387 lines
15 KiB
PHP
387 lines
15 KiB
PHP
<?php
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/*
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================================================================================
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EvalMath - PHP Class to safely evaluate math expressions
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Copyright (C) 2005 Miles Kaufmann <http://www.twmagic.com/>
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================================================================================
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NAME
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EvalMath - safely evaluate math expressions
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SYNOPSIS
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<?
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include('evalmath.class.php');
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$m = new EvalMath;
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// basic evaluation:
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$result = $m->evaluate('2+2');
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// supports: order of operation; parentheses; negation; built-in functions
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$result = $m->evaluate('-8(5/2)^2*(1-sqrt(4))-8');
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// create your own variables
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$m->evaluate('a = e^(ln(pi))');
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// or functions
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$m->evaluate('f(x,y) = x^2 + y^2 - 2x*y + 1');
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// and then use them
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$result = $m->evaluate('3*f(42,a)');
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?>
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DESCRIPTION
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Use the EvalMath class when you want to evaluate mathematical expressions
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from untrusted sources. You can define your own variables and functions,
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which are stored in the object. Try it, it's fun!
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METHODS
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$m->evalute($expr)
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Evaluates the expression and returns the result. If an error occurs,
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prints a warning and returns false. If $expr is a function assignment,
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returns true on success.
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$m->e($expr)
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A synonym for $m->evaluate().
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$m->vars()
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Returns an associative array of all user-defined variables and values.
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$m->funcs()
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Returns an array of all user-defined functions.
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PARAMETERS
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$m->suppress_errors
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Set to true to turn off warnings when evaluating expressions
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$m->last_error
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If the last evaluation failed, contains a string describing the error.
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(Useful when suppress_errors is on).
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AUTHOR INFORMATION
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Copyright 2005, Miles Kaufmann.
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LICENSE
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are
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met:
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1 Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The name of the author may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT,
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INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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*/
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class EvalMath {
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var $suppress_errors = false;
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var $last_error = null;
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var $v = array('e'=>2.71,'pi'=>3.14); // variables (and constants)
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var $f = array(); // user-defined functions
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var $vb = array('e', 'pi'); // constants
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var $fb = array( // built-in functions
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'sin','sinh','arcsin','asin','arcsinh','asinh',
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'cos','cosh','arccos','acos','arccosh','acosh',
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'tan','tanh','arctan','atan','arctanh','atanh',
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'sqrt','abs','ln','log');
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function EvalMath() {
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// make the variables a little more accurate
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$this->v['pi'] = pi();
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$this->v['e'] = exp(1);
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}
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function e($expr) {
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return $this->evaluate($expr);
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}
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function evaluate($expr) {
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$this->last_error = null;
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$expr = trim($expr);
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if (substr($expr, -1, 1) == ';') $expr = substr($expr, 0, strlen($expr)-1); // strip semicolons at the end
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//===============
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// is it a variable assignment?
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if (preg_match('/^\s*([a-z]\w*)\s*=\s*(.+)$/', $expr, $matches)) {
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if (in_array($matches[1], $this->vb)) { // make sure we're not assigning to a constant
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return $this->trigger("cannot assign to constant '$matches[1]'");
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}
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if (($tmp = $this->pfx($this->nfx($matches[2]))) === false) return false; // get the result and make sure it's good
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$this->v[$matches[1]] = $tmp; // if so, stick it in the variable array
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return $this->v[$matches[1]]; // and return the resulting value
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//===============
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// is it a function assignment?
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} elseif (preg_match('/^\s*([a-z]\w*)\s*\(\s*([a-z]\w*(?:\s*,\s*[a-z]\w*)*)\s*\)\s*=\s*(.+)$/', $expr, $matches)) {
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$fnn = $matches[1]; // get the function name
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if (in_array($matches[1], $this->fb)) { // make sure it isn't built in
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return $this->trigger("cannot redefine built-in function '$matches[1]()'");
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}
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$args = explode(",", preg_replace("/\s+/", "", $matches[2])); // get the arguments
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if (($stack = $this->nfx($matches[3])) === false) return false; // see if it can be converted to postfix
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for ($i = 0; $i<count($stack); $i++) { // freeze the state of the non-argument variables
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$token = $stack[$i];
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if (preg_match('/^[a-z]\w*$/', $token) and !in_array($token, $args)) {
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if (array_key_exists($token, $this->v)) {
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$stack[$i] = $this->v[$token];
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} else {
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return $this->trigger("undefined variable '$token' in function definition");
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}
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}
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}
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$this->f[$fnn] = array('args'=>$args, 'func'=>$stack);
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return true;
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//===============
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} else {
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return $this->pfx($this->nfx($expr)); // straight up evaluation, woo
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}
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}
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function vars() {
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$output = $this->v;
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unset($output['pi']);
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unset($output['e']);
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return $output;
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}
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function funcs() {
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$output = array();
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foreach ($this->f as $fnn=>$dat)
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$output[] = $fnn . '(' . implode(',', $dat['args']) . ')';
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return $output;
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}
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//===================== HERE BE INTERNAL METHODS ====================\\
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// Convert infix to postfix notation
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function nfx($expr) {
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$index = 0;
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$stack = new EvalMathStack;
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$output = array(); // postfix form of expression, to be passed to pfx()
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$expr = trim(strtolower($expr));
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$ops = array('+', '-', '*', '/', '^', '_');
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$ops_r = array('+'=>0,'-'=>0,'*'=>0,'/'=>0,'^'=>1); // right-associative operator?
