Language

[Colonel_Panic]

This is the first place online where I have *seen* stuff just like mine.
which makes me feel sort of "at home" I suppose.

LANGUAGE
=======
I have seen stuff like this called a "math module", and its a good description.
it continually asks you for an "expression to evaluate".

you are making variable assignments;
 the variable list "grows" at the top of the screen
if you enter:
x=2
y=3
z=((x*2)+(y*4))/2

you can watch as it keeps track and performs the evaluation(s)

this module, one just like it... is always my "ground zero" if I
am going to do any kind of "make my own language" work. Which is
why its called "language". I have used these routines several times in the past, they never fail me.

this is a stripped down special version, where it stops and shows you, step by step,
each "pass" as it reduces the math expression. In real life, it just SPITS it back out,
it seems instantaneous.

In one of my projects, I might have to calculate algebraic expressions, out of a $string.
this module will obviously be re-purposed for that.

LINUX MINT executable:
 

Language

got code?

Code: QB64: [Select]

1. NumVars = 0
2. DIM VN$(128), VV(128)
3.  
4. AnotherExpression:
5. CLS
6. FOR t = 1 TO NumVars
7.   PRINT VN$(t); " ="; VV(t)
8. NEXT t
9. PRINT "Enter expression to evaluate :";
10. LINE INPUT z$
11. PRINT "-----------------------------"
12. 'strip the spaces; meaningless in a math expression
13. N1$ = ""
14. FOR t = 1 TO LEN(z$)
15.   IF MID$(z$, t, 1) <> " " THEN N1$ = N1$ + MID$(z$, t, 1)
16. NEXT t
17. z$=N1$
18. 'check for assignment
19. VarFlag = 0
20. FOR t = 2 TO LEN(z$)
21.   IF MID$(z$, t, 1) = "=" THEN
22.     GOSUB Assign:
23.     IF VarFlag > 0 THEN z$ = EXP$: GOTO Start:
24.   END IF
25. NEXT t
26.  
27. Start:
28. pErrL = 0: pErrR = 0 'checks L's = R's
29. pErr = 0 'other error(s)
30. FOR t = 1 TO LEN(z$) 'check # of P's match
31.   IF MID$(z$, t, 1) = "(" THEN pErrL = pErrL + 1
32.   IF MID$(z$, t, 1) = ")" THEN pErrR = pErrR + 1
33. NEXT t
34. IF (pErrL <> pErrR) THEN
35.   PRINT "Fatal Error; (="; pErrL; "and )="; pErrR
36.   PRINT "press <ENTER> :";: LINE INPUT nothing$
37.   CLS: GOTO AnotherExpression:
38. END IF
39. pErrL = 0: pErrR = 0
40. FOR t = 1 TO LEN(z$)
41.   IF MID$(z$, t, 1) = "(" THEN pErrL = pErrL + 1
42.   IF MID$(z$, t, 1) = ")" THEN pErrR = pErrR + 1
43.   IF pErrL = 0 AND pErrR = 1 THEN
44.     PRINT "Fatal Error; 1st Paren must be a ("
45.     PRINT "press <ENTER> :";: LINE INPUT nothing$
46.     CLS: GOTO AnotherExpression:
47.   END IF
48. NEXT t
49.  
50. pErrL = 0: pErrR = 0
51. FOR t = LEN(z$) TO 1 STEP -1
52.   IF MID$(z$, t, 1) = "(" THEN pErrL = pErrL + 1
53.   IF MID$(z$, t, 1) = ")" THEN pErrR = pErrR + 1
54.   IF pErrL = 1 AND pErrR = 0 THEN
55.     PRINT "Fatal Error; last Paren must be a )"
56.     PRINT "press <ENTER> :";: LINE INPUT nothing$
57.     CLS: GOTO AnotherExpression
