Quick Test
What if we want a quick and dirty test that determines both the number
of digits a calculator uses and whether or not it gives correct results
to that number of digits?
Of course there is an unlimited number of possibilities of combining
functions and values and I've simply picked one. It uses functions that
most scientific calculators offer (using radians):
| Operation |
8 digit result |
9 digit result |
10 digit result |
11 digit result |
12 digit result |
13 digit result |
14 digit result |
| 100 / 18 |
5.5555556E+0 |
5.55555556E+0 |
5.555555556E+0 |
5.5555555556E+0 |
5.55555555556E+0 |
5.555555555556E+0 |
5.5555555555556E+0 |
| sin |
-6.6510148E-1 |
-6.65101512E-1 |
-6.651014600E-1 |
-6.6510151495E-1 |
-6.65101514976E-1 |
-6.651015149785E-1 |
-6.6510151497879E-1 |
| e^x |
5.1422134E-1 |
5.14221325E-1 |
5.142213410E-1 |
5.1422132390E-1 |
5.14221323892E-1 |
5.142213238903E-1 |
5.1422132389015E-1 |
| asin |
5.4009951E-1 |
5.40099493E-1 |
5.400994918E-1 |
5.4009949158E-1 |
5.40099491570E-1 |
5.400994915684E-1 |
5.4009949156822E-1 |
| tan |
5.9956490E-1 |
5.99564874E-1 |
5.995648720E-1 |
5.9956487171E-1 |
5.99564871699E-1 |
5.995648716971E-1 |
5.9956487169684E-1 |
| * sqrt(2) |
8.4791284E-1 |
8.47912775E-1 |
8.479127733E-1 |
8.4791277311E-1 |
8.47912773077E-1 |
8.479127730765E-1 |
8.4791277307616E-1 |
| ln |
-1.6497743E-1 |
-1.64977508E-1 |
-1.649775102E-1 |
-1.6497751038E-1 |
-1.64977510418E-1 |
-1.649775104190E-1 |
-1.6497751041938E-1 |
| * -5 |
8.2488715E-1 |
8.24887540E-1 |
8.248875510E-1 |
8.2488755190E-1 |
8.24887552090E-1 |
8.248875520950E-1 |
8.2488755209690E-1 |
| atan |
6.8973289E-1 |
6.89733125E-1 |
6.897331320E-1 |
6.8973313254E-1 |
6.89733132652E-1 |
6.897331326549E-1 |
6.8973313265606E-1 |
| Previous precision |
|
6.8973289 E-1 |
6.89733125 E-1 |
6.897331320 E-1 |
6.8973313254 E-1 |
6.89733132652 E-1 |
6.897331326549 E-1 |
| Relative error |
-3.5E-07 |
-1.1E-08 |
-9.5E-10 |
-1.7E-10 |
-6.1E-12 |
-1.9E-12 |
-1.7E-13 |
The sequence of operations is carefully chosen to avoid unnecessary
amplification of errors. But it also assures that errors of one stage are
not cancelled out in the next one: Looking at the row labelled "Previous
precision" it can be observed that at least the last digits of the final
result is usually not correct - regardless of how many digits are used!
This is also expressed by the relative error of the result given in the
last line.
|
Sequence of operations |
| AOS |
| 100 |
/ |
18 |
= |
sin |
e^x |
asin |
tan |
* |
2 |
sqrt |
= |
ln |
* |
-5 |
= |
atan |
|
| RPN |
| 100 |
18 |
/ |
sin |
e^x |
asin |
tan |
2 |
sqrt |
* |
ln |
-5 |
* |
atan |
|
|
|
|