Parsing/RPN calculator algorithm
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Create a stack-based evaluator for an expression in 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:
3 4 2 * 1 5 - 2 3 ^ ^ / +
- Print or display the output here
- Notes
- ^ means exponentiation in the expression above.
- / means division.
- See also
- 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.
Ada
<lang Ada>with Ada.Text_IO, Ada.Containers.Vectors;
procedure RPN_Calculator is
package IIO is new Ada.Text_IO.Float_IO(Float);
package Float_Vec is new Ada.Containers.Vectors
(Index_Type => Positive, Element_Type => Float);
Stack: Float_Vec.Vector;
Input: String := Ada.Text_IO.Get_Line; Cursor: Positive := Input'First; New_Cursor: Positive;
begin
loop
-- read spaces
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
Ada.Text_IO.Put(" ");
IIO.Put(Stack.Element(I), Aft => 5, Exp => 0);
end loop;
Ada.Text_IO.New_Line;
end loop;
Ada.Text_IO.Put("Result = ");
IIO.Put(Item => Stack.Last_Element, Aft => 5, Exp => 0);
end RPN_Calculator;</lang>
- Output:
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
<lang algol68># 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 )
)</lang>
- Output:
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
ANTLR
Java
<lang 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($num.text));}; Digit : '0'..'9'; op : '-' {double x = s.pop(); s.push(s.pop() - x);} | '/' {double x = s.pop(); s.push(s.pop() / x);} | '*' {s.push(s.pop() * s.pop());} | '^' {double x = s.pop(); s.push(Math.pow(s.pop(), x));} | '+' {s.push(s.pop() + s.pop());}; WS : (' ' | '\t'){skip()}; NEWLINE : '\r'? '\n'; </lang> Produces:
>java Test 3 4 2 * 1 5 - 2 3 ^ ^ / + ^Z 3.0001220703125
AutoHotkey
Output is in clipboard. <lang AHK>evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +") evalRPN(s){ stack := [] out := "For RPN expression: '" s "'`r`n`r`nTOKEN`t`tACTION`t`t`tSTACK`r`n" Loop Parse, s If A_LoopField is number t .= A_LoopField else { If t stack.Insert(t) , out .= t "`tPush num onto top of stack`t" stackShow(stack) "`r`n" , t := "" If InStr("+-/*^", l := A_LoopField) { a := stack.Remove(), b := stack.Remove() stack.Insert( l = "+" ? b + a :l = "-" ? b - a :l = "*" ? b * a :l = "/" ? b / a :l = "^" ? b **a :0 ) out .= l "`tApply op " l " to top of stack`t" stackShow(stack) "`r`n" } } r := stack.Remove() out .= "`r`n The final output value is: '" r "'" clipboard := out return r } StackShow(stack){ for each, value in stack out .= A_Space value return subStr(out, 2) }</lang>
- Output:
For RPN expression: '3 4 2 * 1 5 - 2 3 ^ ^ / +' TOKEN ACTION STACK 3 Push num onto top of stack 3 4 Push num onto top of stack 3 4 2 Push num onto top of stack 3 4 2 * Apply op * to top of stack 3 8 1 Push num onto top of stack 3 8 1 5 Push num onto top of stack 3 8 1 5 - Apply op - to top of stack 3 8 -4 2 Push num onto top of stack 3 8 -4 2 3 Push num onto top of stack 3 8 -4 2 3 ^ Apply op ^ to top of stack 3 8 -4 8 ^ Apply op ^ to top of stack 3 8 65536 / Apply op / to top of stack 3 0.000122 + Apply op + to top of stack 3.000122 The final output value is: '3.000122'
BBC BASIC
<lang bbcbasic> @% = &60B
RPN$ = "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%)</lang>
- Output:
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
C
<lang 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; }</lang>
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. <lang c>#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; }</lang>
C++
<lang cpp>#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;
}</lang>
- Output:
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 Final answer: 3.00012
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Globalization; using System.Threading;
namespace RPNEvaluator {
class RPNEvaluator
{
static void Main(string[] args)
{
Thread.CurrentThread.CurrentCulture = CultureInfo.InvariantCulture;
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();
}
}
}</lang>
- Output:
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
<lang>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) { print("``token.string.padTrailing(8)````description.padTrailing(30)````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 { throw Exception("bad syntax"); } } return stack.pop(); }
print(calculate("3 4 2 * 1 5 - 2 3 ^ ^ / +")); }</lang>
- Output:
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. <lang clojure> (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)))
</lang>
- Output:
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
<lang 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))
(arg1 (cadr 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)))))</lang>
- Output:
>(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
<lang scheme>
- 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))
(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 (task rpn)
(define S (stack 'S)) (calculator (text-parse rpn) S ))
</lang>
- Output:
(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
<lang 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</lang>
- Output:
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
<lang d>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]);
}</lang>
- Output:
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
<lang 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").</lang>
- Output:
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
F#
As interactive script
<lang fsharp>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</lang>
- Output:
> 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
+ add 3.000
val it : float list = [3.00012207]
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.<lang Fortran> 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?
