def logsig(x):
    """Compute the log-sigmoid function component-wise."""
    out = np.zeros_like(x)
    idx0 = x < -33
    out[idx0] = x[idx0]
    idx1 = (x >= -33) & (x < -18)
    out[idx1] = x[idx1] - np.exp(x[idx1])
    idx2 = (x >= -18) & (x < 37)
    out[idx2] = -np.log1p(np.exp(-x[idx2]))
    idx3 = x >= 37
    out[idx3] = -np.exp(-x[idx3])
    return out