Code Golf: Evaluating Mathematical Expressions

Question

Challenge

Here is the challenge (of my own invention, though I wouldn't be surprised if it has previously appeared elsewhere on the web).

Write a function that takes a single argument that is a string representation of a simple mathematical expression and evaluates it as a floating point value. A "simple expression" may include any of the following: positive or negative decimal numbers, +, -, *, /, (, ). Expressions use (normal) infix notation. Operators should be evaluated in the order they appear, i.e. not as in BODMAS, though brackets should be correctly observed, of course. The function should return the correct result for any possible expression of this form. However, the function does not have to handle malformed expressions (i.e. ones with bad syntax).

Examples of expressions:

1 + 3 / -8                            = -0.5       (No BODMAS)
2*3*4*5+99                            = 219
4 * (9 - 4) / (2 * 6 - 2) + 8         = 10
1 + ((123 * 3 - 69) / 100)            = 4
2.45/8.5*9.27+(5*0.0023)              = 2.68...

Rules

I anticipate some form of "cheating"/craftiness here, so please let me forewarn against it! By cheating, I refer to the use of the eval or equivalent function in dynamic languages such as JavaScript or PHP, or equally compiling and executing code on the fly. (I think my specification of "no BODMAS" has pretty much guaranteed this however.) Apart from that, there are no restrictions. I anticipate a few Regex solutions here, but it would be nice to see more than just that.

Now, I'm mainly interested in a C#/.NET solution here, but any other language would be perfectly acceptable too (in particular, F# and Python for the functional/mixed approaches). I haven't yet decided whether I'm going to accept the shortest or most ingenious solution (at least for the language) as the answer, but I would welcome any form of solution in any language, except what I've just prohibited above!

My Solution

I've now posted my C# solution here (403 chars). Update: My new solution has beaten the old one significantly at 294 chars, with the help of a bit of lovely regex! I suspected that this will get easily beaten by some of the languages out there with lighter syntax (particularly the funcional/dynamic ones), and have been proved right, but I'd be curious if someone could beat this in C# still.

Update

I've seen some very crafty solutions already. Thanks to everyone who has posted one. Although I haven't tested any of them yet, I'm going to trust people and assume they at least work with all of the given examples.

Just for the note, re-entrancy (i.e. thread-safety) is not a requirement for the function, though it is a bonus.

---

Format

Please post all answers in the following format for the purpose of easy comparison:

Language

Number of characters: ???

Fully obfuscated function:

(code here)

Clear/semi-obfuscated function:

(code here)

Any notes on the algorithm/clever shortcuts it takes.

---

Answer 1

Python

Number of characters: 237

Fully obfuscated function:

from operator import*
def e(s,l=[]):
 if s:l+=list(s.replace(' ','')+')')
 a=0;o=add;d=dict(zip(')*+-/',(0,mul,o,sub,div)));p=l.pop
 while o:
  c=p(0)
  if c=='(':c=e(0)
  while l[0]not in d:c+=p(0)
  a=o(a,float(c));o=d[p(0)]
 return a

Clear/semi-obfuscated function:

import operator

def calc(source, stack=[]):
    if source:
        stack += list(source.replace(' ', '') + ')')

    answer = 0

    ops = {
        ')': 0,
        '*': operator.mul,
        '+': operator.add,
        '-': operator.sub,
        '/': operator.div,
    }

    op = operator.add
    while op:
        cur = stack.pop(0)

        if cur == '(':
            cur = calc(0)

        while stack[0] not in ops:
            cur += stack.pop(0)

        answer = op(answer, float(cur))
        op = ops[stack.pop(0)]

    return answer

Answer 2

Ruby 1.9

(because of the regex)

Number of characters: 296

def d(s)
  while m = s.match(/((?<pg>\((?:\\[()]|[^()]|\g<pg>)*\)))/)
    s.sub!(m[:pg], d(m[:pg][1,m[:pg].size-2]))
  end
  while m = s.match(/(-?\d+(\.\d+)?)\s*([*+\-\/])\s*(-?\d+(\.\d+)?)/)
    r=m[1].to_f.send(m[3],m[4].to_f) if %w{+ - * /}.include?m[3]
    s.sub!(m[0], r.to_s)
  end
  s
end

EDIT: Includes Martin's optimization.

Answer 3

C99

Number of characters: 239 (But see below for 209)

compressed function:

#define S while(*e==32)++e
#define F float
F strtof();char*e;F v();F g(){S;return*e++-40?strtof(e-1,&e):v();}F v(){F b,a=g();for(;;){S;F o=*e++;if(!o|o==41)return a;b=g();a=o==43?a+b:o==45?a-b:o==42?a*b:a/b;}}F f(char*x){e=x;return v();}

decompressed function:

float strtof();

char* e;
float v();

float g() {
    while (*e == ' ') ++e;
    return *e++ != '(' ? strtof(e-1, &e) : v();
}

float v() {
    float b, a = g();
    for (;;) {
        while (*e == ' ') ++e;
        float op = *e++;
        if (op == 0 || op == ')') return a;
        b = g();
        a = op == '+' ? a + b : op == '-' ? a - b : op == '*' ? a * b : a / b;
    }
}

float eval(char* x) {
    e = x;
    return v();
}

Function is not re-entrant.

EDIT from Chris Lutz: I hate to trample on another man's code, but here is a 209-character version:

#define S for(;*e==32;e++)
#define X (*e++-40?strtof(e-1,&e):v())
float strtof();char*e;float v(){float o,a=X;for(;;){S;o=*e++;if(!o|o==41)return a;S;a=o-43?o-45?o-42?a/X:a*X:a-X:a+X;}}
#define f(x) (e=x,v())

Readable (well, not really very readable, but decompressed):

float strtof();
char *e;
float v() {
    float o, a = *e++ != '(' ? strtof(e - 1, &e) : v();
    for(;;) {
        for(; *e == ' '; e++);
        o = *e++;
        if(o == 0 || o==')') return a;
        for(; *e == ' '; e++);
        // I have no idea how to properly indent nested conditionals
        // and this is far too long to fit on one line.
        a = o != '+' ?
          o != '-' ?
            o != '*' ?
              a / (*e++ != '(' ? strtof(e - 1, &e) : v()) :
              a * (*e++ != '(' ? strtof(e - 1, &e) : v()) :
            a - (*e++ != '(' ? strtof(e - 1, &e) : v()) :
          a + (*e++ != '(' ? strtof(e - 1, &e) : v());
      }
}
#define f(x) (e = x, v())

Yeah, f() is a macro, not a function, but it works. The readable version has some of the logic rewritten but not reordered (like o != '+' instead of o - '+'), but is otherwise just an indented (and preprocessed) version of the other one. I keep trying to simplify the if(!o|o==41)return a; part into the for() loop, but it never makes it shorter. I still believe it can be done, but I'm done golfing. If I work on this question anymore, it will be in the language that must not be named.

Answer 4

Python

Number of characters: 492

Mildly obfuscated function (short variable names, no spaces around operators):

def e(s):
    q=[]
    b=1
    v=[]
    for c in s.replace(' ','')+'$':
     if c in '.0123456789' or c in '+-' and b and not v:
      v+=[c]
     else:
      if v:
       q+=[float(''.join(v))]
       v=[]
      while len(q)>=3:
       x,y,z=q[-3:]
       if type(x)==type(z)==float:
        if y=='+':q[-3:]=[x+z]
        elif y=='-':q[-3:]=[x-z]
        elif y=='*':q[-3:]=[x*z]
        elif y=='/':q[-3:]=[x/z]
       elif (x,z)==('(',')'):q[-3:]=[y]
       else:break
      if c=='$':break
      q+=[c]
      b=c!=')'
    return q[0]

I think this is relatively easy to understand. It's a pretty straightforward, naive approach. It doesn't import anything, doesn't use regex, is fully self-contained (single function, no globals, no side-effects), and should handle signed literals (positive or negative). Using more sensible variable names and adhering to recommended Python formatting increases the character count to more like 850-900, a big chunk of that from using four spaces instead of a single tab for indentation.

Answer 5

Haskell

Number of characters: 182

No attempt at cleverness, just some compression: 4 lines, 312 bytes.

import Data.Char;import Text.ParserCombinators.Parsec
q=either(error.show)id.runParser t id"".filter(' '/=);t=do
s<-getState;a<-fmap read(many1$oneOf".-"<|>digit)<|>between(char '('>>setState id)(char ')'>>setState s)t
option(s a)$choice(zipWith(\c o->char c>>return(o$s a))"+-*/"[(+),(-),(*),(/)])>>=setState>>t

And now, really getting into the golf spirit, 3 lines and 182 bytes:

q=snd.(`e`id).filter(' '/=)
e s c|[(f,h)]<-readsPrec 0 s=g h(c f);e('(':s)c=g h(c f)where(')':h,f)=e s id
g('+':h)=e h.(+);g('-':h)=e h.(-);g('*':h)=e h.(*);g('/':h)=e h.(/);g h=(,)h

Exploded:

-- Strip spaces from the input, evaluate with empty accumulator,
-- and output the second field of the result.
q :: String -> Double
q = snd . flip eval id . filter (not . isSpace)

-- eval takes a string and an accumulator, and returns
-- the final value and what’s left unused from the string.
eval :: (Fractional a, Read a) => String -> (a -> a) -> (String, a)

-- If the beginning of the string parses as a number, add it to the accumulator,
-- then try to read an operator and further.
eval str accum | [(num, rest)] <- readsPrec 0 str = oper rest (accum num)

-- If the string starts parentheses, evaluate the inside with a fresh
-- accumulator, and continue after the closing paren.
eval ('(':str) accum = oper rest (accum num) where (')':rest, num) = eval str id

-- oper takes a string and current value, and tries to read an operator
-- to apply to the value.  If there is none, it’s okay.
oper :: (Fractional a, Read a) => String -> a -> (String, a)

-- Handle operations by giving eval a pre-seeded accumulator.
oper ('+':str) num = eval str (num +)
oper ('-':str) num = eval str (num -)
oper ('*':str) num = eval str (num *)
oper ('/':str) num = eval str (num /)

-- If there’s no operation parsable, just return.
oper str num = (str, num)

Answer 6

JavaScript (Not IE compatible)

Number of characters: 268/260

Fully obfuscated function:

function e(x){x=x.replace(/ /g,'')+')'
function P(n){return x[0]=='('?(x=x.substr(1),E()):(n=/^[-+]?[\d.]+/(x)[0],x=x.substr(n.length),+n)}function E(a,o,b){a=P()
for(;;){o=x[0]
x=x.substr(1)
if(o==')')return a
b=P()
a=o=='+'?a+b:o=='-'?a-b:o=='*'?a*b:a/b}}return E()}

or, in JavaScript 1.8 (Firefox 3+), you can save a few characters by using expression closures:

e=function(x,P,E)(x=x.replace(/ /g,'')+')',P=function(n)(x[0]=='('?(x=x.substr(1),E()):(n=/^[-+]?[\d.]+/(x)[0],x=x.substr(n.length),+n)),E=function(a,o,b){a=P()
for(;;){o=x[0]
x=x.substr(1)
if(o==')')return a
b=P()
a=o=='+'?a+b:o=='-'?a-b:o=='*'?a*b:a/b}},E())

Clear/semi-obfuscated function:

function evaluate(x) {
    x = x.replace(/ /g, "") + ")";
    function primary() {
        if (x[0] == '(') {
            x = x.substr(1);
            return expression();
        }

        var n = /^[-+]?\d*\.?\d*/.exec(x)[0];
        x = x.substr(n.length);
        return +n;
    }

    function expression() {
        var a = primary();
        for (;;) {
            var operator = x[0];
            x = x.substr(1);

            if (operator == ')') {
                return a;
            }

            var b = primary();
            a = (operator == '+') ? a + b :
                (operator == '-') ? a - b :
                (operator == '*') ? a * b :
                                    a / b;
        }
    }

    return expression();
}

Neither version will work in IE, because they use array-style subscripting on the string. If you replace both occurrences of x[0] with x.charAt(0), the first one should work everywhere.

I cut out some more characters since the first version by turning variables into function parameters and replacing another if statement with the conditional operator.