58.   END IF
59. NEXT t
60.  
61. 'done error trapping;
62. ' add Paren's to force one pass and contain any ops
63. z$ = "(" + z$ + ")"
64.  
65. RunAgain:
66. hasP = 0
67. FOR t = 1 TO LEN(z$)
68.   IF (MID$(z$, t, 1) = "(") OR (MID$(z$, t, 1) = ")") THEN hasP = 1
69. NEXT t
70. IF hasP = 1 THEN GOTO Find_inner_paren:
71. IF hasP = 0 THEN
72.   PRINT "done, final value ="; z$
73.   IF VarFlag > 0 THEN
74.     VV(VarFlag) = VAL(z$)
75.   END IF
76. END IF
77. PRINT "press <ENTER> :";
78. LINE INPUT nothing$
79. CLS: GOTO AnotherExpression:
80.  
81. Find_inner_paren:
82. PRINT z$
83.  
84. Find_left_paren:
85. FOR t1 = 1 TO LEN(z$) - 1
86.   IF MID$(z$, t1, 1) = "(" THEN
87.     GOSUB Find_Right_Paren:
88.     IF rpFlag <> 0 THEN
89.       lft$ = LEFT$(z$, t1 - 1)
90.       rht$ = RIGHT$(z$, LEN(z$) - rpFlag)
91.       ' PRINT "."; lft$; "."; rht$; ".": END
92.       GOSUB Eval:
93.       z$ = lft$ + LTRIM$(STR$(zval)) + rht$
94.       GOTO RunAgain:
95.     END IF
96.   END IF
97. NEXT t1
98.  
99. '--------------------subroutine Find_Right_Paren:-------------
100. 'driven entirely by Find_Left_Paren:
101. Find_Right_Paren:
102. rpFlag = 0
103. FOR t2 = t1 + 1 TO LEN(z$)
104.   IF MID$(z$, t2, 1) = "(" THEN
105.     rpFlag = 0
106.     RETURN
107.   END IF
108.   IF MID$(z$, t2, 1) = ")" THEN
109.     rpFlag = t2
110.     RETURN
111.   END IF
112. NEXT t2
113. rpFlag = 0: RETURN
114. '--------------------END subroutine Find_Right_Paren:----------
115.  
116. '------------------subroutine Eval:----------------------------
117. 'we are always working at the innermost Paren's
118. 'this routine reduces it to a value one operation at a time
119. Eval:
120. z1$ = MID$(z$, t1, t2 - t1 + 1)
121. EvalAgain:
122.  
123. FOR t3 = 1 TO LEN(z1$)
124.   IF MID$(z1$, t3, 1) = "^" THEN op$ = "^": GOSUB EvalAdd:: GOTO EvalAgain:
125. NEXT t3
126.  
127. FOR t3 = 1 TO LEN(z1$)
128.   IF MID$(z1$, t3, 1) = "*" THEN op$ = "*": GOSUB EvalAdd:: GOTO EvalAgain:
129.   IF MID$(z1$, t3, 1) = "/" THEN op$ = "/": GOSUB EvalAdd:: GOTO EvalAgain:
130. NEXT t3
131.  
132. FOR t3 = 1 TO LEN(z1$)
133.   IF MID$(z1$, t3, 1) = "+" THEN op$ = "+": GOSUB EvalAdd:: GOTO EvalAgain:
134.   IF MID$(z1$, t3, 1) = "-" THEN op$ = "-": GOSUB EvalAdd:: GOTO EvalAgain:
135. NEXT t3
136. GOSUB ReplaceVar:
137. PRINT "no more ops; value = "; z1$
138. zval = VAL(MID$(z1$, 2, LEN(z1$) - 2))
139. RETURN
140. '--------------------END subroutine Eval:---------------------
141.  
142. '--------------------subroutine EvalAdd:----------------------
143. 'performs the actual OPeration(s) when called by Eval:
144. EvalAdd:
145. FOR t5 = t3 - 1 TO 2 STEP -1
146.   IF INSTR("^*/+-", MID$(z1$, t5, 1)) <> 0 THEN
147.     Lend = t5 + 1: GOTO GotLeft:
148.   END IF
149. NEXT t5
150. Lend = 2
151. GotLeft:
152. L1$ = MID$(z1$, Lend, t3 - Lend)
153. FOR t4 = t3 + 1 TO LEN(z1$)
