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".
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(2)[X]. |
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.
The presence of the CLMUL instruction set can be checked by testing one of the CPU feature bits.
x86 is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel based on the Intel 8086 microprocessor and its 8088 variant. The 8086 was introduced in 1978 as a fully 16-bit extension of Intel's 8-bit 8080 microprocessor, with memory segmentation as a solution for addressing more memory than can be covered by a plain 16-bit address. The term "x86" came into being because the names of several successors to Intel's 8086 processor end in "86", including the 80186, 80286, 80386 and 80486 processors.
In computing, Streaming SIMD Extensions (SSE) is a single instruction, multiple data (SIMD) instruction set extension to the x86 architecture, designed by Intel and introduced in 1999 in their Pentium III series of central processing units (CPUs) shortly after the appearance of Advanced Micro Devices (AMD's) 3DNow!. SSE contains 70 new instructions, most of which work on single precision floating-point data. SIMD instructions can greatly increase performance when exactly the same operations are to be performed on multiple data objects. Typical applications are digital signal processing and graphics processing.
In computing, especially digital signal processing, the multiply–accumulate (MAC) or multiply-add (MAD) operation is a common step that computes the product of two numbers and adds that product to an accumulator. The hardware unit that performs the operation is known as a multiplier–accumulator ; the operation itself is also often called a MAC or a MAD operation. The MAC operation modifies an accumulator a:
The x86 instruction set refers to the set of instructions that x86-compatible microprocessors support. The instructions are usually part of an executable program, often stored as a computer file and executed on the processor.
Supplemental Streaming SIMD Extensions 3 is a SIMD instruction set created by Intel and is the fourth iteration of the SSE technology.
SSE4 is a SIMD CPU instruction set used in the Intel Core microarchitecture and AMD K10 (K8L). It was announced on September 27, 2006, at the Fall 2006 Intel Developer Forum, with vague details in a white paper; more precise details of 47 instructions became available at the Spring 2007 Intel Developer Forum in Beijing, in the presentation. SSE4 is fully compatible with software written for previous generations of Intel 64 and IA-32 architecture microprocessors. All existing software continues to run correctly without modification on microprocessors that incorporate SSE4, as well as in the presence of existing and new applications that incorporate SSE4.
The AMD Bulldozer Family 15h is a microprocessor microarchitecture for the FX and Opteron line of processors, developed by AMD for the desktop and server markets. Bulldozer is the codename for this family of microarchitectures. It was released on October 12, 2011, as the successor to the K10 microarchitecture.
The SSE5 was a SIMD instruction set extension proposed by AMD on August 30, 2007 as a supplement to the 128-bit SSE core instructions in the AMD64 architecture.
Advanced Vector Extensions (AVX) are extensions to the x86 instruction set architecture for microprocessors from Intel and Advanced Micro Devices (AMD). They were proposed by Intel in March 2008 and first supported by Intel with the Sandy Bridge processor shipping in Q1 2011 and later by AMD with the Bulldozer processor shipping in Q3 2011. AVX provides new features, new instructions and a new coding scheme.
The XOP instruction set, announced by AMD on May 1, 2009, is an extension to the 128-bit SSE core instructions in the x86 and AMD64 instruction set for the Bulldozer processor core, which was released on October 12, 2011. However AMD removed support for XOP from Zen (microarchitecture) onward.
The VEX prefix and VEX coding scheme are an extension to the x86 and x86-64 instruction set architecture for microprocessors from Intel, AMD and others.
The FMA instruction set is an extension to the 128 and 256-bit Streaming SIMD Extensions instructions in the x86 microprocessor instruction set to perform fused multiply–add (FMA) operations. There are two variants:
An Advanced Encryption Standard instruction set is now integrated into many processors. The purpose of the instruction set is to improve the speed and security of applications performing encryption and decryption using Advanced Encryption Standard (AES).
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 and Skylake-X CPUs; this includes the Core-X series, as well as the new Xeon Scalable Processor Family and Xeon D-2100 Embedded Series. AVX-512 consists of multiple extensions that may be implemented independently. This policy is a departure from the historical requirement of implementing the entire instruction block. Only the core extension AVX-512F is required by all AVX-512 implementations.
The F16C instruction set is an x86 instruction set architecture extension which provides support for converting between half-precision and standard IEEE single-precision floating-point formats.
Bit manipulation instructions sets are extensions to the x86 instruction set architecture for microprocessors from Intel and AMD. The purpose of these instruction sets is to improve the speed of bit manipulation. All the instructions in these sets are non-SIMD and operate only on general-purpose registers.