Answer 7

C#

Number of characters: 396 (updated)

(but fails the test you added with "/ -8", and I'm not inclined to fix it...

static float Eval(string s){int i,j;s=s.Trim();while((i=s.IndexOf(')'))>=0){j=s.LastIndexOf('(',i,i);s=s.Substring(0,j++)+Eval(s.Substring(j,i-j))+s.Substring(i+1);}if((i=s.LastIndexOfAny("+-*/".ToCharArray()))<0) return float.Parse(s);var r=float.Parse(s.Substring(i+1));var l=i>0?Eval(s.Substring(0,i)):(float?)null;return s[i]=='+'?(l??0)+r:(s[i]=='-'?(l??0)-r:(s[i]=='/'?(l??1)/r:(l??1)*r));}

From:

static float Eval(string s)
{
    int i, j;
    s = s.Trim();
    while ((i = s.IndexOf(')')) >= 0)
    {
        j = s.LastIndexOf('(', i, i);
        s = s.Substring(0, j++) + Eval(s.Substring(j, i - j)) + s.Substring(i + 1);
    } 
    if ((i = s.LastIndexOfAny("+-*/".ToCharArray())) < 0) return float.Parse(s);
    var r = float.Parse(s.Substring(i + 1));
    var l = i > 0 ? Eval(s.Substring(0, i)) : (float?)null;
    return s[i] == '+'
        ? (l ?? 0) + r
        : (s[i] == '-'
            ? (l ?? 0) - r
            : (s[i] == '/'
                ? (l ?? 1) / r
                : (l ?? 1) * r));
}

Answer 8

C#

Number of characters: 403

So here's my solution... I'm still waiting for someone to post one in C# that can beat it. (Marc Gravell was close, and may yet do better than me after some more tinkering.)

Fully obfuscated function:

float e(string x){float v=0;if(float.TryParse(x,out v))return v;x+=';';int t=0;
char o,s='?',p='+';float n=0;int l=0;for(int i=0;i<x.Length;i++){o=s;if(
x[i]!=' '){s=x[i];if(char.IsDigit(x[i])|s=='.'|(s=='-'&o!='1'))s='1';if(s==')')
l--;if(s!=o&l==0){if(o=='1'|o==')'){n=e(x.Substring(t,i-t));if(p=='+')v+=n;
if(p=='-')v-=n;if(p=='*')v*=n;if(p=='/')v/=n;p=x[i];}t=i;if(s=='(')t++;}
if(s=='(')l++;}}return v;}

Semi-obfuscated function:

public static float Eval(string expr)
{
    float val = 0;
    if (float.TryParse(expr, out val))
        return val;
    expr += ';';
    int tokenStart = 0;
    char oldState, state = '?', op = '+';
    float num = 0;
    int level = 0;
    for (int i = 0; i < expr.Length; i++)
    {
        oldState = state;
        if (expr[i] != ' ')
        {
            state = expr[i];
            if (char.IsDigit(expr[i]) || state == '.' ||
                (state == '-' && oldState != '1'))
                state = '1';
            if (state == ')')
                level--;
            if (state != oldState && level == 0)
            {
                if (oldState == '1' || oldState == ')')
                {
                    num = Eval(expr.Substring(tokenStart, i - tokenStart));
                    if (op == '+') val += num;
                    if (op == '-') val -= num;
                    if (op == '*') val *= num;
                    if (op == '/') val /= num;
                    op = expr[i];
                }
                tokenStart = i;
                if (state == '(')
                    tokenStart++;
            }
            if (state == '(')
                level++;
        }
    }
    return val;
}

Nothing too clever going on here, it woul seem. The function does however have the advantage of being re-entrant (i.e. thread-safe).

I am also reasonably pleased with the number of chars, given that it's written in C# (valid 1.0, 2.0, and 3.0 I believe).

Answer 9

Ruby 1.8.7

Number of characters: 620

Do try and take it easy on my implementation, it's the first time I've written an expression parser in my life! I guarantee that it isn't the best.

Obfuscated:

def solve_expression(e)
t,r,s,c,n=e.chars.to_a,[],'','',''
while(c=t.shift)
n=t[0]
if (s+c).match(/^(-?)[.\d]+$/) || (!n.nil? && n.match(/\d/) && c=='-')
s+=c
elsif (c=='-' && n=='(') || c=='('
m,o,x=c=='-',1,''
while(c=t.shift)
o+=1 if c=='('
o-=1 if c==')'
x+=c unless c==')' && o==0
break if o==0
end
r.push(m ? -solve_expression(x) : solve_expression(x))
s=''
elsif c.match(/[+\-\/*]/)
r.push(c) and s=''
else
r.push(s) if !s.empty?
s=''
end
end
r.push(s) unless s.empty?
i=1
a=r[0].to_f
while i<r.count
b,c=r[i..i+1]
c=c.to_f
case b
when '+': a=a+c
when '-': a=a-c
when '*': a=a*c
when '/': a=a/c
end
i+=2
end
a
end

Readable:

def solve_expression(expr)
  chars = expr.chars.to_a # characters of the expression
  parts = [] # resulting parts
  s,c,n = '','','' # current string, character, next character

  while(c = chars.shift)
    n = chars[0]
    if (s + c).match(/^(-?)[.\d]+$/) || (!n.nil? && n.match(/\d/) && c == '-') # only concatenate when it is part of a valid number
      s += c
    elsif (c == '-' && n == '(') || c == '(' # begin a sub-expression
      negate = c == '-'
      open = 1
      subExpr = ''
      while(c = chars.shift)
        open += 1 if c == '('
        open -= 1 if c == ')'
        # if the number of open parenthesis equals 0, we've run to the end of the
        # expression.  Make a new expression with the new string, and add it to the
        # stack.
        subExpr += c unless c == ')' && open == 0
        break if open == 0
      end
      parts.push(negate ? -solve_expression(subExpr) : solve_expression(subExpr))
      s = ''
    elsif c.match(/[+\-\/*]/)
      parts.push(c) and s = ''
    else
      parts.push(s) if !s.empty?
      s = ''
    end
  end
  parts.push(s) unless s.empty? # expression exits 1 character too soon.

  # now for some solutions!
  i = 1
  a = parts[0].to_f # left-most value is will become the result
  while i < parts.count
    b,c = parts[i..i+1]
    c = c.to_f
    case b
      when '+': a = a + c
      when '-': a = a - c
      when '*': a = a * c
      when '/': a = a / c
    end
    i += 2
  end
  a
end

Answer 10

PHP

Number of characters: 284

obfuscated:

function f($m){return c($m[1]);}function g($n,$m){$o=$m[0];$m[0]=' ';return$o=='+'?$n+$m:($o=='-'?$n-$m:($o=='*'?$n*$m:$n/$m));}function c($s){while($s!=($t=preg_replace_callback('/\(([^()]*)\)/',f,$s)))$s=$t;preg_match_all('![-+/*].*?[\d.]+!',"+$s",$m);return array_reduce($m[0],g);}

readable:

function callback1($m) {return c($m[1]);}
function callback2($n,$m) {
    $o=$m[0];
    $m[0]=' ';
    return $o=='+' ? $n+$m : ($o=='-' ? $n-$m : ($o=='*' ? $n*$m : $n/$m));
}
function c($s){ 
    while ($s != ($t = preg_replace_callback('/\(([^()]*)\)/','callback1',$s))) $s=$t;
    preg_match_all('![-+/*].*?[\d.]+!', "+$s", $m);
    return array_reduce($m[0], 'callback2');
}


$str = '  2.45/8.5  *  -9.27   +    (   5   *  0.0023  ) ';
var_dump(c($str));
# float(-2.66044117647)

Should work with any valid input (including negative numbers and arbitrary whitespace)

Answer 11

Common Lisp

(SBCL)
Number of characters: 251

(defun g(e)(if(numberp e)e(let((m (g (pop e)))(o(loop for x in e by #'cddr collect x))(n(loop for x in (cdr e)by #'cddr collect (g x))))(mapcar(lambda(x y)(setf m(apply x(list m y))))o n)m)))(defun w(e)(g(read-from-string(concatenate'string"("e")"))))

Proper version (387 chars):

(defun wrapper (exp) (golf-eval (read-from-string (concatenate 'string "(" exp ")"))))

(defun golf-eval (exp)
 (if (numberp exp)
     exp
   (let ((mem (golf-eval (pop exp)))
     (op-list (loop for x in exp by #'cddr collect x))
     (num-list (loop for x in (cdr exp) by #'cddr collect (golf-eval x))))
    (mapcar (lambda (x y) (setf mem (apply x (list mem y)))) op-list num-list)
    mem)))

Input is form w(), which takes one string argument. It uses the trick that nums/operands and operators are in the pattern N O N O N ... and recursively evaluates all operands, and therefore getting nesting very cheap. ;)

Answer 12

Python 3K

(its 3K because / converts the result to a floating point number)

Number of characters: 808

Clear (I cannot write obfuscated code in Python XD):

def parse(line):
  ops = {"+": lambda x,y:x+y,
       "-": lambda x,y:x-y,
       "*": lambda x,y:x*y,
       "/": lambda x,y:x/y}
  def tpp(s, t):
    if len(s) > 0 and s[-1] in ops:
      f = ops[s.pop()]
      t = f(s.pop(), t)
    return t
  line = line + " "
  s = []
  t = 0
  m = None
  for c in line:
    if c in "0123456789":
      if not m:
        m = "i"
      if m == "i":
        t = t*10 + ord(c)-ord("0")
      elif m =="d":
        t = t + e*(ord(c)-ord("0"))
        e*=0.1
    elif c == ".":
      m = "d"
      e = 0.1
    elif m:
      t = tpp(s,t)
      s.append(t)
      m = None
      t = 0

    if c in ops or c == "(":
      s.append(c)
    elif c == ")":
      t = s.pop()
      s.pop()
      s.append(tpp(s,t))
      t = 0
  t = s.pop()
  if int(t) == t:
    t = int(t)
  return t

I'm not using any kind of regular expression, even the number parsing is made by hand ;-)

Quite simple, scans the line, it can be in 3 different modes (m), None that means that there's no number being parsed, "i" that means that it is parsing the integer part and "d" that means that is parsing the decimal part.

It uses a stack to store the temporary computations, when it has finished parsing a number sees if it there was an operator in the stack, in that case evals and pushes. The opening parens are just pushed and the closing parens remove the opening paren and repush the current eval.

Fairly simple and straightfordward :-)

Answer 13

F#

Number of characters: 327

OP was looking for an F# version, here it is. Can be done a lot nicer since I'm abusing a ref here to save characters. It handles most things such as -(1.0), 3 - -3 and even 0 - .5 etc.

let g s=
 let c=ref[for x in System.Text.RegularExpressions.Regex.Matches(s,"[0-9.]+|[^\s]")->x.Value]
 let rec e v=if (!c).IsEmpty then v else 
  let h=(!c).Head
  c:=(!c).Tail
  match h with|"("->e(e 0.0)|")"->v|"+"->e(v+(e 0.0))|"-"->e(v-(e 0.0))|"/"->e(v/(e 0.0))|"*"->e(v*(e 0.0))|x->float x
 e(e 0.0)

Answer 14

Ruby

Number of characters: 302

Semi-obfuscated:

def e(l)
  t=0.0;o=nil
  while l!=''
    l.sub!(/^\s+/,'')
    l.sub!(/^(-?\d+|-?\d+\.\d+)/,'')
    t=o ? t.send(o, $1.to_f) : $1.to_f if $~
    l.sub!(/^(\+|-|\*|\/)/,'')
    o=$1 if $~
    l.sub!(/^\(/,'')
    t=o ? t.send(o, e(l)) : e(l) if $~
    l.sub!(/^\)/,'')
    return t if $~
  end
  t
end

Destroys original string, also assumes expression is well-formed (only valid characters, and matching brackets).

Not obfuscated:

def evaluate_expression(expression)
  result_so_far = 0.0
  last_operator = nil

  while (expression != '')
    # remove any leading whitespace
    expression.sub!(/^\s+/, '') 

    # extract and remove leading integer or decimal number
    expression.sub!(/^(-?\d+|-?\d+\.\d+)/, '')
    if $~
      # match was successful
      number = $1.to_f
      if last_operator.nil?
        # first number, just store it
        result_so_far = number
      else
        # we have an operator, use it!
        # last_operator is a string matching '+', '-', '*' or '/'
        # just invoke the method of that name on our result_so_far
        # since these operators are just method calls in Ruby
        result_so_far = result_so_far.send(last_operator, number)
       end
    end

    # extract and remove leading operator +-*/
    expression.sub!(/^(\+|-|\*|\/)/, '')
    if $~
      # match was successful
      last_operator = $1
    end

    # extract and remove leading open bracket
    l.sub!(/^\(/, '')
    if $~
      # match successful
      if last_operator.nil?
        # first element in the expression is an open bracket
        # so just evaluate its contents recursively
        result_so_far = evaluate_expression(expression)
      else
        # combine the content of the bracketing with the
        # result so far using the last_operator
        result_so_far.send(last_operator, evaluate_expression(expression))
      end
    end

    # extract and remove leading close bracket
    l.sub!(/^\)/, '')
    if $~
      # match successful
      # this must be the end of a recursive call so
      # return the result so far without consuming the rest
      # of the expression
      return result_so_far
    end
  end
  t
end

The recursive call is controlled by the modification of the expression string, which is a bit nasty, but it seems to work.

