From: Marc-Andre Lafortune <redmine@...>
Date: 2009-10-11T02:23:13+09:00
Subject: [ruby-core:26044] [Bug #2189](Open) Math.atanh(1) & Math.atanh(-1) should not raise an error

Issue #2189 has been updated by Marc-Andre Lafortune.

Status changed from Assigned to Open

I should have ran make test-all, I'm sorry. I also should have realized that the correct solution should have been more careful about platform independence. I'll be more careful in the future. I will also have to find out why I currently get 6 failures and 3 errors running test-all...

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As to the question if atanh should raise an error or return +/- infinity, I'd like to point out:

a) The SUSv3 sentence given above continues and states "If x is ��1, a pole error shall occur, and atanh() shall return the value of the macro HUGE_VAL with the same sign as the correct value of the function."

Since it is not possible to both return a value and raise an error in Ruby, a choice must be made even if one wants to follow SUSv3.

Also, isn't a pole error different from a range error or a domain error in that document?

b) In math, atanh(tanh(x)) == x. Since tanh(x=1.0/0) doesn't raise an error, I believe atanh should not raise an error and return x.

c) atanh(��1) returns ��infinity in the following programs:
- Mathematica
- Matlab
- Python
- C++ boost library

I therefore suggest to make an explicit check for ��1 and return ��Infinity in those cases, so to have a result that is:
- platform independent (1.8.x's result is currently platform dependent) 
- useful
- mathematically valid

Thanks
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http://redmine.ruby-lang.org/issues/show/2189

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