I tried to implement [soft-max](https://en.wikipedia.org/wiki/Softmax_function) with the following code (`out_vec` is a `numpy` vector of floats):

```
numerator = np.exp(out_vec)
denominator = np.sum(np.exp(out_vec))
out_vec = numerator/denominator

```

However, I got an overflow error because of `np.exp(out_vec)`. Therefore, I checked (manually) what the upper limit of `np.exp()` is, and found that `np.exp(709)` is a number, but `np.exp(710)` is considered to be `np.inf`. Thus, to try to avoid the overflow error, I modified my code as follows:

```
out_vec[out_vec > 709] = 709 #prevent np.exp overflow
numerator = np.exp(out_vec)
denominator = np.sum(np.exp(out_vec))
out_vec = numerator/denominator

```

Now, I get a different error:

```
RuntimeWarning: invalid value encountered in greater out_vec[out_vec > 709] = 709

```

What's wrong with the line I added? I looked up this specific error and all I found is people's advice on how to ignore the error. Simply ignoring the error won't help me, because every time my code encounters this error it does not give the usual results.