mma_kernel.h

/*
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#ifndef MMA_HIP_KERNEL_H
#define MMA_HIP_KERNEL_H
 
template <typename T>
__global__ void mma_Ljjxinv_kernel(T* __restrict__ Ljjxinv, 
     const T* __restrict__ pjlambda, const T* __restrict__ qjlambda,
     const T* __restrict__ x, const T* __restrict__ low, const T* __restrict__ upp,
     const T* __restrict__ alpha, const T* __restrict__ beta,
     const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    const T xt = x[tj];
    T val = -1.0 / (2.0 * pjlambda[tj] / pow(upp[tj] - xt, 3) +
                    2.0 * qjlambda[tj] / pow(xt - low[tj], 3));
    // Remove the sensitivity for the active primal constraints
    bool is_alpha = xt == alpha[tj];
    bool is_beta  = xt == beta[tj];
    Ljjxinv[tj] = (is_alpha || is_beta) ? T(0.0) : val;
  }
}
 
 
template <typename T>
__global__ void mma_dipsolvesub1_kernel(T* __restrict__ x, 
     const T* __restrict__ pjlambda, const T* __restrict__ qjlambda,
     const T* __restrict__ low, const T* __restrict__ upp,
     const T* __restrict__ alpha, const T* __restrict__ beta,
     const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    T pj = sqrt(pjlambda[tj]);
    T qj = sqrt(qjlambda[tj]);
    T denom = pj + qj;
    T val = (pj * low[tj] + qj * upp[tj]) / denom;
 
    // Clamp x between alpha and beta using branchless min/max
    x[tj] = fmax(fmin(val, beta[tj]), alpha[tj]);
  }
 
}
 
template <typename T>
__global__ void mattrans_v_mul_kernel(T* __restrict__ output, 
     const T* __restrict__ pij, const T* __restrict__ lambda,
     const int m, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    output[tj] = 0.0;
    for (int i = 0; i < m; i++) {
      // output[tj] = output[tj] + pij[tj + i * n] * lambda[i];
      output[tj] = output[tj] + pij[i + tj * m] * lambda[i];
    }
  }
}
 
template <typename T>
__global__ void mma_sub1_kernel(T* __restrict__ xlow, T* __restrict__ xupp,
     const T* __restrict__ x, const T* __restrict__ xmin,
     const T* __restrict__ xmax, const T asyinit, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
     T xgap = xmax[tj] - xmin[tj];
     xlow[tj] = x[tj] - asyinit * xgap;
     xupp[tj] = x[tj] + asyinit * xgap;
  }
}
 
 
template< typename T >
__global__ void mma_sub2_kernel(T* __restrict__ low, T* __restrict__ upp,
     const T* __restrict__ x, const T* __restrict__ xold1,
     const T* __restrict__ xold2, const T* __restrict__ xdiff,
     const T asydecr, const T asyincr, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj >= n) return;
 
  // Load data into registers for faster accessing compare to global memory 
  // when accessing repeatedly)
  const T xval     = x[tj];
  const T xold1val = xold1[tj];
  const T xold2val = xold2[tj];
  const T lowval   = low[tj];
  const T uppval   = upp[tj];
  const T xdiffval = xdiff[tj];
 
  // Compute the product
  const T prod = (xval - xold1val) * (xold1val - xold2val);
 
  // Compute asy_factor without branching
  T asy_factor = (prod < T(0)) ? asydecr :
                 (prod > T(0)) ? asyincr : T(1);
 
  // Update low and upp using fma (fused multiply-add) for numerical stability
  T new_low = fma(-asy_factor, (xold1val - lowval), xval);
  T new_upp = fma(asy_factor,  (uppval - xold1val), xval);
 
  // Apply bounds
  new_low = max(new_low, xval - T(10.0) * xdiffval);
  new_low = min(new_low, xval - T(0.01) * xdiffval);
 
  new_upp = min(new_upp, xval + T(10.0) * xdiffval);
  new_upp = max(new_upp, xval + T(0.01) * xdiffval);
 
