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aruzinsky
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 Posted: Tue Jul 15, 2008 4:16 pm Post subject: Re: Programming skills required by mathematicians? |
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It may interest everyone to know that some CPUs have been designed so
that their assembly languages more or less resemble an HLL. At one
end of the spectrum, you have RISC processors and at the other end,
you have a CPU (32016 ?) made by Nation Semiconductor. Also, there
are CPUs designed just for the HLL, Forth. See http://www.ultratechnology.com/chips.htm
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Pubkeybreaker
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| Posted: Tue Jul 15, 2008 5:48 pm Post subject: Re: Programming skills required by mathematicians? |
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On Jul 15, 12:08 pm, Marshall <marshall.spi...@gmail.com> wrote:
| Quote: |
On Jul 15, 3:41 am, Pubkeybreaker <pubkeybrea...@aol.com> wrote:
I have never claimed otherwise. However the topic under
discussion is programming languages, not numerics.
No. Go back and read the first post. The question was
what languages are good for *mathematicians*. Not software
engineers. Not professional programmers. Mathematicians
use software to COMPUTE. Your sense of the context of this
thread is wrong-headed.
If so, then where are your posts in this thread recommending
specific programming languages for undergrads interested
in math? You haven't made any; I have.
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Fine. An undergrad contemplating doing mathematical coding
needs 3 things.
(1) Knowledge of a symbolic math package: choose from Maple, Magma,
Pari,
Mathematica, etc.
(2) Any HLL *other* than LISP and other than a scripting language
such as PERL. For this purpose Fortran, ANSI C, C++, Forth,
Haskell,
etc. suffice. The exact choice really DOESN'T MATTER. One can even use
[yech! VB]
(3) What does matter for a mathematician is the ability to get close
to
the machine when needed for speed reasons.
Assembler is *essential* anytime speed might become an issue.
However, over-riding all of these concerns for a mathematician is
knowledge of the right **algorithm**.
| Quote: |
I know you've been on usenet a long time, so I know that
you know that what you are saying is dishonest.
|
I know no such thing. My posts in this thread have always been aimed
directly
at the original question.
| Quote: |
There
has been some thread drift. The recent subthreads have
been about a different topic, as you know very well.
|
So? It is this movement away from the original question that
is dishonest. This is a *math* newsgroup, not a software
newsgroup.
| Quote: |
This is also revealed by your failure to
acknowledge that you have been woefully mistaken about
such simple facts as the existence of SSE compilers
or the x%2 -> x&1 optimization.
|
You are putting words in my mouth.
What I have said is that I have never seen SSE code emitted
by a compiler. I did NOT say that such compilers don't exist.
I have written *extensive* numerical code, including many
signal processing/FFT routines. FFT's can make very good
use of parallelism. I have the very Intel compiler of which you
spoke installed into my uSoft Visual Studio compiler, and I have never
seen it emit SSE code.
The ability of any compiler to extract sufficient parallelism from
HLL is extremely limited. Extraction of parallelism is NP-Complete.
For this reason, knowledge of the
*algorithm* is what matters, and the ability to drop into assembler
to take advantage of it. The choice of HLL is almost *irrelevant*.
| Quote: |
etc. by whatever size metric,
is a small thing.
Learn to READ. The topic is "what languages are good for
MATHEMATICIANS". The objectives are totally different.
Re-usability, readability, maintainability are secondary.
SPEED is the second most important criterion (after correctness)
This is not meant to deprecate it; it's clearly
important out of proportion to its market size. But it's small
in comparison to many other things. Signal processing I
will grant you. But how many jobs do you think require
knowledge of, say, numeric analysis, vs. how to write
a SQL query? How many people use encryption
Everyone does.
Everytime you use SSL.
How cute, cutting off a sentence in the middle to change the
meaning and score a cheap point.
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*mathematicians* write encryption software all the time.
You keep forgeting what this thread is about. You keep trying
to shift away from what a mathematician needs towards
general software engineering. This is dishonest on your part.
You seem more interested in invoking a language/software engineering/
software paradigm holy war than answering the original question.
| Quote: |
Instead what's happened is that you've demonstrated that
(some) mathematicians fail at software engineering.
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ROTFLMA. |
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Frederick Williams
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| Posted: Tue Jul 15, 2008 7:20 pm Post subject: Re: Programming skills required by mathematicians? |
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Marshall wrote:
| Quote: |
[...]
software for factoring primes,
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Even I could write a program to do that  .
