My rpn calculator can't compute negative numbers...

[UEZ]

UEZ,

trying to figure out what you just did there,

• first you check what the token is,
• if it is a number:
•     you push it to the stack,
• if it is an operator:
•     Operand1 = first value
•         if the last char of Operand1 is a '-' then Operand1 = '-' & the value of Operand1 without the '-'
•     Operand2 = second value
•         if the last char of Operand2 is a '-' then Operand2 = '-' & the value of Operand2 without the '-'
•         (tell me if i'm wrong here, i'm a noob if it comes to regex..)
•     then let autoit evaluate(Operand1 & operator token & Operand2)

is this correct?

well, the shunting yard algorithm i made returns the tokens token by token, '3-' could never be a single token, to would rather be '3', '-'

 

 

Well, if the token is e.g. 2- then the "-" must be a the beginning to calculate properly.

What 6. and 8. is doing, is to move the "-" to the beginning  by capturing everything before "-" and adding "-" manually to the string.

It is the same as e.g.

$s = "3.125-"
ConsoleWrite("-" & StringTrimRight($s, 1) & @CRLF)

but don't ask me why I used regex.

 

Br,

UEZ

Edited September 7, 2014 by UEZ

[jchd]

Again that will never work in general. Of course you or me or anyone else can exhibit myriads of RPN expressions where sign change and subtract can use the same symbol but that doesn't work in the general case.

You have to decide whether an operator or function is monadic, dyadic, a.s.o. because confusing different arities changes the semantics of the expression.

Consider the input (1 - cos(-x)) / sqrt(5) . In RPN it is:

1 ←

x ←

± ←               ; this is sign change, whatever symbol you use except -

cos ←

- ←

5 ←

sqrt ←

/ ←

Using - as well for unary minus, you get:

1 ←

x ←

- ←               ; this is NOT sign change

cos ←

- ←

5 ←

sqrt ←

/ ←

That is: -cos(1 - x) / sqrt(5)

[TheAutomator]

UEZ,

ok, i get what you did now.

interesting idea, i'm going to test a few things with that code if i may

jchd,

I examined the udf from guinness and saw what he did 

he used whitespace to see which symbol is a minus and which is not..

here some pseudocode:

Func ShuntingYard_Calculate(sExpression)
    aChar = Split(sExpression,""); <<<split to chars>>>
    hStack = array()'Create a stack to push/pop to.
    iNumber1 = 0
    iNumber2 = 2
    sDigits = ""
    sToken = ""
    For i = 0 To UBound(aChar)
        sToken = aChar(i)
        If isnumeric(sToken) Then
            sDigits = sDigits & sToken
        ElseIf isoperator(sToken) Then
            iNumber2 = Pop(hStack)
            iNumber1 = Pop(hStack)
            call Push(rpn(iNumber1, iNumber2, sToken), hStack)
        ElseIf sToken = " " And Not(sDigits = "") Then; <<<TEST FOR '-'>>>
            If isnumeric(sDigits) Then
                iNumber1 = sDigits
                Call Push(iNumber1, hStack)
            End If
            sDigits = ""
            iNumber1 = 0
        End If
    Next
    return= Pop(hStack)
EndFunc

the problem with your code is that you cant use e.g. "1 - 5 -" as input, and this would mean that i have to fully reprogram the tokenizer and find out a way to see

if the '-' is monadic or not and replace it with another symbol if needed..

tell me if i'm wrong or misunderstood you.

Edited September 7, 2014 by TheAutomator

[jchd]

That isn't "a problem with my code", that's how a RPN calculator works. Whatever trick you use to differenciate the operations you do need to use something different. Using a separate symbol is simpler. On actual calculators the key is often marked +/- but there is no such symbol in Unicode. ± is Alt 0177 in western latin.

[guinness]

Thanks jchd.

As I implemented the shunting yard algorithm according to the specification, I see no bug in my code (see signature). 

[jchd]

Let's see where we land:

; Create postfix notation (RPN) from infix notation.
    ConsoleWrite(StringFormat('%s: == %s', '2 ^ ( 1 - - 3 )', ShuntingYard_Parse('2 ^ ( 1 - - 3 )')) & @CRLF)
    ConsoleWrite('Reference: ???' & @CRLF)

We get:

2 ^ ( 1 - - 3 ): == 2 1  - 3 - ^

Feed a rpn processor with that:

2 ←      ; stack is (2)

1 ←      ; stack is (2, 1)

-           ; does 2-1 = 1 so stack is now (1)

3 ←      ; stack is (1, 3)

-           ; does 1-3 = -2 so stack is now (-2)

^          ; error! not enough operands

That's hardly correct.

I'm not saying that you didn't follow the referenced page you linked, I'm saying that one needs distinct symbols for unary vs binary "minus" in the rpn stack. Second point, unary minus (aka sign change) wasn't considered in the algorithm you implemented: it can only deal with binary minus (aka substract) and not unary minus.

[guinness]

Well that should be pointed out in the algorithm specification.

[jchd]

True, that's why it isn't the whole story.

Unary common functions/operators like unary -, inverse (1/x), sqrt, 3root, trig functions, ..., derivative, transpose, determinant, ...

Binary functions/operators like + - * / ^ Mod, so many other

Ternary functions like PowerMod(a,b,n) which is Mod(a ^ b, n), and so on.

...

Take any 4-operation (+ - * /) very basic calculator without parenthesis capability and see how _you_ (human with a brain) handle 2*(1 - -3)

You immediately realize that -3 has to be handled with care unless the calculator offers a +/- sign change key.

Singing that you don't need a calculator for that is silly!

[TheAutomator]

jchd,

 

Ok, I see..

so if i want to do (1 - - 1) i have to replace the last '-' with something else in the tokenizer i guess?

(1 - - 1) becomes (1 - ± 1)

I also noticed that interpreters can handle multiple minus symbols after each other and even with pluses inside of them like: "1+--+-+-+1" 

(1 + - - - 1) becomes (1 + ± ± ± 1)

(- 1) becomes (± 1) then?

guinness,

 

I cant follow you there

Is the minus multiple thing something you are going to implement in your rpn calculator? (last private message you send me)

or are you simply saying that it is the job for the tokenizer to see which minus is what?

regards,

TheAutomator

[guinness]

It's not something I will implement any time soon, sorry. I thought it was an issue with my code, but it would be a workaround for the limitation of Shunting-Yard alogrithm.

I only created the Shunting-Yard algorithm concept as I was bored at the time and just interested in porting something I had previously created in C#.

[jchd]

My intention wasn't to spread FUD (Fear, Uncertainty and Doubt) but simply to draw attention on a possible pitfall that could be painful to fix after the fact.