_out ///<[out] Output matrix
                          )
  {
   const int r = get_global_id(0);
   const int c = get_global_id(1);
   const int d = get_global_id(2);
   const int rows = get_global_size(0);
   const int cols = get_global_size(1);
   const int dimension = get_global_size(2);
//---
   matrix_out[(c * rows + r)*dimension + d] = matrix_in[(r * cols + c) * dimension + d];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void OrthoganalLoss(__global const float *data,
                             __global float *grad,
                             const int add
                            )
  {
   const size_t r = get_global_id(0);
   const size_t c = get_local_id(1);
   const size_t cols = get_local_size(1);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   uint ls = min((uint)cols, (uint)LOCAL_ARRAY_SIZE);
//---
   const int shift1 = r * cols + c;
   const int shift2 = c * cols + r;
   float value1 = IsNaNOrInf(data[shift1],0);
   float value2 = (shift1 == shift2 ? value1 : IsNaNOrInf(data[shift2],0));
   float v2 = IsNaNOrInf(value1 * value2,0);
//---
   for(int i = 0; i < cols; i += ls)
     {
      //---
      if(i <= c && (i + ls) > c)
         Temp[c - i] = (i == 0 ? 0 : Temp[c - i]) + v2;
      BarrierLoc;
     }
//---
   uint count = min(ls, (uint)cols);
   do
     {
      count = (count + 1) / 2;
      if(c < ls)
         Temp[c] += (c < count && (c + count) < cols ? Temp[c + count] : 0);
      if(c + count < ls)
         Temp[c + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//---
   const float sum = Temp[0];
   float loss = -pow((float)(r == c) - sum, 2.0f);
   float g = (2 * (sum - (float)(r == c))) * loss;
   g = 2 * value2 * g;
   if(isinf(g) || isnan(g))
      g = 0;
   if(add == 1)
      grad[shift1] += g;
   else
      grad[shift1] = g;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcDistance(__global const float *data,
                           __global float *distance,
                           const int dimension
                          )
  {
   const size_t main = get_global_id(0);
   const size_t slave = get_local_id(1);
   const int total = (int)get_local_size(1);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   int ls = min((int)total, (int)LOCAL_ARRAY_SIZE);
//---
   const int shift_main = main * dimension;
   const int shift_slave = slave * dimension;
   const int shift_dist = main * total + slave;
//--- calc distance
   float dist = 0;
   if(main != slave)
     {
      //---
      for(int d = 0; d < dimension; d++)
         dist += pow(data[shift_main + d] - data[shift_slave + d], 2.0f);
     }
//--- Look Max
//---
   for(int i = 0; i < total; i += ls)
     {
      if(!isinf(dist) && !isnan(dist))
        {
         if(i <= slave && (i + ls) > slave)
            Temp[slave - i] = max((i == 0 ? 0 : Temp[slave - i]), dist);
        }
      else
         if(i == 0)
            Temp[slave] = 0;
      BarrierLoc;
     }
//---
   int count = ls;
   do
     {
      count = (count + 1) / 2;
      if(slave < count && (slave + count) < ls)
        {
         if(Temp[slave] < Temp[slave + count])
            Temp[slave] = Temp[slave + count];
         Temp[slave + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//--- Normalize
   if(Temp[0] > 0)
      dist /= Temp[0];
   if(isinf(dist) || isnan(dist))
      dist = 1;
//--- result
   distance[shift_dist] = dist;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardLocalMax(__global const float *matrix_i,
                                  __global const float *distance,
                                  __global float *matrix_o,
                                  const float radius
                                 )
  {
   const size_t i = get_global_id(0);
   const size_t total = get_global_size(0);
   const size_t d = get_global_id(1);
   const size_t dimension = get_global_size(1);
//---
   const int shift_dist = i * total;
   const int shift_out = i * dimension + d;
//---
   float result = -3.402823466e+38f;
//---
   for(int k = 0; k < total; k++)
     {
      if(distance[shift_dist + k] > radius)
         continue;
      int shift = k * dimension + d;
      result = max(result, matrix_i[shift]);
     }
   matrix_o[shift_out] = result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcInputGradientLocalMax(__global const float *matrix_i,
                                        __global float *matrix_ig,
                                        __global const float *distance,
                                        __global const float *matrix_o,
                                        __global const float *matrix_g,
                                        const float radius
                                       )
  {
   const size_t i = get_global_id(0);
   const size_t total = get_global_size(0);
   const size_t d = get_global_id(1);
   const size_t dimension = get_global_size(1);
//---
   float result = 0;
   float value = matrix_i[i * dimension + d];
//---
   for(int k = 0; k < total; k++)
     {
      if(distance[k * total + i] > radius)
         continue;
      int shift = k * dimension + d;
      if(fabs(matrix_o[shift] - value) <= 1.192092896e-07f)
         result += matrix_g[shift];
     }
   matrix_ig[i * dimension + d] = result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MHMaskAttentionOut(__global const float *q,     ///<[in] Matrix of Querys
                                 __global const float *kv,    ///<[in] Matrix of Keys
                                 __global float *score,       ///<[out] Matrix of Scores
                                 __global const float *mask,  ///<[in] Mask Matrix
                                 __global float *out,         ///<[out] Matrix of attention
                                 const int dimension,          ///< Dimension of Key
                                 const int heads_kv,
                                 const float mask_level
                                )
  {
//--- init
   const int q_id = get_global_id(0);
   const int k = get_local_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int kunits = get_local_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_k = dimension * (2 *  heads_kv * k + h_kv);
   const int shift_v = dimension * (2 *  heads_kv * k + heads_kv + h_kv);
   const int shift_s = kunits * (q_id *  heads + h) + k;
   const bool b_mask = (mask[shift_s] < mask_level);
   const uint ls = min((uint)get_local_size(1), (uint)LOCAL_ARRAY_SIZE);
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   __local float temp[LOCAL_ARRAY_SIZE];
//--- Score
   float sum = 0;
   if(b_mask)
      sum = MIN_VALUE;
   else
      for(int d = 0; d < dimension; d++)
         sum += q[shift_q + d] * kv[shift_k + d];
   float sc = LocalSoftMax(IsNaNOrInf(sum / koef, MIN_VALUE), 1, temp);
   score[shift_s] = sc;
   BarrierLoc;
//--- out
   for(int d = 0; d < dimension; d++)
     {
      BarrierLoc;
      sum = LocalSum(IsNaNOrInf(kv[shift_v + d] * sc, 0), 1, temp);
      if(k == 0)
         out[shift_q + d] = temp[0];
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MHMaskAttentionInsideGradients(__global const float *q, __global float *q_g,
      __global const float *kv, __global float *kv_g,
      __global const float *mask, __global float *mask_g,
      __global const float *scores, __global const float *gradient,
      const int kunits, const int heads_kv, const float mask_level)
  {
//--- init
   const int q_id = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h) + d;
   const int shift_s = (q_id * heads + h) * kunits;
   const int shift_g = h * dimension + d;
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
//--- Calculating Value's gradients
   int step_score = kunits * heads;
   if(h < heads_kv)
     {
      //---
      for(int v = q_id; v < kunits; v += qunits)
        {
         float grad = 0;
         for(int hq = h; hq < heads; hq += heads_kv)
           {
            int shift_score = hq * kunits + v;
            for(int g = 0; g < qunits; g++)
               grad += gradient[shift_g + dimension * (hq - h + g  * heads)] *
                       scores[shift_score + g * step_score];
           }
         int shift_v = dimension * (2 *  heads_kv * v + heads_kv + h) + d;
         kv_g[shift_v] = grad;
        }
     }
//--- Calculating Query's gradients
   float grad = 0;
   float out_g = gradient[shift_g + q_id * dimension];
   int shift_val = (heads_kv + h_kv) * dimension + d;
   int shift_key = h_kv * dimension + d;
//---
   for(int k = 0; k < kunits; k++)
     {
      float sc_g = 0;
      float sc = scores[shift_s + k];
      if(sc == 0)
         continue;
      for(int v = 0; v < kunits; v++)
         sc_g += scores[shift_s + v] * out_g * kv[shift_val + 2 * v * heads_kv * dimension] *
                 ((float)(k == v) - sc);
      grad += sc_g * kv[shift_key + 2 * k * heads_kv * dimension];
     }
   q_g[shift_q] = grad / koef;
//--- Calculating Key's gradients
   if(h < heads_kv)
     {
      //---
      for(int k = q_id; k < kunits; k += qunits)
        {
         int shift_k = dimension * (2 *  heads_kv * k + h_kv) + d;
         grad = 0;
         for(int hq = h; hq < heads; hq++)
           {
            int shift_score = hq * kunits + k;
            float val = kv[shift_k + heads_kv * dimension];
            for(int scr = 0; scr < qunits; scr++)
              {
               float sc_g = 0;
               int shift_sc = scr * kunits * heads;
               float sc = scores[shift_sc + k];
               if(sc == 0)
                  continue;
               for(int v = 0; v < kunits; v++)
                  sc_g += scores[shift_sc + v] * gradient[shift_g + scr * dimension] *
                          val * ((float)(k == v) - sc);
               grad += sc_g * q[shift_q + scr * dimension];
              }
           }
         kv_g[shift_k] = grad / koef;
        }
     }
//--- Mask's gradient
   for(int k = q_id; k < kunits; k += qunits)
     {
      float m = mask[shift_s + k];
      if(m < mask_level)
         mask_g[shift_s + k] = 0;
      else
         mask_g[shift_s + k] = 1 - m;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcPositionBias(__global const float *data1,
                               __global const float *data2,
                               __global float *result,
                               const int dimension
                              )
  {
   const size_t idx1 = get_global_id(0);
   const size_t idx2 = get_global_id(1);
   const size_t total1 = get_global_size(0);
   const size_t total2 = get_global_size(1);
//---
   const int shift1 = idx1 * dimension;
   const int shift2 = idx2 * dimension;
   const int shift_out = idx1 * total2 + idx2;
//---
   float res = 0;
//---
   for(int i = 0; i < dimension; i++)
      res = pow(data1[shift1 + i] - data2[shift2 + i], 2.0f);
   res = sqrt(res);
   res = exp(-res);
   if(isnan(res) || isinf(res))
      res = 0;
//---
   result[shift_out] = res;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MHPosBiasAttentionOut(__global const float *q,        ///<[in] Matrix of Querys
                                    __global const float *k,        ///<[in] Matrix of Keys
                                    __global const float *v,        ///<[in] Matrix of Values
                                    __global float *score,          ///<[out] Matrix of Scores
                                    __global const float *pos_bias, ///<[in] Position Bias
                                    __global float *out,            ///<[out] Matrix of attention
                                    const int dimension,             ///< Dimension of Key
                                    const int heads_kv,
                                    const int use_pos_bias
                                   )
  {
//--- init
   const int q_id = get_global_id(0);
   const int k_id = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int kunits = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_kv = dimension * (heads_kv * k_id + h_kv);
   const int shift_s = kunits * (q_id *  heads + h) + k_id;
   const int shift_pb = q_id * kunits + k_id;
   const uint ls = min((uint)get_local_size(1), (uint)LOCAL_ARRAY_SIZE);
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   __local float temp[LOCAL_ARRAY_SIZE];
//--- sum of exp
   uint count = 0;
   if(k_id < ls)
     {
      temp[k_id] = 0;
      //---
      do
        {
         if(q_id >= (count * ls + k_id))
            if((count * ls) < (kunits - k_id))
              {
               float sum = 0;
               int sh_k = dimension * heads_kv * count * ls;
               for(int d = 0; d < dimension; d++)
                  sum = q[shift_q + d] * k[shift_kv + d + sh_k];
               sum = exp(sum / koef);
               if(isnan(sum))
                  sum = 0;
               temp[k_id] = temp[k_id] + sum + (use_pos_bias > 0 ? pos_bias[shift_pb + count * ls] : 0);
              }
         count++;
        }
      while((count * ls + k_id) < kunits);
     }
   BarrierLoc;
   count = min(ls, (uint)kunits);
//---
//---
   do
     {
      count = (count + 1) / 2;
      if(k_id < ls)
         temp[k_id] += (k_id < count && (k_id + count) < kunits ? temp[k_id + count] : 0);
      if(k_id + count < ls)
         temp[k_id + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//--- score
   float sum = temp[0];
   float sc = 0;
   if(q_id >= (count * ls + k_id))
      if(sum != 0)
        {
         //---
         for(int d = 0; d < dimension; d++)
            sc = q[shift_q + d] * k[shift_kv + d];
         sc = (exp(sc / koef) + (use_pos_bias > 0 ? pos_bias[shift_pb] : 0)) / sum;
         if(isnan(sc))
            sc = 0;
        }
   score[shift_s] = sc;
   BarrierLoc;
//--- out
//---
   for(int d = 0; d < dimension; d++)
     {
      uint count = 0;
      if(k_id < ls)
         do
           {
            if((count * ls) < (kunits - k_id))
              {
               int sh_v = 2 * dimension * heads_kv * count * ls;
               float sum =
                  v[shift_kv + d + sh_v] * (count == 0 ? sc : score[shift_s + count * ls]);
               if(isnan(sum))
                  sum = 0;
               temp[k_id] = (count > 0 ? temp[k_id] : 0) + sum;
              }
            count++;
           }
         while((count * ls + k_id) < kunits);
      BarrierLoc;
      //---
      count = min(ls, (uint)kunits);
      do
        {
         count = (count + 1) / 2;
         if(k_id < ls)
            temp[k_id] += (k_id < count && (k_id + count) < kunits ? temp[k_id + count] : 0);
         if(k_id + count < ls)
            temp[k_id + count] = 0;
         BarrierLoc;
        }
      while(count > 1);
      //---
      out[shift_q + d] = temp[0];
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MHPosBiasAttentionInsideGradients(__global const float *q, __global float *q_g,
      __global const float *k, __global float *k_g,
      __global const float *v, __global float *v_g,
      __global const float *scores, __global const float *gradient,
      const int kunits, const int heads_kv)
  {
//--- init
   const int q_id = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h) + d;
   const int shift_s = (q_id * heads + h) * kunits;
   const int shift_g = h * dimension + d;
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
//--- Calculating Value's gradients
   int step_score = kunits * heads;
   if(h < heads_kv)
     {
      //---
      for(int v_id = q_id; v_id < kunits; v_id += qunits)
        {
         float grad = 0;
         for(int hq = h; hq < heads; hq += heads_kv)
           {
            int shift_score = hq * kunits + v_id;
            for(int g = 0; g < qunits; g++)
               grad += gradient[shift_g + dimension * (hq - h + g  * heads)] *
                       scores[shift_score + g * step_score];
           }
         int shift_v = dimension * (heads_kv * v_id + h) + d;
         v_g[shift_v] = grad;
        }
     }
//--- Calculating Query's gradients
   float grad = 0;
   float out_g = gradient[shift_g + q_id * dimension];
   int shift_val = h_kv * dimension + d;
   int shift_key = h_kv * dimension + d;
//---
   for(int k_id = 0; k_id < kunits; k_id++)
     {
      float sc_g = 0;
      float sc = scores[shift_s + k_id];
      if(sc == 0)
         continue;
      for(int v_id = 0; v_id < kunits; v_id++)
         sc_g += scores[shift_s + v_id] * out_g * v[shift_val + v_id * heads_kv * dimension] *
                 ((float)(k_id == v_id) - sc);
      grad += sc_g * k[shift_key + k_id * heads_kv * dimension];
     }
   q_g[shift_q] = grad / koef;
//--- Calculating Key's gradients
   if(h < heads_kv)
     {
      //---
      for(int k_id = q_id; k_id < kunits; k_id += qunits)
        {
         int shift_k = dimension * (heads_kv * k_id + h_kv) + d;
         grad = 0;
         for(int hq = h; hq < heads; hq += heads_kv)
           {
            int shift_score = hq * kunits + k_id;
            float val = v[shift_k];
            for(int scr = 0; scr < qunits; scr++)
              {
               float sc_g = 0;
               int shift_sc = scr * kunits * heads;
               float sc = scores[shift_sc + k_id];
               if(sc == 0)
                  continue;
               for(int v_id = 0; v_id < kunits; v_id++)
                  sc_g += scores[shift_sc + v_id] * gradient[shift_g + scr * dimension] *
                          val * ((float)(k_id == v_id) - sc);
               grad += sc_g * q[shift_g + scr * heads * dimension];
              }
           }
         k_g[shift_k] = grad / koef;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DiversityLoss(__global const float *data,
                            __global float *grad,
                            const int activation,
                            const int add
                           )
  {
   const size_t main = get_global_id(0);
   const size_t slave = get_local_id(1);
   const size_t dim = get_local_id(2);
   const size_t total = get_local_size(1);
   const size_t dimension = get_local_size(2);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
//---
   const int shift_main = main * dimension + dim;
   const int shift_slave = slave * dimension + dim;
//---
   const int value_main = data[shift_main];
   const int value_slave = data[shift_slave];
   float delt = value_main - value_slave;
//---
   const int ls = min((int)total, (int)LOCAL_ARRAY_SIZE);
//---
   for(int d = 0; d < dimension; d++)
     {
      for(int i = 0; i < total; i += ls)
        {
         if(d == dim)
           {
            if(i <= slave && (i + ls) > slave)
              {
               int k = i % ls;
               float val = IsNaNOrInf(pow(delt, 2.0f) / total, 0);
               Temp[k] = ((d == 0 && i == 0) ? 0 : Temp[k]) + val;
              }
           }
         BarrierLoc;
        }
     }
//---
   int count = ls;
//---
   do
     {
      count = (count + 1) / 2;
      if(slave < count)
        {
         Temp[slave] += ((slave + count) < ls ? Temp[slave + count] : 0);
         if(slave + count < ls)
            Temp[slave + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//---
   float loss = exp(-Temp[0]);
   float gr = IsNaNOrInf(2 * pow(loss, 2.0f) * delt / total, 0);
//---
//---
   for(int d = 0; d < dimension; d++)
     {
      for(int i = 0; i < total; i += ls)
        {
         if(d == dim)
           {
            if(i <= slave && (i + ls) > slave)
              {
               int k = i % ls;
               Temp[k] = ((d == 0 && i == 0) ? 0 : Temp[k]) + gr;
              }
           }
         BarrierLoc;
        }
      //---
      int count = ls;
      do
        {
         count = (count + 1) / 2;
         if(slave < count && d == dim)
           {
            Temp[slave] += ((slave + count) < ls ? Temp[slave + count] : 0);
            if(slave + count < ls)
               Temp[slave + count] = 0;
           }
         BarrierLoc;
        }
      while(count > 1);
      if(slave == 0 && d == dim)
        {
         if(add > 0)
            grad[shift_main] += Deactivation(IsNaNOrInf(Temp[0], 0), value_main, activation);
         else
            grad[shift_main] = Deactivation(IsNaNOrInf(Temp[0], 0), value_main, activation);