DEED = "Load" !Yes. So, load its value.
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</lang>
Output...
Evaluation of the Reverse Polish string 3 4 2 * 1 5 - 2 3 ^ ^ / + Char Token Action SP:Stack... 1 3 Load 1: 3.000000 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
<lang 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 ) ->
stack = op( stack.tail().head(), stack.head() ) : stack.tail().tail()
println( "perform $token: ${stack.reversed()}" )
None -> error( "unrecognized operator '$token'" )
stack.head()
res = evaluate( '3 4 2 * 1 5 - 2 3 ^ ^ / +' ) println( res + (if res is Integer then else " or ${float(res)}") )</lang>
- Output:
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. <lang go>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])
}</lang>
- Output:
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
<lang 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()
}</lang> Test <lang groovy>println evaluateRPN('3 4 2 * 1 5 - 2 3 ^ ^ / +')</lang>
- 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, 0.0001220703125] +: [3.0001220703125] 3.0001220703125
Haskell
Pure RPN calculator <lang Haskell>calcRPN :: String -> [Double] calcRPN = foldl interprete [] . words
interprete s x
| x `elem` ["+","-","*","/","^"] = operate x s
| otherwise = read 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</lang>
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.
<lang haskell>calcRPNLog :: String -> ([Double],[(String, [Double])]) calcRPNLog input = mkLog $ zip commands $ tail result
where result = scanl interprete [] commands
commands = words input
mkLog [] = ([], [])
mkLog res = (snd $ last res, res)</lang>
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: <lang haskell>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</lang>
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: <lang haskell>class Monad m => 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</lang>
The use case: <lang haskell>calcRPNM :: Logger m => String -> m [Double] calcRPNM = foldM (verbose interprete) [] . words</lang>
- Output:
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")
Icon and Unicon
<lang Icon>procedure main()
EvalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
end
link printf 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</lang>
printf.icn provides formatting
- Output:
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: <lang J> a: , <;._1 ' ' , '3 4 2 * 1 5 - 2 3 ^ ^ / +' ┌┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┐ ││3│4│2│*│1│5│-│2│3│^│^│/│+│ └┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┘</lang> 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. <lang J> 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│ └─┘</lang>
Alternate Implementation
<lang J>rpn=: 3 :0
queue=. |.3 :'|.3 :y 0'::]each;: y
op=. 1 :'2 (u~/@:{.,}.)S:0 ,@]'
ops=. +op`(-op)`(*op)`(%op)`(^op)`(,&;)
choose=. ((;:'+-*/^')&i.@[)
,ops@.choose/queue
)</lang>
Example use:
<lang J> rpn '3 4 2 * 1 5 - 2 3 ^ ^ / +' 3.00012</lang>
To see intermediate result stacks, use this variant (the only difference is the definition of 'op'):
<lang J>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.@[)
,ops@.choose/queue
)</lang>
In other words:
<lang J> 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</lang>
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
Supports multi-digit numbers and negative numbers. <lang java5>import java.util.LinkedList;
public class RPN{ public static void evalRPN(String expr){ String cleanExpr = cleanExpr(expr); LinkedList<Double> stack = new LinkedList<Double>(); 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); } System.out.println("Final answer: " + stack.pop()); }
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 ^ ^ / +"); } }</lang>
- Output:
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] Final answer: 3.0001220703125
JavaScript
<lang 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, '
')
}</lang>
- 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 /: 3,0.0001220703125 +: 3.0001220703125
With checks and messages
<lang javascript>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!
')
}
}</lang>
- Output:
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.)
<lang julia>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 ^ ^ / +")</lang>
- 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, 0.0001220703125 +: 3.0001220703125
(The return value is also 3.0001220703125.)
