Library for evaluating math expresions

htdocs/includes/evalmath/README.md

+evalmath.class.php
+==================
+
+Version 1.0
+
+Taken from http://www.phpclasses.org/browse/file/11680.html, cred to Miles Kaufmann
+
+This repository is cloned for two reasons:
+
+1. To allow downloading the code without signing in to phpclasses.org.
+2. To add very small improvements to the code.

htdocs/includes/evalmath/evalmath.class.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
+    $m->evalute($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).
+
+    $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.
+*/
+
+class EvalMath {
+
+    var $suppress_errors = false;
+    var $last_error = null;
+    var $last_error_code = null;
+    
+    var $v = array('e'=>2.71,'pi'=>3.14); // variables (and constants)
+    var $f = array(); // user-defined functions
+    var $vb = array('e', 'pi'); // constants
+    var $fb = array(  // built-in functions
+        'sin','sinh','arcsin','asin','arcsinh','asinh',
+        'cos','cosh','arccos','acos','arccosh','acosh',
+        'tan','tanh','arctan','atan','arctanh','atanh',
+        'sqrt','abs','ln','log');
+    
+    function EvalMath() {
+        // make the variables a little more accurate
+        $this->v['pi'] = pi();
+        $this->v['e'] = exp(1);
+    }
+    
+    function e($expr) {
+        return $this->evaluate($expr);
+    }
+    
+    function evaluate($expr) {
+        $this->last_error = null;
+        $this->last_error_code = null;
+        $expr = trim($expr);
+        if (substr($expr, -1, 1) == ';') $expr = substr($expr, 0, strlen($expr)-1); // strip semicolons at the end
+        //===============
+        // is it a variable assignment?
+        if (preg_match('/^\s*([a-z]\w*)\s*=\s*(.+)$/', $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
+            for ($i = 0; $i<count($stack); $i++) { // freeze the state of the non-argument variables
+                $token = $stack[$i];
+                if (preg_match('/^[a-z]\w*$/', $token) and !in_array($token, $args)) {
+                    if (array_key_exists($token, $this->v)) {
+                        $stack[$i] = $this->v[$token];
+                    } else {
+                        return $this->trigger(3, "undefined variable '$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() {
+        $output = $this->v;
+        unset($output['pi']);
+        unset($output['e']);
+        return $output;
+    }
+    
+    function funcs() {
+        $output = array();
+        foreach ($this->f as $fnn=>$dat)
+            $output[] = $fnn . '(' . implode(',', $dat['args']) . ')';
+        return $output;
+    }
+
+    //===================== HERE BE INTERNAL METHODS ====================\\
+
+    // Convert infix to postfix notation
+    function nfx($expr) {
+    
+        $index = 0;
+        $stack = new 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
+    
+        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
+            $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 parethesis?
+                    $op = '*'; $index--; // it's an implicit multiplication
+                }
+                // heart of the algorithm:
+                while($stack->count > 0 and ($o2 = $stack->last()) and in_array($o2, $ops) and ($ops_r[$op] ? $ops_p[$op] < $ops_p[$o2] : $ops_p[$op] <= $ops_p[$o2])) {
+                    $output[] = $stack->pop(); // pop stuff off the stack into the output
+                }
+                // many thanks: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_algorithm_in_detail
+                $stack->push($op); // finally put OUR operator onto the stack
+                $index++;
+                $expecting_op = false;
+            //===============
+            } elseif ($op == ')' and $expecting_op) { // ready to close a parenthesis?
+                while (($o2 = $stack->pop()) != '(') { // pop off the stack back to the last (
+                    if (is_null($o2)) return $this->trigger(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 $this->trigger(9, "an unexpected error occured");
+            }
+            if ($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 
+                $index++;                             // into implicit multiplication if no operator is there)
+            }
+        
+        } 
+        while (!is_null($op = $stack->pop())) { // pop everything off the stack and push onto output
+            if ($op == '(') return $this->trigger(11, "expecting ')'", ")"); // if there are (s on the stack, ()s were unbalanced
+            $output[] = $op;
+        }
+        return $output;
+    }
+
+    // evaluate postfix notation
+    function pfx($tokens, $vars = array()) {
+        
+        if ($tokens == false) return false;
+    
+        $stack = new EvalMathStack;
+        
+        foreach ($tokens as $token) { // nice and easy
+            // if the token is a binary operator, pop two values off the stack, do the operation, and push the result back on
+            if (in_array($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') $fnn = 'log';
+                    eval('$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 $stack->pop();
+    }
+    
+    // trigger an error, but nicely, if need be
+    function trigger($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;
+    }
+}
+
+// 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($n=1) {
+        if (isset($this->stack[$this->count-$n])) {
+          return $this->stack[$this->count-$n];
+        }
+        return;
+    }
+}