Changing Of The Guard

04212014, 09:51 PM
Post: #1




Changing Of The Guard
Hi all.
If I recall correctly, Spices/Spikes and prior only maintained 10digit accuracy with no guard digits. So, correct me if I'm wrong. What are the calculation/accuracy forensics for each lineage following? Thanks 

04222014, 12:00 AM
(This post was last modified: 04222014 01:05 AM by Thomas Klemm.)
Post: #2




RE: Changing Of The Guard  
04222014, 01:50 AM
Post: #3




RE: Changing Of The Guard
I believe the first HP with guard digits was the HP91 printing scientific, with 3 guard digits. It would make sense to me that any calcs that came out after it, including the late Woodstock, and all that followed would likely have those guard digits.
Hopefully someone can verify if that's the case. As best I can tell, Spice, Nut and Voyager calcs had about the same level of accuracy. Bob 

04222014, 05:04 AM
(This post was last modified: 04222014 05:26 AM by Mike Morrow.)
Post: #4




RE: Changing Of The Guard
(04222014 01:50 AM)bshoring Wrote: I believe the first HP with guard digits was the HP91 printing scientific... What an odd belief. :) That certainly is not true about the HP91 nor none of the other machines that you mention...nor of the HP67/97, nor the HP41C series, nor the HP15C...etc. etc. etc. AFAIK, no HP calculator used any guard digits until machines based on the Saturn processor were developed. That would be around 1986...the HP28C and later. Even then...the additional digits are strictly internal to the specific calculation and do not survive when the number reaches the display. For example, the HP42S is said to use 15digit precision during calculation. But for a simple example. pushing the PI button produces a display of 3.14159265359. Take the SIN of that, and the exact same result is produced that occurs when you key in 3.14159265359 and take the SIN. There are no hidden digits in the value that is displayed after PI is executed. The same is true for more complex examples. TI machines used three guard digits at least as early as the SR50 in 1974. Those nondisplayed digits still exist when the value is presented for display. Subtracting a manually keyedin value that appears identical to the displayed value will generally show the presence of the guard digits in the original value. Most Casio machines (like the fx115ES Plus) show the same behavior, except that the 115ES has five guard digits! I personally always preferred TI's use of guard digits to HP's refusal to improve the precision of calculations on their machines. HP always bizarrely maintained that their failure to provide guard digits was a positive characteristic, compared to TI. That was pure HP BS. For example, I always got far better accuracy of results, due to far better precision, from a fourthorder RungeKutta program on a TI59 than I ever got from the same program executed on a HP67 or HP97 or 41C. This is just another of many areas where HP screwed the pooch in its mythological age of excellence. :) 

04222014, 05:23 AM
Post: #5




RE: Changing Of The Guard
(04222014 01:50 AM)bshoring Wrote: Hopefully someone can verify if that's the case.The HP35 already had 2 guard digits. You can verify this by calculating 1.0005005^{2}. Actually all 13 digits are calculated. But then the last digit is lost by shifting the result to the right. This was corrected later. Cheers Thomas 

04222014, 05:28 AM
(This post was last modified: 04222014 05:36 AM by Matt Agajanian.)
Post: #6




RE: Changing Of The Guard
Mike, Yes, indeed. Even as I remember from my SR56 days, TI would always reprint that guard digits/ EE/INVEE guard digits example even in its TI58/59 and TI57 manuals among others to show that guard digits were present in calculations.
Thomas, thanks for the verification. Although, as I regard HP in high technological respect, their usage of guard digits in their calcs is quite obscure and I do not recall in any manuals that calculations are carried past 10 digits of accuracy (unless it's explicitely stated in some of their manuals and I must've missed the fine print somwhere). 

04222014, 06:59 AM
(This post was last modified: 04222014 08:25 AM by Thomas Klemm.)
Post: #7




RE: Changing Of The Guard
(04222014 05:04 AM)Mike Morrow Wrote: AFAIK, no HP calculator used any guard digits until machines based on the Saturn processor were developed.These are intermediate results of calculating 1111111*1111111 = 1234567654321. HP35 Before rounding: After rounding: Note: the last digit is lost. HP34C Note: the rounded result is in register c. Cheers Thomas 

04222014, 07:18 AM
Post: #8




RE: Changing Of The Guard
(04222014 05:28 AM)Matt Agajanian Wrote: Thomas, thanks for the verification. Although, as I regard HP in high technological respect, their usage of guard digits in their calcs is quite obscure and I do not recall in any manuals that calculations are carried past 10 digits of accuracy (unless it's explicitely stated in some of their manuals and I must've missed the fine print somwhere). In HP calculators the guard digits are not exposed to the user. The intermediate result is rounded to 10 or 12 digits. You always get what you see. TI calculators only displayed the rounded result while keeping the guard digits internally. This is an advantage if you chain computations but can be confusing because e.g. you see a 2 but internally it is 1.9999999999. Start squaring this number to see what can happen. Cheers Thomas 

04252014, 10:44 AM
Post: #9




RE: Changing Of The Guard
(04222014 05:28 AM)Matt Agajanian Wrote: Although, as I regard HP in high technological respect, their usage of guard digits in their calcs is quite obscure and I do not recall in any manuals that calculations are carried past 10 digits of accuracy (unless it's explicitely stated in some of their manuals and I must've missed the fine print somwhere). It's explained in at least some HP manuals. For example, the 32SII says on page 116, "All numbers are stored with 12digit precision.... During some complicated internal calculations, the calculator uses 15digit precision for intermediate results." Ever since Dennis Harm's famous "The New Accuracy: Making 2^3=8" article was written (HP Journal, October 1976, pages 1617), every HP BCD calculator has used 3 extra digits during internal calculations, and at least some of their manuals have in fact explained this. <0ΙΈ0> Joe 

04252014, 05:46 PM
Post: #10




RE: Changing Of The Guard
(04252014 10:44 AM)Joe Horn Wrote: Ever since Dennis Harm's famous "The New Accuracy: Making 2^3=8" article was written (HP Journal, October 1976, pages 1617), every HP BCD calculator has used 3 extra digits during internal calculations, and at least some of their manuals have in fact explained this. That's a nice reference article, Joe. It may have also come in handy during another recent discussion where trig functions and \(\pi\) were being discussed to show the rationale behind some of the nonCAS results (even if they weren't agreeable). You have an amazing amount of historical info stored away in your head! Thanks for sharing it with us. 

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