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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).
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.
*/
/**
* This class was heavily modified in order to get usefull spreadsheet emulation ;-)
* skodak
* This class was modified to allow comparison operators (<, <=, ==, >=, >)
* and synonyms functions (for the 'if' function). See MDL-14274 for more details.
*/
class EvalMath {
/** @var string Pattern used for a valid function or variable name. Note, var and func names are case insensitive.*/
private static $namepat = '[a-z][a-z0-9_]*';
var $suppress_errors = false;
var $last_error = null;
var $v = array(); // variables (and constants)
var $f = array(); // user-defined functions
var $vb = array(); // 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','exp','floor','ceil');
var $fc = array( // calc functions emulation
'average'=>array(-1), 'max'=>array(-1), 'min'=>array(-1),
'mod'=>array(2), 'pi'=>array(0), 'power'=>array(2),
'round'=>array(1, 2), 'sum'=>array(-1), 'rand_int'=>array(2),
'rand_float'=>array(0), 'ifthenelse'=>array(3), 'cond_and'=>array(-1), 'cond_or'=>array(-1));
var $fcsynonyms = array('if' => 'ifthenelse', 'and' => 'cond_and', 'or' => 'cond_or');
var $allowimplicitmultiplication;
public function __construct($allowconstants = false, $allowimplicitmultiplication = false) {
if ($allowconstants){
$this->v['pi'] = pi();
$this->v['e'] = exp(1);
}
$this->allowimplicitmultiplication = $allowimplicitmultiplication;
}
/**
* Old syntax of class constructor. Deprecated in PHP7.
*
* @deprecated since Moodle 3.1
*/
public function EvalMath($allowconstants = false, $allowimplicitmultiplication = false) {
debugging('Use of class name as constructor is deprecated', DEBUG_DEVELOPER);
self::__construct($allowconstants, $allowimplicitmultiplication);
}
function e($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($expr)-1); // strip semicolons at the end
//===============
// is it a variable assignment?
if (preg_match('/^\s*('.self::$namepat.')\s*=\s*(.+)$/', $expr, $matches)) {
if (in_array($matches[1], $this->vb)) { // make sure we're not assigning to a constant
return $this->trigger(get_string('cannotassigntoconstant', 'mathslib', $matches[1]));
}
if (($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*('.self::$namepat.')\s*\(\s*('.self::$namepat.'(?:\s*,\s*'.self::$namepat.')*)\s*\)\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(get_string('cannotredefinebuiltinfunction', 'mathslib', $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('/^'.self::$namepat.'$/', $token) and !in_array($token, $args)) {
if (array_key_exists($token, $this->v)) {
$stack[$i] = $this->v[$token];
} else {
return $this->trigger(get_string('undefinedvariableinfunctiondefinition', 'mathslib', $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 $this->v;
}
function funcs() {
$output = array();
foreach ($this->f as $fnn=>$dat)
$output[] = $fnn . '(' . implode(',', $dat['args']) . ')';
return $output;
}
/**
* @param string $name
* @return boolean Is this a valid var or function name?
*/
public static function is_valid_var_or_func_name($name){
return preg_match('/'.self::$namepat.'$/iA', $name);
}
//===================== HERE BE INTERNAL METHODS ====================\\
// Convert infix to postfix notation
function nfx($expr) {
$index = 0;
$stack = new EvalMathStack;
$output = array(); // postfix form of expression, to be passed to pfx()
$expr = trim(strtolower($expr));
// MDL-14274: new operators for comparison added.
$ops = array('+', '-', '*', '/', '^', '_', '>', '<', '<=', '>=', '==');
$ops_r = array('+'=>0,'-'=>0,'*'=>0,'/'=>0,'^'=>1); // right-associative operator?
$ops_p = array('+'=>0,'-'=>0,'*'=>1,'/'=>1,'_'=>1,'^'=>2, '>'=>3, '<'=>3, '<='=>3, '>='=>3, '=='=>3); // 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(get_string('illegalcharactergeneral', 'mathslib', $matches[0]));
}
while(1) { // 1 Infinite Loop ;)
// MDL-14274 Test two character operators.
$op = substr($expr, $index, 2);
if (!in_array($op, $ops)) {
// MDL-14274 Get one character operator.
