Statistical registers assignments in HP RPN calculators

[brouhaha]

In the course of deciding how to add basic statistical functions to my hacked 16C firmware, I first looked at what the other Voyager calculators do, and then the 41C. Considering only those calculators, based on the Nut CPU architecture, HP did three different things. That got me to wondering, so I went through all of the HP RPN calculators that have statistical functions and store the accumulated values in numbered registers (which leaves out the HP-80 and HP-32S). I found a total of FOURTEEN different sets of statistical register assignments. I've listed them below.

The HP-80 peforms single-variable statistics using only the stack. The HP-81 has single-variable statistics as noted in the table, but also a separate set of two-variable statistical functions called "Trend Line" (TL), not covered by my table..

For the modified 16C, I'm trying to decide whether to use the 10C/11C/34C register assignments (very easily done), or to make them movable via a ΣREG function like the 41C family (a little more challenging).

EDITED 2023-04-19 - thanks to Dave Britten, Mike, and AndiGer for corrections and updates

Code:


           19C
           29C
           32E                                     12C       41C 
           55                                 15C  37E  10C  41CV
      45   91                       67        33E  38E  11C  41CX    32SII
reg   46   95C  81   22   25   27   97   92   33C  38C  34C  42S     33s    35s
---   ---  ---  ---  ---  ---  ---  ---  ---  ---  ---  ---  ------  -----  ---
n     5    .0   11   7    3    4    S9   Σ0   2    1    0    Σreg+5  ±28    -27
Σx    7    .1   12   9    7    5    S4   Σ1   3    2    1    Σreg+0  ±29    -28
Σx²   6    .2   10   8    6    6    S5   Σ2   4    3    2    Σreg+1  ±31    -30
Σy    8    .3   n/a  6    4    7    S6   Σ3   5    4    3    Σreg+2  ±30    -29
Σy²   n/a  .4   n/a  n/a  n/a  8    S7   Σ4   6    5    4    Σreg+3  ±32    -31
Σxy   n/a  .5   n/a  5    5    9    S8   Σ5   7    6    5    Σreg+4  ±33    -32

[Paul Dale]

Wow, that's pretty crazily mixed up.

[Dave Britten]

Very interesting - and bewildering how much they changed up the assignments over the years.

The 80 is probably the strangest of all: there are no stat registers, everything just sits on the stack!

The 32S and 32SII do in fact have numbered registers, it's just that you don't encounter the numeric identities unless you're using indirect addressing, and the stat registers appear to only be accessible indirectly on the 32SII (according to the manuals). Nevertheless, the assignments on the 32SII appear to match the 33S:

n - 28
Σx - 29
Σy - 30
Σx^2 - 31
Σy^2 - 32
Σxy - 33

[AndiGer]

Just powered my 81.

sum y in stack register Z
sum y square in stack register Y
sum xy in register 12

Register 13 holds highest x value + 1 (x always incrementing when calculating expanded trend line according to the manual example)