        }
      BarrierLoc;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MHRelativeAttentionOut(__global const float *q,        ///<[in] Matrix of Querys
                                     __global const float *k,        ///<[in] Matrix of Keys
                                     __global const float *v,        ///<[in] Matrix of Values
                                     __global const float *bk,       ///<[in] Matrix of Positional Bias Keys
                                     __global const float *bv,       ///<[in] Matrix of Positional Bias Values
                                     __global const float *gc,       ///<[in] Global content bias vector
                                     __global const float *gp,       ///<[in] Global positional bias vector
                                     __global float *score,          ///<[out] Matrix of Scores
                                     __global float *out,            ///<[out] Matrix of attention
                                     const int dimension              ///< Dimension of Key
                                    )
  {
//--- init
   const int q_id = get_global_id(0);
   const int k_id = get_local_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int kunits = get_local_size(1);
   const int heads = get_global_size(2);
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_kv = dimension * (heads * k_id + h);
   const int shift_gc = dimension * h;
   const int shift_s = kunits * (q_id *  heads + h) + k_id;
   const int shift_pb = q_id * kunits + k_id;
   const uint ls = min((uint)get_local_size(1), (uint)LOCAL_ARRAY_SIZE);
   float koef = sqrt((float)dimension);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
//--- score
   float sc = 0;
//---
   for(int d = 0; d < dimension; d++)
     {
      float val_q = q[shift_q + d];
      float val_k = k[shift_kv + d];
      float val_bk = bk[shift_kv + d];
      sc += val_q * val_k + val_q * val_bk + val_k * val_bk + gc[shift_q + d] * val_k + gp[shift_q + d] * val_bk;
     }
   sc = sc / koef;
//--- max value
//---
   for(int cur_k = 0; cur_k < kunits; cur_k += ls)
     {
      if(k_id >= cur_k && k_id < (cur_k + ls))
        {
         int shift_local = k_id % ls;
         temp[shift_local] = (cur_k == 0 ? sc : fmax(temp[shift_local], sc));
        }
      BarrierLoc;
     }
   uint count = min(ls, (uint)kunits);
//---
   do
     {
      count = (count + 1) / 2;
      if(k_id < ls)
         temp[k_id] = (k_id < count && (k_id + count) < kunits ? fmax(temp[k_id + count], temp[k_id]) : temp[k_id]);
      BarrierLoc;
     }
   while(count > 1);
   sc = IsNaNOrInf(exp(fmax(sc - temp[0], -120)), 0);
   BarrierLoc;
//--- sum of exp
//---
   for(int cur_k = 0; cur_k < kunits; cur_k += ls)
     {
      if(k_id >= cur_k && k_id < (cur_k + ls))
        {
         int shift_local = k_id % ls;
         temp[shift_local] = (cur_k == 0 ? 0 : temp[shift_local]) + sc;
        }
      BarrierLoc;
     }
//---
   count = min(ls, (uint)kunits);
   do
     {
      count = (count + 1) / 2;
      if(k_id < ls)
         temp[k_id] += (k_id < count && (k_id + count) < kunits ? temp[k_id + count] : 0);
      if(k_id + count < ls)
         temp[k_id + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//--- score
   float sum = IsNaNOrInf(temp[0], 1);
   if(fabs(sum) <= 1.2e-7f)
      sum = 1;
   sc /= sum;
   score[shift_s] = sc;
   BarrierLoc;
//--- out
//---
   for(int d = 0; d < dimension; d++)
     {
      float val_v = v[shift_kv + d];
      float val_bv = bv[shift_kv + d];
      float val = IsNaNOrInf(sc * (val_v + val_bv), 0);
      //--- sum of value
      for(int cur_v = 0; cur_v < kunits; cur_v += ls)
        {
         if(k_id >= cur_v && k_id < (cur_v + ls))
           {
            int shift_local = k_id % ls;
            temp[shift_local] = (cur_v == 0 ? 0 : temp[shift_local]) + val;
           }
         BarrierLoc;
        }
      //---
      count = min(ls, (uint)kunits);
      do
        {
         count = (count + 1) / 2;
         if(k_id < count && (k_id + count) < kunits)
            temp[k_id] += temp[k_id + count];
         if(k_id + count < ls)
            temp[k_id + count] = 0;
         BarrierLoc;
        }
      while(count > 1);
      //---
      if(k_id == 0)
         out[shift_q + d] = IsNaNOrInf(temp[0], 0);
      BarrierLoc;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MHRelativeAttentionInsideGradients(__global const float *q, __global float *q_g,
      __global const float *k, __global float *k_g,
      __global const float *v, __global float *v_g,
      __global const float *bk, __global float *bk_g,
      __global const float *bv, __global float *bv_g,
      __global const float *gc, __global float *gc_g,
      __global const float *gp, __global float *gp_g,
      __global const float *scores,
      __global const float *gradient,
      const int kunits
                                                )
  {
//--- init
   const int q_id = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int shift_q = dimension * (q_id * heads + h) + d;
   const int shift_s = (q_id * heads + h) * kunits;
   const int shift_g = h * dimension + d;
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
//--- Calculating Value's gradients
   int step_score = kunits * heads;
//---
   for(int v_id = q_id; v_id < kunits; v_id += qunits)
     {
      float grad = 0;
      int shift_score = h * kunits + v_id;
      for(int g = 0; g < qunits; g++)
         grad += gradient[shift_g + dimension * (g  * heads)] *
                 scores[shift_score + g * step_score];
      int shift_v = dimension * (heads * v_id + h) + d;
      grad = IsNaNOrInf(grad, 0);
      v_g[shift_v] = grad;
      bv_g[shift_v] = grad;
     }
//--- Calculating Query's gradients
   float grad_gc = 0;
   float grad_gp = 0;
   float out_g = gradient[shift_g + q_id * dimension];
   int shift_val = h * dimension + d;
   int shift_key = h * dimension + d;
//---
   for(int k_id = 0; k_id < kunits; k_id++)
     {
      float sc_g = 0;
      float sc = scores[shift_s + k_id];
      if(sc == 0)
         continue;
      for(int v_id = 0; v_id < kunits; v_id++)
         sc_g += scores[shift_s + v_id] * out_g *
                 (v[shift_val + v_id * heads * dimension] + bv[shift_val + v_id * heads * dimension]) *
                 ((float)(k_id == v_id) - sc);
      grad_gc += IsNaNOrInf(sc_g * k[shift_key + k_id * heads * dimension], 0);
      grad_gp += IsNaNOrInf(sc_g * bk[shift_key + k_id * heads * dimension], 0);
     }
//---
   q_g[shift_q] = (grad_gc + grad_gp) / koef;
   gc_g[shift_q] = grad_gc / koef;
   gp_g[shift_q] = grad_gp / koef;
//--- Calculating Key's gradients
//---
   for(int k_id = q_id; k_id < kunits; k_id += qunits)
     {
      int shift_k = dimension * (heads * k_id + h) + d;
      float grad = 0;
      float grad_bk = 0;
      int shift_score = h * kunits + k_id;
      float val = (v[shift_k] + bv[shift_k]);
      for(int scr = 0; scr < qunits; scr++)
        {
         float sc_g = 0;
         int shift_sc = scr * kunits * heads;
         float sc = scores[shift_sc + k_id];
         if(sc == 0)
            continue;
         for(int v_id = 0; v_id < kunits; v_id++)
            sc_g += scores[shift_sc + v_id] * gradient[shift_g + scr * dimension] *
                    val * ((float)(k_id == v_id) - sc);
         float _q = q[shift_g + scr * heads * dimension];
         grad += sc_g * (_q + bk[shift_k] + gc[shift_g + scr * heads * dimension]);
         grad_bk += sc_g * (_q + k[shift_k] + gp[shift_g + scr * heads * dimension]);
        }
      k_g[shift_k] = grad / koef;
      bk_g[shift_k] = grad_bk / koef;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcAlignmentGradient(__global const float *matrix_o1,
                                    __global const float *matrix_o2,
                                    __global float *matrix_g1,
                                    __global float *matrix_g2,
                                    const int activation,
                                    const int add)
  {
   int i = get_global_id(0);
   const float out1 = IsNaNOrInf(matrix_o1[i], 0);
   const float out2 = IsNaNOrInf(matrix_o2[i], 0);
   float grad1 = Deactivation(out2 - out1, out1, activation);
   float grad2 = Deactivation(out1 - out2, out2, activation);
//---
   if(add > 0)
     {
      matrix_g1[i] += grad1;
      matrix_g2[i] += grad2;
     }
   else
     {
      matrix_g1[i] = grad1;
      matrix_g2[i] = grad2;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeatureSmoothing(__global const float *feature,
                               __global float *outputs,
                               const int smoothing
                              )
  {
   const size_t pos = get_global_id(0);
   const size_t d = get_global_id(1);
   const size_t total = get_global_size(0);
   const size_t dimension = get_global_size(1);
//---
   const int shift_input = pos * dimension + d;
   const int shift_output = dimension * pos * smoothing + d;
//---
   float value = IsNaNOrInf(feature[shift_input], 0);
   outputs[shift_output] = value;
//---
   for(int s = 1; s <= smoothing; s++)
     {
      if((pos - s) >= 0)
         value += IsNaNOrInf(feature[shift_input - s * dimension], 0);
      if((pos + s) < total)
         value += IsNaNOrInf(feature[shift_input + s * dimension], 0);
      float factor = IsNaNOrInf(1.0f / (min((int)total, (int)(pos + s)) - max((int)(pos - s), 0) + 1), 0);
      float out = IsNaNOrInf(value * factor, 0);
      outputs[shift_output + s * dimension] = out;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeatureSmoothingGradient(__global float *feature_gr,
                                       __global const float *outputs_gr,
                                       const int smoothing
                                      )
  {
   const size_t pos = get_global_id(0);
   const size_t d = get_global_id(1);
   const size_t total = get_global_size(0);
   const size_t dimension = get_global_size(1);
//---
   const int shift_input = pos * dimension + d;
   const int shift_output = dimension * pos * smoothing + d;
   const int step_output = dimension * smoothing;
//---
   float grad = IsNaNOrInf(outputs_gr[shift_output], 0);
//---
   for(int s = 1; s <= smoothing; s++)
     {
      int shift = shift_output + s * dimension;
      float factor = 1.0f / (min((int)total, (int)(pos + s)) - max((int)(pos - s), 0) + 1);
      //---
      float value = IsNaNOrInf(outputs_gr[shift] * factor, 0);
      //---
      if((pos - s) >= 0)
         grad += IsNaNOrInf(outputs_gr[shift - s * step_output] * factor, 0);
      //---
      if((pos + s) < total)
         grad += IsNaNOrInf(outputs_gr[shift + s * step_output] * factor, 0);
     }
//---
   feature_gr[shift_input] = IsNaNOrInf(grad, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void BatchFeedForwardAddNoise(__global const float *inputs, __global float *options,
                                       __global const float *noise, __global float *output,
                                       const int batch, const int optimization,
                                       const int activation, const float alpha)
  {
   if(batch <= 1)
      return;
   int n = get_global_id(0);
   int shift = n * (optimization == 0 ? 7 : 9);
//---
   float inp = inputs[n];
   float mean = (batch > 1 ? (IsNaNOrInf(options[shift], 0) * ((float)batch - 1.0f) + inp) / ((float)batch) : inp);
   float delt = inp - mean;
   float variance = IsNaNOrInf(options[shift + 1], 0) * ((float)batch - 1.0f) + pow(delt, 2);
   if(batch > 0)
      variance /= (float)batch;
   float nx = (variance > 0 ? delt / sqrt(variance) : 0);
   float noisex = sqrt(alpha) * nx + sqrt(1 - alpha) * fabs(noise[n]) * sign(nx);
//---
   float gamma = IsNaNOrInf(options[shift + 3], 0);
   if(gamma == 0)
     {
      options[shift + 3] = 1;
      gamma = 1;
     }
   float betta = IsNaNOrInf(options[shift + 4], 0);
//---
   options[shift] = mean;
   options[shift + 1] = variance;
   options[shift + 2] = nx;
   output[n] = fActivation(gamma * noisex + betta, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void HyperProjection(__global const float *inputs,
                              __global float *outputs
                             )
  {
   const size_t pos = get_global_id(0);
   const size_t d = get_local_id(1);
   const size_t total = get_global_size(0);
   const size_t dimension = get_local_size(1);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const int ls = min((int)dimension, (int)LOCAL_ARRAY_SIZE);
//---
   const int shift_in = pos * dimension + d;
   const int shift_out = pos * (dimension + 1) + d + 1;
//---
   float v = IsNaNOrInf(inputs[shift_in], 0);
//---
   float v2 = IsNaNOrInf(v * v, 0);
//---
   if(d < ls)
      temp[d] = v2;
   BarrierLoc;
//---
   for(int i = ls; i < (int)dimension; i += ls)
     {
      if(d >= i && d < (i + ls))
         temp[d % ls] += v2;
      BarrierLoc;
     }
//---
   int count = min(ls, (int)dimension);
//---
   do
     {
      count = (count + 1) / 2;
      if(d < count)
         temp[d] += ((d + count) < dimension ? temp[d + count] : 0);
      if(d + count < dimension)
         temp[d + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//---
   outputs[shift_out] = v;
   if(d == 0)
     {
      v = IsNaNOrInf(((float)pos) / ((float)total), 0);
      outputs[shift_out - 1] = sqrt(fmax(temp[0] - v * v, 1.2e-07f));
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void HyperProjectionGrad(__global const float *inputs,
                                  __global float *inputs_gr,
                                  __global const float *outputs_gr
                                 )
  {
   const size_t pos = get_global_id(0);
   const size_t d = get_global_id(1);
   const size_t total = get_global_size(0);
   const size_t dimension = get_global_size(1);
//---
   const int shift_in = pos * dimension + d;
   const int shift_start_out = pos * (dimension + 1);
   const int shift_out = shift_start_out + d + 1;
//---
   float v = IsNaNOrInf(inputs[shift_in], 0);
   float grad = IsNaNOrInf(outputs_gr[shift_out], 0);
//---
   v = IsNaNOrInf(v * outputs_gr[shift_start_out], 0);
//---
   inputs_gr[shift_in] = v + grad;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void LogMap(__global const float *features,
                     __global const float *centroids,
                     __global const float *curvatures,
                     __global float *outputs,
                     __global float *product,
                     __global float *distance,
                     __global float *norma
                    )
  {
//--- identify
   const size_t f = get_global_id(0);
   const size_t cent = get_global_id(1);
   const size_t d = get_local_id(2);
   const size_t total_f = get_global_size(0);
   const size_t total_cent = get_global_size(1);
   const size_t dimension = get_local_size(2);
//--- create local array
   __local float temp[LOCAL_ARRAY_SIZE];
   const int ls = min((int)dimension, (int)LOCAL_ARRAY_SIZE);
//--- calc shifts
   const int shift_f = f * dimension + d;
   const int shift_out = (f * total_cent + cent) * dimension + d;
   const int shift_cent = cent * dimension + d;
   const int shift_temporal = f * total_cent + cent;
//--- load inputs
   float feature = IsNaNOrInf(features[shift_f], 0);
   float centroid = IsNaNOrInf(centroids[shift_cent], 0);
   float curv = IsNaNOrInf(curvatures[cent], 1.2e-7f);
//--- dot(features, centroids)
   float fc = IsNaNOrInf(feature * centroid, 0);
//---
   if(d < ls)
      temp[d] = (d > 0 ? fc : -fc);
   BarrierLoc;
//---
   for(int i = ls; i < (int)dimension; i += ls)
     {
      if(d >= i && d < (i + ls))
         temp[d % ls] += fc;
      BarrierLoc;
     }
//---
   int count = min(ls, (int)dimension);
//---
   do
     {
      count = (count + 1) / 2;
      if(d < count)
         temp[d] += ((d + count) < dimension ? temp[d + count] : 0);
      if(d + count < dimension)
         temp[d + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
   float prod = IsNaNOrInf(temp[0], 0);
   product[shift_temporal] = prod;
//--- project
   float u = IsNaNOrInf(feature + prod * centroid * curv, 0);
//--- norm(u)
   float u2 = IsNaNOrInf(u * u, 0);
//---
   if(d < ls)
      temp[d] = (d > 0 ? u2 : -u2);
   BarrierLoc;
//---
   for(int i = ls; i < (int)dimension; i += ls)
     {
      if(d >= i && d < (i + ls))
         temp[d % ls] += u2;
      BarrierLoc;
     }
//---
   count = min(ls, (int)dimension);
//---
   do
     {
      count = (count + 1) / 2;
      if(d < count)
         temp[d] += ((d + count) < dimension ? temp[d + count] : 0);
      if(d + count < dimension)
         temp[d + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
   float normu = IsNaNOrInf(temp[0], 0);
   if(normu <= 0)
      normu = 1.0e-7f;
   normu = sqrt(normu);
   norma[shift_temporal] = normu;
//--- distance features to centroid
   float theta = IsNaNOrInf(-prod * curv, 0);
   theta = fmax(theta, 1.0f + 1.2e-07f);
   float dist = IsNaNOrInf(sqrt(clamp(pow(acosh(theta), 2.0f) / curv, 0.0f, 50.0f)), 0);
   distance[shift_temporal] = dist;
   float proj_u = IsNaNOrInf(dist * u / normu, 0);
//---
   if(d < ls)
      temp[d] = (d > 0 ? proj_u * centroid : 0);
   BarrierLoc;
//---
   for(int i = ls; i < (int)dimension; i += ls)
     {
      if(d >= i && d < (i + ls))
         temp[d % ls] += proj_u * centroid;
      BarrierLoc;
     }
//---
   count = min(ls, (int)dimension);
//---
   do
     {
      count = (count + 1) / 2;
      if(d < count)
         temp[d] += ((d + count) < dimension ? temp[d + count] : 0);
      if(d + count < dimension)
         temp[d + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//---
   if(d == 0)
     {
      proj_u = IsNaNOrInf(temp[0] / centroid, 0);
      proj_u = fmax(u, 1.2e-7f);
     }
//---
   outputs[shift_out] = proj_u;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void LogMapGrad(__global const float *features, __global float *features_gr,
                         __global const float *centroids, __global float *centroids_gr,
                         __global const float *curvatures, __global float *curvatures_gr,
                         __global const float *outputs, __global const float *outputs_gr,
                         __global const float *product,
                         __global const float *distance,
                         __global const float *norma
                        )
  {
//--- identify
   const size_t f = get_global_id(0);
   const size_t cent = get_global_id(1);
   const size_t d = get_local_id(2);
   const size_t total_f = get_global_size(0);
   const size_t total_cent = get_global_size(1);
   const size_t dimension = get_local_size(2);
//--- create local array
   __local float temp[LOCAL_ARRAY_SIZE];
   const int ls = min((int)dimension, (int)LOCAL_ARRAY_SIZE);
//--- calc shifts
   const int shift_f = f * dimension + d;
   const int shift_out = (f * total_cent + cent) * dimension + d;
   const int shift_cent = cent * dimension + d;
   const int shift_temporal = f * total_cent + cent;
//--- load inputs
   float feature = features[shift_f];
   if(isinf(feature) || isnan(feature))
      feature = 0;
   float centroid = centroids[shift_cent];
   if(isinf(centroid) || isnan(centroid))
      centroid = 0;
   float centroid0 = (d > 0 ? centroids[shift_cent - d] : centroid);
   if(isinf(centroid0) || isnan(centroid0) || centroid0 == 0)
      centroid0 = 1.2e-7f;
   float curv = curvatures[cent];
   if(isinf(curv) || isnan(curv))
      curv = 1.2e-7f;
   float prod = product[shift_temporal];
   float dist = distance[shift_temporal];
   float normu = norma[shift_temporal];
   float u = feature + prod * centroid * curv;
   if(isinf(u) || isnan(u))
      u = 0;
//---
   float grad = outputs_gr[shift_out];
   if(isinf(grad) || isnan(grad))
      grad = 0;
   float grad0 = (d > 0 ? outputs_gr[shift_out - d] : grad);
   if(isinf(grad0) || isnan(grad0))
      grad0 = 0;
//---
   float feature_gr = 0;
   float centroid_gr = 0;
   float curv_gr = 0;
   float prod_gr = 0;
   float normu_gr = 0;
   float dist_gr = 0;
