Re: Distributivity and types

    anton@mips.complang.tuwien.ac.at (Anton Ertl) wrote:


> Only if overflows trap. If, OTOH, you use modulo (aka wrap-around)
> arithmetic, this law holds (as do many others, because the cardinal
> numbers modulo 2^N are a field; two's complement numbers are just a
> different interpretation, the operations + and * are the same as for
> unsigned numbers) and you will get the correct answer.


A minor (if slightly off-topic) point: The integers modulo 2^N are
definitely not a field unless N=1. In general, the integers mod d
form a field if and only if d is prime. However, the integers mod d
always form a ring under + and *. I assume this is what you meant.


[An example reveals that the integers mod 4 do not form a field
under + and *.


2 * 0 = 0 (mod 4)
2 * 1 = 2 (mod 4)
2 * 2 = 0 (mod 4)
2 * 3 = 2 (mod 4)


Therefore there is no multiplicative inverse of 2.]


Jonathan

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