Re: math operators
>From: Juergen Luethje <j.lue at gmx.de>
>Subject: Re: math operators
>
>Jon wrote:
>
> >> Lucius Hilley wrote:
> >>
> >> POWER
> >> I would love to see power(4, 5) become 4^5.
> >> I know that we wouldn't be able to get read of power()
> >
> > YES! i prefer "^" but another alternative is "**" (like Ruby)
>
>
>I never saw a program, that uses '++' as alternative for '*', or '--' as
>alternative for '/'. I know, that there are some programs that use '**'
>as alternative for '^', but I don't see any reason, why that should be
>useful.
>
In C, ++ is equivalent to +=1 and -- is equivalent to -=1, in most cases.
Pointers complicate things of course. Powers are repeated multiplication, so
** somewhat makes sense for this, but of course, multiplication is repeated
addition, so someone might just think it is ++. I have seen ** in a few
other languages.
>
>The following text explains, why I prefer 'power(x,y)' to 'x^y':
>
>Math operations of the same priority, such as 7+5+1, are normally
>evaluated from left to right, if no parentheses are used. OK.
>
>And how about the power operator? What is the result of
> 2^3^2 ?
>
>Mathematically, evaluation is right to left for the power operator! So
> 2^3^2 = 2^(3^2) = 2^9 = 512.
>
I think the problem here is that it is hard to tell what you mean when
the exponents are not in superscript. I think the way you see it, 2^3^2 is 2
with a superscript 3 to the upper right, and the 3 has a superscript 2 to
the upper right of it. The "industry standard" sees it as (2^3)^2, ie, 2
with a superscript 3, all in brackets, and then with a superscript 2 for the
brackets. 2^(3^2) translates to 2^9, which is 512, but (2^3)^2 is 2^(3 * 2),
then 2^6, making 64. This is the major problem with the power symbol. It is
too ambigous to tell which form was meant. Even C had this problem, and
decided to go with the pow() function. (For those who thought ^ was power,
it really is bitwise XOR.)
>But there seems to be a kind of "industry standard", that says that such
>expressions should be calculated from left to right. That means:
> 2^3^2 = (2^3)^2 = 8^2 = 64
>
This right-to-left thing really depends on how you think 2^3^2 should look
on paper. Mathematics does say that expressions are evaluated left-to-right,
no matter what. It is because you see it as 2^(3^2) that makes the
difference.
>For example all PowerBASIC versions that I know, and AFAIK also Visual
>Basic calculates such expressions this way.
>I have a pocket calculator that doesn't perform it's calculation until
>the entire expression has been entered (very nice, BTW).
>It returns 64 for 2^3^2, too (which is false, strictly mathematically
>speaking).
>
My calculator, which does the same thing, evaluates it to 64, as well.
>IMHO, this situation is very strange.
>And Euphoria completly avoids this dilemma by using a 'power()' function,
>instead of a power operator!!! I was very pleased, when I noticed that.
>
Yes, this situation is quite annoying. However, proper use of brackets, to
clarify your meaning, will fix the problem.
>So beside Euphorias obvious elegance, it has some "hidden elegance",
>that cannot be seen at the first glance.
>
>
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