arc cosine surprising numeric results

[Ralf Stephan]

Here under the hood, RR.acos gets called. I think this should return meaningful values even if the value is outside the domain.

sage: cos(1.*I)
1.54308063481524        <--- CC element
sage: acos(_)
1.00000000000000*I
sage: acos(1.54308063481524)
NaN
sage: acos(CC(1.54308063481524))
0.999999999999997*I
sage: acos(RR(1.54308063481524))
NaN

Neither SymPy? nor Pari nor Maxima do this:

In [1]: acos(1.543)
Out[1]: 0.999931383282944⋅ⅈ
? acos(1.543)
%1 = 0.99993138328294395810833497263866793658*I
(%i1) acos(1.543);
(%o1)                        0.9999313832829438 %i

[Jeroen Demeyer]

Replying to rws:

why are floats of type RR not CC?

Are you suggesting

sage: parent(1.0)
Complex Field with 53 bits of precision

[Ralf Stephan]

The alternative would be to return complex in RR.acos.

[Ralf Stephan]

It's also a symptom of inconsistency in symbolic/pynac.pyx where we call RR.function, i.e. mpfr but also mpmath directly. Do you have a preference? Maybe it's best to use mpmath throughout in pynac.pyx.

[Ralf Stephan]

I have come to a conclusion, and adapted the ticket description.

[Ralf Stephan]

Ok, since this is at least consistent with arb behaviour I'll file this as oddity not bug. It would be interesting to know what the big Ms return.