| Re: multiplication [message #19617 is a reply to message #19427] |
Tue, 28 March 2000 00:00   |
John-David T. Smith
Messages: 384
Registered: January 2000
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Senior Member |
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James Kuyper wrote:
>
> meron@cars3.uchicago.edu wrote:
>>
>> In article <38E03BDC.868B8396@hotmail.com>, marc <m_schellens@hotmail.com> writes:
>>> Is there a function like TOTAL but for multiplication.
>>> Like the big PI symbol in mathematical notation.
>>> Or this really something for the for loop?
>>>
>>> I.E.
>>>
>>> a=[1,2,3,...]
>>>
>>> result=a[1]*a[2]*a[3]...
>>>
>> if all the elements of a are positive then you can simply do
>>
>> result = exp(total(alog(a)))
> ...
>> If some of the elements are negative, you can still handle it. do
>>
>> dum = where(a lt 0, ndum)
>> sig = (-1)^ndum
>> result = sig*exp(total(alog(abs(a))))
>
> You can't honestly be suggesting that this is a good technique? Ignore
> for a momement what happens if any element of 'a' is 0. That code
> performs two transcendental function evaluations per element of 'a'. IDL
> would have to be very badly engineered (which I suppose is possible),
> for a 'for' loop to execute more slowly than your code.
Only one transcendental is computed for each a, alog(). The exp occurs on the
single value after the total. Results for a 10,000 element random floating
array finely tuned to avoid under or overflow:
Loop Method:
Average Time: 0.017213961
0.00528653
Log Method:
Average Time: 0.0049092293
0.00528580
4 times as fast. Suppose you'd like to do an array with 100,000 double
elements... you get:
Loop Method:
% Loop limit expression too large for loop variable type.
<LONG ( 99999)>.
Log Method:
Average Time: 0.050116260
7.92382e+10
And if you hack it with two nested loops to avoid the loop limit error:
c=1. & for j=0L,n/100-1 do for k=0L,99L do c=c*a[j*100L+k]
you get:
Hacked Loop Method
Average Time: 0.30190306
0.97063262
Log Method:
Average Time: 0.068175601
0.97063262
A full 5 times faster.
And now, just for fun, the same data set, but with multiplication computed in a
heavily optimized C program. The core of the C code is simply the
straightforward: "for(i=0;i<N;i++) res*=a[i]"; The result:
Got 0.97063262 (Average Time: 0.001710 s)
Ouch! Another speedup of by a factor of 40!
Morals: IDL loops are pitifully slow, and you can't loop over very large arrays
without trickery, and for many operations, compiled C is *significantly* faster.
JD
--
J.D. Smith |*| WORK: (607) 255-5842
Cornell University Dept. of Astronomy |*| (607) 255-6263
304 Space Sciences Bldg. |*| FAX: (607) 255-5875
Ithaca, NY 14853 |*|
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