Answer 15

Python with regular expressions

Number of characters: 283

Fully obfuscated function:

import re
from operator import*
def c(e):
 O=dict(zip("+-/*()",(add,sub,truediv,mul)))
 a=[add,0];s=a
 for v,o in re.findall("(-?[.\d]+)|([+-/*()])",e):
  if v:s=[float(v)]+s
  elif o=="(":s=a+s
  elif o!=")":s=[O[o]]+s
  if v or o==")":s[:3]=[s[1](s[2],s[0])]
 return s[0]

Not obfuscated:

import re
from operator import *

def compute(s):
    operators = dict(zip("+-/*()", (add, sub, truediv, mul)))
    stack = [add, 0]
    for val, op in re.findall("(-?[.\d]+)|([+-/*()])", s):
        if val:
            stack = [float(val)] + stack
        elif op == "(":
            stack = [add, 0] + stack
        elif op != ")":
            stack = [operators[op]] + stack
        if val or op == ")":
            stack[:3] = [stack[1](stack[2], stack[0])]
    return stack[0]

I wanted to see if I cab beat the other Python solutions using regular expressions.

Couldn't.

The regular expression I'm using creates a list of pairs (val, op) where only one item in each pair is valid. The rest of the code is a rather standard stack based parser with a neat trick of replacing the top 3 cells in the stack with the result of the computation using Python list assignment syntax. Making this work with negative numbers required only two additional characters (-? in the regex).

Answer 16

C# with Regex Love

Number of characters: 384

Fully-obfuscated:

float E(string i){i=i.Replace(" ","");Regex b=new Regex(@"\((?>[^()]+|\((?<D>)|\)(?<-D>))*(?(D)(?!))\)");i=b.Replace(i,m=>Eval(m.Value.Substring(1,m.Length-2)).ToString());float r=0;foreach(Match m in Regex.Matches(i,@"(?<=^|\D)-?[\d.]+")){float f=float.Parse(m.Value);if(m.Index==0)r=f;else{char o=i[m.Index-1];if(o=='+')r+=f;if(o=='-')r-=f;if(o=='*')r*=f;if(o=='/')r/=f;}}return r;}

Not-obfuscated:

private static float Eval(string input)
{
    input = input.Replace(" ", "");
    Regex balancedMatcher = new Regex(@"\(
                                            (?>
                                                [^()]+
                                            |
                                                \( (?<Depth>)
                                            |
                                                \) (?<-Depth>)
                                            )*
                                            (?(Depth)(?!))
                                        \)", RegexOptions.IgnorePatternWhitespace);
    input = balancedMatcher.Replace(input, m => Eval(m.Value.Substring(1, m.Length - 2)).ToString());

    float result = 0;

    foreach (Match m in Regex.Matches(input, @"(?<=^|\D)-?[\d.]+"))
    {
        float floatVal = float.Parse(m.Value);
        if (m.Index == 0)
        {
            result = floatVal;
        }
        else
        {
            char op = input[m.Index - 1];
            if (op == '+') result += floatVal;
            if (op == '-') result -= floatVal;
            if (op == '*') result *= floatVal;
            if (op == '/') result /= floatVal;
        }
    }

    return result;
}

Takes advantage of .NET's Regex balancing group feature.

Answer 17

F#

Number of characters: 461

Here is Marc Gravell's solution (essentially) converted from C# to F#. The char count is scarecly better, but I thought I'd post it anyway out of interest.

Obfuscated code:

let e x=
 let rec f(s:string)=
  let i=s.IndexOf(')')
  if i>0 then
   let j=s.LastIndexOf('(',i)
   f(s.Substring(0,j)+f(s.Substring(j+1,i-j-1))+s.Substring(i+1))
  else
   let o=[|'+';'-';'*';'/'|]
   let i=s.LastIndexOfAny(o)
   let j=s.IndexOfAny(o,max(i-2)0,2)
   let k=if j<0 then i else j
   if k<0 then s else
    let o=s.[k]
    string((if o='+'then(+)else if o='-'then(-)else if o='*'then(*)else(/))(float(f(s.Substring(0,k))))(float(s.Substring(k+1))))
 float(f x)

Answer 18

Python

Number of characters: 382

Yet another Python solution, heavily using regular expression replacement. Each run through the loop the simplest expressions are computed and the results are put back into the string.

This is the unobfuscated code, unless you consider regular expressions to be obfuscated.

import re
from operator import *    
operators = dict(zip("+-/*", (add, sub, truediv, mul)))    
def compute(s):
    def repl(m):
        v1, op, v2 = m.groups()
        return str(operators[op](float(v1), float(v2)))
    while not re.match("^\d+\.\d+$", s):
        s = re.sub("([.\d]+)\s*([+-/*])\s*([.\d]+)", repl, s)
        s = re.sub("\(([.\d]+)\)", r"\1", s)
    return s

Had this idea just as I was turning in and couldn't let it go until I wrote it down and made it work.

Answer 19

Perl

Number of characters: 93

Fully obfuscated function: (93 characters if you join these three lines into one)

$_="(@ARGV)";s/\s//g;$n=qr/(-?\d+(\.\d+)?)/;
while(s.\($n\)|(?<=\()$n[-+*/]$n.eval$&.e){}
print

Clear/semi-obfuscated function:

$_="(@ARGV)";            # Set the default var to "(" argument ")"
s/\s//g;                 # Strip all spaces from $_
$n=qr/(-?\d+(\.\d+)?)/;  # Compile a regex for "number"

# repeatedly replace the sequence "(" NUM ")" with NUM, or if there aren't
# any of those, replace "(" NUM OP NUM with the result
# of doing an eval on just the NUM OP NUM bit.
while(s{\($n\)|(?<=\()$n[-+*/]$n}{eval$&}e){}

# print $_
print

I think this is pretty well explained in the "clear" version. The two main insights are that you can make the code uniform by surrounding the argument with parentheses at the start (special cases cost characters), and that it is sufficient, albeit massively inefficient, to only process stuff right next to an open parenthesis, replacing it with its result.

It's probably easiest to run this code as:

perl -le '$_="(@ARGV)";s/\s//g;$n=qr/(-?\d+(\.\d+)?)/;while(s.\($n\)|(?<=\()$n[-+*/]$n.eval$&.e){}print' '4 * (9 - 4) / (2 * 6 - 2) + 8'

Answer 20

Fortran 77 (gfortran dialect, now with g77 support)

Number of characters: 2059

Obfuscated version:

      function e(c)
      character*99 c
      character b
      real f(24)                
      integer i(24)             
      nf=0                      
      ni=0                      
 20   nf=kf(0.0,nf,f)
      ni=ki(43,ni,i)         
 30   if (isp(c).eq.1) goto 20
      h=fr(c)
 31   g=fp(nf,f)
      j=ip(ni,i)
      select case(j)
      case (40) 
         goto 20
      case (42)                 
         d=g*h
      case (43)                 
         d=g+h
      case (45)                 
         d=g-h
      case (47)                 
         d=g/h
      end select
 50   nf=kf(d,nf,f)
 60   j=nop(c)
      goto (20, 70, 75, 75, 60, 75, 60, 75) (j-39)
 65   e=fp(nf,f)
      return
 70   h=fp(nf,f)              
      goto 31
 75   ni=ki(j,ni,i)
      goto 30
      end
      function kf(v,n,f)
      real f(24)
      kf=n+1
      f(n+1)=v
      return
      end
      function ki(j,n,i)
      integer i(24)
      ki=n+1
      i(n+1)=j
      return
      end
      function fp(n,f)
      real f(24)
      fp=f(n)
      n=n-1
      return
      end
      function ip(n,i)
      integer i(24)
      ip=i(n)
      n=n-1
      return
      end
      function nop(s)
      character*99 s
      l=1
      do while(s(l:l).eq." ".and.l.lt.99)
         l=l+1
      enddo
      nop=ichar(s(l:l))
      s(l:l)=" "
      return
      end
      function isp(s)
      character*99 s
      isp=0
      l=1
      do while(s(l:l).eq." ".and.l.lt.99)
         l=l+1
      enddo
      isp=41-ichar(s(l:l))
      if (isp.eq.1) s(l:l)=" "
      return
      end
      function fr(s)
      character*99 s
      m=1                      
      n=1                      
      i=1
      do while(i.le.99)
         j=ichar(s(i:i))
         if (j.eq.32) goto 90   
         if (j.ge.48.and.j.lt.58) goto 89
         if (j.eq.43.or.j.eq.45) goto (89,80) m
         if (j.eq.46) goto (83,80) n
 80      exit
 83      n=2
 89      m=2
 90      i=i+1
      enddo
      read(s(1:i-1),*) fr
      do 91 j=1,i-1
         s(j:j)=" "
 91   continue
      return 
      end

Clear version: (3340 characters with scaffold)

      program infixeval
      character*99 c
      do while (.true.)
         do 10 i=1,99
            c(i:i)=" "
 10      continue
         read(*,"(A99)") c
         f=e(c)
         write(*,*)f
      enddo
      end

      function e(c)
      character*99 c
      character b
      real f(24)                ! value stack
      integer i(24)             ! operator stack
      nf=0                      ! number of items on the value stack
      ni=0                      ! number of items on the operator stack
 20   nf=pushf(0.0,nf,f)
      ni=pushi(43,ni,i)         ! ichar(+) = 43
D     write (*,*) "'",c,"'"
 30   if (isp(c).eq.1) goto 20
      h=fr(c)
D     write (*,*) "'",c,"'"
 31   g=fpop(nf,f)
      j=ipop(ni,i)
D     write(*,*) "Opperate ",g," ",char(j)," ",h
      select case(j)
      case (40) 
         goto 20
      case (42)                 ! "*" 
         d=g*h
      case (43)                 ! "+"
         d=g+h
      case (45)                 ! "-"
         d=g-h
      case (47)                 ! "*"
         d=g/h
      end select
 50   nf=pushf(d,nf,f)
 60   j=nop(c)
D     write(*,*) "Got op: ", char(j)
      goto (20, 70, 75, 75, 60, 75, 60, 75) (j-39)
 65   e=fpop(nf,f)
      return
 70   h=fpop(nf,f)              ! Encountered a "("
      goto 31
 75   ni=pushi(j,ni,i)
      goto 30
      end

c     push onto a real stack
c     OB as kf
      function pushf(v,n,f)
      real f(24)
      pushf=n+1
      f(n+1)=v
D     write(*,*) "Push ", v
      return
      end

c     push onto a integer stack
c     OB as ki
      function pushi(j,n,i)
      integer i(24)
      pushi=n+1
      i(n+1)=j
D     write(*,*) "Push ", char(j)
      return
      end

c     pop from real stack
c     OB as fp
      function fpop(n,f)
      real f(24)
      fpop=f(n)
      n=n-1
D      write (*,*) "Pop ", fpop
      return
      end

c     pop from integer stack
c     OB as ip
      function ipop(n,i)
      integer i(24)
      ipop=i(n)
      n=n-1
D      write (*,*) "Pop ", char(ipop)
      return
      end

c     Next OPerator: returns the next nonws character, and removes it
c     from the string
      function nop(s)
      character*99 s
      l=1
      do while(s(l:l).eq." ".and.l.lt.99)
         l=l+1
      enddo
      nop=ichar(s(l:l))
      s(l:l)=" "
      return
      end

c     IS an open Paren: return 1 if the next non-ws character is "("
c     (also overwrite it with a space. Otherwise return not 1
      function isp(s)
      character*99 s
      isp=0
      l=1
      do while(s(l:l).eq." ".and.l.lt.99)
         l=l+1
      enddo
      isp=41-ichar(s(l:l))
      if (isp.eq.1) s(l:l)=" "
      return
      end

c     Float Read: return the next real number in the string and removes the
c     character
      function fr(s)
      character*99 s
      m=1                      ! No sign (Minus or plus) so far
      n=1                      ! No decimal so far
      i=1
      do while(i.le.99)
         j=ichar(s(i:i))
         if (j.eq.32) goto 90   ! skip spaces
         if (j.ge.48.and.j.lt.58) goto 89
         if (j.eq.43.or.j.eq.45) goto (89,80) m
         if (j.eq.46) goto (83,80) n
c     not part of a number
 80      exit
 83      n=2
 89      m=2
 90      i=i+1
      enddo
      read(s(1:i-1),*) fr
      do 91 j=1,i-1
         s(j:j)=" "
 91   continue
      return 
      end

Notes This edited version is rather more evil than my first attempt. Same algorithm, but now inline with a horrible tangle of gotos. I've ditched the co-routines, but am now using a couple of flavors of computed branches. All error checking and reporting has been removed, but this version will silently recover from some classes of unexpected characters in the input. This version also compiles with g77.

