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Issue backdrop#40: Moving EvalMath class from CTools to includes for …
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,386 @@ | ||
| <?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. | ||
| */ | ||
|
|
||
| class EvalMath { | ||
| var $suppress_errors = false; | ||
| var $last_error = 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', | ||
| 'pow', 'exp', | ||
| 'sqrt','abs','ln','log', | ||
| 'time', 'ceil', 'floor', 'min', 'max', 'round'); | ||
|
|
||
| function __construct() { | ||
| // 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; | ||
| $expr = trim($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 $this->trigger("cannot assign to constant '$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 $this->trigger("cannot redefine built-in function '$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 $this->trigger("undefined variable '$token' in function definition"); | ||
| } | ||
| } | ||
| } | ||
| $this->f[$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 $this->trigger("illegal character '{$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 $this->trigger("illegal character '_'"); // but not in the input expression | ||
| //=============== | ||
| } elseif ((in_array($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("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 $this->trigger("too many arguments ($arg_count given, 1 expected)"); | ||
| } elseif (array_key_exists($fnn, $this->f)) { | ||
| if ($arg_count != count($this->f[$fnn]['args'])) | ||
| return $this->trigger("wrong number of arguments ($arg_count given, " . count($this->f[$fnn]['args']) . " expected)"); | ||
| } else { // did we somehow push a non-function on the stack? this should never happen | ||
| return $this->trigger("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("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("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 $this->trigger("unexpected ')'"); | ||
| } elseif (in_array($op, $ops) and !$expecting_op) { | ||
| return $this->trigger("unexpected operator '$op'"); | ||
| } else { // I don't even want to know what you did to get here | ||
| return $this->trigger("an unexpected error occured"); | ||
| } | ||
| if ($index == strlen($expr)) { | ||
| if (in_array($op, $ops)) { // did we end with an operator? bad. | ||
| return $this->trigger("operator '$op' lacks operand"); | ||
| } 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("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; | ||
|
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| $stack = new EvalMathStack; | ||
|
|
||
| foreach ($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 $this->trigger("internal error"); | ||
| if (is_null($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, $op2)); break; | ||
| } | ||
| // if the token is a unary operator, pop one value off the stack, do the operation, and push it back on | ||
| } elseif ($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("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("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 $this->trigger("undefined variable '$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 $stack->pop(); | ||
| } | ||
|
|
||
| // trigger an error, but nicely, if need be | ||
| function trigger($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($n=1) { | ||
| return !empty($this->stack[$this->count-$n]) ? $this->stack[$this->count-$n] : NULL; | ||
| } | ||
| } |
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