# PCLMULQDQ — Carry-Less Multiplication Quadword

Opcode/Instruction | Op/En | 64/32 bit Mode Support | CPUID Feature Flag | Description
--- | --- | --- | --- | ---
66 0F 3A 44 /r ib PCLMULQDQ xmm1, xmm2/m128, imm8 | A | V/V | PCLMULQDQ | Carry-less multiplication of one quadword of xmm1 by one quadword of xmm2/m128, stores the 128-bit result in xmm1. The immediate is used to determine which quadwords of xmm1 and xmm2/m128 should be used.
VEX.128.66.0F3A.WIG 44 /r ib VPCLMULQDQ xmm1, xmm2, xmm3/m128, imm8 | B | V/V | PCLMULQDQ AVX | Carry-less multiplication of one quadword of xmm2 by one quadword of xmm3/m128, stores the 128-bit result in xmm1. The immediate is used to determine which quadwords of xmm2 and xmm3/m128 should be used.
VEX.256.66.0F3A.WIG 44 /r /ib VPCLMULQDQ ymm1, ymm2, ymm3/m256, imm8 | B | V/V | VPCLMULQDQ AVX | Carry-less multiplication of one quadword of ymm2 by one quadword of ymm3/m256, stores the 128-bit result in ymm1. The immediate is used to determine which quadwords of ymm2 and ymm3/m256 should be used.
EVEX.128.66.0F3A.WIG 44 /r /ib VPCLMULQDQ xmm1, xmm2, xmm3/m128, imm8 | C | V/V | VPCLMULQDQ AVX512VL | Carry-less multiplication of one quadword of xmm2 by one quadword of xmm3/m128, stores the 128-bit result in xmm1. The immediate is used to determine which quadwords of xmm2 and xmm3/m128 should be used.
EVEX.256.66.0F3A.WIG 44 /r /ib VPCLMULQDQ ymm1, ymm2, ymm3/m256, imm8 | C | V/V | VPCLMULQDQ AVX512VL | Carry-less multiplication of one quadword of ymm2 by one quadword of ymm3/m256, stores the 128-bit result in ymm1. The immediate is used to determine which quadwords of ymm2 and ymm3/m256 should be used.
EVEX.512.66.0F3A.WIG 44 /r /ib VPCLMULQDQ zmm1, zmm2, zmm3/m512, imm8 | C | V/V | VPCLMULQDQ AVX512F | Carry-less multiplication of one quadword of zmm2 by one quadword of zmm3/m512, stores the 128-bit result in zmm1. The immediate is used to determine which quadwords of zmm2 and zmm3/m512 should be used.

## Instruction Operand Encoding ¶

Op/En | Tuple | Operand 1 | Operand 2 | Operand 3 | Operand 4
--- | --- | --- | --- | --- | ---
A | N/A | ModRM:reg (r, w) | ModRM:r/m (r) | imm8 | N/A
B | N/A | ModRM:reg (w) | VEX.vvvv (r) | ModRM:r/m (r) | imm8
C | Full Mem | ModRM:reg (w) | EVEX.vvvv (r) | ModRM:r/m (r) | imm8 (r)

## Description ¶

Performs a carry-less multiplication of two quadwords, selected from the first source and second source operand according to the value of the immediate byte. Bits 4 and 0 are used to select which 64-bit half of each operand to use according to Table 4-13, other bits of the immediate byte are ignored.

The EVEX encoded form of this instruction does not support memory fault suppression.

Imm[4] | Imm[0] | PCLMULQDQ Operation
--- | --- | ---
0 | 0 | CL_MUL( SRC21[63:0], SRC1[63:0] )
0 | 1 | CL_MUL( SRC2[63:0], SRC1[127:64] )
1 | 0 | CL_MUL( SRC2[127:64], SRC1[63:0] )
1 | 1 | CL_MUL( SRC2[127:64], SRC1[127:64] )

Table 4-13. PCLMULQDQ Quadword Selection of Immediate Byte

> 1. SRC2 denotes the second source operand, which can be a register or memory; SRC1 denotes the first source and destination operand.

