# PMULHRSW — Packed Multiply High With Round and Scale

Opcode/Instruction | Op/En | 64/32 bit Mode Support | CPUID Feature Flag | Description
--- | --- | --- | --- | ---
NP 0F 38 0B /r1 PMULHRSW mm1, mm2/m64 | A | V/V | SSSE3 | Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to mm1.
66 0F 38 0B /r PMULHRSW xmm1, xmm2/m128 | A | V/V | SSSE3 | Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to xmm1.
VEX.128.66.0F38.WIG 0B /r VPMULHRSW xmm1, xmm2, xmm3/m128 | B | V/V | AVX | Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to xmm1.
VEX.256.66.0F38.WIG 0B /r VPMULHRSW ymm1, ymm2, ymm3/m256 | B | V/V | AVX2 | Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to ymm1.
EVEX.128.66.0F38.WIG 0B /r VPMULHRSW xmm1 {k1}{z}, xmm2, xmm3/m128 | C | V/V | AVX512VL AVX512BW | Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to xmm1 under writemask k1.
EVEX.256.66.0F38.WIG 0B /r VPMULHRSW ymm1 {k1}{z}, ymm2, ymm3/m256 | C | V/V | AVX512VL AVX512BW | Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to ymm1 under writemask k1.
EVEX.512.66.0F38.WIG 0B /r VPMULHRSW zmm1 {k1}{z}, zmm2, zmm3/m512 | C | V/V | AVX512BW | Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to zmm1 under writemask k1.

> 1. See note in Section 2.5, “Intel® AVX and Intel® SSE Instruction Exception Classification,” in the Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 2A, and Section 23.25.3, “Exception Conditions of Legacy SIMD Instructions Operating on MMX Registers,” in the Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 3B.

## Instruction Operand Encoding ¶

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

## 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 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;
    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 (__m64 a, __m64 b)

    (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 Table 2-21, “Type 4 Class Exception Conditions.”

EVEX-encoded instruction, see Exceptions Type E4.nb in Table 2-49, “Type E4 Class Exception Conditions.”