  // Write results back
  low[tj] = new_low;
  upp[tj] = new_upp;
}
 
template< typename T >
__global__ void mma_sub3_kernel(const T* __restrict__ x,
     const T* __restrict__ df0dx, const T* __restrict__ dfdx,
     T* __restrict__ low, T* __restrict__ upp, const T* __restrict__ xmin,
   const T* __restrict__ xmax, T* __restrict__ alpha, T* __restrict__ beta,
   T* __restrict__ p0j, T* __restrict__ q0j, T* __restrict__ pij,
   T* __restrict__ qij, const int n, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
     T xgap = xmax[tj] - xmin[tj];
     alpha[tj] = max(max(xmin[tj], low[tj] +
        0.1 * (x[tj] - low[tj])), x[tj] - 0.5 * xgap);
     beta[tj] = min(min(xmax[tj], upp[tj] - 0.1 * (upp[tj] - x[tj])), x[tj] +
        0.5 * xgap);
 
     p0j[tj] = pow(upp[tj] - x[tj], 2) * (1.001 * max(df0dx[tj], 0.0) +
        0.001 * max(-df0dx[tj], 0.0) + 0.00001 / max(0.00001, xgap));
     q0j[tj] = pow(x[tj] - low[tj], 2) * (0.001 * max(df0dx[tj], 0.0) +
        1.001 * max(-df0dx[tj], 0.0) + 0.00001 / max(0.00001, xgap));
 
     for (int i = 0; i < m; i++) {
        pij[i + tj*m] = pow(upp[tj] - x[tj], 2) *
         (1.001 * max(dfdx[i + tj*m], 0.0) + 0.001 *
         max(-dfdx[i + tj*m], 0.0) + 0.00001 / max(0.00001, xgap));
        qij[i + tj*m] = pow(x[tj] - low[tj], 2) *
         (0.001 * max(dfdx[i + tj*m], 0.0) + 1.001 *
       max(-dfdx[i + tj*m], 0.0) + 0.00001 / max(0.00001, xgap));
     }
  }
}
 
 
template< typename T >
__global__ void mma_sub4_kernel(const T* __restrict__ x, T* __restrict__ low,
     T* __restrict__ upp, T* __restrict__ pij, T* __restrict__ qij,
     T* __restrict__ temp, const int n, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
     for (int i = 0; i < m; i++) {
        temp[i + tj*m] = pij[i + tj*m] / (upp[tj] - x[tj]) +
         qij[i + tj*m] / (x[tj] - low[tj]);
     }
  }
}
 
 
template <typename T>
__global__ void mma_max2_kernel(T* __restrict__ xsi, const T* __restrict__ x,
     T* __restrict__ alpha, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
     xsi[tj] = max(1.0, 1.0 / (x[tj] - alpha[tj]));
  }
}
 
 
 
template <typename T>
__global__ void relambda_kernel(T* __restrict__ temp, const T* __restrict__ x,
     const T* __restrict__ xupp, const T* __restrict__ xlow,
     const T* __restrict__ pij, const T* __restrict__ qij, const int n,
   const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
     for (int i = 0; i < m; i++) {
        temp[i + tj*m] = pij[i + tj*m] / (xupp[tj] - x[tj]) +
         qij[i + tj*m] / (x[tj] - xlow[tj]);
     }
  }
}
 
 
template <typename T>
__global__ void sub2cons2_kernel(T* __restrict__ a, const T* __restrict__ b,
     const T* __restrict__ c, const T* __restrict__ d,
     const T e, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
     a[tj] = b[tj]*(c[tj]-d[tj])-e;
  }
}
 
template< typename T>
__inline__ __device__ T max_reduce_warp(T val) {
  val = max(val, __shfl_down(val, 16, 32));
  val = max(val, __shfl_down(val, 8, 32));
  val = max(val, __shfl_down(val, 4, 32));
  val = max(val, __shfl_down(val, 2, 32));
  val = max(val, __shfl_down(val, 1, 32));
  return val;
}
 