154.   IF INSTR("^*/+-", MID$(z1$, t4, 1)) <> 0 THEN
155.     Rend = t4: GOTO GotRite:
156.   END IF
157. NEXT t4
158. Rend = LEN(z1$)
159. GotRite:
160. R1$ = MID$(z1$, t3 + 1, Rend - (t3 + 1))
161. GOSUB ReplaceVars:
162. PRINT L1$; " "; op$; " "; R1$; " = ";
163. IF op$ = "+" THEN res$ = LTRIM$(STR$(VAL(L1$) + VAL(R1$)))
164. IF op$ = "-" THEN res$ = LTRIM$(STR$(VAL(L1$) - VAL(R1$)))
165. IF op$ = "*" THEN res$ = LTRIM$(STR$(VAL(L1$) * VAL(R1$)))
166. IF op$ = "/" THEN res$ = LTRIM$(STR$(VAL(L1$) / VAL(R1$)))
167. IF op$ = "^" THEN res$ = LTRIM$(STR$(VAL(L1$) ^ VAL(R1$)))
168.  
169. z1$ = LEFT$(z1$, Lend - 1) + res$ + RIGHT$(z1$, LEN(z1$) - Rend + 1)
170. PRINT z1$
171.  
172. RETURN
173. '--------------------END EvalAdd:-----------------------------
174.  
175. '--------------subroutine Assign:-----------------------------
176. 'sets up a variable assignment to the expression
177. Assign:
178. VarFlag = 0
179. Epl = t
180. NAM$ = LEFT$(z$, Epl - 1)
181. EXP$ = RIGHT$(z$, LEN(z$) - Epl)
182.  
183. namErr = 0
184. FOR t1 = 1 TO LEN(NAM$) 'legal var names are A-Z, 0-9, a-z, and _ ;cant start with a #
185.   ch$ = MID$(NAM$, t1, 1)
186.   IF t1 > 1 AND ch$ >= "0" AND ch$ <= "9" THEN GOTO DuLast: 'cant start with #
187.   IF ch$ >= "A" AND ch$ <= "Z" THEN GOTO DuLast:
188.   IF ch$ >= "a" AND ch$ <= "z" THEN GOTO DuLast:
189.   IF ch$ = "_" THEN GOTO DuLast:
190.   namErr = namErr + 1
191.   DuLast:
192. NEXT t1
193. IF namErr > 0 THEN
194.   VarFlag = 0
195.   PRINT "Fatal Error; illegal variable name"
196.   PRINT "press <enter> :";
197.   LINE INPUT nothing$
198.   RETURN
199. END IF
200.  
201. IF NumVars = 0 THEN
202.   NumVars = NumVars + 1
203.   VN$(NumVars) = NAM$
204.   VarFlag = NumVars
205.   GOTO DuLast2:
206. END IF
207. IF NumVars > 0 THEN
208.   FOR t1 = 1 TO NumVars
209.     IF NAM$ = VN$(t1) THEN
210.       VarFlag = t1
211.       GOTO DuLast2:
212.     END IF
213.   NEXT t1
214. END IF
215. 'add new variable
216. NumVars = NumVars + 1
217. VN$(NumVars) = NAM$
218. VarFlag = NumVars
219. DuLast2:
220. RETURN
221. '------------------END subroutine Assign:----------------------
222.  
223.  
224. '--------------subroutine ReplaceVars:-------------------------
225. 'checks for operands being variables
226. ReplaceVars:
227. FOR t9 = 1 TO NumVars
228.   IF VN$(t9) = L1$ THEN L1$ = LTRIM$(STR$(VV(t9)))
229.   IF VN$(t9) = R1$ THEN R1$ = LTRIM$(STR$(VV(t9)))
230. NEXT t9
231. RETURN
232. '-----------------END subroutine ReplaceVars:------------------
233.  
234.  
235. '----------------subroutine ReplaceVar:------------------------
236. 'catches case of a variable not being an operand
237. ReplaceVar:
238. chNam$ = MID$(z1$, 2, LEN(z1$) - 2)
239. FOR t9 = 1 TO NumVars
240.   IF VN$(t9) = chNam$ THEN z1$ = "(" + LTRIM$(STR$(VV(t9))) + ")"
241. NEXT t9
242. RETURN
243. '-------------------END subroutine ReplaceVar:-----------------
244.  
245.  

