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Re: TOTAL gives totally different result on identical array [message #76899 is a reply to message #76896]

Fri, 08 July 2011 07:37

Liam Gumley
Messages: 473
Registered: November 1994

Senior Member

[stuff deleted]

The online documentation for the TOTAL function in IDL warns that this
may happen:

---quote begins---
You should be aware that when summing a large number of values, the
result from TOTAL can depend heavily upon the order in which the
numbers are added. Since the thread pool will add values in a
different order, you may obtain a different — but equally correct —
result than that obtained using the standard non-threaded
implementation. This effect occurs because TOTAL uses floating point
arithmetic, and the mantissa of a floating point value has a fixed
number of significant digits. The effect is especially obvious when
using single precision arithmetic, but can also affect double
precision computations. Such differences do not mean that the sums are
incorrect. Rather, they mean that they are equal within the ability of
the floating point representation used to represent them.
---end quote---

In a previous posting, someone mentioned the Kahan algorithm for
computing a numerically stable summation:

http://en.wikipedia.org/wiki/Kahan_summation_algorithm

A translation to IDL looks like this:

function kahansum, input
sum = 0.0
c = 0.0
for i = 0L, n_elements(input) - 1 do begin
y = input[i] - c
t = sum + y
c = (t - sum) - y
sum = t
endfor
return, sum
end

The IDL documentation for TOTAL includes the following example for
demonstrating the impact of array ordering on summation:

IDL> vec = FINDGEN(100000)
IDL> PRINT, TOTAL(vec) - TOTAL(REVERSE(vec))
-87552.0

However the Kahan summation, while considerably slower, does the
summation with much less error:

IDL> PRINT, kahansum(vec) - kahansum(reverse(vec))
0.00000

Cheers,
Liam.
Practical IDL Programming
http://www.gumley.com/

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[Message index]

		Re: TOTAL gives totally different result on identical array By: Michael Galloy on Fri, 08 July 2011 12:10
		Re: TOTAL gives totally different result on identical array By: Liam Gumley on Fri, 08 July 2011 11:48
		Re: TOTAL gives totally different result on identical array By: Foldy Lajos on Fri, 08 July 2011 11:33
		Re: TOTAL gives totally different result on identical array By: Fabzou on Fri, 08 July 2011 10:46
		Re: TOTAL gives totally different result on identical array By: Liam Gumley on Fri, 08 July 2011 10:25
		Re: TOTAL gives totally different result on identical array By: Foldy Lajos on Fri, 08 July 2011 08:44
		Re: TOTAL gives totally different result on identical array By: Liam Gumley on Fri, 08 July 2011 07:37
		Aw: Re: TOTAL gives totally different result on identical array By: M. Suklitsch on Fri, 08 July 2011 05:55
		Re: TOTAL gives totally different result on identical array By: Fabzou on Fri, 08 July 2011 03:34

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