Oh that's an Intel math kernel library. They probably just arbitrarily chose a 32-bit type in one of their FORTRAN interfaces. The x86_64 architecture itself, is pretty much word size agnostic. Arrays can be indexed using a 64-bit index, for example: mov (%rax,%rbx,8),%rcx where %rbx is the 64-bit word index. The only caveat with the instruction encoding is that fixed-size displacements can't be more than 32-bits. So for example, you can access the second 64-bit word in the array as mov 8(%rax),%rcx but you can't say mov 0x1000000000(%rax),%rcx. You'd instead have to load 0x1000000000/8 into %rbx and use the first op. This poses headaches for programs that compile to 3gb executables, since unlike arrays, code is usually referenced using displacement notation, but workarounds exist and it's still fine. All that stuff is abstracted by the compiler.