⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

;Task: Create a stack-based evaluator for an expression in [[wp:Reverse Polish notation|reverse Polish notation (RPN)]] that also shows the changes in the stack as each individual token is processed ''as a table''.

• Assume an input of a correct, space separated, string of tokens of an RPN expression

• Test with the RPN expression generated from the [[Parsing/Shunting-yard algorithm]] task:

```  <big><big><code> 3 4 2 * 1 5 - 2 3 ^ ^ / + </code></big></big>
```
• Print or display the output here

;Notes:

• '''^''' means exponentiation in the expression above.
• '''/''' means division.

• [[Parsing/Shunting-yard algorithm]] for a method of generating an RPN from an infix expression.
• Several solutions to [[24 game/Solve]] make use of RPN evaluators (although tracing how they work is not a part of that task).
• [[Parsing/RPN to infix conversion]].
• [[Arithmetic evaluation]].

## 360 Assembly

{{trans|FORTRAN}} For concision, only integer arithmetic is handled, but input numbers can be of any length. The formal task is not completed, but the spirit of it is.

```*        RPN calculator         RC 25/01/2019
REVPOL   CSECT
USING  REVPOL,R13         base register
B      72(R15)            skip savearea
DC     17F'0'             savearea
STM    R14,R12,12(R13)    save previous context
XPRNT  TEXT,L'TEXT        print expression !?
L      R4,0               js=0  offset in stack
LA     R5,0               ns=0  number of stack items
LA     R6,0               jt=0  offset in text
LA     R7,TEXT            r7=@text
MVC    CC,0(R7)           cc first char of token
DO WHILE=(CLI,CC,NE,X'00')  do while cc<>'0'x
MVC    CTOK,=CL5' '         ctok=''
MVC    CTOK(1),CC           ctok=cc
CLI    CC,C' '              if cc=' '
BE     ITERATE              then goto iterate
IF CLI,CC,GE,C'0',AND,CLI,CC,LE,C'9' THEN
XDECI  R2,0(R7)             r2=cint(text); r1=@text
ST     R2,STACK(R4)         stack(js)=cc
SR     R1,R7                lt  length of token
BCTR   R1,0                 lt-1
EX     R1,MVCV              MVC CTOK("R1"),0(R7)
AR     R6,R1                jt+=lt-1
AR     R7,R1                @text+=lt-1
LA     R4,4(R4)             js+=4
LA     R5,1(R5)             ns++
ELSE     ,                    else
MVC    DEED,=C'Exec'        deed='Exec'
LA     R9,STACK-8(R4)       @stack(j-1)
IF CLI,CC,EQ,C'+' THEN        if cc='+' then
L      R1,STACK-8(R4)         stack(j-1)
A      R1,STACK-4(R4)         stack(j-1)+stack(j)
ST     R1,0(R9)               stack(j-1)=stack(j-1)+stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'-' THEN        if cc='-' then
L      R1,STACK-8(R4)         stack(j-1)
S      R1,STACK-4(R4)         stack(j-1)-stack(j)
ST     R1,0(R9)               stack(j-1)=stack(j-1)-stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'*' THEN        if cc='*' then
L      R3,STACK-8(R4)         stack(j-1)
M      R2,STACK-4(R4)         stack(j-1)*stack(j)
ST     R3,0(R9)               stack(j-1)=stack(j-1)*stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'/' THEN        if cc='/' then
L      R2,STACK-8(R4)         stack(j-1)
SRDA   R2,32                  for sign propagation
D      R2,STACK-4(R4)         stack(j-1)/stack(j)
ST     R3,0(R9)               stack(j-1)=stack(j-1)/stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'^' THEN        if cc='^' then
LA     R3,1                   r3=1
L      R0,STACK-4(R4)         r0=stack(j) [loop count]
EXPONENT M      R2,STACK-8(R4)         r3=r3*stack(j-1)
BCT    R0,EXPONENT            if r0--<>0 then goto exponent
ST     R3,0(R9)               stack(j-1)=stack(j-1)^stack(j)
ENDIF    ,                    endif
S      R4,=F'4'             js-=4
BCTR   R5,0                 ns--
ENDIF    ,                  endif
MVC    PG,=CL80' '          clean buffer
MVC    PG(4),DEED           output deed
MVC    PG+5(5),CTOK         output cc
MVC    PG+11(6),=C'Stack:'  output
LA     R2,1                 i=1
LA     R3,STACK             @stack
LA     R9,PG+18             @buffer
DO WHILE=(CR,R2,LE,R5)        do i=1 to ns
L      R1,0(R3)               stack(i)
XDECO  R1,XDEC                edit stack(i)
MVC    0(5,R9),XDEC+7         output stack(i)
LA     R2,1(R2)               i=i+1
LA     R3,4(R3)               @stack+=4
LA     R9,6(R9)               @buffer+=6
ENDDO    ,                    enddo
XPRNT  PG,L'PG              print
ITERATE  LA     R6,1(R6)             jt++
LA     R7,1(R7)             @text++
MVC    CC,0(R7)             cc next char
ENDDO    ,                  enddo
L      R1,STACK           stack(1)
XDECO  R1,XDEC            edit stack(1)
MVC    XDEC(4),=C'Val='   output
XPRNT  XDEC,L'XDEC        print stack(1)
L      R13,4(0,R13)       restore previous savearea pointer
LM     R14,R12,12(R13)    restore previous context
XR     R15,R15            rc=0
BR     R14                exit
MVCV     MVC    CTOK(0),0(R7)      patern mvc
TEXT     DC     C'3 4 2 * 1 5 - 2 3 ^ ^ / +',X'00'
STACK    DS     16F                stack(16)
DEED     DS     CL4
CC       DS     C
CTOK     DS     CL5
PG       DS     CL80
XDEC     DS     CL12
YREGS
END    REVPOL
```

{{out}}

```
3 4 2 * 1 5 - 2 3 ^ ^ / +
Load 2     Stack:     3     4     2
Exec *     Stack:     3     8
Load 1     Stack:     3     8     1
Load 5     Stack:     3     8     1     5
Exec -     Stack:     3     8    -4
Load 2     Stack:     3     8    -4     2
Load 3     Stack:     3     8    -4     2     3
Exec ^     Stack:     3     8    -4     8
Exec ^     Stack:     3     8 65536
Exec /     Stack:     3     0
Exec +     Stack:     3
Val=       3

```

```with Ada.Text_IO, Ada.Containers.Vectors;

procedure RPN_Calculator is

(Index_Type => Positive, Element_Type => Float);
Stack: Float_Vec.Vector;

Cursor: Positive := Input'First;
New_Cursor: Positive;

begin
loop
while Cursor <= Input'Last and then Input(Cursor)=' ' loop
Cursor := Cursor + 1;
end loop;

exit when Cursor > Input'Last;

New_Cursor := Cursor;
while New_Cursor <= Input'Last and then Input(New_Cursor) /= ' ' loop
New_Cursor := New_Cursor + 1;
end loop;

-- try to read a number and push it to the stack
declare
Last: Positive;
Value: Float;
X, Y: Float;
begin
IIO.Get(From => Input(Cursor .. New_Cursor - 1),
Item => Value,
Last => Last);
Stack.Append(Value);
Cursor := New_Cursor;

exception -- if reading the number fails, try to read an operator token
when others =>
Y := Stack.Last_Element; Stack.Delete_Last; -- pick two elements
X := Stack.Last_Element; Stack.Delete_Last; -- from the stack
case Input(Cursor) is
when '+' => Stack.Append(X+Y);
when '-' => Stack.Append(X-Y);
when '*' => Stack.Append(X*Y);
when '/' => Stack.Append(X/Y);
when '^' => Stack.Append(X ** Integer(Float'Rounding(Y)));
when others => raise Program_Error with "unecpected token '"
& Input(Cursor) & "' at column" & Integer'Image(Cursor);
end case;
Cursor := New_Cursor;
end;

for I in Stack.First_Index .. Stack.Last_Index loop
IIO.Put(Stack.Element(I), Aft => 5, Exp => 0);
end loop;
end loop;

IIO.Put(Item => Stack.Last_Element, Aft => 5, Exp => 0);

end RPN_Calculator;
```

{{out}}

```3 4 2 * 1 5 - 2 3 ^ ^ / +
3.00000
3.00000  4.00000
3.00000  4.00000  2.00000
3.00000  8.00000
3.00000  8.00000  1.00000
3.00000  8.00000  1.00000  5.00000
3.00000  8.00000 -4.00000
3.00000  8.00000 -4.00000  2.00000
3.00000  8.00000 -4.00000  2.00000  3.00000
3.00000  8.00000 -4.00000  8.00000
3.00000  8.00000 65536.00000
3.00000  0.00012
3.00012
Result =  3.00012
```

## ALGOL 68

{{works with|ALGOL 68G|Any - tested with release 2.8.win32}}

```# RPN Expression evaluator - handles numbers and + - * / ^    #
#     the right-hand operand for ^ is converted to an integer #

# expression terminator #
CHAR end of expression character = REPR 12;

# evaluates the specified rpn expression #
PROC evaluate = ( STRING rpn expression )VOID:
BEGIN

[ 256 ]REAL   stack;
INT           stack pos := 0;

# pops an element off the stack #
PROC pop = REAL:
BEGIN
stack pos -:= 1;
stack[ stack pos + 1 ]
END; # pop #

INT rpn pos := LWB rpn expression;

# evaluate tokens from the expression until we get the end of expression #
WHILE

# get the next token from the string #

STRING token type;
REAL   value;

# skip spaces #
WHILE rpn expression[ rpn pos ] = " "
DO
rpn pos +:= 1
OD;

# handle the token #
IF rpn expression[ rpn pos ] = end of expression character
THEN
# no more tokens #
FALSE

ELSE
# have a token #

IF  rpn expression[ rpn pos ] >= "0"
AND rpn expression[ rpn pos ] <= "9"
THEN
# have a number #

# find where the nmumber is in the expression #
INT  number start = rpn pos;
WHILE (   rpn expression[ rpn pos ] >= "0"
AND rpn expression[ rpn pos ] <= "9"
)
OR rpn expression[ rpn pos ] = "."
DO
rpn pos +:= 1
OD;

# read the number from the expression #
FILE number f;
associate( number f
, LOC STRING := rpn expression[ number start : rpn pos - 1 ]
);
get( number f, ( value ) );
close( number f );

token type := "number"

ELSE
# must be an operator #
CHAR op      = rpn expression[ rpn pos ];
rpn pos    +:= 1;

REAL arg1   := pop;
REAL arg2   := pop;
token type  := op;

value := IF   op = "+"
THEN
# add the top two stack elements #
arg1 + arg2
ELIF op = "-"
THEN
# subtract the top two stack elements #
arg2 - arg1
ELIF op = "*"
THEN
# multiply the top two stack elements #
arg2 * arg1
ELIF op = "/"
THEN
# divide the top two stack elements #
arg2 / arg1
ELIF op = "^"
THEN
# raise op2 to the power of op1 #
arg2 ^ ENTIER arg1
ELSE
# unknown operator #
print( ( "Unknown operator: """ + op + """", newline ) );
0
FI

FI;

TRUE
FI
DO
# push the new value on the stack and show the new stack #

stack[ stack pos +:= 1 ] := value;

print( ( ( token type + "            " )[ 1 : 8 ] ) );
FOR element FROM LWB stack TO stack pos
DO
print( ( " ", fixed( stack[ element ], 8, 4 ) ) )
OD;
print( ( newline ) )

OD;

print( ( "Result is: ", fixed( stack[ stack pos ], 12, 8 ), newline ) )

END; # evaluate #

main: (

# get the RPN expresson from the user #

STRING rpn expression;

print( ( "Enter expression: " ) );
read( ( rpn expression, newline ) );

# add a space to terminate the final token and an expression terminator #
rpn expression +:= " " + end of expression character;

# execute the expression #
evaluate( rpn expression )

)
```

{{out}}

```
Enter expression: 3 4 2 * 1 5 - 2 3 ^ ^ / +
number    +3.0000
number    +3.0000  +4.0000
number    +3.0000  +4.0000  +2.0000
*         +3.0000  +8.0000
number    +3.0000  +8.0000  +1.0000
number    +3.0000  +8.0000  +1.0000  +5.0000
-         +3.0000  +8.0000  -4.0000
number    +3.0000  +8.0000  -4.0000  +2.0000
number    +3.0000  +8.0000  -4.0000  +2.0000  +3.0000
^         +3.0000  +8.0000  -4.0000  +8.0000
^         +3.0000  +8.0000 +65536.0
/         +3.0000  +0.0001
+         +3.0001
Result is:  +3.00012207

```

## ANSI Standard BASIC

```1000 DECLARE EXTERNAL SUB rpn
1010 PUBLIC NUMERIC R(64)                             ! stack
1020 PUBLIC STRING expn\$                              ! for keyboard input
1030 PUBLIC NUMERIC i, lenn, n, true, false           ! global values
1040 LET true = -1
1050 LET false = 0
1060 DO
1070    PRINT "enter an RPN expression:"
1080    INPUT expn\$
1090    IF LEN( expn\$ ) = 0 THEN EXIT DO
1100    PRINT "expn: ";expn\$
1110    CALL rpn( expn\$ )
1120 LOOP
1130 END
1140 !
1150 ! interpret reverse polish (postfix) expression
1160 EXTERNAL SUB rpn( expn\$ )
1170 DECLARE EXTERNAL FUNCTION is_digit, get_number
1180 DECLARE EXTERNAL SUB print_stack
1190 DECLARE STRING ch\$
1200 LET expn\$ = expn\$ & " "                          ! must terminate line with space
1210 LET lenn = LEN( expn\$ )
1220 LET i = 0
1230 LET n = 1
1240 LET R(n) = 0.0                                   ! push zero for unary operations
1250 DO
1260    IF i >= lenn THEN EXIT DO                     ! at end of line
1270    LET i = i + 1
1280    IF expn\$(i:i) <> " " THEN                     ! skip white spaces
1290       IF is_digit( expn\$(i:i) ) = true THEN      ! push number onto stack
1300          LET n = n + 1
1310          LET R(n) = get_number
1320          CALL print_stack
1330       ELSEIF expn\$(i:i) = "+" then               ! add and pop stack
1340          IF n < 2 THEN
1350             PRINT "stack underflow"
1360          ELSE
1370             LET R(n-1) = R(n-1) + R(n)
1380             LET n = n - 1
1390             CALL print_stack
1400          END IF
1410       ELSEIF expn\$(i:i) = "-" then               ! subtract and pop stack
1420          IF n < 2 THEN
1430             PRINT "stack underflow"
1440          ELSE
1450             LET R(n-1) = R(n-1) - R(n)
1460             LET n = n - 1
1470             CALL print_stack
1480          END IF
1490       ELSEIF expn\$(i:i) = "*" then               ! multiply and pop stack
1500          IF n < 2 THEN
1510             PRINT "stack underflow"
1520          ELSE
1530             LET R(n-1) = R(n-1) * R(n)
1540             LET n = n - 1
1550             CALL print_stack
1560          END IF
1570       ELSEIF expn\$(i:i) = "/" THEN               ! divide and pop stack
1580          IF n < 2 THEN
1590             PRINT "stack underflow"
1600          ELSE
1610             LET R(n-1) = R(n-1) / R(n)
1620             LET n = n - 1
1630             CALL print_stack
1640          END IF
1650       ELSEIF expn\$(i:i) = "^" THEN               ! raise to power and pop stack
1660          IF n < 2 THEN
1670             PRINT "stack underflow"
1680          ELSE
1690             LET R(n-1) = R(n-1) ^ R(n)
1700             LET n = n - 1
1710             CALL print_stack
1720          END IF
1730       ELSE
1740          PRINT REPEAT\$( " ", i+5 ); "^ error"
1750          EXIT DO
1760       END IF
1770    END IF
1780 LOOP
1790 PRINT "result: "; R(n)                           ! end of main program
1800 END SUB
1810 !
1820 ! extract a number from a string
1830 EXTERNAL FUNCTION get_number
1840 DECLARE EXTERNAL FUNCTION is_digit
1850 LET j = 1                                        ! start of number string
1860 DECLARE STRING number\$                           ! buffer for conversion
1870 DO                                               ! get integer part
1880    LET number\$(j:j) = expn\$(i:i)
1890    LET i = i + 1
1900    LET j = j + 1
1910    IF is_digit( expn\$(i:i) ) = false THEN
1920       IF expn\$(i:i) = "." then
1930          LET number\$(j:j) = expn\$(i:i)           ! include decimal point
1940          LET i = i + 1
1950          LET j = j + 1
1960          DO WHILE is_digit( expn\$(i:i) ) = true  ! get fractional part
1970             LET number\$(j:j) = expn\$(i:i)
1980             LET i = i + 1
1990             LET j = j + 1
2000          LOOP
2010       END IF
2020       EXIT DO
2030    END IF
2040 LOOP
2050 LET get_number = VAL( number\$ )
2060 END FUNCTION
2070 !
2080 ! check for digit character
2090 EXTERNAL FUNCTION is_digit( ch\$ )
2100 IF "0" <= expn\$(i:i) AND expn\$(i:i) <= "9" THEN
2110    LET is_digit = true
2120 ELSE
2130    LET is_digit = false
2140 END IF
2150 END FUNCTION
2160 !
2170 EXTERNAL SUB print_stack
2180 PRINT expn\$(i:i);"    ";
2190 FOR ptr=n TO 2 STEP -1
2200    PRINT USING "-----%.####":R(ptr);
2210 NEXT ptr
2220 PRINT
2230 END SUB
```

## ANTLR

[[File:Rpn.png|left|rpnC]] [[File:rpnCNum.png|left|rpnC]] [[File:RpnCop.png|left|rpnC]]

