Re: Extended modal types

["Robert I. Eachus" <rieachus@attbi.com>]

Florian Weimer wrote:


> (IMHO, modular types whose modular type whose modulus is not a power
> of two should have been avoided altogether.)


Shows your hardware bias. ;-)  There are two very useful applications of 
modular types in Ada.  One where the modulus is an integral power of two 
maps nicely to a lot of hardware device interfaces, etc.  The other is 
in the area of cryptography and hashing, where the modulus tends to be a 
prime, or the product of two primes.  On a lot of hardware (X * Y) mod 
some large prime is a very useful operation, and maps neatly to a 32-bit 
by 32-bit multiply with a 64 (actually 63) bit result, and a divide by a 
32 bit integer keeping the remainder.  Most programming languages have 
no easy way of getting to those hardware instructions.

Are there operations on modular types which are pretty useless for 
non-power of two modulii, and there are operations that are only of 
interest for such modulii.  Ada supports both, and there is a large 
enough set of operations that make sense for both that the two sets of 
types were unified.  (Except in the limits in package System.)