--
He is not here; but far away
The noise of life begins again
And ghastly thro' the drizzling rain
On the bald street breaks the blank day. |
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Herman Rubin
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| Posted: Tue Jul 15, 2008 11:33 pm Post subject: Re: Programming skills required by mathematicians? |
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In article <6b23ea89-cc8b-4b97-9f6f-0c99b5419954@k30g2000hse.googlegroups.com>,
aruzinsky <aruzinsky@general-cathexis.com> wrote:
| Quote: |
On the subject of maximum efficiency, does anyone know of an HLL that
easily allows code to modify itself?
For example, suppose, you have a statement "X += 1234;". The "1234"
is part of the machine code and occupies a 4 byte space between
surrounding machine code. To change it, all you need is a pointer to
its address. Similarly, you can change += to -=, *= , or whatever
fits into the RAM space occupied by +=. I once did this kind of thing
in Forth. The only difficult part is finding the addresses and
knowing what fits where. I assume that I do not need to explain how
this leads to efficiency.
I always thought that this idea should be developed.
|
This was a standard procedure in the "old days". Before
the attempt to keep people from messing things up, there
was no distinction between program and data. I have used
this myself.
In fact, the von Neumann introduction was that of code
modifying itself. Alas, many of the current operating
systems prevent this, in the name of making things
"foolproof".
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Herman Rubin
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| Posted: Wed Jul 16, 2008 1:03 am Post subject: Re: Programming skills required by mathematicians? |
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In article <0fd6e0d1-236f-4c79-9394-e2049879f7f2@d45g2000hsc.googlegroups.com>,
Marshall <marshall.spight@gmail.com> wrote:
| Quote: |
On Jul 14, 7:20 am, hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
Daryl McCullough <stevendaryl3...@yahoo.com> wrote:
Humans do not have to be deprived of the tool of gotos,
any more than they have to be deprived of algebra.
Umm. Okay. I don't see how gotos are comparable to algebra,
but nevermind.
The most important part of algebra is the use of a precise
and concise notation.
I'm no mathematician, but I would have thought that algebraic
identities that permit the provably-correct transformation
of expressions into equivalent expressions was more important
than the notation. Which, coincidentally, is one of the things
that goto destroys.
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NO! It is often necessary to block these provably
correct transformations to preserve accuracy. This
was an often raised point in C, where the early
versions did exactly what you said. The later
versions respect user parentheses. Try computing
x - ln(1+x) to machine precision for all x > -1.
This also occurs in CAS. I asked for the tail of
the exponential series to be computed as such, because
I knew that subtraction the head from the exponential
would introduce errors larger than the final result.
| Quote: |
I don't think I've ever seen a goto in a math book. Am
I missing something? It seems the most mathematically
clean programming languages I've seen are the pure
functional ones, which lack goto.
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The programs translate into gotos. The "standard"
method for computing the error function starts
with the magnitude of the argument and chooses
the algorithm accordingly. In this case, one can
fix the program so than it is efficient, but this
cannot be done in all cases.
It is often necessary to sort the arguments by algorithm,
and on parallel machines, it may be difficult to get any
efficiency at all. Conditionals are a major problem on
them, and tricks are used,
| Quote: |
The CS people do not recognize this,
and are willing to use sesquipedalian variable names, while
the mathematician quibbles at two characters.
Math and industrial programming are distinct domains.
The reason programmers use long variable names and
mathematicians uses short ones is that they are each
using what is most appropriate for their domain. From
what I've seen, however, CS people spend a good deal
more time thinking about notation than math people do.
Which should not be a surprise given the relative age
of the fields.
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| Quote: |
There is
nothing wrong with this, except for readability. The
computer, being a superfast subimbecile, does not know that
there is a difference.
Variable names exist for human readers, not for computers.
The names are gone from the generated machine code. Two
distinct alpha-equivalent programs will generate identical
machine code, regardless of the length of variable names.
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It is not machine code which is kept in the a.out file, or
the equivalent on other systems. A disassembler will produce
the original names. Decently readable disassembler code
would be a great improvement.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Herman Rubin
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| Posted: Wed Jul 16, 2008 1:30 am Post subject: Re: Programming skills required by mathematicians? |
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In article <896a680e-0f01-46c0-a287-71dca78423a7@27g2000hsf.googlegroups.com>,
Marshall <marshall.spight@gmail.com> wrote:
| Quote: |
On Jul 12, 6:15 pm, hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
In article <4879ecb0-c766-4de5-8de0-d1b2ed910...@z72g2000hsb.googlegroups.com>,
They are. I did say that another more complicated routine
can decide to jump to one of the cases; that means they
must have global names to the code fragment combination, so
that they can be jumped to.
They do have global names.
But they are NOT subroutines; they are locations.
As I said, you are specifying the solution as gotos, and then
rejecting any other solution as failing because it isn't gotos.
