On Mon, May 29, 2006 at 03:55:01PM +0200, Maarten Kronenburg wrote:
In my opinion the unsigned integer with a modulus is required, which is generalizing the base type unsigned int (which is modular) to any modulus.
I don't understand your motivation for such a type. IIUC there are two
"Christoph Ludwig" <cludwig@cdc.informatik.tu-darmstadt.de> wrote in message news:20060529163902.GE7459@castellio.textgrid.it.fh-worms.de... lines
of reasoning:
1) There are applications where integers with negative values don't make any sense.
But that is merely a special case of variables with a restricted range. There are also bigint applications where a variable can only take prime values or square free values or... Such restrictions are no less common than the case of non-negative integers, at least in my experience from computer algebra and cryptography.
Therefore, as David Abrahms pointed out, there should rather be a generic solution for restricted types. The unsigned_integer is actually a modular_integer with any modulus, although when the modulus is zero, it can be any non-negative integer. But users can make other integer classes with other restrictions. This is why these member functions and operators are virtual in the first place.
2) The native unsigned type is an integral type with mod 2^n semantics.
Thus,
there should also be a bigint type with mod 2^n semantics.
Then why restrict yourself to the modulus 2^n? All arbitrary length integer packages I am familiar with also provide modular arithmetic for arbitrary modulus N. (Even if you cannot exploit the factorization of the modulus, modular arithmetic is much more efficient than integer arithmetic followed by a modulus operation. In fact, I would have no use for a bigint implementation without efficient modular arithmetic.) Most important is certainly the case that N is prime, but composed moduli are also often needed. The special case N = 2^n may perhaphs be the easiest one to implement, but from a potential user's point of view such a choice seems arbitrary and gratuitous.
As mentioned above, the unsigned_integer is actually a modular_integer with any modulus, that can be set with the static function set_modulus. So it is not restricted to modulus of form 2^n. Users can also make a template with an unsigned_integer data member, and provide the modulus as a template non-type parameter.
Christoph
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