<?php
/**
* @file
* =============================================================================.
*
* 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
* $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!
*
* AUTHOR INFORMATION
* Copyright 2005, Miles Kaufmann.
* Enhancements, 2005 onwards, Drupal Community.
*
* 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.
*/
/**
* ctools_math_expr Class.
*/
class ctools_math_expr {
/**
* If TRUE do not call trigger_error on error other wise do.
*
* @var bool
*/
public $suppress_errors = FALSE;
/**
* The last error message reported.
*
* @var string
*/
public $last_error = NULL;
/**
* List of all errors reported.
*
* @var array
*/
public $errors = array();
/**
* Variable and constant values.
*
* @var array
*/
protected $vars;
/**
* User defined functions.
*
* @var array
*/
protected $userfuncs;
/**
* The names of constants, used to make constants read-only.
*
* @var array
*/
protected $constvars;
/**
* Built in simple (one arg) functions.
* Merged into $this->funcs in constructor.
*
* @var array
*/
protected $simplefuncs;
/**
* Definitions of all built-in functions.
*
* @var array
*/
protected $funcs;
/**
* Operators and their precedence.
*
* @var array
*/
protected $ops;
/**
* The set of operators using two arguments.
*
* @var array
*/
protected $binaryops;
/**
* Public constructor.
*/
public function __construct() {
$this->userfuncs = array();
$this->simplefuncs = array(
'sin',
'sinh',
'asin',
'asinh',
'cos',
'cosh',
'acos',
'acosh',
'tan',
'tanh',
'atan',
'atanh',
'exp',
'sqrt',
'abs',
'log',
'ceil',
'floor',
'round',
);
$this->ops = array(
'+' => array('precedence' => 0),
'-' => array('precedence' => 0),
'*' => array('precedence' => 1),
'/' => array('precedence' => 1),
'^' => array('precedence' => 2, 'right' => TRUE),
'_' => array('precedence' => 1),
'==' => array('precedence' => -1),
'!=' => array('precedence' => -1),
'>=' => array('precedence' => -1),
'<=' => array('precedence' => -1),
'>' => array('precedence' => -1),
'<' => array('precedence' => -1),
);
$this->binaryops = array(
'+', '-', '*', '/', '^', '==', '!=', '<', '<=', '>=', '>',
);
$this->funcs = array(
'ln' => array(
'function' => 'log',
'arguments' => 1,
),
'arcsin' => array(
'function' => 'asin',
'arguments' => 1,
),
'arcsinh' => array(
'function' => 'asinh',
'arguments' => 1,
),
'arccos' => array(
'function' => 'acos',
'arguments' => 1,
),
'arccosh' => array(
'function' => 'acosh',
'arguments' => 1,
),
'arctan' => array(
'function' => 'atan',
'arguments' => 1,
),
'arctanh' => array(
'function' => 'atanh',
'arguments' => 1,
),
'min' => array(
'function' => 'min',
'arguments' => 2,
'max arguments' => 99,
),
'max' => array(
'function' => 'max',
'arguments' => 2,
'max arguments' => 99,
),
'pow' => array(
'function' => 'pow',
'arguments' => 2,
),
'if' => array(
'function' => 'ctools_math_expr_if',
'arguments' => 2,
'max arguments' => 3,
),
'number' => array(
'function' => 'ctools_math_expr_number',
'arguments' => 1,
),
'time' => array(
'function' => 'time',
'arguments' => 0,
),
);
// Allow modules to add custom functions.
$context = array('final' => &$this->funcs);
drupal_alter('ctools_math_expression_functions', $this->simplefuncs, $context);
// Set up the initial constants and mark them read-only.
$this->vars = array('e' => exp(1), 'pi' => pi());
drupal_alter('ctools_math_expression_constants', $this->vars);
$this->constvars = array_keys($this->vars);
// Translate the older, simpler style into the newer, richer style.
foreach ($this->simplefuncs as $function) {
$this->funcs[$function] = array(
'function' => $function,
'arguments' => 1,
);
}
}
/**
* Change the suppress errors flag.
