Control calculator expression logic

[keenlearner]

Hello I am building a PHP scientific calculator, users can perform calculation by just typing like normal mathematical expressions, e.g "(2+3-4^6)/33.3* 4!" so the result will be calculated accordingly, but I have a problem that, when malicious users try to put a mathematical expressions that is very long enough and takes a very heavy load of processing which might make my web server down. Such as

 

"9999999999999999999999999999999999999999999999999999999 * 999999999999999999999999999999"

 

So I thought of limiting the expressions that users can input up to 50 characters long, but this is still not a good idea, because heavy calculations does not necessarily depends on the length of the expressions, such as

 

//This does not make my computer load heavily

"1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1"

 

//But this one takes quite long and consume high processing power.

"999999999^99999"

 

So I want to know, is there a logic that can actually determines the result which might consume high processing which can solve my problem ? or is there a good scientific calculator library that you might want to share ? Thanks a lot.

[teng84]

i see the prob but you can have it work using a nested IF i dodnt see any dificulties with this it will only need to have lot of filtering

[Barand]

Seems like you need to limit the numbers between certain operators and not the whole expression

[keenlearner]

Thanks, for the reply

When I tried it on my localhost, "9999999^9999999999999999999" it really makes my processors lights on without blinking for quite a few seconds and finally makes my apache hang for 1.83 Ghz Duo core processors with 1.5 GB RAM.

I believe there must be logic, because you can try in Google, type "999^99", it gives you result of calculation, but if you tried "999^103" . Google won't give you the result, because it seems that they will not calculate expression that will give result that exceed around 9.02983468 × 10^305

teng84, I have tried a few nested if, but seems that I still can't get the logic close to perfect yet, can you give me a brief algorithm for that ? Thanks

[cooldude832]

what you could do is apply some javascript to it

first don't let the user edit the calculation area (make a javascript onfocus event to blur it)

secondly if someone tries to calculate a ridiculous number like 99^99^99 in the coding do a test if the answer is greater than what max size is for a float. if that is the case tell it to break right away and give an overflow error.  Also make t so they dont' have direct input make buttons like a calculator (you can use hotkeys too to get that feel too).  Also maybe you could use ajaxs to test the output as they are inputting to test for overflows before it goes to that point (i.e 99^99 and they try to enter another ^99 say overflow.)

 

Just a few ideas

[keenlearner]

How if expression that has only one operator 99^999 and also its result is too big to be handled. It's important that we need to decide whether the expressions is too be to be handled BEFORE the calculation is made, because if we can only decide whether to calculate the expression or not AFTER the calculation is made our Apache server already hang. I think it goes the same for browser as well, instead of making our Apache hang, it will make the users browser hang.

 

I have tried something out below but still not solving.

Let's say 999^999 will make my apache server hang, let the base and the power be x and y respectively, x ^ y

So if I limit the x and y to be 900 respectively, 900^900. so the the following should be OK

800^400

700^900

2^900

 

since x or y are equal or less than 900

But problem is this line below should be allowed too, because the result still less than 900^900 and does not make heavy load.

2^1000

But since we limit the y to be 900, this will not be calculated, which is a bad idea too. I so eager to solve this, but so far have not get a good solutions, but I believe there is a logic like Google's. Thanks.

[cooldude832]

set a pair of thresholds amounts for y/x (and secondary thresholds)

i.e

<?php
$ymax = 999;
$xmax = 99999;
$ymax_2 = 9999;
$xmax2 = 9999;
if($_POST['x'] > $xmax){if($_POST['y'] >$ymax_2){//overflow}}
?>

get the idea?

[cooldude832]

set a pair of thresholds amounts for y/x (and secondary thresholds)

i.e

<?php
$ymax = 999;
$xmax = 99999;
$ymax_2 = 9999;
$xmax2 = 9999;
if($_POST['x'] > $xmax){if($_POST['y'] >$ymax_2){//overflow}}
?>

 

[Barand]

if 2^1000 is OK but 999^1000 is not OK then for each x you need an upper y threshold

[keenlearner]

Thanks cooldude832, that is what I did initially but still not solving the problem if

$xmax = 900;
$ymax = 900;

if($_GET['x'] > $xmax && $_GET['y'] > $ ymax) //overflow 

//But we should allowed if 
$_GET['x'] = 2
$_GET['y'] = 1000;
//because this calculation still ok.

