(12C) Signum Function

[Thomas Klemm]

(03-03-2019 07:49 PM)Albert Chan Wrote:  Example, on HP-12C, x = Pi + 0.04 = 3.181592654

If we just look at the mantissa it appears that this only happens for values between \(\sqrt{10} \approx 3.16228\) and \(5\).
And within this interval it happens at about 18.37% of the cases.
Which is close to \(\frac{5 - \sqrt{10}}{10} \approx 0.18377\).
Choosing a number at random leads to a wrong result in about 1 of 27 cases.
I don't think that we can neglect that.

Here's a table with some values \(x\) having only 5 digits after the decimal point and \(\sqrt{x^2}\) as it is calculated by the HP-12C:

Code:

3.16343 3.163429999
3.16466 3.164660001
3.17129 3.171289999
3.19029 3.190289999
3.19434 3.194340001
3.20766 3.207660001
3.22016 3.220160001
3.22092 3.220920001
3.22379 3.223789999
3.23338 3.233379999
3.23869 3.238690001
3.24384 3.243840001
3.25258 3.252580001
3.25807 3.258069999
3.26229 3.262289999
3.28479 3.284789999
3.28807 3.288069999
3.29319 3.293190001
3.29693 3.296929999
3.30756 3.307559999
3.32538 3.325379999
3.32808 3.328080001
3.34906 3.349059999
3.35962 3.359619999
3.36371 3.363709999
3.38234 3.382340001
3.38394 3.383939999
3.38838 3.388379999
3.41781 3.417810001
3.42121 3.421209999
3.42931 3.429310001
3.43142 3.431420001
3.44721 3.447209999
3.44906 3.449059999
3.45719 3.457190001
3.46108 3.461080001
3.47871 3.478709999
3.48116 3.481160001
3.48608 3.486080001
3.48643 3.486429999
3.48821 3.488209999
3.49429 3.494289999
3.49831 3.498310001
3.49921 3.499209999
3.50488 3.504879999
3.51834 3.518340001
3.53331 3.533310001
3.54069 3.540690001
3.54171 3.541709999
3.54388 3.543879999
3.54484 3.544840001
3.55221 3.552209999
3.55792 3.557920001
3.56512 3.565119999
3.57588 3.575879999
3.57734 3.577340001
3.57829 3.578289999
3.57866 3.578660001
3.58194 3.581939999
3.59334 3.593340001
3.59421 3.594209999
3.59556 3.595559999
3.60493 3.604929999
3.60834 3.608340001
3.61407 3.614069999
3.61743 3.617429999
3.61884 3.618840001
3.63366 3.633660001
3.63462 3.634619999
3.63771 3.637709999
3.65793 3.657929999
3.66531 3.665310001
3.67357 3.673569999
3.67557 3.675569999
3.67762 3.677619999
3.68834 3.688340001
3.69693 3.696929999
3.70616 3.706160001
3.71143 3.711429999
3.71466 3.714660001
3.72621 3.726209999
3.74243 3.742429999
3.75288 3.752879999
3.75638 3.756379999
3.75643 3.756429999
3.75938 3.759379999
3.77419 3.774190001
3.78007 3.780069999
3.79638 3.796379999
3.79731 3.797310001
3.80288 3.802879999
3.82866 3.828660001
3.84429 3.844289999
3.85679 3.856789999
3.87116 3.871160001
3.88507 3.885069999
3.89021 3.890209999
3.90788 3.907879999
3.91862 3.918619999
3.94979 3.949789999
3.95034 3.950340001
3.96016 3.960160001
3.96812 3.968119999
3.99571 3.995709999
4.00312 4.003119999
4.01279 4.012789999
4.01316 4.013160001
4.02188 4.021879999
4.07884 4.078840001
4.11312 4.113119999
4.15243 4.152429999
4.17866 4.178660001
4.19862 4.198619999
4.23857 4.238569999
4.24734 4.247340001
4.26734 4.267340001
4.28816 4.288160001
4.29112 4.291119999
4.30134 4.301340001
4.30566 4.305660001
4.33416 4.334160001
4.36738 4.367379999
4.38716 4.387160001
4.40307 4.403069999
4.44193 4.441929999
4.51507 4.515069999
4.51557 4.515569999
4.51793 4.517929999
4.57107 4.571069999
4.58657 4.586569999
4.64793 4.647929999
4.68393 4.683929999
4.72493 4.724929999
4.73393 4.733929999
4.77593 4.775929999
4.84307 4.843069999

Cheers
Thomas