Hyperbolic arc cosine fails on (-1) :: Complex r.
When allowing for complex results, the hyperbolic arc cosine is continuously defined on all ℝ.
In the (x < (-1)) real ray of the complex plane, acosh equals \z -> i * pi + acosh(abs z), which works fine for almost all arguments. Thus, acosh (-1) should equal i * pi; however due to the implementation as
acosh z = log (z + (z+1) * sqrt ((z-1)/(z+1)))where the denominator in the root becomes zero at z = -1, this comes out as NaN :+ NaN.
Could be fixed trivially by adding a special case
acosh ((-1):+0) = 0:+pito the instance (RealFloat a) => Floating (Complex a) in Data.Complex.
Trac metadata
| Trac field | Value |
|---|---|
| Version | 7.6.3 |
| Type | Bug |
| TypeOfFailure | OtherFailure |
| Priority | low |
| Resolution | Unresolved |
| Component | libraries/base |
| Test case | acosh(-1) :: Complex Double |
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