[Help-gsl] acosh, getting consistent results from GSL and Guile

[Marco Maggi]

Ciao,

  for  some values of  the operand  I get  different results
from  'acosh' when  using  GSL (1.8),  Guile  (1.8) and  GNU
Octave (2.1.63).  Other functions give me different results,
too. Below  is the output  of my tests.   I am not at  all a
math expert.

  Browsing Wikipedia for acosh  formulas it seems to me that
GSL is using an equivalent of:

    (log (- x (sqrt (- (* x x) 1))))

while the others are using an equivalent of:

    (log (+ x (sqrt (- (* x x) 1))))

  I'm interested in having equal results from GSL and Guile,
specifically I would  like GSL to yield the  same results of
Guile, not  vice versa.  I  am writing a Guile  interface to
GSL (do not criticise me on this, please).

  I am thinking about replacing 'gsl_complex_arccosh()' (and
some  other functions)  with  my own  implementation, but  I
would like  to know  if there is  a specific reason  for the
different choice in GSL.

Thank You.

*** GSL test of function acosh

acosh(1.000000+0.000000i)       = -0.000000+0.000000i
acosh(1.234000+1.234000i)       = 1.259714+0.865731i
acosh(0.000000+1.000000i)       = 0.881374+1.570796i
acosh(-1.234000+1.234000i)      = 1.259714+2.275862i
acosh(-1.000000+0.000000i)      = -0.000000+3.141593i
acosh(-1.234000+-1.234000i)     = 1.259714+-2.275862i
acosh(0.000000+-1.000000i)      = 0.881374+-1.570796i
acosh(1.234000+-1.234000i)      = 1.259714+-0.865731i
acosh(-5.000000+0.000000i)      = 2.292432+3.141593i
acosh(-10.000000+0.000000i)     = 2.993223+3.141593i

*** Guile test of function acosh

acosh(1.000000+0.000000i)       = 0.000000+0.000000i
acosh(1.234000+1.234000i)       = 1.259714+0.865731i
acosh(0.000000+1.000000i)       = 0.881374+1.570796i
acosh(-1.234000+1.234000i)      = -1.259714-2.275862i
acosh(-1.000000+0.000000i)      = 0.000000+3.141593i
acosh(-1.234000-1.234000i)      = -1.259714+2.275862i
acosh(0.000000-1.000000i)       = -0.881374+1.570796i
acosh(1.234000-1.234000i)       = 1.259714-0.865731i
acosh(-5.000000+0.000000i)      = -2.292432+3.141593i
acosh(-10.000000+0.000000i)     = -2.993223+3.141593i

With formulas from www.wikipedia.org, acosh(-5):
-2.29243166956117+3.14159265358979i     plus version
2.29243166956118+3.14159265358979i      minus version

*** Octave test of function acosh

acosh(1.000000+0.000000i)       = 0.000000+0.000000i
acosh(1.234000+1.234000i)       = 1.259714+0.865731i
acosh(0.000000+1.000000i)       = 0.881374+1.570796i
acosh(-1.234000+1.234000i)      = -1.259714+-2.275862i
acosh(-1.000000+0.000000i)      = 0.000000+3.141593i
acosh(-1.234000+-1.234000i)     = -1.259714+2.275862i
acosh(-0.000000+-1.000000i)     = -0.881374+1.570796i
acosh(1.234000+-1.234000i)      = 1.259714+-0.865731i
acosh(-5.000000+0.000000i)      = -2.292432+3.141593i
acosh(-10.000000+0.000000i)     = -2.993223+3.141593i



--
Marco Maggi

"They say jump!, you say how high?"
Rage Against the Machine - "Bullet in the Head"