AVX2

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Advanced Vector Extensions 2 (AVX2) is an expansion of the AVX instruction set. Support for 256-bit expansions of the SSE2 128-bit integer instructions will be added in AVX2, which was along with BMI2 part of Intel's Haswell architecture in 2013, and since 2015, of AMD's Excavator microarchitecture.

Features

Beside expanding most integer AVX instructions to 256 bit, AVX2 has 3-operand general-purpose bit manipulation and multiply, vector shifts, Double- and Quad Word-granularity any-to-any permutes, and 3-operand fused multiply-accumulate support. An important catch is that not all of the instructions are simply generalizations of their 128-bit equivalents: many work "in-lane", applying the same 128-bit operation to each 128-bit half of the register instead of a 256-bit generalization of the operation. For example:

Set Instruction Result
AVX vpunpckldq xmm0, ABCD, EFGH xmm1 := AEBF
AVX2 vpunpckldq ymm0, ABCDEFGH, IJKLMNOP xmm1 := AIBJEMFN

If vpunpckldq had been expanded in the more intuitive fashion, the result of the AVX2 operation would be AIBJCKDL. The reason for this design might be to allow AVX to be implemented more easily with two separate 128-bit arithmetic units.

Some AVX2 instructions, such as type conversion instructions, take both xmm and ymm registers as arguments. For example:

Set Instruction Operation
AVX vpmovzxbw xmm1, xmm2/m64 xmm1 := Packed_Zero_Extend_Byte_To_Word(xmm2/m64)
AVX2 vpmovzxbw ymm1, xmm2/m128 ymm1 := Packed_Zero_Extend_Byte_To_Word(xmm2/m128)

Individual Vector Shifts

With AVX2 each data element, such as a bitboard of a quad-bitboard, may be shifted left or right individually, as specified by the second source operand, with following Assembly mnemonics and C intrinsic equivalents:

Instruction Description Intrinsic
VPSRLVQ ymm1, ymm2, ymm3/m256 Variable Bit Shift Right Logical _m256i _mm256_srlv_epi64 (_m256i m, _m256i count)
VPSLLVQ ymm1, ymm2, ymm3/m256 Variable Bit Shift Left Logical _m256i _mm256_sllv_epi64 (_m256i m, _m256i count)

Applications

With an appropriate quad-bitboard class, one may generate attacks of up to four different directions using individual shifts, for instance knight attacks or sliding piece attacks with Dumb7Fill to generate all positive or negative sliding ray attacks passing two times orthogonal and diagonal sliding pieces.

Cpwmappinghint.JPG
Code samples and bitboard diagrams rely on Little endian file and rank mapping.

Knight Attacks

        noNoWe    noNoEa
            +15  +17
             |     |
noWeWe  +6 __|     |__+10  noEaEa
              \   /
               >0<
           __ /   \ __
soWeWe -10   |     |   -6  soEaEa
             |     |
            -17  -15
        soSoWe    soSoEa
QBB noEaEa_noNoEa_noNoWe_noWeWe(U64 knights) {
   const QBB qmask  (notAB, notA,notH,notGH);
   const QBB qshift (10,17,15,6);
   QBB qknights (knights);
   return (qknights << qshift) & qmask;
}

QBB soWeWe_soSoWe_soSoEa_soEaEa(U64 knights) {
   const QBB qmask  (notGH,notH,notA,notAB);
   const QBB qshift (10,17,15,6);
   QBB qknights (knights);
   return (qknights >> qshift) & qmask;
}

Dumb7Fill

  northwest    north   northeast
  noWe         nort         noEa
          +7    +8    +9
              \  |  /
  west    -1 <-  0 -> +1    east
              /  |  \
          -9    -8    -7
  soWe         sout         soEa
  southwest    south   southeast
QBB east_nort_noWe_noEa_Attacks(QBB qsliders {rq,rq,bq,bq}, U64 empty) {
   const QBB qmask  (notA,-1,notH,notA);
   const QBB qshift (1,8,7,9);
   QBB qflood (sliders);
   QBB qempty  = QBB(empty) & qmask;
   qflood |= qsliders = (qsliders << qshift) & qempty;
   qflood |= qsliders = (qsliders << qshift) & qempty;
   qflood |= qsliders = (qsliders << qshift) & qempty;
   qflood |= qsliders = (qsliders << qshift) & qempty;
   qflood |= qsliders = (qsliders << qshift) & qempty;
   qflood |=            (qsliders << qshift) & qempty;
   return               (qflood   << qshift) & qmask  
}

QBB west_sout_soEa_soWe_Attacks(QBB qsliders {rq,rq,bq,bq}, U64 empty) {
   const QBB qmask  (notH,-1, notA,notH);
   const QBB qshift (1,8,7,9);
   QBB qflood (sliders);
   QBB qempty  = QBB(empty) & qmask;
   qflood |= qsliders = (qsliders >> qshift) & qempty;
   qflood |= qsliders = (qsliders >> qshift) & qempty;
   qflood |= qsliders = (qsliders >> qshift) & qempty;
   qflood |= qsliders = (qsliders >> qshift) & qempty;
   qflood |= qsliders = (qsliders >> qshift) & qempty;
   qflood |=            (qsliders >> qshift) & qempty;
   return               (qflood   >> qshift) & qmask  
}

Bitboard Permutation

For each bitboard in a destination quad-bitboard, the Qwords Element Permutation (VPERMQ) instruction [1] selects one bitboard of a source quad-bitboard. This permits a bitboard in the source operand to be copied to multiple locations in the destination.

 destQBB.bb[0] = sourceQBB.bb[ (imm8 >> 0) & 3 ]
 destQBB.bb[1] = sourceQBB.bb[ (imm8 >> 2) & 3 ]
 destQBB.bb[2] = sourceQBB.bb[ (imm8 >> 4) & 3 ]
 destQBB.bb[3] = sourceQBB.bb[ (imm8 >> 6) & 3 ]

Vertical Nibble

Following code extracts the piece-code as "vertical nibble" from a quad-bitboard as board representation inside a register, "indexed" by square. The idea is to shift the square bits to the leftmost bit, the sign bit of each bitboard, to perform the VPMOVMSKB instruction to get the sign bits of all 32 bytes into a general purpose register. Unfortunately, there is no VPMOVMSKQ to get only the signs of four bitboards, so some more masking and mapping is required to get the four-bit piece code ...

int getPiece (__m256i qbb, U64 sq) {
   __m128i  shift = _mm_cvtsi32x_si128( sq ^ 63 ); /* left shift amount 63-sq */
   qbb  =  _mm256_sll_epi64( qbb, shift ); /* squares to signs */
   uint32   qbbsigns = _mm256_movemask_epi8( qbb );  /* get sign bits of 32 bytes */
   return ((qbbsigns & 0x80808080) * 0x00204081) >> 28; /* mask, nibble-map, shift */
}

... using these intrinsics ...

... with seven assembly instructions intended, assuming the quad-bitboard passed in ymm0 and the square in rcx

  xor       rcx, 63          ; left shift amount 63-sq
  movd      xmm6, rcx        ; shift amount via xmm
  vpsllq    ymm6, ymm0, xmm6 ; squares to signs
  vpmovmskb eax, ymm6        ; get sign bits of 32 bytes
  and       eax, 0x80808080  ; mask the four bitboard sign bits
  imul      eax, 0x00204081  ; map them to the upper nibble
  shr       eax, 28          ; nibble as piece code

See also

Publications

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