World: r3wp

Brian, I know about IEEE754! :)

I wrote much of the documentation about it.

I just tested, the C function, fmod (3.3, 1.1), also returns 1.1. 
:)

I figured so, since if I knew about it it must be pretty basic :)

I think that the difference between // and MOD is in how they handle 
negative numbers. Modulus (as a math concept, as I recall) isn't 
defined for negative numbers at all. Programming languages tend to 
punt when it comes to this, so // works the most common way, and 
MOD converts it to the next most common way.

The reason is understandable too. When the two decimals tested can 
be divided without remainder (the remainder comes close to zero), 
we can't use the result. It's because the division can be on either 
side of zero, so the rounding will give zero or -1.0.

>> $3.3 // $1.1
== $0

The $ in this case just being a sigil for a different numeric representation 
that works better in this kind of situation.

(Good work on that, Ladislav!)

I also tested, that it takes equal amount of cpu time to do this 
in C, where a and b are of type double:

fmod (a, b)

or

a - floor (a / b) * b

Same can be said for integers, where we would use % in C.

I conclude, it makes sense to drop MOD and MODULO, and then use the 
calculation using floor for both integers and decimals. It will give 
the mathematically best result, and it will perform as good as using 
% and fmod in C.

MOD and MODULO are supposed to be different from // for *negative* 
numbers.

If you look at the source for those functions, you will see that 
MOD calls // internally, and MODULO calls MOD.

Neither call floor (unless // calls it internally).

And if you look in HELP MODULO, it looks like a hack to fix some 
problem:


Wrapper for MOD that handles errors like REMAINDER. Negligible values 
(compared to A and B) are rounded to zero.

Yup. Which is where my math knowledge left off. I can see the math 
they use, but not why it is necessary.

I get MOD, I think: It's that negative values thing. MODULO seems 
to deal with the epsilon, afaict.

Ladislav wrote them, iirc. If he thinks they're necessary I'll take 
his word for it :)

Ops, I said something wrong, when saying, the division can be on 
either side of zero. The division is of course close to a whole number, 
but can be on either side of that number, so the rounding can be 
that number (if the result lie above) or one below that number (if 
the result is below). Using ROUND instead of ROUND/FLOOR solves it.

Use the SOURCE, Luke. ROUND isn't used at all.

I just say Ladislav popping in. Ladislav, if you don't wanna read 
all, my question simple is, if we need all of REMAINDER, MOD and 
MODULO?

Although perhaps it should be. MOD and MODULO were written when ROUND 
was mezzanine. Now that ROUND is native, perhaps MOD and MODULO could 
be optimized by someone who understands the math (not me).

(And maybe you're not the one to answer this question.) :)

When implementing Round as mezzanine, I needed MOD to do it, and 
Gregg thought it might have been useful to make it available;

Good enough :)

Remaninder (//) is handling operands as "exact", MOD uses some "rounding", 
MODULO is more "standard" and uses even more rounding

the difference is as follows:

>> mod 0.3 0.1
== -2.77555756156289e-17

>> remainder 0.3 0.1
== 0.1

>> modulo 0.3 0.1
== 0.0

The fact is, that MOD was necessary for positive values of B only, 
so there is no provision for the negative ones

So the difference is only, when the division give a remainder close 
to zero. Example of same results:

>> mod 0.3 0.2
== 0.1
>> remainder 0.3 0.2
== 0.1
>> modulo 0.3 0.2
== 0.1


And then there are some differences, when dealing with negative numbers.

Should there be? And is more optimization possible?

Should there be? -> Should there be provision for the negative ones, 
Ladislav?

It is even possible to axe the MOD function, ask Gregg, what he thinks 
about it

(or make it "hidden", if the MODULO function remains)

With the MOD function inlined in MODULO, more optimization may be 
possible.

So the difference is only, when the division give a remainder close 
to zero.

 - actually not, the difference is visible, if the Remainder function 
 gives a result close to the B value

(called Value2 in case of the Remainder function)

Yes, more precise formulation.

thanks

If we get rid of MOD and just go with MODULO, should we rename MODULO 
to MOD ?

The disadvantage is that MOD might be a less-specific name.

I do not mind, as far as I remember, I really used it only in the 
mezzanine implementation of Round, although, some stand-alone use 
might make sense

My suggestion is to get rid of moth MOD and MODULO, and then deside 
on a way, REMAINDER should work. People can always make some function 
in special cases. And remember rule no. 1!
K.I.S.S.

moth = both

aha, so you would suggest to change the Remainder behaviour?

If functions like MOD and MODULO is needed, then the real problem 
might be with remainder?

Well, Remainder does not do *any* rounding, which may be what is 
desired, or not.

I'm studying Lua these days, and they just have one function, that 
do:
a - floor (a / b) * b
Simple to understand.

What would be the consequences of such a change? I remember you going 
on about IEEE754 predictability, and this would seem to reduce precision 
- all that rounding...

I saw that implementation before I read about modulus on wikipedia 
and wolfram.