The primary limits are still fortran's rigid formatting, long and ubiquitous keywords, and simple primitives.

Answer 21

Perl (no eval)

Number of characters: 167 106 (see below for the 106 character version)

Fully obfuscated function: (167 characters if you join these three lines into one)

sub e{my$_="($_[0])";s/\s//g;$n=q"(-?\d++(\.\d+)?+)";
@a=(sub{$1},1,sub{$3*$6},sub{$3+$6},4,sub{$3-$6},6,sub{$3/$6});
while(s:\($n\)|(?<=\()$n(.)$n:$a[7&ord$5]():e){}$_}

Clear/deobfuscated version:

sub e {
  my $_ = "($_[0])";
  s/\s//g;
  $n=q"(-?\d++(\.\d+)?+)"; # a regex for "number", including capturing groups
                           # q"foo" in perl means the same as 'foo'
                           # Note the use of ++ and ?+ to tell perl
                           # "no backtracking"

  @a=(sub{$1},             # 0 - no operator found
      1,                   # placeholder
      sub{$3*$6},          # 2 - ord('*') = 052
      sub{$3+$6},          # 3 - ord('+') = 053
      4,                   # placeholder
      sub{$3-$6},          # 5 - ord('-') = 055
      6,                   # placeholder
      sub{$3/$6});         # 7 - ord('/') = 057

  # The (?<=... bit means "find a NUM WHATEVER NUM sequence that happens
  # immediately after a left paren", without including the left
  # paren.  The while loop repeatedly replaces "(" NUM WHATEVER NUM with
  # "(" RESULT and "(" NUM ")" with NUM.  The while loop keeps going
  # so long as those replacements can be made.

  while(s:\($n\)|(?<=\()$n(.)$n:$a[7&ord$5]():e){}

  # A perl function returns the value of the last statement
  $_
}

I had misread the rules initially, so I'd submitted a version with "eval". Here's a version without it.

The latest bit of insight came when I realized that the last octal digit in the character codes for +, -, /, and * is different, and that ord(undef) is 0. This lets me set up the dispatch table @a as an array, and just invoke the code at the location 7 & ord($3).

There's an obvious spot to shave off one more character - change q"" into '' - but that would make it harder to cut-and-paste into the shell.

Even shorter

Number of characters: 124 106

Taking edits by ephemient into account, it's now down to 124 characters: (join the two lines into one)

sub e{$_=$_[0];s/\s//g;$n=q"(-?\d++(\.\d+)?+)";
1while s:\($n\)|$n(.)$n:($1,1,$3*$6,$3+$6,4,$3-$6,6,$6&&$3/$6)[7&ord$5]:e;$_}

Shorter still

Number of characters: 110 106

The ruby solution down below is pushing me further, though I can't reach its 104 characters:

sub e{($_)=@_;$n='( *-?[.\d]++ *)';
s:\($n\)|$n(.)$n:(($1,$2-$4,$4&&$2/$4,$2*$4,$2+$4)x9)[.8*ord$3]:e?e($_):$_}

I had to give in and use ''. That ruby send trick is really useful for this problem.

Squeezing water from a stone

Number of characters: 106

A small contortion to avoid the divide-by-zero check.

sub e{($_)=@_;$n='( *-?[.\d]++ *)';
s:\($n\)|$n(.)$n:($1,0,$2*$4,$2+$4,0,$2-$4)[7&ord$3]//$2/$4:e?e($_):$_}

Here's the test harness for this function:

perl -le 'sub e{($_)=@_;$n='\''( *-?[.\d]++ *)'\'';s:\($n\)|$n(.)$n:($1,0,$2*$4,$2+$4,0,$2-$4)[7&ord$3]//$2/$4:e?e($_):$_}' -e 'print e($_) for @ARGV' '1 + 3' '1 + ((123 * 3 - 69) / 100)' '4 * (9 - 4) / (2 * 6 - 2) + 8' '2*3*4*5+99' '2.45/8.5*9.27+(5*0.0023) ' '1 + 3 / -8'

Answer 22

Python

Number of characters: 235

Fully obfuscated function:

def g(a):
 i=len(a)
 while i:
  try:m=g(a[i+1:]);n=g(a[:i]);a=str({'+':n+m,'-':n-m,'*':n*m,'/':n/(m or 1)}[a[i]])
  except:i-=1;j=a.rfind('(')+1
  if j:k=a.find(')',j);a=a[:j-1]+str(g(a[j:k]))+a[k+1:]
 return float(a.replace('--',''))

Semi-obfuscated:

def g(a):
    i=len(a);
    # do the math
    while i:
        try:
            # recursively evaluate left and right
            m=g(a[i+1:])
            n=g(a[:i])
            # try to do the math assuming that a[i] is an operator
            a=str({'+':n+m,'-':n-m,'*':n*m,'/':n/(m or 1)}[a[i]])
        except:
            # failure -> next try
            i-=1
            j=a.rfind('(')+1
        # replace brackets in parallel (this part is executed first)
        if j:
            k=a.find(')',j)
            a=a[:j-1]+str(g(a[j:k]))+a[k+1:]
    return float(a.replace('--',''))

FWIW, the n+1th Python solution. In a blatant abuse of try-except I use a trial-and-error approach. It should handle all cases properly including stuff like -(8), --8 and g('-(1 - 3)'). It is re-entrant. Without support for the -- case which many implementations don't support, it is at 217 chars (see previous revision).

Thanks for an interesting hour on a Sunday and another 30 mins on Monday. Thanks to krubo for his nice dict.

Answer 23

Ruby

Number of characters: 170

Obfuscated:

def s(x)
while x.sub!(/\(([^\(\)]*?)\)/){s($1)}
x.gsub!('--','')
end
while x.sub!(/(-?[\d.]+)[ ]*([+\-*\/])[ ]*(-?[\d.]+)/){$1.to_f.send($2,$3.to_f)}
end
x.strip.to_f
end

Readable:

def s(x)
while x.sub!(/\(([^\(\)]*?)\)/){s($1)}
x.gsub!('--','')
end
while x.sub!(/(-?[\d.]+)[ ]*([+\-*\/])[ ]*(-?[\d.]+)/){$1.to_f.send($2,$3.to_f)}
end
x.strip.to_f
end

[
  ['1 + 3 / -8', -0.5],
  ['2*3*4*5+99', 219],
  ['4 * (9 - 4) / (2 * 6 - 2) + 8', 10],
  ['1 + ((123 * 3 - 69) / 100)', 4],
  ['2.45/8.5*9.27+(5*0.0023)',2.68344117647059],
  ['(3+7) - (5+2)', 3]
].each do |pair|
  a,b = s(String.new(pair[0])),pair[1]
  print pair[0].ljust(25), ' = ', b, ' (', a==b, ')'
  puts
end

There is no real obfuscation to this one, which I decided to post fresh since it's wildly different from my first. I should have seen this from the start. The process is a very simple process of elimination: find and resolve the highest pair of parenthesis (the most nested) into a number until no more are found, then resolve all the existing numbers and operations into the result. And, while resolving parenthetical statements I have it strip all double-dashes (Float.to_f doesn't know what to do with them).

So, it supports positive and negative numbers (+3, 3, & -3) and even negated sub-expressions within the parenthesis just by the order of processing. The only shorter implementation is the Perl (w/o eval) one.

Edit: I'm still chasing Perl, but this is the second smallest answer right now. I shrunk it with changes to the second regex and by changing the treatment of the string to be destructive (replaces the old string). This eliminated the need to duplicate the string, which I found out to just be a new pointer to the string. And renaming the function to s from solve saved a few characters.

Answer 24

Python (without importing anything)

Number of characters: 222

I stole many tricks from Dave's answer, but I managed to shave off some more characters.

def e(s,l=0,n=0,f='+'):
 if s:l=[c for c in s+')'if' '!=c]
 while f!=')':
  p=l.pop;m=p(0)
  if m=='(':m=e(0,l)
  while l[0]not in'+-*/)':m+=p(0)
  m=float(m);n={'+':n+m,'-':n-m,'*':n*m,'/':n/(m or 1)}[f];f=p(0)
 return n

Commented version:

def evaluate(stringexpr, listexpr=0, n=0, f_operation='+'):
    # start out as taking 0 + the expression... (or could use 1 * ;)

    # We'll prefer to keep the expression as a list of characters,
    # so we can use .pop(0) to eat up the expression as we go.
    if stringexpr:
        listexpr = [c for c in stringexpr+')' if c!=' ']

    # use ')' as sentinel to return the answer
    while f_operation != ')':
        m_next = listexpr.pop(0)
        if m_next == '(':
            # lists are passed by reference, so this call will eat the (parexp)
            m_next = evaluate(None, listexpr)

        else:
            # rebuild any upcoming numeric chars into a string
            while listexpr[0] not in '+-*/)':
                m_next += listexpr.pop(0)

        # Update n as the current answer.  But never divide by 0.
        m = float(m_next)
        n = {'+':n+m, '-':n-m, '*':n*m, '/':n/(m or 1)}[f_operation]

        # prepare the next operation (known to be one of '+-*/)')
        f_operation = listexpr.pop(0)

    return n

Answer 25

J

Number of characters: 208

After Jeff Moser's comment, I realized that I had completely forgotten about this language... I'm no expert, but my first attempt went rather well.

e=:>@{:@f@;:
f=:''&(4 :0)
'y x'=.x g y
while.($y)*-.')'={.>{.y do.'y x'=.(x,>(-.'/'={.>{.y){('%';y))g}.y end.y;x
)
g=:4 :0
z=.>{.y
if.z='('do.'y z'=.f}.y else.if.z='-'do.z=.'_',>{.}.y end.end.(}.y);":".x,z
)

It's a bit annoying, having to map x/y and -z into J's x%y and _z. Without that, maybe 50% of this code could disappear.

Answer 26

Visual Basic.NET

Number of characters: 9759

I'm more of a bowler myself.

NOTE: does not take nested parentheses into account. Also, untested, but I'm pretty sure it works.