*
* When errors are not suppressed, trigger_error is used to cause a PHP error
* when an evaluation error occurs, as a result of calling trigger(). With
* errors suppressed this doesn't happen.
*
* @param bool $enable
* If FALSE, enable triggering of php errors when expression errors occurs.
* otherwise, suppress triggering the errors.
*
* @return bool
* The new (current) state of the flag.
*
* @see ctools_math_expr::trigger()
*/
public function set_suppress_errors($enable) {
return $this->suppress_errors = (bool) $enable;
}
/**
* Backwards compatible wrapper for evaluate().
*
* @see ctools_math_expr::evaluate()
*/
public function e($expr) {
return $this->evaluate($expr);
}
/**
* Evaluate the expression.
*
* @param string $expr
* The expression to evaluate.
*
* @return string|bool
* The result of the expression, or FALSE if an error occurred, or TRUE if
* an user-defined function was created.
*/
public function evaluate($expr) {
$this->last_error = NULL;
$expr = trim($expr);
// Strip possible semicolons at the end.
if (substr($expr, -1, 1) == ';') {
$expr = (string) substr($expr, 0, -1);
}
// Is it a variable assignment?
if (preg_match('/^\s*([a-z]\w*)\s*=\s*(.+)$/', $expr, $matches)) {
// Make sure we're not assigning to a constant.
if (in_array($matches[1], $this->constvars)) {
return $this->trigger("cannot assign to constant '$matches[1]'");
}
// Get the result and make sure it's good:
if (($tmp = $this->pfx($this->nfx($matches[2]))) === FALSE) {
return FALSE;
}
// If so, stick it in the variable array...
$this->vars[$matches[1]] = $tmp;
// ...and return the resulting value:
return $this->vars[$matches[1]];
}
// 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)) {
// Get the function name.
$fnn = $matches[1];
// Make sure it isn't built in:
if (isset($this->funcs[$matches[1]])) {
return $this->trigger("cannot redefine built-in function '$matches[1]()'");
}
// Get the arguments.
$args = explode(",", preg_replace("/\s+/", "", $matches[2]));
// See if it can be converted to postfix.
$stack = $this->nfx($matches[3]);
if ($stack === FALSE) {
return FALSE;
}
// Freeze the state of the non-argument variables.
for ($i = 0; $i < count($stack); $i++) {
$token = (string) $stack[$i];
if (preg_match('/^[a-z]\w*$/', $token) and !in_array($token, $args)) {
if (array_key_exists($token, $this->vars)) {
$stack[$i] = $this->vars[$token];
}
else {
return $this->trigger("undefined variable '$token' in function definition");
}
}
}
$this->userfuncs[$fnn] = array('args' => $args, 'func' => $stack);
return TRUE;
}
else {
// Straight up evaluation.
return trim($this->pfx($this->nfx($expr)), '"');
}
}
/**
* Fetch an array of variables used in the expression.
*
* @return array
* Array of name : value pairs, one for each variable defined.
*/
public function vars() {
$output = $this->vars;
// @todo: Is this supposed to remove all constants? we should remove all
// those in $this->constvars!
unset($output['pi']);
unset($output['e']);
return $output;
}
/**
* Fetch all user defined functions in the expression.
*
* @return array
* Array of name : string pairs, one for each function defined. The string
* will be of the form fname(arg1,arg2). The function body is not returned.
*/
public function funcs() {
$output = array();
foreach ($this->userfuncs as $fnn => $dat) {
$output[] = $fnn . '(' . implode(',', $dat['args']) . ')';
}
return $output;
}
/**
* Convert infix to postfix notation.
*
* @param string $expr
* The expression to convert.
*
* @return array|bool
* The expression as an ordered list of postfix action tokens.
*/
private function nfx($expr) {
$index = 0;
$stack = new ctools_math_expr_stack();
// Postfix form of expression, to be passed to pfx().
$output = array();
// @todo: Because the expr can contain string operands, using strtolower here is a bug.
$expr = trim(strtolower($expr));
// We use this in syntax-checking the expression and determining when
// '-' is a negation.