 
 
template< typename T >
__global__ void maxval_kernel(const T*  __restrict__ a, T *temp, const int n) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
 
  __shared__ T shared[32];
  T maxval = 0.0;
  for (int i = idx; i < n; i += str) {
     maxval = max(maxval, abs(a[i]));
  }
 
  maxval = max_reduce_warp<T>(maxval);
  if (lane == 0)
     shared[wid] = maxval;
  __syncthreads();
 
  maxval = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0.0;
  if (wid == 0)
     maxval = max_reduce_warp<T>(maxval);
 
  if (threadIdx.x == 0)
    temp[blockIdx.x] = maxval;
 
}
 
template <typename T>
__global__ void max_reduce_kernel(T*  __restrict__ bufred, const int n) {
 
  T maxval = 0.0;
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
  for (int i = idx; i < n; i += str)
  {
    maxval =max(maxval, bufred[i]);
  }
 
  __shared__ T shared[32];
  unsigned int lane = threadIdx.x % warpSize;
  unsigned int wid = threadIdx.x / warpSize;
 
  maxval = max_reduce_warp<T>(maxval);
  if (lane == 0)
    shared[wid] = maxval;
  __syncthreads();
 
  maxval = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0.0;
  if (wid == 0)
    maxval = max_reduce_warp<T>(maxval);
 
  if (threadIdx.x == 0)
    bufred[blockIdx.x] = maxval;
}
 
template <typename T>
__global__ void delx_kernel(T* __restrict__ delx, const T* __restrict__ x,
     const T* __restrict__ xlow, const T* __restrict__ xupp,
     const T* __restrict__ pij, const T* __restrict__ qij,
   const T* __restrict__ p0j, const T* __restrict__ q0j,
     const T* __restrict__ alpha, const T* __restrict__ beta,
   const T* __restrict__ lambda, const T epsi, const int n, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    delx[tj]=0;
    for (int i = 0; i < m; i++) {
      delx[tj] = delx[tj] + pij[i + tj * m] *
         lambda[i] / pow(xupp[tj] - x[tj], 2) -
           qij[i + tj * m] * lambda[i] / pow(x[tj] - xlow[tj], 2);
    }
    delx[tj] = delx[tj] + p0j[tj] / pow(xupp[tj] - x[tj], 2) -
       q0j[tj] / pow(x[tj] - xlow[tj], 2) - epsi / (x[tj] - alpha[tj])
         + epsi / (beta[tj] - x[tj]);
  }
}
 
 
template <typename T>
__global__ void GG_kernel(T* __restrict__ GG, const T* __restrict__ x,
     const T* __restrict__ xlow, const T* __restrict__ xupp,
     const T* __restrict__ pij, const T* __restrict__ qij, const int n,
     const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    for (int ggdumiter = 0; ggdumiter < m; ggdumiter++) {
      GG[ggdumiter  + m*tj] = pij[ggdumiter + m*tj] / pow(xupp[tj] - x[tj], 2) -
         qij[ggdumiter + m*tj] / pow(x[tj] - xlow[tj], 2);
    }
  }
}
template <typename T>
__global__ void diagx_kernel(T* __restrict__ diagx, const T* __restrict__ x,
     const T* __restrict__ xsi, const T* __restrict__ xlow,
     const T* __restrict__ xupp, const T* __restrict__ p0j,
   const T* __restrict__ q0j, const T* __restrict__ pij,
   const T* __restrict__ qij, const T* alpha, const T*  beta,
   const T*  eta, const T* lambda, const int n, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    T sum = 0;
    T sum1 = 0;
    for (int i = 0; i < m; i++) {
      sum = sum + pij[tj *m+ i] * lambda[i];
      sum1 = sum1 + qij[tj*m + i] * lambda[i];
    }
    diagx[tj] = (p0j[tj] + sum) / pow(xupp[tj] - x[tj], 3) +
       (q0j[tj] + sum1) / pow(x[tj] - xlow[tj], 3);
    diagx[tj] = 2.0 * diagx[tj] + xsi[tj] / (x[tj] - alpha[tj]) +
       eta[tj] / (beta[tj] - x[tj]);
  }
}
 
