Re: Programming skills required by mathematicians?

In article
<7b49f964-7b90-445e-8df5-b52754301e2e@[EMAIL PROTECTED]
>,
aruzinsky  <aruzinsky@[EMAIL PROTECTED]
> wrote:
>On Jul 1, 10:16=A0am, hru...@[EMAIL PROTECTED]
 (Herman Rubin) wrote:
>> In article
<84498550-6584-4d29-8703-d737ffe2e...@[EMAIL PROTECTED]
>com>,

>> aruzinsky =A0<aruzin...@[EMAIL PROTECTED]
> wrote:
>> >On Jun 25, 2:40=3DA0am, rAgAv <ragav.pa...@[EMAIL PROTECTED]
> wrote:
>> >> Hello,

			.....................

>> Computers have been used in number theory, algebraic geometry,
>> computational problems which are more abstract than concrete,
>> as well as more "practical" problems. =A0My technical re****ts,
>> available from the Purdue Statistics Department, are a combination
>> of an odd type of numerical analysis, and involve using Boolean
>> operations on the bit patter of floats, something which is not
>> in any HLL to my knowledge.

>> Efficient random number procedures can be mainly done in HLL,
>> but not with full efficiency. =A0And I doubt that anyone can
>> get a full accuracy efficient procedure to generate
>> f(x) =3D x - ln(1+x) to full machine precision without using
>> the hardware structure. =A0Also, on most machines, multiple
>> precision (I consider what is called "double" to be single)
>> arithmetic is a mess because of the forced normalization of
>> floats and the hidden bit. =A0The factor may be higher than 10.
>> This is partly due to the HLLs, which have discounted fixed
>> point arithmetic.

>> >If you were an "applied mathematician," I would recommend Fortran and
>> >Algol only because there are many legacy programs written in these
>> >languages. =A0In particular, the Collected Algorithms from ACM Vol I
to
>> >III are mostly in Algol and Fortran.

>> At that time, those were the only moderately well known HLLs.
>> Machine independence is fine, but one must take into account
>> the machine to get efficiency.

>With modern compilers, one can easily mix a HLL with assembly
>language.  For example, Visual C++ object code can be disassembled
>into assembly language, modified, and then recompiled back to object
>code.

This is not good with the usual assemblers.  Often,
the compiled code is "optimized" in such a way that
it is hard to follow.  Optimization is needed later,
not at compile time.

Few current assembler languages are concise enough
for easy coding.  Typing 50 characters when 5 would
suffice leads to errors.  Something like the Cray
assembler language with simplifications and overloading
is needed.

>For mental exercise and development, I recommend learning Forth which
>uses Reverse Polish Notation (RPN), i.e. operands precede operators,
>as in reality.  Forth and RPN foster efficient programming and
>utilization of RAM. Standard Forth does not use floating point, but
>Forth can be modified to do anything because it is easily extensible.
>Some modified versions directly use the PC FPU stack very efficiently.

RPN is moderately easy to write, and is my choice for
a calculator.  I am less fond of the stack idea of
Forth for a computer.  I do know how to juggle registers,
and providing the appropriate information for a machine
which offers many registers is quite different from doing
good programming on a stack machine.

-- 
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@[EMAIL PROTECTED]
         Phone: (765)494-6054   FAX: (765)494-0558