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
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
Kahan summation algorithm

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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 Messages In This Thread Kahan summation algorithm - Thomas Klemm - 12-19-2014 09:12 PM RE: Kahan summation algorithm - Gerald H - 12-20-2014, 09:47 AM RE: Kahan summation algorithm - Werner - 12-21-2014, 08:52 AM