### Java

```
grammar rpnC ;
//
//  rpn Calculator
//
//  Nigel Galloway - April 7th., 2012
//
@members {
Stack<Double> s = new Stack<Double>();
}
rpn	:	(WS* (num|op) (WS | WS* NEWLINE {System.out.println(s.pop());}))*;
num	:	'-'? Digit+ ('.' Digit+)? {s.push(Double.parseDouble(\$num.text));};
Digit	:	'0'..'9';
op	:	'-' {double x = s.pop(); s.push(s.pop() - x);}
|	'/' {double x = s.pop(); s.push(s.pop() / x);}
|	'*' {s.push(s.pop() * s.pop());}
|	'^' {double x = s.pop(); s.push(Math.pow(s.pop(), x));}
|	'+' {s.push(s.pop() + s.pop());};
WS	:	(' ' | '\t'){skip()};
NEWLINE	:	'\r'? '\n';

```

Produces:

```
>java Test
3 4 2 * 1 5 - 2 3 ^ ^ / +
^Z
3.0001220703125

```

## AutoHotkey

{{works with|AutoHotkey_L}} Output is in clipboard.

```evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
evalRPN(s){
stack := []
out := "For RPN expression: '" s "'`r`n`r`nTOKEN`t`tACTION`t`t`tSTACK`r`n"
Loop Parse, s
If A_LoopField is number
t .= A_LoopField
else
{
If t
stack.Insert(t)
, out .= t "`tPush num onto top of stack`t" stackShow(stack) "`r`n"
, t := ""
If InStr("+-/*^", l := A_LoopField)
{
a := stack.Remove(), b := stack.Remove()
stack.Insert(	 l = "+" ? b + a
:l = "-" ? b - a
:l = "*" ? b * a
:l = "/" ? b / a
:l = "^" ? b **a
:0	)
out .= l "`tApply op " l " to top of stack`t" stackShow(stack) "`r`n"
}
}
r := stack.Remove()
out .= "`r`n The final output value is: '" r "'"
clipboard := out
return r
}
StackShow(stack){
for each, value in stack
out .= A_Space value
return subStr(out, 2)
}
```

{{out}}

```For RPN expression: '3 4 2 * 1 5 - 2 3 ^ ^ / +'

TOKEN		ACTION			STACK
3	Push num onto top of stack	3
4	Push num onto top of stack	3 4
2	Push num onto top of stack	3 4 2
*	Apply op * to top of stack	3 8
1	Push num onto top of stack	3 8 1
5	Push num onto top of stack	3 8 1 5
-	Apply op - to top of stack	3 8 -4
2	Push num onto top of stack	3 8 -4 2
3	Push num onto top of stack	3 8 -4 2 3
^	Apply op ^ to top of stack	3 8 -4 8
^	Apply op ^ to top of stack	3 8 65536
/	Apply op / to top of stack	3 0.000122
+	Apply op + to top of stack	3.000122

The final output value is: '3.000122'
```

## BBC BASIC

```      @% = &60B
RPN\$ = "3 4 2 * 1 5 - 2 3 ^ ^ / +"

DIM Stack(1000)
SP% = 0

FOR i% = 1 TO LEN(RPN\$)
Token\$ = MID\$(RPN\$,i%,1)
IF Token\$ <> " " THEN
PRINT Token\$ " :";
CASE Token\$ OF
WHEN "+": PROCpush(FNpop + FNpop)
WHEN "-": PROCpush(-FNpop + FNpop)
WHEN "*": PROCpush(FNpop * FNpop)
WHEN "/": n = FNpop : PROCpush(FNpop / n)
WHEN "^": n = FNpop : PROCpush(FNpop ^ n)
WHEN "0","1","2","3","4","5","6","7","8","9":
PROCpush(VALMID\$(RPN\$,i%))
WHILE ASCMID\$(RPN\$,i%)>=48 AND ASCMID\$(RPN\$,1)<=57
i% += 1
ENDWHILE
ENDCASE
FOR j% = SP%-1 TO 0 STEP -1 : PRINT Stack(j%); : NEXT
PRINT
ENDIF
NEXT i%
END

DEF PROCpush(n)
IF SP% > DIM(Stack(),1) ERROR 100, "Stack full"
Stack(SP%) = n
SP% += 1
ENDPROC

DEF FNpop
IF SP% = 0 ERROR 100, "Stack empty"
SP% -= 1
= Stack(SP%)
```

{{out}}

```
3 :          3
4 :          4          3
2 :          2          4          3
* :          8          3
1 :          1          8          3
5 :          5          1          8          3
- :         -4          8          3
2 :          2         -4          8          3
3 :          3          2         -4          8          3
^ :          8         -4          8          3
^ :      65536          8          3
/ : 0.00012207          3
+ :    3.00012

```

## Bracmat

```(  ( show
=   line a
.   \n:?line
&   whl
' (!arg:%?a ?arg&!a " " !line:?line)
& put\$(str\$!line)
)
& :?stack
&   map
\$ ( (
=   a b
.   show\$(!arg !stack)
&     (     !arg
: ( "+"
| "-"
| "*"
| "/"
| "^"
)
& !stack:%?a %?b ?stack
& ( !arg:"+"&!a+!b
| !arg:"-"&-1*!a+!b
| !arg:"*"&!a*!b
| !arg:"/"&!a*!b^-1
| !a^!b
)
| !arg
)
!stack
: ?stack
)
. vap\$((=.!arg).get'(,STR)." ")
)
& out\$!stack
)
```

Input from keyboard:

```3 4 2 * 1 5 - 2 3 ^ ^ / +
```

Output:

```3
3 4
3 4 2
3 4 2 *
3 8 1
3 8 1 5
3 8 1 5 -
3 8 -4 2
3 8 -4 2 3
3 8 -4 2 3 ^
3 8 -4 9 ^
3 8 1/6561 /
3 1/52488 +
157465/52488
{!} 157465/52488
```

## C

```#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

void die(const char *msg)
{
fprintf(stderr, "%s", msg);
abort();
}

#define MAX_D 256
double stack[MAX_D];
int depth;

void push(double v)
{
if (depth >= MAX_D) die("stack overflow\n");
stack[depth++] = v;
}

double pop()
{
if (!depth) die("stack underflow\n");
return stack[--depth];
}

double rpn(char *s)
{
double a, b;
int i;
char *e, *w = " \t\n\r\f";

for (s = strtok(s, w); s; s = strtok(0, w)) {
a = strtod(s, &e);
if (e > s)		printf(" :"), push(a);
#define binop(x) printf("%c:", *s), b = pop(), a = pop(), push(x)
else if (*s == '+')	binop(a + b);
else if (*s == '-')	binop(a - b);
else if (*s == '*')	binop(a * b);
else if (*s == '/')	binop(a / b);
else if (*s == '^')	binop(pow(a, b));
#undef binop
else {
fprintf(stderr, "'%c': ", *s);
die("unknown oeprator\n");
}
for (i = depth; i-- || 0 * putchar('\n'); )
printf(" %g", stack[i]);
}

if (depth != 1) die("stack leftover\n");

return pop();
}

int main(void)
{
char s[] = " 3 4 2 * 1 5 - 2 3 ^ ^ / + ";
printf("%g\n", rpn(s));
return 0;
}
```

It's also possible to parse RPN string backwards and recursively; good luck printing out your token stack ''as a table'': there isn't one.

```#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <string.h>
#include <math.h>

#define die(msg) fprintf(stderr, msg"\n"), abort();
double get(const char *s, const char *e, char **new_e)
{
const char *t;
double a, b;

for (e--; e >= s && isspace(*e); e--);
for (t = e; t > s && !isspace(t[-1]); t--);

if (t < s) die("underflow");

#define get2(expr) b = get(s, t, (char **)&t), a = get(s, t, (char **)&t), a = expr
a = strtod(t, (char **)&e);
if (e <= t) {
if	(t[0] == '+') get2(a + b);
else if (t[0] == '-') get2(a - b);
else if (t[0] == '*') get2(a * b);
else if (t[0] == '/') get2(a / b);
else if (t[0] == '^') get2(pow(a, b));
else {
fprintf(stderr, "'%c': ", t[0]);
die("unknown token");
}
}
#undef get2

*(const char **)new_e = t;
return a;
}

double rpn(const char *s)
{
const char *e = s + strlen(s);
double v = get(s, e, (char**)&e);

while (e > s && isspace(e[-1])) e--;
if (e == s) return v;

fprintf(stderr, "\"%.*s\": ", e - s, s);
die("front garbage");
}

int main(void)
{
printf("%g\n", rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +"));
return 0;
}
```

## C++

```#include <vector>
#include <string>
#include <sstream>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <iterator>
#include <cstdlib>

double rpn(const std::string &expr){
std::istringstream iss(expr);
std::vector<double> stack;
std::cout << "Input\tOperation\tStack after" << std::endl;
std::string token;
while (iss >> token) {
std::cout << token << "\t";
double tokenNum;
if (std::istringstream(token) >> tokenNum) {
std::cout << "Push\t\t";
stack.push_back(tokenNum);
} else {
std::cout << "Operate\t\t";
double secondOperand = stack.back();
stack.pop_back();
double firstOperand = stack.back();
stack.pop_back();
if (token == "*")
stack.push_back(firstOperand * secondOperand);
else if (token == "/")
stack.push_back(firstOperand / secondOperand);
else if (token == "-")
stack.push_back(firstOperand - secondOperand);
else if (token == "+")
stack.push_back(firstOperand + secondOperand);
else if (token == "^")
stack.push_back(std::pow(firstOperand, secondOperand));
else { //just in case
std::cerr << "Error" << std::endl;
std::exit(1);
}
}
std::copy(stack.begin(), stack.end(), std::ostream_iterator<double>(std::cout, " "));
std::cout << std::endl;
}
return stack.back();
}

int main() {
std::string s = " 3 4 2 * 1 5 - 2 3 ^ ^ / + ";
std::cout << "Final answer: " << rpn(s) << std::endl;

return 0;
}
```

{{out}}

```
Input	Operation	Stack after
3	Push		3
4	Push		3 4
2	Push		3 4 2
*	Operate		3 8
1	Push		3 8 1
5	Push		3 8 1 5
-	Operate		3 8 -4
2	Push		3 8 -4 2
3	Push		3 8 -4 2 3
^	Operate		3 8 -4 8
^	Operate		3 8 65536
/	Operate		3 0.00012207
+	Operate		3.00012

```

## C#

```using System;
using System.Collections.Generic;
using System.Linq;
using System.Globalization;

namespace RPNEvaluator
{
class RPNEvaluator
{
static void Main(string[] args)
{

string rpn = "3 4 2 * 1 5 - 2 3 ^ ^ / +";
Console.WriteLine("{0}\n", rpn);

decimal result = CalculateRPN(rpn);
Console.WriteLine("\nResult is {0}", result);
}

static decimal CalculateRPN(string rpn)
{
string[] rpnTokens = rpn.Split(' ');
Stack<decimal> stack = new Stack<decimal>();
decimal number = decimal.Zero;

foreach (string token in rpnTokens)
{
if (decimal.TryParse(token, out number))
{
stack.Push(number);
}
else
{
switch (token)
{
case "^":
case "pow":
{
number = stack.Pop();
stack.Push((decimal)Math.Pow((double)stack.Pop(), (double)number));
break;
}
case "ln":
{
stack.Push((decimal)Math.Log((double)stack.Pop(), Math.E));
break;
}
case "sqrt":
{
stack.Push((decimal)Math.Sqrt((double)stack.Pop()));
break;
}
case "*":
{
stack.Push(stack.Pop() * stack.Pop());
break;
}
case "/":
{
number = stack.Pop();
stack.Push(stack.Pop() / number);
break;
}
case "+":
{
stack.Push(stack.Pop() + stack.Pop());
break;
}
case "-":
{
number = stack.Pop();
stack.Push(stack.Pop() - number);
break;
}
default:
Console.WriteLine("Error in CalculateRPN(string) Method!");
break;
}
}
PrintState(stack);
}

return stack.Pop();
}

static void PrintState(Stack<decimal> stack)
{
decimal[] arr = stack.ToArray();

for (int i = arr.Length - 1; i >= 0; i--)
{
Console.Write("{0,-8:F3}", arr[i]);
}

Console.WriteLine();
}
}
}
```

{{out}}

```
3 4 2 * 1 5 - 2 3 ^ ^ / +

3.000
3.000   4.000
3.000   4.000   2.000
3.000   8.000
3.000   8.000   1.000
3.000   8.000   1.000   5.000
3.000   8.000   -4.000
3.000   8.000   -4.000  2.000
3.000   8.000   -4.000  2.000   3.000
3.000   8.000   -4.000  8.000
3.000   8.000   65536.000
3.000   0.000
3.000

Result is 3.0001220703125

```

## Ceylon

import ceylon.collection {

```ArrayList
```

}

shared void run() {

```value ops = map {
"+" -> plus<Float>,
"*" -> times<Float>,
"-" -> ((Float a, Float b) => a - b),
"/" -> ((Float a, Float b) => a / b),
"^" -> ((Float a, Float b) => a ^ b)
};

void printTableRow(String|Float token, String description, {Float*} stack) {
}

function calculate(String input) {

value stack = ArrayList<Float>();
value tokens = input.split().map((String element)
=> if(ops.keys.contains(element)) then element else parseFloat(element));

print("Token   Operation                     Stack");

for(token in tokens.coalesced) {
if(is Float token) {
stack.push(token);
printTableRow(token, "push", stack);
} else if(exists op = ops[token], exists first = stack.pop(), exists second = stack.pop()) {
value result = op(second, first);
stack.push(result);
printTableRow(token, "perform ``token`` on ``formatFloat(second, 1, 1)`` and ``formatFloat(first, 1, 1)``", stack);
} else {
}
}
return stack.pop();
}

print(calculate("3 4 2 * 1 5 - 2 3 ^ ^ / +"));
```

}

```
{{out}}

```txt
Token   Operation                     Stack
3.0     push                          { 3.0 }
4.0     push                          { 3.0, 4.0 }
2.0     push                          { 3.0, 4.0, 2.0 }
*       perform * on 4.0 and 2.0      { 3.0, 8.0 }
1.0     push                          { 3.0, 8.0, 1.0 }
5.0     push                          { 3.0, 8.0, 1.0, 5.0 }
-       perform - on 1.0 and 5.0      { 3.0, 8.0, -4.0 }
2.0     push                          { 3.0, 8.0, -4.0, 2.0 }
3.0     push                          { 3.0, 8.0, -4.0, 2.0, 3.0 }
^       perform ^ on 2.0 and 3.0      { 3.0, 8.0, -4.0, 8.0 }
^       perform ^ on -4.0 and 8.0     { 3.0, 8.0, 65536.0 }
/       perform / on 8.0 and 65536.0  { 3.0, 1.220703125E-4 }
+       perform + on 3.0 and 0.0      { 3.0001220703125 }
3.0001220703125

```

## Clojure

This would be a lot simpler and generic if we were allowed to use something other than ^ for exponentiation. ^ isn't a legal clojure symbol.

```
(ns rosettacode.parsing-rpn-calculator-algorithm
(:require clojure.math.numeric-tower
clojure.string
clojure.pprint))

(def operators
"the only allowable operators for our calculator"
{"+" +
"-" -
"*" *
"/" /
"^" clojure.math.numeric-tower/expt})

(defn rpn
"takes a string and returns a lazy-seq of all the stacks"
[string]
(letfn [(rpn-reducer [stack item] ; this takes a stack and one item and makes a new stack
(if (contains? operators item)
(let [operand-1 (peek stack) ; if we used lists instead of vectors, we could use destructuring, but stacks would look backwards
stack-1 (pop stack)]   ;we're assuming that all the operators are binary
(conj (pop stack-1)
((operators item) (peek stack-1) operand-1)))
(conj stack (Long. item))))] ; if it wasn't an operator, we'll assume it's a long. Could choose bigint, or even read-line
(reductions rpn-reducer [] (clojure.string/split string #"\s+")))) ;reductions is like reduce only shows all the intermediate steps

(let [stacks (rpn "3 4 2 * 1 5 - 2 3 ^ ^ / +")] ;bind it so we can output the answer separately.
(println "stacks: ")
(clojure.pprint/pprint stacks)
(print "answer:" (->> stacks last first)))

```

{{out}} stacks: ([] [3] [3 4] [3 4 2] [3 8] [3 8 1] [3 8 1 5] [3 8 -4] [3 8 -4 2] [3 8 -4 2 3] [3 8 -4 8] [3 8 65536] [3 1/8192] [24577/8192]) answer: 24577/8192

## Common Lisp

```(setf (symbol-function '^) #'expt)  ; Make ^ an alias for EXPT

(defun print-stack (token stack)
(format T "~a: ~{~a ~}~%" token (reverse stack)))

(defun rpn (tokens &key stack verbose )
(cond
((and (not tokens) (not stack)) 0)
((not tokens) (car stack))
(T
(let* ((current (car tokens))
(next-stack (if (numberp current)
(cons current stack)
(let* ((arg2 (car stack))
(fun (car tokens)))
(cons (funcall fun arg1 arg2) (cddr stack))))))
(when verbose
(print-stack current next-stack))
(rpn (cdr tokens) :stack next-stack :verbose verbose)))))
```

{{Out}}

```>(defparameter *tokens* '(3 4 2 * 1 5 - 2 3 ^ ^ / +))

*TOKENS*
> (rpn *tokens*)

24577/8192
> (rpn *tokens* :verbose T)
3: 3
4: 3 4
2: 3 4 2
*: 3 8
1: 3 8 1
5: 3 8 1 5
-: 3 8 -4
2: 3 8 -4 2
3: 3 8 -4 2 3
^: 3 8 -4 8
^: 3 8 65536
/: 3 1/8192
+: 24577/8192
24577/8192
```

## EchoLisp

```
;; RPN (postfix) evaluator

(lib 'hash)

(define OPS (make-hash))
(hash-set OPS "^" expt)
(hash-set OPS "*" *)
(hash-set OPS "/" //) ;; float divide
(hash-set OPS "+" +)
(hash-set OPS "-" -)

(define (op? op) (hash-ref OPS op))

;; algorithm : https://en.wikipedia.org/wiki/Reverse_Polish_notation#Postfix_algorithm

(define (calculator rpn S)
(for ((token rpn))
(if (op? token)
(let [(op2 (pop S)) (op1 (pop S))]
(unless (and op1 op2) (error "cannot calculate expression at:" token))
(push S ((op? token) op1 op2))
(writeln op1 token op2 "→" (stack-top S)))
(push S (string->number token))))
(pop S))

