Fast sigmoid function for neural networks

[British0zzy]

Hi, I'm looking for a very fast implementation of a sigmoid function for use in a neural network. Does anyone know of papers they can reference me to which have analysis on different sigmoid functions used in neural networks?
Posting of any freely available code which approximates a sigmoid function is also acceptable :)

Also, I need more knowledge on choosing a learning rate, or more specifically, varying the learning rate according to parameters.

Any help is appreciated,
Thanks!