pmulhrsw

Packed Multiply High with Round and Scale

PMULHRSW xmm1, xmm2/m128

Multiplies signed 16-bit words, rounds, and scales.

Details

Multiplies signed 16-bit integers from destination and source operands, returning the scaled and rounded high 16 bits of the 32-bit product (result = (product + 0x4000) >> 15). Saturation occurs if the result exceeds the signed 16-bit range. No CPU flags are affected by this instruction.

Pseudocode Operation

for i ← 0 to 7 do
  product[i] ← dest[i*16:i*16+15] * src[i*16:i*16+15]
  intermediate[i] ← product[i] + 0x4000
  result[i] ← intermediate[i] >> 15
  if result[i] > 32767 then
    dest[i*16:i*16+15] ← 32767
  else if result[i] < -32768 then
    dest[i*16:i*16+15] ← -32768
  else
    dest[i*16:i*16+15] ← result[i]
  end if
end for

Example

PMULHRSW xmm1, xmm2/m128

Encoding

Binary Layout
66
+0
0F
+1
38
+2
0B
+3
 
Format SSSE3
Opcode 66 0F 38 0B
Extension SSSE3

Operands

  • dest
    128-bit XMM SIMD register
  • src
    128-bit XMM SIMD register or Memory operand

Reference (Intel® SDM)

Instruction Forms

Opcode Instruction Op/En 64/32-bit Mode CPUID 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 AND AVX512BW) OR AVX10.1 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 AND AVX512BW) OR AVX10.1 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 OR AVX10.1 Multiply 16-bit signed words, scale and round signed doublewords, pack high 16 bits to zmm1 under writemask k1.

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 32bit 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. PMULHRSW—Packed Multiply High With Round and Scale Vol. 2B 4-375 128-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]



PMULHRSW—Packed Multiply High With Round and Scale                                                                                       Vol. 2B 4-376
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





PMULHRSW—Packed Multiply High With Round and Scale                                                                                       Vol. 2B 4-377
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 Equivalent

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)

Exceptions

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 2-51, “Type E4 Class Exception Conditions.” PMULHRSW—Packed Multiply High With Round and Scale Vol. 2B 4-378