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As OPEN subroutines, they save a little time while
adding space. But if they are long, the time lost
by not transferring control might get things out of
cache.
Also, as transfers to case 3 and case 2 have no
conditionals, there would not even be a saving
of a transfer by going to those cases, as they
drop into case 1. So the inline improvement does
not even occur, as I thought it before.
| Quote: |
Also, is switch(n) any more
intelligible than goto what you have?
It won't be to anyone who learned how to read code in
the 1970s and doesn't want to learn anything more recent
than that. To everyone else, yes it will.
If switch is more intelligible to anyone than the goto
program, it is because the person has not learned how
to use gotos, and for no other reason.
That is plainly false.
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| Quote: |
BTW, for your code to be implemented properly, min3, min2,
min1, and high should be LOCATIONS, not called
subroutines. The location of case3 is min3, of case 2 is
min2, so you would have to use gotos rather than calls.
In other words, you are evaluating any response to your
challenge solely on the basis of how much it conforms
to your goto-based solution. How intellectually honest of you.
No, your approach would use
I have not proposed an approach.
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| Quote: |
I do not trust the compiler writer
This is amply clear. Probably when you did your analyses
of generated code in the late 1970s, you saw some things
that left a big impression.
It was clear that they did not understand mathematics at
all, and were more writing a means of generating a working
hack. C is an excellent example of that, and its bad
parts have continued in C++.
You appear entirely unaware of the vast majority of what
goes on in the world of software development. Are you aware
of the existence of languages outside of C/C++, and Fortran?
Are you going to tell me that, for example, Ken Thompson
"cannot understand mathematics"? You complain
about CS notation a lot; can you design a more terse
notation than Thompson's notation for regular expressions?
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I am aware of these. I am discussing the problem of
mathematical and related results, not for regular
expressions, and I am not convinced that Thompson's
notation is that great.
Understanding mathematics means being able to see the
problems of computation, not to make jobs of low
computational complexity, such as my algorithm, so
hard to implement as (in this case) to be noncompetitive.
| Quote: |
We need unlimited types, and a struct is not quite a type.
A struct is a type. And if you're going to start claiming that
C's type system isn't very good, that's a point that was
generally accepted decades ago. Do the names
"Hindley/Milner" mean anything to you? If they don't,
you should *really* avoid saying anything about type
systems.
Notice how I'm not presuming to lecture you on
how numerical analysis should be done?
|
So give me the tools to carry out numerical
analysis. The early hardware had it, and when
Fortran was introduced, it was introduced as a
kludge to eliminate some work. It was not until
Algol that there was an attempt to make a general
language, and in an attempt to simplify, they
eliminated actions known to mathematicians, such
as those who understood flow diagrams.
| Quote: |
Also, the notation is designed for people who cannot
understand mathematics. The system subroutines in the
supposedly well-designed C were written by fools.
Now you're just trolling.
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I have seen some of them.
| Quote: |
One thing missing in ALL languages is having a list,
not a struct, before the replacement statement.
I'm assuming here you refer to multiple assignment,
since list assignment is trivially supported in almost
every language I know of. But plenty of languages
have multiple assignment. When you say "missing
in ALL languages" you mean that it's present in
neither Fortran nor C?
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Multiple assignment in complicated languages like Lisp?
If I have to type anything more than
q,r = a/b
as a notation for division giving integer quotient and
remainder of the appropriate type, it is lacking.
Look at the postings by Pubkeybreaker.
| Quote: |
Generated assembler code is DESIGNED to be unreadable.
Probably this is the result of some sort of conspiracy against you.
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It is a conspiracy against anyone who wants to use
anything other than HLLs.
| Quote: |
Do you understand gotos? Could you read a Fortran
program of the 1970's?
What is to understand? Gotos are less than trivial.
I probably wrote my first goto in ~1972, although I
don't think I've written one in twenty years. I probably
couldn't read Fortran very well today, but I spent years
writing Fortran in the early 1980s.
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| Quote: |
Can you create a flow diagram? I have rarely written
one, but I have one in my head when I code.
Can I draw a flowchart, is that what you're asking?!
Um, yeah. Yeah I can.
Do you know what Continuation Passing Style is?
(You might even like it.)
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| Quote: |
We need more versatility; trying to make code so that
someone who can only follow rules can maintain it can
only permanently reduce capability.
Any time you want machine language, you know where
to find it.
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Are you sure? It was a major job to find a list of the
computer instructions for the POWER machines, and the
explanations were all long and written for people who
cannot understand mathematics. Also, there was no timing
information or indication of parallelism or caching.