 
template< typename T>
__inline__ __device__ T reduce_warp(T val) {
  val += __shfl_down(val, 16, 32);
  val += __shfl_down(val, 8, 32);
  val += __shfl_down(val, 4, 32);
  val += __shfl_down(val, 2, 32);
  val += __shfl_down(val, 1, 32);
  return val;
}
 
template <typename T>
__global__ void mmareduce_kernel(T* __restrict__ bufred, const int n) {
 
  T sum = 0;
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
  for (int i = idx; i < n; i += str)
  {
    sum += bufred[i];
  }
 
  __shared__ T shared[32];
  unsigned int lane = threadIdx.x % warpSize;
  unsigned int wid = threadIdx.x / warpSize;
 
  sum = reduce_warp<T>(sum);
  if (lane == 0)
    shared[wid] = sum;
  __syncthreads();
 
  sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
  if (wid == 0)
    sum = reduce_warp<T>(sum);
 
  if (threadIdx.x == 0)
    bufred[blockIdx.x] = sum;
}
 
 
template< typename T >
__global__ void mmasum_kernel(const T*  __restrict__ a, T*  __restrict__ buf_h,
     const int n, const int m, const int k) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
 
  __shared__ T shared[32];
  T sum = 0;
  for (int i = idx; i < n; i += str)
  {
    sum += a[m * i + k ];
  }
 
  sum = reduce_warp<T>(sum);
  if (lane == 0)
    shared[wid] = sum;
  __syncthreads();
 
  sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
  if (wid == 0)
    sum = reduce_warp<T>(sum);
 
  if (threadIdx.x == 0)
    buf_h[blockIdx.x] = sum;
 
}
template< typename T >
__global__ void mmasumbb_kernel(const T*  __restrict__ GG,
     const T*  __restrict__ delx, const T*  __restrict__ diagx,
     T*  __restrict__ buf_h, const int n, const int m, const int k) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
 
  __shared__ T shared[32];
  T sum = 0;
  for (int i = idx; i < n; i += str)
  {
    sum += GG[ k + i * m] * delx[i] / diagx[i];
  }
 
  sum = reduce_warp<T>(sum);
  if (lane == 0)
    shared[wid] = sum;
  __syncthreads();
 
  sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
  if (wid == 0)
    sum = reduce_warp<T>(sum);
 
  if (threadIdx.x == 0)
    buf_h[blockIdx.x] = sum;
 
}
 
template< typename T >
__global__ void mmasumHess_kernel(const T*  __restrict__ hijx,
     const T*  __restrict__ Ljjxinv, T*  __restrict__ buf_h, const int n,
   const int m, const int k0, const int k1) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
  // this is similar to mmasumAA_kernel but with Ljjxinv_d = 1/diagx
  __shared__ T shared[32];
  T sum = 0;
  for (int i = idx; i < n; i += str)
  {
    sum += hijx[ k0 + i * m] * Ljjxinv[i]  * hijx[ k1 + i * m];
  }
 
  sum = reduce_warp<T>(sum);
  if (lane == 0)
    shared[wid] = sum;
  __syncthreads();
 
  sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
  if (wid == 0)
    sum = reduce_warp<T>(sum);
 
  if (threadIdx.x == 0)
    buf_h[blockIdx.x] = sum;
 
}
 
template< typename T >
__global__ void mmasumAA_kernel(const T*  __restrict__ GG,
     const T*  __restrict__ diagx, T*  __restrict__ buf_h, const int n,
   const int m, const int k0, const int k1) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
 
