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 RMI V/V PCLMUL-QDQ Carry-less multiplication of one quadword of xmm1 by one quadword of xmm2/m128, stores the 128-bit result in xmm1. The imme-diate is used to determine which quadwords of xmm1 and xmm2/m128 should be used.
VEX.NDS.128.66.0F3A.WIG 44 /r ib VPCLMULQDQ xmm1, xmm2, xmm3/m128, imm8 RVMI V/V Both PCL-MULQDQ and AVX flags Carry-less multiplication of one quadword of xmm2 by one quadword of xmm3/m128, stores the 128-bit result in xmm1. The imme-diate is used to determine which quadwords of xmm2 and xmm3/m128 should be used.

Instruction Operand Encoding

Op/En Operand 1 Operand2 Operand3 Operand4
RMI ModRM:reg (r, w) ModRM:r/m (r) imm8 NA
RVMI ModRM:reg (w) VEX.vvvv (r) ModRM:r/m (r) imm8

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 4-10, other bits of the immediate byte are ignored.

Table 4-10. PCLMULQDQ Quadword Selection of Immediate Byte

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] )

NOTES:

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

and.

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

Compilers and assemblers may implement the following pseudo-op syntax to simply programming and emit the required encoding for Imm8.

Table 4-11. Pseudo-Op and PCLMULQDQ Implementation

Pseudo-Op Imm8 Encoding
PCLMULLQLQDQ xmm1, xmm2 0000_0000B
PCLMULHQLQDQ xmm1, xmm2 0000_0001B
PCLMULLQHDQ xmm1, xmm2 0001_0000B
PCLMULHQHDQ xmm1, xmm2 0001_0001B

Operation

PCLMULQDQ

IF (Imm8[0] = 0 )
    THEN
         TEMP1 ← SRC1 [63:0];
    ELSE
         TEMP1 ← SRC1 [127:64];
FI
IF (Imm8[4] = 0 )
    THEN
         TEMP2 ← SRC2 [63:0];
    ELSE
         TEMP2 ← SRC2 [127:64];
FI
For i = 0 to 63 {
    TmpB [ i ] ← (TEMP1[ 0 ] and TEMP2[ i ]);
    For j = 1 to i {
         TmpB [ i ] ← TmpB [ i ] xor (TEMP1[ j ] and TEMP2[ i - j ])
    }
    DEST[ i ] ← TmpB[ i ];
}
For i = 64 to 126 {
    TmpB [ i ] ← 0;
    For j = i - 63 to 63 {
         TmpB [ i ] ← TmpB [ i ] xor (TEMP1[ j ] and TEMP2[ i - j ])
    }
    DEST[ i ] ← TmpB[ i ];
}
DEST[127] ← 0;
DEST[VLMAX-1:128] (Unmodified)

VPCLMULQDQ

IF (Imm8[0] = 0 )
    THEN
         TEMP1 ← SRC1 [63:0];
    ELSE
         TEMP1 ← SRC1 [127:64];
FI
IF (Imm8[4] = 0 )
    THEN
         TEMP2 ← SRC2 [63:0];
    ELSE
         TEMP2 ← SRC2 [127:64];
FI
For i = 0 to 63 {
    TmpB [ i ] ← (TEMP1[ 0 ] and TEMP2[ i ]);
    For j = 1 to i {
         TmpB [i] ← TmpB [i] xor (TEMP1[ j ] and TEMP2[ i - j ])
    }
    DEST[i] ← TmpB[i];
}
For i = 64 to 126 {
    TmpB [ i ] ← 0;
    For j = i - 63 to 63 {
         TmpB [i] ← TmpB [i] xor (TEMP1[ j ] and TEMP2[ i - j ])
    }
    DEST[i] ← TmpB[i];
}
DEST[VLMAX-1:127] ← 0;

Intel C/C++ Compiler Intrinsic Equivalent

(V)PCLMULQDQ:

__m128i _mm_clmulepi64_si128 (__m128i, __m128i, const int)

SIMD Floating-Point Exceptions

None.

Other Exceptions

See Exceptions Type 4.