> For the complete documentation index, see [llms.txt](https://json007.gitbook.io/svm/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://json007.gitbook.io/svm/lr/overflow_and_underflow.md).

# Overflow and Underflow

$$e^{1000} = \inf$$ 上溢出\
$$e^{-1000} = 0$$ 下溢出。浮点数只有64位。

所以一般对式子做一些变形，比如：\
$$\log \sum\_{n=1}^N \exp X\_n = a + \log \sum\_{n=1}^N \exp {X\_n -a }$$\
对于任意a都成立，一般取X中最大的值： $$a=\max\_n X\_n$$

[计算指数函数的和的对数](http://www.hankcs.com/ml/computing-log-sum-exp.html)\
[Softmax loss 和 NAN](https://www.zybuluo.com/nrailgun/note/325347)