SAXPY is an algorithm in high-performance computing (HPC).

Let $\mathbf{y}^{(t)}, \mathbf{x}^{(t)}\in\mathbb{R}^n$ be vectors over real numbers at some discrete time $t\in\mathbb{N}$ and let $a\in\mathbb{R}$ be a real parameter.

SAXPY is defined as a vector update of $\mathbf{y}$ at time $t+1$ according to the formula:

$$\mathbf{y}^{(t+1)} = a\mathbf{x}^{(t)} + \mathbf{y}^{(t)}$$

We can write $\mathbf{y}^{(t)} = (y_0^{(t)}, y_1^{(t)}, \dots, y_n^{(t)})$ and $\mathbf{x}^{(t)} = (x_0^{(t)}, x_1^{(t)}, \dots, x_n^{(t)})$

Thus if we look at individual vector elements, where $k\in\{0, 1, \dots, n\}$, we have the following formula: $$y_k^{(t + 1)} = a\cdot x_k^{(t)} + y_k^{(t)}$$

// y - Y vector
// x - X vector
// a - parameter
// N - size of both vectors
void saxpy(float* y, float* x, float a, size_t N)
{
    size_t i;
    for (i = 0; i < N; i++) {
        y[i] = a * x[i] + y[i];
    }
}