PMULHRSW — Packed Multiply High with Round and Scale

1. See note in Section 2.4, “AVX and SSE Instruction Exception Specification” in the Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 2A and Section 22.25.3, “Exception Conditions of Legacy SIMD Instructions Operating on MMX Registers” in the Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 3A.

Instruction Operand Encoding ¶

Description ¶

PMULHRSW multiplies vertically each signed 16-bit integer from the destination operand (first operand) with the corresponding signed 16-bit integer of the source operand (second operand), producing intermediate, signed 32-bit integers. Each intermediate 32-bit integer is truncated to the 18 most significant bits. Rounding is always performed by adding 1 to the least significant bit of the 18-bit intermediate result. The final result is obtained by selecting the 16 bits immediately to the right of the most significant bit of each 18-bit intermediate result and packed to the destination operand.

When the source operand is a 128-bit memory operand, the operand must be aligned on a 16-byte boundary or a general-protection exception (#GP) will be generated.

In 64-bit mode and not encoded with VEX/EVEX, use the REX prefix to access XMM8-XMM15 registers.

Legacy SSE version 64-bit operand: Both operands can be MMX registers. The second source operand is an MMX register or a 64-bit memory location.

128-bit Legacy SSE version: The first source and destination operands are XMM registers. The second source operand is an XMM register or a 128-bit memory location. Bits (MAXVL-1:128) of the corresponding YMM destination register remain unchanged.

VEX.128 encoded version: The first source and destination operands are XMM registers. The second source operand is an XMM register or a 128-bit memory location. Bits (MAXVL-1:128) of the destination YMM register are zeroed.

VEX.256 encoded version: The second source operand can be an YMM register or a 256-bit memory location. The first source and destination operands are YMM registers.

EVEX encoded versions: The first source operand is a ZMM/YMM/XMM register. The second source operand can be a ZMM/YMM/XMM register, a 512/256/128-bit memory location. The destination operand is a ZMM/YMM/XMM register conditionally updated with writemask k1.

Operation ¶

PMULHRSW (with 64-bit operands) ¶

temp0[31:0] = INT32 ((DEST[15:0] * SRC[15:0]) >>14) + 1;
temp1[31:0] = INT32 ((DEST[31:16] * SRC[31:16]) >>14) + 1;
temp2[31:0] = INT32 ((DEST[47:32] * SRC[47:32]) >> 14) + 1;
temp3[31:0] = INT32 ((DEST[63:48] * SRc[63:48]) >> 14) + 1;
DEST[15:0] = temp0[16:1];
DEST[31:16] = temp1[16:1];
DEST[47:32] = temp2[16:1];
DEST[63:48] = temp3[16:1];

PMULHRSW (with 128-bit operand) ¶

temp0[31:0] = INT32 ((DEST[15:0] * SRC[15:0]) >>14) + 1;
temp1[31:0] = INT32 ((DEST[31:16] * SRC[31:16]) >>14) + 1;
temp2[31:0] = INT32 ((DEST[47:32] * SRC[47:32]) >>14) + 1;
temp3[31:0] = INT32 ((DEST[63:48] * SRC[63:48]) >>14) + 1;
temp4[31:0] = INT32 ((DEST[79:64] * SRC[79:64]) >>14) + 1;
temp5[31:0] = INT32 ((DEST[95:80] * SRC[95:80]) >>14) + 1;
temp6[31:0] = INT32 ((DEST[111:96] * SRC[111:96]) >>14) + 1;
temp7[31:0] = INT32 ((DEST[127:112] * SRC[127:112) >>14) + 1;
DEST[15:0] = temp0[16:1];
DEST[31:16] = temp1[16:1];
DEST[47:32] = temp2[16:1];
DEST[63:48] = temp3[16:1];
DEST[79:64] = temp4[16:1];
DEST[95:80] = temp5[16:1];
DEST[111:96] = temp6[16:1];
DEST[127:112] = temp7[16:1];

VPMULHRSW (VEX.128 encoded version) ¶

temp0[31:0]←INT32 ((SRC1[15:0] * SRC2[15:0]) >>14) + 1
temp1[31:0]←INT32 ((SRC1[31:16] * SRC2[31:16]) >>14) + 1
temp2[31:0]←INT32 ((SRC1[47:32] * SRC2[47:32]) >>14) + 1
temp3[31:0]←INT32 ((SRC1[63:48] * SRC2[63:48]) >>14) + 1
temp4[31:0]←INT32 ((SRC1[79:64] * SRC2[79:64]) >>14) + 1
temp5[31:0]←INT32 ((SRC1[95:80] * SRC2[95:80]) >>14) + 1
temp6[31:0]←INT32 ((SRC1[111:96] * SRC2[111:96]) >>14) + 1
temp7[31:0]←INT32 ((SRC1[127:112] * SRC2[127:112) >>14) + 1
DEST[15:0] ← temp0[16:1]
DEST[31:16] ← temp1[16:1]
DEST[47:32] ← temp2[16:1]
DEST[63:48] ← temp3[16:1]
DEST[79:64] ← temp4[16:1]
DEST[95:80] ← temp5[16:1]
DEST[111:96] ← temp6[16:1]
DEST[127:112] ← temp7[16:1]
DEST[MAXVL-1:128] ← 0

