Vintage logarithm round up Message #1 Posted by McAllan on 15 Mar 2012, 4:59 p.m.
I've played around a little with the logarithms or more accurately the powers function of a small selection of vintage calculators. Here I've done some very interesting discoveries.
While 2^8 gives more or less correct answers on all (like 259.9999999 or just above 256 on the hidden digits) especially interesting seems the two cases 2^26 and 2^30.
Before I start I should add that only the SR50 seems to use hidden digits in an "honest way". I suspect the SR51II uses hidden digits too but if that's the case they're very hard to get for logarithms (easy for Pi). Most likely it's using hidden digits but the result of the isolated calculation is rounded to 10 (as many as can be displayed). HP and Canon for logarithm only seems to use as many digits as can be displayed  that is I can't seem to extract any more digits of the result that is displayed. Perhaps someone has something to add?
The results for 2^26
Correct result: 67.108.864  please note I'm using European format ;)
HP35: 67.108.863,69
HP25: 67.108.863,69
TI SR50: 67.108.864 + 8ee5
TI SR51II: 67.108.864 (+ 0)
Canon F71: 67.108.863,9 (note only 9 digits while it's a 10 digit machine)
Canon F7: 67.108.857
The results for 2^30
Correct result: 1.073.741.824
HP35: 1.073.741.827
HP25: 1.073.741.827
TI SR50: 1.073.741.824 + 1ee3
TI SR51II: 1.073.741.824 (+ 0)
Canon F71: 1.073.741.820
Canon F7: 1,0737417ee9
Seems a bit odd. Especially HP and Canon seems to have some quirks. While the F7 seems quite bad at 2^26 the HP is even worse if you take into account that is has more digits available. F7 is off by 7 at the least significant digit while HP is off by 31(!). To add to oddity the F7 seems substantially more precise if doing powers manually:
Keystrokes: 26 [x] 2 [ln] [)] [e^x]
Which results in: 67.108.863. Not 100% correct but very acceptable considering it's available digits.Using that method 2^8 is spot on.
On closer look it actually seems like F71 rounds to 9 significant digits on powers despite is has 10 on the display for mantissa. Playing a little using the manually method on F71 gets 2^26 = 67.108.864,03 and 2^30 = 1.073.741.825. While not 100% correct then a litte more correct than using dedicated power function  and with the 10th digit available... Odd... :S
On HP "manual" always seems to get same result as the dedicated button.
Seems like TI is really trumps the others. On the other hand the SR50 seems to use logarithms to calculate square root. It's slower and sqrt(256) = 16  7ee11. All others get square root 100% correct and are significantly faster here despite more or less same speed on other functions. The SR51 (not the II) seems equal to the SR50 except for square root where it is also spot on. Perhaps the SR50 implements it using logarithms because of ROM space (the SR51 and SR51II has two ROMs where SR50 only has one  so perhaps it's fully stuffed).
Regarding trigonometric I haven't found any real deal breakers although I should say I haven't played that much around with those functions. The largest reason I've found the SR50 to be superior is because of it's larger internal precision. The SR50 seems to use all 13 internal digits for triginometrics while the others only seems to use as many digits as is displayed. So after all the F7 isn't as bad as writtin on some site. It may not beat neither HP nor SR50 but it still beats the TI30. May do trigonometric round up when I've played a little bit more with those functions.
Despite their flaws I somehow still like the Canons. They're well built and has nice reliable buttons. They got something about the casing and buttons correct. Second best imho SR50 followed closely by it's replacement SR50A then the HPs and last SR51II with it's low cost version of the "Klixon". Oh and who doesn't don't like the conversions on the F7? While likely not much used they're well implemented and easy reachable in contrast to SR51 or very limited like on SR51II.
