Rounding error or something

[RedDwarf]

So, I was messing around with some program or another on my 84+SE and ended up doing something where I took the iPart of log(16)/log(2). Confused when the program didn't work, I went to the home screen and did iPart(log(16)/log(2)) - which should return 4 - and it returned 3. I then tried fPart(log(16)/log(2)) and that returned 1. What's going on here? I tried it on several different 83+ series calculators and all of them did the same thing. My friend's 89 Titanium, however, worked properly. I admit myself to be thoroughly confused. Maybe this has been discussed before but I couldn't find anything.

[Weregoose]

Welcome to United-TI! :)

The TI-83+ and similar models (which includes the TI-84+SE) use floating-point arithmetic, which means that calculations are only accurate to a certain number of decimal places. If it's off by a mere 10^-14, then this could cause the unexpected behavior like what you described. To correct this behavior, oftentimes all you need is round(value,#decimals, where the second argument defaults to 10 if left omitted, which by itself is usually sufficient. So, try using iPart(round(log(16)/log(2 instead.

About the fPart( being equal to one: log(16)/log(2) actually evaluates to 3.9999999999999 on the calculator, and the fractional part is very close to an integer, so it will be displayed as such. While up to 14 digits are retained between calculations, the home screen will only display up to 10. However, the result itself isn't rounded – just the display is.

[RedDwarf]

That's pretty much what I expected and round is exactly what I need for this program. But as far as I can tell, this only happens for 16: iPart(log(32)/log(2))=5, iPart(log(64)/log(2))=6, etc. Why just 16?

[Weregoose]

Actually, it messes up slightly in the positive direction for exponents of six through eight, and then fails to reach its mark at nine, but gets its act together for every input past that. I couldn't offer an explanation as to why that is. There'd likely be problems for powers of other bases as well. I'll look more into this. (Edit: The distribution's a mess – can't find a pattern.)

[thornahawk]

For some "fun", try plotting iPart(log(X^N)/log(X)) for various values of N (not just integers). You'd be surprised at how often you'll see "combs".

I have a feeling it's the approximation algorithm within log( (and ln(, for that matter) that causes the trouble. Without a way to find out what TI exactly uses (I don't think they'd tell. ), you won't make headway towards understanding why this is so.

thornahawk