What is the purpose of numpy.log1p( )?
For real-valued input,
log1pis accurate also forxso small that1 + x == 1in floating-point accuracy.
So for example let's add a tiny non-zero number and 1.0. Rounding errors make it a 1.0.
>>> 1e-100 == 0.0False>>> 1e-100 + 1.0 == 1.0TrueIf we try to take the log of that incorrect sum, we get an incorrect result (compare to WolframAlpha):
>>> np.log(1e-100 + 1)0.0But if we use log1p(), we get the correct result
>>> np.log1p(1e-100)1e-100The same principle holds for exp1m() and logaddexp(): The're more accurate for small x.
