如何评估 PHP 中作为字符串传递的公式？

Question

只是想找出正确且更安全的方法来执行作为字符串传递的数学运算。 在我的场景中，它是从图像 EXIF 数据中获取的值。

经过一番研究后，我发现了两种方法。

首先，使用eval：

function calculator1($str){
    eval("\$str = $str;");
    return $str;
}

第二，使用create_function：

function calculator2($str){
    $fn = create_function("", "return ({$str});" );
    return $fn();
};

这两个示例都需要字符串清理以避免恶意代码执行。 还有其他或更短的方法吗？

Answer 1

这可能会有所帮助。

http://www.phpclasses.org/browse/package/2695.html

下载需要烦人的登录。 我把它复制粘贴在这里给你。

• 此类可用于安全地计算数学表达式。
• 该类可以采用文本字符串中的表达式，并通过替换变量值并计算数学函数和运算的结果来对其进行评估。
• 它支持隐式乘法、多变量函数和嵌套函数。
• 它可用于评估来自不受信任来源的表达式。 它提供强大的错误检查，并且仅评估一组有限的函数。
• 它可用于从公式表达式生成图表。

    /*
    ================================================================================

    EvalMath - PHP Class to safely evaluate math expressions
    Copyright (C) 2005 Miles Kaufmann <http://www.twmagic.com/>

    ================================================================================

    NAME
        EvalMath - safely evaluate math expressions

    SYNOPSIS
        <?
          include('evalmath.class.php');
          $m = new EvalMath;
          // basic evaluation:
          $result = $m->evaluate('2+2');
          // supports: order of operation; parentheses; negation; built-in functions
          $result = $m->evaluate('-8(5/2)^2*(1-sqrt(4))-8');
          // create your own variables
          $m->evaluate('a = e^(ln(pi))');
          // or functions
          $m->evaluate('f(x,y) = x^2 + y^2 - 2x*y + 1');
          // and then use them
          $result = $m->evaluate('3*f(42,a)');
        ?>

    DESCRIPTION
        Use the EvalMath class when you want to evaluate mathematical expressions 
        from untrusted sources.  You can define your own variables and functions,
        which are stored in the object.  Try it, it's fun!

    METHODS
        $m->evalute($expr)
            Evaluates the expression and returns the result.  If an error occurs,
            prints a warning and returns false.  If $expr is a function assignment,
            returns true on success.

        $m->e($expr)
            A synonym for $m->evaluate().

        $m->vars()
            Returns an associative array of all user-defined variables and values.

        $m->funcs()
            Returns an array of all user-defined functions.

    PARAMETERS
        $m->suppress_errors
            Set to true to turn off warnings when evaluating expressions

        $m->last_error
            If the last evaluation failed, contains a string describing the error.
            (Useful when suppress_errors is on).

    AUTHOR INFORMATION
        Copyright 2005, Miles Kaufmann.

    LICENSE
        Redistribution and use in source and binary forms, with or without
        modification, are permitted provided that the following conditions are
        met:

        1   Redistributions of source code must retain the above copyright
            notice, this list of conditions and the following disclaimer.
        2.  Redistributions in binary form must reproduce the above copyright
            notice, this list of conditions and the following disclaimer in the
            documentation and/or other materials provided with the distribution.
        3.  The name of the author may not be used to endorse or promote
            products derived from this software without specific prior written
            permission.

        THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
        IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
        WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
        DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT,
        INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
        (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
        SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
        HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
        STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
        ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
        POSSIBILITY OF SUCH DAMAGE.

