Management of memory heap space for data files accessible to programs operating in different addressing modes

A method and apparatus for managing heap memory for an application program in a data processing system. The system supports a basic addressing mode and an extended addressing mode. Programs operating in the basic addressing mode are limited to addressing using a first number of bits, program operating in the extended addressing mode are limited to addressing using a second number of bits, and the first number of bits is less than the second number of bits. One or more heap banks are established for an application program, with each heap bank having a quantity of memory space that is addressable by the program operating in basic addressing mode. The heap banks are managed by a system program operating in extended addressing mode. In response to each request from the application program that requires a quantity of memory space, one of the heap banks is selected for allocating the memory. An additional heap bank is established if none of the heap banks has a quantity of available memory space that satisfies the required quantity.