I do not know if I can find it for Windows machines; I
can for the AMD processors.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Herman Rubin
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| Posted: Wed Jul 16, 2008 1:46 am Post subject: Re: Programming skills required by mathematicians? |
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In article <3c13c$487c524b$82a1e228$799@news1.tudelft.nl>,
Han de Bruijn <Han.deBruijn@DTO.TUDelft.NL> wrote:
| Quote: |
Pubkeybreaker wrote:
This is the sort of thing Herman refers to, although he has not
presented his case very well. The machine has instructions
which speed these kinds of mathematical computations, yet compilers
seem lousy at making good use of them.
That's certainly true. It's true for every program that generates lower
level code from higher level code. Very much the same if e.g. PostScript
is generated from LaTex. You can squeeze such generated code easily by
a factor 10 or more when done by hand (thereby enhancing accompanying
efficiency with the same factor). Clearly it's difficult to be specific
enough when writing a "general" compiler.
Han de Bruijn
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Fortran was originally written to perform a good job for
numerical operations on a particular class of machines.
It did a fairly good job on those, as long as one did not
try too hard to make it difficult. Fortran 1A allowed the
addition of assembler instructions. It was not intended
that other than job subroutines should be written in Fortran.
Fortran was written for mathematical operations. It was
not written for typing "Hello world" or anything like that.
It had its weaknesses, but not the ones of the present
languages, in effectively making things difficult, nor did
it prevent using the power of the machines.
Algol was an attempt to come up with a "general" compiler
for numerical operations. The best grade I could give it
is a D; for one, it involved too much typing, and for
another, it left far too much out.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Herman Rubin
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| Posted: Wed Jul 16, 2008 2:54 am Post subject: Re: Programming skills required by mathematicians? |
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In article <b612f4e7-45d2-4835-bffc-edd7ec8b2770@x35g2000hsb.googlegroups.com>,
Jason Glumidge <Jason.Glumidge@gmail.com> wrote:
| Quote: |
On Jul 14, 3:13 pm, hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
snipped
I am not "still thinking in Fortran", although I have used
it, as well as assembler, from way back. Although Fortran
was used for this a lot later, Fortran was intended as a
convenience, not a panacea. I am thinking as a supposedly
rather good mathematician, and thinking of how to do the
mathematics.
Where on earth is the goto statement in mathematics!? Time to learn a
functional programming language maybe?
|
If (something) do (something), where some of the somethings
done are the same. Flow diagrams are natural in many
computational methods. One even has this for proofs, where
the same lemma may be used at different times. Also, there
can be cases.
Now in mathematics, it apparently does not make a difference
whether one looks at gotos or subroutine calls. But for a
computer, a goto, especially conditional, is not likely to
be good, while a subroutine call, other than inlining, is
likely to greatly add to execution time.
When it comes to the generation of nonuniform random variables,
most are done by acceptance-rejection methods, or possibly
acceptance-replacement methods. These can have gotos, but
usually can be done in C. However, if it comes to vector
or parallel machines, this is not a good way, but another,
which also can be done in HLL, is better. However, in
considering the process, it is naturally goto, but using
HLL conventions.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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herbzet
Guest
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| Posted: Wed Jul 16, 2008 10:33 am Post subject: Re: Programming skills required by mathematicians? |
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Frederick Williams wrote:
| Quote: |
Marshall wrote:
[...]
software for factoring primes,
Even I could write a program to do that .
|
Took me a minute ... LOL!
--
hz |
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Han de Bruijn
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| Posted: Wed Jul 16, 2008 11:01 am Post subject: Re: Programming skills required by mathematicians? |
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aruzinsky wrote:
| Quote: |
It may interest everyone to know that some CPUs have been designed so
that their assembly languages more or less resemble an HLL. At one
end of the spectrum, you have RISC processors and at the other end,
you have a CPU (32016 ?) made by Nation Semiconductor. Also, there
are CPUs designed just for the HLL, Forth.
See http://www.ultratechnology.com/chips.htm
.
|
Oh well, if you find that FORTH is a High Level Language ..
( http://hdebruijn.soo.dto.tudelft.nl/www/muziek/midicode.htm )
Han de Bruijn |
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Han de Bruijn
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| Posted: Wed Jul 16, 2008 11:01 am Post subject: Re: Programming skills required by mathematicians? |
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Pubkeybreaker wrote:
| Quote: |
(2) Any HLL *other* than LISP and other than a scripting language
such as PERL. For this purpose Fortran, ANSI C, C++, Forth,
Haskell, etc. suffice. The exact choice really DOESN'T MATTER.
