[Boost-bugs] [Boost C++ Libraries] #5113: math/special_functions/acosh.hpp wrong approximation for x near 1

Subject: [Boost-bugs] [Boost C++ Libraries] #5113: math/special_functions/acosh.hpp wrong approximation for x near 1
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2011-01-24 08:32:09

#5113: math/special_functions/acosh.hpp wrong approximation for x near 1
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 Reporter:  SebastianLuther@…       |       Owner:  johnmaddock
     Type:  Bugs                    |      Status:  new        
Milestone:  To Be Determined        |   Component:  math       
  Version:  Boost 1.45.0            |    Severity:  Problem    
 Keywords:                          |  
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 The documentation and the code have different bugs for the approximation
 of acosh(x) for x near 1.

 First of all they use different definitions of y. The documentation has
 y=1-x and the code has y=x-1. They both use the formula
 {{{(1+(1/12)*y+(3/160)*y^2)*sqrt(2*y)}}}, but neither of them is correct.

 correct formulas [1]

 {{{y=1-x -> (1+(1/12)*y+(3/160)*y^2)*sqrt(-2*y)}}}

 {{{y=x-1 -> (1-(1/12)*y+(3/160)*y^2)*sqrt(2*y)}}}

 [1]
 http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/

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Ticket URL: <https://svn.boost.org/trac/boost/ticket/5113>
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