# d199: Fast sigmoid algorithm [nd009, study materials]

Fast sigmoid algorithm: http://stackoverflow.com/questions/10732027/fast-sigmoid-algorithm

``````(*fun)(xs[i]);

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``````
``````xs[i] = (*fun)(xs[i]);

atan(pi*x/2)*2/pi    9.2 ns
atan(x)              7.9 ns
1/(1+exp(-x))       19.3 ns
1/sqrt(1+x^2)       10.8 ns
erf(sqrt(pi)*x/2)    6.5 ns
tanh(x)             15.4 ns
x/(1+|x|)            4.4 ns``````
``````xs[i] = (*fun)(xs[i]) + 0.5;

atan(pi*x/2)*2/pi   20.5 ns
atan(x)             19.4 ns
1/(1+exp(-x))       19.3 ns
1/sqrt(1+x^2)       10.8 ns
erf(sqrt(pi)*x/2)   49.9 ns
tanh(x)             28.1 ns
x/(1+|x|)            2.5 ns``````

Source: https://gist.github.com/astanin/5270668 (‘Benchmark various sigmoid functions’ by https://github.com/astanin)

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