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$ops_p = array('+'=>0,'-'=>0,'*'=>1,'/'=>1,'_'=>1,'^'=>2); // operator precedence
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$expecting_op = false; // we use this in syntax-checking the expression
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// and determining when a - is a negation
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if (preg_match("/[^\w\s+*^\/()\.,-]/", $expr, $matches)) { // make sure the characters are all good
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return $this->trigger("illegal character '{$matches[0]}'");
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}
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while(1) { // 1 Infinite Loop ;)
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$op = substr($expr, $index, 1); // get the first character at the current index
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// find out if we're currently at the beginning of a number/variable/function/parenthesis/operand
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$ex = preg_match('/^([a-z]\w*\(?|\d+(?:\.\d*)?|\.\d+|\()/', substr($expr, $index), $match);
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//===============
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if ($op == '-' and !$expecting_op) { // is it a negation instead of a minus?
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$stack->push('_'); // put a negation on the stack
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$index++;
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} elseif ($op == '_') { // we have to explicitly deny this, because it's legal on the stack
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return $this->trigger("illegal character '_'"); // but not in the input expression
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//===============
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} elseif ((in_array($op, $ops) or $ex) and $expecting_op) { // are we putting an operator on the stack?
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if ($ex) { // are we expecting an operator but have a number/variable/function/opening parethesis?
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$op = '*'; $index--; // it's an implicit multiplication
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}
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// heart of the algorithm:
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while($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])) {
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$output[] = $stack->pop(); // pop stuff off the stack into the output
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}
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// many thanks: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_algorithm_in_detail
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$stack->push($op); // finally put OUR operator onto the stack
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$index++;
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$expecting_op = false;
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//===============
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} elseif ($op == ')' and $expecting_op) { // ready to close a parenthesis?
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while (($o2 = $stack->pop()) != '(') { // pop off the stack back to the last (
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if (is_null($o2)) return $this->trigger("unexpected ')'");
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else $output[] = $o2;
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}
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if (preg_match("/^([a-z]\w*)\($/", $stack->last(2), $matches)) { // did we just close a function?
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$fnn = $matches[1]; // get the function name
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$arg_count = $stack->pop(); // see how many arguments there were (cleverly stored on the stack, thank you)
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$output[] = $stack->pop(); // pop the function and push onto the output
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if (in_array($fnn, $this->fb)) { // check the argument count
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if($arg_count > 1)
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return $this->trigger("too many arguments ($arg_count given, 1 expected)");
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} elseif (array_key_exists($fnn, $this->f)) {
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if ($arg_count != count($this->f[$fnn]['args']))
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return $this->trigger("wrong number of arguments ($arg_count given, " . count($this->f[$fnn]['args']) . " expected)");
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} else { // did we somehow push a non-function on the stack? this should never happen
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return $this->trigger("internal error");
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}
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}
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$index++;
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//===============
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} elseif ($op == ',' and $expecting_op) { // did we just finish a function argument?
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while (($o2 = $stack->pop()) != '(') {
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if (is_null($o2)) return $this->trigger("unexpected ','"); // oops, never had a (
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else $output[] = $o2; // pop the argument expression stuff and push onto the output
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}
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// make sure there was a function
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if (!preg_match("/^([a-z]\w*)\($/", $stack->last(2), $matches))
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return $this->trigger("unexpected ','");
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$stack->push($stack->pop()+1); // increment the argument count
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$stack->push('('); // put the ( back on, we'll need to pop back to it again
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$index++;
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$expecting_op = false;
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//===============
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} elseif ($op == '(' and !$expecting_op) {
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$stack->push('('); // that was easy
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$index++;
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$allow_neg = true;
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//===============
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} elseif ($ex and !$expecting_op) { // do we now have a function/variable/number?
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$expecting_op = true;
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$val = $match[1];
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if (preg_match("/^([a-z]\w*)\($/", $val, $matches)) { // may be func, or variable w/ implicit multiplication against parentheses...
