Compute log-softmax over the last dimension of x without calling torch.softmax, torch.log_softmax, F.softmax or F.log_softmax.

It must stay finite for very large logits. Exponentiating first overflows to inf and then produces nan; subtracting the row maximum before exponentiating leaves the result unchanged mathematically and keeps every intermediate in range.

Input

tensor([[1., 2., 3.],
        [0., 0., 0.]])

Output

tensor([[-2.4076, -1.4076, -0.4076],
        [-1.0986, -1.0986, -1.0986]])