Re: Larger matrices

On Fri, 08 Aug 2008 17:40:16 +0200, Georg Bauhaus wrote:

Dmitry A. Kazakov schrieb:

They are not. Lisp is a list-oriented language, Prolog is a logical
inference language.

Lisp and Prolog with FFI(!) are not universal? Come on.

Of course they are not. Both are domain-specific languages.

This notion of "purpose" is not very specific.
Let me put is this way: Ada has to be especially good at
systems programming, hence it has to be fairly low level.

Wrong. Where that follows from? Systems programming need not to be
low-level.

A systems programming language must provide for the low
level.

Nope, it must provide systems programming domain abstractions. Ada does
this. This does not make it low-level.

It seems that you are confusing different concepts of abstraction. Level
depends on where is the ground, the underlying computational environment.
This is not necessarily the hardware, but it can be one.

1. Considering hardware as the environment. Ada running on an Ada-hardware
(if such existed) would make this implementation of Ada low-level. But it
would not make Ada low-level, because it also runs on the hardware
requiring much work to create an Ada compiler. Therefore Ada in general is
high level relatively to the hardware.

2. Considering programming paradigms as the environment, i.e. the terms in
which programs are thought an composed. Ada is again very high level, as it
supports up to 3rd set abstractions:

value -> type (sets of) -> class / generic (sets of)

OO decomposition, concurrency etc.

A language that does not provide for the low level
is not a systems programming language.

A logical fallacy: A => B does not imply A = B.

Ada has many features
that provide for low level programming. It lacks a numer of
features used in higher level programming (E.g. function
environments, unbounded numbers, ...).

Since when unbounded numbers became high level? Consider it used to
implement modular arithmetic or ASCII characters. How low-level!

Systems programming
is not the same as low level programming or high level programming;
rather, the set of objects is typically not as abstract as
some mathematical N-array of numbers.

I don't see how interrupt, task or I/O port are less abstract than array.

What hardware?

Vector processors.

OK, I wasn't aware that the LA packages were made for vector
processors only.

Take Intel x86 instead, if you don't like vector processor.

Assume data flow hardware, and assume a way
to put the function result in the input box of the next processing unit.
What now?

Nothing, Ada.Numerics.Generic_Real_Arrays was not designed in order to
support this hardware.

Aha? I see that GNAT delegates to Fortran libraries. Traditionally,
Fortran is certainly an associate of non-PC hardware.

That was not the point, it was as it reads, the design did not target any
hardware and will be *relatively* inefficient on any existing hardware.
Relatively, because it most likely will beat both Lisp and Prolog.

I don't see how prototyping a hypertext graph algorithm
requires a maximally efficient implementation of matrix
computations.

Because of the problem size. Incidence matrices grow as O(n**2), i.e.
extremely fast.

O(N**2) is not extremely fast; many non-extreme algorithms
are in this class. The case discussed hits some memory barrier
at n = 5_000 and that's it. We get elaborate array indexing support
in some array programming languages. If chosing one of those
PLs costs me a constant factor of 10, I get all the indexing
stuff in return, it seems worth the cost during prototyping.

No chance. O(N**2) is only memory complexity. You should also consider the
number of operations required per element. Naive matrix multiplication is
O(N**3). Factor 10 means (N x 10)**3 thousand times slower! And this is
only the lower bound. But all this is in order learn that the fancy
language X is greatly slower than Ada and is totally unsuitable for
production code? I know it in advance!

--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
.

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