Imports Microsoft.VisualBasic
Imports System.Text
Imports System.Collections.Generic
Public Class Main
Public Shared Function DoArithmaticFunctionFromStringInput(ByVal MathematicalString As String) As Double
 Dim numberList As New List(Of Number)
 Dim operationsList As New List(Of IOperatable)
 Dim currentNumber As New Number
 Dim currentParentheticalStatement As New Parenthetical
 Dim isInParentheticalMode As Boolean = False
 Dim allCharactersInString() As Char = MathematicalString.ToCharArray
 For Each mathChar In allCharactersInString
  If mathChar = Number.ZERO_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.ONE_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.TWO_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.THREE_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.FOUR_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.FIVE_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.SIX_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.SEVEN_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.EIGHT_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.NINE_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Number.DECIMAL_POINT_STRING_REPRESENTATION Then
   currentNumber.UpdateNumber(mathChar)
  ElseIf mathChar = Addition.ADDITION_STRING_REPRESENTATION Then
   Dim addition As New Addition

   If Not isInParentheticalMode Then
    operationsList.Add(addition)
    numberList.Add(currentNumber)
   Else
    currentParentheticalStatement.AllNumbers.Add(currentNumber)
    currentParentheticalStatement.AllOperators.Add(addition)
   End If

   currentNumber = New Number
  ElseIf mathChar = Number.NEGATIVE_NUMBER_STRING_REPRESENTATION Then
   If currentNumber.StringOfNumbers.Length > 0 Then
    currentNumber.UpdateNumber(mathChar)

    Dim subtraction As New Addition
    If Not isInParentheticalMode Then
     operationsList.Add(subtraction)
     numberList.Add(currentNumber)
    Else
     currentParentheticalStatement.AllNumbers.Add(currentNumber)
     currentParentheticalStatement.AllOperators.Add(subtraction)
    End If

    currentNumber = New Number
   Else
    currentNumber.UpdateNumber(mathChar)
   End If
  ElseIf mathChar = Multiplication.MULTIPLICATION_STRING_REPRESENTATION Then
   Dim multiplication As New Multiplication

   If Not isInParentheticalMode Then
    operationsList.Add(multiplication)
    numberList.Add(currentNumber)
   Else
    currentParentheticalStatement.AllNumbers.Add(currentNumber)
    currentParentheticalStatement.AllOperators.Add(multiplication)
   End If
   currentNumber = New Number
  ElseIf mathChar = Division.DIVISION_STRING_REPRESENTATION Then
   Dim division As New Division

   If Not isInParentheticalMode Then
    operationsList.Add(division)
    numberList.Add(currentNumber)
   Else
    currentParentheticalStatement.AllNumbers.Add(currentNumber)
    currentParentheticalStatement.AllOperators.Add(division)
   End If
   currentNumber = New Number
  ElseIf mathChar = Parenthetical.LEFT_PARENTHESIS_STRING_REPRESENTATION Then
   isInParentheticalMode = True
  ElseIf mathChar = Parenthetical.RIGHT_PARENTHESIS_STRING_REPRESENTATION Then
   currentNumber = currentParentheticalStatement.EvaluateParentheticalStatement
   numberList.Add(currentNumber)
   isInParentheticalMode = False
  End If
 Next

 Dim result As Double = 0
 Dim operationIndex As Integer = 0
 For Each numberOnWhichToPerformOperations As Number In numberList
  result = operationsList(operationIndex).PerformOperation(result, numberOnWhichToPerformOperations)
  operationIndex = operationIndex + 1
 Next

 Return result

End Function
Public Class Number
 Public Const DECIMAL_POINT_STRING_REPRESENTATION As Char = "."
 Public Const NEGATIVE_NUMBER_STRING_REPRESENTATION As Char = "-"
 Public Const ZERO_STRING_REPRESENTATION As Char = "0"
 Public Const ONE_STRING_REPRESENTATION As Char = "1"
 Public Const TWO_STRING_REPRESENTATION As Char = "2"
 Public Const THREE_STRING_REPRESENTATION As Char = "3"
 Public Const FOUR_STRING_REPRESENTATION As Char = "4"
 Public Const FIVE_STRING_REPRESENTATION As Char = "5"
 Public Const SIX_STRING_REPRESENTATION As Char = "6"
 Public Const SEVEN_STRING_REPRESENTATION As Char = "7"
 Public Const EIGHT_STRING_REPRESENTATION As Char = "8"
 Public Const NINE_STRING_REPRESENTATION As Char = "9"

 Private _isNegative As Boolean
 Public ReadOnly Property IsNegative() As Boolean
  Get
   Return _isNegative
  End Get
 End Property
 Public ReadOnly Property ActualNumber() As Double
  Get
   Dim result As String = ""
   If HasDecimal Then
    If DecimalIndex = StringOfNumbers.Length - 1 Then
     result = StringOfNumbers.ToString
    Else
     result = StringOfNumbers.Insert(DecimalIndex, DECIMAL_POINT_STRING_REPRESENTATION).ToString
    End If
   Else
    result = StringOfNumbers.ToString
   End If
   If IsNegative Then
    result = NEGATIVE_NUMBER_STRING_REPRESENTATION & result
   End If
   Return CType(result, Double)
  End Get
 End Property
 Private _hasDecimal As Boolean
 Public ReadOnly Property HasDecimal() As Boolean
  Get
   Return _hasDecimal
  End Get
 End Property
 Private _decimalIndex As Integer
 Public ReadOnly Property DecimalIndex() As Integer
  Get
   Return _decimalIndex
  End Get
 End Property
 Private _stringOfNumbers As New StringBuilder
 Public ReadOnly Property StringOfNumbers() As StringBuilder
  Get
   Return _stringOfNumbers
  End Get
 End Property
 Public Sub UpdateNumber(ByVal theDigitToAppend As Char)
  If IsNumeric(theDigitToAppend) Then
   Me._stringOfNumbers.Append(theDigitToAppend)
  ElseIf theDigitToAppend = DECIMAL_POINT_STRING_REPRESENTATION Then
   Me._hasDecimal = True
   Me._decimalIndex = Me._stringOfNumbers.Length
  ElseIf theDigitToAppend = NEGATIVE_NUMBER_STRING_REPRESENTATION Then
   Me._isNegative = Not Me._isNegative
  End If
 End Sub
 Public Shared Function ConvertDoubleToNumber(ByVal numberThatIsADouble As Double) As Number
  Dim numberResult As New Number
  For Each character As Char In numberThatIsADouble.ToString.ToCharArray
   numberResult.UpdateNumber(character)
  Next
  Return numberResult
 End Function
End Class
Public MustInherit Class Operation
 Protected _firstnumber As New Number
 Protected _secondnumber As New Number
 Public Property FirstNumber() As Number
  Get
   Return _firstnumber
  End Get
  Set(ByVal value As Number)
   _firstnumber = value
  End Set
 End Property
 Public Property SecondNumber() As Number
  Get
   Return _secondnumber
  End Get
  Set(ByVal value As Number)
   _secondnumber = value
  End Set
 End Property
End Class
Public Interface IOperatable
 Function PerformOperation(ByVal number1 As Double, ByVal number2 As Number) As Double
End Interface
Public Class Addition
 Inherits Operation
 Implements IOperatable
 Public Const ADDITION_STRING_REPRESENTATION As String = "+"
 Public Sub New()

 End Sub
 Public Function PerformOperation(ByVal number1 As Double, ByVal number2 As Number) As Double Implements IOperatable.PerformOperation
  Dim result As Double = 0
  result = number1 + number2.ActualNumber
  Return result
 End Function
End Class
Public Class Multiplication
 Inherits Operation
 Implements IOperatable
 Public Const MULTIPLICATION_STRING_REPRESENTATION As String = "*"
 Public Sub New()

 End Sub
 Public Function PerformOperation(ByVal number1 As Double, ByVal number2 As Number) As Double Implements IOperatable.PerformOperation
  Dim result As Double = 0
  result = number1 * number2.ActualNumber
  Return result
 End Function
End Class
Public Class Division
 Inherits Operation
 Implements IOperatable
 Public Const DIVISION_STRING_REPRESENTATION As String = "/"
 Public Const DIVIDE_BY_ZERO_ERROR_MESSAGE As String = "I took a lot of time to write this program. Please don't be a child and try to defile it by dividing by zero. Nobody thinks you are funny."
 Public Sub New()

 End Sub
 Public Function PerformOperation(ByVal number1 As Double, ByVal number2 As Number) As Double Implements IOperatable.PerformOperation
  If Not number2.ActualNumber = 0 Then
   Dim result As Double = 0
   result = number1 / number2.ActualNumber
   Return result
  Else
   Dim divideByZeroException As New Exception(DIVIDE_BY_ZERO_ERROR_MESSAGE)
   Throw divideByZeroException
  End If
 End Function
End Class
Public Class Parenthetical
 Public Const LEFT_PARENTHESIS_STRING_REPRESENTATION As String = "("
 Public Const RIGHT_PARENTHESIS_STRING_REPRESENTATION As String = ")"
 Private _allNumbers As New List(Of Number)
 Public Property AllNumbers() As List(Of Number)
  Get
   Return _allNumbers
  End Get
  Set(ByVal value As List(Of Number))
   _allNumbers = value
  End Set
 End Property
 Private _allOperators As New List(Of IOperatable)
 Public Property AllOperators() As List(Of IOperatable)
  Get
   Return _allOperators
  End Get
  Set(ByVal value As List(Of IOperatable))
   _allOperators = value
  End Set
 End Property
 Public Sub New()

 End Sub
 Public Function EvaluateParentheticalStatement() As Number
  Dim result As Double = 0
  Dim operationIndex As Integer = 0
  For Each numberOnWhichToPerformOperations As Number In AllNumbers
   result = AllOperators(operationIndex).PerformOperation(result, numberOnWhichToPerformOperations)
   operationIndex = operationIndex + 1
  Next

  Dim numberToReturn As New Number
  numberToReturn = Number.ConvertDoubleToNumber(result)
  Return numberToReturn
 End Function
End Class
End Class

Answer 27

Here comes another one:

Shell script (using sed+awk)

Number of characters: 295

obfuscated:

e(){ a="$1";while echo "$a"|grep -q \(;do eval "`echo "$a"|sed 's/\(.*\)(\([^()]*\))\(.*\)/a="\1\`e \"\2\"\`\3"/'`";done; echo "$a"|sed 's/\([-+*/]\) *\(-\?\) */ \1 \2/g'|awk '{t=$1;for(i=2;i<NF;i+=2){j=$(i+1);if($i=="+") t+=j; else if($i=="-") t-=j; else if($i=="*") t*=j; else t/=j}print t}';}

readable

e () {
    a="$1"
    # Recursively process bracket-expressions
    while echo "$a"|grep -q \(; do
        eval "`echo "$a"|
            sed 's/\(.*\)(\([^()]*\))\(.*\)/a="\1\`e \"\2\"\`\3"/'`"
    done
    # Compute expression without brackets
    echo "$a"|
        sed 's/\([-+*/]\) *\(-\?\) */ \1 \2/g'|
        awk '{
            t=$1;
            for(i=2;i<NF;i+=2){
                j=$(i+1);
                if($i=="+") t+=j;
                else if($i=="-") t-=j;
                else if($i=="*") t*=j;
                else t/=j
            }
            print t
        }'
}

Test:

str='  2.45 / 8.5  *  9.27   +    (   5   *  0.0023  ) '
echo "$str"|bc -l
e "$str"

Result:

2.68344117647058823526
2.68344

Answer 28

Java

Number of Characters: 376

Updated version, now with more ? operator abuse!

Fully obfuscated solution:

static double e(String t){t="("+t+")";for(String s:new String[]{"+","-","*","/","(",")"})t=t.replace(s," "+s+" ");return f(new Scanner(t));}static double f(Scanner s){s.next();double a,v=s.hasNextDouble()?s.nextDouble():f(s);while(s.hasNext("[^)]")){char o=s.next().charAt(0);a=s.hasNextDouble()?s.nextDouble():f(s);v=o=='+'?v+a:o=='-'?v-a:o=='*'?v*a:v/a;}s.next();return v;}

Clear/semi-obfuscated function:

static double evaluate(String text) {
 text = "(" + text + ")";
 for (String s : new String[] {"+", "-", "*", "/", "(", ")" }) {
  text = text.replace(s, " " + s + " ");
 }
 return innerEval(new Scanner(text));
}

static double innerEval(Scanner s) {
 s.next();
 double arg, val = s.hasNextDouble() ? s.nextDouble() : innerEval(s);
 while (s.hasNext("[^)]")) {
  char op = s.next().charAt(0);
  arg = s.hasNextDouble() ? s.nextDouble() : innerEval(s);
  val =
   op == '+' ? val + arg :
   op == '-' ? val - arg :
   op == '*' ? val * arg :
   val / arg;
 }
 s.next();
 return val;
}

Answer 29

I'm surprised nobody did it in Lex / Yacc or equivalent.

That would seem to yield the shortest source code that was also readable / maintainable.

Answer 30

Ruby

Number of characters: 217 179

This is the shortest ruby solution up to now (one heavily based on RegExp yields incorrect answers when string contains few groups of parenthesis) -- no longer true. Solutions based on regex and substitution are shorter. This one is based on stack of accumulators and parses whole expression from left to right. It is re-entrant, and does not modify input string. It could be accused of breaking the rules of not using eval, as it calls Float's methods with identical names as their mathematical mnemonics (+,-,/,*).

