Kahan summation algorithm

[Thomas Klemm]

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

[Gerald H]

Thank you. Never seen this before.

[Werner]

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