530 lines
17 KiB
PHP
530 lines
17 KiB
PHP
<?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
|
|
* $m->evaluate($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.
|
|
*/
|
|
|
|
/**
|
|
* \file core/class/evalmath.class.php
|
|
* \ingroup core
|
|
* \brief This file for Math evaluation
|
|
*/
|
|
|
|
/**
|
|
* Class EvalMath
|
|
*/
|
|
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',
|
|
);
|
|
|
|
/**
|
|
* Constructor
|
|
*/
|
|
public function __construct()
|
|
{
|
|
// make the variables a little more accurate
|
|
$this->v['pi'] = pi();
|
|
$this->v['e'] = exp(1);
|
|
}
|
|
|
|
/**
|
|
* Evaluate
|
|
*
|
|
* @param string $expr String
|
|
* @return boolean|int|float|NULL|mixed Result
|
|
*/
|
|
public function e($expr)
|
|
{
|
|
return $this->evaluate($expr);
|
|
}
|
|
|
|
/**
|
|
* Evaluate
|
|
*
|
|
* @param string $expr String
|
|
* @return boolean|int|float|NULL|mixed Result
|
|
*/
|
|
public function evaluate($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
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Function vars
|
|
*
|
|
* @return array Output
|
|
*/
|
|
public function vars()
|
|
{
|
|
$output = $this->v;
|
|
unset($output['pi']);
|
|
unset($output['e']);
|
|
return $output;
|
|
}
|
|
|
|
/**
|
|
* Function funcs
|
|
*
|
|
* @return array Output
|
|
*/
|
|
private function funcs() // @phpstan-ignore-line
|
|
{
|
|
$output = array();
|
|
foreach ($this->f as $fnn => $dat) {
|
|
$output[] = $fnn.'('.implode(',', $dat['args']).')';
|
|
}
|
|
return $output;
|
|
}
|
|
|
|
// ===================== HERE BE INTERNAL METHODS ====================\\
|
|
|
|
/**
|
|
* Convert infix to postfix notation
|
|
*
|
|
* @param string $expr Expression
|
|
* @return boolean|array Output
|
|
*/
|
|
private function nfx($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 parenthesis?
|
|
$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 $this->trigger(9, "an unexpected error occurred");
|
|
}
|
|
if ($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
|
|
$index++; // into implicit multiplication if no operator is there)
|
|
}
|
|
}
|
|
while (!is_null($ope = $stack->pop())) { // pop everything off the stack and push onto output
|
|
if ($ope == '(') {
|
|
return $this->trigger(11, "expecting ')'", ")"); // if there are (s on the stack, ()s were unbalanced
|
|
}
|
|
$output[] = $ope;
|
|
}
|
|
|
|
return $output;
|
|
}
|
|
|
|
/**
|
|
* Evaluate postfix notation
|
|
*
|
|
* @param array $tokens Expression
|
|
* @param array $vars Array
|
|
* @return string|false Output or false if error
|
|
*/
|
|
private function pfx($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') {
|
|
$fnn = 'log';
|
|
}
|
|
// @phan-suppress-next-line PhanPluginUnsafeEval
|
|
eval('$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();
|
|
}
|
|
|
|
/**
|
|
* trigger an error, but nicely, if need be
|
|
*
|
|
* @param string $code Code
|
|
* @param string $msg Msg
|
|
* @param string|null $info String
|
|
* @return false
|
|
*/
|
|
public function trigger($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 for internal use
|
|
*/
|
|
class EvalMathStack
|
|
{
|
|
/** @var mixed[] */
|
|
public $stack = array();
|
|
|
|
/** @var int */
|
|
public $count = 0;
|
|
|
|
/**
|
|
* push
|
|
*
|
|
* @param string $val Val
|
|
* @return void
|
|
*/
|
|
public function push($val)
|
|
{
|
|
$this->stack[$this->count] = $val;
|
|
$this->count++;
|
|
}
|
|
|
|
/**
|
|
* pop
|
|
*
|
|
* @return ?mixed Stack element
|
|
*/
|
|
public function pop()
|
|
{
|
|
if ($this->count > 0) {
|
|
$this->count--;
|
|
return $this->stack[$this->count];
|
|
}
|
|
return null;
|
|
}
|
|
|
|
/**
|
|
* last
|
|
*
|
|
* @param int $n N
|
|
* @return mixed Stack
|
|
*/
|
|
public function last($n = 1)
|
|
{
|
|
if (isset($this->stack[$this->count - $n])) {
|
|
return $this->stack[$this->count - $n];
|
|
}
|
|
|
|
return '';
|
|
}
|
|
}
|