[Maxima-bugs] [ maxima-Bugs-1369693 ] tanh and atanh not accurate for small bigfloats

[SourceForge.net <no...@so...>]

Bugs item #1369693, was opened at 2005-11-29 21:17
Message generated for change (Tracker Item Submitted) made by Item Submitter
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1369693&group_id=4933

Please note that this message will contain a full copy of the comment thread,
including the initial issue submission, for this request,
not just the latest update.
Category: Lisp Core
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Raymond Toy (rtoy)
Assigned to: Nobody/Anonymous (nobody)
Summary: tanh and atanh not accurate for small bigfloats

Initial Comment:
tanh and atanh are not very accurate for small bigfloats.

(%i21) taylor(atanh(x),x,0,5);
(%o21) x+x^3/3+x^5/5
(%i22) atanh(1b-6);
(%o22) 1.0000000000003328136B-6
(%i24) x+x^3/3+x^5/5;
(%o24) x^5/5+x^3/3+x
(%i25) ev(%o24,x=1b-6);
(%o25) 1.0000000000003333333B-6

Compare %o25 with %o22.  %o25 is right.

(%i26) tanh(1b-6);
(%o26) 9.9999999999966745551B-7
(%i27) taylor(tanh(x),x,0,5);
(%o27) x-x^3/3+2*x^5/15
(%i28) x-x^3/3+2*x^5/15;
(%o28) 2*x^5/15-x^3/3+x
(%i29) ev(%,x=1b-6);
(%o29) 9.9999999999966666667B-7

Compare %o26 with %o29.  %o29 is right.


----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1369693&group_id=4933