  __shared__ T shared[32];
  T sum = 0;
  for (int i = idx; i < n; i += str)
  {
    sum += GG[ k0 + i * m] /diagx[i]  * GG[ k1 + i * m];
  }
 
  sum = reduce_warp<T>(sum);
  if (lane == 0)
    shared[wid] = sum;
  __syncthreads();
 
  sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
  if (wid == 0)
    sum = reduce_warp<T>(sum);
 
  if (threadIdx.x == 0)
    buf_h[blockIdx.x] = sum;
 
}
 
 
template <typename T>
__global__ void mma_copy_kernel(T* __restrict__ a, const T* __restrict__ b,
     const int n, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
    if(tj<n)
      a[tj+m]=b[tj];
}
 
 
 
template <typename T>
__global__ void AA_kernel(T* __restrict__ temp, const T* __restrict__ GG,
     const T* __restrict__ diagx, const int n, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    for (int i0 = 0; i0 < m; i0++) {
      for (int i1 = 0; i1 < m; i1++) {
        temp[tj + i0 * (n + 1) + i1 * (m + 1) * (n + 1)] = GG[i0 * n + tj] *
         (1.0 / diagx[tj]) * GG[i1 * n + tj];
      }
    }
  }
}
 
 
template <typename T>
__global__ void dx_kernel(T* __restrict__ dx, const T* __restrict__ delx,
     const T* __restrict__ diagx, const T* __restrict__ GG,
     const T* __restrict__ dlambda, const int n, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    dx[tj] = -delx[tj]/diagx[tj];
    for(int i=0;i<m;i++){
      dx[tj] =dx[tj] - GG[tj*m+i]*dlambda[i]/diagx[tj];
    }
  }
}
 
 
 
template <typename T>
__global__ void dxsi_kernel(T* __restrict__ dxsi, const T* __restrict__ xsi,
     const T* __restrict__ dx, const T* __restrict__ x,
     const T* __restrict__ alpha, const T epsi, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    dxsi[tj]= -xsi[tj] + (epsi-dx[tj]*xsi[tj])/(x[tj] - alpha[tj]);
  }
}
 
 
template <typename T>
__global__ void deta_kernel(T* __restrict__ deta, const T* __restrict__ eta,
     const T* __restrict__ dx, const T* __restrict__ x,
     const T* __restrict__ beta, const T epsi, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    deta[tj] = -eta[tj] + (epsi + dx[tj] * eta[tj]) / (beta[tj] - x[tj]);
  }
}
 
 
 
template <typename T>
__global__ void RexCalculation_kernel(T* __restrict__ rex,
     const T* __restrict__ x, const T* __restrict__ xlow,
   const T* __restrict__ xupp, const T* __restrict__ pij,
   const T* __restrict__ p0j, const T* __restrict__ qij,
   const T* __restrict__ q0j, const T* __restrict__ lambda,
   const T* __restrict__ xsi, const T* __restrict__ eta, const int n,
   const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    rex[tj] = 0.0;
    for (int i = 0; i < m; i++) {
      rex[tj] = rex[tj] + pij[i +tj*m] * lambda[i] / pow(xupp[tj] - x[tj], 2) -
         qij[i +tj*m] * lambda[i] / pow(x[tj] - xlow[tj], 2);
    }
    rex[tj] = rex[tj] + p0j[tj] / pow(xupp[tj] - x[tj], 2) -
       q0j[tj] / pow(x[tj] - xlow[tj], 2) - xsi[tj] + eta[tj];
  }
}
 
template <typename T>
__global__ void rey_calculation_kernel(T* __restrict__ rey,
     const T* __restrict__ c, const T* __restrict__ d, const T* __restrict__ y,
     const T* __restrict__ lambda, const T* __restrict__ mu, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    rey[tj] = c[tj] + d[tj] * y[tj] - lambda[tj] - mu[tj];
  }
}
 
 
template< typename T >
__global__ void norm_kernel(const T*  __restrict__ a, T*  __restrict__ buf_h,
     const int n) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
 
