There was a mini-challenge involving rounding back in 2003:

I said at the time:

"It should be noted that the reason some of these various algorithms are failing with the test values of Meyers and Prange is due to a property of the floating point system on the HP48. There is a largest odd number that can be represented on the 48 and that is

999999999999. Numbers greater than this are all even integers; their fractional parts are zero. Adding one to a number greater than 999999999999 on the 48 will not change it from even to odd (these remarks don't apply to internal 15 form numbers; their threshold is higher). Any algorithm that expects this property (change of parity with addition of unity) to hold for all integers may fail."

There are probably some on this forum who didn't see or participate in that topic. It might be interesting to look at it again.