HP65 accuracy error

12162019, 04:51 PM
Post: #1




HP65 accuracy error
Everyone who uses the HP65 needs to be aware of the known accuracy error in the y^x function for larger values.
10 ENTER 6 Y^X yields 1000000 as expected 10 ENTER 7 Y^X yields 9999999.99 10 ENTER 8 Y^X yields 99999999.60 the error gets greater the larger you go. Just be aware. 

12162019, 05:26 PM
Post: #2




RE: HP65 accuracy error
(12162019 04:51 PM)Don Shepherd Wrote: Everyone who uses the HP65 needs to be aware of the known accuracy error in the y^x function for larger values. I think that 45 years after its introduction, most people know by now! Tom L Cui bono? 

12162019, 05:44 PM
Post: #3




RE: HP65 accuracy error
(12162019 05:26 PM)toml_12953 Wrote: I think that 45 years after its introduction, most people know by now! Yeah, those who have collected and used and programmed the 65 probably do, but I've seen some people here on the forum who are restoring and newly acquiring the 65, and they may not know this. I mention it because last night I entered a new 65 program and it didn't give the expected results, and I traced it down to this y^x accuracy error. 

12162019, 06:38 PM
Post: #4




RE: HP65 accuracy error
If I recall correctly, the early marketing literature of the HP21/25 mentioned the improvement of exponentiation functions. (or later?)
TomC (12162019 05:44 PM)Don Shepherd Wrote:(12162019 05:26 PM)toml_12953 Wrote: I think that 45 years after its introduction, most people know by now! 

12162019, 06:53 PM
Post: #5




RE: HP65 accuracy error
(12162019 04:51 PM)Don Shepherd Wrote: Everyone who uses the HP65 needs to be aware of the known accuracy error in the y^x function for larger values. Common with all the classics and HP21. cheers Tony 

12162019, 07:10 PM
Post: #6




RE: HP65 accuracy error
Article was titled something like "The new accuracy  making 2^3 = 8"


12162019, 08:55 PM
Post: #7




RE: HP65 accuracy error
(12162019 07:10 PM)Gene Wrote: Article was titled something like "The new accuracy  making 2^3 = 8" That article, "The New Accuracy: Making 2^3 = 8", written by Dennis Harms, appeared on page 16 of the HewlettPackard Journal from November 1976, with the cover story being the HP67/97. At the end, Dennis acknowledges Dave Cochran, Professor William Kahn and Bill Egbert. For those keeping score at home, Dave Cochran spoke at the HHC2018 conference in San Jose, William Kahn spoke at the original HP conference in 1979 in Santa Clara and Bill Egbert spoke at the 1981 conference in Corvallis, Oregon, where he presented the Saturn CPU to the public for the first time. Jake 

12162019, 09:48 PM
Post: #8




RE: HP65 accuracy error  
12162019, 11:02 PM
(This post was last modified: 12172019 11:55 PM by Don Shepherd.)
Post: #9




RE: HP65 accuracy error
(12162019 09:48 PM)SlideRule Wrote: Any hints as to the identity of the the 65 program (my curiosity)?Yes, it's a little encryption/decryption program I adapted for the 65 from a version I wrote for the 12c. For the 65, you press A to display no decimals, then press E to encrypt five 2digit numbers representing letters of your message. The encryption results in a big base 10 number from the 5 2digit numbers in base 40, and entering E decrypts the big base 10 number back into the original 2digit base 40 numbers. Except it doesn't give you the same 2digit numbers you started with because of the Y^X error. The 12c version of this program works fine. updated on Dec. 17, 2019  I modified the program below to remove the two Y^X operations and just used regular multiplication to adjust the multipliers in each loop instead of the Y^X operations, and now the program works fine. If anyone is interested, I'll post the new code. It's good to know that there is a relatively easy workaround for this problem. Here is the 65 version that does not work correctly (lowercase for ease of entry): lbl a dsp . 0 rtn lbl d (decode) sto 1 0 sto 2 sto 3 lbl 2 rcl 1 40 / sto 4 lst x x<>y frac x 10 rcl 3 y^x generates the wrong number x sto + 2 rcl 4 int sto 1 0 x=y goto 3 2 sto + 3 goto 2 lbl 3 rcl 2 rtn lbl e (encode) sto 1 0 sto 2 sto 3 lbl 1 rcl 1 100 / int sto 1 lst x frac 100 x 40 rcl 2 y^x x sto + 3 1 sto + 2 4 rcl 2 x<=y goto 1 rcl 3 rtn 

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