(define S (stack 'S))
(calculator (text-parse rpn) S ))

```

{{out}}

```
(task "3 4 2 * 1 5 - 2 3 ^ ^ / +")

4      *     2     →     8
1      -     5     →     -4
2      ^     3     →     8
-4     ^     8     →     65536
8     /     65536     →     0.0001220703125
3     +     0.0001220703125     →     3.0001220703125

→ 3.0001220703125

;; RATIONAL CALCULATOR
(hash-set OPS "/" /) ;; rational divide
(task "3 4 2 * 1 5 - 2 3 ^ ^ / +")

4      *     2     →     8
1      -     5     →     -4
2      ^     3     →     8
-4     ^     8     →     65536
8     /     65536     →     1/8192
3     +     1/8192     →     24577/8192

→ 24577/8192

```

## Ela

```open string generic monad io

type OpType = Push | Operate
deriving Show

type Op = Op (OpType typ) input stack
deriving Show

parse str = split " " str

eval stack []      = []
eval stack (x::xs) = op :: eval nst xs
where (op, nst)  = conv x stack
conv "+"@x = operate x (+)
conv "-"@x = operate x (-)
conv "*"@x = operate x (*)
conv "/"@x = operate x (/)
conv "^"@x = operate x (**)
conv x     = \stack ->
let n = gread x::stack in
(Op Push x n, n)
operate input fn (x::y::ys) =
let n = (y `fn` x) :: ys in
(Op Operate input n, n)

print_line (Op typ input stack) = do
putStr input
putStr "\t"
put typ
putStr "\t\t"
putLn stack

print ((Op typ input stack)@x::xs) lv = print_line x `seq` print xs (head stack)
print [] lv = lv

print_result xs = do
putStrLn "Input\tOperation\tStack after"
res <- return \$ print xs 0
putStrLn ("Result: " ++ show res)

res = parse "3 4 2 * 1 5 - 2 3 ^ ^ / +" |> eval []
print_result res ::: IO
```

{{out}}

```Input	Operation	Stack after
3	Push		[3]
4	Push		[4,3]
2	Push		[2,4,3]
*	Operate		[8,3]
1	Push		[1,8,3]
5	Push		[5,1,8,3]
-	Operate		[-4,8,3]
2	Push		[2,-4,8,3]
3	Push		[3,2,-4,8,3]
^	Operate		[8,-4,8,3]
^	Operate		[65536,8,3]
/	Operate		[0.0001220703f,3]
+	Operate		[3.000122f]
Result: 3.000122f
```

## D

{{trans|Go}}

```import std.stdio, std.string, std.conv, std.typetuple;

void main() {
auto input = "3 4 2 * 1 5 - 2 3 ^ ^ / +";
writeln("For postfix expression: ", input);
writeln("\nToken            Action            Stack");
real[] stack;
foreach (tok; input.split()) {
auto action = "Apply op to top of stack";
switch (tok) {
foreach (o; TypeTuple!("+", "-", "*", "/", "^")) {
case o:
mixin("stack[\$ - 2]" ~
(o == "^" ? "^^" : o) ~ "=stack[\$ - 1];");
stack.length--;
break;
}
break;
default:
action = "Push num onto top of stack";
stack ~= to!real(tok);
}
writefln("%3s    %-26s  %s", tok, action, stack);
}
writeln("\nThe final value is ", stack[0]);
}
```

{{out}}

```For postfix expression: 3 4 2 * 1 5 - 2 3 ^ ^ / +

Token            Action            Stack
3    Push num onto top of stack  [3]
4    Push num onto top of stack  [3, 4]
2    Push num onto top of stack  [3, 4, 2]
*    Apply op to top of stack    [3, 8]
1    Push num onto top of stack  [3, 8, 1]
5    Push num onto top of stack  [3, 8, 1, 5]
-    Apply op to top of stack    [3, 8, -4]
2    Push num onto top of stack  [3, 8, -4, 2]
3    Push num onto top of stack  [3, 8, -4, 2, 3]
^    Apply op to top of stack    [3, 8, -4, 8]
^    Apply op to top of stack    [3, 8, 65536]
/    Apply op to top of stack    [3, 0.00012207]
+    Apply op to top of stack    [3.00012]

The final value is 3.00012
```

## Erlang

```-module(rpn).
-export([eval/1]).

parse(Expression) ->
parse(string:tokens(Expression," "),[]).

parse([],Expression) ->
lists:reverse(Expression);
parse(["+"|Xs],Expression) ->
parse(Xs,[fun erlang:'+'/2|Expression]);
parse(["-"|Xs],Expression) ->
parse(Xs,[fun erlang:'-'/2|Expression]);
parse(["*"|Xs],Expression) ->
parse(Xs,[fun erlang:'*'/2|Expression]);
parse(["/"|Xs],Expression) ->
parse(Xs,[fun erlang:'/'/2|Expression]);
parse(["^"|Xs],Expression) ->
parse(Xs,[fun math:pow/2|Expression]);
parse([X|Xs],Expression) ->
{N,_} = string:to_integer(X),
parse(Xs,[N|Expression]).

%% The expression should be entered as a string of numbers and
%% operators separated by spaces. No error handling is included if
%% another string format is used.
eval(Expression) ->
eval(parse(Expression),[]).

eval([],[N]) ->
N;
eval([N|Exp],Stack) when is_number(N) ->
NewStack = [N|Stack],
print(NewStack),
eval(Exp,NewStack);
eval([F|Exp],[X,Y|Stack]) ->
NewStack = [F(Y,X)|Stack],
print(NewStack),
eval(Exp,NewStack).

print(Stack) ->
lists:map(fun (X) when is_integer(X) -> io:format("~12.12b ",[X]);
(X) when is_float(X) -> io:format("~12f ",[X]) end, Stack),
io:format("~n").
```

{{out}}

```145> rpn:eval("3 4 2 * 1 5 - 2 3 ^ ^ / +").
3
4            3
2            4            3
8            3
1            8            3
5            1            8            3
-4            8            3
2           -4            8            3
3            2           -4            8            3
8.000000           -4            8            3
65536.000000            8            3
0.000122            3
3.000122
3.0001220703125
```

As interactive script

```let reduce op = function
| b::a::r -> (op a b)::r
| _ -> failwith "invalid expression"

let interprete s = function
| "+" -> "add",    reduce ( + ) s
| "-" -> "subtr",  reduce ( - ) s
| "*" -> "mult",   reduce ( * ) s
| "/" -> "divide", reduce ( / ) s
| "^" -> "exp",    reduce ( ** ) s
| str -> "push", (System.Double.Parse str) :: s

let interp_and_show s inp =
let op,s'' = interprete s inp
printf "%5s%8s " inp op
List.iter (printf " %-6.3F") (List.rev s'')
printf "\n";
s''

let eval str =
printfn "Token  Action  Stack";
let ss = str.ToString().Split() |> Array.toList
List.fold interp_and_show [] ss
```

{{out}}

```> eval "3 4 2 * 1 5 - 2 3 ^ ^ / +";;
Token  Action  Stack
3    push  3.000
4    push  3.000  4.000
2    push  3.000  4.000  2.000
*    mult  3.000  8.000
1    push  3.000  8.000  1.000
5    push  3.000  8.000  1.000  5.000
-   subtr  3.000  8.000  -4.000
2    push  3.000  8.000  -4.000 2.000
3    push  3.000  8.000  -4.000 2.000  3.000
^     exp  3.000  8.000  -4.000 8.000
^     exp  3.000  8.000  65536.000
/  divide  3.000  0.000
val it : float list = [3.00012207]
```

## Factor

Factor is a stack-based evaluator for an expression in reverse Polish notation. In the listener:

```IN: scratchpad 3 4 2 * 1 5 - 2 3 ^ ^ / +

--- Data stack:
3+1/8192
```

To show intermediate steps:

```{ 3 4 2 * 1 5 - 2 3 ^ ^ / + } [ 1quotation ] map
[ dup pprint bl call datastack . ] each
```

{{out}}

```
[ 3 ] { 3 }
[ 4 ] { 3 4 }
[ 2 ] { 3 4 2 }
[ * ] { 3 8 }
[ 1 ] { 3 8 1 }
[ 5 ] { 3 8 1 5 }
[ - ] { 3 8 -4 }
[ 2 ] { 3 8 -4 2 }
[ 3 ] { 3 8 -4 2 3 }
[ ^ ] { 3 8 -4 8 }
[ ^ ] { 3 8 65536 }
[ / ] { 3 1/8192 }
[ + ] { 3+1/8192 }

```

## Fortran

Since the project is to demonstrate the workings of the scheme to evaluate a RPN text sequence, and the test example contains only single-digit numbers and single-character operators, there is no need to escalate to reading full integers or floating-point numbers, the code for which would swamp the details of the RPN evaluator. As a result, it is easy to scan the text via a DO-loop that works one character at a time since there is no backstepping, probing ahead, nor multi-symbol items that must be combined into a single "token" with states that must be remembered from one character to the next. With multi-character tokens, the scan would be changed to invocations of NEXTTOKEN that would lurch ahead accordingly.

The method is simple (the whole point of RPN) and the function prints a schedule of actions at each step. Possibly this semi-tabular output is what is meant by "as a table". Conveniently, all the operators take two operands and return one, so the SP accountancy can be shared. Unlike ! for example.

The source style is essentially F77 except for the trivial use of the PARAMETER statement, and CYCLE to GO TO the end of the loop when a space is encountered. With the introduction of unfixed-format source style came also the possible use of semicolons to cram more than one statement part on a line so that the CASE and its action statement can be spread across the page rather than use two lines in alternation: for this case a tabular layout results that is easier to read and check. Because the F90 MODULE protocol is not used, the function's type should be declared in the calling routine but the default type suffices.

```      REAL FUNCTION EVALRP(TEXT)	!Evaluates a Reverse Polish string.
Caution: deals with single digits only.
CHARACTER*(*) TEXT	!The RPN string.
INTEGER SP,STACKLIMIT		!Needed for the evaluation.
PARAMETER (STACKLIMIT = 6)	!This should do.
REAL*8 STACK(STACKLIMIT)		!Though with ^ there's no upper limit.
INTEGER L,D		!Assistants for the scan.
CHARACTER*4 DEED		!A scratchpad for the annotation.
CHARACTER*1 C		!The character of the moment.
WRITE (6,1) TEXT	!A function that writes messages... Improper.
1   FORMAT ("Evaluation of the Reverse Polish string ",A,//	!Still, it's good to see stuff.
1   "Char Token Action  SP:Stack...")	!Such as a heading for the trace.
SP = 0			!Commence with the stack empty.
STACK = -666		!This value should cause trouble.
DO L = 1,LEN(TEXT)	!Step through the text.
C = TEXT(L:L)			!Grab a character.
IF (C.LE." ") CYCLE		!Boring.
D = ICHAR(C) - ICHAR("0")	!Uncouth test to check for a digit.
IF (D.GE.0 .AND. D.LE.9) THEN	!Is it one?
SP = SP + 1				!By going up one.
IF (SP.GT.STACKLIMIT) STOP "Stack overflow!"	!Or, maybe not.
STACK(SP) = D			!And stashing the value.
ELSE				!Otherwise, it must be an operator.
IF (SP.LT.2) STOP "Stack underflow!"	!They all require two operands.
DEED = "XEQ"		!So, I'm about to do so.
SELECT CASE(C)		!Which one this time?
CASE("+"); STACK(SP - 1) = STACK(SP - 1) + STACK(SP)	!A + B = B + A, so it is easy.
CASE("-"); STACK(SP - 1) = STACK(SP - 1) - STACK(SP)	!A is in STACK(SP - 1), B in STACK(SP)
CASE("*"); STACK(SP - 1) = STACK(SP - 1)*STACK(SP)		!Again, order doesn't count.
CASE("/"); STACK(SP - 1) = STACK(SP - 1)/STACK(SP)		!But for division, A/B becomes A B /
CASE("^"); STACK(SP - 1) = STACK(SP - 1)**STACK(SP)	!So, this way around.
CASE DEFAULT		!This should never happen!
STOP "Unknown operator!"	!If the RPN script is indeed correct.
END SELECT			!So much for that operator.
SP = SP - 1		!All of them take two operands and make one.
END IF		!So much for that item.
WRITE (6,2) L,C,DEED,SP,STACK(1:SP)	!Reveal the state now.
2     FORMAT (I4,A6,A7,I4,":",66F14.6)	!Aligned with the heading of FORMAT 1.
END DO			!On to the next symbol.
EVALRP = STACK(1)	!The RPN string being correct, this is the result.
END	!Simple enough!

PROGRAM HSILOP
REAL V
V = EVALRP("3 4 2 * 1 5 - 2 3 ^ ^ / +")	!The specified example.
WRITE (6,*) "Result is...",V
END
```

Output...

```
Evaluation of the Reverse Polish string 3 4 2 * 1 5 - 2 3 ^ ^ / +

Char Token Action  SP:Stack...
3     4   Load   2:      3.000000      4.000000
5     2   Load   3:      3.000000      4.000000      2.000000
7     *   XEQ    2:      3.000000      8.000000
9     1   Load   3:      3.000000      8.000000      1.000000
11     5   Load   4:      3.000000      8.000000      1.000000      5.000000
13     -   XEQ    3:      3.000000      8.000000     -4.000000
15     2   Load   4:      3.000000      8.000000     -4.000000      2.000000
17     3   Load   5:      3.000000      8.000000     -4.000000      2.000000      3.000000
19     ^   XEQ    4:      3.000000      8.000000     -4.000000      8.000000
21     ^   XEQ    3:      3.000000      8.000000  65536.000000
23     /   XEQ    2:      3.000000      0.000122
25     +   XEQ    1:      3.000122
Result is...   3.000122
```

## FunL

```def evaluate( expr ) =
stack = []

for token <- expr.split( '''\s+''' )
case number( token )
Some( n ) ->
stack = n : stack
println( "push \$token: \${stack.reversed()}" )
None ->
case {'+': (+), '-': (-), '*': (*), '/': (/), '^': (^)}.>get( token )
Some( op ) ->
println( "perform \$token: \${stack.reversed()}" )
None -> error( "unrecognized operator '\$token'" )

res = evaluate( '3 4 2 * 1 5 - 2 3 ^ ^ / +' )
println( res + (if res is Integer then '' else " or \${float(res)}") )
```

{{out}}

```
push 3: [3]
push 4: [3, 4]
push 2: [3, 4, 2]
perform *: [3, 8]
push 1: [3, 8, 1]
push 5: [3, 8, 1, 5]
perform -: [3, 8, -4]
push 2: [3, 8, -4, 2]
push 3: [3, 8, -4, 2, 3]
perform ^: [3, 8, -4, 8]
perform ^: [3, 8, 65536]
perform /: [3, 1/8192]
perform +: [24577/8192]
24577/8192 or 3.0001220703125

```

## Go

No error checking.

```package main

import (
"fmt"
"math"
"strconv"
"strings"
)

var input = "3 4 2 * 1 5 - 2 3 ^ ^ / +"

func main() {
fmt.Printf("For postfix %q\n", input)
fmt.Println("\nToken            Action            Stack")
var stack []float64
for _, tok := range strings.Fields(input) {
action := "Apply op to top of stack"
switch tok {
case "+":
stack[len(stack)-2] += stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "-":
stack[len(stack)-2] -= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "*":
stack[len(stack)-2] *= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "/":
stack[len(stack)-2] /= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "^":
stack[len(stack)-2] =
math.Pow(stack[len(stack)-2], stack[len(stack)-1])
stack = stack[:len(stack)-1]
default:
action = "Push num onto top of stack"
f, _ := strconv.ParseFloat(tok, 64)
stack = append(stack, f)
}
fmt.Printf("%3s    %-26s  %v\n", tok, action, stack)
}
fmt.Println("\nThe final value is", stack[0])
}
```

{{out}}

```
For postfix "3 4 2 * 1 5 - 2 3 ^ ^ / +"

Token            Action            Stack
3    Push num onto top of stack  [3]
4    Push num onto top of stack  [3 4]
2    Push num onto top of stack  [3 4 2]
*    Apply op to top of stack    [3 8]
1    Push num onto top of stack  [3 8 1]
5    Push num onto top of stack  [3 8 1 5]
-    Apply op to top of stack    [3 8 -4]
2    Push num onto top of stack  [3 8 -4 2]
3    Push num onto top of stack  [3 8 -4 2 3]
^    Apply op to top of stack    [3 8 -4 8]
^    Apply op to top of stack    [3 8 65536]
/    Apply op to top of stack    [3 0.0001220703125]
+    Apply op to top of stack    [3.0001220703125]

The final value is 3.0001220703125

```

## Groovy

```def evaluateRPN(expression) {
def stack = [] as Stack
def binaryOp = { action -> return { action.call(stack.pop(), stack.pop()) } }
def actions = [
'+': binaryOp { a, b -> b + a },
'-': binaryOp { a, b -> b - a },
'*': binaryOp { a, b -> b * a },
'/': binaryOp { a, b -> b / a },
'^': binaryOp { a, b -> b ** a }
]
expression.split(' ').each { item ->
def action = actions[item] ?: { item as BigDecimal }
stack.push(action.call())

println "\$item: \$stack"
}
assert stack.size() == 1 : "Unbalanced Expression: \$expression (\$stack)"
stack.pop()
}
```

Test

```println evaluateRPN('3 4 2 * 1 5 - 2 3 ^ ^ / +')
```

{{out}}

```3: [3]
4: [3, 4]
2: [3, 4, 2]
*: [3, 8]
1: [3, 8, 1]
5: [3, 8, 1, 5]
-: [3, 8, -4]
2: [3, 8, -4, 2]
3: [3, 8, -4, 2, 3]
^: [3, 8, -4, 8]
^: [3, 8, 65536]
/: [3, 0.0001220703125]
+: [3.0001220703125]
3.0001220703125
```

Pure RPN calculator

```calcRPN :: String -> [Double]
calcRPN = foldl interprete [] . words

interprete s x
| x `elem` ["+","-","*","/","^"] = operate x s
where
operate op (x:y:s) = case op of
"+" -> x + y:s
"-" -> y - x:s
"*" -> x * y:s
"/" -> y / x:s
"^" -> y ** x:s
```
```λ> calcRPN "3 4 +"
[7.0]

λ> calcRPN "3 4 2 * 1 5 - 2 3 ^ ^ / +"
[3.0001220703125]

```

'''Calculation logging'''

''Pure logging''. Log as well as a result could be used as a data.

