evalmath.class.php

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<?php
/*
 * ================================================================================
 *
 * 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).
 *
 * $m->last_error_code
 * If the last evaluation failed, 2 element array with numeric code and extra info
 *
 * 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
{
  public $suppress_errors = false;
 
  public $last_error = null;
 
  public $last_error_code = null;
 
  public $v = array('e' => 2.71, 'pi' => 3.14159);
 
  // variables (and constants)
  public $f = array();
 
  // user-defined functions
  public $vb = array('e', 'pi');
 
  // constants
  public $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', 'intval', 'ceil',
  );
 
  public function __construct()
  {
    // make the variables a little more accurate
    $this->v['pi'] = pi();
    $this->v['e'] = exp(1);
  }
 
  public function e($expr)
  {
    return $this->evaluate($expr);
  }
 
  public function evaluate($expr)
  {
    if (empty($expr)) {
      return false;
    }
 
    $this->last_error = null;
    $this->last_error_code = 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?
    $matches = array();
    if (preg_match('/^\s*([a-z]\w*)\s*=\s*(.+)$/', $expr, $matches)) {
      if (in_array($matches[1], $this->vb)) { // make sure we're not assigning to a constant
        return $this->trigger(1, "cannot assign to constant '$matches[1]'", $matches[1]);
      }
      if (($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 $this->trigger(2, "cannot redefine built-in function '$matches[1]()'", $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
      }
      $nbstack = count($stack);
      for ($i = 0; $i < $nbstack; $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 $this->trigger(3, "undefined variable '$token' in function definition", $token);
          }
        }
      }
      $this->f[$fnn] = array('args' => $args, 'func' => $stack);
      return true;
      // ===============
    } else {
      return $this->pfx($this->nfx($expr)); // straight up evaluation, woo
    }
  }
 
  public function vars()
  {
    $output = $this->v;
    unset($output['pi']);
    unset($output['e']);
    return $output;
  }
 
  private function funcs()
  {
    $output = array();
    foreach ($this->f as $fnn => $dat) {
      $output[] = $fnn.'('.implode(',', $dat['args']).')';
    }
    return $output;
  }
 
  // ===================== HERE BE INTERNAL METHODS ====================\\
 
  private 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
 
    $matches = array();
    if (preg_match("/[^\w\s+*^\/()\.,-]/", $expr, $matches)) { // make sure the characters are all good
      return $this->trigger(4, "illegal character '".$matches[0]."'", $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
      $match = array();
      $ex = preg_match('/^([a-z]\w*\‍(?|\d+(?:\.\d*)?|\.\d+|\‍()/', substr($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 $this->trigger(4, "illegal character '_'", "_"); // but not in the input expression
                                    // ===============
      } elseif ((in_array($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(5, "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 $this->trigger(6, "wrong number of arguments ($arg_count given, 1 expected)", array($arg_count, 1));
            }
          } elseif (array_key_exists($fnn, $this->f)) {
            if ($arg_count != count($this->f[$fnn]['args'])) {
              return $this->trigger(6, "wrong number of arguments ($arg_count given, ".count($this->f[$fnn]['args'])." expected)", array($arg_count, count($this->f[$fnn]['args'])));
            }
          } else { // did we somehow push a non-function on the stack? this should never happen
            return $this->trigger(7, "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(5, "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(5, "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 $this->trigger(5, "unexpected ')'", ")");
      } elseif (in_array($op, $ops) and !$expecting_op) {
        return $this->trigger(8, "unexpected operator '$op'", $op);
      } else { // I don't even want to know what you did to get here
        return $this->trigger(9, "an unexpected error occured");
      }
      if ($index == strlen($expr)) {
        if (in_array($op, $ops)) { // did we end with an operator? bad.
          return $this->trigger(10, "operator '$op' lacks operand", $op);
        } else {
          break;
        }
      }
      while (substr($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(11, "expecting ')'", ")"); // if there are (s on the stack, ()s were unbalanced
      }
      $output[] = $op;
    }
 
    return $output;
  }
 
  private function pfx($tokens, $vars = array())
  {
    $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
      $matches = array();
      if (in_array($token, array('+', '-', '*', '/', '^'))) {
        if (is_null($op2 = $stack->pop())) {
          return $this->trigger(12, "internal error");
        }
        if (is_null($op1 = $stack->pop())) {
          return $this->trigger(13, "internal error");
        }
        switch ($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(14, "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(15, "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(16, "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 $this->trigger(17, "undefined variable '$token'", $token);
        }
      }
    }
    // when we're out of tokens, the stack should have a single element, the final result
    if ($stack->count != 1) {
      return $this->trigger(18, "internal error");
    }
    return $stack->pop();
  }
 
  public function trigger($code, $msg, $info = null)
  {
    $this->last_error = $msg;
    $this->last_error_code = array($code, $info);
    if (!$this->suppress_errors) {
      trigger_error($msg, E_USER_WARNING);
    }
    return false;
  }
}
 
class EvalMathStack
{
  public $stack = array();
 
  public $count = 0;
 
  public function push($val)
  {
    $this->stack[$this->count] = $val;
    $this->count++;
  }
 
  public function pop()
  {
    if ($this->count > 0) {
      $this->count--;
      return $this->stack[$this->count];
    }
    return null;
  }
 
  public function last($n = 1)
  {
    if (isset($this->stack[$this->count - $n])) {
      return $this->stack[$this->count - $n];
    }
 
    return '';
  }
}