[Maxima-bugs] [ maxima-Bugs-3587295 ] erf inaccurate for small bigfloat values

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Bugs item #3587295, was opened at 2012-11-14 15:38
Message generated for change (Tracker Item Submitted) made by rtoy
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Category: Lisp Core - Floating point
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Raymond Toy (rtoy)
Assigned to: Nobody/Anonymous (nobody)
Summary: erf inaccurate for small bigfloat values

Initial Comment:
erf(1b-20) -> 1.387778780781446b-17

The correct answer is closer to 1.128379167095513b-20.

This is caused by bfloat-erf computing erf using 1-gamma_incomplete(1/2,x^2)/sqrt(%pi).  For small x, gamma_incomplete(1/2,x^2) is very close to sqrt(%pi), so we lose lots of precision using this formula. 

For small x, we should just use the taylor series.

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