$op = substr($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
$ex = preg_match('/^('.self::$namepat.'\(?|\d+(?:\.\d*)?(?:(e[+-]?)\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 $this->trigger(get_string('illegalcharacterunderscore', 'mathslib')); // but not in the input expression
//===============
} elseif ((in_array($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?
if (!$this->allowimplicitmultiplication){
return $this->trigger(get_string('implicitmultiplicationnotallowed', 'mathslib'));
} else {// it's an implicit multiplication
$op = '*';
$index--;
}
}
// heart of the algorithm:
while($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
$index += strlen($op);
$expecting_op = false;
//===============
} elseif ($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(get_string('unexpectedclosingbracket', 'mathslib'));
else $output[] = $o2;
}
if (preg_match('/^('.self::$namepat.')\($/', $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)
$fn = $stack->pop();
$output[] = array('fn'=>$fn, 'fnn'=>$fnn, 'argcount'=>$arg_count); // send function to output
if (in_array($fnn, $this->fb)) { // check the argument count
if($arg_count > 1) {
$a= new stdClass();
$a->expected = 1;
$a->given = $arg_count;
return $this->trigger(get_string('wrongnumberofarguments', 'mathslib', $a));
}
} elseif ($this->get_native_function_name($fnn)) {
$fnn = $this->get_native_function_name($fnn); // Resolve synonyms.
$counts = $this->fc[$fnn];
if (in_array(-1, $counts) and $arg_count > 0) {}
elseif (!in_array($arg_count, $counts)) {
$a= new stdClass();
$a->expected = implode('/',$this->fc[$fnn]);
$a->given = $arg_count;
return $this->trigger(get_string('wrongnumberofarguments', 'mathslib', $a));
}
} elseif (array_key_exists($fnn, $this->f)) {
if ($arg_count != count($this->f[$fnn]['args'])) {
$a= new stdClass();
$a->expected = count($this->f[$fnn]['args']);
$a->given = $arg_count;
return $this->trigger(get_string('wrongnumberofarguments', 'mathslib', $a));
}
} else { // did we somehow push a non-function on the stack? this should never happen
return $this->trigger(get_string('internalerror', 'mathslib'));
}
}
$index++;
//===============
} elseif ($op == ',' and $expecting_op) { // did we just finish a function argument?
while (($o2 = $stack->pop()) != '(') {
if (is_null($o2)) return $this->trigger(get_string('unexpectedcomma', 'mathslib')); // oops, never had a (
else $output[] = $o2; // pop the argument expression stuff and push onto the output
}
// make sure there was a function
if (!preg_match('/^('.self::$namepat.')\($/', $stack->last(2), $matches))
return $this->trigger(get_string('unexpectedcomma', 'mathslib'));
$stack->push($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 = $match[1];
if (preg_match('/^('.self::$namepat.')\($/', $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) or
$this->get_native_function_name($matches[1])){ // 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 ($op == ')') {
//it could be only custom function with no params or general error
if ($stack->last() != '(' or $stack->last(2) != 1) return $this->trigger(get_string('unexpectedclosingbracket', 'mathslib'));
if (preg_match('/^('.self::$namepat.')\($/', $stack->last(3), $matches)) { // did we just close a function?
$stack->pop();// (
$stack->pop();// 1
$fn = $stack->pop();
$fnn = $matches[1]; // get the function name
$fnn = $this->get_native_function_name($fnn); // Resolve synonyms.
$counts = $this->fc[$fnn];
if (!in_array(0, $counts)){
$a= new stdClass();
$a->expected = $this->fc[$fnn];
$a->given = 0;
return $this->trigger(get_string('wrongnumberofarguments', 'mathslib', $a));
}
$output[] = array('fn'=>$fn, 'fnn'=>$fnn, 'argcount'=>0); // send function to output
$index++;
$expecting_op = true;
} else {
return $this->trigger(get_string('unexpectedclosingbracket', 'mathslib'));
}
//===============
} elseif (in_array($op, $ops) and !$expecting_op) { // miscellaneous error checking
return $this->trigger(get_string('unexpectedoperator', 'mathslib', $op));
} else { // I don't even want to know what you did to get here
return $this->trigger(get_string('anunexpectederroroccured', 'mathslib'));
}
if ($index == strlen($expr)) {
if (in_array($op, $ops)) { // did we end with an operator? bad.
return $this->trigger(get_string('operatorlacksoperand', 'mathslib', $op));
} else {
break;
}
}
while (substr($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(get_string('expectingaclosingbracket', 'mathslib')); // if there are (s on the stack, ()s were unbalanced
$output[] = $op;
}
return $output;
}
/**
*
* @param string $fnn
* @return string|boolean false if function name unknown.
*/
function get_native_function_name($fnn) {
if (array_key_exists($fnn, $this->fcsynonyms)) {
return $this->fcsynonyms[$fnn];
} else if (array_key_exists($fnn, $this->fc)) {
return $fnn;
} else {
return false;
}
}
// evaluate postfix notation
function pfx($tokens, $vars = array()) {
if ($tokens == false) return false;
$stack = new EvalMathStack;
foreach ($tokens as $token) { // nice and easy
// if the token is a function, pop arguments off the stack, hand them to the function, and push the result back on
if (is_array($token)) { // it's a function!