    */

    class EvalMath {

        var $suppress_errors = false;
        var $last_error = null;

        var $v = array('e'=>2.71,'pi'=>3.14); // variables (and constants)
        var $f = array(); // user-defined functions
        var $vb = array('e', 'pi'); // constants
        var $fb = array(  // built-in functions
            'sin','sinh','arcsin','asin','arcsinh','asinh',
            'cos','cosh','arccos','acos','arccosh','acosh',
            'tan','tanh','arctan','atan','arctanh','atanh',
            'sqrt','abs','ln','log');

        function EvalMath() {
            // make the variables a little more accurate
            $this->v['pi'] = pi();
            $this->v['e'] = exp(1);
        }

        function e($expr) {
            return $this->evaluate($expr);
        }

        function evaluate($expr) {
            $this->last_error = null;
            $expr = trim($expr);
            if (substr($expr, -1, 1) == ';') $expr = substr($expr, 0, strlen($expr)-1); // strip semicolons at the end
            //===============
            // is it a variable assignment?
            if (preg_match('/^\s*([a-z]\w*)\s*=\s*(.+)$/', $expr, $matches)) {
                if (in_array($matches[1], $this->vb)) { // make sure we're not assigning to a constant
                    return $this->trigger("cannot assign to constant '$matches[1]'");
                }
                if (($tmp = $this->pfx($this->nfx($matches[2]))) === false) return false; // get the result and make sure it's good
                $this->v[$matches[1]] = $tmp; // if so, stick it in the variable array
                return $this->v[$matches[1]]; // and return the resulting value
            //===============
            // is it a function assignment?
            } elseif (preg_match('/^\s*([a-z]\w*)\s*\(\s*([a-z]\w*(?:\s*,\s*[a-z]\w*)*)\s*\)\s*=\s*(.+)$/', $expr, $matches)) {
                $fnn = $matches[1]; // get the function name
                if (in_array($matches[1], $this->fb)) { // make sure it isn't built in
                    return $this->trigger("cannot redefine built-in function '$matches[1]()'");
                }
                $args = explode(",", preg_replace("/\s+/", "", $matches[2])); // get the arguments
                if (($stack = $this->nfx($matches[3])) === false) return false; // see if it can be converted to postfix
                for ($i = 0; $i<count($stack); $i++) { // freeze the state of the non-argument variables
                    $token = $stack[$i];
                    if (preg_match('/^[a-z]\w*$/', $token) and !in_array($token, $args)) {
                        if (array_key_exists($token, $this->v)) {
                            $stack[$i] = $this->v[$token];
                        } else {
                            return $this->trigger("undefined variable '$token' in function definition");
                        }
                    }
                }
                $this->f[$fnn] = array('args'=>$args, 'func'=>$stack);
                return true;
            //===============
            } else {
                return $this->pfx($this->nfx($expr)); // straight up evaluation, woo
            }
        }

        function vars() {
            $output = $this->v;
            unset($output['pi']);
            unset($output['e']);
            return $output;
        }

        function funcs() {
            $output = array();
            foreach ($this->f as $fnn=>$dat)
                $output[] = $fnn . '(' . implode(',', $dat['args']) . ')';
            return $output;
        }

        //===================== HERE BE INTERNAL METHODS ====================\\

        // Convert infix to postfix notation
        function nfx($expr) {

            $index = 0;
            $stack = new EvalMathStack;
            $output = array(); // postfix form of expression, to be passed to pfx()
            $expr = trim(strtolower($expr));

            $ops   = array('+', '-', '*', '/', '^', '_');
            $ops_r = array('+'=>0,'-'=>0,'*'=>0,'/'=>0,'^'=>1); // right-associative operator?  
            $ops_p = array('+'=>0,'-'=>0,'*'=>1,'/'=>1,'_'=>1,'^'=>2); // operator precedence

            $expecting_op = false; // we use this in syntax-checking the expression
                                   // and determining when a - is a negation

            if (preg_match("/[^\w\s+*^\/()\.,-]/", $expr, $matches)) { // make sure the characters are all good
                return $this->trigger("illegal character '{$matches[0]}'");
            }