```calcRPNLog :: String -> ([Double],[(String, [Double])])
where result = scanl interprete [] commands
commands = words input
mkLog [] = ([], [])
mkLog res = (snd \$ last res, res)
```
```λ> calcRPNLog "3 4 +"
([7.0],[("3",[3.0]),("4",[4.0,3.0]),("+",[7.0])])

λ> mapM_ print \$ snd \$ calcRPNLog "3 4 2 * 1 5 - 2 3 ^ ^ / +"
("3",[3.0])
("4",[4.0,3.0])
("2",[2.0,4.0,3.0])
("*",[8.0,3.0])
("1",[1.0,8.0,3.0])
("5",[5.0,1.0,8.0,3.0])
("-",[-4.0,8.0,3.0])
("2",[2.0,-4.0,8.0,3.0])
("3",[3.0,2.0,-4.0,8.0,3.0])
("^",[8.0,-4.0,8.0,3.0])
("^",[65536.0,8.0,3.0])
("/",[1.220703125e-4,3.0])
("+",[3.0001220703125])
```

''Logging as a side effect.'' Calculator returns result in IO context:

```import Control.Monad (foldM)

calcRPNIO :: String -> IO [Double]
calcRPNIO = foldM (verbose interprete) [] . words

verbose f s x = write (x ++ "\t" ++ show res ++ "\n") >> return res
where res = f s x
```
```λ> calcRPNIO "3 4 +"
3	[3.0]
4	[4.0,3.0]
+	[7.0]
[7.0]

λ> calcRPNIO "3 4 2 * 1 5 - 2 3 ^ ^ / +"
3	[3.0]
4	[4.0,3.0]
2	[2.0,4.0,3.0]
*	[8.0,3.0]
1	[1.0,8.0,3.0]
5	[5.0,1.0,8.0,3.0]
-	[-4.0,8.0,3.0]
2	[2.0,-4.0,8.0,3.0]
3	[3.0,2.0,-4.0,8.0,3.0]
^	[8.0,-4.0,8.0,3.0]
^	[65536.0,8.0,3.0]
/	[1.220703125e-4,3.0]
+	[3.0001220703125]
[3.0001220703125]
```

Or even more general (requires FlexibleInstances and TypeFamilies extensions).

Some universal definitions:

``` Logger m where
write :: String -> m ()

instance Logger IO where write = putStr
instance a ~ String => Logger (Writer a) where write = tell

verbose2 f x y = write (show x ++ " " ++
show y ++ " ==> " ++
show res ++ "\n") >> return res
where res = f x y
```

The use case:

``` String -> m [Double]
calcRPNM = foldM (verbose interprete) [] . words
```

{{out}} in REPL

```λ> calcRPNM "3 4 2 * 1 5 - 2 3 ^ ^ / +"
[] "3" ==> [3.0]
[3.0] "4" ==> [4.0,3.0]
[4.0,3.0] "2" ==> [2.0,4.0,3.0]
[2.0,4.0,3.0] "*" ==> [8.0,3.0]
[8.0,3.0] "1" ==> [1.0,8.0,3.0]
[1.0,8.0,3.0] "5" ==> [5.0,1.0,8.0,3.0]
[5.0,1.0,8.0,3.0] "-" ==> [-4.0,8.0,3.0]
[-4.0,8.0,3.0] "2" ==> [2.0,-4.0,8.0,3.0]
[2.0,-4.0,8.0,3.0] "3" ==> [3.0,2.0,-4.0,8.0,3.0]
[3.0,2.0,-4.0,8.0,3.0] "^" ==> [8.0,-4.0,8.0,3.0]
[8.0,-4.0,8.0,3.0] "^" ==> [65536.0,8.0,3.0]
[65536.0,8.0,3.0] "/" ==> [1.220703125e-4,3.0]
[1.220703125e-4,3.0] "+" ==> [3.0001220703125]
[3.0001220703125]

λ> runWriter \$ calcRPNM "3 4 +"
([7.0],"[] \"3\" ==> [3.0]\n[3.0] \"4\" ==> [4.0,3.0]\n[4.0,3.0] \"+\" ==> [7.0]\n")
```

```procedure main()
EvalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
end

invocable all

procedure EvalRPN(expr)          #: evaluate (and trace stack) an RPN string

stack := []
expr ? until pos(0) do {
tab(many(' '))                         # consume previous seperator
token := tab(upto(' ')|0)              # get token
if token := numeric(token) then {      # ... numeric
push(stack,token)
printf("pushed numeric   %i : %s\n",token,list2string(stack))
}
else {                                 # ... operator
every b|a := pop(stack)             # pop & reverse operands
case token of {
"+"|"-"|"*"|"^"   : push(stack,token(a,b))
"/"               : push(stack,token(real(a),b))
default           : runerr(205,token)
}
printf("applied operator %s : %s\n",token,list2string(stack))
}
}
end

procedure list2string(L)         #: format list as a string
every (s := "[ ") ||:= !L || " "
return s || "]"
end
```

{{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/printf.icn printf.icn provides formatting]

{{out}}

```pushed numeric   3 : [ 3 ]
pushed numeric   4 : [ 4 3 ]
pushed numeric   2 : [ 2 4 3 ]
applied operator * : [ 8 3 ]
pushed numeric   1 : [ 1 8 3 ]
pushed numeric   5 : [ 5 1 8 3 ]
applied operator - : [ -4 8 3 ]
pushed numeric   2 : [ 2 -4 8 3 ]
pushed numeric   3 : [ 3 2 -4 8 3 ]
applied operator ^ : [ 8 -4 8 3 ]
applied operator ^ : [ 65536 8 3 ]
applied operator / : [ 0.0001220703125 3 ]
applied operator + : [ 3.0001220703125 ]
```

## J

This task's operations are all dyadic - having two arguments. So on each step we may either "shift" a number to the stack or "reduce" two topmost stack items to one.

Our implementation will be a monadic verb: it will take a single argument, which contains both the accumulated stack and the tokens to be processed. First, create initial state of the input:

```   a: , <;._1 ' ' , '3 4 2 * 1 5 - 2 3 ^ ^ / +'
┌┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┐
││3│4│2│*│1│5│-│2│3│^│^│/│+│
└┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┘
```

As an example, let's also add monadic operation _ which inverses the sign of the stack top element.

We're going to read tokens from input one by one. Each time we read a token, we're checking if it's a number - in this case we put the number to the stack - or an operation - in this case we apply the operation to the stack. The monad which returns 1 (true) for a token representing an operation and 0 (false) otherwise is "isOp". The dyad, which moves an input token to the stack, is "doShift". Applying the operation to the stack is "doApply".

There are 6 operations - one monadic "_" and five dyadic "+", "-", "*", "/", "^". For operation, we need to translate input token into operation and apply it to the stack. The dyad which converts the input token to the operation is "dispatch". It uses two miscellaneous adverbs, one for monadic operations - "mo" - and another for dyadic - "dy".

The RPN driver is the monad "consume", which handles one token. The output is the state of the program after the token was consumed - stack in the 0th box, and remaining input afterwards. As a side effect, "consume" is going to print the resulting stack, so running "consume" once for each token will produce intermediate states of the stack.

```   isOp=: '_+-*/^' e.~ {.@>@{.
mo=: 1 :'(}: , u@{:) @ ['
dy=: 1 :'(_2&}. , u/@(_2&{.)) @ ['
dispatch=: (-mo)`(+dy)`(-dy)`(*dy)`(%dy)`(^dy)@.('_+-*/^' i. {.@>@])
doShift=: (<@, ".@>@{.) , }.@]
doApply=: }.@] ,~ [ <@dispatch {.@]
consume=: [: ([ smoutput@>@{.) >@{. doShift`doApply@.(isOp@]) }.
consume ^: (<:@#) a: , <;._1 ' ' , '3 4 2 * 1 5 - 2 3 ^ ^ / +'
3
3 4
3 4 2
3 8
3 8 1
3 8 1 5
3 8 _4
3 8 _4 2
3 8 _4 2 3
3 8 _4 8
3 8 65536
3 0.00012207
3.00012
┌───────┐
│3.00012│
└───────┘
consume ^: (<:@#) a: , <;._1 ' ' , '3 _ 4 +'
3
_3
_3 4
1
┌─┐
│1│
└─┘
```

### Alternate Implementation

```rpn=: 3 :0
queue=. |.3 :'|.3 :y 0'::]each;: y
op=. 1 :'2 (u~/@:{.,}.)S:0 ,@]'
ops=. +op`(-op)`(*op)`(%op)`(^op)`(,&;)
choose=. ((;:'+-*/^')&i.@[)
,[email protected]/queue
)
```

Example use:

```   rpn '3 4 2 * 1 5 - 2 3 ^ ^ / +'
3.00012
```

To see intermediate result stacks, use this variant (the only difference is the definition of 'op'):

```rpnD=: 3 :0
queue=. |.3 :'|.3 :y 0'::]each;: y
op=. 1 :'2 (u~/@:{.,}.)S:0 ,@([smoutput)@]'
ops=. +op`(-op)`(*op)`(%op)`(^op)`(,&;)
choose=. ((;:'+-*/^')&i.@[)
,[email protected]/queue
)
```

In other words:

```   rpnD '3 4 2 * 1 5 - 2 3 ^ ^ / +'
┌─────┐
│2 4 3│
└─────┘
5 1 8 3
3 2 _4 8 3
8 _4 8 3
65536 8 3
0.00012207 3
3.00012
```

Note that the seed stack is boxed while computed stacks are not. Note that top of stack here is on the left. Note also that adjacent constants are bundled in the parsing phase. Finally, note that the result of rpn (and of rpnD - lines previous to the last line in the rpnD example here are output and not a part of the result) is the final state of the stack - in the general case it may not contain exactly one value.

## Java

{{works with|Java|1.5+}} Supports multi-digit numbers and negative numbers.

```import java.util.LinkedList;

public class RPN{
public static void evalRPN(String expr){
String cleanExpr = cleanExpr(expr);
System.out.println("Input\tOperation\tStack after");
for(String token:cleanExpr.split("\\s")){
System.out.print(token+"\t");
Double tokenNum = null;
try{
tokenNum = Double.parseDouble(token);
}catch(NumberFormatException e){}
if(tokenNum != null){
System.out.print("Push\t\t");
stack.push(Double.parseDouble(token+""));
}else if(token.equals("*")){
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand * secondOperand);
}else if(token.equals("/")){
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand / secondOperand);
}else if(token.equals("-")){
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand - secondOperand);
}else if(token.equals("+")){
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand + secondOperand);
}else if(token.equals("^")){
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(Math.pow(firstOperand, secondOperand));
}else{//just in case
System.out.println("Error");
return;
}
System.out.println(stack);
}
}

private static String cleanExpr(String expr){
//remove all non-operators, non-whitespace, and non digit chars
return expr.replaceAll("[^\\^\\*\\+\\-\\d/\\s]", "");
}

public static void main(String[] args){
evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +");
}
}
```

{{out}}

```Input	Operation	Stack after
3	Push		[3.0]
4	Push		[4.0, 3.0]
2	Push		[2.0, 4.0, 3.0]
*	Operate		[8.0, 3.0]
1	Push		[1.0, 8.0, 3.0]
5	Push		[5.0, 1.0, 8.0, 3.0]
-	Operate		[-4.0, 8.0, 3.0]
2	Push		[2.0, -4.0, 8.0, 3.0]
3	Push		[3.0, 2.0, -4.0, 8.0, 3.0]
^	Operate		[8.0, -4.0, 8.0, 3.0]
^	Operate		[65536.0, 8.0, 3.0]
/	Operate		[1.220703125E-4, 3.0]
+	Operate		[3.0001220703125]
```

## JavaScript

```var e = '3 4 2 * 1 5 - 2 3 ^ ^ / +'
var s=[], e=e.split(' ')
for (var i in e) {
var t=e[i], n=+t
if (n == t)
s.push(n)
else {
var o2=s.pop(), o1=s.pop()
switch (t) {
case '+': s.push(o1+o2); break;
case '-': s.push(o1-o2); break;
case '*': s.push(o1*o2); break;
case '/': s.push(o1/o2); break;
case '^': s.push(Math.pow(o1,o2)); break;
}
}
document.write(t, ': ', s, '
')
}
```

{{out}}

```
3: 3
4: 3,4
2: 3,4,2
*: 3,8
1: 3,8,1
5: 3,8,1,5
-: 3,8,-4
2: 3,8,-4,2
3: 3,8,-4,2,3
^: 3,8,-4,8
^: 3,8,65536
/: 3,0.0001220703125
+: 3.0001220703125

```

### = With checks and messages =

```var e = '3 4 2 * 1 5 - 2 3 ^ ^ / +'
eval: {
document.write(e, '
')
var s=[], e=e.split(' ')
for (var i in e) {
var t=e[i], n=+t
if (!t) continue
if (n == t)
s.push(n)
else {
if ('+-*/^'.indexOf(t) == -1) {
document.write(t, ': ', s, '
', 'Unknown operator!
')
break eval
}
if (s.length<2) {
document.write(t, ': ', s, '
', 'Insufficient operands!
')
break eval
}
var o2=s.pop(), o1=s.pop()
switch (t) {
case '+': s.push(o1+o2); break
case '-': s.push(o1-o2); break
case '*': s.push(o1*o2); break
case '/': s.push(o1/o2); break
case '^': s.push(Math.pow(o1,o2))
}
}
document.write(t, ': ', s, '
')
}
if (s.length>1) {
document.write('Insufficient operators!
')
}
}
```

{{out}}

```
3 4 2 * 1 5 - 2 3 ^ ^ / +
3: 3
4: 3,4
2: 3,4,2
*: 3,8
1: 3,8,1
5: 3,8,1,5
-: 3,8,-4
2: 3,8,-4,2
3: 3,8,-4,2,3
^: 3,8,-4,8
^: 3,8,65536
/: 3,0.0001220703125
+: 3.0001220703125

```

## Julia

(This code takes advantage of the fact that all of the operands and functions in the specified RPN syntax are valid Julia expressions, so we can use the built-in `parse` and `eval` functions to turn them into numbers and the corresponding Julia functions.)

```function rpn(s)
stack = Any[]
for op in map(eval, map(parse, split(s)))
if isa(op, Function)
arg2 = pop!(stack)
arg1 = pop!(stack)
push!(stack, op(arg1, arg2))
else
push!(stack, op)
end
println("\$op: ", join(stack, ", "))
end
length(stack) != 1 && error("invalid RPN expression \$s")
return stack[1]
end
rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +")
```

{{out}}

```3: 3
4: 3, 4
2: 3, 4, 2
*: 3, 8
1: 3, 8, 1
5: 3, 8, 1, 5
-: 3, 8, -4
2: 3, 8, -4, 2
3: 3, 8, -4, 2, 3
^: 3, 8, -4, 8
^: 3, 8, 65536
/: 3, 0.0001220703125
+: 3.0001220703125
```

(The return value is also `3.0001220703125`.)

## Kotlin

```// version 1.1.2

fun rpnCalculate(expr: String) {
if (expr.isEmpty()) throw IllegalArgumentException("Expresssion cannot be empty")
println("For expression = \$expr\n")
println("Token           Action             Stack")
val tokens = expr.split(' ').filter { it != "" }
val stack = mutableListOf<Double>()
for (token in tokens) {
val d = token.toDoubleOrNull()
if (d != null) {
println(" \$d   Push num onto top of stack  \$stack")
}
else if ((token.length > 1) || (token !in "+-*/^")) {
throw IllegalArgumentException("\$token is not a valid token")
}
else if (stack.size < 2) {
throw IllegalArgumentException("Stack contains too few operands")
}
else {
val d1 = stack.removeAt(stack.lastIndex)
val d2 = stack.removeAt(stack.lastIndex)
"+"  -> d2 + d1
"-"  -> d2 - d1
"*"  -> d2 * d1
"/"  -> d2 / d1
else -> Math.pow(d2, d1)
})
println(" \$token     Apply op to top of stack    \$stack")
}
}
println("\nThe final value is \${stack[0]}")
}

fun main(args: Array<String>) {
val expr = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
rpnCalculate(expr)
}
```

{{out}}

```
For expression = 3 4 2 * 1 5 - 2 3 ^ ^ / +

Token           Action             Stack
3.0   Push num onto top of stack  [3.0]
4.0   Push num onto top of stack  [3.0, 4.0]
2.0   Push num onto top of stack  [3.0, 4.0, 2.0]
*     Apply op to top of stack    [3.0, 8.0]
1.0   Push num onto top of stack  [3.0, 8.0, 1.0]
5.0   Push num onto top of stack  [3.0, 8.0, 1.0, 5.0]
-     Apply op to top of stack    [3.0, 8.0, -4.0]
2.0   Push num onto top of stack  [3.0, 8.0, -4.0, 2.0]
3.0   Push num onto top of stack  [3.0, 8.0, -4.0, 2.0, 3.0]
^     Apply op to top of stack    [3.0, 8.0, -4.0, 8.0]
^     Apply op to top of stack    [3.0, 8.0, 65536.0]
/     Apply op to top of stack    [3.0, 1.220703125E-4]
+     Apply op to top of stack    [3.0001220703125]

