Alastair Reid
On Thursday 19 June 2003 2:59 pm, Ketil Z. Malde wrote:
What about CPUs with only native 32bit support,
All you need to implement arbitrary sized N-bit arithmetic is a CPU which provides 'add with carry', 'subtract with carry', etc. All CPUs I have every used provide these operations and I think it's a safe bet that all future CPUs will provide them.
I'm not saying it'll be impossible to implement, just that if you only have shorter operands, any opertaion on 64-bit entities must be implemented as a much larger number of operations (around 64 muls and 16 adds if you use byte operations¹)
What about computers with a >64 bit native type?
Processors which provide 2*N*8-bit arithmetic sometimes provide N*8-bit arithmetic too
...again, it would be *possible*, but not efficient. On the other hand, Integers will be optimized to use whatever features available on a specific platform; it could use a single byte for small numbers in the first case, or it could use the full 128 bit operations for large numbers. I'm not saying it's a very relevant problem; and I'd be the first to agree that most CPUs now and in the future provide 64- or at least 32-bit operations (and probably not 128-bit ones).
I suspect Integer could be optimized (by recognizing that most uses of Integer are for values that fit in 31 bits) so that the difference is pretty minimal.
GMP (which I thought was used to implement Integer) is supposed to be pretty good.
But this would have limited effect on a date like 19 June 2003 which is (very roughly) 2^69 picoseconds since the epoch.
Yes. And, as I mentioned previously, I don't think any application spends a significant amount of time computing times. The focus should be on what't practical and simple from an API point of view, rather than efficiency. IMHO. -kzm ¹ OK, so that's fairly naive, and can surely be implemented more efficiently. But who multiplies times, anyway? Or, for that matter, runs Haskell on an 8-bit CPU? :-) -- If I haven't seen further, it is by standing in the footprints of giants