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:

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: =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:

=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.

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 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 ...
 * _mm_cvtsi64x_si128
 * _mm256_sll_epi64
 * _mm256_movemask_epi8

... 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=
 * CFish - AVX2 Attacks
 * DirGolem
 * NNUE
 * SIMD and SWAR Techniques

=SIMD=
 * AltiVec
 * AVX
 * AVX-512
 * BMI2
 * MMX
 * SSE
 * SSE2
 * SSE3
 * SSSE3
 * SSE4

=Publications=
 * Wojciech Muła, Nathan Kurz, Daniel Lemire (2016). Faster Population Counts Using AVX2 Instructions. arXiv:1611.07612 » AVX-512, Population Count
 * Wojciech Muła, Daniel Lemire (2017). Faster Base64 Encoding and Decoding Using AVX2 Instructions. arXiv:1704.00605 » Base64

=Manuals=
 * Intel® Architecture Instruction Set Extensions Programming Reference (pdf)
 * Intel® 64 and IA-32 Architectures Optimization Reference Manual (pdf)

=Forum Posts=
 * Re: Tapered Eval between 4 phases by Youri Matiounine, CCC, October 16, 2017 » Tapered Eval
 * Re: Ryzen 2 and BMI2? by Joost Buijs, CCC, May 18, 2020 » AMD, BMI2

=External Links=
 * Advanced Vector Extensions 2 from Wikipedia
 * Overview: Intrinsics for Intel® Advanced Vector Extensions 2 (Intel® AVX2) Instructions | Intel® Software
 * Intel Intrinsics Guide - AVX2
 * Intel Software Development Emulator, which can be used to experiment with AVX and AVX2 on a CPU that doesn't support them.
 * Stop the instruction set war by Agner Fog
 * Processing Arrays of Bits with Intel® Advanced Vector Extensions 2 (Intel® AVX2) | Intel® Developer Zone by Thomas Willhalm, May 17, 2013
 * Haswell Instructions Latency

=References= Up one Level