The INT32 API contains the type int32, a vector type
simple-int32-vector and accessor, functions to convert int32 to and from integer, some constant int32 values, and a full range of operators for mod 2^32 arithmetic.
You can find all these by evaluating
(apropos "INT32" "SYSTEM" t)
For details for each, see the entries starting with int32 in The SYSTEM Package.