How could two equal numbers not be equal in PHP

I have two numbers which are supposed to be equal to return a difference, I doesn't make sense...

The only way to be able to reproduce this problem here I had to base64_encode my arrays,

here is the script:

basically the script will fix numbers like "1 234,5" to "1234.5" and does calculations, but at the ends it returns

            First Number: 4784.47
            Second Number: 4784.47
            Difference: 9.0949470177293E-13

I just don't understand????????

            $aa = '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开发者_如何学GoOiJBbW91bnQiO3M6MjoiMTUiO3M6MTI6IkR1cmF0aW9uVGltZSI7czoxOiItIjtzOjEyOiJOZXRVbml0UHJpY2UiO3M6NToiMTUsMjAiO3M6OToiTmV0QW1vdW50IjtzOjY6IjE1MiwwMCI7czoxMDoiVkFUUGVyY2VudCI7czozOiIyNSUiO3M6MzoiVkFUIjtzOjU6IjM4LDAwIjtzOjExOiJHcm9zc0Ftb3VudCI7czo2OiIxOTAsMDAiO3M6ODoiSXRlbUNvZGUiO3M6NjoiU01TX09OIjt9fQ==';

            $tt = 'YTozOntzOjE2OiJTdW1tYXJ5SXRlbU5ldHRvIjtzOjg6IjMgODI3LDU4IjtzOjE0OiJTdW1tYXJ5SXRlbVZBVCI7czo2OiI5NTYsODkiO3M6MTc6IlN1bW1hcnlJdGVtQnJ1dHRvIjtzOjg6IjQgNzg0LDQ3Ijt9';

            $a = unserialize(base64_decode($aa));
            $t = unserialize(base64_decode($tt));


            function calculate_call_fees($a,$t){

                $or_item = 0;

                foreach($a as $k => $r) {
                    $or_item += fix_num($r['GrossAmount']); 
                }        

                $br =  fix_num($t['SummaryItemBrutto']);   

                if($br>$or_item){
                    $diff = $br-$or_item;
                } else {
                    $diff = 0;
                }

                echo 'First Number: ' . $br.'<br/>';
                echo 'Second Number: ' . $or_item.'<br />';
                echo 'Difference: ' . $diff.'<br />';

                echo '<hr />';
                echo '<pre>';
                print_r($a);
                echo '</pre>';
                echo '<hr />';
                echo '<pre>';
                print_r($t);
                echo '</pre>';    

            }

            function fix_num($n){
                return floatval(str_replace(Array(" ",","),array("","."),$n));
            }

            calculate_call_fees($a,$t);

Using "equals" comparison with floating point numbers is dangerous because of floating point limited precision - you're liable to get small differences due to the rounding involved.

Instead, if you want to see if two floating point numbers are "the same", just see if their difference is below a certain threshold:

if( abs($a - $b) < 0.00000001) {
    // a and b are "equal"
}

It is not just PHP. There is a general problem of representing fractional numbers in the computer. It's subject for various types of overflows, underflows, precision issues and so on. PHP's manual shed some light on the topic.

The general rule - if you demand for two 'seem-equal' numbers to be guaranteed equal - don't use floating point data types (float, double), but fixed point (decimal, numeric)

It appears as this is "Machine epsilon" issue: http://en.wikipedia.org/wiki/Machine_epsilon

Try to compare the difference between them with 0.000001 instead of comparing them directly.