Obfuscated code (old version, tweaked below):

def f(p);a,o=[0],['+']
p.sub(/-/,'+-').scan(/(?:(-?\d+(?:\.\d+)?)|(.))\s*/).each{|n|
q,w=n;case w;when'(';a<<0;o<<'+';when')';q=a.pop;else;o<<w
end if q.nil?;a[-1]=a[-1].method(o.pop).call(q.to_f) if !q.nil?};a[0];end

More obfuscated code:

def f(p);a,o=[0],[:+]
p.scan(/(?:(-?\d+(?:\.\d+)?)|(.))\s*/).each{|n|q,w=n;case w
when'(';a<<0;o<<:+;when')';q=a.pop;else;o<<w;end if !q
a<<a.pop.send(o.pop,q.to_f)if q};a[0];end

Clean code:

def f(p)
  accumulators, operands = [0], ['+']
  p.gsub(/-/,'+-').scan(/(?:(-?\d+(?:\.\d+)?)|(.))\s*/).each do |n|
    number, operand = n
    case operand
      when '('
        accumulators << 0
        operands << '+'
      when ')'
        number = accumulators.pop
        operands.pop
      else 
        operands[-1] = operand
    end if number.nil?
    accumulators[-1] = accumulators.last.method(operands[-1]).call(number.to_f) unless number.nil?
  end
  accumulators.first
end

Answer 31

MATLAB (v7.8.0)

Number of characters: 239

Obfuscated function:

function [v,s]=m(s),r=1;while s,s=regexp(s,'( ?)(?(1)-?)[\.\d]+|\S','match');c=s{end};s=[s{1:end-1}];if any(c>47),v=str2num(c);elseif c>41,[l,s]=m(s);v=[l/v l*v l+v l-v];v=v(c=='/*+-');if r,break;end;r=1;elseif c<41,break;end;r=r&c~=41;end

Clear(er) function:

function [value,str] = math(str)
  returnNow = 1;
  while str,
    str = regexp(str,'( ?)(?(1)-?)[\.\d]+|\S','match');
    current = str{end};
    str = [str{1:end-1}];
    if any(current > 47),
      value = str2num(current);
    elseif current > 41,
      [leftValue,str] = math(str);
      value = [leftValue/value leftValue*value ...
               leftValue+value leftValue-value];
      value = value(current == '/*+-');
      if returnNow,
        break;
      end;
      returnNow = 1;
    elseif current < 41,
      break;
    end;
    returnNow = returnNow & (c ~= 41);
  end

Test:

>> [math('1 + 3 / -8'); ...
math('2*3*4*5+99'); ...
math('4 * (9 - 4) / (2 * 6 - 2) + 8'); ...
math('1 + ((123 * 3 - 69) / 100)'); ...
math('2.45/8.5*9.27+(5*0.0023)')]

ans =

   -0.5000
  219.0000
   10.0000
    4.0000
    2.6834

Synopsis: A mixture of regular expressions and recursion. Pretty much the best I have been able to do so far, without cheating and using EVAL.

Answer 32

Assembler

427 bytes

Obfuscated, assembled with the excellent A86 into a .com executable:

dd 0db9b1f89h, 081bee3h, 0e8af789h, 0d9080080h, 0bdac7674h, 013b40286h
dd 07400463ah, 0ccfe4508h, 08ce9f675h, 02fc8000h, 013b0057eh, 0feaac42ah
dd 0bedf75c9h, 0ba680081h, 04de801h, 04874f73bh, 04474103ch, 0e8e8b60fh
dd 08e8a003fh, 0e880290h, 0de0153h, 08b57e6ebh, 0d902a93eh, 046d891dh
dd 08906c783h, 05f02a93eh, 03cffcee8h, 057197510h, 02a93e8bh, 08b06ef83h
dd 05d9046dh, 02a93e89h, 03bc9d95fh, 0ac0174f7h, 074f73bc3h, 0f3cac24h
dd 0eed9c474h, 0197f0b3ch, 07cc4940fh, 074f73b09h, 0103cac09h, 0a3ce274h
dd 0e40a537eh, 0e0d90274h, 02a3bac3h, 021cd09b4h, 03e8b20cdh, 0ff8102a9h
dd 0ed7502abh, 0474103ch, 0e57d0b3ch, 0be02a3bfh, 014d903a3h, 0800344f6h
dd 02db00574h, 0d9e0d9aah, 0d9029f2eh, 0bb34dfc0h, 08a0009h, 01c75f0a8h
dd 020750fa8h, 0b0f3794bh, 021e9aa30h, 0de607400h, 08802990eh, 0de07df07h
dd 0c392ebc1h, 0e8c0008ah, 0aa300404h, 0f24008ah, 04baa3004h, 02eb0ee79h
dd 03005c6aah, 0c0d90ab1h, 0e9defcd9h, 02a116deh, 0e480e0dfh, 040fc8045h
dd 0ede1274h, 0c0d90299h, 015dffcd9h, 047300580h, 0de75c9feh, 0303d804fh
dd 03d80fa74h, 04f01752eh, 0240145c6h, 0dfff52e9h, 0d9029906h, 0f73b025fh
dd 03caca174h, 07fed740ah, 0df07889ah, 0277d807h, 047d9c1deh, 0990ede02h
dd 025fd902h, 03130e0ebh, 035343332h, 039383736h, 02f2b2d2eh, 02029282ah
dd 0e9000a09h, 07fc9f9c1h, 04500000fh, 0726f7272h
db 024h, 0abh, 02h

EDIT: Unobfuscated source:

  mov [bx],bx
  finit
  mov si,81h
  mov di,si
  mov cl,[80h]
  or cl,bl
  jz ret
 l1:
  lodsb
  mov bp,d1
  mov ah,19
 l2:
  cmp al,[bp]
  je l3
  inc bp
  dec ah
  jne l2
  jmp exit
 l3:
  cmp ah,2
  jle l4
  mov al,19
  sub al,ah
  stosb
 l4:
  dec cl
  jnz l1
  mov si,81h
  push done

 decode:
 l5:
  call l7
 l50:
  cmp si,di
  je ret
  cmp al,16
  je ret
  db 0fh, 0b6h, 0e8h ; movzx bp,al
  call l7
  mov cl,[bp+op-11]
  mov byte ptr [sm1],cl
  db 0deh
 sm1:db ?
  jmp l50

 open:
  push di
  mov di,word ptr [s]
  fstp dword ptr [di]
  mov [di+4],bp
  add di,6
  mov word ptr [s],di
  pop di
  call decode
  cmp al,16
  jne ret
  push di
  mov di,word ptr [s]
  sub di,6
  mov bp,[di+4]
  fld dword ptr [di]
  mov word ptr [s],di
  pop di
  fxch st(1)
  cmp si,di
  je ret
  lodsb
  ret



 l7: cmp si,di
  je exit
  lodsb
  cmp al,15
  je open
  fldz
  cmp al,11
  jg exit
  db 0fh, 94h, 0c4h ; sete ah 
  jl l10
 l9:
  cmp si,di
  je l12
  lodsb
  cmp al,16
  je ret
 l10:
  cmp al,10
  jle l12i

 l12:
  or ah,ah
  je l13
  fchs
 l13:
  ret

 exit:
  mov dx,offset res
  mov ah,9
  int 21h
  int 20h

 done:
  mov di,word ptr [s]
  cmp di,(offset s)+2
  jne exit
  cmp al,16
  je ok
  cmp al,11
  jge exit
 ok:
  mov di,res
  mov si,res+100h
  fst dword ptr [si]
  test byte ptr [si+3],80h
  jz pos
  mov al,'-'
  stosb
  fchs
 pos:
  fldcw word ptr [cw]
  fld st(0)
  fbstp [si]
  mov bx,9
 l1000:
  mov al,[si+bx]
  test al,0f0h
  jne startu
  test al,0fh
  jne startl
  dec bx
  jns l1000
  mov al,'0'
  stosb
  jmp frac

 l12i:
  je l11
  fimul word ptr [d3]
  mov [bx],al
  fild word ptr [bx]
  faddp
  jmp l9
  ret

 startu:
  mov al,[si+bx]
  shr al,4
  add al,'0'
  stosb
 startl:
  mov al,[si+bx]
  and al,0fh
  add al,'0'
  stosb
  dec bx
  jns startu

 frac:
  mov al,'.'
  stosb
  mov byte ptr [di],'0'
  mov cl,10
  fld st(0)
  frndint
 frac1: 
  fsubp st(1)
  ficom word ptr [zero]
  fstsw ax
  and ah,045h
  cmp ah,040h
  je finished
  fimul word ptr [d3]
  fld st(0)
  frndint
  fist word ptr [di]
  add byte ptr [di],'0'
  inc di
  dec cl
  jnz frac1

 finished: 
  dec di
  cmp byte ptr [di],'0'
  je finished
  cmp byte ptr [di],'.'
  jne f2
  dec di
 f2:
  mov byte ptr [di+1],'$'
 exit2:
  jmp exit


 l11:
  fild word ptr [d3]
  fstp dword ptr [bx+2]
 l111:
  cmp si,di
  je ret
  lodsb
  cmp al,10
  je exit2
  jg ret
  mov [bx],al
  fild word ptr [bx]
  fdiv dword ptr [bx+2]
  faddp
  fld dword ptr [bx+2]
  fimul word ptr [d3]
  fstp dword ptr [bx+2]
  jmp l111


 d1: db '0123456789.-+/*()', 32, 9
 d3: dw 10
 op: db 0e9h, 0c1h, 0f9h, 0c9h
 cw: dw 0f7fh
 zero: dw 0
 res:db 'Error$'
 s:  dw (offset s)+2

Skizz

Answer 33

Ruby

Number of characters: 103

N='( *-?[\d.]+ *)'
def e x
x.sub!(/\(#{N}\)|#{N}([^.\d])#{N}/){$1or(e$2).send$3,e($4)}?e(x):x.to_f
end

This is a non-recursive version of The Wicked Flea's solution. Parenthesized sub-expressions are evaluated bottom-up instead of top-down.

Edit: Converting the 'while' to a conditional + tail recursion has saved a few characters, so it is no longer non-recursive (though the recursion is not semantically necessary.)

Edit: Borrowing Daniel Martin's idea of merging the regexps saves another 11 characters!

Edit: That recursion is even more useful than I first thought! x.to_f can be rewritten as e(x), if x happens to contain a single number.

Edit: Using 'or' instead of '||' allows a pair of parentheses to be dropped.

Long version:

# Decimal number, as a capturing group, for substitution
# in the main regexp below.
N='( *-?[\d.]+ *)'

# The evaluation function
def e(x)
  matched = x.sub!(/\(#{N}\)|#{N}([^\d.])#{N}/) do
    # Group 1 is a numeric literal in parentheses.  If this is present then
    # just return it.
    if $1
      $1
    # Otherwise, $3 is an operator symbol and $2 and $4 are the operands
    else
      # Recursively call e to parse the operands (we already know from the
      # regexp that they are numeric literals, and this is slightly shorter
      # than using :to_f)
      e($2).send($3, e($4))
      # We could have converted $3 to a symbol ($3.to_s) or converted the
      # result back to string form, but both are done automatically anyway
    end
  end
  if matched then
    # We did one reduction. Now recurse back and look for more.
    e(x)
  else
    # If the string doesn't look like a non-trivial expression, assume it is a
    # string representation of a real number and attempt to parse it
    x.to_f
  end
end

Answer 34

C++

Chars: 1670

 // not trying to be terse here
#define DIGIT(c)((c)>='0' && (c) <= '9')
#define WHITE(pc) while(*pc == ' ') pc++
#define LP '('
#define RP ')'

bool SeeNum(const char* &pc, float& fNum){
    WHITE(pc);
    if (!(DIGIT(*pc) || (*pc=='.'&& DIGIT(pc[1])))) return false;
    const char* pc0 = pc;
    while(DIGIT(*pc)) pc++;
    if (*pc == '.'){
        pc++;
        while(DIGIT(*pc)) pc++;
    }
    char buf[200];
    int len = pc - pc0;
    strncpy(buf, pc0, len); buf[len] = 0;
    fNum = atof(buf);
    return true;
}

bool SeeChar(const char* &pc, char c){
    WHITE(pc);
    if (*pc != c) return false;
    pc++;
    return true;
}

void ParsExpr(const char* &pc, float &fNum);

void ParsPrim(const char* &pc, float &fNum){
    if (SeeNum(pc, fNum));
    else if (SeeChar(pc, LP)){
        ParsExpr(pc, fNum);
        if (!SeeChar(pc, RP)) exit(0);
    }
    else exit(0); // you can abort better than this
}

void ParsUnary(const char* &pc, float &fNum){
    if (SeeChar(pc, '-')){
        pc+;
        ParsUnary(pc, fNum);
        fNum = -fNum;
    }
    else {
        ParsPrim(pc, fNum);
    }
}

void ParsExpr(const char* &pc, float &fNum){
    ParsUnary(pc, fNum);
    float f1 = 0;
    while(true){
        if (SeeChar(pc, '+')){
            ParsUnary(pc, f1);
            fNum += f1;
        }
        else if (SeeChar(pc, '-')){
            ParsUnary(pc, f1);
            fNum -= f1;
        }
        else if (SeeChar(pc, '*')){
            ParsUnary(pc, f1);
            fNum *= f1;
        }
        else if (SeeChar(pc, '/')){
            ParsUnary(pc, f1);
            fNum /= f1;
        }
        else break;
    }
}

This is just LL1 (recursive descent). I like to do it this way (although I use doubles) because it's plenty fast, and easy to insert routines to handle precedence levels.

