Mmap() an entire large file
MAP_PRIVATE mappings require a memory reservation, as writing to these pages may result in copy-on-write allocations. This means that you can't map something too much larger than your physical ram + swap. Try using a MAP_SHARED mapping instead. This means that writes to the mapping will be reflected on disk - as such, the kernel knows it can always free up memory by doing writeback, so it won't limit you.
I also note that you're mapping with PROT_WRITE, but you then go on and read from the memory mapping. You also opened the file with O_RDONLY - this itself may be another problem for you; you must specify O_RDWR if you want to use PROT_WRITE with MAP_SHARED.
As for PROT_WRITE only, this happens to work on x86, because x86 doesn't support write-only mappings, but may cause segfaults on other platforms. Request PROT_READ|PROT_WRITE - or, if you only need to read, PROT_READ.
On my system (VPS with 676MB RAM, 256MB swap), I reproduced your problem; changing to MAP_SHARED results in an EPERM error (since I'm not allowed to write to the backing file opened with O_RDONLY). Changing to PROT_READ and MAP_SHARED allows the mapping to succeed.
If you need to modify bytes in the file, one option would be to make private just the ranges of the file you're going to write to. That is, munmap and remap with MAP_PRIVATE the areas you intend to write to. Of course, if you intend to write to the entire file then you need 8GB of memory to do so.
Alternately, you can write 1 to /proc/sys/vm/overcommit_memory. This will allow the mapping request to succeed; however, keep in mind that if you actually try to use the full 8GB of COW memory, your program (or some other program!) will be killed by the OOM killer.
You don't have enough virtual memory to handle that mapping.
As an example, I have a machine here with 8G RAM, and ~8G swap (so 16G total virtual memory available).
If I run your code on a VirtualBox snapshot that is ~8G, it works fine:
$ ls -lh /media/vms/.../snap.vdi
-rw------- 1 me users 9.2G Aug 6 16:02 /media/vms/.../snap.vdi
$ ./a.out /media/vms/.../snap.vdi
Size: 9820000256
[0]=3C [1]=3C [2]=3C [3]=20 [4]=4F [5]=72 [6]=61 [7]=63 [8]=6C [9]=65
Now, if I drop the swap, I'm left with 8G total memory. (Don't run this on an active server.) And the result is:
$ sudo swapoff -a
$ ./a.out /media/vms/.../snap.vdi
Size: 9820000256
mmap: Cannot allocate memory
So make sure you have enough virtual memory to hold that mapping (even if you only touch a few pages in that file).
Linux (and apparently a few other UNIX systems) have the MAP_NORESERVE flag for mmap(2), which can be used to explicitly enable swap space overcommitting. This can be useful when you wish to map a file larger than the amount of free memory available on your system.
This is particularly handy when used with MAP_PRIVATE and only intend to write to a small portion of the memory mapped range, since this would otherwise trigger swap space reservation of the entire file (or cause the system to return ENOMEM, if system wide overcommitting hasn't been enabled and you exceed the free memory of the system).
The issue to watch out for is that if you do write to a large portion of this memory, the lazy swap space reservation may cause your application to consume all the free RAM and swap on the system, eventually triggering the OOM killer (Linux) or causing your app to receive a SIGSEGV.