$expecting_op = FALSE;
while (TRUE) {
$op = substr($expr, $index, 1);
// Get the first character at the current index, and if the second
// character is an =, add it to our op as well (accounts for <=).
if (substr($expr, $index + 1, 1) === '=') {
$op = substr($expr, $index, 2);
$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+|\()/', (string) substr($expr, $index), $match);
// Is it a negation instead of a minus?
if ($op === '-' and !$expecting_op) {
// Put a negation on the stack.
$stack->push('_');
$index++;
}
// We have to explicitly deny this, because it's legal on the stack but
// not in the input expression.
elseif ($op == '_') {
return $this->trigger("illegal character '_'");
}
// Are we putting an operator on the stack?
elseif ((isset($this->ops[$op]) || $ex) && $expecting_op) {
// Are we expecting an operator but have a num, var, func, or
// open-paren?
if ($ex) {
$op = '*';
// It's an implicit multiplication.
$index--;
}
// Heart of the algorithm:
while ($stack->count() > 0 &&
($o2 = $stack->last()) &&
isset($this->ops[$o2]) &&
(!empty($this->ops[$op]['right']) ?
$this->ops[$op]['precedence'] < $this->ops[$o2]['precedence'] :
$this->ops[$op]['precedence'] <= $this->ops[$o2]['precedence'])) {
// Pop stuff off the stack into the output.
$output[] = $stack->pop();
}
// Many thanks: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_algorithm_in_detail
// finally put OUR operator onto the stack.
$stack->push($op);
$index++;
$expecting_op = FALSE;
}
// Ready to close a parenthesis?
elseif ($op === ')') {
// Pop off the stack back to the last '('.
while (($o2 = $stack->pop()) !== '(') {
if (is_null($o2)) {
return $this->trigger("unexpected ')'");
}
else {
$output[] = $o2;
}
}
// Did we just close a function?
if (preg_match("/^([a-z]\w*)\($/", (string) $stack->last(2), $matches)) {
// Get the function name.
$fnn = $matches[1];
// See how many arguments there were (cleverly stored on the stack,
// thank you).
$arg_count = $stack->pop();
// Pop the function and push onto the output.
$output[] = $stack->pop();
// Check the argument count:
if (isset($this->funcs[$fnn])) {
$fdef = $this->funcs[$fnn];
$max_arguments = isset($fdef['max arguments']) ? $fdef['max arguments'] : $fdef['arguments'];
if ($arg_count > $max_arguments) {
return $this->trigger("too many arguments ($arg_count given, $max_arguments expected)");
}
}
elseif (array_key_exists($fnn, $this->userfuncs)) {
$fdef = $this->userfuncs[$fnn];
if ($arg_count !== count($fdef['args'])) {
return $this->trigger("wrong number of arguments ($arg_count given, " . count($fdef['args']) . ' expected)');
}
}
else {
// Did we somehow push a non-function on the stack? this should
// never happen.
return $this->trigger('internal error');
}
}
$index++;
}
// Did we just finish a function argument?
elseif ($op === ',' && $expecting_op) {
$index++;
$expecting_op = FALSE;
}
elseif ($op === '(' && !$expecting_op) {
$stack->push('(');
$index++;
}
elseif ($ex && !$expecting_op) {
// Make sure there was a function.
if (preg_match("/^([a-z]\w*)\($/", (string) $stack->last(3), $matches)) {
// Pop the argument expression stuff and push onto the output:
while (($o2 = $stack->pop()) !== '(') {
// Oops, never had a '('.
if (is_null($o2)) {
return $this->trigger("unexpected argument in $expr $o2");
}
else {
$output[] = $o2;
}
}
// Increment the argument count.
$stack->push($stack->pop() + 1);
// Put the ( back on, we'll need to pop back to it again.
$stack->push('(');
}
// Do we now have a function/variable/number?
