First of all, beware of NASM bugs with the macho64 output format with 64-bit absolute addressing (NASM 2.13.02+) and with RIP-relative in NASM 2.11.08. 64-bit absolute addressing is not recommended, so this answer should work even for buggy NASM 2.13.02 and higher. (The bugs don't cause this error, they lead to wrong addresses being used at runtime.)
[data_items + edi*4] is a 32-bit addressing mode. Even [data_items + rdi*4] can only use a 32-bit absolute displacement, so it wouldn't work either. Note that using an address as a 32-bit (sign-extended) immediate like cmp rdi, data_items is also a problem: only mov allows a 64-bit immediate.
64-bit code on OS X can't use 32-bit absolute addressing at all. Executables are loaded at a base address above 4GiB, so label addresses just plain don't fit in 32-bit integers, with zero- or sign-extension. RIP-relative addressing is the best / most efficient solution, whether you need it to be position-independent or not1.
In NASM, default rel at the top of your file will make all [] memory operands prefer RIP-relative addressing. See also Section 3.3 Effective Addresses in the NASM manual.
default rel ; near the top of file; affects all instructions
my_func:
...
mov ecx, [data_items] ; uses the default: RIP-relative
;mov ecx, [abs data_items] ; override to absolute [disp32], unusuable
mov ecx, [rel data_items] ; explicitly RIP-relative
But RIP-relative is only possible when there are no other registers involved, so for indexing a static array you need to get the address in a register first. Use a RIP-relative lea rsi, [rel data_items].
lea rsi, [data_items] ; can be outside the loop
...
mov eax, [rsi + rdi*4]
Or you could add rsi, 4 inside the loop and use a simpler addressing mode like mov eax, [rsi].
Note that mov rsi, data_items will work for getting an address into a register, but you don't want that because it's less efficient.
Technically, any address within +-2GiB of your array will work, so if you have multiple arrays you can address the others relative to one common base address, only tieing up one register with a pointer. e.g. lea rbx, [arr1] / ... / mov eax, [rbx + rdi*4 + arr2-arr1]. Relative Addressing errors - Mac 10.10 mentions that Agner Fog's "optimizing assembly" guide has some examples of array addressing, including one using the __mh_execute_header as a reference point. (The code in that question looks like another attempt to port this 32-bit Linux example from the PGU book to 64-bit OS X, at the same time as learning asm in the first place.)
Note that on Linux, position-dependent executables are loaded in the low 32 bits of virtual address space, so you will see code like mov eax, [array + rdi*4] or mov edi, symbol_name in Linux examples or compiler output on http://gcc.godbolt.org/. gcc -pie -fPIE will make position-independent executables on Linux, and is the default on many recent distros, but not Godbolt.
This doesn't help you on MacOS, but I mention it in case anyone's confused about code they've seen for other OSes, or why AMD64 architects bothered to allow [disp32] addressing modes at all on x86-64.
And BTW, prefer using 64-bit addressing modes in 64-bit code. e.g. use [rsi + rdi*4], not [esi + edi*4]. You usually don't want to truncate pointers to 32-bit, and it costs an extra address-size prefix to encode.
Similarly, you should be using syscall to make 64-bit system calls, not int 0x80. What are the calling conventions for UNIX & Linux system calls on i386 and x86-64 for the differences in which registers to pass args in.
Footnote 1:
64-bit absolute addressing is supported on OS X, but only in position-dependent executables (non-PIE). This related question x64 nasm: pushing memory addresses onto the stack & call function includes an ld warning from using gcc main.o to link:
ld: warning: PIE disabled. Absolute addressing (perhaps -mdynamic-no-pic) not
allowed in code signed PIE, but used in _main from main.o. To fix this warning,
don't compile with -mdynamic-no-pic or link with -Wl,-no_pie
So the linker checks if any 64-bit absolute relocations are used, and if so disables creation of a Position-Independent Executable. A PIE can benefit from ASLR for security. I think shared-library code always has to be position-independent on OS X; I don't know if jump tables or other cases of pointers-as-data are allowed (i.e. fixed up by the dynamic linker), or if they need to be initialized at runtime if you aren't making a position-dependent executable.
mov r64, imm64 is larger (10 bytes) and not faster than lea r64, [RIP_rel32] (7 bytes).
So you could use mov rsi, qword data_items instead of a RIP-relative LEA which runs about as fast, and takes less space in code caches and the uop cache. 64-bit immediates also have a uop-cache fetch penalty for on Sandybridge-family (http://agner.org/optimize/): they take 2 cycles to read from a uop cache line instead of 1.
x86 also has a form of mov that loads/store from/to a 64-bit absolute address, but only for AL/AX/EAX/RAX. See http://felixcloutier.com/x86/MOV.html. You don't want this either, because it's larger and not faster than mov eax, [rel foo].
(Related: an AT&T syntax version of the same question)