One can even use [yech! VB]
|
With Forth as his/her choice he/she will be busy all day with
re-organizing the data stack. Don't know if _that_ should be the
primary occupation of a mathematics undergraduate. Note: I've
been a Forth and native PostScript programmer myself, so I know
what I'm talking about. I'd rather recommend (Delphi) Pascal and
let the institute organize a cheap license for it (TU Delft has).
Han de Bruijn |
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Han de Bruijn
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| Posted: Wed Jul 16, 2008 11:01 am Post subject: Re: Programming skills required by mathematicians? |
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Herman Rubin wrote:
| Quote: |
In article <6b23ea89-cc8b-4b97-9f6f-0c99b5419954@k30g2000hse.googlegroups.com>,
aruzinsky <aruzinsky@general-cathexis.com> wrote:
On the subject of maximum efficiency, does anyone know of an HLL that
easily allows code to modify itself?
For example, suppose, you have a statement "X += 1234;". The "1234"
is part of the machine code and occupies a 4 byte space between
surrounding machine code. To change it, all you need is a pointer to
its address. Similarly, you can change += to -=, *= , or whatever
fits into the RAM space occupied by +=. I once did this kind of thing
in Forth. The only difficult part is finding the addresses and
knowing what fits where. I assume that I do not need to explain how
this leads to efficiency.
I always thought that this idea should be developed.
This was a standard procedure in the "old days". Before
the attempt to keep people from messing things up, there
was no distinction between program and data. I have used
this myself.
|
Uh no ! Even COBOL already has a separate "Data Division" and "Procedure
Division". Talking about the "old days" ..
| Quote: |
In fact, the von Neumann introduction was that of code
modifying itself. Alas, many of the current operating
systems prevent this, in the name of making things
"foolproof".
|
I've seen dreadful examples of such "self modifying code" (in assembler)
and I would discourage everybody to use such code. Are you deliberately
provoking everybody, Herman ? I've been a programmer for many years and
I don't feel any need to go back to those dark ages of bad programming
practices, with gotos, and with self modifying code.
Han de Bruijn |
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Han de Bruijn
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| Posted: Wed Jul 16, 2008 11:01 am Post subject: Re: Programming skills required by mathematicians? |
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Herman Rubin wrote:
| Quote: |
Fortran was written for mathematical operations. It was
not written for typing "Hello world" or anything like that.
It had its weaknesses, but not the ones of the present
languages, in effectively making things difficult, nor did
it prevent using the power of the machines.
|
In fact, Fortran is still persistent in the present languages, meaning
that the formula translator of these languages is an almost exact _copy_
of the FORmula TRANslator designed with Fortran. So there is hardly any
difference with respect to Fortran's essentials. What _is_ different in
the modern languages are the control structures. But I'd rather consider
the latter as a _vast_ improvement over Fortran(66) instead of a "making
things difficult".
Han de Bruijn |
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Han de Bruijn
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| Posted: Wed Jul 16, 2008 11:01 am Post subject: Re: Programming skills required by mathematicians? |
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herbzet wrote:
| Quote: |
Frederick Williams wrote:
Marshall wrote:
[...]
software for factoring primes,
Even I could write a program to do that .
Took me a minute ... LOL!
|
Threw away the program and did it on the backside of an envelope :-)
Han de Bruijn |
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aruzinsky
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| Posted: Wed Jul 16, 2008 4:02 pm Post subject: Re: Programming skills required by mathematicians? |
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On Jul 16, 1:26 am, Han de Bruijn <Han.deBru...@DTO.TUDelft.NL> wrote:
| Quote: |
Pubkeybreaker wrote:
(2) Any HLL *other* than LISP and other than a scripting language
such as PERL. For this purpose Fortran, ANSI C, C++, Forth,
Haskell, etc. suffice. The exact choice really DOESN'T MATTER.
One can even use [yech! VB]
With Forth as his/her choice he/she will be busy all day with
re-organizing the data stack. Don't know if _that_ should be the
primary occupation of a mathematics undergraduate. Note: I've
been a Forth and native PostScript programmer myself, so I know
what I'm talking about. I'd rather recommend (Delphi) Pascal and
let the institute organize a cheap license for it (TU Delft has).
Han de Bruijn
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You don't know what you are talking about, possibly because you have a
low mental aptitude for Forth.
I did much of the programming leading to my 1989 Ph.D. thesis,
Sequential Least Absolute Deviations Estimation of Autoregressive
Parameters, in Forth and I wasn't "busy all day with re-organizing the
data stack." I remember the opposite. Forth is commonly recognized
as a "write only" language and that is true. Experienced users can
write programs very fast in Forth, but others typically can't read
them. That is why the programs printed in my thesis are in Basic. |
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