//---
   float proj_u_gr = (d > 0 ? grad + grad0 / centroid0 * centroid : 0);
   if(d == 0)
      centroid_gr += outputs[shift_out] / centroid * grad;
   else
      centroid_gr += grad0 / centroid0 * outputs[shift_out];
   if(isnan(centroid_gr) || isinf(centroid_gr))
      centroid_gr = 0;
//---
   dist_gr = u / normu * proj_u_gr;
   float u_gr = dist / normu * proj_u_gr;
   normu_gr = dist * u / (normu * normu) * proj_u_gr;
//---
   if(d < ls)
      temp[d] = dist_gr;
   BarrierLoc;
//---
   for(int id = ls; id < (int)dimension; id += ls)
     {
      if(d >= id && d < (id + ls))
         temp[d % ls] += dist_gr;
      BarrierLoc;
     }
//---
   int count = min(ls, (int)dimension);
//---
   do
     {
      count = (count + 1) / 2;
      if(d < count)
         temp[d] += ((d + count) < dimension ? temp[d + count] : 0);
      if(d + count < dimension)
         temp[d + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
   if(isinf(temp[0]) || isnan(temp[0]))
      temp[0] = 0;
   dist_gr = temp[0];
//---
   if(d == 0)
     {
      float theta = -prod * curv;
      float theta_gr = 1.0f / sqrt(curv * (theta * theta - 1)) * dist_gr;
      if(isinf(theta_gr) || isnan(theta_gr))
         theta_gr = 0;
      curv_gr += -pow(acosh(theta), 2.0f) / (2 * sqrt(pow(curv, 3.0f))) * dist_gr;
      if(isinf(curv_gr) || isnan(curv_gr))
         curv_gr = 0;
      temp[0] = -curv * theta_gr;
      if(isinf(temp[0]) || isnan(temp[0]))
         temp[0] = 0;
      curv_gr += -prod * theta_gr;
      if(isinf(curv_gr) || isnan(curv_gr))
         curv_gr = 0;
     }
   BarrierLoc;
//---
   prod_gr += temp[0];
   BarrierLoc;
//---
   if(d < ls)
      temp[d] = normu_gr;
   BarrierLoc;
//---
   for(int id = ls; id < (int)dimension; id += ls)
     {
      if(d >= id && d < (id + ls))
         temp[d % ls] += normu_gr;
      BarrierLoc;
     }
//---
   count = min(ls, (int)dimension);
//---
   do
     {
      count = (count + 1) / 2;
      if(d < count)
         temp[d] += ((d + count) < dimension ? temp[d + count] : 0);
      if(d + count < dimension)
         temp[d + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
   normu_gr = temp[0];
   if(isinf(normu_gr) || isnan(normu_gr))
      normu_gr = 1.2e-7f;
   u_gr += u / normu * normu_gr;
   if(isnan(u_gr) || isinf(u_gr))
      u_gr = 0;
//---
   feature_gr += u_gr;
   centroid_gr += prod * curv * u_gr;
   BarrierLoc;
//--- dot (u_gr * centroid)
   if(d < ls)
      temp[d] = u_gr * centroid;
   BarrierLoc;
//---
   for(int id = ls; id < (int)dimension; id += ls)
     {
      if(d >= id && d < (id + ls))
         temp[d % ls] += u_gr * centroid;
      BarrierLoc;
     }
//---
   count = min(ls, (int)dimension);
//---
   do
     {
      count = (count + 1) / 2;
      if(d < count)
         temp[d] += ((d + count) < dimension ? temp[d + count] : 0);
      if(d + count < dimension)
         temp[d + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
   if(d == 0)
     {
      if(isinf(temp[0]) || isnan(temp[0]))
         temp[0] = 0;
      prod_gr += temp[0] * curv;
      if(isinf(prod_gr) || isnan(prod_gr))
         prod_gr = 0;
      curv_gr += temp[0] * prod;
      if(isinf(curv_gr) || isnan(curv_gr))
         curv_gr = 0;
      temp[0] = prod_gr;
     }
   BarrierLoc;
//---
   prod_gr = temp[0];
   feature_gr += prod_gr * centroid * (d > 0 ? 1 : -1);
   centroid_gr += prod_gr * feature * (d > 0 ? 1 : -1);
//--- result
   features_gr[shift_f] += feature_gr;
   centroids_gr[shift_cent] += centroid_gr;
   if(f == 0 && d == 0)
      curvatures_gr[cent] += curv;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcEpsilonWeights(__global const float *matrix_w,
                                 __global const float *matrix_g,
                                 __global const float *matrix_i,
                                 __global float *matrix_epsw,
                                 const float rho
                                )
  {
   const size_t inp = get_local_id(0);
   const size_t inputs = get_local_size(0) - 1;
   const size_t out = get_global_id(1);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const int ls = min((int)inputs, (int)LOCAL_ARRAY_SIZE);
//---
   const int shift_w = out * (inputs + 1) + inp;
   const float w = IsNaNOrInf(matrix_w[shift_w], 0);
   float grad = fabs(w) * IsNaNOrInf(matrix_g[out], 0) * (inputs == inp ? 1.0f : IsNaNOrInf(matrix_i[inp], 0));
//---
   const int local_shift = inp % ls;
//---
   for(int i = 0; i <= inputs; i += ls)
     {
      if(i <= inp && inp < (i + ls))
         temp[local_shift] = (i == 0 ? 0 : temp[local_shift]) + IsNaNOrInf(grad * grad, 0);
      BarrierLoc;
     }
//---
   int count = ls;
   do
     {
      count = (count + 1) / 2;
      if(inp < count)
         temp[inp] += ((inp + count) < inputs ? IsNaNOrInf(temp[inp + count], 0) : 0);
      if(inp + count < inputs)
         temp[inp + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//---
   float norm = sqrt(IsNaNOrInf(temp[0], 0));
   float epsw = IsNaNOrInf(w * w * grad * rho / (norm + 1.2e-7f), w);
//---
   matrix_epsw[shift_w] = epsw;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcEpsilonWeightsConv(__global const float *matrix_w,
                                     __global const float *matrix_g,
                                     __global const float *matrix_i,
                                     __global float *matrix_epsw,
                                     const int inputs,
                                     const float rho,
                                     const int step
                                    )
  {
//---
   const size_t inp = get_local_id(0);
   const size_t window_in = get_local_size(0) - 1;
   const size_t out = get_global_id(1);
   const size_t window_out = get_global_size(1);
   const size_t v = get_global_id(2);
   const size_t variables = get_global_size(2);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const int ls = min((int)(window_in + 1), (int)LOCAL_ARRAY_SIZE);
//---
   const int shift_w = (out + v * window_out) * (window_in + 1) + inp;
   const int total = (inputs - window_in + step - 1) / step;
   const int shift_out = v * total * window_out + out;
   const int shift_in = v * inputs + inp;
   const float w = IsNaNOrInf(matrix_w[shift_w], 0);
//---
   float grad = 0;
//---
   for(int t = 0; t < total; t++)
     {
      if(inp != window_in && (inp + t * step) >= inputs)
         break;
      float g = IsNaNOrInf(matrix_g[t * window_out + shift_out], 0);
      float i = IsNaNOrInf(inp == window_in ? 1.0f : matrix_i[t * step + shift_in], 0);
      grad += IsNaNOrInf(g * i, 0);
     }
   grad *= fabs(w);
//---
   const int local_shift = inp % ls;
//---
   for(int i = 0; i <= inputs; i += ls)
     {
      if(i <= inp && inp < (i + ls))
         temp[local_shift] = (i == 0 ? 0 : temp[local_shift]) + IsNaNOrInf(grad * grad, 0);
      BarrierLoc;
     }
//---
   int count = ls;
   do
     {
      count = (count + 1) / 2;
      if(inp < count && (inp + count) < inputs)
        {
         temp[inp] += IsNaNOrInf(temp[inp + count], 0);
         temp[inp + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//---
   float norm = sqrt(IsNaNOrInf(temp[0], 0));
   float epsw = IsNaNOrInf(w * w * grad * rho / (norm + 1.2e-7f), w);
//---
   matrix_epsw[shift_w] = epsw;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PLRMultiAgents(__global const float *inputs,
                             __global float *outputs,
                             __global int *isttp,
                             const int transpose,
                             __global const float *min_step
                            )
  {
   const size_t i = get_global_id(0);
   const size_t lenth = get_global_size(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
   const size_t a = get_global_id(2);
   const size_t agents = get_global_size(2);
//--- constants
   const int shift_in = ((bool)transpose ? (i * variables + v) : (v * lenth + i));
   const int step_in = ((bool)transpose ? variables : 1);
   const int shift_ag = a * lenth * variables;
//--- look for ttp
   float value = IsNaNOrInf(inputs[shift_in], 0);
   bool bttp = false;
   if(i == 0 || i == lenth - 1)
      bttp = true;
   else
     {
      float prev = value;
      int prev_pos = i;
      float max_v = value;
      float max_pos = i;
      float min_v = value;
      float min_pos = i;
      while(fmax(fabs(prev - max_v), fabs(prev - min_v)) < min_step[a] && prev_pos > 0)
        {
         prev_pos--;
         prev = IsNaNOrInf(inputs[shift_in - (i - prev_pos) * step_in], 0);
         if(prev >= max_v && (prev - min_v) < min_step[a])
           {
            max_v = prev;
            max_pos = prev_pos;
           }
         if(prev <= min_v && (max_v - prev) < min_step[a])
           {
            min_v = prev;
            min_pos = prev_pos;
           }
        }
      //---
      float next = value;
      int next_pos = i;
      while(fmax(fabs(next - max_v), fabs(next - min_v)) < min_step[a] && next_pos < (lenth - 1))
        {
         next_pos++;
         next = IsNaNOrInf(inputs[shift_in + (next_pos - i) * step_in], 0);
         if(next > max_v && (next - min_v) < min_step[a])
           {
            max_v = next;
            max_pos = next_pos;
           }
         if(next < min_v && (max_v - next) < min_step[a])
           {
            min_v = next;
            min_pos = next_pos;
           }
        }
      //---
      if(
         (value >= prev && value > next) ||
         (value > prev && value == next) ||
         (value <= prev && value < next) ||
         (value < prev && value == next)
      )
         if(max_pos == i || min_pos == i)
            bttp = true;
     }
//---
   isttp[shift_in + shift_ag] = (int)bttp;
   outputs[shift_in + shift_ag] = 0;
   BarrierLoc;
//--- calc position
   int pos = -1;
   int prev_in = 0;
   int prev_ttp = 0;
   if(bttp)
     {
      pos = 0;
      //---
      for(int p = 0; p < i; p++)
        {
         int current_in = ((bool)transpose ? (p * variables + v) : (v * lenth + p));
         if((bool)isttp[current_in + shift_ag])
           {
            pos++;
            prev_ttp = p;
            prev_in = current_in;
           }
        }
     }
//--- cacl tendency
   if(pos > 0 && pos < (lenth / 3))
     {
      float sum_x = 0;
      float sum_y = 0;
      float sum_xy = 0;
      float sum_xx = 0;
      int dist = i - prev_ttp;
      //---
      for(int p = 0; p < dist; p++)
        {
         float x = (float)(p);
         float y = IsNaNOrInf(inputs[prev_in + p * step_in], 0);
         sum_x += x;
         sum_y += y;
         sum_xy += x * y;
         sum_xx += x * x;
        }
      float slope = IsNaNOrInf((dist * sum_xy - sum_x * sum_y) / (dist > 1 ? (dist * sum_xx - sum_x * sum_x) : 1), 0);
      float intercept = IsNaNOrInf((sum_y - slope * sum_x) / dist, 0);
      int shift_out = ((bool)transpose ? ((pos - 1) * 3 * variables + v) : (v * lenth + (pos - 1) * 3)) + shift_ag;
      outputs[shift_out] = slope;
      outputs[shift_out + step_in] = intercept;
      outputs[shift_out + 2 * step_in] = ((float)dist) / lenth;
     }
   else
     {
      if(pos == (lenth / 3))
        {
         float sum_x = 0;
         float sum_y = 0;
         float sum_xy = 0;
         float sum_xx = 0;
         int dist = lenth - prev_ttp;
         //---
         for(int p = 0; p < dist; p++)
           {
            float x = (float)(p);
            float y = IsNaNOrInf(inputs[prev_in + p * step_in], 0);
            sum_x += x;
            sum_y += y;
            sum_xy += x * y;
            sum_xx += x * x;
           }
         float slope = IsNaNOrInf((dist * sum_xy - sum_x * sum_y) / (dist > 1 ? (dist * sum_xx - sum_x * sum_x) : 1), 0);
         float intercept = IsNaNOrInf((sum_y - slope * sum_x) / dist, 0);
         int shift_out = ((bool)transpose ? ((pos - 1) * 3 * variables + v) : (v * lenth + (pos - 1) * 3)) + shift_ag;
         outputs[shift_out] = slope;
         outputs[shift_out + step_in] = intercept;
         outputs[shift_out + 2 * step_in] = IsNaNOrInf((float)dist / lenth, 0);
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PLRMultiAgentsGradient(__global float *inputs_gr,
                                     __global const float *outputs,
                                     __global const float *outputs_gr,
                                     const int transpose,
                                     const int agents
                                    )
  {
   const size_t i = get_global_id(0);
   const size_t lenth = get_global_size(0);
   const size_t v = get_global_id(1);
   const size_t variables = get_global_size(1);
//--- constants
   const int shift_in = ((bool)transpose ? (i * variables + v) : (v * lenth + i));
   const int step_in = ((bool)transpose ? variables : 1);
   const int shift_out = ((bool)transpose ? v : (v * lenth));
   const int step_out = 3 * step_in;
   const int shift_ag = lenth * variables;
//--- Sum gradient
   float grad = 0;
//---
   for(int a = 0; a < agents; a++)
     {
      //--- calc position
      int pos = -1;
      int prev_in = 0;
      int dist = 0;
      do
        {
         pos++;
         prev_in += dist;
         dist = (int)fmax(outputs[shift_out + pos * step_out + 2 * step_in + a * shift_ag] * lenth, 1);
        }
      while(!(prev_in <= i && (prev_in + dist) > i));
      //--- calc constants
      float sum_x = 0;
      float sum_xx = 0;
      for(int p = 0; p < dist; p++)
        {
         float x = (float)(p);
         sum_x += x;
         sum_xx += x * x;
        }
      //--- get output gradient
      float grad_slope = IsNaNOrInf(outputs_gr[shift_out + pos * step_out + a * shift_ag], 0);
      float grad_intercept = IsNaNOrInf(outputs_gr[shift_out + pos * step_out + step_in + a * shift_ag], 0);
      //--- calc gradient
      grad_slope -= IsNaNOrInf(sum_x / dist * grad_intercept, 0);
      grad_slope /= fmax(IsNaNOrInf(dist * sum_xx - sum_x * sum_x, 0), 1);
      grad += IsNaNOrInf(grad_intercept / dist, 0);
      grad += IsNaNOrInf((dist * (i - prev_in) - sum_x) * grad_slope, 0);
     }
   grad = clamp(IsNaNOrInf(grad / agents, 0), -MAX_GRAD, MAX_GRAD);
//--- save result
   inputs_gr[shift_in] = grad;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardMHConv(__global float *matrix_w,
                                __global float *matrix_i,
                                __global float *matrix_o,
                                const int inputs,
                                const int step,
                                const int window_in,
                                const int window_out,
                                const int activation
                               )
  {
   const size_t i = get_global_id(0);
   const size_t h = get_global_id(1);
   const size_t v = get_global_id(2);
   const size_t total = get_global_size(0);
   const size_t heads = get_global_size(1);
//---
   const int window_in_h = (window_in + heads - 1) / heads;
   const int window_out_h = (window_out + heads - 1) / heads;
   const int shift_out = window_out * i + window_out_h * h;
   const int shift_in = step * i + window_in_h * h;
//---
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * window_out * total;
   const int shift_var_w = v * window_out * (window_in_h + 1);
   const int shift_w_h = h * window_out_h * (window_in_h + 1);
//---
   float sum = 0;
   float4 inp, weight;
   int stop = (window_in_h <= (inputs - shift_in) ? window_in_h : (inputs - shift_in));
   stop = min(stop, (int)(window_in - h * window_in_h));
//---
//---
   for(int out = 0; (out < window_out_h && (window_out_h * h + out) < window_out); out++)
     {
      int shift = (window_in_h + 1) * out + shift_w_h;
      for(int k = 0; k <= stop; k += 4)
        {
         switch(stop - k)
           {
            case 0:
               inp = (float4)(1, 0, 0, 0);
               weight = (float4)(matrix_w[shift_var_w + shift + window_in_h], 0, 0, 0);
               break;
            case 1:
               inp = (float4)(matrix_i[shift_var_in + shift_in + k], 1, 0, 0);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + window_in_h], 0, 0);
               break;
            case 2:
               inp = (float4)(matrix_i[shift_var_in + shift_in + k],
                              matrix_i[shift_var_in + shift_in + k + 1], 1, 0);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + k + 1],
                                 matrix_w[shift_var_w + shift + window_in_h], 0);
               break;
            case 3:
               inp = (float4)(matrix_i[shift_var_in + shift_in + k], matrix_i[shift_var_in + shift_in + k + 1],
                              matrix_i[shift_var_in + shift_in + k + 2], 1);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + k + 1],
                                 matrix_w[shift_var_w + shift + k + 2], matrix_w[shift_var_w + shift + shift_w_h]);
               break;
            default:
               inp = (float4)(matrix_i[shift_var_in + shift_in + k], matrix_i[shift_var_in + shift_in + k + 1],
                              matrix_i[shift_var_in + shift_in + k + 2], matrix_i[shift_var_in + shift_in + k + 3]);
               weight = (float4)(matrix_w[shift_var_w + shift + k], matrix_w[shift_var_w + shift + k + 1],
                                 matrix_w[shift_var_w + shift + k + 2], matrix_w[shift_var_w + shift + k + 3]);
               break;
           }
         sum += IsNaNOrInf(dot(inp, weight), 0);
        }
      sum = IsNaNOrInf(sum, 0);
      //---
      matrix_o[shift_var_out + out + shift_out] = fActivation(sum, activation);;
     }
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_gr
/// Kernel of the Convolution neuron to transfer gradient
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientMHConv(__global float *matrix_w,
                                       __global float *matrix_g,
                                       __global float *matrix_o,
                                       __global float *matrix_ig,
                                       const int outputs,
                                       const int step,
                                       const int window_in,
                                       const int window_out,
                                       const int activation,
                                       const int shift_out,
                                       const int heads
                                      )
  {
   const size_t i = get_global_id(0);
   const size_t inputs = get_global_size(0);
   const size_t v = get_global_id(1);
//---
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * outputs;
   const int shift_var_w = v * window_out * (window_in + 1);
   const int window_in_h = (window_in + heads - 1) / heads;
   const int window_out_h = (window_out + heads - 1) / heads;
//---
   float sum = 0;
   float out = matrix_o[shift_var_in + i];
   const int w_start = i % step;
   const int start = max((int)((i - window_in + step) / step), 0);
   int stop = (w_start + step - 1) / step;
   stop = min((int)((i + step - 1) / step + 1), stop) + start;
   if(stop > (outputs / window_out))
      stop = outputs / window_out;
//---
   for(int k = start; k < stop; k++)
     {
      int head = (k % window_out) / window_out_h;
      for(int h = 0; h < window_out_h; h ++)
        {
         if((head * window_out_h + h) >= window_out)
            break;
         int shift_g = k * window_out + head * window_out_h + h;
         int shift_w = (stop - k - 1) * step + (i % step) / window_in_h +
                       head * (window_in_h + 1) + h * (window_in_h + 1);
         if(shift_g >= outputs || shift_w >= (window_in_h + 1) * window_out)
            break;
         sum += IsNaNOrInf(matrix_g[shift_out + shift_g + shift_var_out] * matrix_w[shift_w + shift_var_w], 0);
        }
     }
//---
   matrix_ig[shift_var_in + i] = Deactivation(sum, out, activation);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_opt Convolution Neuron Adam optimization Updating
/// Weights Calculation kernel
/// Describes the process of Adam optimization weights for the Convolution
/// Neuron (#CNeuronConvOCL).
