CLMUL instruction set

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Carry-less Multiplication (CLMUL) is an extension to the x86 instruction set used by microprocessors from Intel and AMD which was proposed by Intel in March 2008[1] and made available in the Intel Westmere processors announced in early 2010. Mathematically, the instruction implements multiplication of polynomials over the finite field GF(2) where the bitstring represents the polynomial . The CLMUL instruction also allows a more efficient implementation of the closely related multiplication of larger finite fields GF(2k) than the traditional instruction set.[2]

One use of these instructions is to improve the speed of applications doing block cipher encryption in Galois/Counter Mode, which depends on finite field GF(2k) multiplication. Another application is the fast calculation of CRC values,[3] including those used to implement the LZ77 sliding window DEFLATE algorithm in zlib and pngcrush.[4]

ARMv8 also has a version of CLMUL. SPARC calls their version XMULX, for "XOR multiplication".

New instructions[edit]

The instruction computes the 128-bit carry-less product 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 specifying specific values of the immediate operand are also defined:

Instruction Opcode Description
PCLMULQDQ xmmreg,xmmrm,imm [rmi: 66 0f 3a 44 /r ib] Perform a carry-less multiplication of two 64-bit polynomials over the finite field GF(2k).
PCLMULLQLQDQ xmmreg,xmmrm [rm:  66 0f 3a 44 /r 00] Multiply the low halves of the two registers.
PCLMULHQLQDQ xmmreg,xmmrm [rm:  66 0f 3a 44 /r 01] Multiply the high half of the destination register by the low half of the source register.
PCLMULLQHQDQ xmmreg,xmmrm [rm:  66 0f 3a 44 /r 10] Multiply the low half of the destination register by the high half of the source register.
PCLMULHQHQDQ xmmreg,xmmrm [rm:  66 0f 3a 44 /r 11] Multiply the high halves of the two registers.

A EVEX vectorized version (VPCLMULQDQ) is seen in AVX-512.

CPUs with CLMUL instruction set[edit]

The presence of the CLMUL instruction set can be checked by testing one of the CPU feature bits.

See also[edit]


  1. ^ "Intel Software Network". Intel. Archived from the original on 2008-04-07. Retrieved 2008-04-05.
  2. ^ Shay Gueron (2011-04-13). "Intel Carry-Less Multiplication Instruction and its Usage for Computing the GCM Mode – Rev 2". Intel.
  3. ^ "Fast CRC Computation for Generic Polynomials Using PCLMULQDQ" (PDF).
  4. ^ Vlad Krasnov (2015-07-08). "Fighting Cancer: The Unexpected Benefit Of Open Sourcing Our Code". CloudFlare. Retrieved 2016-09-04.
  5. ^ Johan De Gelas (2017-03-31). "The Intel Xeon E5 v4 Review: Testing Broadwell-EP With Demanding Server Workloads". Anandtech. p. 3.
  6. ^ "Slide detailing improvements of Jaguar over Bobcat". AMD. Retrieved August 3, 2013.
  7. ^ Dave Christie (6 May 2009). "Striking a balance". AMD Developer blogs. Archived from the original on 9 November 2013. Retrieved 2011-03-11.