Should positive * pos_inf be pos_inf instead of zero_pm_inf?

[postmath]

I've seen your comments that you feel that the various non-number values in arb are not well enough defined, but I think this should be a case where there is a reasonable mathematically correct interpretation.

In arb_mul (and arb_mul_arf), if you multiply an arb_t (or an arf_t) representing a signed infinity by a non-exact finite arb_t, then the result's radius is infinite. It seems like it would be mathematically sound to test whether the finite arb_t is either all positive or all negative, and if so, set the result's radius to be finite instead -- correct? That would give answers that users might expect more, even though of course the current result is also correct. I would be happy to prepare a patch.

[fredrik-johansson]

Yes, this seems reasonable.