$fnn = $token['fnn'];
$count = $token['argcount'];
if (in_array($fnn, $this->fb)) { // built-in function:
if (is_null($op1 = $stack->pop())) return $this->trigger(get_string('internalerror', 'mathslib'));
$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 ($this->get_native_function_name($fnn)) { // calc emulation function
$fnn = $this->get_native_function_name($fnn); // Resolve synonyms.
// get args
$args = array();
for ($i = $count-1; $i >= 0; $i--) {
if (is_null($args[] = $stack->pop())) return $this->trigger(get_string('internalerror', 'mathslib'));
}
$res = call_user_func_array(array('EvalMathFuncs', $fnn), array_reverse($args));
if ($res === FALSE) {
return $this->trigger(get_string('internalerror', 'mathslib'));
}
$stack->push($res);
} 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(get_string('internalerror', 'mathslib'));
}
$stack->push($this->pfx($this->f[$fnn]['func'], $args)); // yay... recursion!!!!
}
// if the token is a binary operator, pop two values off the stack, do the operation, and push the result back on
} elseif (in_array($token, array('+', '-', '*', '/', '^', '>', '<', '==', '<=', '>='), true)) {
if (is_null($op2 = $stack->pop())) return $this->trigger(get_string('internalerror', 'mathslib'));
if (is_null($op1 = $stack->pop())) return $this->trigger(get_string('internalerror', 'mathslib'));
switch ($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(get_string('divisionbyzero', 'mathslib'));
$stack->push($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 >= $op2)); break;
}
// if the token is a unary operator, pop one value off the stack, do the operation, and push it back on
} elseif ($token == "_") {
$stack->push(-1*$stack->pop());
// if the token is a 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(get_string('undefinedvariable', 'mathslib', $token));
}
}
}
// when we're out of tokens, the stack should have a single element, the final result
if ($stack->count != 1) return $this->trigger(get_string('internalerror', 'mathslib'));
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($n=1) {
if ($this->count - $n >= 0) {
return $this->stack[$this->count-$n];
}
return null;
}
}
// spreadsheet functions emulation
class EvalMathFuncs {
/**
* MDL-14274 new conditional function.
* @param boolean $condition boolean for conditional.
* @param variant $then value if condition is true.
* @param unknown $else value if condition is false.
* @author Juan Pablo de Castro <juan.pablo.de.castro@gmail.com>
* @return unknown
*/
static function ifthenelse($condition, $then, $else) {
if ($condition == true) {
return $then;
} else {
return $else;
}
}
static function cond_and() {
$args = func_get_args();
foreach($args as $a) {
if ($a == false) {
return 0;
}
}
return 1;
}
static function cond_or() {
$args = func_get_args();
foreach($args as $a) {
if($a == true) {
return 1;
}
}
return 0;
}
static function average() {
$args = func_get_args();
return (call_user_func_array(array('self', 'sum'), $args) / count($args));
}
static function max() {
$args = func_get_args();
$res = array_pop($args);
foreach($args as $a) {
if ($res < $a) {
$res = $a;
}
}
return $res;
}
static function min() {
$args = func_get_args();
$res = array_pop($args);
foreach($args as $a) {
if ($res > $a) {
$res = $a;
}
}
return $res;
}
static function mod($op1, $op2) {
return $op1 % $op2;
}
static function pi() {
return pi();
}
static function power($op1, $op2) {
return pow($op1, $op2);
}
static function round($val, $precision = 0) {
return round($val, $precision);
}
static function sum() {
$args = func_get_args();
$res = 0;
foreach($args as $a) {
$res += $a;
}
return $res;
}
protected static $randomseed = null;
static function set_random_seed($randomseed) {
self::$randomseed = $randomseed;
}
static function get_random_seed() {
if (is_null(self::$randomseed)){
return microtime();
} else {
return self::$randomseed;
}
}
static function rand_int($min, $max){
if ($min >= $max) {
return false; //error
}
$noofchars = ceil(log($max + 1 - $min, '16'));
$md5string = md5(self::get_random_seed());
$stringoffset = 0;
do {
while (($stringoffset + $noofchars) > strlen($md5string)){
$md5string .= md5($md5string);
}
$randomno = hexdec(substr($md5string, $stringoffset, $noofchars));
$stringoffset += $noofchars;
} while (($min + $randomno) > $max);
return $min + $randomno;
}
static function rand_float() {
$randomvalues = unpack('v', md5(self::get_random_seed(), true));
return array_shift($randomvalues) / 65536;
}
}