$expecting_op = TRUE;
$val = (string) $match[1];
if (preg_match("/^([a-z]\w*)\($/", $val, $matches)) {
// May be func, or variable w/ implicit multiplication against
// parentheses...
if (isset($this->funcs[$matches[1]]) or array_key_exists($matches[1], $this->userfuncs)) {
$stack->push($val);
$stack->push(0);
$stack->push('(');
$expecting_op = FALSE;
}
// it's a var w/ implicit multiplication.
else {
$val = $matches[1];
$output[] = $val;
}
}
// it's a plain old var or num.
else {
$output[] = $val;
}
$index += strlen($val);
}
elseif ($op === ')') {
// Miscellaneous error checking.
return $this->trigger("unexpected ')'");
}
elseif (isset($this->ops[$op]) and !$expecting_op) {
return $this->trigger("unexpected operator '$op'");
}
elseif ($op === '"') {
// Fetch a quoted string.
$string = (string) substr($expr, $index);
if (preg_match('/"[^"\\\\]*(?:\\\\.[^"\\\\]*)*"/s', $string, $matches)) {
$string = $matches[0];
// Trim the quotes off:
$output[] = $string;
$index += strlen($string);
$expecting_op = TRUE;
}
else {
return $this->trigger('open quote without close quote.');
}
}
else {
// I don't even want to know what you did to get here.
return $this->trigger("an unexpected error occurred at $op");
}
if ($index === strlen($expr)) {
if (isset($this->ops[$op])) {
// Did we end with an operator? bad.
return $this->trigger("operator '$op' lacks operand");
}
else {
break;
}
}
// Step the index past whitespace (pretty much turns whitespace into
// implicit multiplication if no operator is there).
while (substr($expr, $index, 1) === ' ') {
$index++;
}
}
// Pop everything off the stack and push onto output:
while (!is_null($op = $stack->pop())) {
// If there are (s on the stack, ()s were unbalanced.
if ($op === '(') {
return $this->trigger("expecting ')'");
}
$output[] = $op;
}
return $output;
}
/**
* Evaluate a prefix-operator stack expression.
*
* @param array $tokens
* The array of token values to evaluate. A token is a string value
* representing either an operation to perform, a variable, or a value.
* Literal values are checked using is_numeric(), or a value that starts
* with a double-quote; functions and variables by existence in the
* appropriate tables.
* If FALSE is passed in the function terminates immediately, returning
* FALSE.
* @param array $vars
* Additional variable values to use when evaluating the expression. These
* variables do not override internal variables with the same name.
*
* @return bool|mixed
* The expression's value, otherwise FALSE is returned if there is an error
* detected unless php error handling intervenes: see suppress_error.
*/
public function pfx(array $tokens, array $vars = array()) {
if ($tokens == FALSE) {
return FALSE;
}
$stack = new ctools_math_expr_stack();
foreach ($tokens as $token) {
// If the token is a binary operator, pop two values off the stack, do
// the operation, and push the result back on again.
if (in_array($token, $this->binaryops)) {
if (is_null($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;
case '==':
$stack->push((int) ($op1 == $op2));
break;
case '!=':
$stack->push((int) ($op1 != $op2));
break;
case '<=':
$stack->push((int) ($op1 <= $op2));
break;
case '<':
$stack->push((int) ($op1 < $op2));
break;
case '>=':
$stack->push((int) ($op1 >= $op2));
break;
case '>':
$stack->push((int) ($op1 > $op2));
break;
}
}
// If the token is a unary operator, pop one value off the stack, do the
// operation, and push it back on again.
elseif ($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 again.
elseif (preg_match("/^([a-z]\w*)\($/", (string) $token, $matches)) {
$fnn = $matches[1];
// Check for a built-in function.
if (isset($this->funcs[$fnn])) {
$args = array();
// Collect all required args from the stack.
for ($i = 0; $i < $this->funcs[$fnn]['arguments']; $i++) {
if (is_null($op1 = $stack->pop())) {
return $this->trigger("function $fnn missing argument $i");
}
$args[] = $op1;
}
// If func allows additional args, collect them too, stopping on a
// NULL arg.