VPMULHRSW (VEX.256 encoded version) ¶

temp0[31:0]←INT32 ((SRC1[15:0] * SRC2[15:0]) >>14) + 1
temp1[31:0]←INT32 ((SRC1[31:16] * SRC2[31:16]) >>14) + 1
temp2[31:0]←INT32 ((SRC1[47:32] * SRC2[47:32]) >>14) + 1
temp3[31:0]←INT32 ((SRC1[63:48] * SRC2[63:48]) >>14) + 1
temp4[31:0]←INT32 ((SRC1[79:64] * SRC2[79:64]) >>14) + 1
temp5[31:0]←INT32 ((SRC1[95:80] * SRC2[95:80]) >>14) + 1
temp6[31:0]←INT32 ((SRC1[111:96] * SRC2[111:96]) >>14) + 1
temp7[31:0]←INT32 ((SRC1[127:112] * SRC2[127:112) >>14) + 1
temp8[31:0]←INT32 ((SRC1[143:128] * SRC2[143:128]) >>14) + 1
temp9[31:0]←INT32 ((SRC1[159:144] * SRC2[159:144]) >>14) + 1
temp10[31:0]←INT32 ((SRC1[75:160] * SRC2[175:160]) >>14) + 1
temp11[31:0]←INT32 ((SRC1[191:176] * SRC2[191:176]) >>14) + 1
temp12[31:0]←INT32 ((SRC1[207:192] * SRC2[207:192]) >>14) + 1
temp13[31:0]←INT32 ((SRC1[223:208] * SRC2[223:208]) >>14) + 1
temp14[31:0]←INT32 ((SRC1[239:224] * SRC2[239:224]) >>14) + 1
temp15[31:0]←INT32 ((SRC1[255:240] * SRC2[255:240) >>14) + 1
DEST[15:0] ← temp0[16:1]
DEST[31:16] ← temp1[16:1]
DEST[47:32] ← temp2[16:1]
DEST[63:48] ← temp3[16:1]
DEST[79:64] ← temp4[16:1]
DEST[95:80] ← temp5[16:1]
DEST[111:96] ← temp6[16:1]
DEST[127:112] ← temp7[16:1]
DEST[143:128] ← temp8[16:1]
DEST[159:144] ← temp9[16:1]
DEST[175:160] ← temp10[16:1]
DEST[191:176] ← temp11[16:1]
DEST[207:192] ← temp12[16:1]
DEST[223:208] ← temp13[16:1]
DEST[239:224] ← temp14[16:1]
DEST[255:240] ← temp15[16:1]
DEST[MAXVL-1:256] ← 0

VPMULHRSW (EVEX encoded version) ¶

(KL, VL) = (8, 128), (16, 256), (32, 512)
FOR j←0 TO KL-1
    i←j * 16
    IF k1[j] OR *no writemask*
        THEN
            temp[31:0]←((SRC1[i+15:i] * SRC2[i+15:i]) >>14) + 1
            DEST[i+15:i] ← tmp[16:1]
        ELSE
            IF *merging-masking* ; merging-masking
                THEN *DEST[i+15:i] remains unchanged*
                ELSE *zeroing-masking*
                        ; zeroing-masking
                    DEST[i+15:i] ← 0
            FI
    FI;
ENDFOR
DEST[MAXVL-1:VL] ← 0

Intel C/C++ Compiler Intrinsic Equivalents ¶

VPMULHRSW __m512i _mm512_mulhrs_epi16(__m512i a, __m512i b);

VPMULHRSW __m512i _mm512_mask_mulhrs_epi16(__m512i s, __mmask32 k, __m512i a, __m512i b);

VPMULHRSW __m512i _mm512_maskz_mulhrs_epi16( __mmask32 k, __m512i a, __m512i b);

VPMULHRSW __m256i _mm256_mask_mulhrs_epi16(__m256i s, __mmask16 k, __m256i a, __m256i b);

VPMULHRSW __m256i _mm256_maskz_mulhrs_epi16( __mmask16 k, __m256i a, __m256i b);

VPMULHRSW __m128i _mm_mask_mulhrs_epi16(__m128i s, __mmask8 k, __m128i a, __m128i b);

VPMULHRSW __m128i _mm_maskz_mulhrs_epi16( __mmask8 k, __m128i a, __m128i b);

PMULHRSW: __m64_mm_mulhrs_pi16(__m64a,__m64b)

(V)PMULHRSW: __m128i _mm_mulhrs_epi16 (__m128i a, __m128i b)

VPMULHRSW:__m256i _mm256_mulhrs_epi16 (__m256i a, __m256i b)

SIMD Floating-Point Exceptions ¶

None.

Other Exceptions ¶

Non-EVEX-encoded instruction, see Exceptions Type 4.

EVEX-encoded instruction, see Exceptions Type E4.nb.