//+------------------------------------------------------------------+
__kernel void UpdateWeightsMHConvAdam(__global float *matrix_w,   ///<[in,out] Weights matrix (m+1)*n, where m -
                                      ///< input window and n - output window
                                      __global const float *matrix_g, ///<[in] Tensor of gradients at current layer
                                      __global const float *matrix_i, ///<[in] Inputs tensor
                                      __global float *matrix_m,      ///<[in] Matrix of first momentum
                                      __global float *matrix_v,      ///<[in] Matrix of seconfd momentum
                                      const int inputs,               ///< Number of inputs
                                      const float l,                  ///< Learning rates
                                      const float b1,                 ///< First momentum multiplier
                                      const float b2,                 ///< Second momentum multiplier
                                      const int window_in,                  ///< Size of input window
                                      const int window_out,                 ///< Size of output window
                                      const int step,                        ///< Step size
                                      const int heads
                                     )
  {
   const size_t i = get_global_id(0);
//---
   const int window_in_h = (window_in + heads - 1) / heads;
   const int v = i / ((window_in_h + 1) * window_out);
   const int shift = i % window_out;
   const int shift_out = i / (window_in_h + 1) - v;
   const int total = (inputs - window_in + step - 1) / step;
//---
   const int shift_var_in = v * inputs;
   const int shift_var_out = v * total * window_out;
//---
   float grad = 0;
//---
   for(int t = 0; t < total; t++)
     {
      if(shift != window_in_h && (shift + t * window_in) >= inputs)
         break;
      grad += IsNaNOrInf(matrix_g[t * window_out + shift_out + shift_var_out] *
                         (shift == window_in_h ? 1 : matrix_i[shift + t * step + shift_var_in]), 0);
     }
   float mt = IsNaNOrInf(clamp(b1 * matrix_m[i] + (1 - b1) * grad, -1.0e5f, 1.0e5f), 0);
   float vt = IsNaNOrInf(clamp(b2 * matrix_v[i] + (1 - b2) * pow(grad, 2), 1.0e-6f, 1.0e6f), 1.0e-6f);
   float weight = clamp(matrix_w[i] + l * mt / sqrt(vt), -MAX_WEIGHT, MAX_WEIGHT);
   matrix_w[i] = weight;
   matrix_m[i] = mt;
   matrix_v[i] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MoreLessEqual(__global const float *input,
                            __global float *output)
  {
   const size_t i = get_global_id(0);
   const float value = IsNaNOrInf(input[i], 0);
   float result = 0;
   if(fabs(value) > 1.2e-7f)
     {
      if(value > 0)
         result = 1;
      else
         result = -1;
     }
   output[i] = result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MultiScaleRelativeAttentionOut(__global const float *q,        ///<[in] Matrix of Querys
      __global const float *k,        ///<[in] Matrix of Keys
      __global const float *v,        ///<[in] Matrix of Values
      __global const float *bk,       ///<[in] Matrix of Positional Bias Keys
      __global const float *bv,       ///<[in] Matrix of Positional Bias Values
      __global const float *gc,       ///<[in] Global content bias vector
      __global const float *gp,       ///<[in] Global positional bias vector
      __global float *score,          ///<[out] Matrix of Scores
      __global float *out,            ///<[out] Matrix of attention
      const int dimension              ///< Dimension of Key
                                            )
  {
//--- init
   const uint q_id = get_global_id(0);
   const uint k_id = get_local_id(1);
   const uint h = get_global_id(2);
   const uint qunits = get_global_size(0);
   const uint kunits = get_local_size(1);
   const uint heads = get_global_size(2);
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_kv = dimension * (heads * k_id + h);
   const int shift_gc = dimension * h;
   const int shift_s = kunits * (q_id *  heads + h) + k_id;
   const int shift_pb = q_id * kunits + k_id;
   const uint ls = min((uint)get_local_size(1), (uint)LOCAL_ARRAY_SIZE);
   const uint window = max((uint)((kunits + h) / (h + 1)), min((uint)3, kunits));
   float koef = sqrt((float)dimension);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
//--- score
   float sc = 0;
   if(k_id < window)
     {
      //---
      for(int d = 0; d < dimension; d++)
        {
         float val_q = q[shift_q + d];
         float val_k = k[shift_kv + d];
         float val_bk = bk[shift_kv + d];
         sc += val_q * val_k + val_q * val_bk + val_k * val_bk + gc[shift_q + d] * val_k + gp[shift_q + d] * val_bk;
        }
      sc = sc / koef;
     }
//--- max value
//---
   for(int cur_k = 0; cur_k < kunits; cur_k += ls)
     {
      if(k_id < window)
         if(k_id >= cur_k && k_id < (cur_k + ls))
           {
            int shift_local = k_id % ls;
            temp[shift_local] = (cur_k == 0 ? sc : fmax(temp[shift_local], sc));
           }
      BarrierLoc;
     }
   uint count = min(ls, kunits);
//---
//---
   do
     {
      count = (count + 1) / 2;
      if(k_id < (window + 1) / 2)
         if(k_id < ls)
            temp[k_id] = (k_id < count && (k_id + count) < kunits ? fmax(temp[k_id + count], temp[k_id]) : temp[k_id]);
      BarrierLoc;
     }
   while(count > 1);
   if(k_id < window)
      sc = IsNaNOrInf(exp(fmax(sc - temp[0], -120)), 0);
   BarrierLoc;
//--- sum of exp
//---
   for(int cur_k = 0; cur_k < kunits; cur_k += ls)
     {
      if(k_id >= cur_k && k_id < (cur_k + ls))
        {
         int shift_local = k_id % ls;
         temp[shift_local] = (cur_k == 0 ? 0 : temp[shift_local]) + sc;
        }
      BarrierLoc;
     }
//---
   count = min(ls, (uint)kunits);
   do
     {
      count = (count + 1) / 2;
      if(k_id < count && k_id < (window + 1) / 2)
         temp[k_id] += ((k_id + count) < kunits ? temp[k_id + count] : 0);
      if(k_id + count < ls)
         temp[k_id + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//--- score
   float sum = IsNaNOrInf(temp[0], 1);
   if(sum <= 1.2e-7f)
      sum = 1;
   sc /= sum;
   score[shift_s] = sc;
   BarrierLoc;
//--- out
   int shift_local = k_id % ls;
//---
   for(int d = 0; d < dimension; d++)
     {
      float val_v = v[shift_kv + d];
      float val_bv = bv[shift_kv + d];
      float val = IsNaNOrInf(sc * (val_v + val_bv), 0);
      //--- sum of value
      for(int cur_v = 0; cur_v < kunits; cur_v += ls)
        {
         if(k_id >= cur_v && k_id < (cur_v + ls))
            temp[shift_local] = (cur_v == 0 ? 0 : temp[shift_local]) + val;
         BarrierLoc;
        }
      //---
      count = min(ls, (uint)kunits);
      do
        {
         count = (count + 1) / 2;
         if(k_id < count && (k_id + count) < kunits)
            temp[k_id] += temp[k_id + count];
         if(k_id + count < ls)
            temp[k_id + count] = 0;
         BarrierLoc;
        }
      while(count > 1);
      //---
      if(k_id == 0)
         out[shift_q + d] = IsNaNOrInf(temp[0], 0);
      BarrierLoc;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SSM2D_FeedForward(__global const float *ah,
                                __global const float *b_time,
                                __global const float *b_var,
                                __global const float *px_time,
                                __global const float *px_var,
                                __global const float *c_time,
                                __global const float *c_var,
                                __global const float *delta_time,
                                __global const float *delta_var,
                                __global       float *hidden,
                                __global       float *y
                               )
  {
   const size_t n = get_local_id(0);
   const size_t d = get_global_id(1);
   const size_t n_total = get_local_size(0);
   const size_t d_total = get_global_size(1);
//--- Hidden state
//---
   for(int h = 0; h < 2; h++)
     {
      float new_h = ah[(2 * n + h) * d_total + d] + ah[(2 * n_total + 2 * n + h) * d_total + d];
      if(h == 0)
         new_h += b_time[n] * px_time[n * d_total + d];
      else
         new_h += b_var[n] * px_var[n * d_total + d];
      hidden[(h * n_total + n)*d_total + d] = IsNaNOrInf(new_h, 0);
     }
   BarrierLoc;
//--- Output
   uint shift_c = n;
   uint shift_h1 = d;
   uint shift_h2 = shift_h1 + n_total * d_total;
   float value = 0;
//---
   for(int i = 0; i < n_total; i++)
     {
      value += IsNaNOrInf(c_time[shift_c] * delta_time[shift_c] * hidden[shift_h1], 0);
      value += IsNaNOrInf(c_var[shift_c] * delta_var[shift_c] * hidden[shift_h2], 0);
      shift_c += n_total;
      shift_h1 += d_total;
      shift_h2 += d_total;
     }
//---
   y[n * d_total + d] = IsNaNOrInf(value, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SSM2D_CalcHiddenGradient(__global const float *ah,
                                       __global       float *grad_ah,         // Gradient with respect to ah
                                       __global const float *b_time,
                                       __global       float *grad_b_time,     // Gradient with respect to b_time
                                       __global const float *b_var,
                                       __global       float *grad_b_var,      // Gradient with respect to b_var
                                       __global const float *px_time,
                                       __global       float *grad_px_time,    // Gradient with respect to px_time
                                       __global const float *px_var,
                                       __global       float *grad_px_var,     // Gradient with respect to px_var
                                       __global const float *c_time,
                                       __global       float *grad_c_time,     // Gradient with respect to c_time
                                       __global const float *c_var,
                                       __global       float *grad_c_var,      // Gradient with respect to c_var
                                       __global const float *delta_time,
                                       __global       float *grad_delta_time, // Gradient with respect to delta_time
                                       __global const float *delta_var,
                                       __global       float *grad_delta_var,  // Gradient with respect to delta_var
                                       __global const float *hidden,
                                       __global const float *grad_y           // Gradient of loss with respect to y
                                      )
  {
//---
   const size_t n = get_global_id(0);
   const size_t d = get_local_id(1);
   const size_t n_total = get_global_size(0);
   const size_t d_total = get_local_size(1);
//--- Initialize indices for data access
   uint shift_c = n;
   uint shift_h1 = d;
   uint shift_h2 = shift_h1 + n_total * d_total;
   float grad_hidden1 = 0;
   float grad_hidden2 = 0;
//--- Backpropagation: compute hidden gradients from y
//---
   for(int i = 0; i < n_total; i++)
     {
      float grad = grad_y[i * d_total + d];
      float c_t = c_time[shift_c];
      float c_v = c_var[shift_c];
      float delta_t = delta_time[shift_c];
      float delta_v = delta_var[shift_c];
      float h1 = hidden[shift_h1];
      float h2 = hidden[shift_h2];
      //-- Accumulate gradients for hidden states
      grad_hidden1 += IsNaNOrInf(grad * c_t * delta_t, 0);
      grad_hidden2 += IsNaNOrInf(grad * c_v * delta_v, 0);
      //--- Compute gradients for c_time, c_var, delta_time, delta_var
      grad_c_time[shift_c] += grad * delta_t * h1;
      grad_c_var[shift_c]  += grad * delta_v * h2;
      grad_delta_time[shift_c] += grad * c_t * h1;
      grad_delta_var[shift_c]  += grad * c_v * h2;
      //--- Update indices for the next element
      shift_c += n_total;
      shift_h1 += d_total;
      shift_h2 += d_total;
     }
//--- Backpropagate through hidden -> ah, b_time, px_time
//---
   for(int h = 0; h < 2; h++)
     {
      float grad_h = (h == 0) ? grad_hidden1 : grad_hidden2;
      //--- Store gradients in ah (considering its influence on two elements)
      grad_ah[(2 * n + h) * d_total + d] = grad_h;
      grad_ah[(2 * (n_total + n) + h) * d_total + d] = grad_h;
     }
//--- Backpropagate through px_time and px_var (influenced by b_time and b_var)
   grad_px_time[n * d_total + d] = grad_hidden1 * b_time[n];
   grad_px_var[n * d_total + d] = grad_hidden2 * b_var[n];
   if(d == 0)
     {
      grad_b_time[n] = 0;
      grad_b_var[n] = 0;
     }
   BarrierLoc;
//--- Sum gradients over all d for b_time and b_var
   grad_b_time[n] += grad_hidden1 * px_time[n * d_total + d];
   grad_b_var[n] += grad_hidden2 * px_var[n * d_total + d];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PScan(__global const float* A,
                    __global const float* X,
                    __global const float* H,
                    __global float* X_out)
  {
   const size_t idx = get_local_id(0);
   const size_t dim = get_global_id(1);
   const size_t L = get_local_size(0);
   const size_t D = get_global_size(1);
   const int num_steps = (int)log2((float)L);
//---
   __local float local_A[1024];
   __local float local_X[1024];
   __local float local_H[1024];
//--- Load data to local memory
   int offset = dim + idx * D;
   local_A[idx] = A[offset];
   local_X[idx] = X[offset];
   local_H[idx] = H[offset];
   BarrierLoc;
//--- Scan
//---
   for(int step = 0; step < num_steps; step++)
     {
      int halfT = L >> (step + 1);
      if(idx < halfT)
        {
         int base = idx * 2;
         local_X[base + 1] += local_A[base + 1] * local_X[base];
         local_X[base + 1] *= local_H[base + 1];
         local_A[base + 1] *= local_A[base];
        }
      BarrierLoc;
     }
//--- Save result
   X_out[offset] = local_X[idx];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PScan_CalcHiddenGradient(__global const float* A,
                                       __global float*  grad_A,
                                       __global const float* X,
                                       __global float*  grad_X,
                                       __global const float* H,
                                       __global float*  grad_H,
                                       __global const float* grad_X_out)
  {
   const size_t idx = get_local_id(0);
   const size_t dim = get_global_id(1);
   const size_t L = get_local_size(0);
   const size_t D = get_global_size(1);
   const int num_steps = (int)log2((float)L);
//---
   __local float local_A[1024];
   __local float local_X[1024];
   __local float local_H[1024];
   __local float local_grad_X[1024];
   __local float local_grad_A[1024];
   __local float local_grad_H[1024];
//--- Load data to local memory
   int offset = idx * D + dim;
   local_A[idx] = A[offset];
   local_X[idx] = X[offset];
   local_H[idx] = H[offset];
   local_grad_X[idx] = grad_X_out[offset];
   local_grad_A[idx] = 0.0f;
   local_grad_H[idx] = 0.0f;
   BarrierLoc;
//--- Reverse Scan (Backward)
//---
   for(int step = num_steps - 1; step >= 0; step--)
     {
      int halfT = L >> (step + 1);
      if(idx < halfT)
        {
         int base = idx * 2;
         // Compute gradients
         float grad_next = local_grad_X[base + 1] * local_H[base + 1];
         local_grad_H[base + 1] = local_grad_X[base + 1] * local_X[base];
         local_grad_A[base + 1] = local_grad_X[base + 1] * local_X[base];
         local_grad_X[base] += local_A[base + 1] * grad_next;
        }
      BarrierLoc;
     }
//--- Save gradients
   grad_A[offset] = local_grad_A[idx];
   grad_X[offset] = local_grad_X[idx];
   grad_H[offset] = local_grad_H[idx];
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DiagMatMult(__global const float *diag,
                          __global const float *matr,
                          __global float *result,
                          int activation)
  {
   size_t row = get_global_id(0);
   size_t col = get_local_id(1);
   size_t var = get_global_id(2);
   size_t rows = get_global_size(0);
   size_t cols = get_local_size(1);
//---
   __local float local_diag[1];
   if(cols == 0)
      local_diag[0] = diag[row + var * rows];
   BarrierLoc;
//---
   int shift = (row  + var * rows) * cols + col;
//---
   float res = local_diag[0] * matr[shift];
//---
   result[shift] = fActivation(res, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DiagMatMultGrad(__global const float *diag,
                              __global float *grad_diag,
                              __global const float *matr,
                              __global float *grad_matr,
                              __global const float *grad_result)
  {
   size_t row = get_global_id(0);
   size_t col = get_local_id(1);
   size_t var = get_global_id(2);
   size_t rows = get_global_size(0);
   size_t cols = get_local_size(1);
   size_t vars = get_global_size(2);
//---
   __local float local_diag[LOCAL_ARRAY_SIZE];
   if(cols == 0)
      local_diag[0] = diag[row + var * rows];
   BarrierLoc;
//---
   int shift = (row  + var * rows) * cols + col;
//---
   float grad = grad_result[shift];
   float inp = matr[shift];
//---
   grad_matr[shift] = IsNaNOrInf(local_diag[0] * grad, 0);
   BarrierLoc;
//---
   int loc = col % LOCAL_ARRAY_SIZE;
//---
   for(int c = 0; c < cols; c += LOCAL_ARRAY_SIZE)
     {
      if(c <= col && (c + LOCAL_ARRAY_SIZE) > col)
        {
         if(c == 0)
            local_diag[loc] = IsNaNOrInf(grad * inp, 0);
         else
            local_diag[loc] += IsNaNOrInf(grad * inp, 0);
        }
      BarrierLoc;
     }
//---
   int count = min(LOCAL_ARRAY_SIZE, (int)cols);
   int ls = count;
//---
   do
     {
      count = (count + 1) / 2;
      if((col + count) < ls)
        {
         local_diag[col] += local_diag[col + count];
         local_diag[col + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//---
   if(col == 0)
      grad_diag[row + var * rows] = IsNaNOrInf(local_diag[0], 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void TopKgates(__global const float *inputs,
                        __global const float *noises,
                        __global float *gates,
                        const uint k)
  {
   size_t idx = get_local_id(0);
   size_t var = get_global_id(1);
   size_t window = get_local_size(0);
   size_t vars = get_global_size(1);
//---
   const int shift_logit = var * 2 * window + idx;
   const int shift_std = shift_logit + window;
   const int shift_gate = var * window + idx;
//---
   float logit = IsNaNOrInf(inputs[shift_logit], MIN_VALUE);
   float noise = IsNaNOrInf(noises[shift_gate], 0);
   if(noise != 0)
     {
      noise *= fActivation(inputs[shift_std], 3);
      logit += IsNaNOrInf(noise, 0);
     }
//---
   __local float temp[LOCAL_ARRAY_SIZE];
//---
   const uint ls = min((uint)window, (uint)LOCAL_ARRAY_SIZE);
   uint bigger = 0;
   float max_logit = logit;
//--- Top K
   for(int i = 0; i < window; i += ls)
     {
      if(idx >= i && idx < (i + ls))
         temp[idx % ls] = logit;
      BarrierLoc;
      for(int i1 = 0; (i1 < min((int)ls, (int)(window - i)) && bigger <= k); i1++)
        {
         if(temp[i1] > logit)
            bigger++;
         if(temp[i1] > max_logit)
            max_logit = temp[i1];
        }
      BarrierLoc;
     }
//---
   if(bigger <= k)
      gates[shift_gate] = logit - max_logit;
   else
      gates[shift_gate] = MIN_VALUE;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void TopKgatesGrad(__global const float *inputs,
                            __global float *grad_inputs,
                            __global const float *noises,
                            __global const float *gates,
                            __global float *grad_gates)
  {
   size_t idx = get_global_id(0);
   size_t var = get_global_id(1);
   size_t window = get_global_size(0);
   size_t vars = get_global_size(1);
//---
   const int shift_logit = var * 2 * window + idx;
   const int shift_std = shift_logit + window;
   const int shift_gate = var * window + idx;
//---
   float grad = IsNaNOrInf(grad_gates[shift_gate], 0);
   grad_inputs[shift_logit] = grad;
//---
   float noise = IsNaNOrInf(noises[shift_gate], 0);
   if(noise == 0)
     {
      grad_inputs[shift_std] = 0;
      return;
     }
//---
   grad *= noise;
   grad_inputs[shift_std] = Deactivation(grad, fActivation(inputs[shift_std], 3), 3);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MaskByDistance(__global const float *buf_real,
                             __global const float *buf_imag,
                             __global float *mask,
                             const int dimension
                            )
  {
   const size_t main = get_global_id(0);
   const size_t slave = get_local_id(1);
   const int total = (int)get_local_size(1);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   int ls = min((int)total, (int)LOCAL_ARRAY_SIZE);
//---
