a colleague of mine recently noticed that the description of the
inverse hyperbolic functions in the gfortran manual is not quite
correct, i.e. ATANH is not the "hyperbolic arctangent" but the
"hyperbolic area tangent". Same goes for ASINH and ACOSH. Note that
the F08 standard simply speaks about ATANH as the "inverse hyperbolic
tangent".
I will commit the attached patch to trunk and 4.5 shortly (tested with
"make pdf").
OK, I finally found a reference to "area" function by perusing the German
Wikipedia (http://de.wikipedia.org/wiki/Hyperbolischer_Tangens),
you don't need to look into the German Wikipedia to find that. As
Hendrik already noted, the English version has it as well
(http://en.wikipedia.org/wiki/Artanh):
"The inverses of the hyperbolic functions are the area hyperbolic
functions. The names hint at the fact that they give the area of a
sector of the unit hyperbola x2 - y2 = 1 in the same way that the
inverse trigonometric functions give the arclength of a sector on the
unit circle x2 + y2 = 1. The abbreviations arcsinh, arccosh, etc., are
commonly used, even though they are misnomers, since the prefix arc is
the abbreviation for arcus, while the prefix ar stands for area."