The P1D performs best on primary (non-rechargeable) CR123 cells. Don't worry whether it has an "a" on the end of it, as there are numerous names in the industry for this size cell. The P1D is an excellent flashlight with a lot of punch from a compact size and will deliver very reasonable runtimes when used with standard CR123 disposable cells.
However, when we throw an "R" in front of "CR123." We are discussing a different breed of cell. While they share the same dimensions as CR123 primary cells, they are rechargeable, re-usable cells. The problem is that there are a wide variety of these cells on the markets designed for different applications, with different chemistries, different output voltages, and different safety features. The P1D is compatible with "3.0V" varieties of these rechargeable cells, but keep in mind that this comes at the cost of substantially reduced runtime as these cells have much less capacity than their non-rechargeable siblings. There are also many 3.7V rechargeable R123 cells on the market, in the case of the P1D, these should be avoided to maintain all of the P1Ds functionalities. (many have used the higher voltage cells in the P1D, but it causes the lower output settings not to function correctly).
If you like the concept of simply replacing the cell when it is dead with a new one, and are willing to buy CR123s online (~$1-2 each depending where you get em) to keep the costs reasonable, then the P1D is an excellent choice. If you think you're more likely to use rechargeable cells, it'd be worth considering alternatives.
Eric