   const int shift_main = main * dimension;
   const int shift_slave = slave * dimension;
   const int shift_mask = main * total + slave;
//--- calc distance
   float dist = 0;
   if(main != slave)
     {
      //---
      for(int d = 0; d < dimension; d++)
         dist += pow(ComplexAbs((float2)(buf_real[shift_main + d], buf_imag[shift_main + d])) -
                     ComplexAbs((float2)(buf_real[shift_slave + d], buf_imag[shift_slave + d])), 2.0f);
      dist = sqrt(dist);
     }
//--- Look Max
//---
   for(int i = 0; i < total; i += ls)
     {
      if(i <= slave && (i + ls) > slave)
         Temp[slave % ls] = fmax((i == 0 ? 0 : Temp[slave % ls]), IsNaNOrInf(dist, 0));
      BarrierLoc;
     }
//---
   int count = ls;
   do
     {
      count = (count + 1) / 2;
      if(slave < count && (slave + count) < ls)
        {
         if(Temp[slave] < Temp[slave + count])
            Temp[slave] = Temp[slave + count];
         Temp[slave + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//--- Normalize
   if(Temp[0] > 0)
      dist /= Temp[0];
//--- result
   mask[shift_mask] = 1 - IsNaNOrInf(dist, 1);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MaskAttention(__global const float *q,     ///<[in] Matrix of Querys
                            __global const float *kv,    ///<[in] Matrix of Keys
                            __global float *scores,       ///<[out] Matrix of Scores
                            __global const float *masks,  ///<[in] Mask Matrix
                            __global float *out,         ///<[out] Matrix of attention
                            const int dimension,          ///< Dimension of Key
                            const int heads_kv
                           )
  {
//--- init
   const int q_id = get_global_id(0);
   const int k = get_local_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int kunits = get_local_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_k = dimension * (2 *  heads_kv * k + h_kv);
   const int shift_v = dimension * (2 *  heads_kv * k + heads_kv + h_kv);
   const int shift_s = kunits * (q_id *  heads + h) + k;
   const float mask = IsNaNOrInf(masks[q_id * kunits + k], 0);
   const uint ls = min((uint)kunits, (uint)LOCAL_ARRAY_SIZE);
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
   __local float temp[LOCAL_ARRAY_SIZE];
//--- Score
   float score = 0;
   if(mask != 0)
     {
      for(int d = 0; d < dimension; d++)
         score += IsNaNOrInf(q[shift_q + d] * kv[shift_k + d], 0);
      score = IsNaNOrInf(exp(score / koef) * mask, 0);
     }
//--- sum of exp
//---
   for(int i = 0; i < kunits; i += ls)
     {
      if(k >= i && k < (i + ls))
         temp[k % ls] = (i == 0 ? 0 : temp[k % ls]) + score;
      BarrierLoc;
     }
//---
   uint count = ls;
//---
   do
     {
      count = (count + 1) / 2;
      if(k < ls)
         temp[k] += (k < count && (k + count) < kunits ? temp[k + count] : 0);
      if(k + count < ls)
         temp[k + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//--- score
   if(temp[0] > 0)
      score /= temp[0];
   scores[shift_s] = score;
//--- out
//---
   for(int d = 0; d < dimension; d++)
     {
      float val = kv[shift_v + d] * score;
      //---
      for(int i = 0; i < kunits; i += ls)
        {
         if(k >= i && k < (i + ls))
            temp[k % ls] = (i == 0 ? 0 : temp[k % ls]) + val;
         BarrierLoc;
        }
      //---
      uint count = ls;
      //---
      do
        {
         count = (count + 1) / 2;
         if(k < ls)
            temp[k] += (k < count && (k + count) < kunits ? temp[k + count] : 0);
         if((k + count) < ls)
            temp[k + count] = 0;
         BarrierLoc;
        }
      while(count > 1);
      //---
      if(k == 0)
         out[shift_q + d] = temp[0];
      BarrierLoc;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MaskAttentionGradients(__global const float *q, __global float *q_g,
                                     __global const float *kv, __global float *kv_g,
                                     __global const float *scores,
                                     __global const float *gradient,
                                     const int kunits, const int heads_kv
                                    )
  {
//--- init
   const int q_id = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h) + d;
   const int shift_s = (q_id * heads + h) * kunits;
   const int shift_g = h * dimension + d;
   float koef = sqrt((float)dimension);
   if(koef < 1)
      koef = 1;
//--- Calculating Value's gradients
   int step_score = kunits * heads;
   if(h < heads_kv)
     {
      //---
      for(int v = q_id; v < kunits; v += qunits)
        {
         float grad = 0;
         for(int hq = h; hq < heads; hq += heads_kv)
           {
            int shift_score = hq * kunits + v;
            for(int g = 0; g < qunits; g++)
               grad += gradient[shift_g + dimension * (hq - h + g  * heads)] *
                       scores[shift_score + g * step_score];
           }
         int shift_v = dimension * (2 *  heads_kv * v + heads_kv + h) + d;
         kv_g[shift_v] = grad;
        }
     }
//--- Calculating Query's gradients
   float grad = 0;
   float out_g = IsNaNOrInf(gradient[shift_g + q_id * dimension], 0);
   int shift_val = (heads_kv + h_kv) * dimension + d;
   int shift_key = h_kv * dimension + d;
//---
   for(int k = 0; (k < kunits && out_g != 0); k++)
     {
      float sc_g = 0;
      float sc = scores[shift_s + k];
      if(sc == 0)
         continue;
      for(int v = 0; v < kunits; v++)
         sc_g += scores[shift_s + v] * out_g * kv[shift_val + 2 * v * heads_kv * dimension] *
                 ((float)(k == v) - sc);
      grad += sc_g * kv[shift_key + 2 * k * heads_kv * dimension];
     }
   q_g[shift_q] = grad / koef;
//--- Calculating Key's gradients
   if(h < heads_kv)
     {
      //---
      for(int k = q_id; k < kunits; k += qunits)
        {
         int shift_k = dimension * (2 *  heads_kv * k + h_kv) + d;
         grad = 0;
         for(int hq = h; hq < heads; hq++)
           {
            int shift_score = hq * kunits + k;
            float val = kv[shift_k + heads_kv * dimension];
            for(int scr = 0; scr < qunits; scr++)
              {
               float sc_g = 0;
               int shift_sc = scr * kunits * heads;
               float sc = scores[shift_sc + k];
               if(sc == 0)
                  continue;
               for(int v = 0; v < kunits; v++)
                  sc_g += scores[shift_sc + v] * gradient[shift_g + scr * dimension] *
                          val * ((float)(k == v) - sc);
               grad += sc_g * q[dimension * (h + scr * heads) + d];
              }
           }
         kv_g[shift_k] = grad / koef;
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardMultWinConv(__global const float *matrix_w,
                                     __global const float *matrix_i,
                                     __global float *matrix_o,
                                     __global const int *windows_in,
                                     const int inputs,
                                     const int windows_total,
                                     const int window_out,
                                     const int activation
                                    )
  {
   const size_t i = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t outputs = get_global_size(0);
//---
   const int id = i % (window_out * windows_total);
//---
   int step = 0;
   int shift_in = 0;
   int shift_weight = 0;
   int window_in = 0;
   int window = 0;
//---
   for(int w = 0; w < windows_total; w++)
     {
      int win = windows_in[w];
      step += win;
      if((w * window_out) < id)
        {
         shift_in = step;
         window_in = win;
         shift_weight += (win + 1) * window_out;
        }
     }
//---
   int steps = (int)(i / (window_out * windows_total));
   shift_in += steps * step + v * inputs;
   shift_weight += (id % window_out) * (window_in + 1);
   float sum = matrix_w[shift_weight + window_in];
//---
   for(int w = 0; w < window_in; w++)
      if((shift_in + w) < inputs)
         sum += IsNaNOrInf(matrix_i[shift_in + w], 0) * matrix_w[shift_weight + w];
//---
   matrix_o[v * outputs + i] = fActivation(sum, activation);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_gr
/// Kernel of the Convolution neuron to transfer gradient
/// to previous layer (#CNeuronConvOCL)
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientMultWinConv(__global const float *matrix_w,
      __global const float *matrix_i,
      __global float *matrix_ig,
      __global const float *matrix_og,
      __global const int *windows_in,
      const int outputs,
      const int windows_total,
      const int window_out,
      const int activation
                                           )
  {
   const size_t i = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t inputs = get_global_size(0);
//---
   int step = 0;
//---
   for(int w = 0; w < windows_total; w++)
      step += windows_in[w];
//---
   int steps = (int)(i / step);
   int id = i % step;
   int window = 0;
   int before = 0;
   int window_in = 0;
//---
   for(int w = 0; w < windows_total; w++)
     {
      window_in = windows_in[w];
      if((before + window_in) >= id)
         break;
      window = w + 1;
      before += window_in;
     }
//---
   int shift_weight = (before + window) * window_out + id - before;
   int shift_out = (steps * windows_total + window) * window_out + v * outputs;
   float sum = 0;
//---
   for(int w = 0; w < window_out; w++)
      sum += IsNaNOrInf(matrix_og[shift_out + w], 0) * matrix_w[shift_weight + w * (window_in + 1)];
//---
   matrix_ig[v * inputs + i] = Deactivation(sum, matrix_i[v * inputs + i], activation);
  }
//+------------------------------------------------------------------+
///\ingroup neuron_conv_opt Convolution Neuron Adam optimization Updating
/// Weights Calculation kernel
/// Describes the process of Adam optimization weights for the Convolution
/// Neuron (#CNeuronConvOCL).
//+------------------------------------------------------------------+
__kernel void UpdateWeightsMultWinConvAdam(__global float *matrix_w,
      __global const float *matrix_og,
      __global const float *matrix_i,
      __global float *matrix_m,
      __global float *matrix_v,
      __global const int *windows_in,
      const int windows_total,
      const int window_out,
      const int inputs,
      const int outputs,
      const float l,
      const float b1,
      const float b2
                                          )
  {
   const size_t i = get_global_id(0);  // weight shift
   const size_t v = get_local_id(1);   // variable
   const size_t variables = get_local_size(1);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
//---
   int step_out = window_out * windows_total;
//---
   int step_in = 0;
   int shift_in = 0;
   int shift_out = 0;
   int window = 0;
   int number_w = 0;
//---
   for(int w = 0; w < windows_total; w++)
     {
      int win = windows_in[w];
      if((step_in + w)*window_out <= i &&
         (step_in + win + w + 1)*window_out > i)
        {
         shift_in = step_in;
         shift_out = (step_in + w + 1) * window_out;
         window = win;
         number_w = w;
        }
      step_in += win;
     }
   bool bias = ((i - (shift_in + number_w) * window_out) % (window + 1) == window);
   int t = (i - (shift_in + number_w) * window_out) / (window + 1);
   shift_out += t + v * outputs;
   shift_in += (i - (shift_in + number_w) * window_out) % (window + 1) + v * inputs;
//---
   float grad = 0;
   int total = (inputs + step_in - 1) / step_in;
//---
   for(int t = 0; t < total; t++)
     {
      int sh_out = t * step_out + shift_out;
      if(bias && sh_out < outputs)
        {
         grad += IsNaNOrInf(matrix_og[sh_out], 0);
         continue;
        }
      //---
      int sh_in = t * step_in + shift_in;
      if(sh_in >= inputs)
         break;
      grad += IsNaNOrInf(matrix_og[sh_out] * matrix_i[sh_in], 0);
     }
//--- sum
   const uint ls = min((uint)variables, (uint)LOCAL_ARRAY_SIZE);
//---
   for(int s = 0; s < (int)variables; s += ls)
     {
      if(v >= s && v < (s + ls))
         temp[v % ls] = (i == 0 ? 0 : temp[v % ls]) + grad;
      BarrierLoc;
     }
//---
   uint count = ls;
//---
   do
     {
      count = (count + 1) / 2;
      if(v < ls)
         temp[v] += (v < count && (v + count) < ls ? temp[v + count] : 0);
      if(v + count < ls)
         temp[v + count] = 0;
      BarrierLoc;
     }
   while(count > 1);
//---
   if(v == 0)
     {
      grad = temp[0];
      float mt = IsNaNOrInf(clamp(b1 * matrix_m[i] + (1 - b1) * grad, -1.0e5f, 1.0e5f), 0);
      float vt = IsNaNOrInf(clamp(b2 * matrix_v[i] + (1 - b2) * pow(grad, 2), 1.0e-6f, 1.0e6f), 1.0e-6f);
      float weight = clamp(matrix_w[i] + IsNaNOrInf(l * mt / sqrt(vt), 0), -MAX_WEIGHT, MAX_WEIGHT);
      matrix_w[i] = weight;
      matrix_m[i] = mt;
      matrix_v[i] = vt;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MaskAttentionComplex(__global const float2* __attribute__((aligned(8)))q,     ///<[in] Matrix of Querys
                                   __global const float2* __attribute__((aligned(8)))kv,    ///<[in] Matrix of Keys
                                   __global float *scores,       ///<[out] Matrix of Scores
                                   __global const float *masks,  ///<[in] Mask Matrix
                                   __global float2* __attribute__((aligned(8)))out,         ///<[out] Matrix of attention
                                   const int dimension,          ///< Dimension of Key
                                   const int heads_kv
                                  )
  {
//--- init
   const int q_id = get_global_id(0);
   const int k = get_local_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int kunits = get_local_size(1);
   const int heads = get_global_size(2);
//---
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_k = dimension * (2 *  heads_kv * k + h_kv);
   const int shift_v = dimension * (2 *  heads_kv * k + heads_kv + h_kv);
   const int shift_s = kunits * (q_id *  heads + h) + k;
   const float mask = IsNaNOrInf(masks[shift_s], 0);
   const uint ls = min((uint)kunits, (uint)LOCAL_ARRAY_SIZE);
   float2 koef = (float2)(fmax((float)sqrt((float)dimension), (float)1), 0);
   __local float2 temp[LOCAL_ARRAY_SIZE];
//--- Score
   float score = 0;
   float2 score2 = (float2)0;
   if(ComplexAbs(mask) >= 0.01f)
     {
      for(int d = 0; d < dimension; d++)
         score2 += IsNaNOrInf2(ComplexMul(q[shift_q + d], kv[shift_k + d]), (float2)0);
      score = IsNaNOrInf(ComplexAbs(ComplexExp(ComplexDiv(score, koef))) * mask, 0);
     }
//--- sum of exp
//---
   for(int i = 0; i < kunits; i += ls)
     {
      if(k >= i && k < (i + ls))
         temp[k % ls].x = (i == 0 ? 0 : temp[k % ls].x) + score;
      BarrierLoc;
     }
//---
   uint count = ls;
//---
   do
     {
      count = (count + 1) / 2;
      if(k < ls)
         temp[k].x += (k < count && (k + count) < kunits ? temp[k + count].x : 0);
      if(k + count < ls)
         temp[k + count].x = 0;
      BarrierLoc;
     }
   while(count > 1);
//--- score
   if(temp[0].x > 0)
      score = score / temp[0].x;
   scores[shift_s] = score;
//--- out
//---
   for(int d = 0; d < dimension; d++)
     {
      float2 val = (score > 0 ? ComplexMul(kv[shift_v + d], (float2)(score, 0)) : (float2)0);
      //---
      for(int i = 0; i < kunits; i += ls)
        {
         if(k >= i && k < (i + ls))
            temp[k % ls] = (i == 0 ? (float2)0 : temp[k % ls]) + val;
         BarrierLoc;
        }
      //---
      uint count = ls;
      //---
      do
        {
         count = (count + 1) / 2;
         if(k < ls)
            temp[k] += (k < count && (k + count) < kunits ? temp[k + count] : (float2)0);
         if((k + count) < ls)
            temp[k + count] = (float2)0;
         BarrierLoc;
        }
      while(count > 1);
      //---
      if(k == 0)
         out[shift_q + d] = temp[0];
      BarrierLoc;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MaskAttentionGradientsComplex(__global const float2* __attribute__((aligned(8)))q, __global float2* __attribute__((aligned(8)))q_g,
      __global const float2* __attribute__((aligned(8)))kv, __global float2* __attribute__((aligned(8)))kv_g,
      __global const float *scores,
      __global const float *mask, __global float *mask_g,
      __global const float2* __attribute__((aligned(8)))gradient,
      const int kunits, const int heads_kv
                                           )
  {
//--- init
   const int q_id = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int shift_q = dimension * (q_id * heads + h) + d;
   const int shift_s = (q_id * heads + h) * kunits;
   const int shift_g = h * dimension + d;
   float2 koef = (float2)(fmax(sqrt((float)dimension), (float)1), 0);
//--- Calculating Value's gradients
   int step_score = kunits * heads;
   if(h < heads_kv)
     {
      //---
      for(int v = q_id; v < kunits; v += qunits)
        {
         float2 grad = (float2)0;
         for(int hq = h; hq < heads; hq += heads_kv)
           {
            int shift_score = hq * kunits + v;
            for(int g = 0; g < qunits; g++)
              {
               float sc = IsNaNOrInf(scores[shift_score + g * step_score], 0);
               if(sc > 0)
                  grad += ComplexMul(gradient[shift_g + dimension * (hq - h + g  * heads)],
                                     (float2)(sc, 0));
              }
           }
         int shift_v = dimension * (2 *  heads_kv * v + heads_kv + h) + d;
         kv_g[shift_v] = grad;
        }
     }
//--- Calculating Query's gradients
   float2 grad = 0;
   float2 out_g = IsNaNOrInf2(gradient[shift_g + q_id * dimension], (float2)0);
   int shift_val = (heads_kv + h_kv) * dimension + d;
   int shift_key = h_kv * dimension + d;
//---
   for(int k = 0; (k < kunits && ComplexAbs(out_g) != 0); k++)
     {
      float2 sc_g = 0;
      float2 sc = (float2)(scores[shift_s + k], 0);
      for(int v = 0; v < kunits; v++)
         sc_g += IsNaNOrInf2(ComplexMul(
                                ComplexMul((float2)(scores[shift_s + v], 0),
                                           out_g * kv[shift_val + 2 * v * heads_kv * dimension]),
                                ((float2)(k == v, 0) - sc)), (float2)0);
      float m = mask[shift_s + k];
      mask_g[shift_s + k] = IsNaNOrInf(sc.x / m * sc_g.x + sc.y / m * sc_g.y, 0);
      grad += IsNaNOrInf2(ComplexMul(sc_g, kv[shift_key + 2 * k * heads_kv * dimension]), (float2)0);
     }
   q_g[shift_q] = IsNaNOrInf2(ComplexDiv(grad, koef), (float2)0);
//--- Calculating Key's gradients
   if(h < heads_kv)
     {
      //---
      for(int k = q_id; k < kunits; k += qunits)
        {
         int shift_k = dimension * (2 *  heads_kv * k + h_kv) + d;
         grad = 0;
         for(int hq = h; hq < heads; hq++)
           {
            int shift_score = hq * kunits + k;
            float2 val = IsNaNOrInf2(kv[shift_k + heads_kv * dimension], (float2)0);
            for(int scr = 0; scr < qunits; scr++)
              {
               float2 sc_g = (float2)0;
               int shift_sc = scr * kunits * heads;
               float2 sc = (float2)(IsNaNOrInf(scores[shift_sc + k], 0), 0);
               if(ComplexAbs(sc) == 0)
                  continue;
               for(int v = 0; v < kunits; v++)
                  sc_g += IsNaNOrInf2(
                             ComplexMul(
                                ComplexMul((float2)(scores[shift_sc + v], 0),
                                           gradient[shift_g + scr * dimension]),
                                ComplexMul(val, ((float2)(k == v, 0) - sc))),
                             (float2)0);
               grad += IsNaNOrInf2(ComplexMul(sc_g, q[(h + scr * heads) * dimension + d]), (float2)0);
              }
           }
         kv_g[shift_k] = IsNaNOrInf2(ComplexDiv(grad, koef), (float2)0);
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CSLSTM_FeedForward(__global const float4* __attribute__((aligned(16))) concatenated,
                                 __global float *memory,
                                 __global float *output)
  {
   uint id = (uint)get_global_id(0);
   uint total = (uint)get_global_size(0);       // hidden size
   uint idv = (uint)get_global_id(1);
   uint total_v = (uint)get_global_size(1);     // variables
//---
   uint shift = id + total * idv;
   float4 concat = concatenated[shift];
//---
   float fg = 1 - fActivation(1 - 1 / pow(fActivation(concat.s0, ActFunc_SIGMOID), 2), ActFunc_TANH);
   float ig = fActivation(fActivation(concat.s1, ActFunc_SIGMOID), ActFunc_TANH);
   float nc = fActivation(concat.s2, ActFunc_TANH);
   float og = fActivation(concat.s3, ActFunc_SIGMOID);
   float mem = IsNaNOrInf(memory[shift] * fg + ig * nc, 0);
   float out = IsNaNOrInf(og * fActivation(mem, ActFunc_TANH), 0);
//---
   memory[shift] = mem;
   output[shift] = out;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CSLSTM_CalcHiddenGradient(__global const float4* __attribute__((aligned(16))) concatenated,    // Input from forward pass (W*x + U*h + b)
