Timing comparison for diffeq program in c++, Maple and Maxima

On 8/9/2012 7:18 AM, Dennis Darland wrote:
> I am using just basic math like you say. In maple I can use higher precision floating point by setting "Digits". (Though it only seems to work up to about 32 digits). I expected to be able to do something similar in Maxima. Maxima does have "big floats". I tried them, but, as far as I could tell, they did not support trig functions, etc. (You only get about 16 digits and a lot of warning messages).
bigfloats work with trig functions, but the compiler works on (declared) 
machine floats.

>    If  big floats can me made to support trig functions, etc., I would like to know about it.
Sure. don't compile that part.
>   I plan to look also for a c++ library for extended precision floating point numbers.
There are libraries for quad double and also arbitrary precision like MPFR.
I doubt that these are really the first port of call for improving the 
code for this application (solving ODEs)
>   I am also interested in what is called "interval arithmetic."
Same comment.
>
> I also used Maxima as well as Maple as it is more affordable, and I like to support open source. I am not trying to criticize Maple or Maxima, only to ascertain the facts. It is interesting that c++ is so much faster, in that it makes solving some problems more practical.
If your program is oriented toward producing C code, then it is quite 
reasonable to
expect that the C code it produces will run fastest with a C compiler, 
and simulating
this environment on Maxima or Maple can be quite slow unless those 
programs can
take advantage of the knowledge that "everything is simply a number"  and no
symbolic computation at all should happen.
>
> The program was debugged in Maple and Maxima together. Both, in some cases gave better error messages than the other. I doubt I could have debugged it in c or c++, which most likely have crashed instead of giving an error message. (The code to generate c or c++ is not released yet, as I am just beginning to test it, but it seems to work OK so far)
>
> The reason I started subscripts at 1 was Dr Chang's work started subscripts at 1, and thus it was a lot easier. I used the formulas from his draft of a book he started. He was working in FORTRAN, but my program is not at all a translation of his program. (He wrote as program in FORTRAN which generated a FORTRAN program,) His program is beyond my comprehension.  Also other languages I may want to use in the future may not permit "0" subscripts. I doubt I will ever support FORTRAN.
>
> Dennis J. Darland
> dennis.darland at yahoo.com
> http://dennisdarland.com/
> http://dennisdarland.com/dennisdaze/
> http://dennisdarland.com/philosophy/
> http://sode.sourceforge.net/
> "According to the World Health Organization, the warming of the planet caused an additional 140,000 deaths in 2004, as compared with the number of deaths there would have been had average global temperatures remained as they were during the period 1961 to 1990. This means that climate change is already causing, every week, as many deaths as occurred in the terrorist attacks on September 11, 2001"
> -- Peter Singer _Practical Ethics, Third Edition_, p. 216.
>
>
> --- On Thu, 8/9/12, Rupert Swarbrick <rswarbrick at gmail.com> wrote:
>
>> From: Rupert Swarbrick <rswarbrick at gmail.com>
>> Subject: Re: [Maxima] Timing comparison for diffeq program in c++, Maple and Maxima
>> To: maxima at math.utexas.edu
>> Date: Thursday, August 9, 2012, 7:32 AM
>> Dennis Darland <dennis.darland at yahoo.com>
>> writes:
>>> I ran a timing test comparison for c++, Maple and
>> Maxima.
>>> All three programs generated by omnisode - a set of
>> Ruby programs.
>>> Set time limit to 1 minute.
>>> Maximum iteration was sufficient to solve entire
>> problem.
>>> Problem was sin.ode for all three.
>>> Output was redirected to file only - none to screen
>>> Results:
>>> c++ solved entire problem in 23 seconds (140001
>> iterations)
>>> Maple performed 11542 iterations in 60 seconds
>>> Maxima performed 372 iterations in 60 seconds
>>> That amounts to:
>>> c++ 6,087 iterations/second
>>> Maple 192 iterations/second
>>> Maxima 6.2 iterations/second
>>> c++ is almost 32 times faster than Maple which is
>> almost 31 times faster than Maxima.
>>> So c++ is almost 982 times faster than Maxima.
>>>
>>> More info on omnisode at:
>>> http://sode.sourceforge.net/
>> Right, I just tried to look up the Maxima code you're
>> generating and
>> found things like [1]. Since I'm clearly not going to read
>> through that
>> carefully, and I presume no-one else is either, can you
>> explain exactly
>> what you're measuring?
>>
>> Your code looks to me like a C/FORTRAN program translated
>> to
>> Maxima. Unsurprisingly, it runs very slowly. What are you
>> actually
>> trying to do? What capabilities of Maple or Maxima are you
>> using other
>> than basic arithmetic?
>>
>> Or should we interpret your message as
>>
>>    "Writing bare-metal calculations in Maple and running
>> them is
>>     marginally less slow that writing them in
>> Maxima and running
>>     them. But it would have been easier to do
>> it in C anyway"
>>
>>   ?
>>
>>
>> Rupert
>>
>> [1] http://sode.sourceforge.net/omniresults/special_cases_007/diffeq.tan_sqrt_lin.mxt.txt
>>
>> -----Inline Attachment Follows-----
>>
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