Kahan summation algorithm - Printable Version

Kahan summation algorithm - Printable Version

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Kahan summation algorithm - Thomas Klemm - 12-19-2014 09:12 PM

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

RE: Kahan summation algorithm - Gerald H - 12-20-2014 09:47 AM

Thank you. Never seen this before.

RE: Kahan summation algorithm - Werner - 12-21-2014 08:52 AM

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