double precisoin type

Hello,

postgres [1264904]=# select 123456789.123456789123456::double precision;
┌────────────────────┐
│ float8 │
├────────────────────┤
│ 123456789.12345679 │
└────────────────────┘
(1 row)

I do not understand why this number is truncated at 123456789.12345679 that
is 17 digits and not 15 digits

Any idea

Fabrice

Documentation says:
double precision 8 bytes variable-precision, inexact 15 decimal digits
precision