Kotlin
<lang scala>// 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) {
stack.add(d)
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)
stack.add(when (token) {
"+" -> 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 ${stack[0]}")
}
fun main(args: Array<String>) {
val expr = "3 4 2 * 1 5 - 2 3 ^ ^ / +" rpnCalculate(expr)
}</lang>
- Output:
For expression = 3 4 2 * 1 5 - 2 3 ^ ^ / + Token Action Stack 3.0 Push num onto top of stack [3.0] 4.0 Push num onto top of stack [3.0, 4.0] 2.0 Push num onto top of stack [3.0, 4.0, 2.0] * Apply op to top of stack [3.0, 8.0] 1.0 Push num onto top of stack [3.0, 8.0, 1.0] 5.0 Push num onto top of stack [3.0, 8.0, 1.0, 5.0] - Apply op to top of stack [3.0, 8.0, -4.0] 2.0 Push num onto top of stack [3.0, 8.0, -4.0, 2.0] 3.0 Push num onto top of stack [3.0, 8.0, -4.0, 2.0, 3.0] ^ Apply op to top of stack [3.0, 8.0, -4.0, 8.0] ^ Apply op to top of stack [3.0, 8.0, 65536.0] / Apply op to top of stack [3.0, 1.220703125E-4] + Apply op to top of stack [3.0001220703125] The final value is 3.0001220703125
Liberty BASIC
<lang lb> global stack$
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 </lang>
- Output:
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
<lang 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 *" )</lang>
- Output:
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 + add 3.0001220703125 result: 3.0001220703125 INPUT OP STACK 22 push 22 11 push 22 11 * mul 242 result: 242.0000000000000
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".) <lang 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 ^ ^ / +"]];</lang>
- 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 1/8192 +: 24577/8192
NetRexx
<lang 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
</lang>
- Output:
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
<lang 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 ""</lang>
- Output:
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
<lang 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();
}
}
} </lang>
- Output:
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
<lang 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</lang>
Evaluation of the test expression:
# 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.
<lang Oforth>"3 4 2 * 1 5 - 2 3 ^ ^ / +" eval println</lang>
- Output:
3
To show the changes in the stack, we can use .l after evaluating each word :
<lang Oforth>: rpn(s) { s words apply(#[ eval .l ]) }
rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +")</lang>
- 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 | 0 | 3 |
ooRexx
<lang 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</lang>
- Output:
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
Perl
<lang Perl>
- RPN calculator
- Nigel Galloway April 2nd., 2012
$WSb = '(?:^|\s+)'; $WSa = '(?:\s+|$)'; $num = '([+-/]?(?:\.\d+|\d+(?:\.\d*)?))'; $op = '([-+*/^])'; sub myE {
my $a = '('.$1.')'.$3.'('.$2.')';
$a =~ s/\^/**/;
return eval($a);
} while (<>) {
while (s/$WSb$num\s+$num\s+$op$WSa/' '.myE().' '/e) {}
print ($_, "\n");
} </lang> Produces:
>rpnC.pl 3 4 2 * 1 5 - 2 3 ^ ^ / + 3.0001220703125
Perl 6
<lang 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($proggie);</lang>
- Output:
3 () 4 (3) 2 (3 4) * (3 4 2) 1 (3 8) 5 (3 8 1) - (3 8 1 5) 2 (3 8 -4) 3 (3 8 -4 2) ^ (3 8 -4 2 3) ^ (3 8 -4 8) / (3 8 65536) + (3 0.0001220703125) 3.0001220703125
Phix
<lang Phix>procedure evalRPN(string s) sequence stack = {} sequence ops = split(s)
for i=1 to length(ops) do
string op = ops[i]
switch op
case "+": stack[-2] = stack[-2]+stack[-1]; stack = stack[1..-2]
case "-": stack[-2] = stack[-2]-stack[-1]; stack = stack[1..-2]
case "*": stack[-2] = stack[-2]*stack[-1]; stack = stack[1..-2]
case "/": stack[-2] = stack[-2]/stack[-1]; stack = stack[1..-2]
case "^": stack[-2] = power(stack[-2],stack[-1]); stack = stack[1..-2]
default : stack = append(stack,scanf(op,"%d")[1][1])
end switch
?{op,stack}
end for
end procedure evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")</lang>
- Output:
"started"
{"3",{3}}
{"4",{3,4}}
{"2",{3,4,2}}
{"*",{3,8}}
{"1",{3,8,1}}
{"5",{3,8,1,5}}
{"-",{3,8,-4}}
{"2",{3,8,-4,2}}
{"3",{3,8,-4,2,3}}
{"^",{3,8,-4,8}}
{"^",{3,8,65536}}
{"/",{3,0.0001220703125}}
{"+",{3.00012207}}
PHP
<lang php> <?php function rpn($postFix){
$stack = Array(); echo "Input\tOperation\tStack\tafter\n" ;
$token = explode(" ", trim($postFix)); $count = count($token);
for($i = 0 ; $i<$count;$i++)
{
echo $token[$i] ." \t";
$tokenNum = "";
if (is_numeric($token[$i])) {
echo "Push";
array_push($stack,$token[$i]);
}
else
{
echo "Operate";
$secondOperand = end($stack);
array_pop($stack);
$firstOperand = end($stack);
array_pop($stack);
if ($token[$i] == "*")
array_push($stack,$firstOperand * $secondOperand);
else if ($token[$i] == "/")
array_push($stack,$firstOperand / $secondOperand);
else if ($token[$i] == "-")
array_push($stack,$firstOperand - $secondOperand);
else if ($token[$i] == "+")
array_push($stack,$firstOperand + $secondOperand);
else if ($token[$i] == "^")