if (!empty($this->funcs[$fnn]['max arguments'])) {
for (; $i < $this->funcs[$fnn]['max arguments']; $i++) {
$arg = $stack->pop();
if (!isset($arg)) {
break;
}
$args[] = $arg;
}
}
$stack->push(
call_user_func_array($this->funcs[$fnn]['function'], array_reverse($args))
);
}
// Check for a user function.
elseif (isset($fnn, $this->userfuncs)) {
$args = array();
for ($i = count($this->userfuncs[$fnn]['args']) - 1; $i >= 0; $i--) {
$value = $stack->pop();
$args[$this->userfuncs[$fnn]['args'][$i]] = $value;
if (is_null($value)) {
return $this->trigger('internal error');
}
}
// yay... recursion!!!!
$stack->push($this->pfx($this->userfuncs[$fnn]['func'], $args));
}
}
// If the token is a number or variable, push it on the stack.
else {
if (is_numeric($token) || $token[0] == '"') {
$stack->push($token);
}
elseif (array_key_exists($token, $this->vars)) {
$stack->push($this->vars[$token]);
}
elseif (array_key_exists($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.
*
* @param string $msg
* Message to add to trigger error.
*
* @return bool
* Can trigger error, then returns FALSE.
*/
protected function trigger($msg) {
$this->errors[] = $msg;
$this->last_error = $msg;
if (!$this->suppress_errors) {
trigger_error($msg, E_USER_WARNING);
}
return FALSE;
}
}
/**
* Class implementing a simple stack structure, used by ctools_math_expr.
*/
class ctools_math_expr_stack {
/**
* The stack.
*
* @var array
*/
private $stack;
/**
* The stack pointer, points at the first empty space.
*
* @var int
*/
private $count;
/**
* Ctools_math_expr_stack constructor.
*/
public function __construct() {
$this->stack = array();
$this->count = 0;
}
/**
* Push the value onto the stack.
*
* @param mixed $val
*/
public function push($val) {
$this->stack[$this->count] = $val;
$this->count++;
}
/**
* Remove the most recently pushed value and return it.
*
* @return mixed|null
* The most recently pushed value, or NULL if the stack was empty.
*/
public function pop() {
if ($this->count > 0) {
$this->count--;
return $this->stack[$this->count];
}
return NULL;
}
/**
* "Peek" the stack, or Return a value from the stack without removing it.
*
* @param int $n
* Integer indicating which value to return. 1 is the topmost (i.e. the
* value that pop() would return), 2 indicates the next, 3 the third, etc.
*
* @return mixed|null
* A value pushed onto the stack at the nth position, or NULL if the stack
* was empty.
*/
public function last($n = 1) {
return !empty($this->stack[$this->count - $n]) ? $this->stack[$this->count - $n] : NULL;
}
/**
* Return the number of items on the stack.
*
* @return int
* The number of items.
*/
public function count() {
return $this->count;
}
}
/**
* Helper function for evaluating 'if' condition.
*
* @param int $expr
* The expression to test: if <> 0 then the $if expression is returned.
* @param mixed $if
* The expression returned if the condition is true.
* @param mixed $else
* Optional. The expression returned if the expression is false.
*
* @return mixed|null
* The result. NULL is returned when an If condition is False and no Else
* expression is provided.
*/
function ctools_math_expr_if($expr, $if, $else = NULL) {
return $expr ? $if : $else;
}
/**
* Remove any non-digits so that numbers like $4,511.23 still work.
*
* It might be good for those using the 12,345.67 format, but is awful for
* those using other conventions.
* Use of the php 'intl' module might work here, if the correct locale can be
* derived, but that seems unlikely to be true in all cases.
*
* @todo: locale could break this since in some locales that's $4.512,33 so
* there needs to be a way to detect that and make it work properly.
*
* @param mixed $arg
* A number string with possible leading chars.
*
* @return mixed
* Returns a number string.
*/
function ctools_math_expr_number($arg) {
// @todo: A really bad idea: It might be good for those using the 12,345.67
// format, but is awful for those using other conventions.
// $arg = preg_replace("/[^0-9\.]/", '', $arg);.
return $arg;
}