Floating point rounding error php ...how can I make sure it works correctly?

Question

I have the following function that determines if I sale is fully paid for. I don't remember why I did it this way, but it has been working so far and I don't remember why I had to do it this way.

function _payments_cover_total()
{
    //get_payments is a list of payment amounts such as:
    //10.20, 10.21, or even 10.1010101101 (10 decimals max) 

    $total_payments = 0;

    foreach($this->sale_lib->get_payments() as $payment)
    {
        $total_payments += $payment['payment_amount'];
    }

    //to_currency_no_money rounds total to 2 decimal places
    if (to_currency_no_money($this->sale_lib->get_total()) - $total_payments ) > 1e-6 ) )
    {
        return false;
    }

    return true;
}

I am wondering if there is ever a case where due to a rounding error that this function would return false when it shouldn't.

The main part I have a question about is:

 > 1e-6

I think before I had, but it was causing problems in some cases.

> 0

Answer 1

I think you are doing what is mentioned on php floating help page. To quote it directly :

To test floating point values for equality, an upper bound on the relative error due to rounding is used. This value is known as the machine epsilon, or unit roundoff, and is the smallest acceptable difference in calculations.

$a and $b are equal to 5 digits of precision.

<?php
$a = 1.23456789;
$b = 1.23456780;
$epsilon = 0.00001;

if(abs($a-$b) < $epsilon) {
    echo "true";
}
?>

So in your case:

(to_currency_no_money($this->sale_lib->get_total()) - $total_payments) > 1e-6

relative error due to rounding should not be great than 1e-6 or 0.000001

if you are not sure about left operand being greater than right 100% time,then you should add abs() e.g for correctness.

$relative_error=to_currency_no_money($this->sale_lib->get_total()) - $total_payments;
 if(abs($relative_error) > 1e-6){
   return false
 }
 return true;