            while(1) { // 1 Infinite Loop ;)
                $op = substr($expr, $index, 1); // get the first character at the current index
                // find out if we're currently at the beginning of a number/variable/function/parenthesis/operand
                $ex = preg_match('/^([a-z]\w*\(?|\d+(?:\.\d*)?|\.\d+|\()/', substr($expr, $index), $match);
                //===============
                if ($op == '-' and !$expecting_op) { // is it a negation instead of a minus?
                    $stack->push('_'); // put a negation on the stack
                    $index++;
                } elseif ($op == '_') { // we have to explicitly deny this, because it's legal on the stack 
                    return $this->trigger("illegal character '_'"); // but not in the input expression
                //===============
                } elseif ((in_array($op, $ops) or $ex) and $expecting_op) { // are we putting an operator on the stack?
                    if ($ex) { // are we expecting an operator but have a number/variable/function/opening parethesis?
                        $op = '*'; $index--; // it's an implicit multiplication
                    }
                    // heart of the algorithm:
                    while($stack->count > 0 and ($o2 = $stack->last()) and in_array($o2, $ops) and ($ops_r[$op] ? $ops_p[$op] < $ops_p[$o2] : $ops_p[$op] <= $ops_p[$o2])) {
                        $output[] = $stack->pop(); // pop stuff off the stack into the output
                    }
                    // many thanks: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_algorithm_in_detail
                    $stack->push($op); // finally put OUR operator onto the stack
                    $index++;
                    $expecting_op = false;
                //===============
                } elseif ($op == ')' and $expecting_op) { // ready to close a parenthesis?
                    while (($o2 = $stack->pop()) != '(') { // pop off the stack back to the last (
                        if (is_null($o2)) return $this->trigger("unexpected ')'");
                        else $output[] = $o2;
                    }
                    if (preg_match("/^([a-z]\w*)\($/", $stack->last(2), $matches)) { // did we just close a function?
                        $fnn = $matches[1]; // get the function name
                        $arg_count = $stack->pop(); // see how many arguments there were (cleverly stored on the stack, thank you)
                        $output[] = $stack->pop(); // pop the function and push onto the output
                        if (in_array($fnn, $this->fb)) { // check the argument count
                            if($arg_count > 1)
                                return $this->trigger("too many arguments ($arg_count given, 1 expected)");
                        } elseif (array_key_exists($fnn, $this->f)) {
                            if ($arg_count != count($this->f[$fnn]['args']))
                                return $this->trigger("wrong number of arguments ($arg_count given, " . count($this->f[$fnn]['args']) . " expected)");
                        } else { // did we somehow push a non-function on the stack? this should never happen
                            return $this->trigger("internal error");
                        }
                    }
                    $index++;
                //===============
                } elseif ($op == ',' and $expecting_op) { // did we just finish a function argument?
                    while (($o2 = $stack->pop()) != '(') { 
                        if (is_null($o2)) return $this->trigger("unexpected ','"); // oops, never had a (
                        else $output[] = $o2; // pop the argument expression stuff and push onto the output
                    }
                    // make sure there was a function
                    if (!preg_match("/^([a-z]\w*)\($/", $stack->last(2), $matches))
                        return $this->trigger("unexpected ','");
                    $stack->push($stack->pop()+1); // increment the argument count
                    $stack->push('('); // put the ( back on, we'll need to pop back to it again
                    $index++;
                    $expecting_op = false;
                //===============
                } elseif ($op == '(' and !$expecting_op) {
                    $stack->push('('); // that was easy
                    $index++;
                    $allow_neg = true;
                //===============
                } elseif ($ex and !$expecting_op) { // do we now have a function/variable/number?
                    $expecting_op = true;
                    $val = $match[1];
                    if (preg_match("/^([a-z]\w*)\($/", $val, $matches)) { // may be func, or variable w/ implicit multiplication against parentheses...
                        if (in_array($matches[1], $this->fb) or array_key_exists($matches[1], $this->f)) { // it's a func
                            $stack->push($val);
                            $stack->push(1);
                            $stack->push('(');
                            $expecting_op = false;
                        } else { // it's a var w/ implicit multiplication
                            $val = $matches[1];
                            $output[] = $val;
                        }
                    } else { // it's a plain old var or num
                        $output[] = $val;
                    }
                    $index += strlen($val);
                //===============
                } elseif ($op == ')') { // miscellaneous error checking
                    return $this->trigger("unexpected ')'");
                } elseif (in_array($op, $ops) and !$expecting_op) {
                    return $this->trigger("unexpected operator '$op'");
                } else { // I don't even want to know what you did to get here
                    return $this->trigger("an unexpected error occured");
                }
                if ($index == strlen($expr)) {
                    if (in_array($op, $ops)) { // did we end with an operator? bad.
                        return $this->trigger("operator '$op' lacks operand");
                    } else {
                        break;
                    }
                }
                while (substr($expr, $index, 1) == ' ') { // step the index past whitespace (pretty much turns whitespace 
                    $index++;                             // into implicit multiplication if no operator is there)
                }

