[ clisp-Bugs-1436987 ] atanh branch cut strangeness

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Bugs item #1436987, was opened at 2006-02-22 13:53
Message generated for change (Comment added) made by robert_dodier
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Robert Dodier (robert_dodier)
Assigned to: Nobody/Anonymous (nobody)
Summary: atanh branch cut strangeness

Initial Comment:
So far as I can tell, Clisp 2.34 (Linux, compiled w/
gcc 3.3.2) handles branch cuts of atanh incorrectly. I
also checked asin and acos and those two functions seem OK.

(1) acos and asin: CLHS says
(http://www.lispworks.com/documentation/HyperSpec/Body/f_asin_.htm)
that the branch cut on [1, \infty) is continuous w/ 4th
quadrant and on (-\infty, -1] is continuous w/ 2nd
quadrant.

Clisp: conforms to spec

(2) atanh: CLHS says
(http://www.lispworks.com/documentation/HyperSpec/Body/f_sinh_.htm)
that the branch cut on [1, \infty) is continuous w/ 
1st quadrant and on (-\infty, -1] is continuous w/ 3rd
quadrant.

Clisp: continuous w/ 4th and 2nd quadrants respectively

PS. Here's a test script:
(cl:asin #C(2.5 0.01))
(cl:asin 2.5)
(cl:asin #C(2.5 -0.01))

(cl:asin #C(-2.5 0.01))
(cl:asin -2.5)
(cl:asin #C(-2.5 -0.01))

(cl:acos #C(2.5 0.01))
(cl:acos 2.5)
(cl:acos #C(2.5 -0.01))

(cl:acos #C(-2.5 0.01))
(cl:acos -2.5)
(cl:acos #C(-2.5 -0.01))

(cl:atanh #C(2.5 0.01))
(cl:atanh 2.5)
(cl:atanh #C(2.5 -0.01))

(cl:atanh #C(-2.5 0.01))
(cl:atanh -2.5)
(cl:atanh #C(-2.5 -0.01))

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>Comment By: Robert Dodier (robert_dodier)
Date: 2006-03-05 09:56

Message:
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user_id=501686

After further study of CLHS, I've concluded the statements
about branch cuts for ATANH are inconsistent with the
formula (log(1 + x) - log(1 - x))/2. The branch cuts as
derived from the formula are (-\infty, -1) continuous w/ 2nd
quadrant and (1, \infty) continuous w/ 4th. I think the only
way to read the spec for ATANH is to read the stuff about
branch cuts as commentary and ignore it (i.e., observe the
formula and ignore the commentary).

That said, there is still some strangeness in ATANH, namely
that (ATANH -2.5) => #C(-0.42364892 1.5707964) which is
different from (ATANH #C(-2.5 0.0)) => #C(-0.42364892
-1.5707964). Since Clisp doesn't recognize signed zero, I
don't see how that can be. For the record, (IMAGPART -2.5)
=> 0 and (PHASE -2.5) => 3.1415927.

In order to be consistent w/ (log(1 + x) - log(1 - x))/2,
(ATANH #C(-2.5 0.0)) should yield #C(-0.42364892 1.5707964).

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