While there are currently no mainstream general-purpose processors built to operate on 128-bitintegers or addresses, a number of processors do have specialized ways to operate on 128-bit chunks of data. The IBM System/370 could be considered the first simple 128-bit computer, as it used 128-bit floating point registers. Most modern CPUs feature SIMD instruction sets (SSE, AltiVec etc.) where 128-bit vector registers are used to store several smaller numbers, such as four 32-bit floating-point numbers. A single instruction can then operate on all these values in parallel. However, these processors do not operate on individual numbers that are 128 binary digits in length, only their registers have the size of 128-bits.
The DEC VAX supported operations on 128-bit integer ('O' or octaword) and 128-bit floating-point ('H-float' or HFLOAT) datatypes. Support for such operations was an upgrade option rather than being a standard feature. Since the VAX's registers were 32 bits wide, a 128-bit operation used four consecutive registers or four longwords in memory.
In the same way that compilers emulate e.g. 64 bit integer arithmetic on architectures with register sizes less than 64 bit, some compilers also support 128 bit integer arithmetic. For example, the GCC C compiler has a __int128_t 128 bit integer type. For the C programming language, this is a compiler-specific extension, as C11 itself doesn't support 128 bit integers.
128-bit processors could be used for addressing directly up to 2128 (over 3.40 × 1038) bytes, which would greatly exceed the total data stored on Earth as of 2010, which has been estimated to be around 1.2 zettabytes (1.42 × 1021 bytes).
The AS/400 virtual instruction set defines all pointers as 128-bit. This gets translated to the hardware's real instruction set as required, allowing the underlying hardware to change without needing to recompile the software. Past hardware was 48-bit CISC, while current hardware is 64-bit PowerPC. Because pointers are defined to be 128-bit, future hardware may be 128-bit without software incompatibility.
^Suzuoki, M.; Kutaragi, K.; Hiroi, T.; Magoshi, H.; Okamoto, S.; Oka, M.; Ohba, A.; Yamamoto, Y.; Furuhashi, M.; Tanaka, M.; Yutaka, T.; Okada, T.; Nagamatsu, M.; Urakawa, Y.; Funyu, M.; Kunimatsu, A.; Goto, H.; Hashimoto, K.; Ide, N.; Murakami, H.; Ohtaguro, Y.; Aono, A. (1999). "A microprocessor with a 128-bit CPU, ten floating-point MAC's, four floating-point dividers, and an MPEG-2 decoder". IEEE Journal of Solid-State Circuits34 (11): 1608. doi:10.1109/4.799870.edit