Re: types, was New Book: The School of Niklaus Wirth

  Jerry Leichter <jerrold.leichter@smarts.com> writes:
>For *division*, however, things break down: 1/-1 is -1 in signed
>arithmetic, but 0 in unsigned arithmetic. The unsigned form gives you
>the division in the ring of integers mod 2^n,


If you mean "ring of (integers mod 2^n)", then you are wrong. E.g.,


3*6=2 (mod 16)
i.e.,
2/3=6 (mod 16)


In contrast, the integer division in all programming languages I know
gives 0 for 2/3.


>I don't remember off-hand how multiplication works out


Multiplication is just like addition: unsigned multiply also serves as
2s-complement multiply, unless you try to mix precisions (i.e., you
need different signed and unsigned multiplies for 32bit*32bit=64bit).


>> You may be confusing this with C, where signed arithmetic overflow
>> has undefined behaviour (probably because modulo arithmetic for
>> signed integers was considered too unimportant and too variant to be
>> a useful part of the standard).
>
>Actually, this has to do with what hardware can implement cheaply.


Yes. In particular there is probably no way to define a result for
signed arithmetic overflow that can be implemented cheaply on
2s-complement, 1s-complement, and sign-magnitude machines.


- anton
--
M. Anton Ertl Some things have to be seen to be believed
anton@mips.complang.tuwien.ac.at Most things have to be believed to be seen
http://www.complang.tuwien.ac.at/anton/home.html

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