[Colonel_Panic]

it is *supposed* to do:

addition, subtraction, multiplication, division, exponent

if you peek at the code around line 120+ you will see where "any operation"
between 2 values, the operand could easily be inserted and the result calculated.
fairly easy to add math operations one at a time to get your library going.
I always stayed pretty "lean" and didnt ask it to do much beyond reduce algebraic.

What I do, is I check a string... and if it starts with a VARIABLE followed by an equals sign,
 then this module is a go.
If I am doing ARRAYS? I will want more than straight integer numbers, the end user
 of my software will expect to have algebraic equations for array indexes, like any programmer
 needs. This module?

well... its a STRING, and its surrounded by PARENTHESIS... the module automatically spits back the
 array index. If its a integer index, fine. if its a variable index, thats fine too. If the index of the array
 reference is an algebraic equation of existing variable assignments? Hey, it spits back the result.

if the STRING isnt a variable name followed by an equals sign?
Then its probably a COMMAND, and I would then search a list of commands in a string array.
take appropriate action.

NOTE: this is not "the actual code" I used twice before; I recreated it because I have done it a
  couple times before. If you can "trip it up" and prove it makes a parenthetical or order of operations error? That's good work on your part.

[Ed Davis]

it is *supposed* to do:

addition, subtraction, multiplication, division, exponent

...

NOTE: this is not "the actual code" I used twice before; I recreated it because I have done it a
  couple times before. If you can "trip it up" and prove it makes a parenthetical or order of operations error? That's good work on your part.

Pretty cool!

I did notice one problem - it gets:

Code: QB64: [Select]

1. -2^-3^-4

  wrong.  For instance, in QB64, the answer is:



(https://www.qb64.org/forum/data:image/png;base64,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)


However, in the posted code, the above loops:


(https://www.qb64.org/forum/data:image/png;base64,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)




The QB64 IDE also gets it wrong too, so you're in good company!




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)


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)



Hmmm.  Not sure why the pictures pasted from the clipboard didn't come through.  They looked fine on this end :(

Anyway, the answer from QB64 is:  -0.9914792

However, the IDE Math Tool gets 4096, and the posted code just loops.

Again, very cool, and thanks for sharing!

[SMcNeill]

-2^-3^-4

With the images goofed up, I can't see what the results were, but I'd suspect your expectations are wrong.

-2^-3^-4...  I'm expecting you think that's a NEGATIVE 2 there, don't you?

How about if I write it as:  0 - 2 ^ -3 ^ -4

Now, isn't that a MINUS in front of that 2?

By order of precedence, we do powers before subtraction, so that minus is evaluated last.  I'm guessing what you want is (-2) ^ -3 ^ -4 for your answer.

[Ed Davis]

-2^-3^-4

With the images goofed up, I can't see what the results were, but I'd suspect your expectations are wrong.

-2^-3^-4...  I'm expecting you think that's a NEGATIVE 2 there, don't you?

How about if I write it as:  0 - 2 ^ -3 ^ -4

Now, isn't that a MINUS in front of that 2?

By order of precedence, we do powers before subtraction, so that minus is evaluated last.  I'm guessing what you want is (-2) ^ -3 ^ -4 for your answer.

I was simply testing it.

