Mathematical expression of LogSoftmax

I was checking the C code for LogSoftmax, then I came to this line,

Now LogSoftmax can be expressed as, x_i - log( exp(x).sum() )
But what is the significance of adding maxinput with log( exp(x).sum() )?

Subtracting max_input from the argument of the exp function prevents numerical overflow due to large numbers, see LogSumExp in Wikipedia.