HP35 exp(ln(x)) bug, a new number found. - Printable Version +- HP Forums ( https://archived.hpcalc.org/museumforum)+-- Forum: HP Museum Forums ( https://archived.hpcalc.org/museumforum/forum-1.html)+--- Forum: Old HP Forum Archives ( https://archived.hpcalc.org/museumforum/forum-2.html)+--- Thread: HP35 exp(ln(x)) bug, a new number found. ( /thread-171052.html) |

HP35 exp(ln(x)) bug, a new number found. - Kiwi Geoff - 08-25-2010
The famous exp(ln(2.02)) bug on the original HP35 resulted in HP printing an Errata, part of which said:
" The numbers are 0.7030975114 and 0.995033085 x 10E-2,
I was curious as to whether there were any other numbers that
Doing a numerical search, I did find another number that does exp(ln(1.12211)) = 1.111 After a little more number crunching, it seems the full list of original HP35 exp(ln(x)) errors are as follows. They all produce values that need to be multiplied by 1.01 to give the correct answer: exp(ln(1.0201)) exp(ln(1.04060401)) exp(ln(1.12211)) exp(ln(2.02)) exp(ln(2.060602)) Only 5 numbers, from an astronomical number of correct results. A true needle in a haystack problem. For those who do not have an original HP35 (circa 1972) calculator, you can try the above numbers on this If anyone can find more than the above 5 numbers - I would be very interested. Story of the new number and the HP35 Errata.
Regards, Geoff Hitchcox (Christchurch, New Zealand).
Re: HP35 exp(ln(x)) bug, a new number found. - Chuck - 08-26-2010
Was this error barring internal rounding error? I tried exp(ln(3.2001)) and got 3.2000999999. Re: HP35 exp(ln(x)) bug, a new number found. - Kiwi Geoff - 08-26-2010
Quote:
Hi Chuck, I should have explained what the bug is. It's when you go
The example you gave is simply a "rounding" issue Chuck, if we take your answer of 3.200099999 and multiply by 1.01 we get 3.232101
Quote: The "bug" is at the 1% level Chuck. It is fascinating to study why this bug happened, because it's every programmer's nightmare, where an issue way down in the 12th place, can suddenly become a very much larger error. The original HP35 firmware was an absolute wonder (mainly by Dave Cochran)- even the exp(ln(x)) bug is still a salient lesson for modern programmers. If interested, Jacques Laporte has a great web resource discussing the bug, and how the HP 35 works internally.
Regards, Geoff Hitchcox, (Christchurch, New Zealand).
Re: HP35 exp(ln(x)) bug, a new number found. - Namir - 08-26-2010
Thanks for the link to Jacques Laport site. What a wealth of info!!!
Re: HP35 exp(ln(x)) bug, a new number found. - Dieter - 08-27-2010
Chuck wrote: Quote:
Well, this is one of the many cases where the calculator seems to give a wrong result just because it works perfectly correct. :-) |