  __shared__ T shared[32];
  T sum = 0;
  for (int i = idx; i < n; i += str)
  {
    sum += pow(a[i], 2);
  }
 
  sum = reduce_warp<T>(sum);
  if (lane == 0)
    shared[wid] = sum;
  __syncthreads();
 
  sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
  if (wid == 0)
    sum = reduce_warp<T>(sum);
 
  if (threadIdx.x == 0)
    buf_h[blockIdx.x] = sum;
 
}
 
 
 
template <typename T>
__global__ void sub2cons_kernel(T* __restrict__ a, const T* __restrict__ b,
     const T* __restrict__ c,
  const T d, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    a[tj] = b[tj]*c[tj]-d;
  }
}
 
 
template <typename T>
__global__ void dely_kernel(T* __restrict__ dely, const T* __restrict__ c,
     const T* __restrict__ d, const T* __restrict__ y,
     const T* __restrict__ lambda, const T epsi, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    dely[tj] = c[tj] + d[tj]*y[tj] - lambda[tj] - epsi/y[tj];
  }
}
 
 
 
template< typename T >
__global__ void maxval2_kernel(const T* __restrict__ a, const T* __restrict__ b,
     T* __restrict__ temp, const T cons, const int n) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
 
  __shared__ T shared[32];
  T maxval = cons * a[0] / b[0];
  for (int i = idx; i < n; i += str)
  {
    maxval = max(maxval, cons * a[i] / b[i]);
  }
 
  maxval = max_reduce_warp<T>(maxval);
  if (lane == 0)
    shared[wid] = maxval;
  __syncthreads();
 
  maxval = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0.0;
  if (wid == 0)
    maxval = max_reduce_warp<T>(maxval);
 
  if (threadIdx.x == 0)
    temp[blockIdx.x] = maxval;
 
}
 
 
template< typename T >
__global__ void maxval3_kernel(const T* __restrict__ a, const T* __restrict__ b,
     const T* __restrict__ c, T* __restrict__ temp, const T cons, const int n) {
 
  const int idx = blockIdx.x * blockDim.x + threadIdx.x;
  const int str = blockDim.x * gridDim.x;
 
  const unsigned int lane = threadIdx.x % warpSize;
  const unsigned int wid = threadIdx.x / warpSize;
 
  __shared__ T shared[32];
  T maxval = cons * a[0] / b[0];
  for (int i = idx; i < n; i += str)
  {
    maxval = max(maxval, cons * a[i] / (b[i] - c[i]));
  }
 
  maxval = max_reduce_warp<T>(maxval);
  if (lane == 0)
    shared[wid] = maxval;
  __syncthreads();
 
  maxval = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
  if (wid == 0)
    maxval = max_reduce_warp<T>(maxval);
 
  if (threadIdx.x == 0)
    temp[blockIdx.x] = maxval;
 
}
 
 
template <typename T>
__global__ void kkt_rex_kernel(T* __restrict__ rex, const T* __restrict__ df0dx,
     const T* __restrict__ dfdx, const T* __restrict__ xsi,
     const T* __restrict__ eta, const T* __restrict__ lambda, const int n,
   const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    rex[tj] = 0.0;
    for (int i = 0; i < m; i++) {
      rex[tj] = rex[tj] + dfdx[i + tj*m] * lambda[i];
    }
    rex[tj] += df0dx[tj] - xsi[tj] + eta[tj];
  }
}
 
 
template <typename T>
__global__ void maxcons_kernel(T* __restrict__ a, const T b,
     const T c, const T* __restrict__ d, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    a[tj] = max(b, c * d[tj]);
  }
}
 
 template< typename T >
 __global__ void glsum_kernel(const T * a, T * buf_h, const int n) {
   const int idx = blockIdx.x * blockDim.x + threadIdx.x;
   const int str = blockDim.x * gridDim.x;
 
   const unsigned int lane = threadIdx.x % warpSize;
   const unsigned int wid = threadIdx.x / warpSize;
 
