Carry-less Multiplication (CLMUL) is an extension to the x86 instruction set used by

microprocessor A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit, or a small number of integrated circuits. The microprocessor contains the arithmetic, logic, and control circu ...

s from

Intel Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the devel ...

and AMD which was proposed by Intel in March 2008 and made available in the Intel Westmere processors announced in early 2010. Mathematically, the instruction implements multiplication of polynomials over the

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subt ...

GF(2) where the bitstring

a_0a_1\ldots a_

represents the polynomial

a_0 + a_1X + a_2X^2 + \cdots + a_X^

. The CLMUL instruction also allows a more efficient implementation of the closely related multiplication of larger finite fields GF(2^''k'') than the traditional instruction set. One use of these instructions is to improve the speed of applications doing block cipher encryption in

Galois/Counter Mode In cryptography, Galois/Counter Mode (GCM) is a mode of operation for symmetric-key cryptographic block ciphers which is widely adopted for its performance. GCM throughput rates for state-of-the-art, high-speed communication channels can be achie ...

, which depends on finite field GF(2^''k'') multiplication. Another application is the fast calculation of CRC values, including those used to implement the LZ77

sliding window A sliding window protocol is a feature of packet-based data transmission protocols. Sliding window protocols are used where reliable in-order delivery of packets is required, such as in the data link layer ( OSI layer 2) as well as in the Tran ...

DEFLATE algorithm in zlib and pngcrush. ARMv8 also has a version of CLMUL. SPARC calls their version XMULX, for "XOR multiplication".

New instructions

The instruction computes the 128-bit

carry-less product The carry-less product of two binary numbers is the result of carry-less multiplication of these numbers. This operation conceptually works like long multiplication except for the fact that the carry is discarded instead of applied to the more si ...

of two 64-bit values. The destination is a 128-bit XMM register. The source may be another XMM register or memory. An immediate operand specifies which halves of the 128-bit operands are multiplied.

Mnemonics A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imager ...

specifying specific values of the immediate operand are also defined: A EVEX vectorized version (VPCLMULQDQ) is seen in

AVX-512 AVX-512 are 512-bit extensions to the 256-bit Advanced Vector Extensions SIMD instructions for x86 instruction set architecture (ISA) proposed by Intel in July 2013, and implemented in Intel's Xeon Phi x200 (Knights Landing) and Skylake-X CPUs; ...

CPUs with CLMUL instruction set

** Westmere processor (March 2010). ** Sandy Bridge processor ** Ivy Bridge processor ** Haswell processor ** Broadwell processor (with increased throughput and lower latency) **

Skylake Skylake or Sky Lake may refer to: * Skylake (microarchitecture), the codename for a processor microarchitecture developed by Intel as the successor to Broadwell * Skylake (Mysia), a town of ancient Mysia, now in Turkey * Sky Lake, Florida Sky La ...

(and later) processor ** Goldmont processor * AMD: ** Jaguar-based processors and newer ** Puma-based processors and newer ** "Heavy Equipment" processors *** Bulldozer-based processors *** Piledriver-based processors *** Steamroller-based processors *** Excavator-based processors and newer **

Zen Zen ( zh, t=禪, p=Chán; ja, text= 禅, translit=zen; ko, text=선, translit=Seon; vi, text=Thiền) is a school of Mahayana Buddhism that originated in China during the Tang dynasty, known as the Chan School (''Chánzong'' 禪宗), and ...

processors ** Zen+ processors ** Zen2 (and later) processors The presence of the CLMUL instruction set can be checked by testing one of the CPU feature bits.

References

{{Multimedia extensions, state=uncollapsed X86 architecture X86 instructions

New instructions

CPUs with CLMUL instruction set

See also

References