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] ) |
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 |
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.”