import numpy as np


def reference(master, exp_avg, exp_avg_sq, grad, out_bf16, hp):
    h = hp[0].astype(np.float64)
    g = grad.astype(np.float64)
    m = h[0] * exp_avg + h[1] * g
    v = h[2] * exp_avg_sq + (h[3] * g) ** 2
    p = (master + h[6] * m / (np.sqrt(v * h[4]) + h[5])) * h[7]
    return p, m, v, p