Re: Possreps and numeric types
Date: Mon, 26 Mar 2007 01:11:31 GMT
Message-ID: <75FNh.73199$zU1.30763_at_pd7urf1no>
Marshall wrote:
> On Mar 25, 1:30 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
>>Marshall wrote: >> >> >>>So what if we had an internal representation for >>>integer similar to java.math.BigInteger, and an >>>internal representation for rational that was a pair >>>of integers. We can define *exact* operators for >>>these types for basic arithmetic functions. >> >>I disagree. Unless one has infinite precision, rational is >>always an approximation.
>
>
> "Approximation" is perhaps not the best choice of words.
> We certainly have resource limits in our finite computers.
> There are computations that we can't do because
> we don't have the resources. For example, a computer
> might be able to add together two one billion digit
> integers, but not be able to add together two ten billion
> digit integers because it didn't have enough memory.
> That doesn't mean the result of adding the two
> one billion digit integers is approximate; on the
> contrary, it is precise and exact. Or consider
> java.util.BigInteger. Any answer you get from it
> will be precise, and it can handle up to four
> billion digit numbers. If it can't give you an answer,
> it'll fail in a way that can't be mistaken for an
> answer.
> ...
>
What amazes me is that consumer cpu's don't have any kind of long decimal support, the most common kind of number consumer and business arithmetic needs and binary float instructions continue to dominate what's built. When I paid attention to instruction sets, until about fifteen or twenty years ago, I noticed over and over how the cpu engineers would study current OS softwares in order to decide their instruction sets. Naturally, the OS people studied those hardware instruction sets. It seemed the most absurd kind of bio-feedback to me, an idiotic stifling of progress.
At the same time, the OS people were almost totally ignorant of the issues dbms builders face. As a result, the dbms people learned quickly not to depend on much in the way of OS services for their locking, indexing and accessing mechanisms and invented their own.
Also, I can't blame entirely blame Intel for holding back progress by insisting that its early generations all be backward-compatible, but that attitude has wasted quite a few years of my lifetime and that of many others, I'm sure.
Another thing that hasn't changed is that the hardware that gets sold today isn't necessarily what people need, the mfrs push what they've got not what is usually needed. Same goes for Microsoft, big time, eg., pushing SQL, the database equivalent of Howard Hughes' Spruce Goose, more than IBM ever did.
My rant for today,
p
Received on Mon Mar 26 2007 - 03:11:31 CEST