The final value is 3.0001220703125

```

## Liberty BASIC

```
global stack\$

expr\$ = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
print "Expression:"
print expr\$
print

print "Input","Operation","Stack after"

stack\$=""
token\$ = "#"
i = 1
token\$ = word\$(expr\$, i)
token2\$ = " "+token\$+" "

do
print "Token ";i;": ";token\$,
select case
'operation
case instr("+-*/^",token\$)<>0
print "operate",
op2\$=pop\$()
op1\$=pop\$()
if op1\$=""  then
print "Error: stack empty for ";i;"-th token: ";token\$
end
end if

op1=val(op1\$)
op2=val(op2\$)

select case token\$
case "+"
res = op1+op2
case "-"
res = op1-op2
case "*"
res = op1*op2
case "/"
res = op1/op2
case "^"
res = op1^op2
end select

call push str\$(res)
'default:number
case else
print "push",
call push token\$
end select
print "Stack: ";reverse\$(stack\$)
i = i+1
token\$ = word\$(expr\$, i)
token2\$ = " "+token\$+" "
loop until token\$ =""

res\$=pop\$()
print
print "Result:" ;res\$
extra\$=pop\$()
if extra\$<>"" then
print "Error: extra things on a stack: ";extra\$
end if
end

'---------------------------------------
function reverse\$(s\$)
reverse\$ = ""
token\$="#"
while token\$<>""
i=i+1
token\$=word\$(s\$,i,"|")
reverse\$ = token\$;" ";reverse\$
wend
end function
'---------------------------------------
sub push s\$
stack\$=s\$+"|"+stack\$    'stack
end sub

function pop\$()
'it does return empty on empty stack
pop\$=word\$(stack\$,1,"|")
stack\$=mid\$(stack\$,instr(stack\$,"|")+1)
end function

```

{{out}}

```
Expression:
3 4 2 * 1 5 - 2 3 ^ ^ / +

Input         Operation     Stack after
Token 1: 3    push          Stack:  3
Token 2: 4    push          Stack:  3 4
Token 3: 2    push          Stack:  3 4 2
Token 4: *    operate       Stack:  3 8
Token 5: 1    push          Stack:  3 8 1
Token 6: 5    push          Stack:  3 8 1 5
Token 7: -    operate       Stack:  3 8 -4
Token 8: 2    push          Stack:  3 8 -4 2
Token 9: 3    push          Stack:  3 8 -4 2 3
Token 10: ^   operate       Stack:  3 8 -4 8
Token 11: ^   operate       Stack:  3 8 65536
Token 12: /   operate       Stack:  3 0.12207031e-3
Token 13: +   operate       Stack:  3.00012207

Result:3.00012207

```

## Lua

```
local stack = {}
function push( a ) table.insert( stack, 1, a ) end
function pop()
if #stack == 0 then return nil end
return table.remove( stack, 1 )
end
function writeStack()
for i = #stack, 1, -1 do
io.write( stack[i], " " )
end
print()
end
function operate( a )
local s
if a == "+" then
push( pop() + pop() )
io.write( a .. "\tadd\t" ); writeStack()
elseif a == "-" then
s = pop(); push( pop() - s )
io.write( a .. "\tsub\t" ); writeStack()
elseif a == "*" then
push( pop() * pop() )
io.write( a .. "\tmul\t" ); writeStack()
elseif a == "/" then
s = pop(); push( pop() / s )
io.write( a .. "\tdiv\t" ); writeStack()
elseif a == "^" then
s = pop(); push( pop() ^ s )
io.write( a .. "\tpow\t" ); writeStack()
elseif a == "%" then
s = pop(); push( pop() % s )
io.write( a .. "\tmod\t" ); writeStack()
else
push( tonumber( a ) )
io.write( a .. "\tpush\t" ); writeStack()
end
end
function calc( s )
local t, a = "", ""
print( "\nINPUT", "OP", "STACK" )
for i = 1, #s do
a = s:sub( i, i )
if a == " " then operate( t ); t = ""
else t = t .. a
end
end
if a ~= "" then operate( a ) end
print( string.format( "\nresult: %.13f", pop() ) )
end
--[[ entry point ]]--
calc( "3 4 2 * 1 5 - 2 3 ^ ^ / +" )
calc( "22 11 *" )
```

{{out}}

```
INPUT   OP      STACK
3       push    3
4       push    3 4
2       push    3 4 2
*       mul     3 8
1       push    3 8 1
5       push    3 8 1 5
-       sub     3 8 -4
2       push    3 8 -4 2
3       push    3 8 -4 2 3
^       pow     3 8 -4 8
^       pow     3 8 65536
/       div     3 0.0001220703125

result: 3.0001220703125

INPUT   OP      STACK
22      push    22
11      push    22 11
*       mul     242

result: 242.0000000000000
```

## M2000 Interpreter

```
Module Rpn_Calc {
Rem Form 80,60
function rpn_calc(a\$) {
def m=0
dim token\$()
token\$()=piece\$(a\$," ")
l=len(token\$())
dim type(l)=0, reg(l)
where=-1
for i=0 to  l-1
c=val(token\$(i),"",m)
if m>-1 then
where++
reg(where)=c
else
reg(where-1)=eval(str\$(reg(where-1))+token\$(i)+str\$(reg(where)))
where--
end if
inf=each(reg(),1, where+1)
while inf
export\$<=token\$(i)+" ["+str\$(inf^,"")+"] "+ str\$(array(inf))+{
}
token\$(i)=" "
end while
next i
=reg(0)
}
Global export\$
document export\$
example1=rpn_calc("3 4 2 * 1 5 - 2 3 ^ ^ / +")
example2=rpn_calc("1 2 + 3 4 + ^ 5 6 + ^")
Print example1, example2
Rem Print #-2, Export\$
ClipBoard Export\$
}
Rpn_Calc

```

{{out}}