                                        __global float4* __attribute__((aligned(16))) grad_concat,           // Output: gradients w.r.t. gate pre-activations
                                        __global const float* memory,                                        // Updated memory (after forward pass)
                                        __global const float* grad_output                                    // dL/dOutput from the next layer
                                       )
  {
   uint id = get_global_id(0);              // Index within sequences
   uint total = get_global_size(0);         // Total size of sequences
   uint idv = get_global_id(1);             // Index over independent univariate sequences (e.g., features or channels) in a multivariate time series
   uint shift = id + total * idv;           // Flattened index
//---
   float4 concat = concatenated[shift];     // Pre-activation values for all 4 gates
// --- Forward reconstruction of gates ---
   float fg_s = fActivation(concat.s0, ActFunc_SIGMOID);
   float fg = 1.0f - fActivation(1.0f - 1.0f / pow(fg_s, 2), ActFunc_TANH);  // Forget gate (ft)
   float ig_s = fActivation(concat.s1, ActFunc_SIGMOID);
   float ig = fActivation(ig_s, ActFunc_TANH);            // Input gate (it)
   float nc = fActivation(concat.s2, ActFunc_TANH);         // Candidate (ct~)
   float og = fActivation(concat.s3, ActFunc_SIGMOID);      // Output gate (ot)
   float mem = memory[shift];                              // New memory state (ct)
   float mem_t = fActivation(mem, ActFunc_TANH);         // tanh(ct)
// --- Reconstruct previous memory state (t-1) ---
   float prev_mem = IsNaNOrInf((mem - ig * nc) / fg, 0);
// --- Gradients computation ---
   float out_g = grad_output[shift];
   float og_g = Deactivation(out_g * mem_t, og, ActFunc_SIGMOID);
   float mem_g = Deactivation(out_g * og, mem_t, ActFunc_TANH);
   float nc_g = Deactivation(mem_g * ig, nc, ActFunc_TANH);
   float ig_g = Deactivation(Deactivation(mem_g * nc, ig, ActFunc_TANH), ig_s, ActFunc_SIGMOID);
// ∂L/∂fg = ∂L/∂ct * mem_(t-1)
   float fg_g = mem_g * prev_mem;
// Derivative of the complex forget gate:
// f(z) = 1 - tanh(1 - 1 / σ(z)^2)
   float fg_s_g = 2 / pow(fg_s, 3) * Deactivation(-fg_g, fg, ActFunc_TANH);
   fg_g = Deactivation(fg_s_g, fg_s, ActFunc_SIGMOID);
// --- Write back gradients ---
   grad_concat[shift] = (float4)(fg_g, ig_g, nc_g, og_g);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ProbAttentionQeuryImp(__global const float* querys,
                                    __global const float2* __attribute__((aligned(8))) keys_values,
                                    __global const float* index_keys,
                                    __global float* querys_imp,
                                    const int dimension
                                   )
  {
   const size_t id_q = get_global_id(0);
   const size_t total_q = get_global_size(0);
   const size_t ind_k = get_local_id(1);
   const size_t total_ind = get_local_size(1);
   const size_t id_h = get_global_id(2);
   const size_t total_h = get_global_size(2);
//---
   __local float temp[LOCAL_ARRAY_SIZE][2];
   const int ls = min((int)total_ind, (int)LOCAL_ARRAY_SIZE);
//---
   const int shift_q = dimension * (id_q * total_h + id_h);
   const int id_k = index_keys[ind_k * total_h + id_h];
   const int shift_k = dimension * (id_k * total_h + id_h);
//---
   float sum = 0;
//---
   for(int d = 0; d < dimension; d++)
      sum += IsNaNOrInf(querys[shift_q + d] * keys_values[shift_k + d].s0, 0);
//---
   int id_t = ind_k % ls;
//---
   for(int i = 0; i < total_ind; i += ls)
     {
      if(i <= ind_k || (i + ls) > ind_k)
        {
         temp[id_t][0] = IsNaNOrInf((i == 0 ? 0 : temp[id_t][0]) + sum, 0);
         temp[id_t][1] = (i == 0 ? IsNaNOrInf(sum, MIN_VALUE) : fmax(temp[id_t][1], IsNaNOrInf(sum, MIN_VALUE)));
         BarrierLoc;
        }
     }
   int count = ls;
//---
   do
     {
      count = (count + 1) / 2;
      if(ind_k < count && (ind_k + count) < ls)
        {
         temp[ind_k][0] += temp[ind_k + count][0];
         temp[ind_k + count][0] = 0;
         temp[ind_k][1] = fmax(temp[ind_k + count][1], temp[ind_k][1]);
        }
      BarrierLoc;
     }
   while(count > 1);
   if(ind_k == 0)
      querys_imp[id_q * total_h + id_h] = IsNaNOrInf(temp[0][1] - temp[0][0] / total_ind, MIN_VALUE);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void TopKImportanceToIndex(__global const float* importance,
                                    __global float* indexes,
                                    const int top_k
                                   )
  {
   const size_t id_q = get_global_id(0);
   const size_t total_q = get_global_size(0);
   const size_t id_h = get_global_id(1);
   const size_t total_h = get_global_size(1);
//---
   float imp = importance[id_q * total_h + id_h];
   int pos = 0;
//---
   for(int i = 0; i < total_q; i++)
     {
      if(i == id_q)
         continue;
      float val = importance[i * total_h + id_h];
      if(val > imp || (i < id_q && val >= imp))
         pos++;
      if(pos >= top_k)
         break;
     }
//---
   if(pos < top_k)
      indexes[pos * total_h + id_h] = (float)id_q;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void QIndexAttention(__global const float *q,     ///<[in] Matrix of Querys
                              __global const float2* kv,    ///<[in] Matrix of Keys
                              __global float *scores,       ///<[out] Matrix of Scores
                              __global const float *indexes,  ///<[in] Querys Indexes
                              __global float *out,         ///<[out] Matrix of attention
                              const int dimension,          ///< Dimension of Key
                              const int heads_kv
                             )
  {
//--- init
   const int ind_q = get_global_id(0);
   const int k = get_local_id(1);
   const int h = get_global_id(2);
   const int total_q = get_global_size(0);
   const int total_k = get_local_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int q_id = (int)(indexes[ind_q * heads + h] + 0.001f);
   const int shift_q = dimension * (q_id * heads + h);
   const int shift_kv = dimension * (heads_kv * k + h_kv);
   const int shift_s = total_k * (ind_q *  heads + h) + k;
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const uint ls = min((uint)total_k, (uint)LOCAL_ARRAY_SIZE);
//--- Score
   float score = 0;
   if(q_id >= 0)
     {
      //---
      for(int d = 0; d < dimension; d++)
         score += IsNaNOrInf(q[shift_q + d] * kv[shift_kv + d].s0, 0);
     }
   else
      score = MIN_VALUE;
//--- max of score
   for(int i = 0; i < total_k; i += ls)
     {
      if(k >= i && k < (i + ls))
         temp[k % ls] = (i == 0 ? score : fmax(temp[k % ls], score));
      BarrierLoc;
     }
//---
   uint count = ls;
   do
     {
      count = (count + 1) / 2;
      if(k < count && (k + count) < ls)
         temp[k] = fmax(temp[k + count], temp[k]);
      BarrierLoc;
     }
   while(count > 1);
//---
   score = IsNaNOrInf(exp(score - temp[0]), 0);
//--- sum of exp
   for(int i = 0; i < total_k; i += ls)
     {
      if(k >= i && k < (i + ls))
         temp[k % ls] = (i == 0 ? 0 : temp[k % ls]) + score;
      BarrierLoc;
     }
//---
   count = ls;
//---
   do
     {
      count = (count + 1) / 2;
      if(k < count && (k + count) < ls)
        {
         temp[k] += temp[k + count];
         temp[k + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//--- score
   if(temp[0] > 0)
      score /= temp[0];
   scores[shift_s] = IsNaNOrInf(score, 0);
//--- out
   for(int d = 0; d < dimension; d++)
     {
      float val = kv[shift_kv + d].s1 * score;
      //---
      for(int i = 0; i < total_k; i += ls)
        {
         if(k >= i && k < (i + ls))
            temp[k % ls] = (i == 0 ? 0 : temp[k % ls]) + val;
         BarrierLoc;
        }
      //---
      uint count = ls;
      //---
      do
        {
         count = (count + 1) / 2;
         if(k < count && (k + count) < ls)
           {
            temp[k] += temp[k + count];
            temp[k + count] = 0;
           }
         BarrierLoc;
        }
      while(count > 1);
      //---
      if(k == 0)
         out[dimension * (ind_q * heads + h) + d] = temp[0];
      BarrierLoc;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void QIndexAttentionGradients(__global const float* q,
                                       __global float* q_g,
                                       __global const float2* kv,
                                       __global float2* kv_g,
                                       __global const float* indexes,
                                       __global const float* scores,
                                       __global const float* gradient,
                                       const int kunits, const int heads_kv
                                      )
  {
//--- init
   const int ind_q = get_global_id(0);
   const int d = get_global_id(1);
   const int h = get_global_id(2);
   const int qunits = get_global_size(0);
   const int dimension = get_global_size(1);
   const int heads = get_global_size(2);
   const int h_kv = h % heads_kv;
   const int q_id = (int)(indexes[ind_q * heads + h] + 0.001f);
   const int shift_q = dimension * (q_id * heads + h) + d;
   const int shift_s = (ind_q * heads + h) * kunits;
   const int shift_g = h * dimension + d;
//--- Calculating Value's gradients
   int step_score = kunits * heads;
   if(h < heads_kv)
     {
      //---
      for(int v = ind_q; v < kunits; v += qunits)
        {
         float grad = 0;
         for(int hq = h; hq < heads; hq += heads_kv)
           {
            int shift_score = hq * kunits + v;
            for(int g = 0; g < qunits; g++)
               grad += IsNaNOrInf(gradient[shift_g + dimension * (hq - h + g  * heads)], 0) *
                       scores[shift_score + g * step_score];
           }
         int shift_v = dimension * (heads_kv * v + h) + d;
         kv_g[shift_v].s1 = IsNaNOrInf(grad, 0);
        }
     }
//--- Calculating Query's gradients
   float grad = 0;
   float out_g = IsNaNOrInf(gradient[shift_g + ind_q * dimension], 0);
   int shift_kv = h_kv * dimension + d;
//---
   for(int k = 0; (k < kunits && out_g != 0); k++)
     {
      float sc_g = 0;
      float sc = scores[shift_s + k];
      if(sc == 0)
         continue;
      for(int v = 0; v < kunits; v++)
         sc_g += scores[shift_s + v] * out_g * kv[shift_kv + v * heads_kv * dimension].s1 *
                 ((float)(k == v) - sc);
      grad += sc_g * kv[shift_kv + k * heads_kv * dimension].s0;
     }
   q_g[shift_q] = grad;
//--- Calculating Key's gradients
   if(h < heads_kv)
     {
      //---
      for(int k = ind_q; k < kunits; k += qunits)
        {
         int shift_k = dimension * (heads_kv * k + h_kv) + d;
         grad = 0;
         for(int hq = h; hq < heads; hq++)
           {
            int shift_score = hq * kunits + k;
            float val = kv[shift_k + heads_kv * dimension].s1;
            for(int scr = 0; scr < qunits; scr++)
              {
               float sc_g = 0;
               int shift_sc = scr * kunits * heads;
               float sc = scores[shift_sc + k];
               if(sc == 0)
                  continue;
               for(int v = 0; v < kunits; v++)
                  sc_g += scores[shift_sc + v] * gradient[shift_g + scr * dimension] *
                          val * ((float)(k == v) - sc);
               grad += IsNaNOrInf(sc_g * q[(hq + (int)(indexes[scr * heads + hq] + 0.001f) * heads) * dimension + d], 0);
              }
           }
         kv_g[shift_k].s0 = IsNaNOrInf(grad, 0);
        }
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void TSPositonEncoder(__global const float2* __attribute__((aligned(8))) data,
                               __global const float* time,
                               __global float2* __attribute__((aligned(8))) output,
                               __global const float* period
                              )
  {
   const int id = get_global_id(0);
   const int freq = get_global_id(1);
   const int p = get_global_id(2);
   const int total = get_global_size(0);
   const int freqs = get_global_size(1);
   const int periods = get_global_size(2);
//---
   const int shift = id * freqs + freq;
   const float2 d = data[shift * periods + p];
   const float t = time[id] / period[p];
   float val = M_PI_F * t * pow(2.0f, freq + 1);
//---
   output[shift * periods + p] = (float2)(d.s0 + sin(val), d.s1 + cos(val));
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardMultWinConvWPad(__global const float *matrix_w,
      __global const float *matrix_i,
      __global float *matrix_o,
      __global const int *windows_in,
      const int inputs,
      const int step,
      const int window_out,
      const int activation
                                        )
  {
   const size_t id = get_global_id(0);
   const size_t id_w = get_global_id(1);
   const size_t v = get_global_id(2);
   const size_t outputs = get_global_size(0);
   const size_t windows_total = get_global_size(1);
//---
   int window_in = windows_in[id_w];
   int mid_win = (window_in + 1) / 2;
   int shift_in = id * step - mid_win;
   int shift_in_var = v * inputs;
   int shift_weight = 0;
//---
   for(int w = 0; w < id_w; w++)
      shift_weight += (windows_in[w] + 1) * window_out;
//---
   for(int w_out = 0; w_out < window_out; w_out++)
     {
      float sum = matrix_w[shift_weight + window_in];
      //---
      for(int w = 0; w < window_in; w++)
         if((shift_in + w) >= 0 && (shift_in + w) < inputs)
            sum += IsNaNOrInf(matrix_i[shift_in_var + shift_in + w] * matrix_w[shift_weight + w], 0);
      //---
      int shift_out = (v * outputs + id) * window_out + w_out;
      matrix_o[shift_out] = fActivation(sum, activation);
      shift_weight += window_in + 1;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientMultWinConvWPad(__global const float *matrix_w,
      __global const float *matrix_i,
      __global float *matrix_ig,
      __global const float *matrix_og,
      __global const int *windows_in,
      const int outputs,
      const int step,
      const int window_out,
      const int activation
                                               )
  {
   const size_t id_x = get_global_id(0);
   const size_t id_loc = get_local_id(1);
   const size_t id_win = id_loc / window_out;
   const size_t id_f = id_loc % window_out;
   const size_t v = get_global_id(2);
   const size_t inputs = get_global_size(0);
   const size_t size_loc = get_local_size(1);
   const size_t windows_total = size_loc / window_out;
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const uint ls = min((uint)size_loc, (uint)LOCAL_ARRAY_SIZE);
//---
   int window_in = windows_in[id_win];
   int shift_weight = id_f * (window_in + 1);
   for(int w = 0; w < id_win; w++)
      shift_weight += (windows_in[w] + 1) * window_out;
//---
   int shift_out = max((int)((id_x - window_in) / step), 0);
//---
   float grad = 0;
   int mid_win = (window_in + 1) / 2;
   for(int out = shift_out; out < outputs; out++)
     {
      int shift_in = out * step - mid_win;
      if(shift_in > id_x)
         break;
      int shift_w = id_x - shift_in;
      if(shift_w >= window_in)
         continue;
      int shift_g = ((v * outputs + out) * windows_total + id_win) * window_out + id_f;
      grad += IsNaNOrInf(matrix_w[shift_w + shift_weight] * matrix_og[shift_g], 0);
     }
//---
   for(int i = 0; i < size_loc; i += ls)
     {
      if(i <= id_loc && (i + ls) > id_loc)
         temp[id_loc % ls] = (i == 0 ? 0 : temp[id_loc % ls]) + grad;
      BarrierLoc;
     }
//---
   uint count = ls;
   do
     {
      count = (count + 1) / 2;
      if(id_loc < count && (id_loc + count) < ls)
        {
         temp[id_loc] += temp[id_loc + count];
         temp[id_loc + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//---
   if(id_loc == 0)
      matrix_ig[v * inputs + id_x] = Deactivation(temp[0], matrix_i[v * inputs + id_x], activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsMultWinConvAdamWPad(__global float *matrix_w,
      __global const float *matrix_og,
      __global const float *matrix_i,
      __global float *matrix_m,
      __global float *matrix_v,
      __global const int *windows_in,
      const int windows_total,
      const int window_out,
      const int inputs,
      const int step,
      const int outputs,
      const float l,
      const float b1,
      const float b2
                                              )
  {
   const size_t i = get_global_id(0);  // weight shift
   const size_t v = get_local_id(1);   // variable
   const size_t variables = get_local_size(1);
//---
   __local float temp[LOCAL_ARRAY_SIZE];
   const uint ls = min((uint)variables, (uint)LOCAL_ARRAY_SIZE);
//---
   int step_out = window_out * windows_total;
//---
   int shift_before = 0;
   int window = 0;
   int number_w = 0;
   for(int w = 0; w < windows_total; w++)
     {
      int win = windows_in[w];
      if(shift_before <= i &&
         (win + 1)*window_out > (i - shift_before))
        {
         window = win;
         number_w = w;
        }
      else
         shift_before += (win + 1) * window_out;
     }
//---
   int shift_in = (i - shift_before) % (window + 1);
   int shift_in_var = v * inputs;
   bool bias = (shift_in == window);
   int mid_win = (window + 1) / 2;
   int id_f = (i - shift_before) / (window + 1);
   int shift_out = number_w * window_out + id_f;
   int shift_out_var = v * outputs * step_out;
//---
   float grad = 0;
   if(!bias)
     {
      for(int out = 0; out < outputs; out++)
        {
         int in = out * step - mid_win + shift_in;
         if(in >= inputs)
            break;
         if(in < 0)
            continue;
         //---
         grad += IsNaNOrInf(matrix_og[shift_out_var + shift_out + out * step_out] * matrix_i[shift_in_var + in], 0);
        }
     }
   else
     {
      for(int out = 0; out < outputs; out++)
         grad += IsNaNOrInf(matrix_og[shift_out_var + shift_out + out * step_out], 0);
     }
//--- sum
   for(int s = 0; s < (int)variables; s += ls)
     {
      if(v >= s && v < (s + ls))
         temp[v % ls] = (s == 0 ? 0 : temp[v % ls]) + grad;
      BarrierLoc;
     }
//---
   uint count = ls;
   do
     {
      count = (count + 1) / 2;
      if(v < count && (v + count) < ls)
        {
         temp[v] += temp[v + count];
         temp[v + count] = 0;
        }
      BarrierLoc;
     }
   while(count > 1);
//---
   if(v == 0)
     {
      grad = temp[0];
      float mt = IsNaNOrInf(clamp(b1 * matrix_m[i] + (1 - b1) * grad, -1.0e5f, 1.0e5f), 0);
      float vt = IsNaNOrInf(clamp(b2 * matrix_v[i] + (1 - b2) * pow(grad, 2), 1.0e-6f, 1.0e6f), 1.0e-6f);
      float weight = clamp(matrix_w[i] + IsNaNOrInf(l * mt / sqrt(vt), 0), -MAX_WEIGHT, MAX_WEIGHT);
      matrix_w[i] = weight;
      matrix_m[i] = mt;
      matrix_v[i] = vt;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ConcatDiff(__global const float* data,
                         __global float* output,
                         const int step)
  {
   const size_t i = get_global_id(0);
   const size_t v = get_local_id(1);
   const size_t inputs = get_local_size(0);
   const size_t variables = get_local_size(1);
//---
   const int shift = i * variables;
   const float d = data[shift + v];
   float diff = 0;
   if(step > 0 && (i + step) < inputs)
      diff = IsNaNOrInf(d - data[shift + step * variables + v], 0);
//---
   output[2 * shift + v] = d;
   output[2 * shift + v + variables] = diff;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardMaskMultWinConv(__global const float *matrix_w,
      __global const float *matrix_i,
      __global const float *masks,
      __global float *matrix_o,
      const int inputs,
      const int window_in,
      const int windows_total,
      const int activation
                                        )
  {
   const size_t u = get_global_id(0);
   const size_t w = get_global_id(1);
   const size_t v = get_global_id(2);
   const size_t units = get_global_size(0);
   const size_t window_out = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const int shift_in = u * window_in * windows_total;
   const int shift_in_var =  v * units * window_in * windows_total;
   const int shift_out = (u + v * units) * window_out + w;
   const int shift_mask = (u + v * units) * windows_total;
   const int shift_weight = (v * window_out * windows_total + w) * (window_in + 1);
   const int step_weight = window_out * (window_in + 1);
//---
   float sum = 0;
   for(int w_in = 0; w_in < windows_total; w_in++)
     {
      float m = IsNaNOrInf(masks[shift_mask + w_in], 0);
      if(m < FLT_EPSILON)
         continue;
      const int shift_in_loc = shift_in + w_in * window_in;
      const int shift_weight_loc = shift_weight + w_in * step_weight;
      for(int i = 0; i < window_in; i++)
         if((shift_in_loc + i) < (inputs / variables))
            sum += IsNaNOrInf(matrix_i[shift_in_var + shift_in_loc + i], 0) *
                   matrix_w[shift_weight_loc + i] * m;
      sum += matrix_w[shift_weight_loc + window_in] * m;
     }
//---
