bigint integers up to 19 digits.

Greetings,

I have a column that is a bigint that needs to store integers up to 19
digits long. For the most part this works but we sometimes have
numbers that are greater than 9223372036854775807.

I was thinking of changing this to a real or double precision field,
but read in the docs that the value stored is not always the value
inserted. From the docs " Inexact means that some values cannot be
converted exactly to the internal format and are stored as
approximations, so that storing and printing back out a value may show
slight discrepancies".

Is it known what level of precision is provided by the double data
type. My number will always be 19 digits long and always an integer.

I looked into the numeric data type, but the docs say that it can be slow.

Any feedback would be appreciated.
Thanks
Tory