Answer 35

C#

Number of Characters: 355

I took Noldorin's Answer and modified it, so give Noldorin 99% of the credit for this. Best I could do with the algorithm was using was 408 characters. See Noldorin's Answer for the clearer code version.

Changes made:
Change char comparisons to compare against numbers.
Removed some default declarations and combined same type of declarations.
Re-worked some of the if statments.

float q(string x){float v,n;if(!float.TryParse(x,out v)){x+=';';int t=0,l=0,i=0;char o,s='?',p='+';for(;i<x.Length;i++){o=s;if(x[i]!=32){s=x[i];if(char.IsDigit(x[i])|s==46|(s==45&o!=49))s='1';if(s==41)l--;if(s!=o&l==0){if(o==49|o==41){n=q(x.Substring(t,i-t));v=p==43?v+n:p==45?v-n:p==42?v*n:p==47?v/n:v;p=x[i];}t=i;if(s==40)t++;}if(s==40)l++;}}}return v;}

Edit: knocked it down some more, from 361 to 355, by removing one of the return statments.

Answer 36

C# with Regex

Number of characters: 294

This is partially based off Jeff Moser's answer, but with a significantly simplified evaluation technique. There might even be further ways to reduce the char count, but I'm quite pleased now that there's a C# solution under 300 chars!

Fully obfuscated code:

float e(string x){while(x.Contains("("))x=Regex.Replace(x,@"\(([^\(]*?)\)",m=>e(m.Groups[1].Value).ToString());float r=0;foreach(Match m in Regex.Matches("+"+x,@"\D ?-?[\d.]+")){var o=m.Value[0];var v=float.Parse(m.Value.Substring(1));r=o=='+'?r+v:o=='-'?r-v:o=='*'?r*v:r/v;}return r;}

Clearer code:

float e(string x)
{
    while (x.Contains("("))
        x = Regex.Replace(x, @"\(([^\(]*?)\)", m => e(m.Groups[1].Value).ToString());
    float r = 0;
    foreach (Match m in Regex.Matches("+" + x, @"\D ?-?[\d.]+"))
    {
        var o = m.Value[0];
        var v = float.Parse(m.Value.Substring(1));
        r = o == '+' ? r + v : o == '-' ? r - v : o == '*' ? r * v : r / v;
    }
    return r;
}

Answer 37

C (VS2005)

Number of Characters: 1360

Abuse of preprocessor and warnings for fun code layout (scroll down to see):

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define b main
#define c(a) b(a,0)
#define d -1
#define e -2
#define g break
#define h case
#define hh h
#define hhh h
#define w(i) case i
#define i return
#define j switch
#define k float
#define l realloc
#define m sscanf
#define n int _
#define o char
#define t(u) #u
#define q(r) "%f" t(r)  "n"
#define s while
#define v default
#define ex exit
#define W printf
#define x fn()
#define y strcat
#define z strcpy
#define Z strlen

char*p    =0    ;k    *b    (n,o**    a){k*f
;j(_){    hh   e:     i*    p==40?    (++p,c
(d        ))  :(      f=        l(        0,
4)        ,m (p       ,q        (%        ),
f,&_),    p+=_        ,f       );        hh
d:f=c(    e);s        (1      ){        j(
    *p    ++ ){       hh     0:        hh
    41    :i  f;      hh    43        :*
f+=*c(    e)   ;g     ;h    45:*f=    *f-*c(
e);g;h    42    :*    f=    *f**c(    e);g;h

47:*f      /=*c      (e);     g;   v:    c(0);}
}w(1):    if(p&&    printf    (q  ((     "\\"))
,*  c(    d)  ))    g;  hh    0: ex      (W
(x  ))    ;v  :p    =(        p?y:       z)(l(p
,Z(1[     a]  )+    (p        ?Z(p           )+
1:1))     ,1  [a    ])  ;b    (_ -1          ,a
+1  );    g;  }i    0;};fn    ()  {n     =42,p=
43  ;i     "Er"      "ro"     t(   r)    "\n";}

Skizz

Answer 38

PowerBASIC

Number of characters: ~400

A bit ugly, but it works. :) I'm sure regexp would have made it even smaller.

DEFDBL E,f,i,z,q,a,v,o  
DEFSTR s,c,k,p

FUNCTION E(s)  

    i=LEN(s)  
    DO  
        IF MID$(s,i,1)="("THEN  
            q=INSTR(i,s,")")  
            s=LEFT$(s,i-1)+STR$(E(MID$(s,i+1,q-i-1)))+MID$(s,q+1)  
        END IF  
        i-=1  
    LOOP UNTIL i=0  

    k="+-*/"  
    DIM p(PARSECOUNT(s,ANY k))  
    PARSE s,p(),ANY k  

    a=VAL(p(0))

    FOR i=1TO LEN(s)
        c=MID$(s,i,1)
        q=INSTR(k,c)
        IF q THEN
            z+=1
            IF o=0 THEN o=q ELSE p(z)=c+p(z)
            IF TRIM$(p(z))<>"" THEN
                v=VAL(p(z))
                a=CHOOSE(o,a+v,a-v,a*v,a/v)
                o=0
            END IF
        END IF
    NEXT

    E=a  
END FUNCTION

Answer 39

C#, 264 characters

Strategy: the first 2 lines get rid of parentheses by induction. Then I split by \-?[\d.]+ to get numbers and operators. then using aggregate to reduce the string array to a double value.

Variable explanations

m is parenthesized expression with no nested parentheses.
d is a placeholder for that awkward TryParse syntax.
v is the accumulator for the final value
t is the current token.

float E(string s){var d=999f;while(d-->1)s=Regex.Replace(s,@"(([^(]?))",m=>E(m.Groups[1].Value)+"");return Regex.Split(s,@"(-?[\d.]+)").Aggregate(d,(v,t)=>(t=t.Trim()).Length==0?v:!float.TryParse(t,out d)?(s=t)==""?0:v:s=="/"?v/d:s=="-"?v-d:s==""?v*d:v+d);}

    float F(string s) {
        var d=999f;
        while(d-->1)
            s=Regex.Replace(s,@"\(([^\(]*?)\)",m=>F(m.Groups[1].Value)+"");
        return Regex.Split(s, @"(\-?[\d\.]+)")
            .Aggregate(d, (v, t) => 
                (t=t.Trim()).Length == 0 ? v :
                !float.TryParse(t, out d) ? (s=t) == "" ? 0 : v :
                s == "/" ? v / d :
                s == "-" ? v - d :
                s == "*" ? v * d :
                           v + d);
    }

EDIT: shamelessly stole parts from noldorin's answer, reused s as the operator variable.

EDIT: 999 nested parentheses should be enough for anyone.

Answer 40

SQL (SQL Server 2008)

Number of characters: 4202

Fully obfuscated function:

WITH Input(id,str)AS(SELECT 1,'1 + 3 / -8'UNION ALL SELECT 2,'2*3*4*5+99'UNION ALL SELECT 3,'4 * (9 - 4)/ (2 * 6 - 2)+ 8'UNION ALL SELECT 4,'1 + ((123 * 3 - 69)/ 100)'UNION ALL SELECT 5,'2.45/8.5*9.27+(5*0.0023)'),Separators(i,ch,str_src,priority)AS(SELECT 1,'-',1,1UNION ALL SELECT 2,'+',1,1UNION ALL SELECT 3,'*',1,1UNION ALL SELECT 4,'/',1,1UNION ALL SELECT 5,'(',0,0UNION ALL SELECT 6,')',0,0),SeparatorsStrSrc(str,i)AS(SELECT CAST('['AS varchar(max)),0UNION ALL SELECT str+ch,SSS.i+1FROM SeparatorsStrSrc SSS INNER JOIN Separators S ON SSS.i=S.i-1WHERE str_src<>0),SeparatorsStr(str)AS(SELECT str+']'FROM SeparatorsStrSrc WHERE i=(SELECT COUNT(*)FROM Separators WHERE str_src<>0)),ExprElementsSrc(id,i,tmp,ele,pre_ch,input_str)AS(SELECT id,1,CAST(LEFT(str,1)AS varchar(max)),CAST(''AS varchar(max)),CAST(' 'AS char(1)),SUBSTRING(str,2,LEN(str))FROM Input UNION ALL SELECT id,CASE ele WHEN''THEN i ELSE i+1 END,CAST(CASE WHEN LEFT(input_str,1)=' 'THEN''WHEN tmp='-'THEN CASE WHEN pre_ch LIKE(SELECT str FROM SeparatorsStr)THEN tmp+LEFT(input_str,1)ELSE LEFT(input_str,1)END WHEN LEFT(input_str,1)IN(SELECT ch FROM Separators)OR tmp IN(SELECT ch FROM Separators)THEN LEFT(input_str,1)ELSE tmp+LEFT(input_str,1)END AS varchar(max)),CAST(CASE WHEN LEFT(input_str,1)=' 'THEN tmp WHEN LEFT(input_str,1)='-'THEN CASE WHEN tmp IN(SELECT ch FROM Separators)THEN tmp ELSE''END WHEN LEFT(input_str,1)IN(SELECT ch FROM Separators)OR tmp IN(SELECT ch FROM Separators)THEN CASE WHEN tmp='-'AND pre_ch LIKE(SELECT str FROM SeparatorsStr)THEN''ELSE tmp END ELSE''END AS varchar(max)),CAST(LEFT(ele,1)AS char(1)),SUBSTRING(input_str,2,LEN(input_str))FROM ExprElementsSrc WHERE input_str<>''OR tmp<>''),ExprElements(id,i,ele)AS(SELECT id,i,ele FROM ExprElementsSrc WHERE ele<>''),Scanner(id,i,val)AS(SELECT id,i,CAST(ele AS varchar(max))FROM ExprElements WHERE ele<>''UNION ALL SELECT id,MAX(i)+1,NULL FROM ExprElements GROUP BY id),Operator(op,priority)AS(SELECT ch,priority FROM Separators WHERE priority<>0),Calc(id,c,i,pop_count,s0,s1,s2,stack,status)AS(SELECT Scanner.id,1,1,0,CAST(scanner.val AS varchar(max)),CAST(NULL AS varchar(max)),CAST(NULL AS varchar(max)),CAST(''AS varchar(max)),CAST('init'AS varchar(max))FROM Scanner WHERE Scanner.i=1UNION ALL SELECT Calc.id,Calc.c+1,Calc.i,3,NULL,NULL,NULL,CASE Calc.s1 WHEN'+'THEN CAST(CAST(Calc.s2 AS real)+CAST(Calc.s0 AS real)AS varchar(max))WHEN'-'THEN CAST(CAST(Calc.s2 AS real)-CAST(Calc.s0 AS real)AS varchar(max))WHEN'*'THEN CAST(CAST(Calc.s2 AS real)*CAST(Calc.s0 AS real)AS varchar(max))WHEN'/'THEN CAST(CAST(Calc.s2 AS real)/CAST(Calc.s0 AS real)AS varchar(max))ELSE NULL END+' '+stack,CAST('calc '+Calc.s1 AS varchar(max))FROM Calc INNER JOIN Scanner NextVal ON Calc.id=NextVal.id AND Calc.i+1=NextVal.i WHERE Calc.pop_count=0AND ISNUMERIC(Calc.s2)=1AND Calc.s1 IN(SELECT op FROM Operator)AND ISNUMERIC(Calc.s0)=1AND(SELECT priority FROM Operator WHERE op=Calc.s1)>=COALESCE((SELECT priority FROM Operator WHERE op=NextVal.val),0)UNION ALL SELECT Calc.id,Calc.c+1,Calc.i,3,NULL,NULL,NULL,s1+' '+stack,CAST('paren'AS varchar(max))FROM Calc WHERE pop_count=0AND s2='('AND ISNUMERIC(s1)=1AND s0=')'UNION ALL SELECT Calc.id,Calc.c+1,Calc.i,Calc.pop_count-1,s1,s2,CASE WHEN LEN(stack)>0THEN SUBSTRING(stack,1,CHARINDEX(' ',stack)-1)ELSE NULL END,CASE WHEN LEN(stack)>0THEN SUBSTRING(stack,CHARINDEX(' ',stack)+1,LEN(stack))ELSE''END,CAST('pop'AS varchar(max))FROM Calc WHERE Calc.pop_count>0UNION ALL SELECT Calc.id,Calc.c+1,Calc.i+1,Calc.pop_count,CAST(NextVal.val AS varchar(max)),s0,s1,coalesce(s2,'')+' '+stack,cast('read'as varchar(max))FROM Calc INNER JOIN Scanner NextVal ON Calc.id=NextVal.id AND Calc.i+1=NextVal.i WHERE NextVal.val IS NOT NULL AND Calc.pop_count=0AND((Calc.s0 IS NULL OR calc.s1 IS NULL OR calc.s2 IS NULL)OR NOT(ISNUMERIC(Calc.s2)=1AND Calc.s1 IN(SELECT op FROM Operator)AND ISNUMERIC(calc.s0)=1AND (SELECT priority FROM Operator WHERE op=Calc.s1)>=COALESCE((SELECT priority FROM Operator WHERE op=NextVal.val),0))AND NOT(s2='('AND ISNUMERIC(s1)=1AND s0=')')))SELECT Calc.id,Input.str,Calc.s0 AS result FROM Calc INNER JOIN Input ON Calc.id=Input.id WHERE Calc.c=(SELECT MAX(c)FROM Calc calc2 WHERE Calc.id=Calc2.id)ORDER BY id

