Here is function that works correctly:

function bcmod( $op, $mod, $scale )
{
   while( ($t = bcsub( $op, $mod, $scale )) > 0 ) $op = $t;
   return $op;
}

Correction, need ">= 0":

function bcmod( $op, $mod, $scale )
{
   while( ($t = bcsub( $op, $mod, $scale )) >= 0 ) $op = $t;
   return $op;
}

Sorry, but your problem does not imply a bug in PHP itself.  For a
list of more appropriate places to ask for help using PHP, please
visit http://www.php.net/support.php as this bug system is not the
appropriate forum for asking support questions.  Due to the volume
of reports we can not explain in detail here why your report is not
a bug.  The support channels will be able to provide an explanation
for you.

Thank you for your interest in PHP.

Not a PHP bug.

Is it your position that the bug is in a 3rd party library that PHP uses for the 
BC math API?

If yes, is it your position that marking a bug as bogus, is okay even while the 
API performs erroneous to the documentation?

Thanks for providing yet another evidence that bug reporting is a waste of time.