28/48 Accuracy
09-15-2022, 10:10 PM
Post: #1
 Matt Agajanian Senior Member Posts: 986 Joined: Dec 2013
28/48 Accuracy
Hi all.

With the RPL era, what was the internal calculation accuracy?

Thank you.
09-16-2022, 11:31 AM
Post: #2
 Maximilian Hohmann Senior Member Posts: 1,231 Joined: Dec 2013
RE: 28/48 Accuracy
Hello,

this exhaustive "quick reference" here: https://www.thimet.de/CalcCollection/Cal...erence.pdf gives a figure of 56bits for the mantissa (12 decimal places) and an exponent range of +/-499.

Regards
Max
09-16-2022, 12:16 PM (This post was last modified: 09-16-2022 12:17 PM by J-F Garnier.)
Post: #3
 J-F Garnier Senior Member Posts: 906 Joined: Dec 2013
RE: 28/48 Accuracy
(09-16-2022 11:31 AM)Maximilian Hohmann Wrote:  this exhaustive "quick reference" here: https://www.thimet.de/CalcCollection/Cal...erence.pdf gives a figure of 56bits for the mantissa (12 decimal places) and an exponent range of +/-499.

This is obviously wrong, 12 decimal places are using 12*4=48 bits.

(09-15-2022 10:10 PM)Matt Agajanian Wrote:  With the RPL era, what was the internal calculation accuracy?
User numeric results have 12 digits, whereas internal calculations are done on 15 digits, for all Saturn-based machines, whatever RPL, RPN, Algebraic or BASIC. And whatever based on System RPL or pure assembly language firmware. The math core is basically unchanged since the HP-71B.

J-F
09-16-2022, 03:52 PM (This post was last modified: 09-16-2022 04:04 PM by John Keith.)
Post: #4
 John Keith Senior Member Posts: 993 Joined: Dec 2013
RE: 28/48 Accuracy
(09-16-2022 12:16 PM)J-F Garnier Wrote:  User numeric results have 12 digits, whereas internal calculations are done on 15 digits, for all Saturn-based machines, whatever RPL, RPN, Algebraic or BASIC. And whatever based on System RPL or pure assembly language firmware. The math core is basically unchanged since the HP-71B.

This also applies to Home mode on the Prime, which almost always returns identical results to the Saturn
calculators because the algorithms used are based on those from the Saturn era. The Prime CAS uses binary numbers, not BCD and often returns slightly different results in the least significant digit(s).

Quote:This is obviously wrong, 12 decimal places are using 12*4=48 bits.

IIRC, the least significant 48 bits are the mantissa, bits 48-51 are the mantissa sign (with some other data?) and the most significant 12 bits are the signed exponent (-500..499).
Something like this:

|e e e|s|m m m m m m m m m m m m|
09-16-2022, 04:20 PM
Post: #5
 Werner Senior Member Posts: 854 Joined: Dec 2013
RE: 28/48 Accuracy
(09-16-2022 03:52 PM)John Keith Wrote:  IIRC, the least significant 48 bits are the mantissa, bits 48-51 are the mantissa sign (with some other data?) and the most significant 12 bits are the signed exponent (-500..499).
Something like this:

|e e e|s|m m m m m m m m m m m m|

No, it's
012 3456789ABCDE F
XXX MMMMMMMMMMMM S

Cheers, Werner

41CVâ€ ,42S,48GX,49G,DM42,DM41X,17BII,15CE,DM15L,12C,16CE
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