```3 [0]  3
4 [0]  3
[1]  4
2 [0]  3
[1]  4
[2]  2
* [0]  3
[1]  8
1 [0]  3
[1]  8
[2]  1
5 [0]  3
[1]  8
[2]  1
[3]  5
- [0]  3
[1]  8
[2] -4
2 [0]  3
[1]  8
[2] -4
[3]  2
3 [0]  3
[1]  8
[2] -4
[3]  2
[4]  3
^ [0]  3
[1]  8
[2] -4
[3]  8
^ [0]  3
[1]  8
[2]  65536
/ [0]  3
[1]  .0001220703125
+ [0]  3.0001220703125
1 [0]  1
2 [0]  1
[1]  2
+ [0]  3
3 [0]  3
[1]  3
4 [0]  3
[1]  3
[2]  4
+ [0]  3
[1]  7
^ [0]  2187
5 [0]  2187
[1]  5
6 [0]  2187
[1]  5
[2]  6
+ [0]  2187
[1]  11
^ [0]  5.47440108942022E+36

```
## Mathematica (This code takes advantage of the fact that all of the operands and functions in the specified RPN syntax can be used to form valid Mathematica expressions, so we can use the built-in ToExpression function to turn them into numbers and the corresponding Mathematica functions. Note that we need to add braces around arguments, otherwise "-4^8" would be parsed as "-(4^8)" instead of "(-4)^8".) ```Mathematica calc[rpn_] := Module[{tokens = StringSplit[rpn], s = "(" <> ToString@InputForm@# <> ")" &, op, steps}, op[o_, x_, y_] := ToExpression[s@x <> o <> s@y]; steps = FoldList[Switch[#2, _?DigitQ, Append[#, FromDigits[#2]], _, Append[#[[;; -3]], op[#2, #[[-2]], #[[-1]]]] ] &, {}, tokens][[2 ;;]]; Grid[Transpose[{# <> ":" & /@ tokens, StringRiffle[ToString[#, InputForm] & /@ #] & /@ steps}]]]; Print[calc["3 4 2 * 1 5 - 2 3 ^ ^ / +"]]; ``` {{out}} ```txt 3: 3 4: 3 4 2: 3 4 2 *: 3 8 1: 3 8 1 5: 3 8 1 5 -: 3 8 -4 2: 3 8 -4 2 3: 3 8 -4 2 3 ^: 3 8 -4 8 ^: 3 8 65536 /: 3 1/8192 +: 24577/8192 ``` ## Maxima ```Maxima rmod(i, j) := mod(j, i)\$ rpow(x, y) := y^x\$ rpn(sexpr) := ( operands: [], expr: charlist(sexpr), for token in expr do ( if token = "+" then ( push(pop(operands) + pop(operands), operands) ) elseif token = "-" then ( push(-1 * (pop(operands) - pop(operands)), operands) ) elseif token = "*" then ( push(pop(operands) * pop(operands), operands) ) elseif token = "/" then ( push(1 / (pop(operands) / pop(operands)), operands) ) elseif token = "%" then ( push(rmod(pop(operands), pop(operands)), operands) ) elseif token = "^" then ( push(rpow(pop(operands), pop(operands)), operands) ) elseif token # " " then ( push(parse_string(token), operands) ), if token # " " then ( print(token, " : ", operands) ) ), pop(operands) )\$ rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +"), numer; ``` ### Output (%i5) ev(rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +"),numer) 3 : [3] 4 : [4, 3] 2 : [2, 4, 3] * : [8, 3] 1 : [1, 8, 3] 5 : [5, 1, 8, 3] - : [- 4, 8, 3] 2 : [2, - 4, 8, 3] 3 : [3, 2, - 4, 8, 3] ^ : [8, - 4, 8, 3] ^ : [65536, 8, 3] / : [1.220703125e-4, 3] + : [3.0001220703125] (%o5) 3.0001220703125 ``` ## MiniScript ```MiniScript RPN = function(inputText) tokens = inputText.split stack = [] while tokens tok = tokens.pull if "+-*/^".indexOf(tok) != null then b = stack.pop a = stack.pop if tok == "+" then stack.push a + b if tok == "-" then stack.push a - b if tok == "*" then stack.push a * b if tok == "/" then stack.push a / b if tok == "^" then stack.push a ^ b else stack.push val(tok) end if print tok + " --> " + stack end while return stack[0] end function print RPN("3 4 2 * 1 5 - 2 3 ^ ^ / +") ``` {{out}} ```txt 3 --> [3] 4 --> [3, 4] 2 --> [3, 4, 2] * --> [3, 8] 1 --> [3, 8, 1] 5 --> [3, 8, 1, 5] - --> [3, 8, -4] 2 --> [3, 8, -4, 2] 3 --> [3, 8, -4, 2, 3] ^ --> [3, 8, -4, 8] ^ --> [3, 8, 65536] / --> [3, 0.000122] + --> [3.000122] 3.000122 ``` ## N/t/roff ===Classically-oriented version=== This implementation does not take advantage of GNU TROFF's ability to handle numerical registers of more than 2 characters. {{works with|GNU TROFF|1.22.2}} ```N/t/roff .ig RPN parser implementation in TROFF .. .\" \(*A stack implementation .nr Ac 0 .af Ac 1 .de APUSH .if (\\n(Ac>=0)&(\\n(Ac<27) \{ \ . nr Ac +1 . af Ac A . nr A\\n(Ac \\\$1 . af Ac 1 \} .. .de APOP .if (\\n(Ac>0)&(\\n(Ac<27) \{ \ . af Ac A . rr A\\n(Ac \\\$1 . af Ac 1 . nr Ac -1 .. .\" Facility to print entire stack .de L2 .af Ac 1 .if \\n(Li<=\\n(Ac \{ \ . af Li A \\n(A\\n(Li . af Li 1 . nr Li +1 . L2 \} .. .de APRINT .nr Li 1 .L2 .br .. .\" Integer exponentiation algorithm .de L1 .if \\n(Li<\\\$2 \{ \ . nr Rs \\n(Rs*\\\$1 . nr Li +1 . L1 \\\$1 \\\$2 \} .. .de EXP .nr Li 0 .nr Rs 1 .L1 \\\$1 \\\$2 .. .\" RPN Parser .de REAP .af Ac A .nr O2 \\n(A\\n(Ac .af Ac 1 .nr Ai \\n(Ac-1 .af Ai A .nr O1 \\n(A\\n(Ai .APOP .APOP .. .de RPNPUSH .ie '\\\$1'+' \{ \ . REAP . nr Rs \\n(O1+\\n(O2 \} .el \{ \ . ie '\\\$1'-' \{ \ . REAP . nr Rs \\n(O1-\\n(O2 \} . el \{ \ . ie '\\\$1'*' \{ \ . REAP . nr Rs \\n(O1*\\n(O2 \} . el \{ \ . ie '\\\$1'/' \{ \ . REAP . nr Rs \\n(O1/\\n(O2 \} . el \{ \ . ie '\\\$1'%' \{ \ . REAP . nr Rs \\n(O1%\\n(O2 \} . el \{ \ . ie '\\\$1'^' \{ \ . REAP . EXP \\n(O1 \\n(O2 \} . el .nr Rs \\\$1 \} \} \} \} \} .APUSH \\n(Rs .APRINT .. .de RPNPRINT .if \\n(Ac>1 .tm ERROR (rpn.roff): Malformed input expression. Evaluation stack size: \\n(Ac > 1 . \\n(AA .. .de RPNPARSE .RPNPUSH \\\$1 .ie \\n(.\$>1 \{ \ . shift . RPNPARSE \\\$@ \} .el .RPNPRINT .. .RPNPARSE 3 4 2 * 1 5 - 2 3 ^ ^ / + \" Our input expression ``` ### =Output= 3 3 4 3 4 2 3 8 3 8 1 3 8 1 5 3 8 ‐4 3 8 ‐4 2 3 8 ‐4 2 3 3 8 ‐4 8 3 8 16 3 0 3 3 ``` ### Modern version This version sees great improvement on syntax, stacks can now be as big as they want, and modern GNU Troff constructs are used. {{works with|GNU Troff|1.22.2}} ```N/t/roff .ig ### ===================== Array implementation ### ===================== .. .de end .. .de array . nr \\\$1.c 0 1 . de \\\$1.push end . nr \\\$1..\\\\n+[\\\$1.c] \\\\\$1 . end . de \\\$1.pop end . if \\\\n[\\\$1.c]>0 \{ \ . rr \\\$1..\\\\n[\\\$1.c] . nr \\\$1.c -1\ . \} . end . de \\\$1.dump end . nr i 0 1 . rm ou . while \\\\n+i<=\\\\n[\\\$1.c] \{ \ . as ou "\\\\n[\\\$1..\\\\ni] . \} . tm \\\\*(ou . rr i . end .. .ig ### ==================== End array implementation ### ==================== .. .array stack .de hyper3 . nr rs 1 . nr i 0 1 . while \\n+i<=\\\$2 .nr rs \\n(rs*\\\$1 . rr i .. .de pop2 . nr O2 \\n[\\\$1..\\n[\\\$1.c]] . \\\$1.pop . nr O1 \\n[\\\$1..\\n[\\\$1.c]] . \\\$1.pop .. .de rpn . ie '\\\$1'+' \{ \ . pop2 stack . nr rs \\n(O1+\\n(O2 . \} . el \{ \ . ie '\\\$1'-' \{ \ . pop2 stack . nr rs \\n(O1-\\n(O2 . \} . el \{ \ . ie '\\\$1'*' \{ \ . pop2 stack . nr rs \\n(O1*\\n(O2 . \} . el \{ \ . ie '\\\$1'/' \{ \ . pop2 stack . nr rs \\n(O1/\\n(O2 . \} . el \{ \ . ie '\\\$1'%' \{ \ . pop2 stack . nr rs \\n(O1%\\n(O2 . \} . el \{ \ . ie '\\\$1'^' \{ \ . pop2 stack . hyper3 \\n(O1 \\n(O2 . \} . el .nr rs \\\$1 . \}\}\}\}\} . . stack.push \\n(rs . stack.dump . . if \\n(.\$>1 \{ \ . shift . rpn \\\$@ . \} .. .rpn 3 4 2 * 1 5 - 2 3 ^ ^ / + .stack.dump ``` ### =Output= 3 3 4 3 4 2 3 8 3 8 1 3 8 1 5 3 8 -4 3 8 -4 2 3 8 -4 2 3 3 8 -4 8 3 8 16 3 0 3 3 ``` ## NetRexx {{trans|Java}} ```NetRexx /* NetRexx */ options replace format comments java crossref symbols nobinary numeric digits 20 rpnDefaultExpression = '3 4 2 * 1 5 - 2 3 ^ ^ / +' EODAD = '.*' parse arg rpnString if rpnString = '.' then rpnString = rpnDefaultExpression if rpnString = '' then do say 'Enter numbers or operators [to stop enter' EODAD']:' loop label rpnloop forever rpnval = ask if rpnval == EODAD then leave rpnloop rpnString = rpnString rpnval end rpnloop end rpnString = rpnString.space(1) say rpnString':' evaluateRPN(rpnString) return -- ----------------------------------------------------------------------------- method evaluateRPN(rpnString) public static returns Rexx stack = LinkedList() op = 0 L = 'L' R = 'R' rpnString = rpnString.strip('b') say 'Input\tOperation\tStack after' loop label rpn while rpnString.length > 0 parse rpnString token rest rpnString = rest.strip('b') say token || '\t\-' select label tox case token when '*' then do say 'Operate\t\t\-' op[R] = Rexx stack.pop() op[L] = Rexx stack.pop() stack.push(op[L] * op[R]) end when '/' then do say 'Operate\t\t\-' op[R] = Rexx stack.pop() op[L] = Rexx stack.pop() stack.push(op[L] / op[R]) end when '+' then do say 'Operate\t\t\-' op[R] = Rexx stack.pop() op[L] = Rexx stack.pop() stack.push(op[L] + op[R]) end when '-' then do say 'Operate\t\t\-' op[R] = Rexx stack.pop() op[L] = Rexx stack.pop() stack.push(op[L] - op[R]) end when '^' then do say 'Operate\t\t\-' op[R] = Rexx stack.pop() op[L] = Rexx stack.pop() -- If exponent is a whole number use Rexx built-in exponentiation operation, otherwise use Math.pow() op[R] = op[R] + 0 if op[R].datatype('w') then stack.push(op[L] ** op[R]) else stack.push(Rexx Math.pow(op[L], op[R])) end otherwise do if token.datatype('n') then do say 'Push\t\t\-' stack.push(token) end else do say 'Error\t\t\-' end end end tox calc = Rexx say stack.toString end rpn say calc = stack.toString return calc ``` {{out}} ```txt Input Operation Stack after 3 Push [3] 4 Push [4, 3] 2 Push [2, 4, 3] * Operate [8, 3] 1 Push [1, 8, 3] 5 Push [5, 1, 8, 3] - Operate [-4, 8, 3] 2 Push [2, -4, 8, 3] 3 Push [3, 2, -4, 8, 3] ^ Operate [8, -4, 8, 3] ^ Operate [65536, 8, 3] / Operate [0.0001220703125, 3] + Operate [3.0001220703125] 3 4 2 * 1 5 - 2 3 ^ ^ / +: [3.0001220703125] ``` ## Nim {{trans|Python}} ```nim import math, rdstdin, strutils, tables type Stack = seq[float] proc lalign(s, x): string = s & repeatChar(x - s.len, ' ') proc opPow(s: var Stack) = let b = s.pop let a = s.pop s.add a.pow b proc opMul(s: var Stack) = let b = s.pop let a = s.pop s.add a * b proc opDiv(s: var Stack) = let b = s.pop let a = s.pop s.add a / b proc opAdd(s: var Stack) = let b = s.pop let a = s.pop s.add a + b proc opSub(s: var Stack) = let b = s.pop let a = s.pop s.add a - b proc opNum(s: var Stack, num) = s.add num let ops = toTable({"^": opPow, "*": opMul, "/": opDiv, "+": opAdd, "-": opSub}) proc getInput(inp = ""): seq[string] = var inp = inp if inp.len == 0: inp = readLineFromStdin "Expression: " result = inp.strip.split proc rpnCalc(tokens): auto = var s: Stack = @[] result = @[@["TOKEN","ACTION","STACK"]] for token in tokens: var action = "" if ops.hasKey token: action = "Apply op to top of stack" ops[token](s) else: action = "Push num onto top of stack" s.opNum token.parseFloat result.add(@[token, action, s.map(proc (x: float): string = \$x).join(" ")]) let rpn = "3 4 2 * 1 5 - 2 3 ^ ^ / +" echo "For RPN expression: ", rpn let rp = rpnCalc rpn.getInput var maxColWidths = newSeq[int](rp[0].len) for i in 0 .. rp[0].high: for x in rp: maxColWidths[i] = max(maxColWidths[i], x[i].len) for x in rp: for i, y in x: stdout.write y.lalign(maxColWidths[i]), " " echo "" ``` {{out}} ```txt For RPN expression: 3 4 2 * 1 5 - 2 3 ^ ^ / + TOKEN ACTION STACK 3 Push num onto top of stack 3.0 4 Push num onto top of stack 3.0 4.0 2 Push num onto top of stack 3.0 4.0 2.0 * Apply op to top of stack 3.0 8.0 1 Push num onto top of stack 3.0 8.0 1.0 5 Push num onto top of stack 3.0 8.0 1.0 5.0 - Apply op to top of stack 3.0 8.0 -4.0 2 Push num onto top of stack 3.0 8.0 -4.0 2.0 3 Push num onto top of stack 3.0 8.0 -4.0 2.0 3.0 ^ Apply op to top of stack 3.0 8.0 -4.0 8.0 ^ Apply op to top of stack 3.0 8.0 65536.0 / Apply op to top of stack 3.0 0.0001220703125 + Apply op to top of stack 3.0001220703125 ``` ## Objeck ```objeck use IO; use Struct; bundle Default { class RpnCalc { function : Main(args : String[]) ~ Nil { Caculate("3 4 2 * 1 5 - 2 3 ^ ^ / +"); } function : native : Caculate(rpn : String) ~ Nil { rpn->PrintLine(); tokens := rpn->Split(" "); stack := FloatVector->New(); each(i : tokens) { token := tokens[i]->Trim(); if(token->Size() > 0) { if(token->Get(0)->IsDigit()) { stack->AddBack(token->ToFloat()); } else { right := stack->Get(stack->Size() - 1); stack->RemoveBack(); left := stack->Get(stack->Size() - 1); stack->RemoveBack(); select(token->Get(0)) { label '+': { stack->AddBack(left + right); } label '-': { stack->AddBack(left - right); } label '*': { stack->AddBack(left * right); } label '/': { stack->AddBack(left / right); } label '^': { stack->AddBack(right->Power(left)); } }; }; PrintStack(stack); }; }; Console->Print("result: ")->PrintLine(stack->Get(0)); } function : PrintStack(stack : FloatVector) ~ Nil { " ["->Print(); each(i : stack) { stack->Get(i)->Print(); if(i + 1< stack->Size()) { ", "->Print(); }; }; ']'->PrintLine(); } } } ``` {{out}} ```txt 3 4 2 * 1 5 - 2 3 ^ ^ / + [3] [3, 4] [3, 4, 2] [3, 8] [3, 8, 1] [3, 8, 1, 5] [3, 8, -4] [3, 8, -4, 2] [3, 8, -4, 2, 3] [3, 8, -4, 8] [3, 8, 65536] [3, 0.00012207] [3.00012] result: 3.00012 ``` ## OCaml ```ocaml (* binop : ('a -> 'a -> 'a) -> 'a list -> 'a list *) let binop op = function | b::a::r -> (op a b)::r | _ -> failwith "invalid expression" (* interp : float list -> string -> string * float list *) let interp s = function | "+" -> "add", binop ( +. ) s | "-" -> "subtr", binop ( -. ) s | "*" -> "mult", binop ( *. ) s | "/" -> "divide", binop ( /. ) s | "^" -> "exp", binop ( ** ) s | str -> "push", (float_of_string str) :: s (* interp_and_show : float list -> string -> float list *) let interp_and_show s inp = let op,s' = interp s inp in Printf.printf "%s\t%s\t" inp op; List.(iter (Printf.printf "%F ") (rev s')); print_newline (); s' (* rpn_eval : string -> float list *) let rpn_eval str = Printf.printf "Token\tAction\tStack\n"; let ss = Str.(split (regexp_string " ") str) in List.fold_left interp_and_show [] ss ``` Evaluation of the test expression: ```txt # rpn_eval "3 4 2 * 1 5 - 2 3 ^ ^ / +";; Token Action Stack 3 push 3. 4 push 3. 4. 2 push 3. 4. 2. * mult 3. 8. 1 push 3. 8. 1. 5 push 3. 8. 1. 5. - subtr 3. 8. -4. 2 push 3. 8. -4. 2. 3 push 3. 8. -4. 2. 3. ^ exp 3. 8. -4. 8. ^ exp 3. 8. 65536. / divide 3. 0.0001220703125 + add 3.00012207031 - : float list = [3.0001220703125] ``` ## Oforth Oforth uses RPN and natively parse RPN. ```Oforth "3 4 2 * 1 5 - 2 3 ^ ^ / +" eval println ``` {{out}} ```txt 3 ``` To show the changes in the stack, we can use .l after evaluating each word : ```Oforth : rpn(s) { s words apply(#[ eval .l ]) } rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +") ``` {{out}} ```txt 3 | 3 | 4 | 3 | 4 | 2 | 3 | 8 | 3 | 8 | 1 | 3 | 8 | 1 | 5 | 3 | 8 | -4 | 3 | 8 | -4 | 2 | 3 | 8 | -4 | 2 | 3 | 3 | 8 | -4 | 8 | 3 | 8 | 65536 | 3 | 0 | 3 | ``` ## ooRexx ```ooRexx /* ooRexx ************************************************************* * 10.11.2012 Walter Pachl translated from PL/I via REXX **********************************************************************/ fid='rpl.txt' ex=linein(fid) Say 'Input:' ex /* ex=' 3 4 2 * 1 5 - 2 3 ^ ^ / +' */ Numeric Digits 15 expr='' st=.circularqueue~new(100) Say 'Stack contents:' do While ex<>'' Parse Var ex ch +1 ex expr=expr||ch; if ch<>' ' then do If pos(ch,'0123456789')>0 Then /* a digit goes onto stack */ st~push(ch) Else Do /* an operator */ op=st~pull /* get top element */ select /* and modify the (now) top el*/ when ch='+' Then st~push(st~pull + op) when ch='-' Then st~push(st~pull - op) when ch='*' Then st~push(st~pull * op) when ch='/' Then st~push(st~pull / op) when ch='^' Then st~push(st~pull ** op) end; Say st~string(' ','L') /* show stack in LIFO order */ end end end Say 'The reverse polish expression = 'expr Say 'The evaluated expression = 'st~pull ``` {{out}} ```txt Input: 3 4 2 * 1 5 - 2 3 ^ ^ / + Stack contents: 3 8 3 8 -4 3 8 -4 8 3 8 65536 3 0.0001220703125 3.0001220703125 The reverse polish expression = 3 4 2 * 1 5 - 2 3 ^ ^ / + The evaluated expression = 3.0001220703125 ``` ## PARI/GP Due to the nature of the language, it is not trivial to process an expression as a simple space-separated string. Though, this could be done if one calls an external shell program such as `sed` and pipes the result back hither. ```parigp estack = []; epush(x) = { estack = vector(#estack + 1, i, if(i <= #estack, estack[i], x)); return(#estack); }; epop() = { local(val = estack[#estack]); estack = vector(#estack - 1, i, estack[i]); return(val); }; registerRPNToken(t) = { local(o1, o2); if(type(t) == "t_STR", if(t == "+", o2 = epop(); o1 = epop(); epush(o1 + o2), if(t == "-", o2 = epop(); o1 = epop(); epush(o1 - o2), if(t == "*", o2 = epop(); o1 = epop(); epush(o1 * o2), if(t == "/", o2 = epop(); o1 = epop(); epush(o1 / o2), if(t == "%", o2 = epop(); o1 = epop(); epush(o1 % o2), if(t == "^", o2 = epop(); o1 = epop(); epush(o1 ^ o2) )))))), if(type(t) == "t_INT" || type(t) == "t_REAL" || type(t) == "t_FRAC", epush(t)) ); print(estack); }; parseRPN(s) = { estack = []; for(i = 1, #s, registerRPNToken(s[i])); if(#estack > 1, error("Malformed postfix expression.")); return(estack[1]); }; parseRPN([3, 4, 2, "*", 1, 5, "-", 2, 3, "^", "^", "/", "+"]); \\ Our input expression ``` ### Output [3] [3, 4] [3, 4, 2] [3, 8] [3, 8, 1] [3, 8, 1, 5] [3, 8, -4] [3, 8, -4, 2] [3, 8, -4, 2, 3] [3, 8, -4, 8] [3, 8, 65536] [3, 1/8192] [24577/8192] ``` Whenever possible, PARI/GP tries to manipulate and return results in the simplest form it can. In this case, it deems fractions the most suitable form of output. Nonetheless, converting the fraction `24577/8192` yields `3.0001220703125` as expected. ## Perl ```perl use strict; use warnings; use feature 'say'; my \$number = '[+-]?(?:\.\d+|\d+(?:\.