Re: Is intrinsic MIN inefficient?
From: James Giles (jamesgiles_at_worldnet.att.net)
Date: 05/12/04
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Date: Wed, 12 May 2004 17:15:58 GMT
Steven G. Kargl wrote:
>> It is a summation of terms like
>>
>> (array(a,b) - array(a,b-1))**2
>>
>> with "b" and "b-1" changing slightly within the terms of the series. The
>> "a" and "b" arguments are unaffected by the limits of the DO loop (i.e.
>> DO i=c,d).
>
>
> How large is "a"? If it is sufficiently large, you will
> flush the memory cache for each subtraction operation.
> The elements array(a,b) and array(a,b-1) are stored
> "a" * sizeof(array(a,b)) bytes apart in memory.
Actually, the memory locations are not specified by the
language (though the requirements of storage association,
if it occurs, usually impose the same memory layout for
all implementations). Given the usual choice of storage
order, the elements array(a,b) and array(a,b-1) are
SIZE(array,1) numeric storage units apart, assuming the
data type is default REAL. The variable "a" is presumably
just an integer that's within the bounds of the first dimension
of ARRAY. It's specific value is irrelevant to the calculation
of how far apart the two elements are.
Not also that the efficiency may not be all that adversely
effected (affected? I never get those straight) by the distance
between thos two elements. It depends on how "a" and "b"
vary with "i" in the loop. For example:
DO i=start,end
result(i)=MIN(array(i,j)-array(i,j-1)**2, ..., 1d6)
END DO
Here, "a" and "b" are "i" and "j" respectively. But, the cache
will load up several elements of array beginning at array(i,j)
*and* beginning at array(i,j-1). So, the program will still be
reasonably efficient. However, if the loop is:
DO i=start,end
result(i)=MIN(array(j,i)-array(j,i-1)**2, ..., 1d6)
END DO
You are now cutting "across the grain" of the array. The cache
will indeed be a problem (unless it has the ability to load with
stride).
I suspect the original problem actually has entries in the MIN
function of both the above configurations. He'd probably be
better off with several separate loops (recoded as whole array
operations):
result(start:end)=array(start:end,j)-array(start:end,j-1)**2
result(start:end)=MIN(array(j,start:end)-array(j,start-1:end-1)**2,
result(start:end))
...
result(start:end)=MIN(result(start:end), 1d6)
Now the cache has less load on it and at least *some* of the
expressions may not be "across the grain".
-- J. Giles
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