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

It's best to measure on your hardware first. Just a quick benchmark script shows, that on my machine 1/(1+|x|) is the fastest, and tanh(x) is the close second. Error function erf is pretty fast too.

% gcc -Wall -O2 -lm -o sigmoid-bench{,.c} -std=c99 && ./sigmoid-bench
atan(pi*x/2)*2/pi   24.1 ns
atan(x)             23.0 ns
1/(1+exp(-x))       20.4 ns
1/sqrt(1+x^2)       13.4 ns
erf(sqrt(pi)*x/2)    6.7 ns
tanh(x)              5.5 ns
x/(1+|x|)            5.5 ns

I expect that the results may vary depending on architecture and the compiler used, but erf(x) (since C99), tanh(x) and x/(1.0+fabs(x)) are likely to be the fast performers.