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.
What about computers with a >64 bit native type?
Processors which provide 2*N*8-bit arithmetic sometimes provide N*8-bit arithmetic too (e.g., 32-bit processors sometimes provide 16 bit arithmetic too) so, if their native type is a power of 2 times 64, we should be ok. For any other processors, we can implement it the way 8 and 16-bit arithmetic is currently implemented on Hugs: we coerce the operands to 32 bits, perform the 32-bit operation and coerce the operands back to the desired result size. Coercing up takes, at most, a register-register move and coercing down takes an and operation.
...and I don't think it's entirely given that two 64 bit numbers will be faster than one Integer.
I do. the implementation of Integer requires traversing additional indirections to an array of bits, reading the size of the operands, allocating space for the result, etc. It's a lot of work even if the arguments and result are simple values like 0 or 1. 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. but this would have limited effect on a date like 19 June 2003 which is (very roughly) 2^69 picoseconds since the epoch. Which is all to say that whatever sound reasons may exist, future portability concerns or performance are not reasons to prefer using a single Integer or a Rational. -- Alastair Reid