/**
 * Ultra-optimized CUDA kernel for Runge-Kutta 4th order stage 4
 * Computes k4 = h * f(t + h, y + k3) for RK4 method
 * 
 * This kernel implements the final stage of RK4 with:
 * - Maximum throughput optimization
 * - Minimal memory latency
 * - Optimized for high occupancy
 */

extern "C" __global__ void rk4_stage4(
    const double* __restrict__ y,     // Input solution vector
    const double* __restrict__ k3,    // k3 from stage 3
    double* __restrict__ k4,          // Output k4 vector
    const double t,                   // Current time
    const double h,                   // Step size
    const int n                       // Problem dimension
) {
    const int idx = blockIdx.x * blockDim.x + threadIdx.x;
    
    if (idx >= n) return;
    
    // Load values with coalesced memory access
    const double y_val = y[idx];
    const double k3_val = k3[idx];
    
    // For RK4 stage 4: k4 = h * f(t + h, y + k3)
    const double t_next = t + h;
    const double y_next = y_val + k3_val;
    
    // Placeholder ODE function: dy/dt = -y (exponential decay)
    // In practice, this would evaluate f(t_next, y_next)
    const double dydt = -y_next;
    
    // Compute k4 = h * f(t + h, y + k3)
    const double k4_val = h * dydt;
    
    // Store result
    k4[idx] = k4_val;
}

/**
 * Single-precision version
 */
extern "C" __global__ void rk4_stage4_f32(
    const float* __restrict__ y,
    const float* __restrict__ k3,
    float* __restrict__ k4,
    const float t,
    const float h,
    const int n
) {
    const int idx = blockIdx.x * blockDim.x + threadIdx.x;
    
    if (idx >= n) return;
    
    const float y_val = y[idx];
    const float k3_val = k3[idx];
    
    const float t_next = t + h;
    const float y_next = y_val + k3_val;
    
    const float dydt = -y_next;  // Placeholder ODE function
    const float k4_val = h * dydt;
    
    k4[idx] = k4_val;
}