            } 
            while (!is_null($op = $stack->pop())) { // pop everything off the stack and push onto output
                if ($op == '(') return $this->trigger("expecting ')'"); // if there are (s on the stack, ()s were unbalanced
                $output[] = $op;
            }
            return $output;
        }

        // evaluate postfix notation
        function pfx($tokens, $vars = array()) {

            if ($tokens == false) return false;

            $stack = new EvalMathStack;

            foreach ($tokens as $token) { // nice and easy
                // if the token is a binary operator, pop two values off the stack, do the operation, and push the result back on
                if (in_array($token, array('+', '-', '*', '/', '^'))) {
                    if (is_null($op2 = $stack->pop())) return $this->trigger("internal error");
                    if (is_null($op1 = $stack->pop())) return $this->trigger("internal error");
                    switch ($token) {
                        case '+':
                            $stack->push($op1+$op2); break;
                        case '-':
                            $stack->push($op1-$op2); break;
                        case '*':
                            $stack->push($op1*$op2); break;
                        case '/':
                            if ($op2 == 0) return $this->trigger("division by zero");
                            $stack->push($op1/$op2); break;
                        case '^':
                            $stack->push(pow($op1, $op2)); break;
                    }
                // if the token is a unary operator, pop one value off the stack, do the operation, and push it back on
                } elseif ($token == "_") {
                    $stack->push(-1*$stack->pop());
                // if the token is a function, pop arguments off the stack, hand them to the function, and push the result back on
                } elseif (preg_match("/^([a-z]\w*)\($/", $token, $matches)) { // it's a function!
                    $fnn = $matches[1];
                    if (in_array($fnn, $this->fb)) { // built-in function:
                        if (is_null($op1 = $stack->pop())) return $this->trigger("internal error");
                        $fnn = preg_replace("/^arc/", "a", $fnn); // for the 'arc' trig synonyms
                        if ($fnn == 'ln') $fnn = 'log';
                        eval('$stack->push(' . $fnn . '($op1));'); // perfectly safe eval()
                    } elseif (array_key_exists($fnn, $this->f)) { // user function
                        // get args
                        $args = array();
                        for ($i = count($this->f[$fnn]['args'])-1; $i >= 0; $i--) {
                            if (is_null($args[$this->f[$fnn]['args'][$i]] = $stack->pop())) return $this->trigger("internal error");
                        }
                        $stack->push($this->pfx($this->f[$fnn]['func'], $args)); // yay... recursion!!!!
                    }
                // if the token is a number or variable, push it on the stack
                } else {
                    if (is_numeric($token)) {
                        $stack->push($token);
                    } elseif (array_key_exists($token, $this->v)) {
                        $stack->push($this->v[$token]);
                    } elseif (array_key_exists($token, $vars)) {
                        $stack->push($vars[$token]);
                    } else {
                        return $this->trigger("undefined variable '$token'");
                    }
                }
            }
            // when we're out of tokens, the stack should have a single element, the final result
            if ($stack->count != 1) return $this->trigger("internal error");
            return $stack->pop();
        }

        // trigger an error, but nicely, if need be
        function trigger($msg) {
            $this->last_error = $msg;
            if (!$this->suppress_errors) trigger_error($msg, E_USER_WARNING);
            return false;
        }
    }

    // for internal use
    class EvalMathStack {

        var $stack = array();
        var $count = 0;

        function push($val) {
            $this->stack[$this->count] = $val;
            $this->count++;
        }

        function pop() {
            if ($this->count > 0) {
                $this->count--;
                return $this->stack[$this->count];
            }
            return null;
        }

        function last($n=1) {
            return $this->stack[$this->count-$n];
        }
    }