The first source operand and the destination operand are the same and must be a ZMM/YMM/XMM register. The second source operand can be a ZMM/YMM/XMM register or a 512/256/128-bit memory location. Bits (VL_MAX-1:128) of the corresponding YMM destination register remain unchanged.

Compilers and assemblers may implement the following pseudo-op syntax to simplify programming and emit the required encoding for imm8.

Pseudo-Op | Imm8 Encoding
--- | ---
PCLMULLQLQDQ xmm1, xmm2 | 0000_0000B
PCLMULHQLQDQ xmm1, xmm2 | 0000_0001B
PCLMULLQHQDQ xmm1, xmm2 | 0001_0000B
PCLMULHQHQDQ xmm1, xmm2 | 0001_0001B

Table 4-14. Pseudo-Op and PCLMULQDQ Implementation

## Operation ¶

    define PCLMUL128(X,Y): // helper function
        FOR i := 0 to 63:
            TMP [ i ] := X[ 0 ] and Y[ i ]
            FOR j := 1 to i:
                TMP [ i ] := TMP [ i ] xor (X[ j ] and Y[ i - j ])
            DEST[ i ] := TMP[ i ]
        FOR i := 64 to 126:
            TMP [ i ] := 0
            FOR j := i - 63 to 63:
                TMP [ i ] := TMP [ i ] xor (X[ j ] and Y[ i - j ])
            DEST[ i ] := TMP[ i ]
        DEST[127] := 0;
        RETURN DEST // 128b vector

### PCLMULQDQ (SSE Version) ¶

    IF imm8[0] = 0:
        TEMP1 := SRC1.qword[0]
    ELSE:
        TEMP1 := SRC1.qword[1]
    IF imm8[4] = 0:
        TEMP2 := SRC2.qword[0]
    ELSE:
        TEMP2 := SRC2.qword[1]
    DEST[127:0] := PCLMUL128(TEMP1, TEMP2)
    DEST[MAXVL-1:128] (Unmodified)

### VPCLMULQDQ (128b and 256b VEX Encoded Versions) ¶

    (KL,VL) = (1,128), (2,256)
    FOR i= 0 to KL-1:
        IF imm8[0] = 0:
            TEMP1 := SRC1.xmm[i].qword[0]
        ELSE:
            TEMP1 := SRC1.xmm[i].qword[1]
        IF imm8[4] = 0:
            TEMP2 := SRC2.xmm[i].qword[0]
        ELSE:
            TEMP2 := SRC2.xmm[i].qword[1]
        DEST.xmm[i] := PCLMUL128(TEMP1, TEMP2)
    DEST[MAXVL-1:VL] := 0

### VPCLMULQDQ (EVEX Encoded Version) ¶

    (KL,VL) = (1,128), (2,256), (4,512)
    FOR i = 0 to KL-1:
        IF imm8[0] = 0:
            TEMP1 := SRC1.xmm[i].qword[0]
        ELSE:
            TEMP1 := SRC1.xmm[i].qword[1]
        IF imm8[4] = 0:
            TEMP2 := SRC2.xmm[i].qword[0]
        ELSE:
            TEMP2 := SRC2.xmm[i].qword[1]
        DEST.xmm[i] := PCLMUL128(TEMP1, TEMP2)
    DEST[MAXVL-1:VL] := 0

## Intel C/C++ Compiler Intrinsic Equivalent ¶

    (V)PCLMULQDQ __m128i _mm_clmulepi64_si128 (__m128i, __m128i, const int)

    VPCLMULQDQ __m256i _mm256_clmulepi64_epi128(__m256i, __m256i, const int);

    VPCLMULQDQ __m512i _mm512_clmulepi64_epi128(__m512i, __m512i, const int);

## SIMD Floating-Point Exceptions ¶

None.

## Other Exceptions ¶

See Table 2-21, “Type 4 Class Exception Conditions,” additionally:

#UD | If VEX.L = 1.

EVEX-encoded: See Table 2-50, “Type E4NF Class Exception Conditions.”