HP-35 Bug Question

[Joe Horn]

(04-20-2014 11:28 PM)Gerson W. Barbosa Wrote:  

(04-20-2014 10:23 PM)Katie Wasserman Wrote:  The early HP calculators didn't calculate integer exponentiation exactly, they used logs and anti-logs to compute them in order save space in ROM.

My guess is they still do, the guard digts rounding the results properly.

The HP-71B IDS shows that your guess is correct for at least the '71 and all models that use the same code. For normal inputs, it calculates "the usual e^(x*ln y) calculation" (comment at ROM address 0D2EE), performing each step to 15 internal digits, and only rounding the final result to 12 digits.

However #1: that code also sometimes calls entry point EXP16M (a 16-digit e^x), which in turn calls entry point DXP100 (a "double-precision" e^x, with the low-order digits of the double-precision argument in R0). I don't understand when these routines are called, or how accurate they make the y^x function; perhaps a Saturn-code expert can either decipher that section of the 71 IDS, or peruse the code in the HP 50g with Jazz or Nosy and figure out what it's doing.

However #2: What the HP Prime does can only be answered by Cyrille (for Home's x^y) or Bernard (for CAS's x^y), because they wrote that code from scratch (respectively), not merely porting it from the Saturn code.