array_push($stack,pow($firstOperand,$secondOperand));
else {
die("Error");
}
}
echo "\t\t" . implode(" ", $stack) . "\n";
} return end($stack);
}
echo "Compute Value: " . rpn("3 4 2 * 1 5 - 2 3 ^ ^ / + "); ?> </lang>
- Output:
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: <lang 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)) ) )</lang>
Test (note that the top-of-stack is in the left-most position): <lang 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</lang>
PL/I
<lang 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;</lang>
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:
/* 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
<lang 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 </lang>
- Output:
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. <lang 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', 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', 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.</lang>
- Output:
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
<lang 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])</lang>
- Output:
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
<lang 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</lang>
- Output:
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
<lang 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)))])))
</lang> Test case
-> (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: <lang racket> (calculate-RPN (in-port read (open-input-string "3.0 4 2 * 1 5 - 2 3 ^ ^ / +"))) </lang>
REXX
version 1
<lang 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</lang>
- Output:
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. <lang 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*/ $= /*nullify the stack (completely empty).*/
do k=1 for tokens; ?=@.k; ??=? /*process each token from the @. list.*/
#=words($) /*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</lang> output when using the default input:
─────────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 ||
<lang 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.*/ $= /*nullify the stack (completely empty).*/
do k=1 for tokens; ?=@.k; ??=? /*process each token from the @. list.*/
#=words($); 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($), L); return</lang>
output is identical to the 2nd REXX version.
Ruby
See Parsing/RPN/Ruby <lang ruby>rpn = RPNExpression("3 4 2 * 1 5 - 2 3 ^ ^ / +") value = rpn.eval</lang>
- Output:
for RPN expression: 3 4 2 * 1 5 - 2 3 ^ ^ / + Term Action Stack 3 PUSH [3] 4 PUSH [3, 4] 2 PUSH [3, 4, 2] * MUL [3, 8] 1 PUSH [3, 8, 1] 5 PUSH [3, 8, 1, 5] - SUB [3, 8, -4] 2 PUSH [3, 8, -4, 2] 3 PUSH [3, 8, -4, 2, 3] ^ EXP [3, 8, -4, 8] ^ EXP [3, 8, 65536] / DIV [3, 0.0001220703125] + ADD [3.0001220703125] Value = 3.0001220703125
Run BASIC
<lang runbasic>prn$ = "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</lang>
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
<lang 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
}
}
}</lang>
- Output:
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
<lang 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)</lang>
- Output:
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
Swift
<lang Swift>let opa = [
"^": (prec: 4, rAssoc: true), "*": (prec: 3, rAssoc: false), "/": (prec: 3, rAssoc: false), "+": (prec: 2, rAssoc: false), "-": (prec: 2, rAssoc: false),
]
func rpn(tokens: [String]) -> [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))"</lang>
- Output:
"postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / +"
Tcl
<lang 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 $stack end]
}
puts [evaluate {3 4 2 * 1 5 - 2 3 ^ ^ / +}]</lang>
- Output:
3 push 3 4 push 3 4 2 push 3 4 2 * apply 3 8 1 push 3 8 1 5 push 3 8 1 5 - apply 3 8 -4 2 push 3 8 -4 2 3 push 3 8 -4 2 3 ^ apply 3 8 -4 8 ^ apply 3 8 65536 / apply 3 0.0001220703125 + apply 3.0001220703125 3.0001220703125
VBA
<lang VBA>Global stack$
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</lang>
- Output:
?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
<lang 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</lang>
- Output:
?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
<lang 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])
}</lang> <lang zkl>tests:=T("3 4 2 * 1 5 - 2 3 ^ ^ / +"); foreach t in (tests) { parseRPN(t) }</lang>
- Output:
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
- Programming Tasks
- Solutions by Programming Task
- Ada
- ALGOL 68
- ANTLR
- AutoHotkey
- BBC BASIC
- C
- C++
- C sharp
- Ceylon
- Clojure
- Common Lisp
- EchoLisp
- Ela
- D
- Erlang
- F Sharp
- Fortran
- FunL
- Go
- Groovy
- Haskell
- Icon
- Unicon
- Icon Programming Library
- J
- Java
- JavaScript
- Julia
- Kotlin
- Liberty BASIC
- Lua
- Mathematica
- NetRexx
- Nim
- Objeck
- OCaml
- Oforth
- OoRexx
- Perl
- Perl 6
- Phix
- PHP
- PicoLisp
- PL/I
- PowerShell
- Prolog
- Python
- Racket
- REXX
- Ruby
- Run BASIC
- Scala
- Sidef
- Swift
- Tcl
- VBA
- Xojo
- Zkl