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if (in_array($matches[1], $this->fb) or array_key_exists($matches[1], $this->f)) { // it's a func
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$stack->push($val);
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$stack->push(1);
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$stack->push('(');
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$expecting_op = false;
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} else { // it's a var w/ implicit multiplication
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$val = $matches[1];
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$output[] = $val;
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}
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} else { // it's a plain old var or num
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$output[] = $val;
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}
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$index += strlen($val);
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//===============
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} elseif ($op == ')') { // miscellaneous error checking
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return $this->trigger("unexpected ')'");
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} elseif (in_array($op, $ops) and !$expecting_op) {
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return $this->trigger("unexpected operator '$op'");
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} else { // I don't even want to know what you did to get here
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return $this->trigger("an unexpected error occured");
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}
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if ($index == strlen($expr)) {
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if (in_array($op, $ops)) { // did we end with an operator? bad.
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return $this->trigger("operator '$op' lacks operand");
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} else {
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break;
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}
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}
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while (substr($expr, $index, 1) == ' ') { // step the index past whitespace (pretty much turns whitespace
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$index++; // into implicit multiplication if no operator is there)
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}
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}
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while (!is_null($op = $stack->pop())) { // pop everything off the stack and push onto output
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if ($op == '(') return $this->trigger("expecting ')'"); // if there are (s on the stack, ()s were unbalanced
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$output[] = $op;
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}
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return $output;
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}
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// evaluate postfix notation
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function pfx($tokens, $vars = array()) {
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if ($tokens == false) return false;
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$stack = new EvalMathStack;
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foreach ($tokens as $token) { // nice and easy
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// if the token is a binary operator, pop two values off the stack, do the operation, and push the result back on
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if (in_array($token, array('+', '-', '*', '/', '^'))) {
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if (is_null($op2 = $stack->pop())) return $this->trigger("internal error");
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if (is_null($op1 = $stack->pop())) return $this->trigger("internal error");
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switch ($token) {
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case '+':
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$stack->push($op1+$op2); break;
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case '-':
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$stack->push($op1-$op2); break;
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case '*':
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$stack->push($op1*$op2); break;
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case '/':
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if ($op2 == 0) return $this->trigger("division by zero");
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$stack->push($op1/$op2); break;
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case '^':
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$stack->push(pow($op1, $op2)); break;
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}
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// if the token is a unary operator, pop one value off the stack, do the operation, and push it back on
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} elseif ($token == "_") {
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$stack->push(-1*$stack->pop());
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// if the token is a function, pop arguments off the stack, hand them to the function, and push the result back on
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} elseif (preg_match("/^([a-z]\w*)\($/", $token, $matches)) { // it's a function!
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$fnn = $matches[1];
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if (in_array($fnn, $this->fb)) { // built-in function:
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if (is_null($op1 = $stack->pop())) return $this->trigger("internal error");
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$fnn = preg_replace("/^arc/", "a", $fnn); // for the 'arc' trig synonyms
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if ($fnn == 'ln') $fnn = 'log';
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eval('$stack->push(' . $fnn . '($op1));'); // perfectly safe eval()
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} elseif (array_key_exists($fnn, $this->f)) { // user function
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// get args
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$args = array();
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for ($i = count($this->f[$fnn]['args'])-1; $i >= 0; $i--) {
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if (is_null($args[$this->f[$fnn]['args'][$i]] = $stack->pop())) return $this->trigger("internal error");
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}
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$stack->push($this->pfx($this->f[$fnn]['func'], $args)); // yay... recursion!!!!
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}
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// if the token is a number or variable, push it on the stack
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} else {
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if (is_numeric($token)) {
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$stack->push($token);
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} elseif (array_key_exists($token, $this->v)) {
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$stack->push($this->v[$token]);
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} elseif (array_key_exists($token, $vars)) {
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$stack->push($vars[$token]);
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} else {
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return $this->trigger("undefined variable '$token'");
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}
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}
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}
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// when we're out of tokens, the stack should have a single element, the final result
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if ($stack->count != 1) return $this->trigger("internal error");
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return $stack->pop();
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}
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// trigger an error, but nicely, if need be
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function trigger($msg) {
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$this->last_error = $msg;
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if (!$this->suppress_errors) trigger_error($msg, E_USER_WARNING);
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return false;
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}
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}
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// for internal use
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class EvalMathStack {
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var $stack = array();
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var $count = 0;
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function push($val) {
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$this->stack[$this->count] = $val;
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$this->count++;
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}
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function pop() {
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if ($this->count > 0) {
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$this->count--;
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return $this->stack[$this->count];
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}
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return null;
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}
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function last($n=1) {
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return $this->stack[$this->count-$n];
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}
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}
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