   matrix_o[shift_out] = fActivation(sum, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientMaskMultWinConv(__global const float *matrix_w,
      __global const float *matrix_i,
      __global float *matrix_ig,
      __global const float *matrix_og,
      __global const float *masks,
      __global float *masks_g,
      const int outputs,
      const int window_in,
      const int window_out,
      const int activation
                                               )
  {
   const size_t u = get_global_id(0);
   const size_t w_in = get_global_id(1);
   const size_t v = get_global_id(2);
   const size_t units = get_global_size(0);
   const size_t windows_total = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const int shift_in = (u + v * units) * window_in * windows_total + w_in * window_in;
   const int shift_out = u * window_out;
   const int shift_out_var = v * units * window_out;
   const int shift_mask = (u + v * units) * windows_total + w_in;
   const int shift_weight = (v * window_out * windows_total + w_in * window_out) * (window_in + 1);
//---
   const float m = IsNaNOrInf(masks[shift_mask], 0);
   for(int i = 0; i < window_in; i++)
     {
      float sum = 0;
      if(m >= FLT_EPSILON)
        {
         for(int out = 0; out < window_out; out++)
           {
            if((shift_out + out) >= (outputs / variables))
               continue;
            sum += IsNaNOrInf(matrix_og[shift_out_var + shift_out + out] *
                              matrix_w[shift_weight + out * (window_in + 1) + i] *
                              m, 0);
           }
        }
      matrix_ig[shift_in + i] = Deactivation(sum, matrix_i[shift_in + i], activation);
     }
//---
   float sum = 0;
   for(int out = 0; out < window_out; out++)
     {
      int shift_weight_loc = out * (window_in + 1) + shift_weight;
      float temp = matrix_w[shift_weight_loc + window_in];
      for(int i = 0; i < window_in; i++)
         temp += IsNaNOrInf(matrix_i[shift_in + i], 0) * matrix_w[shift_weight_loc + i];
      sum += IsNaNOrInf(temp * matrix_og[shift_out_var + shift_out + out], 0);
     }
   masks_g[shift_mask] = IsNaNOrInf(sum, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsMaskMultWinConvAdam(__global float *matrix_w,
      __global const float *matrix_og,
      __global const float *matrix_i,
      __global const float *masks,
      __global float *matrix_m,
      __global float *matrix_v,
      const int windows_total,
      const int inputs,
      const int outputs,
      const float l,
      const float b1,
      const float b2
                                              )
  {
   const size_t id_in = get_global_id(0);    // input shift
   const size_t id_out = get_global_id(1);   // filter shift
   const size_t id_v = get_global_id(2);     // variable
   const size_t window_in = get_global_size(0) / windows_total - 1;
   const size_t window_out = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const int w_id = id_in / (window_in + 1);
   const int shift_in = id_in - w_id;
   const int step_in = window_in * windows_total;
   const int units = outputs / window_out;
   const int shift_in_var = id_v * inputs;
   const int shift_out_var = id_v * outputs;
   const int shift_mask_var = id_v * units * windows_total;
   const int shift_weight = ((id_v * windows_total + w_id) * window_out + id_out) *
                            (window_in + 1) + id_in % (window_in + 1);
   const bool bias = (id_in % (window_in + 1) == window_in);
//---
   float grad = 0;
   for(int u = 0; u < units; u++)
     {
      const int shift_in_loc = shift_in + u * step_in;
      if(shift_in < inputs)
         continue;
      float m = IsNaNOrInf(masks[shift_mask_var + u * windows_total + w_id], 0);
      if(m < FLT_EPSILON)
         continue;
      float inp = (bias ? 1 : IsNaNOrInf(matrix_i[shift_in_var + shift_in_loc], 0));
      grad += IsNaNOrInf(inp * m * matrix_og[shift_out_var + u * window_out + id_out], 0);
     }
   float mt = IsNaNOrInf(clamp(b1 * matrix_m[shift_weight] + (1 - b1) * grad, -1.0e5f, 1.0e5f), 0);
   float vt = IsNaNOrInf(clamp(b2 * matrix_v[shift_weight] + (1 - b2) * pow(grad, 2), 1.0e-6f, 1.0e6f), 1.0e-6f);
   float weight = clamp(matrix_w[shift_weight] + IsNaNOrInf(l * mt / sqrt(vt), 0), -MAX_WEIGHT, MAX_WEIGHT);
   matrix_w[shift_weight] = weight;
   matrix_m[shift_weight] = mt;
   matrix_v[shift_weight] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void MainFreq(__global const float* freq_r,
                       __global const float* freq_im,
                       __global float *main_freq,
                       int dimension
                      )
  {
   if(dimension <= 0)
      return;
//---
   size_t n = get_global_id(0);
   const int shift = n * dimension;
//---
   float max_f = 0;
   float max_id = 0;
   float energy;
//---
   for(int i = 1; i < dimension; i++)
     {
      float2 freq = (float2)(freq_r[shift + i], freq_im[shift + i]);
      energy = ComplexAbs(freq);
      if(max_f < energy)
        {
         max_f = energy;
         max_id = i + 1;
        }
     }
   main_freq[n] = max_id;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void FeedForwardAdaptConv(__global const float *matrix_w,
                                   __global const float *matrix_i,
                                   __global float *matrix_o,
                                   __global const float *main_freq,
                                   const int inputs,
                                   const int window_in,
                                   const int activation
                                  )
  {
   const size_t u = get_global_id(0);
   const size_t f = get_global_id(1);
   const size_t v = get_global_id(2);
   const size_t units = get_global_size(0);
   const size_t filters = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const int freq = main_freq[v];
   int window = (inputs / variables + freq - 1) / freq;
   const int step = (int)(inputs / variables + units + 1) / (units + 2);
   if(window < step)
      window = (int)((step + window - 1) / window) * window;
   if(window > window_in)
      window = window_in;
//---
   const int shift_in = (u < (units - 1) ? u * step : inputs / variables - window);
   const int shift_in_var =  v * inputs / variables;
   const int shift_out = (u + v * units) * filters + f;
   const int shift_weight = (v * filters + f) * (window_in + 1);
//---
   float sum = matrix_w[shift_weight + window_in];
   for(int i = 0; i < window; i++)
      if((shift_in + i) < (inputs / variables))
         sum += IsNaNOrInf(matrix_i[shift_in_var + shift_in + i], 0) *
                matrix_w[shift_weight + i];
//---
   matrix_o[shift_out] = fActivation(sum, activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradientAdaptConv(__global const float *matrix_w,
      __global const float *matrix_i,
      __global float *matrix_ig,
      __global const float *matrix_og,
      __global const float *main_freq,
      const int outputs,
      const int window_in,
      const int window_out,
      const int activation
                                         )
  {
   const size_t inp = get_global_id(0);
   const size_t v = get_global_id(1);
   const size_t inputs = get_global_size(0);
   const size_t variables = get_global_size(1);
//---
   const int units = outputs / (window_out * variables);
   const int freq = main_freq[v];
   int window = (inputs / variables + freq - 1) / freq;
   const int step = (int)(inputs + units + 1) / (units + 2);
   if(window < step)
      window = (int)((step + window - 1) / window) * window;
   if(window > window_in)
      window = window_in;
//---
   const int shift_in = v * inputs + inp;
   int u = inp / step;
   int shift_out_var = v * (outputs / variables);
   int shift_weight_var = (v * window_out) * (window_in + 1);
//---
   float sum = 0;
   while(u * step <= inp && u < (units - 1))
     {
      int pos = inp - u * step;
      if(pos >= window)
        {
         u++;
         continue;
        }
      int shift_out = u * window_out;
      int shift_weight = pos + shift_weight_var;
      for(int out = 0; out < window_out; out++)
        {
         if((shift_out + out) >= (outputs / variables))
            continue;
         sum += IsNaNOrInf(matrix_og[shift_out_var + shift_out + out] *
                           matrix_w[shift_weight + out * (window_in + 1)], 0);
        }
      u++;
     }
   if(inp >= (inputs - window))
     {
      int pos = inp + window - inputs;
      int shift_out = (units - 1) * window_out;
      int shift_weight = pos + shift_weight_var;
      for(int out = 0; out < window_out; out++)
        {
         if((shift_out + out) >= (outputs / variables))
            continue;
         sum += IsNaNOrInf(matrix_og[shift_out_var + shift_out + out] *
                           matrix_w[shift_weight + out * (window_in + 1)], 0);
        }
     }
   matrix_ig[shift_in] = Deactivation(sum, matrix_i[shift_in], activation);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void UpdateWeightsAdaptConvAdam(__global float *matrix_w,
      __global const float *matrix_og,
      __global const float *matrix_i,
      __global float *matrix_m,
      __global float *matrix_v,
      __global float *main_freq,
      const int inputs,
      const int outputs,
      const float l,
      const float b1,
      const float b2
                                        )
  {
   const size_t id_in = get_global_id(0);    // input shift
   const size_t id_out = get_global_id(1);   // filter shift
   const size_t id_v = get_global_id(2);     // variable
   const size_t window_in = get_global_size(0) - 1;
   const size_t window_out = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const int units = outputs / (window_out * variables);
   const int freq = main_freq[id_v];
   int window = (inputs / variables + freq - 1) / freq;
   const int step = (int)(inputs / variables + units + 1) / (units + 2);
   if(window < step)
      window = (int)((step + window - 1) / window) * window;
   if(window > window_in)
      window = window_in;
//---
   if(id_in != window_in &&
      id_in >= window)
      return;
//---
   const int shift_in_var = id_v * inputs / variables;
   const int shift_out_var = id_v * outputs / variables;
   const int shift_weight = (id_v * window_out + id_out) *
                            (window_in + 1) + id_in;
   const bool bias = (id_in == window_in);
//---
   float grad = 0;
   for(int u = 0; u < (units - 1); u++)
     {
      const int shift_in_loc = id_in + u * step;
      if(shift_in_loc >= (inputs / variables))
         continue;
      float inp = (bias ? 1 : IsNaNOrInf(matrix_i[shift_in_var + shift_in_loc], 0));
      grad += IsNaNOrInf(inp * matrix_og[shift_out_var + u * window_out + id_out], 0);
     }
     {
      const int shift_in_loc = id_in + inputs / variables - window;
      if(shift_in_loc < (inputs / variables))
        {
         float inp = (bias ? 1 : IsNaNOrInf(matrix_i[shift_in_var + shift_in_loc], 0));
         grad += IsNaNOrInf(inp * matrix_og[shift_out_var + (units - 1) * window_out + id_out], 0);
        }
     }
   float mt = IsNaNOrInf(clamp(b1 * matrix_m[shift_weight] + (1 - b1) * grad, -1.0e5f, 1.0e5f), 0);
   float vt = IsNaNOrInf(clamp(b2 * matrix_v[shift_weight] + (1 - b2) * pow(grad, 2), 1.0e-6f, 1.0e6f), 1.0e-6f);
   float weight = clamp(matrix_w[shift_weight] + IsNaNOrInf(l * mt / sqrt(vt), 0), -MAX_WEIGHT, MAX_WEIGHT);
   matrix_w[shift_weight] = weight;
   matrix_m[shift_weight] = mt;
   matrix_v[shift_weight] = vt;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void RoPE(__global const float2* __attribute__((aligned(8))) inputs,
                   __global const float2* __attribute__((aligned(8))) position_emb,
                   __global float2* __attribute__((aligned(8))) outputs
                  )
  {
   const size_t id_d = get_global_id(0);     // dimension
   const size_t id_u = get_global_id(1);     // unit
   const size_t id_v = get_global_id(2);     // variable
   const size_t dimension = get_global_size(0);
   const size_t units = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const int shift_in = (id_v * units + id_u) * dimension + id_d;
   const int shift_pos = id_u * dimension + id_d;
   const float2 inp = inputs[shift_in];
   const float2 pe = position_emb[shift_pos];
//---
   float2 result = 0;
   result.s0 = inp.s0 * pe.s0 - inp.s1 * pe.s1;
   result.s1 = inp.s0 * pe.s1 + inp.s1 * pe.s0;
//---
   outputs[shift_in] = result;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void CalcHiddenGradRoPE(__global float2* __attribute__((aligned(8))) inputs_gr,
                                 __global const float2* __attribute__((aligned(8))) position_emb,
                                 __global const float2* __attribute__((aligned(8))) outputs_gr
                                )
  {
   const size_t id_d = get_global_id(0);     // dimension
   const size_t id_u = get_global_id(1);     // unit
   const size_t id_v = get_global_id(2);     // variable
   const size_t dimension = get_global_size(0);
   const size_t units = get_global_size(1);
   const size_t variables = get_global_size(2);
//---
   const int shift_in = (id_v * units + id_u) * dimension + id_d;
   const int shift_pos = id_u * dimension + id_d;
   const float2 grad = outputs_gr[shift_in];
   const float2 pe = position_emb[shift_pos];
//---
   float2 grad_x;
   grad_x.s0 = grad.s0 * pe.s0 + grad.s1 * pe.s1;
   grad_x.s1 = grad.s1 * pe.s0 - grad.s0 * pe.s1;
//---
   inputs_gr[shift_in] = grad_x;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DifMatrix(__global const float *matrix1,    ///<[in] First matrix
                        __global const float *matrix2,    ///<[in] Second matrix
                        __global float *matrix_out, ///<[out] Output matrix
                        const float multiplyer,           ///< Multiplyer for output
                        const int shift_in1,              ///< Shift for input 1
                        const int shift_in2,              ///< Shift for input 2
                        const int shift_out               ///< Shift for output
                       )
  {
   const int i = get_global_id(0);
   const int d = get_global_id(1);
   const int step = get_global_size(0);
   const int dimension = get_global_size(1);
//---
   int index = i * dimension + d;
   matrix_out[i * shift_out + index] =
      IsNaNOrInf((matrix1[i * shift_in1 + index] - matrix2[i * shift_in2 + index]) * multiplyer, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void DifMatrixGrad(__global float *matrix1,    ///<[in] First matrix
                            __global float *matrix2,    ///<[in] Second matrix
                            __global const float *matrix_out, ///<[out] Output matrix
                            const float multiplyer,           ///< Multiplyer for output
                            const int shift_in1,              ///< Shift for input 1
                            const int shift_in2,              ///< Shift for input 2
                            const int shift_out               ///< Shift for output
                           )
  {
   const int i = get_global_id(0);
   const int d = get_global_id(1);
   const int step = get_global_size(0);
   const int dimension = get_global_size(1);
//---
   int index = i * dimension + d;
   float grad = IsNaNOrInf(matrix_out[i * shift_out + index] * multiplyer, 0);
   matrix1[i * shift_in1 + index] = grad;
   matrix2[i * shift_in2 + index] = -grad;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void IdentitySumMatrix(__global const float *matrix_in,
                                __global float *matrix_out,
                                const float multiplyer,
                                const int shift_in,
                                const int shift_out
                               )
  {
   const int i = get_global_id(0);
   const int d = get_global_id(1);
   const int step = get_global_size(0);
   const int dimension = get_global_size(1);
//---
   int index = i * dimension + d;
   matrix_out[i * shift_out + index] =
      IsNaNOrInf(((int)(i == d) + matrix_in[i * shift_in + index]) * multiplyer, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void IdentityDifMatrix(__global const float *matrix_in,
                                __global float *matrix_out,
                                const float multiplyer,
                                const int shift_in,
                                const int shift_out
                               )
  {
   const int i = get_global_id(0);
   const int d = get_global_id(1);
   const int step = get_global_size(0);
   const int dimension = get_global_size(1);
//---
   int index = i * dimension + d;
   matrix_out[i * shift_out + index] =
      IsNaNOrInf(((int)(i == d) - matrix_in[i * shift_in + index]) * multiplyer, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void IdentityDifMatrixGrad(__global float *matrix_in,
                                    __global const float *matrix_out,
                                    const float multiplyer,
                                    const int shift_in,
                                    const int shift_out
                                   )
  {
   const int i = get_global_id(0);
   const int d = get_global_id(1);
   const int step = get_global_size(0);
   const int dimension = get_global_size(1);
//---
   int index = i * dimension + d;
   matrix_in[i * shift_in + index] = IsNaNOrInf(-multiplyer * matrix_out[i * shift_out + index], 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SumVecMatrix(__global const float *vector_in,
                           __global const float *matrix_in,
                           __global float *matrix_out,
                           const float multiplyer,           ///< Multiplyer for output
                           const int shift_in1,              ///< Shift for input 1
                           const int shift_in2,              ///< Shift for input 2
                           const int shift_out               ///< Shift for output
                          )
  {
   const int i = get_global_id(0);
   const int d = get_global_id(1);
   const int step = get_global_size(0);
   const int dimension = get_global_size(1);
//---
   int index = i * dimension + d;
   float grad = matrix_out[i * shift_out + index] =
                   (vector_in[shift_in1 + d] + matrix_in[i * shift_in2 + index]) * multiplyer;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void SumVecMatrixGrad(__global float *vector_in,
                               __global float *matrix_in,
                               __global const float *matrix_out,
                               const float multiplyer,           ///< Multiplyer for output
                               const int shift_in1,              ///< Shift for input 1
                               const int shift_in2,              ///< Shift for input 2
                               const int shift_out               ///< Shift for output
                              )
  {
   const int i = get_global_id(0);
   const int d = get_global_id(1);
   const int step = get_global_size(0);
   const int dimension = get_global_size(1);
//---
   int index = i * dimension + d;
   float grad = IsNaNOrInf(matrix_out[i * shift_out + index] * multiplyer, 0);
   matrix_in[i * shift_in2 + index] = grad;
//---
   if(i == 0)
     {
      for(int i1 = 1; i1 < step; i1++)
        {
         index = i1 * dimension + d;
         grad += IsNaNOrInf(matrix_out[i1 * shift_out + index] * multiplyer, 0);
        }
      vector_in[shift_in1 + d] = IsNaNOrInf(grad / step, 0);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void InterpolationAttention(__global const float* matrix_in,
                                     __global const float* W,
                                     __global const float* A,
                                     __global const float* GL,
                                     __global float* Adj,
                                     __global float* H,
                                     __global float* Atten,
                                     __global float* matrix_out,
                                     const int dimension
                                    )
  {
   const size_t i = get_global_id(0);
   const size_t j = get_local_id(1);
   const size_t total = get_global_size(0);
   const size_t total_loc = get_local_size(1);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   const int shift_i = i * dimension;
   const int shift_j = j * dimension;
   const int shift_adj = i * total_loc + j;
//---
   float adj = 0;
   for(int d = 0; d < dimension; d++)
      adj += IsNaNOrInf(GL[shift_i + d] * GL[shift_j + d], 0);
   adj = max(IsNaNOrInf(adj, 0), 0.0f);
   adj = LocalSoftMax(adj, 1, Temp);
   Adj[shift_adj] = adj;
   adj += (float)(i == j);
//---
   for(int id_h = 0; id_h < dimension; id_h += total_loc)
     {
      if(j >= (dimension - id_h))
         break;
      float h = 0;
      for(int w = 0; w < dimension; w++)
         h += IsNaNOrInf(matrix_in[shift_i + w] * W[(id_h + j) * dimension + w], 0);
      H[shift_i + id_h + j] = h;
      BarrierLoc;
     }
   float e = 1e-12f;
   if(adj > 0)
     {
      e = 0;
      for(int a = 0; a < dimension; a++)