 

I think the solutions might be something closed to Barand's, but so still we need to type a lot of threshold number (thousands)

if 2^1000 is OK but 999^1000 is not OK then for each x you need an upper y threshold

 

But I bet there is a formula to determine the heavy calculations, of it.

[Barand]

<?php
function safePow($x, $y)
{
    $r = pow($x,$y);
    return $r < 1.79e308 ? $r : 'overflow!';
}

$expr = '2^99';
list ($x, $y) = explode('^', $expr);

echo safePow ($x, $y);

?>

[keenlearner]

Thanks Barand, I am still looking up for solutions until now.

 

It's important that we need to decide whether the expressions is too big to be handled BEFORE the calculation is made, because if we can only decide whether to calculate the expression AFTER the calculation is made, our Apache server will/already hang.

<?php
function safePow($x, $y)
{
    $r = pow($x,$y);
    return $r < 1.79e308 ? $r : 'overflow!';
}

//if we check whether this is safePow
echo safePow(999, 9999999999999); 
//my apache server could already hang before it return the result.
?>

 

I still believe there is a formula.

[Barand]

Suggest change of server

 

<?php
function safePow($x, $y)
{
    $r = pow($x,$y);
    return $r < 1.79e308 ? $r : 'overflow!';
}

$inputs = array (
           '999^9999999999999',
           '2^9999',
           '99^99',
           '9^9'
        );

echo '<pre>';

printf ("\n%-20s : %25s : %8s\n", 'expression', 'result', 'seconds'); 
printf ("\n%-20s : %25s : %8s\n", '--------------------', '-------------------------', '--------'); 

foreach ($inputs as $expr)
{
    list ($x, $y) = explode('^', $expr);

    $t1 = microtime(1);
    $p = safePow ($x, $y);
    $t2 = microtime(1);
    printf ("\n%-20s : %25s : %0.6f\n", $expr, $p, $t2-$t1); 
}

echo '</pre>';
?>

 

Results -->[pre]

expression          :                    result :  seconds

 

-------------------- : ------------------------- : --------

 

999^9999999999999    :                overflow! : 0.000097

 

2^9999              :                overflow! : 0.000025

 

99^99                :        3.6972963765E+197 : 0.000020

 

9^9                  :                387420489 : 0.000019

 

 

[/pre]

[keenlearner]

You cannot use pow function to calculated pow(999,9999999999999); because it does not actually calculate but instead gives you the word "INF", because pow() cannot handle big number.

 

try

<?php
echo pow(999,9999999999999); //gives INF
?>

 

should use bcpow instead, try at your own risk. you will either have execution timeout or slow down your computer

<?php
echo bcpow(999,9999999);
?>

 

That mean, php code itself has the logic that actually determines the number that is too big to be processed, as I just discovered about

pow() will give INF, if the number is too big.

[Barand]

I was aware of the INF, which is why I was testing against 1.79e308 which is about as big as a float type will store.

 

I changed to bcpow().

 

The one that didn't work (999^9999999999999) took only 0.000089 secs to give a result of 1

 

<?php
function safePow($x, $y)
{
    $r = bcpow($x,$y);
    return $r  ? $r : 'overflow!';
}

$inputs = array (
           '999^9999999999999',
           '9^9999',
           '99^99',
           '9^9'
        );

echo '<table border="1">';

echo  '<tr><td>expression</td><td>result</td><td>seconds</td></tr>'; 

foreach ($inputs as $expr)
{
    list ($x, $y) = explode('^', $expr);

    $t1 = microtime(1);
    $p = safePow ($x, $y);
    $t2 = microtime(1);
    $t = sprintf ("%0.6f", $t2-$t1);
    $p = wordwrap ($p, 50, '<br/>', true); 
    echo  "<tr valign='top'><td>$expr</td><td>$p</td><td>$t</td></tr>"; 

}

echo '</table>';

 

results -->

expression        |  result                                               | seconds
------------------+-------------------------------------------------------+---------
999^9999999999999 |  1                                                    | 0.000089
------------------+-------------------------------------------------------+---------
9^9999            | 29570038080193553244202241247182381904736703321559    | 0.080060
                  | 61671705236976632770045817648617101476387353131190    |
                    07794052755117226772246089286497411108107780037148
                    36325316042186166990796173111553392470503228770292
                    61635989747700682249026677170831101015638735481375
                    95348355198673095302780092160210144684226186834160
                    85201240881900696792962780195582937398604502704630
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------------------+-------------------------------------------------------+---------
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