Bug: HP Prime can't do Log's

[davimle]

OK, I was fascinated and curious about the numerical methods pathological cases posed in the paper linked by @Fortin. Now that my daughter is home with her Prime, I figured it was time for a calculator smack-down! Here are the contenders:

• HP Prime (in Home mode) ~$150
• HP Prime (in CAS mode) ~$150
• Sharp EL-W516X ~$20 (a few years back at Target)
• iOS built-in calculator "Free" (if you already have an iPhone or iPad)
• pCalc app $10
  

The Sharp EL-W516X is a cheap but surprisingly sophisticated little calculator. (I like that it keeps everything as fractions until you ask it to evaluate.) It is reported to have 15-digit precision with 10 digits shown. For fun, I also decided to thrown in results from iOS built-in calculator and also pCalc (a popular RPN calculator app). I tried both the iOS and Mac versions of pCalc and got the same answers from both, which makes sense as they probably run the same code.

Now onto the rounds....

For the classic: 1/3 * 3 - 1

Code:

  Prime (Home):  -0.000000000001
  Prime (CAS):    0
  EL-W516X:       0
  iOS calc:       0
  pCalc app:      0

And the slightly more complicated: 1/3 * 3 - 0.99 - 0.01

Code:

  Prime (Home):  -0.000000000001
  Prime (CAS):    1.60982338571E-15
  EL-W516X:       0
  iOS calc:       0
  pCalc app:      8.6736173799E-18

OK, Prime in regular mode makes perfect sense. CAS mode is "huh"? where did the 1.6 come from? Sharp doesn't advertise CAS, but showed an intermediate answer of 1/100 so it seems to carry around some sort of "symbolic" view. (e.g. I have also seen values such as Pi/2, etc.) pCalc answer just makes me wonder....

Now for the very small differences: 1 + 1E-13 - 1
[Note: I debated about whether I should adjust this to 1E-14 for the calculators that are using 15 digits, however, it seems their threshold is also 1E-13.]

Code:

  Prime (Home):   0
  Prime (CAS):    9.94759830064E-14
  EL-W516X:       0
  iOS calc:       1E-13
  pCalc app:      9.9999977916E-14

So it would seem that Prime in regular mode employs some of the same tricks as attributed to TI in the paper. CAS mode is again, just strange (why can't it get the precise answer?). The Sharp is clearly rounding. iOS calculator is clearly the winner in this round. pCalc gets so close, but not quite.

Now for the very small differences: 1 + 1E-13 - 0.99 - 0.01

Code:

  Prime (Home):   0
  Prime (CAS):    1.01252339846E-13
  EL-W516X:       0
  iOS calc:       1E-13
  pCalc app:      1.0000865153E-13

No change here, for the Prime in regular mode, as I think the information was lost in the addition. CAS mode is still unexplainable to me. Sharp seems to have lost the info in the addition so no difference when it gets to the subtraction. iOS surprises again! pCalc is so close, not sure why it isn't just precise.

So surprisingly, the iOS "free" built-in calculator was the only one to get the correct answer in all 4 calculator torture tests. Too bad it is such a pain to use. I am disappointed that pCalc compares so badly to the calculator that comes bundled for free. Seems they should compare results across several other calculators.

Now if I could just have an HP Prime calculator app for my iPhone 6+.