In the QB64 IDE running:

print -2^-3^-4

Shows:  -.9914792

Are you saying that is wrong?

The IDE math tool gives 4096.

Google calculator returns:

-0.99147913749

I think QB64, google calc (and various other eval/calc programs) are correct, and the IDE math tool is wrong.

[SMcNeill]

I don't "want" anything :)

I was simply testing it.

In the QB64 IDE running:

print -2^-3^-4

Shows:  -.9914792

Are you saying that is wrong?

And the math tool gives 4096.

The google calculator returns:

-0.99147913749

I think QB64, google calc (and various other eval/calc programs) are correct, and the IDE math tool is wrong.

Of the math tool is showing 4096, it's definitely wrong.  I'll dig into it when I get some freetime (which might be after the holidays).  Thanks for reporting the issue -- the math tool is the same math which CONST uses to calculate values, so if it's wrong, CONST probably would be as well.

[david_uwi]

-2^-3^-4 evaluating left to right...
-2^-3=(1/-2)^3=-1/8
(-1/8)^-4=-8^4=4096

[FellippeHeitor]

@SMcNeill We have been discussing for a while now on Discord to replace the custom math interpreter entirely and make CONSTs "fake consts" - that is - have them be regular variables, have QB64 evaluate them at runtime, not at compile time, and just set a "don't change" flag so they are treated as consts. There's a lot to figure - scope, for instance, but that's the trending idea in the dev lounge right now.

[SMcNeill]

-2^-3^-4 evaluating left to right...
-2^-3=(1/-2)^3=-1/8
(-1/8)^-4=-8^4=4096

Even this is wrong...   That -2 in front of the 2 should be processed last as a minus sign.

Guys, run this little demo and you'll see that the math evaluator is all messed in -- in ALL cases in QB64 -- for this type of math problem:

Code: QB64: [Select]

1. Screen _NewImage(1024, 720, 32)
2.  
3. Print "Let's establish what happens when we have a minus number raised to a power: -2 ^ 2 = "; -2 ^ 2
4. Print "Order of Operations says we solve powers over subtraction, so we get -4, not 4."
5. Print
6. Print
7. Print "So let's solve the equation for -2 ^ -3 ^ -4 with that in mind:"
8. x = 2 ^ -3
9. y = x ^ -4
10.  
11. Print "- 2 ^ -3 ^ -4"
12. Print "-"; x; " ^ -4"
13. Print "-"; y
14. Print -y
15. Print
16. Print
17.  
18. Print "The true solution *should* be -4096 and not +4096."
19. Print "Somewhere along the way processing, that minus changes from minus to negative and then gets powered out to a positive..."
20. Print "Which, it really shouldn't do..."
21. Print
22. Print "But a +4096 is much more reliable of an answer than "; -2 ^ -3 ^ -4
23. Print
24. Print "How the heck do we get that anyway??"
25.  
26. Print
27. Print "Another way to do this problem is by multiplying powers:"
28. Print "For example:   x ^ y ^ z is the same as x ^ (y * z)"
29. Print "(From Power of a Power Property of Exponent)"
30. Print
31. Print "So in this case, we get -2 ^ -3 ^ -4 as being the exact same as -2 ^ (-3 * -4) = -2 ^ 12."
32. Print "And, if we solve it like before, we get:"; -2 ^ 12
33. Print
34. Print
35. Print "If we count that - in front of the two as a minus, the result is -4096."
36. Print "If it's a negation symbol, the answer is +4096."
37. Print
38. Print "Either way, it shouldn't be "; -2 ^ -3 ^ -4
39.  

The math evaluator is *almost* right, but it swaps that minus over to a negative at some point and loses track of it.

-2 ^ -3 - ^ -4 is the same as -2 ^ (-3 * -4), or -2 ^ 12 -- and that answer is -4096.

