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Kahan summation algorithm
12-19-2014, 09:12 PM (This post was last modified: 12-19-2014 09:48 PM by Thomas Klemm.)
Post: #1
Kahan summation algorithm
For details please consult Wikipedia.

Program for the HP-42S:
Code:
00 { 19-Byte Prgm }
01 LBL "KAHAN"
02 +
03 ENTER
04 RCL+ ST Z
05 STO- ST Z
06 X<> ST Z
07 +
08 END

Worked example: \(10^{10}+\pi+e\)

CLST
E10
ENTER
0
PI
XEQ "KAHAN"
1
E↑X
R/S

y: 10,000,000,005.9
x: -0.04012551795


This is the correctly rounded result.

The classic addition is not the same:

E10
PI
+
1
E↑X
+

y: 0
x: 10,000,000,005.8


Cheers
Thomas
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12-20-2014, 09:47 AM
Post: #2
RE: Kahan summation algorithm
Thank you. Never seen this before.
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12-21-2014, 08:52 AM
Post: #3
RE: Kahan summation algorithm
What I have never seen mentioned is the fact that this algorithm is meant for binary floating point. Try adding x=y= 1e12-2
You'll get
s := 2e12
c := -2, while it should be -4

BTW my version reads:

Code:
*LBL "K+"
 +
 RCL+ ST Y
 STO- ST Y
 X<>Y
 RCL+ ST L
 END

same size.

Werner
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