   __shared__ T shared[32];
   T sum = 0;
   for (int i = idx; i<n ; i += str)
   {
     sum += a[i];
   }
 
   sum = reduce_warp<T>(sum);
   if (lane == 0)
     shared[wid] = sum;
   __syncthreads();
 
   sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
   if (wid == 0)
     sum = reduce_warp<T>(sum);
 
   if (threadIdx.x == 0)
     buf_h[blockIdx.x] = sum;
 
 }
  template< typename T >
__global__ void glsc2_kernel(const T * a,
                              const T * b,
                              T * buf_h,
                              const int n) {
 
   const int idx = blockIdx.x * blockDim.x + threadIdx.x;
   const int str = blockDim.x * gridDim.x;
 
   const unsigned int lane = threadIdx.x % warpSize;
   const unsigned int wid = threadIdx.x / warpSize;
 
   __shared__ T shared[32];
   T sum = 0.0;
   for (int i = idx; i < n; i+= str) {
     sum += a[i] * b[i];
   }
 
   sum = reduce_warp<T>(sum);
   if (lane == 0)
     shared[wid] = sum;
   __syncthreads();
 
   sum = (threadIdx.x < blockDim.x / warpSize) ? shared[lane] : 0;
   if (wid == 0)
     sum = reduce_warp<T>(sum);
 
   if (threadIdx.x == 0)
     buf_h[blockIdx.x] = sum;
 
 }
 
 
 
 
 
template <typename T>
__global__ void add2inv2_kernel(T* __restrict__ a, const T* __restrict__ b,
     const T c, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    a[tj] = a[tj]+c/b[tj];
  }
}
 
template <typename T>
__global__ void max2_kernel(T* __restrict__ a, const T b,
     const T* __restrict__ c, const T d, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if (tj < n) {
    a[tj]=max(b, d*c[tj]);
  }
}
 
template <typename T>
__global__ void updatebb_kernel(T* __restrict__ bb,
     const T* __restrict__ dellambda, const T* __restrict__ dely,
   const T* __restrict__ d, const T* __restrict__ mu,
   const T* __restrict__ y, const T delz, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if(tj<m)
    bb[tj]=dellambda[tj] + dely[tj]/(d[tj] + mu[tj]/y[tj]) - bb[tj];
  else if(tj<m+1)
    bb[tj]=delz;
}
 
 
 
template <typename T>
__global__ void updateAA_kernel(T* __restrict__ AA,
     const T* __restrict__ globaltmp_mm, const T* __restrict__ s,
   const T* __restrict__ lambda, const T* __restrict__ d,
     const T* __restrict__ mu, const T* __restrict__ y, const T* __restrict__ a,
   const T zeta, const T z, const int m) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if(tj<m)
    {
      AA[tj+tj*(m+1)]=globaltmp_mm[tj+tj*m] + (s[tj] / lambda[tj] +
         1.0/ (d[tj] + mu[tj] / y[tj]));
      AA[tj+m*(m+1)]=a[tj];
      AA[m+tj*(m+1)]=a[tj];
    }
  else if(tj<m+1)
    AA[tj+tj*(m+1)]= -zeta/z;
}
 
template <typename T>
__global__ void dy_kernel(T* __restrict__ dy, const T* __restrict__ dely,
     const T* __restrict__ dlambda, const T* __restrict__ d,
     const T* __restrict__ mu, const T* __restrict__ y, const int n) {
  int tj = blockIdx.x * blockDim.x + threadIdx.x;
  if(tj<n)
    dy[tj] = (-dely[tj]+dlambda[tj])/(d[tj] + mu[tj]/y[tj]);
}
 
#endif