         e += IsNaNOrInf(H[shift_i + a] * A[a], 0) + IsNaNOrInf(H[shift_j + a] * A[dimension + a], 0);
     }
   e = LocalSoftMax(e, 1, Temp);
   Atten[shift_adj] = e;
//--- Scale output by attention
   for(int d = 0; d < dimension; d += total_loc)
     {
      if(j >= (dimension - d))
         break;
      float out = 0;
      int shift_h = d + j;
      int shift_att = i * total_loc;
      int shift_out = i * dimension + shift_h;
      for(int n = 0; n < total_loc; n++)
         out += IsNaNOrInf(H[shift_h + n * dimension] * Atten[shift_att + n], 0);
      matrix_out[shift_out] = fActivation(out, ActFunc_LReLU);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void InterpolationAttentionGrad(__global const float* matrix_in,
      __global float* matrix_in_gr,
      __global const float* W,
      __global float* W_gr,
      __global const float* A,
      __global float* A_gr,
      __global const float* GL,
      __global float* GL_gr,
      __global float* Adj,
      __global float* H,
      __global float* H_gr,
      __global float* Atten,
      __global float* matrix_out_gr,
      const int dimension
                                        )
  {
   const size_t i = get_global_id(0);
   const size_t j = get_local_id(1);
   const size_t total = get_global_size(0);
   const size_t total_loc = get_local_size(1);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   const int shift_i = i * dimension;
   const int shift_j = j * dimension;
   const int shift_adj = i * total_loc + j;
//--- H Gradient
   for(int d = 0; d < dimension; d += total_loc)
     {
      if(j >= (dimension - d))
         break;
      float h_grad = 0;
      int shift_h = shift_i + d + j;
      int shift_att = i;
      int shift_out = d + j;
      for(int n = 0; n < total_loc; n++)
        {
         float gr = matrix_out_gr[shift_out + n * dimension];
         h_grad += IsNaNOrInf(
                      Deactivation(gr, gr, ActFunc_LReLU) * Atten[shift_att + n * total_loc], 0);
        }
      H_gr[shift_h] = h_grad;
      BarrierLoc;
     }
//--- Attention Gradient
   float att_grad = 0;
   for(int d = 0; d < dimension; d++)
     {
      float gr = matrix_out_gr[shift_i + d];
      gr = Deactivation(gr, gr, ActFunc_LReLU);
      att_grad += IsNaNOrInf(gr * H[shift_j + d], 0);
     }
   att_grad = LocalSoftMaxGrad(Atten[shift_adj], att_grad, 1, Temp);
//--- Add H Gradient
   for(int d = 0; d < dimension; d++)
     {
      float h_grad = att_grad * A[d];
      h_grad = LocalSum(h_grad, 1, Temp);
      if(j == 0)
         H_gr[shift_i + d] += h_grad;
      h_grad = att_grad * A[dimension + d];
      h_grad = LocalSum(h_grad, 1, Temp);
      if(j == 0)
         H_gr[shift_j + d] += h_grad;
      float a_grad = att_grad * H[shift_i + d];
      a_grad = LocalSum(a_grad, 1, Temp);
      A_gr[d] += a_grad;
      a_grad = att_grad * H[shift_j + d];
      a_grad = LocalSum(a_grad, 1, Temp);
      A_gr[dimension + d] += a_grad;
     }
//--- Inputs' Gradient
   for(int d = 0; d < dimension; d += total_loc)
     {
      if(j >= (dimension + d))
         break;
      float grad = 0;
      for(int w = 0; w < dimension; w++)
         grad += IsNaNOrInf(H_gr[shift_i + w] * W[(d + j) + dimension * w], 0);
      matrix_in_gr[shift_i + d + j] = grad;
      BarrierLoc;
     }
//--- Adj Gradient
   float grad = LocalSoftMaxGrad(Adj[shift_adj], att_grad, 1, Temp);
   for(int d = 0; d < dimension; d++)
     {
      GL_gr[shift_i + d] += IsNaNOrInf(grad * GL[shift_j + d], 0);
      GL_gr[shift_j + d] += IsNaNOrInf(grad * GL[shift_i + d], 0);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PeriodNorm(__global const float* inputs,
                         __global float2* mean_stdevs,
                         __global float* outputs,
                         const int total_inputs
                        )
  {
   const size_t i = get_global_id(0);
   const size_t p = get_local_id(1);
   const size_t v = get_global_id(2);
   const size_t windows = get_global_size(0);
   const size_t period = get_local_size(1);
   const size_t variable = get_global_size(2);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   const int shift_i = i * period + p;
   const int shift_v = v * total_inputs;
   const int shift_ms = v * windows + i;
//---
   float val = 0;
   if((shift_i) < total_inputs)
      val = IsNaNOrInf(inputs[shift_v + shift_i], 0);
   float mean = IsNaNOrInf(LocalSum(val, 1, Temp) / period, 0);
   val -= mean;
   BarrierLoc;
   float stdev = LocalSum(val * val, 1, Temp) / period;
   stdev = IsNaNOrInf(sqrt(stdev), 1);
//---
   mean_stdevs[shift_ms] = (float2)(mean, stdev);
   if((shift_i) < total_inputs)
      outputs[shift_v + shift_i] = IsNaNOrInf(val / stdev, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void PeriodNormGrad(__global const float* inputs,
                             __global float* inputs_gr,
                             __global const float2* mean_stdevs,
                             __global const float2* mean_stdevs_gr,
                             __global const float* outputs,
                             __global const float* outputs_gr,
                             const int total_inputs
                            )
  {
   const size_t i = get_global_id(0);
   const size_t p = get_local_id(1);
   const size_t v = get_global_id(2);
   const size_t windows = get_global_size(0);
   const size_t period = get_local_size(1);
   const size_t variable = get_global_size(2);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   const int shift_i = i * period + p;
   const int shift_v = v * total_inputs;
   const int shift_ms = v * windows + i;
//---
   float inp = 0;
   float inp_gr = 0;
   float out = 0;
   float out_gr = 0;
   const float2 mean_stdev = mean_stdevs[shift_ms];
   const float2 mean_stdev_gr = mean_stdevs_gr[shift_ms];
   if((shift_i) < total_inputs)
     {
      inp = IsNaNOrInf(inputs[shift_v + shift_i], 0);
      out = IsNaNOrInf(outputs[shift_v + shift_i], 0);
      out_gr = IsNaNOrInf(outputs_gr[shift_v + shift_i], 0);
     }
   float mean_gr = LocalSum(out_gr, 1, Temp) / period + IsNaNOrInf(mean_stdev.x, 0);
   BarrierLoc;
   float stdev_gr = out * LocalSum(IsNaNOrInf(out * out_gr, 0), 1, Temp) / period + IsNaNOrInf(mean_stdev.y, 0);
   inp_gr = (out_gr - mean_gr - stdev_gr) / IsNaNOrInf(mean_stdev.y, 1);
//---
   if((shift_i) < total_inputs)
      inputs_gr[shift_v + shift_i] = IsNaNOrInf(inp_gr, 0);
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void AdaptSpatialNorm(__global const float* inputs,
                               __global const float* attention,
                               __global float2* mean_stdevs,
                               __global float* outputs
                              )
  {
   const size_t i = get_global_id(0);
   const size_t a = get_local_id(1);
   const size_t v = get_global_id(2);
   const size_t total_inputs = get_global_size(0);
   const size_t total_local = get_local_size(1);
   const size_t variables = get_global_size(2);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   const int shift_v = v * total_inputs;
   const int shift_out = shift_v + i;
//---
   float mean = 0, stdev = 0;
   for(uint l = 0; l < variables; l += total_local)
     {
      const int shift_at = v * variables + (a + l);
      float val = IsNaNOrInf(inputs[(a + l) * total_inputs + i], 0);
      float att = IsNaNOrInf(attention[shift_at], 0);
      mean += val * att;
      stdev += val * val * att;
     }
   mean = LocalSum(mean, 1, Temp);
   BarrierLoc;
   stdev = LocalSum(stdev, 1, Temp);
//---
   if(a == 0)
     {
      stdev -= mean * mean;
      stdev = IsNaNOrInf(sqrt(stdev), 1);
      if(stdev <= 0)
         stdev = 1;
      mean_stdevs[shift_out] = (float2)(mean, stdev);
      outputs[shift_out] = IsNaNOrInf((inputs[shift_out] - mean) / stdev, 0);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void AdaptSpatialNormGrad(__global const float* inputs,
                                   __global float* inputs_gr,
                                   __global const float* attention,
                                   __global float* attention_gr,
                                   __global const float2* mean_stdevs,
                                   __global const float2* mean_stdevs_gr,
                                   __global const float* outputs_gr,
                                   const uint total_inputs
                                  )
  {
   const size_t i = get_global_id(0);              // main
   const size_t loc = get_local_id(1);             // local to sum
   const size_t v = get_global_id(2);              // variable
   const size_t total_main = get_global_size(0);   // total
   const size_t total_loc = get_local_size(1);     // local dimension
   const size_t variables = get_global_size(2);    // total variables
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
//--- Inputs gradient
     {
      int shift_in = v * total_inputs + i;
      float grad = 0;
      if(i < total_inputs)
        {
         float x = IsNaNOrInf(inputs[shift_in], 0);
         for(int l = 0; l < variables; l += total_loc)
           {
            if((l + loc) >= variables)
               break;
            int shift_out = i + (l + loc) * total_inputs;
            float att = IsNaNOrInf(attention[(l + loc) * variables + v], 0);
            float out_gr = IsNaNOrInf(outputs_gr[shift_out], 0);
            float2 ms = mean_stdevs[shift_out];
            float2 ms_gr = mean_stdevs_gr[shift_out];
            float dy = (1 - att) * (1 / ms.y - (x - ms.x) * att * x / pow(ms.y, 3.0f));
            float dmean = IsNaNOrInf(ms_gr.x * att, 0);
            float dstd = IsNaNOrInf(ms_gr.y * x * (att - att * att) / ms.y, 0);
            grad += IsNaNOrInf(dy * out_gr + dmean + dstd, 0);
           }
        }
      grad = LocalSum(grad, 1, Temp);
      if(loc == 0 && i < total_inputs)
         inputs_gr[shift_in] = grad;
      BarrierLoc;
     }
//--- Attention gradient
     {
      int shift_att = v * variables + i;
      float grad = 0;
      if(i < variables)
        {
         float att = IsNaNOrInf(attention[shift_att], 0);
         for(int l = 0; l < total_inputs; l += total_loc)
           {
            if((l + loc) >= total_inputs)
               break;
            int shift_out = (l + loc) + v * total_inputs;
            int shift_in = (l + loc) + i * total_inputs;
            float x = IsNaNOrInf(inputs[shift_in], 0);
            float out_gr = IsNaNOrInf(outputs_gr[shift_out], 0);
            float2 ms = mean_stdevs[shift_out];
            float2 ms_gr = mean_stdevs_gr[shift_out];
            float dy = -x / ms.y - (x - ms.x) * x * x * (1 - 2 * att) / (2 * pow(ms.y, 3.0f));
            float dmean = IsNaNOrInf(ms_gr.x * x, 0);
            float dstd = IsNaNOrInf(ms_gr.y * x * x * (1 - 2 * att) / (2 * ms.y), 0);
            grad += IsNaNOrInf(dy * out_gr + dmean + dstd, 0);
           }
        }
      grad = LocalSum(grad, 1, Temp);
      if(loc == 0 && i < variables)
         attention_gr[shift_att] = grad;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void AttentNorm(__global const float* inputs,
                         __global const float* attention,
                         __global float* means,
                         __global float* stdevs,
                         __global float* outputs,
                         const int total_inputs,
                         const int segment_size
                        )
  {
   const size_t s = get_global_id(0);
   const size_t i = get_local_id(1);
   const size_t v = get_global_id(2);
   const size_t total_segments = get_global_size(0);
   const size_t total_local = get_local_size(1);
   const size_t variables = get_global_size(2);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
   const int shift = v * total_inputs + s * segment_size + i;
//---
   float mean = 0, stdev = 0;
   float val = 0;
   for(uint l = 0; l < segment_size; l += total_local)
     {
      if((l + i) >= segment_size ||
         (s * segment_size + l + i) >= total_inputs)
         break;
      float val_l = IsNaNOrInf(inputs[shift + l], 0);
      if(l == 0)
         val = val_l;
      float att = IsNaNOrInf(attention[v * segment_size + l + i], 0);
      mean += val_l * att;
      stdev += val_l * val_l * att;
     }
   mean = LocalSum(mean, 1, Temp);
   BarrierLoc;
   stdev = LocalSum(stdev, 1, Temp);
//---
   stdev -= mean * mean;
   stdev = IsNaNOrInf(sqrt(stdev), 1);
   if(stdev <= 0)
      stdev = 1;
//---
   if(i == 0)
     {
      int shift_ms = v * total_segments + s;
      means[shift_ms] = mean;
      stdevs[shift_ms] = stdev;
     }
   for(uint l = 0; l < segment_size; l += total_local)
     {
      if((l + i) >= segment_size ||
         (s * segment_size + l + i) >= total_inputs)
         break;
      if(l > 0)
         val = inputs[shift + l];
      outputs[shift + l] = IsNaNOrInf((val - mean) / stdev, 0);
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void AttentNormGrad(__global const float* inputs,
                             __global float* inputs_gr,
                             __global const float* attention,
                             __global float* attention_gr,
                             __global const float* means,
                             __global const float* stdevs,
                             __global const float* means_gr,
                             __global const float* outputs_gr,
                             const int total_inputs,
                             const int segment_size
                            )
  {
   const size_t i = get_global_id(0);              // main
   const size_t loc = get_local_id(1);             // local to sum
   const size_t v = get_global_id(2);              // variable
   const size_t total_main = get_global_size(0);   // total
   const size_t total_loc = get_local_size(1);     // local dimension
   const size_t variables = get_global_size(2);    // total variables
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
//--- Inputs gradient
     {
      const int s = i / segment_size;
      const int shift_in = v * total_inputs + i;
      const int shift_ms = v * segment_size + s;
      float grad = 0;
      if(loc == 0 && i < total_inputs)
        {
         Temp[0] = IsNaNOrInf(inputs[shift_in], 0);
         Temp[1] = IsNaNOrInf(means[shift_ms], 0);
         Temp[2] = IsNaNOrInf(stdevs[shift_ms], 1);
         Temp[3] = IsNaNOrInf(means_gr[shift_ms], 0);
         Temp[4] = IsNaNOrInf(attention[(v - s) * segment_size + i], 0);
        }
      BarrierLoc;
      if(i < total_inputs)
        {
         float x = Temp[0];
         float mean = Temp[1];
         float stdev = Temp[2];
         float mean_gr = Temp[3];
         float att = Temp[4];
         for(int l = 0; l < segment_size; l += total_loc)
           {
            if((l + loc) >= segment_size ||
               (i * segment_size + loc + l) >= total_inputs)
               break;
            float out_gr = IsNaNOrInf(outputs_gr[v * total_inputs + s * segment_size + loc + l], 0);
            bool same = (i - s * segment_size) == (loc + l);
            float xl = x;
            if(!same)
               xl = IsNaNOrInf(inputs[v * total_inputs + s * segment_size + loc + l], 0);
            float dy = ((int)same - att) * (1 / stdev - (xl - mean) * att * x / pow(stdev, 3.0f));
            float dmean = (same ? IsNaNOrInf(mean_gr * att, 0) : 0);
            grad += IsNaNOrInf(dy * out_gr + dmean, 0);
           }
        }
      grad = LocalSum(grad, 1, Temp);
      if(loc == 0 && i < total_inputs)
         inputs_gr[shift_in] = grad;
      BarrierLoc;
     }
//--- Attention gradient
     {
      float grad = 0;
      int shift_att = v * segment_size + i;
      if(i < segment_size)
        {
         float att = IsNaNOrInf(attention[shift_att], 0);
         for(int l = 0; l < total_inputs; l += total_loc)
           {
            if((l + loc) >= total_inputs)
               break;
            int shift_out = (l + loc) + v * total_inputs;
            int s = (l + loc) / segment_size;
            int shift_in = v * total_inputs + s * segment_size + i;
            float x = IsNaNOrInf(inputs[shift_in], 0);
            float out_gr = IsNaNOrInf(outputs_gr[shift_out], 0);
            float mean = means[v * segment_size + s];
            float stdev = stdevs[v * segment_size + s];
            float mean_gr = means_gr[v * segment_size + s];
            bool same = (i - s * segment_size) == (loc + l);
            float xl = x;
            if(!same)
               xl = IsNaNOrInf(inputs[shift_out], 0);
            float dy = -x / stdev - (xl - mean) * x * x * (1 - 2 * att) / (2 * pow(stdev, 3.0f));
            float dmean = IsNaNOrInf(mean_gr * x, 0);
            grad += IsNaNOrInf(dy * out_gr + dmean, 0);
           }
        }
      grad = LocalSum(grad, 1, Temp);
      if(loc == 0 && i < segment_size)
         attention_gr[shift_att] = grad;
     }
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ChebStep(__global const float* support,
                       __global float* outputs,
                       const int step
                      )
  {
   const size_t l = get_local_id(0);
   const size_t r = get_global_id(1);
   const size_t c = get_global_id(2);
   const size_t total_l = get_local_size(0);
   const size_t total_r = get_global_size(1);
   const size_t total_c = get_global_size(2);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
//---
   if(step <= 0 || total_r!=total_c)
      return;
//---
   if(step <= 3)
     {
      const float diag = (r == c ? 1.0f : 0.0f);
      if(l == 0)
         outputs[RCtoFlat(r, c, total_r, total_c, 0)] = diag;
      if(step < 2)
         return;
      if(l == 0)
        {
         const float s = IsNaNOrInf(support[RCtoFlat(r, c, total_r, total_c, 0)], 0);
         outputs[RCtoFlat(r, c, total_r, total_c, 1)] = s;
        }
      if(step < 3)
         return;
      float out = 0;
      for(int t = 0; t < total_c; t += total_l)
        {
         const float s1 = IsNaNOrInf(support[RCtoFlat(r, t + l, total_r, total_c, 0)], 0);
         const float s2 = IsNaNOrInf(support[RCtoFlat(t + l, c, total_r, total_c, 0)], 0);
         out += IsNaNOrInf(s1 * s2, 0);
        }
      out = 2 * LocalSum(out, 0, Temp);
      if(l == 0)
        {
         out -= diag;
         outputs[RCtoFlat(r, c, total_r, total_c, 2)] = IsNaNOrInf(out, 0);
        }
      return;
     }
//---
   float out = 0;
   for(int t = 0; t < total_c; t += total_l)
     {
      if((t + l) >= total_c)
         continue;
      const float s1 = IsNaNOrInf(support[RCtoFlat(r, t + l, total_r, total_c, 0)], 0);
      const float s2 = IsNaNOrInf(outputs[RCtoFlat(t + l, c, total_r, total_c, step - 2)], 0);
      out += IsNaNOrInf(s1 * s2, 0);
     }
   out = 2 * LocalSum(out, 0, Temp);
   if(l == 0)
     {
      out -= IsNaNOrInf(outputs[RCtoFlat(r, c, total_r, total_c, step - 3)], 0);
      outputs[RCtoFlat(r, c, total_r, total_c, step - 1)] = IsNaNOrInf(out, 0);
     }
   return;
  }
//+------------------------------------------------------------------+
//|                                                                  |
//+------------------------------------------------------------------+
__kernel void ChebStepGrad(__global const float* support,
                           __global float* support_g,
                           __global const float* outputs,
                           __global float* outputs_g,
                           const int step
                          )
  {
   const size_t l = get_local_id(0);
   const size_t r = get_global_id(1);
   const size_t c = get_global_id(2);
   const size_t total_l = get_local_size(0);
   const size_t total_r = get_global_size(1);
   const size_t total_c = get_global_size(2);
//---
   __local float Temp[LOCAL_ARRAY_SIZE];
//---
   if(step < 1 || total_r!=total_c)
      return;
//---
   if(step >= 2)
     {
      float grad = IsNaNOrInf(outputs_g[RCtoFlat(r, c, total_r, total_c, step)], 0);
      if(l == 0)
         outputs_g[RCtoFlat(r, c, total_r, total_c, step - 2)] -= grad;
      //--- support grad
      grad = 0;
      for(int t = 0; t < total_c; t += total_l)
        {
         if((t + l) >= total_c)
            continue;
         const float s2 = IsNaNOrInf(outputs[RCtoFlat(c, t + l, total_r, total_c, step - 2)], 0);
         grad += IsNaNOrInf(outputs_g[RCtoFlat(r, t + l, total_r, total_c, step)] * s2, 0);
        }
      grad = LocalSum(grad, 0, Temp);
      if(l == 0)
         outputs_g[RCtoFlat(r, c, total_r, total_c, 1)] += grad;
      BarrierLoc;
      //--- T(k-1) grad
      grad = 0;
      for(int t = 0; t < total_c; t += total_l)
        {
         if((t + l) >= total_c)
            continue;
         const float s2 = IsNaNOrInf(support[RCtoFlat(t + l, r, total_r, total_c, 0)], 0);
         grad += IsNaNOrInf(outputs_g[RCtoFlat(t + l, c, total_r, total_c, step)] * s2, 0);
        }
      grad = LocalSum(grad, 0, Temp);
      if(l == 0)
         outputs_g[RCtoFlat(r, c, total_r, total_c, step - 1)] += grad;
     }
//---
   if(step <= 2)
     {
      if(l == 0)
         support_g[RCtoFlat(r, c, total_r, total_c, 0)] = outputs_g[RCtoFlat(r, c, total_r, total_c, 1)];
      return;
     }
  }
//+------------------------------------------------------------------+
