Fast sigmoid algorithm

Question

The sigmoid function is defined as

I found that using the C built-in function exp() to calculate the value of f(x) is slow. Is th

Answer 1

This answer probably isn't relevant for most cases, but just wanted to throw out there that for CUDA computing I've found x/sqrt(1+x^2) to be the fastest function by far.

For example, done with single precision float intrinsics:

__device__ void fooCudaKernel(/* some arguments */) {
    float foo, sigmoid;
    // some code defining foo
    sigmoid = __fmul_rz(rsqrtf(__fmaf_rz(foo,foo,1)),foo);
}