\d*)?)'; my \$operator = '[-+*/^]'; my @tests = ('3 4 2 * 1 5 - 2 3 ^ ^ / +'); for (@tests) { while ( s/ \s* ((?\$number)) # 1st operand \s+ ((?\$number)) # 2nd operand \s+ ((?\$operator)) # operator (?:\s+|\$) # more to parse, or done? / ' '.evaluate().' ' # substitute results of evaluation /ex ) {} say; } sub evaluate { (my \$a = "(\$+{left})\$+{op}(\$+{right})") =~ s/\^/**/; say \$a; eval \$a; } ``` {{out}} ```txt (4)*(2) (1)-(5) (2)**(3) (-4)**(8) (8)/(65536) (3)+(0.0001220703125) 3.0001220703125 ``` ## Perl 6 {{works with|rakudo|2015-09-25}} ```perl6 my \$proggie = '3 4 2 * 1 5 - 2 3 ^ ^ / +'; class RPN is Array { method binop(&op) { self.push: self.pop R[&op] self.pop } method run(\$p) { for \$p.words { say "\$_ ({self})"; when /\d/ { self.push: \$_ } when '+' { self.binop: &[+] } when '-' { self.binop: &[-] } when '*' { self.binop: &[*] } when '/' { self.binop: &[/] } when '^' { self.binop: &[**] } default { die "\$_ is bogus" } } say self; } } RPN.new.run(\$proggie); ``` {{out}} ```txt 3 () 4 (3) 2 (3 4) * (3 4 2) 1 (3 8) 5 (3 8 1) - (3 8 1 5) 2 (3 8 -4) 3 (3 8 -4 2) ^ (3 8 -4 2 3) ^ (3 8 -4 8) / (3 8 65536) + (3 0.0001220703125) 3.0001220703125 ``` ## Phix ```Phix procedure evalRPN(string s) sequence stack = {} sequence ops = split(s) for i=1 to length(ops) do string op = ops[i] switch op case "+": stack[-2] = stack[-2]+stack[-1]; stack = stack[1..-2] case "-": stack[-2] = stack[-2]-stack[-1]; stack = stack[1..-2] case "*": stack[-2] = stack[-2]*stack[-1]; stack = stack[1..-2] case "/": stack[-2] = stack[-2]/stack[-1]; stack = stack[1..-2] case "^": stack[-2] = power(stack[-2],stack[-1]); stack = stack[1..-2] default : stack = append(stack,scanf(op,"%d")[1][1]) end switch ?{op,stack} end for end procedure evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +") ``` {{out}} ```txt "started" {"3",{3}} {"4",{3,4}} {"2",{3,4,2}} {"*",{3,8}} {"1",{3,8,1}} {"5",{3,8,1,5}} {"-",{3,8,-4}} {"2",{3,8,-4,2}} {"3",{3,8,-4,2,3}} {"^",{3,8,-4,8}} {"^",{3,8,65536}} {"/",{3,0.0001220703125}} {"+",{3.00012207}} ``` ## PHP ```php ``` {{out}} ```txt Input Operation Stack after 3 Push 3 4 Push 3 4 2 Push 3 4 2 * Operate 3 8 1 Push 3 8 1 5 Push 3 8 1 5 - Operate 3 8 -4 2 Push 3 8 -4 2 3 Push 3 8 -4 2 3 ^ Operate 3 8 -4 8 ^ Operate 3 8 65536 / Operate 3 0.0001220703125 + Operate 3.0001220703125 Compute Value: 3.0001220703125 ``` ## PicoLisp This is an integer-only calculator: ```PicoLisp (de rpnCalculator (Str) (let (^ ** Stack) # Define '^' from the built-in '**' (prinl "Token Stack") (for Token (str Str "*+-/\^") (if (num? Token) (push 'Stack @) (set (cdr Stack) ((intern Token) (cadr Stack) (pop 'Stack)) ) ) (prin Token) (space 6) (println Stack) ) (println (car Stack)) ) ) ``` Test (note that the top-of-stack is in the left-most position): ```PicoLisp : (rpnCalculator "3 4 2 * 1 5 - 2 3 \^ \^ / +") Token Stack 3 (3) 4 (4 3) 2 (2 4 3) * (8 3) 1 (1 8 3) 5 (5 1 8 3) - (-4 8 3) 2 (2 -4 8 3) 3 (3 2 -4 8 3) ^ (8 -4 8 3) ^ (65536 8 3) / (0 3) + (3) 3 -> 3 ``` ## PL/I ```PL/I Calculator: procedure options (main); /* 14 Sept. 2012 */ declare expression character (100) varying initial (''); declare ch character (1); declare (stack controlled, operand) float (18); declare in file input; open file (in) title ('/CALCULAT.DAT,type(text),recsize(100)'); on endfile (in) go to done; put ('Stack contents:'); main_loop: do forever; get file (in) edit (ch) (a(1)); expression = expression || ch; if ch = ' ' then iterate; select (ch); when ('0', '1', '2', '3', '4', '5', '6', '7', '8', '9') do; allocate stack; stack = ch; iterate main_loop; end; when ('+') do; operand = stack; free stack; stack = stack + operand; end; when ('-') do; operand = stack; free stack; stack = stack - operand; end; when ('*') do; operand = stack; free stack; stack = stack * operand; end; when ('/') do; operand = stack; free stack; stack = stack / operand; end; when ('^') do; operand = stack; free stack; stack = stack ** operand; end; end; call show_stack; end; done: put skip list ('The reverse polish expression = ' || expression); put skip list ('The evaluated expression = ' || stack); end Calculator; ``` ```txt Stack contents: 3.0000000000 8.0000000000 3.0000000000 8.0000000000 -4.0000000000 3.0000000000 8.0000000000 -4.0000000000 8.0000000000 3.0000000000 8.0000000000 65536.0000000000 3.0000000000 0.0001220703 3.0001220703 The reverse polish expression = 3 4 2 * 1 5 - 2 3 ^ ^ / + The evaluated expression = 3.00012207031250000E+0000 ``` The procedure to display the stack: ```txt /* As the stack is push-down pop-up, need to pop it to see what's inside. */ show_stack: procedure; declare ts float (18) controlled; do while (allocation(stack) > 0); allocate ts; ts = stack; free stack; end; put skip; do while (allocation(ts) > 0); allocate stack; stack = ts; free ts; put edit (stack) (f(18,10)); end; end show_stack; ``` ## PowerShell ```PowerShell function Invoke-Rpn { <# .SYNOPSIS A stack-based evaluator for an expression in reverse Polish notation. .DESCRIPTION A stack-based evaluator for an expression in reverse Polish notation. All methods in the Math and Decimal classes are available. .PARAMETER Expression A space separated, string of tokens. .PARAMETER DisplayState This switch shows the changes in the stack as each individual token is processed as a table. .EXAMPLE Invoke-Rpn -Expression "3 4 Max" .EXAMPLE Invoke-Rpn -Expression "3 4 Log2" .EXAMPLE Invoke-Rpn -Expression "3 4 2 * 1 5 - 2 3 ^ ^ / +" .EXAMPLE Invoke-Rpn -Expression "3 4 2 * 1 5 - 2 3 ^ ^ / +" -DisplayState #> [CmdletBinding()] Param ( [Parameter(Mandatory=\$true)] [AllowEmptyString()] [string] \$Expression, [Parameter(Mandatory=\$false)] [switch] \$DisplayState ) Begin { function Out-State ([System.Collections.Stack]\$Stack) { \$array = \$Stack.ToArray() [Array]::Reverse(\$array) \$array | ForEach-Object -Process { Write-Host ("{0,-8:F3}" -f \$_) -NoNewline } -End { Write-Host } } function New-RpnEvaluation { \$stack = New-Object -Type System.Collections.Stack \$shortcuts = @{ "+" = "Add"; "-" = "Subtract"; "/" = "Divide"; "*" = "Multiply"; "%" = "Remainder"; "^" = "Pow" } :ARGUMENT_LOOP foreach (\$argument in \$args) { if (\$DisplayState -and \$stack.Count) { Out-State \$stack } if (\$shortcuts[\$argument]) { \$argument = \$shortcuts[\$argument] } try { \$stack.Push([decimal]\$argument) continue } catch { } \$argCountList = \$argument -replace "(\D+)(\d*)",‘\$2’ \$operation = \$argument.Substring(0, \$argument.Length – \$argCountList.Length) foreach(\$type in [Decimal],[Math]) { if (\$definition = \$type::\$operation) { if (-not \$argCountList) { \$argCountList = \$definition.OverloadDefinitions | Foreach-Object { (\$_ -split ", ").Count } | Sort-Object -Unique } foreach (\$argCount in \$argCountList) { try { \$methodArguments = \$stack.ToArray()[(\$argCount–1)..0] \$result = \$type::\$operation.Invoke(\$methodArguments) \$null = 1..\$argCount | Foreach-Object { \$stack.Pop() } \$stack.Push(\$result) continue ARGUMENT_LOOP } catch { ## If error, try with the next number of arguments } } } } } if (\$DisplayState -and \$stack.Count) { Out-State \$stack if (\$stack.Count) { Write-Host "`nResult = \$(\$stack.Peek())" } } else { \$stack } } } Process { Invoke-Expression -Command "New-RpnEvaluation \$Expression" } End { } } Invoke-Rpn -Expression "3 4 2 * 1 5 - 2 3 ^ ^ / +" -DisplayState ``` {{Out}} ```txt 3.000 3.000 4.000 3.000 4.000 2.000 3.000 8.000 3.000 8.000 1.000 3.000 8.000 1.000 5.000 3.000 8.000 -4.000 3.000 8.000 -4.000 2.000 3.000 8.000 -4.000 2.000 3.000 3.000 8.000 -4.000 8.000 3.000 8.000 65536.000 3.000 0.000 3.000 Result = 3.0001220703125 ``` ## Prolog Works with SWI-Prolog. ```Prolog rpn(L) :- writeln('Token Action Stack'), parse(L, [],[X] ,[]), format('~nThe final output value is ~w~n', [X]). % skip spaces parse([X|L], St) --> {char_type(X, white)}, parse(L, St). % detect operators parse([Op|L], [Y, X | St]) --> { is_op(Op, X, Y, V), writef(' %s', [[Op]]), with_output_to(atom(Str2), writef('Apply %s on top of stack', [[Op]])), writef(' %35l', [Str2]), writef('%w\n', [[V | St]])}, parse(L, [V | St]). % detect number parse([N|L], St) --> {char_type(N, digit)}, parse_number(L, [N], St). % string is finished parse([], St) --> St. % compute numbers parse_number([N|L], NC, St) --> {char_type(N, digit)}, parse_number(L, [N|NC], St). parse_number(S, NC, St) --> { reverse(NC, RNC), number_chars(V, RNC), writef('%5r', [V]), with_output_to(atom(Str2), writef('Push num %w on top of stack', [V])), writef(' %35l', [Str2]), writef('%w\n', [[V | St]])}, parse(S, [V|St]). % defining operations is_op(42, X, Y, V) :- V is X*Y. is_op(43, X, Y, V) :- V is X+Y. is_op(45, X, Y, V) :- V is X-Y. is_op(47, X, Y, V) :- V is X/Y. is_op(94, X, Y, V) :- V is X**Y. ``` {{out}} ```txt 5 ?- rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +"). Token Action Stack 3 'Push num 3 on top of stack' [3] 4 'Push num 4 on top of stack' [4,3] 2 'Push num 2 on top of stack' [2,4,3] * 'Apply * on top of stack' [8,3] 1 'Push num 1 on top of stack' [1,8,3] 5 'Push num 5 on top of stack' [5,1,8,3] - 'Apply - on top of stack' [-4,8,3] 2 'Push num 2 on top of stack' [2,-4,8,3] 3 'Push num 3 on top of stack' [3,2,-4,8,3] ^ 'Apply ^ on top of stack' [8,-4,8,3] ^ 'Apply ^ on top of stack' [65536,8,3] / 'Apply / on top of stack' [0.0001220703125,3] + 'Apply + on top of stack' [3.0001220703125] The final output value is 3.0001220703125 true . ``` ## Python ### Version 1 ```python def op_pow(stack): b = stack.pop(); a = stack.pop() stack.append( a ** b ) def op_mul(stack): b = stack.pop(); a = stack.pop() stack.append( a * b ) def op_div(stack): b = stack.pop(); a = stack.pop() stack.append( a / b ) def op_add(stack): b = stack.pop(); a = stack.pop() stack.append( a + b ) def op_sub(stack): b = stack.pop(); a = stack.pop() stack.append( a - b ) def op_num(stack, num): stack.append( num ) ops = { '^': op_pow, '*': op_mul, '/': op_div, '+': op_add, '-': op_sub, } def get_input(inp = None): 'Inputs an expression and returns list of tokens' if inp is None: inp = input('expression: ') tokens = inp.strip().split() return tokens def rpn_calc(tokens): stack = [] table = ['TOKEN,ACTION,STACK'.split(',')] for token in tokens: if token in ops: action = 'Apply op to top of stack' ops[token](stack) table.append( (token, action, ' '.join(str(s) for s in stack)) ) else: action = 'Push num onto top of stack' op_num(stack, eval(token)) table.append( (token, action, ' '.join(str(s) for s in stack)) ) return table if __name__ == '__main__': rpn = '3 4 2 * 1 5 - 2 3 ^ ^ / +' print( 'For RPN expression: %r\n' % rpn ) rp = rpn_calc(get_input(rpn)) maxcolwidths = [max(len(y) for y in x) for x in zip(*rp)] row = rp[0] print( ' '.join('{cell:^{width}}'.format(width=width, cell=cell) for (width, cell) in zip(maxcolwidths, row))) for row in rp[1:]: print( ' '.join('{cell:<{width}}'.format(width=width, cell=cell) for (width, cell) in zip(maxcolwidths, row))) print('\n The final output value is: %r' % rp[-1][2]) ``` {{out}} ```txt For RPN expression: '3 4 2 * 1 5 - 2 3 ^ ^ / +' TOKEN ACTION STACK 3 Push num onto top of stack 3 4 Push num onto top of stack 3 4 2 Push num onto top of stack 3 4 2 * Apply op to top of stack 3 8 1 Push num onto top of stack 3 8 1 5 Push num onto top of stack 3 8 1 5 - Apply op to top of stack 3 8 -4 2 Push num onto top of stack 3 8 -4 2 3 Push num onto top of stack 3 8 -4 2 3 ^ Apply op to top of stack 3 8 -4 8 ^ Apply op to top of stack 3 8 65536 / Apply op to top of stack 3 0.0001220703125 + Apply op to top of stack 3.0001220703125 The final output value is: '3.0001220703125' ``` ### Version 2 ```python a=[] b={'+': lambda x,y: y+x, '-': lambda x,y: y-x, '*': lambda x,y: y*x,'/': lambda x,y:y/x,'^': lambda x,y:y**x} for c in '3 4 2 * 1 5 - 2 3 ^ ^ / +'.split(): if c in b: a.append(b[c](a.pop(),a.pop())) else: a.append(float(c)) print c, a ``` {{out}} ```txt 3 [3.0] 4 [3.0, 4.0] 2 [3.0, 4.0, 2.0] * [3.0, 8.0] 1 [3.0, 8.0, 1.0] 5 [3.0, 8.0, 1.0, 5.0] - [3.0, 8.0, -4.0] 2 [3.0, 8.0, -4.0, 2.0] 3 [3.0, 8.0, -4.0, 2.0, 3.0] ^ [3.0, 8.0, -4.0, 8.0] ^ [3.0, 8.0, 65536.0] / [3.0, 0.0001220703125] + [3.0001220703125] ``` ## Racket ```racket #lang racket (define (calculate-RPN expr) (for/fold ([stack '()]) ([token expr]) (printf "~a\t -> ~a~N" token stack) (match* (token stack) [((? number? n) s) (cons n s)] [('+ (list x y s ___)) (cons (+ x y) s)] [('- (list x y s ___)) (cons (- y x) s)] [('* (list x y s ___)) (cons (* x y) s)] [('/ (list x y s ___)) (cons (/ y x) s)] [('^ (list x y s ___)) (cons (expt y x) s)] [(x s) (error "calculate-RPN: Cannot calculate the expression:" (reverse (cons x s)))]))) ``` Test case ```txt -> (calculate-RPN '(3.0 4 2 * 1 5 - 2 3 ^ ^ / +)) 3.0 -> () 4 -> (3.0) 2 -> (4 3.0) * -> (2 4 3.0) 1 -> (8 3.0) 5 -> (1 8 3.0) - -> (5 1 8 3.0) 2 -> (-4 8 3.0) 3 -> (2 -4 8 3.0) ^ -> (3 2 -4 8 3.0) ^ -> (8 -4 8 3.0) / -> (65536 8 3.0) + -> (1/8192 3.0) 3.0001220703125 ``` Reading from a string: ```racket (calculate-RPN (in-port read (open-input-string "3.0 4 2 * 1 5 - 2 3 ^ ^ / +"))) ``` ## REXX ### version 1 ```rexx /* REXX *************************************************************** * 09.11.2012 Walter Pachl translates from PL/I **********************************************************************/ fid='rpl.txt' ex=linein(fid) Say 'Input:' ex /* ex=' 3 4 2 * 1 5 - 2 3 ^ ^ / +' */ Numeric Digits 15 expr='' st.=0 Say 'Stack contents:' do While ex<>'' Parse Var ex ch +1 ex expr=expr||ch; if ch<>' ' then do select When pos(ch,'0123456789')>0 Then Do Call stack ch Iterate End when ch='+' Then do; operand=getstack(); st.sti = st.sti + operand; end; when ch='-' Then do; operand=getstack(); st.sti = st.sti - operand; end; when ch='*' Then do; operand=getstack(); st.sti = st.sti * operand; end; when ch='/' Then do; operand=getstack(); st.sti = st.sti / operand; end; when ch='^' Then do; operand=getstack(); st.sti = st.sti ** operand; end; end; call show_stack end end Say 'The reverse polish expression = 'expr Say 'The evaluated expression = 'st.1 Exit stack: Procedure Expose st. /* put the argument on top of the stack */ z=st.0+1 st.z=arg(1) st.0=z Return getstack: Procedure Expose st. sti /* remove and return the stack's top element */ z=st.0 stk=st.z st.0=st.0-1 sti=st.0 Return stk show_stack: procedure Expose st. /* show the stack's contents */ ol='' do i=1 To st.0 ol=ol format(st.i,5,10) End Say ol Return ``` {{out}} ```txt Input: 3 4 2 * 1 5 - 2 3 ^ ^ / + Stack contents: 3.0000000000 8.0000000000 3.0000000000 8.0000000000 -4.0000000000 3.0000000000 8.0000000000 -4.0000000000 8.0000000000 3.0000000000 8.0000000000 65536.0000000000 3.0000000000 0.0001220703 3.0001220703 The reverse polish expression = 3 4 2 * 1 5 - 2 3 ^ ^ / + The evaluated expression = 3.0001220703125 ``` ### version 2 This REXX version handles tokens (not characters) so that the RPN could be (for instance): :::: 3.0 .4e1 2e0 * +1. 5 - 2 3 ** ** / + which is the essentially the same as the default used by the REXX program. ```REXX /*REXX program evaluates a ═════ Reverse Polish notation (RPN) ═════ expression. */ parse arg x /*obtain optional arguments from the CL*/ if x='' then x= "3 4 2 * 1 5 - 2 3 ^ ^ / +" /*Not specified? Then use the default.*/ tokens=words(x) /*save the number of tokens " ". */ showSteps=1 /*set to 0 if working steps not wanted.*/ ox=x /*save the original value of X. */ do i=1 for tokens; @.i=word(x,i) /*assign the input tokens to an array. */ end /*i*/ x=space(x) /*remove any superfluous blanks in X. */ L=max(20, length(x)) /*use 20 for the minimum display width.*/ numeric digits L /*ensure enough decimal digits for ans.*/ say center('operand', L, "─") center('stack', L+L, "─") /*display title*/ \$= /*nullify the stack (completely empty).*/ do k=1 for tokens; [email protected]; ??=? /*process each token from the @. list.*/ #=words(\$) /*stack the count (the number entries).*/ if datatype(?,'N') then do; \$=\$ ?; call show "add to───►stack"; iterate; end if ?=='^' then ??= "**" /*REXXify ^ ───► ** (make legal).*/ interpret 'y='word(\$,#-1) ?? word(\$,#) /*compute via the famous REXX INTERPRET*/ if datatype(y,'N') then y=y/1 /*normalize the number with ÷ by unity.*/ \$=subword(\$, 1, #-2) y /*rebuild the stack with the answer. */ call show ? /*display steps (tracing into), maybe.*/ end /*k*/ say /*display a blank line, better perusing*/ say ' RPN input:' ox; say " answer──►"\$ /*display original input; display ans.*/ parse source upper . y . /*invoked via C.L. or via a REXX pgm?*/ if y=='COMMAND' | \datatype(\$,"W") then exit /*stick a fork in it, we're all done. */ else exit \$ /*return the answer ───► the invoker.