编辑： Jitters 想要支持反向波兰表示法的版本。 让我想起了我的大学时光，当时我有一个惠普计算器:)

    <?php
    /* This Class can be useful for writting RPN macros or FORTH like parsers 
           @Author: Arturo Gonzalez-Mata Santana (Spain)
                 [email protected]
        @copyright 2007: www.phpsqlasp.com

        It is part of a project to recover "macros" from some old aplications 

    This code is free software; you can redistribute it and/or
    modify it under the terms of the GNU General Public License
    as published by the Free Software Foundation; either version 3
    of the License, or (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program; if not, write to the Free Software
    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
    */
    class RPNstack
    {
        var $data=array();
        var $compare=0;
        function pop() {return array_shift ($this->data);}
        function push($x) {array_unshift($this->data, $x);}
        function count() {return count($this->data);}
        function first() {return $this->data[0];}
        function top() {return end($this->data);}  //last element of 
        function swap() { // interchange tow elements
            $t = $this->data[1];
            $this->data[1] = $this->data[0];
            $this->data[0] = $t;
            }
        function dup() {  // put a copy of X element in the stack
            array_unshift($this->data, $this->data[0]);
            }

        function dump(){ // dump array data for debuging
            print_r($this->data);
            }

        function parse($tok)  // execute actions with the stack for each token
        {
            $r = null;
            $tok = strtoupper(trim($tok));
            //$this->dump(); // this line is for debugging purpose only
            switch ($tok) :
                // FIRST "IF THEN" AND OTHER FLOW CONTROLS
                case ('THEN'): break;
                case('IF'):
                    if ($this->pop() == 0) do {  // if condition is false do nothing until "THEN"
                        $tok = strtoupper(strtok (" "));
                        } while ($tok <> "THEN");  // IF THERE IS NO "THEN" THIS SHALL BE AN ENLESS LOOP
                    break;

                //   basic math operators   //OPERADORES MATEMATICOS BASICOS
                case('+'):
                    $r = $this->pop() + $this->pop();
                    // $r = array_shift($this->data) + array_shift($this->data);  // is more efficient but less understable
                    break;        
                case('-'):
                    $r = $this->pop(); $r = $this->pop()-$r;
                    break;
                case('*'):
                    $r = $this->pop() *  $this->pop();
                    break;
                case('/'):
                    $r = $this->pop(); $r = $this->pop() / $r;
                    break;
                // stack operators  //OPERADORES DE PILA  
                case ('DUP'):
                    $r=$this->dup();
                    break;
                case ('SWAP'):
                    $this->swap();
                    break;

                // COMPARISON OPERATORS
                case ('='):
                    if ($this->data[0] == $this->data[1]) $r = $this->push(1);
                    else $r = $this->push(0);
                    break;
                case ('<>'):
                    if ($this->data[0] <> $this->data[1]) $r = $this->push(1);
                    else $r = $this->push(0);
                    break;
                case ('<'):
                    if ($this->data[0] < $this->data[1]) $r = $this->push(1);  
                    else $r = $this->push(0);                            
                    break;
                case ('>'):
                    if ($this->data[0] > $this->data[1])  $r = $this->push(1);  
                    else $r = $this->push(0);                            
                    break;
                case ('>='):
                    if ($this->data[0] >= $this->data[1])  $r = $this->push(1);  
                    else $r = $this->push(0);                            
                    break;
                case ('<='):
                    if ($this->data[0] <= $this->data[1])  $r = $this->push(1);  
                    else $r = $this->push(0);                            
                    break;

                // WARNING FOR NON IMPLEMENTED FUNCTIONS
                default:
                        return sprintf('I don\'t know how to "%s" ', $tok);
            endswitch;
            if (!is_null($r)) $this->push($r); 
            return $r;
        } // parse


        function parse_line($cadena)
        {
            $tok = strtok ($cadena," ");
            while ($tok!= '') {
                if (is_numeric ($tok)) {
                    $this->push($tok);
                } else {
                    $r = $this->parse($tok);
                }
                $tok = strtok (" ");
            }
            return $r;
        }

    } // class RPN



    ?>