Add ^ operator for power

[osaris]

Reference #25

[Hywan]

Are we sure that ^ has not the same priority (precedence) than an other existing operator?

[osaris]

According to many sources found on Google (!!), ^ priority is lower than multiplication and division operators.

[Hywan]

Since PHP5.6, we have the ** operator with the following precedence: http://php.net/manual/en/language.operators.precedence.php. It is a right associative operator. Is it the case here?

[Metalaka]

As said here,

• the common ^ operator is left associative (according to my mind and my calculator (2^3^2=64))
• the PHP ** operator is right associative (2 ** 3 ** 2 == 512).

What about Hoa\Math^ operator ?

[osaris]

It's right associative here (2^3^2 == 512) like the ** operator.

[Metalaka]

Ok, it seem my mind and my college calculator were wrong ;)
https://en.wikipedia.org/wiki/Order_of_operations#Special_cases

[Hywan]

So, do we have the same associativity than in PHP? If yes, why not using **? We will be able to fix test suites directly too.

[Hywan]

Are tests green?

[Hywan]

Thanks for the PR!

[Hywan]

Can you explain this part please?

[osaris]

Short answer, no. Longer, I have basically copy/pasted what is done for #multiplication and updated the operation ?

[Hywan]

Ok. Are tests green?

[Hywan]

Funny: 147a38d.

[Hywan]

We have to talk about testing :-). We use ^ while PHP uses ** and we don't use the same associativity. So the problem is the following: To test Hoa\Math\Arithmetic, we generate expressions and then evaluate them against PHP and Hoa\Math\Visitor\Arithmetic (our implementation). If the result is the same, then we consider our implementation correct. However, PHP uses **, not ^, so its more difficult to test. And yes, the associativity is not the same too. And ** has been introduced in PHP5.6, while 5.4 is the lowest required PHP version for Hoa so we cannot test this feature on all platforms.

Any proposal (I have several ones, but I would like your opinion first 😉)?

[Savageman]

Maybe we can have both ^ with left-associativity and ** with right associativity?

[Hywan]

@Savageman Ole. Nop. Stop. Nada. Too much dangerous :-p. We have the pow function, which is unambiguous. I don't really understand the need for ^ or ** to be frank :-/.

[Hywan]

Let me re-phrase: I don't really understand the need for ^ or **but I am ok to implement on of them. Not both however.

[Savageman]

Then I think we should only implement ^ with left-associativity. When writing math on a paper sheet (you know, with a pen), everyone knows what ^ is and how to calculate it.

[Hywan]

@Savageman Agree. @osaris Thought? Is this PR left-associative?

[Metalaka]

As said here, PR is right associative.

@Savageman, I was thinking like you before read this:

… addition, subtraction, multiplication, and division operators are usually left-associative while an exponentiation operator is right-associative.
https://en.wikipedia.org/wiki/Operator_associativity#Examples

[Hywan]

ping?

[Savageman]

After reading the comment from @Metalaka, other sources and how its done in other languages, I now think it's best to implement with right-associativity. It makes more sense in the programming world.

[Hywan]

Ok. @osaris?

[osaris]

My PR is right-associative so what should I do now ?

[Hywan]

@osaris Write test cases.

[Hywan]

@osaris Currently, how do we test the grammar? We generated expressions based on the arithmetic grammar, and then we evaluate them twice: By PHP and by our visitor. We must obtain the same results. If we don't, either there is an error in PHP or there is an error in our visitor.

The problem is: We use ^ and PHP use **. So we are going to generate expressions with ^ while PHP expects **. Hopefully for us, both operators are right-associatives. So I reckon we could simply replace ^ by ** and it might work. Give it a try.