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ show: if showSteps then say center(arg(1), L) left(space(\$), L); return ``` '''output''' when using the default input: ```txt ─────────operand───────── ──────────────────────stack─────────────────────── add to───►stack 3 add to───►stack 3 4 add to───►stack 3 4 2 * 3 8 add to───►stack 3 8 1 add to───►stack 3 8 1 5 - 3 8 -4 add to───►stack 3 8 -4 2 add to───►stack 3 8 -4 2 3 ^ 3 8 -4 8 ^ 3 8 65536 / 3 0.0001220703125 + 3.0001220703125 RPN input: 3 4 2 * 1 5 - 2 3 ^ ^ / + answer───► 3.0001220703125 ``` ===version 3 (error checking)=== This REXX version is the same as above, but also checks for various errors and allows more operators: ::* checks for illegal operator ::* checks for illegal number ::* checks for illegal bit (logical) values ::* checks for malformed RPN expression ::* checks for division by zero ::* allows alternative exponentiation symbol ** ::* allows logical operations & && | ::* allows alternative division symbol ÷ ::* allows integer division % ::* allows remainder division // ::* allows concatenation || ```REXX /*REXX program evaluates a ═════ Reverse Polish notation (RPN) ═════ expression. */ parse arg x /*obtain optional arguments from the CL*/ if x='' then x= "3 4 2 * 1 5 - 2 3 ^ ^ / +" /*Not specified? Then use the default.*/ tokens=words(x) /*save the number of tokens " ". */ showSteps=1 /*set to 0 if working steps not wanted.*/ ox=x /*save the original value of X. */ do i=1 for tokens; @.i=word(x,i) /*assign the input tokens to an array. */ end /*i*/ x=space(x) /*remove any superfluous blanks in X. */ L=max(20, length(x)) /*use 20 for the minimum display width.*/ numeric digits L /*ensure enough decimal digits for ans.*/ say center('operand', L, "─") center('stack', L+L, "─") /*display title*/ Dop= '/ // % ÷'; Bop='& | &&' /*division operators; binary operands.*/ Aop= '- + * ^ **' Dop Bop; Lop=Aop "||" /*arithmetic operators; legal operands.*/ \$= /*nullify the stack (completely empty).*/ do k=1 for tokens; [email protected]; ??=? /*process each token from the @. list.*/ #=words(\$); b=word(\$, max(1, #) ) /*the stack count; the last entry. */ a=word(\$, max(1, #-1) ) /*stack's "first" operand. */ division =wordpos(?, Dop)\==0 /*flag: doing a some kind of division.*/ arith =wordpos(?, Aop)\==0 /*flag: doing arithmetic. */ bitOp =wordpos(?, Bop)\==0 /*flag: doing some kind of binary oper*/ if datatype(?, 'N') then do; \$=\$ ?; call show "add to───►stack"; iterate; end if wordpos(?, Lop)==0 then do; \$=e 'illegal operator:' ?; leave; end if w<2 then do; \$=e 'illegal RPN expression.'; leave; end if ?=='^' then ??= "**" /*REXXify ^ ──► ** (make it legal). */ if ?=='÷' then ??= "/" /*REXXify ÷ ──► / (make it legal). */ if division & b=0 then do; \$=e 'division by zero.' ; leave; end if bitOp & \isBit(a) then do; \$=e "token isn't logical: " a; leave; end if bitOp & \isBit(b) then do; \$=e "token isn't logical: " b; leave; end interpret 'y=' a ?? b /*compute with two stack operands*/ if datatype(y, 'W') then y=y/1 /*normalize the number with ÷ by unity.*/ _=subword(\$, 1, #-2); \$=_ y /*rebuild the stack with the answer. */ call show ? /*display (possibly) a working step. */ end /*k*/ say /*display a blank line, better perusing*/ if word(\$,1)==e then \$= /*handle the special case of errors. */ say ' RPN input:' ox; say " answer───►"\$ /*display original input; display ans.*/ parse source upper . y . /*invoked via C.L. or via a REXX pgm?*/ if y=='COMMAND' | \datatype(\$,"W") then exit /*stick a fork in it, we're all done. */ else exit \$ /*return the answer ───► the invoker.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ isBit: return arg(1)==0 | arg(1)==1 /*returns 1 if arg1 is a binary bit*/ show: if showSteps then say center(arg(1), L) left(space(\$), L); return ``` '''output''' is identical to the 2nd REXX version. ## Ruby See [[Parsing/RPN/Ruby]] ```ruby rpn = RPNExpression("3 4 2 * 1 5 - 2 3 ^ ^ / +") value = rpn.eval ``` {{out}} ```txt for RPN expression: 3 4 2 * 1 5 - 2 3 ^ ^ / + Term Action Stack 3 PUSH [3] 4 PUSH [3, 4] 2 PUSH [3, 4, 2] * MUL [3, 8] 1 PUSH [3, 8, 1] 5 PUSH [3, 8, 1, 5] - SUB [3, 8, -4] 2 PUSH [3, 8, -4, 2] 3 PUSH [3, 8, -4, 2, 3] ^ EXP [3, 8, -4, 8] ^ EXP [3, 8, 65536] / DIV [3, 0.0001220703125] + ADD [3.0001220703125] Value = 3.0001220703125 ``` ## Run BASIC ```runbasic prn\$ = "3 4 2 * 1 5 - 2 3 ^ ^ / + " j = 0 while word\$(prn\$,i + 1," ") <> "" i = i + 1 n\$ = word\$(prn\$,i," ") if n\$ < "0" or n\$ > "9" then num1 = val(word\$(stack\$,s," ")) num2 = val(word\$(stack\$,s-1," ")) n = op(n\$,num2,num1) s = s - 1 stack\$ = stk\$(stack\$,s -1,str\$(n)) print "Push Opr ";n\$;" to stack: ";stack\$ else s = s + 1 stack\$ = stack\$ + n\$ + " " print "Push Num ";n\$;" to stack: ";stack\$ end if wend function stk\$(stack\$,s,a\$) for i = 1 to s stk\$ = stk\$ + word\$(stack\$,i," ") + " " next i stk\$ = stk\$ + a\$ + " " end function FUNCTION op(op\$,a,b) if op\$ = "*" then op = a * b if op\$ = "/" then op = a / b if op\$ = "^" then op = a ^ b if op\$ = "+" then op = a + b if op\$ = "-" then op = a - b end function ``` ```txt Push Num 3 to stack: 3 Push Num 4 to stack: 3 4 Push Num 2 to stack: 3 4 2 Push Opr * to stack: 3 8 Push Num 1 to stack: 3 8 1 Push Num 5 to stack: 3 8 1 5 Push Opr - to stack: 3 8 -4 Push Num 2 to stack: 3 8 -4 2 Push Num 3 to stack: 3 8 -4 2 3 Push Opr ^ to stack: 3 8 -4 8 Push Opr ^ to stack: 3 8 65536 Push Opr / to stack: 3 1.22070312e-4 Push Opr + to stack: 3.00012207 ``` ## Scala ```Scala object RPN { val PRINT_STACK_CONTENTS: Boolean = true def main(args: Array[String]): Unit = { val result = evaluate("3 4 2 * 1 5 - 2 3 ^ ^ / +".split(" ").toList) println("Answer: " + result) } def evaluate(tokens: List[String]): Double = { import scala.collection.mutable.Stack val stack: Stack[Double] = new Stack[Double] for (token <- tokens) { if (isOperator(token)) token match { case "+" => stack.push(stack.pop + stack.pop) case "-" => val x = stack.pop; stack.push(stack.pop - x) case "*" => stack.push(stack.pop * stack.pop) case "/" => val x = stack.pop; stack.push(stack.pop / x) case "^" => val x = stack.pop; stack.push(math.pow(stack.pop, x)) case _ => throw new RuntimeException( s""""\$token" is not an operator""") } else stack.push(token.toDouble) if (PRINT_STACK_CONTENTS) { print("Input: " + token) print(" Stack: ") for (element <- stack.seq.reverse) print(element + " "); println("") } } stack.pop } def isOperator(token: String): Boolean = { token match { case "+" => true; case "-" => true; case "*" => true; case "/" => true; case "^" => true case _ => false } } } ``` {{out}} ```txt Input: 3 Stack: 3.0 Input: 4 Stack: 3.0 4.0 Input: 2 Stack: 3.0 4.0 2.0 Input: * Stack: 3.0 8.0 Input: 1 Stack: 3.0 8.0 1.0 Input: 5 Stack: 3.0 8.0 1.0 5.0 Input: - Stack: 3.0 8.0 -4.0 Input: 2 Stack: 3.0 8.0 -4.0 2.0 Input: 3 Stack: 3.0 8.0 -4.0 2.0 3.0 Input: ^ Stack: 3.0 8.0 -4.0 8.0 Input: ^ Stack: 3.0 8.0 65536.0 Input: / Stack: 3.0 1.220703125E-4 Input: + Stack: 3.0001220703125 Answer: 3.0001220703125 ``` ## Sidef {{trans|Perl 6}} ```ruby var proggie = '3 4 2 * 1 5 - 2 3 ^ ^ / +' class RPN(arr=[]) { method binop(op) { var x = arr.pop var y = arr.pop arr << y.(op)(x) } method run(p) { p.each_word { |w| say "#{w} (#{arr})" given (w) { when (/\d/) { arr << Num(w) } when (<+ - * />) { self.binop(w) } when ('^') { self.binop('**') } default { die "#{w} is bogus" } } } say arr[0] } } RPN.new.run(proggie) ``` {{out}} ```txt 3 () 4 (3) 2 (3 4) * (3 4 2) 1 (3 8) 5 (3 8 1) - (3 8 1 5) 2 (3 8 -4) 3 (3 8 -4 2) ^ (3 8 -4 2 3) ^ (3 8 -4 8) / (3 8 65536) + (3 0.0001220703125) 3.0001220703125 ``` ## Sinclair ZX81 BASIC If you only have 1k of RAM, this program will correctly evaluate the test expression with fewer than 10 bytes to spare. (I know that because I tried running it with the first line modified to allow a stack depth of 7, i.e. allocating space for two more 40-bit floats, and it crashed with an "out of memory" error code before it could print the result of the final addition.) If we desperately needed a few extra bytes there are ways they could be shaved out of the current program; but this version works, and editing a program that takes up almost all your available RAM isn't very comfortable, and to make it really useful for practical purposes you would still want to have 2k or more anyway. The ZX81 character set doesn't include `^`, so we have to use `**` instead. Note that this is not two separate stars, although that's what it looks like: you have to enter it by typing `SHIFT`+`H`. No attempt is made to check for invalid syntax, stack overflow or underflow, etc. ```basic 10 DIM S(5) 20 LET P=1 30 INPUT E\$ 40 LET I=0 50 LET I=I+1 60 IF E\$(I)=" " THEN GOTO 110 70 IF I [String] { var rpn : [String] = [] var stack : [String] = [] // holds operators and left parenthesis for tok in tokens { switch tok { case "(": stack += [tok] // push "(" to stack case ")": while !stack.isEmpty { let op = stack.removeLast() // pop item from stack if op == "(" { break // discard "(" } else { rpn += [op] // add operator to result } } default: if let o1 = opa[tok] { // token is an operator? for op in stack.reverse() { if let o2 = opa[op] { if !(o1.prec > o2.prec || (o1.prec == o2.prec && o1.rAssoc)) { // top item is an operator that needs to come off rpn += [stack.removeLast()] // pop and add it to the result continue } } break } stack += [tok] // push operator (the new one) to stack } else { // token is not an operator rpn += [tok] // add operand to result } } } return rpn + stack.reverse() } func parseInfix(e: String) -> String { let tokens = e.characters.split{ \$0 == " " }.map(String.init) return rpn(tokens).joinWithSeparator(" ") } var input : String input = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3" "infix: \(input)" "postfix: \(parseInfix(input))" ``` {{out}} ```txt "postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / +" ``` ## Tcl ```tcl # Helper proc pop stk { upvar 1 \$stk s set val [lindex \$s end] set s [lreplace \$s end end] return \$val } proc evaluate rpn { set stack {} foreach token \$rpn { set act "apply" switch \$token { "^" { # Non-commutative operation set a [pop stack] lappend stack [expr {[pop stack] ** \$a}] } "/" { # Non-commutative, special float handling set a [pop stack] set b [expr {[pop stack] / double(\$a)}] if {\$b == round(\$b)} {set b [expr {round(\$b)}]} lappend stack \$b } "*" { # Commutative operation lappend stack [expr {[pop stack] * [pop stack]}] } "-" { # Non-commutative operation set a [pop stack] lappend stack [expr {[pop stack] - \$a}] } "+" { # Commutative operation lappend stack [expr {[pop stack] + [pop stack]}] } default { set act "push" lappend stack \$token } } puts "\$token\t\$act\t\$stack" } return [lindex \$stack end] } puts [evaluate {3 4 2 * 1 5 - 2 3 ^ ^ / +}] ``` {{out}} ```txt 3 push 3 4 push 3 4 2 push 3 4 2 * apply 3 8 1 push 3 8 1 5 push 3 8 1 5 - apply 3 8 -4 2 push 3 8 -4 2 3 push 3 8 -4 2 3 ^ apply 3 8 -4 8 ^ apply 3 8 65536 / apply 3 0.0001220703125 + apply 3.0001220703125 3.0001220703125 ``` ## UNIX Shell Please note that the asterisk `*` within the argument string needs to be escaped or quoted, otherwise the shell will interpret and expand it. Technically, this implementation uses a string to represent a stack and lines to delimit each item of the stack, not spaces as you might expect. However, the input is parsed pretty much as a space-separated argument string, but only with the asterisk quoted. ```bash #!/bin/sh exp() { R=1 local i=1 while [ \$i -le \$2 ]; do R=\$((\$R * \$1)) i=\$((\$i + 1)) done } rpn() { local O1 O2 stack while [ \$# -ge 1 ]; do grep -iE '^-?[0-9]+\$' <<< "\$1" > /dev/null 2>&1 if [ "\$?" -eq 0 ]; then stack=`sed -e '\$a'"\$1" -e '/^\$/d' <<< "\$stack"` else grep -iE '^[-\+\*\/\%\^]\$' <<< "\$1" > /dev/null 2>&1 if [ "\$?" -eq 0 ]; then O2=`sed -n '\$p' <<< "\$stack"` stack=`sed '\$d' <<< "\$stack"` O1=`sed -n '\$p' <<< "\$stack"` case "\$1" in '+') stack=`sed -e '\$a'"\$((\$O1 + \$O2))" -e '/^\$/d' -e '\$d' \ <<< "\$stack"`;; '-') stack=`sed -e '\$a'"\$((\$O1 - \$O2))" -e '/^\$/d' -e '\$d' \ <<< "\$stack"`;; '*') stack=`sed -e '\$a'"\$((\$O1 * \$O2))" -e '/^\$/d' -e '\$d' \ <<< "\$stack"`;; '/') stack=`sed -e '\$a'"\$((\$O1 / \$O2))" -e '/^\$/d' -e '\$d' \ <<< "\$stack"`;; '%') stack=`sed -e '\$a'"\$((\$O1 % \$O2))" -e '/^\$/d' -e '\$d' \ <<< "\$stack"`;; '^') exp \$O1 \$O2 stack=`sed -e '\$a'"\$((\$R))" -e '/^\$/d' -e '\$d' <<< \ "\$stack"`;; esac else echo "Unknown RPN token \`\`\$1''" fi fi echo "\$1" ":" \$stack shift done sed -n '1p' <<< "\$stack" if [ "`wc -l <<< "\$stack"`" -gt 1 ]; then echo "Malformed input expression" > /dev/stderr return 1 else return 0 fi } rpn 3 4 2 '*' 1 5 '-' 2 3 '^' '^' '/' '+' ``` ### Output 3 : 3 4 : 3 4 2 : 3 4 2 * : 3 8 1 : 3 8 1 5 : 3 8 1 5 - : 3 8 -4 2 : 3 8 -4 2 3 : 3 8 -4 2 3 ^ : 3 8 -4 8 ^ : 3 8 65536 / : 3 0 + : 3 3 ``` ## VBA {{trans|Liberty BASIC}} ```VBA Global stack\$ Function RPN(expr\$) Debug.Print "Expression:" Debug.Print expr\$ Debug.Print "Input", "Operation", "Stack after" stack\$ = "" token\$ = "#" i = 1 token\$ = Split(expr\$)(i - 1) 'split is base 0 token2\$ = " " + token\$ + " " Do Debug.Print "Token "; i; ": "; token\$, 'operation If InStr("+-*/^", token\$) <> 0 Then Debug.Print "operate", op2\$ = pop\$() op1\$ = pop\$() If op1\$ = "" Then Debug.Print "Error: stack empty for "; i; "-th token: "; token\$ End End If op1 = Val(op1\$) op2 = Val(op2\$) Select Case token\$ Case "+" res = CDbl(op1) + CDbl(op2) Case "-" res = CDbl(op1) - CDbl(op2) Case "*" res = CDbl(op1) * CDbl(op2) Case "/" res = CDbl(op1) / CDbl(op2) Case "^" res = CDbl(op1) ^ CDbl(op2) End Select Call push2(str\$(res)) 'default:number Else Debug.Print "push", Call push2(token\$) End If Debug.Print "Stack: "; reverse\$(stack\$) i = i + 1 If i > Len(Join(Split(expr, " "), "")) Then token\$ = "" Else token\$ = Split(expr\$)(i - 1) 'base 0 token2\$ = " " + token\$ + " " End If Loop Until token\$ = "" Debug.Print Debug.Print "Result:"; pop\$() 'extra\$ = pop\$() If stack <> "" Then Debug.Print "Error: extra things on a stack: "; stack\$ End If End End Function '--------------------------------------- Function reverse\$(s\$) reverse\$ = "" token\$ = "#" While token\$ <> "" i = i + 1 token\$ = Split(s\$, "|")(i - 1) 'split is base 0 reverse\$ = token\$ & " " & reverse\$ Wend End Function '--------------------------------------- Sub push2(s\$) stack\$ = s\$ + "|" + stack\$ 'stack End Sub Function pop\$() 'it does return empty on empty stack pop\$ = Split(stack\$, "|")(0) stack\$ = Mid\$(stack\$, InStr(stack\$, "|") + 1) End Function ``` {{out}} ```txt ?RPN("3 4 2 * 1 5 - 2 3 ^ ^ / +") Expression: 3 4 2 * 1 5 - 2 3 ^ ^ / + Input Operation Stack after Token 1 : 3 push Stack: 3 Token 2 : 4 push Stack: 3 4 Token 3 : 2 push Stack: 3 4 2 Token 4 : * operate Stack: 3 8 Token 5 : 1 push Stack: 3 8 1 Token 6 : 5 push Stack: 3 8 1 5 Token 7 : - operate Stack: 3 8 -4 Token 8 : 2 push Stack: 3 8 -4 2 Token 9 : 3 push Stack: 3 8 -4 2 3 Token 10 : ^ operate Stack: 3 8 -4 8 Token 11 : ^ operate Stack: 3 8 65536 Token 12 : / operate Stack: 3 .0001220703125 Token 13 : + operate Stack: 3.0001220703125 Result: 3.0001220703125 ``` ## Xojo {{trans|VBA}} ```Xojo Function RPN(expr As String) As String Dim tokenArray() As String Dim stack() As String Dim Wert1 As Double Dim Wert2 As Double 'Initialize array (removed later) ReDim tokenArray(1) ReDim stack(1) tokenArray = Split(expr, " ") Dim i As integer i = 0 While i <= tokenArray.Ubound If tokenArray(i) = "+" Then Wert2 = Val(stack.pop) Wert1 = Val(stack.pop) stack.Append(Str(Wert1+Wert2)) ElseIf tokenArray(i) = "-" Then Wert2 = Val(stack.pop) Wert1 = Val(stack.pop) stack.Append(Str(Wert1-Wert2)) ElseIf tokenArray(i) = "*" Then Wert2 = Val(stack.pop) Wert1 = Val(stack.pop) stack.Append(Str(Wert1*Wert2)) ElseIf tokenArray(i) = "/" Then Wert2 = Val(stack.pop) Wert1 = Val(stack.pop) stack.Append(Str(Wert1/Wert2)) ElseIf tokenArray(i) = "^" Then Wert2 = Val(stack.pop) Wert1 = Val(stack.pop) stack.Append(Str(pow(Wert1,Wert2))) Else stack.Append(tokenArray(i)) End If i = i +1 Wend Return stack(2) End Function ``` {{out}} ```txt ?RPN("3 4 2 * 1 5 - 2 3 ^ ^ / +") Expression: 3 4 2 * 1 5 - 2 3 ^ ^ / + Input Operation Stack after Token 1 : 3 push Stack: 3 Token 2 : 4 push Stack: 3 4 Token 3 : 2 push Stack: 3 4 2 Token 4 : * operate Stack: 3 8 Token 5 : 1 push Stack: 3 8 1 Token 6 : 5 push Stack: 3 8 1 5 Token 7 : - operate Stack: 3 8 -4 Token 8 : 2 push Stack: 3 8 -4 2 Token 9 : 3 push Stack: 3 8 -4 2 3 Token 10 : ^ operate Stack: 3 8 -4 8 Token 11 : ^ operate Stack: 3 8 65536 Token 12 : / operate Stack: 3 .000122 Token 13 : + operate Stack: 3.000122 Result: 3.000122 ``` ## zkl ```zkl var ops=D("^",True, "*",'*, "/",'/, "+",'+, "-",'-); fcn parseRPN(e){ println("\npostfix: ", e); stack:=L(); foreach tok in (e.split()){ op:=ops.find(tok); if(op){ y := stack.pop(); x := stack.pop(); if(True==op) x=x.pow(y); else x=op(x,y); stack.append(x); } else stack.append(tok.toFloat()); println(tok," --> ",stack); } println("result: ", stack[0]) } ``` ```zkl tests:=T("3 4 2 * 1 5 - 2 3 ^ ^ / +"); foreach t in (tests) { parseRPN(t) } ``` {{out}} ```txt postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / + 3 --> L(3) 4 --> L(3,4) 2 --> L(3,4,2) * --> L(3,8) 1 --> L(3,8,1) 5 --> L(3,8,1,5) - --> L(3,8,-4) 2 --> L(3,8,-4,2) 3 --> L(3,8,-4,2,3) ^ --> L(3,8,-4,8) ^ --> L(3,8,65536) / --> L(3,0.00012207) + --> L(3.00012) result: 3.00012 ```