[SMcNeill]

@SMcNeill We have been discussing for a while now on Discord to replace the custom math interpreter entirely and make CONSTs "fake consts" - that is - have them be regular variables, have QB64 evaluate them at runtime, not at compile time, and just set a "don't change" flag so they are treated as consts. There's a lot to figure - scope, for instance, but that's the trending idea in the dev lounge right now.

It'd kind of defeat the purpose of CONST, but it wouldn't upset me any.  All these edge cases in math are crazy, but in this case QB64's normal evaluation methods are terribly crazy. 

The only way to get the 0.9 result is if we count the negation in ^ -3 as a minus:
x = 3 ^ -4
y = -2 ^ -x
Print y

With that a minus 3, rather than a negative 3, we'd do our power first, like above.

It's all goofed up!  :P

Honestly, if it's evaluating as I think it is, I'd expect it to error out on us just from trying to work two math operations without any value between them -- the minus and the power. 

You can't divide divide //
You can't multiply multiply **
Why can you exponent subtract ^-

That should be an exponent negation, not an exponent subtraction in there. 

[SMcNeill]

@BSpinoza  -- The problem is with how you deal with that leading minus.

In example 2, you count it as (-2 ^ -3), setting the result as a negative value you then deal with.

After that, however, you keep the two separate: PRINT -2 ^ (-3 ^ -4)

Try a simple:  PRINT -2 ^ 2.   The answer is -4, not +4, as that minus comes after the exponents are finished.  Your second example should be -(2 ^ -3) ^ -4), if we're going to stick to the same order as we do with -2 ^ 2.

It's all goofy.  Or, if it isn't, I need a *LOT* more coffee to understand why we're gettingthe results we are.

PRINT (-2) ^ (-3 ^ -4) ends up giving as a positive number, instead of a negative, after all.

[SMcNeill]

What we're doing is - (2 ^ - (3 ^ - (4)))...  Powers over negation.  None of those are negative numbers; they're all evaluated as negation operations.

Anyone who doesn't use parentheses for these type of formulas are just crazy.

[FellippeHeitor]

To be very honest with you all, all that matters to me is that this:

 

Results in the same as this:

 

 

[bplus]

+1 with Fellippe and BSpinoza.

Very interesting problem and BSinoza explained issue that Power is like Division not Communitive.

BTW Oh Interpreter would make you say p[-2,p[-3,-4]] or p[p[-2,-3],-4] ie forcing to pick which is to be done 1st and 2nd. * Gold Star for it ;-))
Update: well it did this for one:

p{p{-2,-3},-4} = 4096

and for the other it called an error,
 

It's saying the answer is a complex number!


A expression with a leading minus (separated from number by space) should force an error IMHO, or the minus is assumed to reverse(+/-) the number value immediately to the right like - -2 = 2 or - 2 = -2.

[SMcNeill]

@bplus -- you must've missed this:

What we're doing is - (2 ^ - (3 ^ - (4)))...  Powers over negation.  None of those are negative numbers; they're all evaluated as negation operations.

For proof, try this little code:

Code: QB64: [Select]

1. Print -(2 ^ -(3 ^ -(4)))
2. Print -2 ^ -3 ^ -4

And for the love of God, can somebody explain why the BEEP PRINT is printing different levels of precision here?  I thought we printed to SINGLE precision by default.  How does adding a parenthesis suddenly give us DOUBLE precision? 

EDIT:

When using powers of powers, you multiply the exponents together.

https://www.mtsac.edu/marcs/worksheet/general_topics/11properties_exponents.pdf#:~:text=not%20present%20%20%20Properties%20%20%20,%20%18%13%01%0E%17%08%14%20%20%203%20more%20rows%20

 

Since we solve left to right,

x^2^3 is the same as (x^2) ^ 3, which makes the answer x ^ 6.

In this case, if those are negative numbers, it'd be:
-2 ^ - 3 ^ -4
- 2 ^ 12
4096

But QB64 doesn't count ANY of those as negative numbers.  Instead, it counts them as negation operators.  (ie X = -X)

negate (2 ^ negate (3 ^ negate (4)))