Kahan summation algorithm - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: General Forum (/forum-4.html) +--- Thread: Kahan summation algorithm (/thread-2668.html) 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