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A nommu system does not use a memory management unit, which is the part of the processor that translates virtual addresses into physical addresses. In a nommu system, all addresses are physical addresses, which means:
No demand faulting: memory is allocated directly by malloc(), which returns NULL a lot more often.
In a system with an mmu, malloc() doesn't actually allocate memory. The new virtual address range starts with a redundant copy-on-write mapping of the "zero page" (so all reads return zero but are actually reading from the same physical page over and over), and then writes are intercepted and new memory allocated to hold them as needed by the page fault handler.
On an mmu system, malloc() only returns zero when your process has run out of virtual address space (which only ever really happens on 32 bit systems, and even then you've several gigabytes per process). Actual memory exhaustion is handled by the OOM killer. Because of this, mmu Linux programmers often get out of the habit checking for NULL because it almost never happens. (See the Memory FAQ for details on how this works in the mmu case.)
A nommu system hasn't got virtual address, any "mappings" are just the kernel keeping track of what physical memory is allocated and what's free. Instead allocations on nommu must locate a contiguous region of physical memory, memset it to zero, and return a pointer to the start of it. This means malloc() will return NULL if it can't find a sufficiently large contiguous chunk of memory.
This means that large speculative mappings, such as megabytes of stack "just in case", are a bad idea on nommu.
All program text must be relocatable: so we can't use standard ELF binaries.
Every process in a nommu system uses/sees the same addresses. Most ELF programs specify what address to map each segment at, and the code/data in those segments uses fixed addresses, (plus other details like the program's entry point). This doesn't work on nommu because you don't know what other programs are running on the system, and if you want to run two instances of the same program each needs its own bss and data segments.
So we link programs differently, turning the .o files into either a a binflt binary (a file format that's sort of a relocatable version of the old a.out binaries, built using the elf2flt tool), or an FDPIC binary (a modified ELF variant where everything is relocatable, basically static PIE with extensions to share text and rodata segments between processes). Either way requires a toolchain that knows how to produce these output formats, and a kernel with the relevant binary format loader (CONFIG_BINFMT_FLAT or CONFIG_BINFMT_ELF_FDPIC) enabled.
For example, for the sh2 target the Aboriginal Linux project builds a binflt cross-compiler-sh2eb using uClibc, and the musl-libc project has an fdpic toolchain build using musl.
Fixed stack size specified at compile time
Both nommu output formats require you to specify an explicit stack size at compile time, because a nommu system can't automatically grow the stack (no "guard page" faults). These stacks should be as small as you can get away with because the entire size is allocated at program launch (requiring a contiguous unshareable allocation), and if the system can't get that memory the exec fails. The default size (8k) is basically a kernel stack. The standard Linux assumption of megabytes of stack is not a good fit for nommu systems.
Memory fragmentation is a big deal
A system with an mmu can populate a virtual mapping with scattered physical pages, not just glossing over gaps but mapping them out of order.
A nommu system needs a contiguous physical address range, which may be hard to come by on a system with lots of existing allocations. Even when there's lots of total free memory, a small chunk allocated out of the middle of it will halve the size of the largest allocation that can be satisfied. After a while, the largest available chunk of memory tends to be far smaller than the total amount of free memory.
The system needs contiguous allocations for program code, for for process stacks and environment space, and to satisfy malloc(). The smaller these allocations can be, the more likely they are to fit into available chunks space on a fragmented system. (Conversely, the more small long-lived allocations you make, the more fragmented memory gets.)
Because of this, your libc probably won't put large mappings in the heap (which is itself a large contiguous mapping), but may instead ask the kernel to mmap() larger allocations so they can fit into available space. (The tradeoff is making such allocations larger by rounding up to page size.)
No fork(): vfork() instead
Using fork would be expensive even if it wasn't almost impossible: you have to copy all the program's writeable data to fresh allocations, and most likely immediately discard them again by performing an exec().
The "almost impossible" part is because any pointers in your new copy of the heap/stack would point to memory in the OLD heap/stack, because every process sees the same addresses. Going through the heap and stack to relocate all these pointers turns out to be really hard (see "garbage collection in C").
Instead we use vfork(), which halts the parent process when it creates a new child process so the child can use the parent's memory (definitely the heap, it might or might not get a new stack). When the child calls exec() or _exit(), the parent process resumes.
The vfork()ed child has to be careful not to corrupt the parent's heap (and shouldn't return from the function that called vfork() in case it's using the same stack).
If the child can't exec() a new process, it should call _exit() instead of exit() becaue the first is a system call and the latter does various cleanup work like stdio flushing and running atexit() calls and destructors that are properties of the parent process, and none of the child's business.
(Similarly, the brk() system call is a lot less useful because of the memory fragmentation issue. On some nommu systems, brk() just returns -ENOSYS. This is mostly a concern for people implementing C libraries with nommu support.)