[cmucl] #90: (atanh -2)?

[cmucl]

#90: (atanh -2)?
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 Reporter:  rtoy    |       Owner:  somebody
     Type:  defect  |      Status:  new     
 Priority:  major   |   Milestone:          
Component:  Core    |     Version:  2013-12 
 Keywords:          |  
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 CMUCL 20e says {{{(atanh -2)}}} is {{{#C(-0.54930615 -1.5707964)}}}.  This
 is consistent with what the CLHS says about {{{atanh}}} for {{{x < -1}}}
 being continuous with Quadrant III because {{{(atanh #c(-2.0 -0.0))}}} is
 the same.

 However, from the definition
 {{{
   atanh(z) = 1/2*(log(1+z) - log(1-z))
 }}}
 we have
 {{{
   atanh(-2) = 1/2*(log(-1) - log(3))
             = 1/2*(i*pi - log(3))
             = -log(3)/2 + i*pi/2
 }}}
 That is, the imaginary part should be positive.  This would be consistent
 with the rule that atanh is continuous with Quadrant II.

-- 
Ticket URL: <http://trac.common-lisp.net/cmucl/ticket/90>
cmucl <http://common-lisp.net/project/cmucl>
Cmucl is a high-performance, free Common Lisp implementation.