Clear/semi-obfuscated function:

WITH
  Input(id, str) AS (    
    SELECT 1, '1 + 3 / -8'
    UNION ALL SELECT 2, '2*3*4*5+99'
    UNION ALL SELECT 3, '4 * (9 - 4) / (2 * 6 - 2) + 8'
    UNION ALL SELECT 4, '1 + ((123 * 3 - 69) / 100)'
    UNION ALL SELECT 5, '2.45/8.5*9.27+(5*0.0023)'
  )
, Separators(i, ch, str_src, priority) AS (
    SELECT 1, '-', 1, 1
    UNION ALL SELECT 2, '+', 1, 1
    UNION ALL SELECT 3, '*', 1, 1
    UNION ALL SELECT 4, '/', 1, 1
    UNION ALL SELECT 5, '(', 0, 0
    UNION ALL SELECT 6, ')', 0, 0
  )
, SeparatorsStrSrc(str, i) AS (
    SELECT CAST('[' AS varchar(max)), 0
    UNION ALL
    SELECT
        str + ch
      , SSS.i + 1
    FROM
        SeparatorsStrSrc SSS
          INNER JOIN Separators S ON SSS.i = S.i - 1
    WHERE
        str_src <> 0
  )
, SeparatorsStr(str) AS (
    SELECT str + ']' FROM SeparatorsStrSrc
    WHERE i = (SELECT COUNT(*) FROM Separators WHERE str_src <> 0)
  )
, ExprElementsSrc(id, i, tmp, ele, pre_ch, input_str) AS (
    SELECT
        id
      , 1
      , CAST(LEFT(str, 1) AS varchar(max))
      , CAST('' AS varchar(max))
      , CAST(' ' AS char(1))
      , SUBSTRING(str, 2, LEN(str))
    FROM
        Input
    UNION ALL
    SELECT
        id
      , CASE ele
        WHEN '' THEN i
                ELSE i + 1
        END
      , CAST(
          CASE
          WHEN LEFT(input_str, 1) = ' '
            THEN ''
          WHEN tmp = '-'
            THEN CASE
                 WHEN pre_ch LIKE (SELECT str FROM SeparatorsStr)
                   THEN tmp + LEFT(input_str, 1)
                   ELSE LEFT(input_str, 1)
                 END
          WHEN LEFT(input_str, 1) IN (SELECT ch FROM Separators)
               OR
               tmp IN (SELECT ch FROM Separators)
            THEN LEFT(input_str, 1)
            ELSE tmp + LEFT(input_str, 1)
          END
        AS varchar(max))
      , CAST(
          CASE
          WHEN LEFT(input_str, 1) = ' '
            THEN tmp
          WHEN LEFT(input_str, 1) = '-'
            THEN CASE
                 WHEN tmp IN (SELECT ch FROM Separators)
                   THEN tmp
                   ELSE ''
                 END
          WHEN LEFT(input_str, 1) IN (SELECT ch FROM Separators)
               OR
               tmp IN (SELECT ch FROM Separators)
            THEN CASE
                 WHEN tmp = '-' AND pre_ch LIKE (SELECT str FROM SeparatorsStr)
                   THEN ''
                   ELSE tmp
                 END
            ELSE ''
          END
        AS varchar(max))
      , CAST(LEFT(ele, 1) AS char(1))
      , SUBSTRING(input_str, 2, LEN(input_str))
    FROM
        ExprElementsSrc
    WHERE
        input_str <> ''
        OR
        tmp <> ''
  )
, ExprElements(id, i, ele) AS (
    SELECT
        id
      , i
      , ele
    FROM
        ExprElementsSrc
    WHERE
        ele <> ''
  )
, Scanner(id, i, val) AS (
    SELECT
        id
      , i
      , CAST(ele AS varchar(max))
    FROM
        ExprElements
    WHERE
        ele <> ''
    UNION ALL
    SELECT
        id
      , MAX(i) + 1
      , NULL
    FROM
        ExprElements
    GROUP BY
        id
  )
, Operator(op, priority) AS (
    SELECT
        ch
      , priority 
    FROM
        Separators
    WHERE
        priority <> 0
  )
, Calc(id, c, i, pop_count, s0, s1, s2, stack, status) AS (
    SELECT
        Scanner.id
      , 1
      , 1
      , 0
      , CAST(scanner.val AS varchar(max))
      , CAST(NULL AS varchar(max))
      , CAST(NULL AS varchar(max))
      , CAST('' AS varchar(max))
      , CAST('init' AS varchar(max))
    FROM
        Scanner
    WHERE
        Scanner.i = 1
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i
      , 3
      , NULL
      , NULL
      , NULL
      , CASE Calc.s1
        WHEN '+' THEN CAST(CAST(Calc.s2 AS real) + CAST(Calc.s0 AS real) AS varchar(max))
        WHEN '-' THEN CAST(CAST(Calc.s2 AS real) - CAST(Calc.s0 AS real) AS varchar(max))
        WHEN '*' THEN CAST(CAST(Calc.s2 AS real) * CAST(Calc.s0 AS real) AS varchar(max))
        WHEN '/' THEN CAST(CAST(Calc.s2 AS real) / CAST(Calc.s0 AS real) AS varchar(max))
                 ELSE NULL
        END
          + ' '
          + stack
      , CAST('calc ' + Calc.s1 AS varchar(max))
    FROM
        Calc
          INNER JOIN Scanner NextVal ON Calc.id = NextVal.id
                                          AND Calc.i + 1 = NextVal.i
    WHERE
        Calc.pop_count = 0
          AND ISNUMERIC(Calc.s2) = 1
          AND Calc.s1 IN (SELECT op FROM Operator)
          AND ISNUMERIC(Calc.s0) = 1
          AND (SELECT priority FROM Operator WHERE op = Calc.s1)
            >= COALESCE((SELECT priority FROM Operator WHERE op = NextVal.val), 0)
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i
      , 3
      , NULL
      , NULL
      , NULL
      , s1 + ' ' + stack
      , CAST('paren' AS varchar(max))
    FROM
        Calc
    WHERE
        pop_count = 0
          AND s2 = '('
          AND ISNUMERIC(s1) = 1
          AND s0 = ')'
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i
      , Calc.pop_count - 1
      , s1
      , s2
      , CASE
        WHEN LEN(stack) > 0
          THEN SUBSTRING(stack, 1, CHARINDEX(' ', stack) - 1)
          ELSE NULL
        END
      , CASE
        WHEN LEN(stack) > 0
          THEN SUBSTRING(stack, CHARINDEX(' ', stack) + 1, LEN(stack))
          ELSE ''
        END
      , CAST('pop' AS varchar(max))
    FROM
        Calc
    WHERE
        Calc.pop_count > 0
    UNION ALL
    SELECT
        Calc.id
      , Calc.c + 1
      , Calc.i + 1
      , Calc.pop_count
      , CAST(NextVal.val AS varchar(max))
      , s0
      , s1
      , coalesce(s2, '') + ' ' + stack
      , cast('read' as varchar(max))
    FROM
        Calc
          INNER JOIN Scanner NextVal ON Calc.id = NextVal.id
                                          AND Calc.i + 1 = NextVal.i
    WHERE
        NextVal.val IS NOT NULL
          AND Calc.pop_count = 0
          AND (
            (Calc.s0 IS NULL or calc.s1 is null or calc.s2 is null)
            OR
            NOT(
              ISNUMERIC(Calc.s2) = 1
                AND Calc.s1 IN (SELECT op FROM Operator)
                AND ISNUMERIC(calc.s0) = 1
                AND (SELECT priority FROM Operator WHERE op = Calc.s1)
                  >= COALESCE((SELECT priority FROM Operator WHERE op = NextVal.val), 0)
            )
              AND NOT(s2 = '(' AND ISNUMERIC(s1) = 1 AND s0 = ')')
          )
  )
SELECT
    Calc.id
  , Input.str
  , Calc.s0 AS result
FROM
    Calc
      INNER JOIN Input ON Calc.id = Input.id
WHERE
    Calc.c = (SELECT MAX(c) FROM Calc calc2
              WHERE Calc.id = Calc2.id)
ORDER BY
    id

It is not shortest. But I think that it is very flexible for SQL. It's easy to add new operators. It's easy to change priority of operators.

Answer 41

PHP

Number of characters: 170

Fully obfuscated function:

function a($a,$c='#\(([^()]*)\)#e',$d='a("$1","#^ *-?[\d.]+ *\S *-?[\d.]+ *#e","\$0")'){$e='preg_replace';while($a!=$b=$e($c,$d,$a))$a = $b;return$e('#^(.*)$#e',$d,$a);}

Clearer function:

function a($a, $c = '#\(([^()]*)\)#e', $d = 'a("$1", "#^ *-?[\d.]+ *\S *-?[\d.]+ *#e", "\$0")') {
 $e = 'preg_replace';
 while ($a != $b = $e($c, $d, $a)) {
  $a = $b;
 }
 return $e('#^(.*)$#e', $d, $a);
}

Tests:

assert(a('1 + 3 / -8') === '-0.5');
assert(a('2*3*4*5+99') === '219');
assert(a('4 * (9 - 4) / (2 * 6 - 2) + 8') === '10');
assert(a('1 + ((123 * 3 - 69) / 100)') === '4');
assert(a('2.45/8.5*9.27+(5*0.0023)') === '2.68344117647');
assert(a(' 2 * 3 * 4 * 5 + 99 ') === '219');

Answer 42

Is there any code with optimization? Such as multiplication on zero or serial infix minus. On Python or C.

Answer 43

OCaml using Camlp4 directly:

open Camlp4.PreCast

let expr = Gram.Entry.mk "expr"

EXTEND Gram
  expr:
  [   [ e1 = expr; "+"; e2 = expr -> e1 + e2
      | e1 = expr; "-"; e2 = expr -> e1 - e2 ]
  |   [ e1 = expr; "*"; e2 = expr -> e1 * e2
      | e1 = expr; "/"; e2 = expr -> e1 / e2 ]
  |   [ n = INT -> int_of_string n
      | "("; e = expr; ")" -> e ]   ];
END

let () = Gram.parse expr Loc.ghost (Stream.of_string "1-2+3*4")

OCaml using the Camlp4 stream parser extension:

open Genlex

let lex = make_lexer ["+"; "-"; "*"; "/"; "("; ")"]

let rec parse_atom = parser
  | [< 'Int n >] -> n
  | [< 'Kwd "("; e=parse_expr; 'Kwd ")" >] -> e
and parse_factor = parser
  | [< e1=parse_atom; stream >] ->
      (parser
         | [< 'Kwd "*"; e2=parse_factor >] -> e1 * e2
         | [< 'Kwd "/"; e2=parse_factor >] -> e1 / e2
         | [< >] -> e1) stream
and parse_expr = parser
  | [< e1=parse_factor; stream >] ->
      (parser
         | [< 'Kwd "+"; e2=parse_expr >] -> e1 + e2
         | [< 'Kwd "-"; e2=parse_expr >] -> e1 - e2
         | [< >] -> e1) stream

let () =
  Printf.printf "%d\n" (parse_expr(lex(Stream.of_string "1 + 2 * (3 + 4)")));;