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- <?php
- /*
- ================================================================================
- ctools_math_expr - PHP Class to safely evaluate math expressions
- Copyright (C) 2005 Miles Kaufmann <http://www.twmagic.com/>
- ================================================================================
- NAME
- ctools_math_expr - safely evaluate math expressions
- SYNOPSIS
- include('ctools_math_expr.class.php');
- $m = new ctools_math_expr;
- // 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 ctools_math_expr 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 ctools_math_expr {
- 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',
- 'pow', 'exp',
- 'sqrt','abs','ln','log',
- 'time', 'ceil', 'floor', 'min', 'max', 'round');
- function __construct() {
- // make the variables a little more accurate
- $this->v['pi'] = pi();
- $this->v['e'] = exp(1);
- drupal_alter('ctools_math_expression_functions', $this->fb);
- }
- function e($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 ctools_math_expr_stack;
- $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 $this->trigger("an unexpected error occurred");
- }
- if ($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;
- $stack = new ctools_math_expr_stack;
- foreach ($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 ctools_math_expr_stack {
- 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($n=1) {
- return !empty($this->stack[$this->count-$n]) ? $this->stack[$this->count-$n] : NULL;
- }
- }
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