How many aligned address space can I allocate via mmap?

Suppose I want to allocate a naturally aligned piece of memory through mmap(), say I want to allocate a 16KB block of memory aligned to 16KB, what is the greatest amount of memory inside the address space I could allocate in that way? What if I want to allocate 4MB aligned to 4MB? Or 16MB aligned to 16MB? The table is the result in number of that sized chunks and the total amount in GB.

OS	4KB	16KB	4MB	16MB	64MB
Mac OS X 10.5.8	900227 (3.43GB)	225056 (3.43GB)	877 (3.43GB)	217 (3.39GB)	52 (3.25GB)
Linux 2.6.18 (32-bit)	1048173 (4.00GB)	262040 (4.00GB)	1020 (3.98GB)	252 (3.94GB)	59 (3.69GB)
Linux 2.6.18 (64-bit)	6168666 (23.53GB)	1540236 (23.50GB)	6016 (23.5GB)	1504 (23.5GB)	376 (23.5GB)

The machine that ran the 64-bit test is an AMD Opteron 8220 SE with 40 bit physical address lines (1024 GB) and 48 bit virtual address lines (262144 GB). However, I can't seem to actually allocate that much memory at all.

The source of the program can be found here (alignedmmap.c). Note that since the address is never touched, this does not allocate any actual memory, and the program is so tiny that it hasn't loaded very many shared objects besides standard C library.