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samhocevar / lolremez

📈 Polynomial Approximations using the Remez Algorithm
Do What The F*ck You Want To Public License
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Approximating erf #4

Closed jdh8 closed 3 years ago

jdh8 commented 6 years ago

I'm trying to approximate erf. How do I extend or link to lolremez?

samhocevar commented 6 years ago

Are you compiling lolremez from source? The real functions are declared in lol/src/lol/math/real.h and implemented in lol/src/math/real.cpp (note that lol is a Git submodule). You could for instance look for exp( in these files and implement erf in a similar fashion, e.g. using a Taylor/Maclaurin series.

It looks like a Bürmann series might have a good convergence rate.

samhocevar commented 6 years ago

erf() is now available if you compile from source, and will be in the next release. It’s a quick and dirty implementation for now, and I don’t know how to test its accuracy properly, but I tested the precision by computing (erf(x+ε)-erf(x))/ε which should be close to the derivative of erf, aka 2/sqrt(π)*exp(-x²):

# lolremez '(erf(4+1e-50)-erf(4))/1e-50'
1.269823467186655826835016359930571628776564403116531674080842983563179750336408e-7
# lolremez '2/sqrt(π)*exp(-4²)'
1.269823467186655826835016359930571628776564403116582467019530449796253150990805e-7
                                                   ^ first differing digit