Some observations on the new HP30S


I just bought a new HP30S. Its serial number is was made in China. The construction quality is pretty poor compare to past HPs including the HP20S. The answer results are to 24 digits with the first 10 showing in the needs to subtract what displays to get the digits beyond the initial 10 digits. The HP30S computes the infamous 2^301 example that is in the Advanced functions handbook of the former HP15C to 15 correct significant digits. Saturn CPU calculators from the 48 to the 20S etc compute 3^201 to 11 significant digits. so the HP30S adds 4 more correct digits. based on the fact that the saturn CPUs computer internally to 15 digits, the HP30S computes internaly to 19 digits...being the results are 24 digits there is something weid about all of that..displaying more than is computerd usualy is the other way around. I also noticed perhaps a "bug" in the square root may be deliberate though. For example, if one uses the square root key to compute the square root of 2, the answer is correct to 12 digits..if one uses the Y^X power key though by doing 2^.5 the answer is correct to 17 digits..that is 5 more significant digits. The square root key method is faster though than the power key method. Also, the HP20S for example computes the SIN of exactly 3.141592654 radians correctly to 12 digits..the HP30S computes it to 11 correct digits, so it is one significant digit less accurate with that tricky Sin function. That is another strong sign that the HP30S does not compute internally to a full 24 digits but computers to a lessor amount and merely shows the result to 24 digits. If it computer to 24 internal digits the SIN example would not have one less digit of accuracy compared to the HP48 and HP20S etc when computing the SIN of exactly 3.141592654 Radians.



That's very interesting. The additional digits by the way may be artifacts of the final binary-to-decimal conversion of the result; many older calculators used BCD arithmetic (so the conversion was always exact) but newer machines, that may use true binary arithmetic, would exhibit this behavior.

You can also see this behavior on a PC. For example, a simple C program I wrote prints the square root of two to 20 significant digits as sqrt(2)=1.41421356237309510000. But if I subtract the first 10 digits, then suddenly and magically, additional digits appear: sqrt(2)-1.414213562=0.00000000037309511036. This is just a consequence of the fact that what may be an exact decimal fraction cannot always be expressed as an exact binary fraction.



..I think you are correct. When one does 4?3 on the HP30S, you get all 3s till 24 digits, then you get a bunch of other seemingly random get numbers all the way up to a total of at least 40 digits..maybe more, I have not checked how many yet.


"The HP30S computes the infamous 2^301 example that is in the Advanced functions handbook of the former HP15C"

Not 2^301; it was 3^201 ( = 27^67 = 729^33.5 )

That example was also a "worst case known" for a final 10-digit mantissa (maybe 13-digit internal intermediate mantissa); each different system, whether differing in number of BCD digits, or using binary FP, etc., may have its own different "jawbreakers" :)

The different equivalents also provided a method of comparing the accuracy for different (but theoretically equal-valued) problems; finally, 7.29^33.5 must end up having the same *decimal* mantissa digits (1/10^67 of the original answer), but is usually more accurately computed.

You can, of course, now get the *exact* answer, right down to the last digit, on your HP49G :)

Best wishes from:

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