将字段中的位扩展到掩码中所有（重叠+相邻）集位的最快方法？

假设我有 2 个名为 IN 和 MASK 的二进制输入。实际字段大小可能是 32 到 256 位，具体取决于用于完成任务的指令集。每次调用时两个输入都会改变。

Inputs:
IN   = ...1100010010010100...
MASK = ...0001111010111011...
Output:
OUT  = ...0001111010111000...

编辑：一些评论讨论的另一个示例结果

IN   = ...11111110011010110...
MASK = ...01011011001111110...
Output:
OUT  = ...01011011001111110...

我想要获取 IN 的 1 位所在的 MASK 的连续相邻 1 位。 （这种操作有通用术语吗？也许我没有正确表达我的搜索。）我正在尝试找到一种更快的方法来执行此操作。我愿意使用任何可以在最少 CPU 周期内完成此任务的 x86 或 x86 SIMD 扩展。更广泛的数据类型 SIMD 是首选，因为它允许我一次处理更多数据。

我想出的最好的简单解决方案是以下伪代码，它手动向左移动，直到没有更多匹配位，然后重复向右移动：

// (using the variables above)
testL = testR = OUT = (IN & MASK);

LoopL:
testL = (testL << 1) & MASK;
if (testL != 0) {
    OUT = OUT | testL;
    goto LoopL;
}

LoopR:
testR = (testR >> 1) & MASK;
if (testR != 0) {
    OUT = OUT | testR;
    goto LoopR;
}

return OUT;

我想@fuz 的评论是在正确的轨道上。 以下示例显示了下面的 SSE 和 AVX2 代码的工作原理。 该算法开始于IN_reduced = IN & MASK因为我们不感兴趣 在IN位置处的位MASK is 0.

IN                                  = . . . 0 0 0 0 . . . . p q r s . . .
MASK                                = . . 0 1 1 1 1 0 . . 0 1 1 1 1 0 . . 
IN_reduced = IN & MASK              = . . 0 0 0 0 0 0 . . 0 p q r s 0 . .

如果有任何一个p q r s位是1, then IN_reduced + MASK有一个进位位1在位置X，即右左 请求连续位。

MASK                                = . . 0 1 1 1 1 0 . . 0 1 1 1 1 0 . . 
IN_reduced                          = . . 0 0 0 0 0 0 . . 0 p q r s 0 . .
IN_reduced + MASK                   = . . 0 1 1 1 1 . . . 1 . . . . . .
                                                          X
(IN_reduced + MASK) >>1             = . . . 0 1 1 1 1 . . . 1 . . . . . .

With >> 1这个进位位1移位到与位相同的列p（连续位的第一位）。 现在，(IN_reduced + MASK) >>1实际上是平均值IN_reduced and MASK。 为了避免加法可能溢出，我们使用以下内容 平均的：avg(a, b) = (a & b) + ((a ^ b) >> 1)（参见@Harold 的评论， 也可以看看here https://stackoverflow.com/a/14884757 and here https://stackoverflow.com/a/10470235.) With average = avg(IN_reduced, MASK) we get

MASK                                = . . 0 1 1 1 1 0 . . 0 1 1 1 1 0 . . 
IN_reduced                          = . . 0 0 0 0 0 0 . . 0 p q r s 0 . .
average                             = . . . 0 1 1 1 1 . . . 1 . . . . . .
MASK >> 1                           = . . . 0 1 1 1 1 0 . . 0 1 1 1 1 0 .  
leading_bits = (~(MASK>>1))&average = . . . 0 0 0 0 0 . . . 1 0 0 0 0 . .  

我们可以隔离前导进位位leading_bits = (~(MASK>>1) ) & average因为MASK>>1在这些位置为零 进位位 我们感兴趣的。

正常加法时，进位从右向左传播。这里我们使用一个 反向加法：从左到右进位。 反向添加MASK and leading_bits: rev_added = bit_swap(bit_swap(MASK) + bit_swap(leading_bits)), 这会将位归零 想要的职位。 和OUT = (~rev_added) & MASK我们得到了结果。

MASK                                = . . 0 1 1 1 1 0 . . 0 1 1 1 1 0 . . 
leading_bits                        = . . . 0 0 0 0 0 . . . 1 0 0 0 0 . .  
rev_added (MASK,leading_bits)       = . . . 1 1 1 1 0 . . . 0 0 0 0 1 . .
OUT = ~rev_added & MASK             = . . 0 0 0 0 0 0 . . . 1 1 1 1 0 . .

该算法尚未经过彻底测试，但输出看起来不错。

下面的代码块包含两个单独的代码： 上半部分是SSE代码， 下半部分是AVX2代码。 （为了避免 用两个大的代码块使答案变得过于膨胀。） SSE 算法适用于 2 x 64 位元素，AVX2 版本适用于 4 x 64 位元素。

使用 gcc 9.1，该算法编译为大约 29 条指令 https://godbolt.org/z/KWeNzc, 除了 4vmovdqa-s 用于加载一些常量，这些常量可能是 在现实世界的应用程序中被提升到循环之外（内联后）。 这 29 条指令是 9 次洗牌的良好组合（vpshufb）执行 在 Intel Skylake 上的端口 5 (p5) 上，以及许多其他经常可能出现的指令 在 p0、p1 或 p5 上执行。

因此，每个周期执行大约 3 条指令是可能的。 在这种情况下，吞吐量约为 1 次函数调用（内联） 每 10 个周期。在 AVX2 情况下，这意味着 4uint64_t OUT结果每 约10个周期。

请注意，性能与数据无关（！），这是一个很好的 我认为这个答案的好处。该解决方案是无分支、无循环的，并且 不会遭受分支预测失败的影响。

/*  gcc -O3 -m64 -Wall -march=skylake select_bits.c    */
#include <immintrin.h>
#include <stdio.h>
#include <stdint.h>

int print_sse_128_bin(__m128i x);
__m128i bit_128_k(unsigned int k);
__m128i mm_bitreverse_epi64(__m128i x);
__m128i mm_revadd_epi64(__m128i x, __m128i y);


/* Select specific pieces of contiguous bits from `MASK` based on selector `IN`  */
__m128i mm_select_bits_epi64(__m128i IN, __m128i MASK){
    __m128i IN_reduced   = _mm_and_si128(IN, MASK);
    /* Compute the average of IN_reduced and MASK with avg(a,b)=(a&b)+((a^b)>>1)  */
    /* (IN_reduced & MASK) + ((IN_reduced ^ MASK) >>1) =                          */
    /* ((IN & MASK) & MASK) + ((IN_reduced ^ MASK) >>1) =                         */
    /* IN_reduced + ((IN_reduced ^ MASK) >>1)                                     */
    __m128i tmp          = _mm_xor_si128(IN_reduced, MASK);
    __m128i tmp_div2     = _mm_srli_epi64(tmp, 1);
    __m128i average      = _mm_add_epi64(IN_reduced, tmp_div2);   /* average is the average */
    __m128i MASK_div2    = _mm_srli_epi64(MASK, 1);
    __m128i leading_bits = _mm_andnot_si128(MASK_div2, average);
    __m128i rev_added    = mm_revadd_epi64(MASK, leading_bits);
    __m128i OUT          = _mm_andnot_si128(rev_added, MASK);
    /* Uncomment the next lines to check the arithmetic */ /*   
    printf("IN           ");print_sse_128_bin(IN           );       
    printf("MASK         ");print_sse_128_bin(MASK         ); 
    printf("IN_reduced   ");print_sse_128_bin(IN_reduced   );       
    printf("tmp          ");print_sse_128_bin(tmp          );       
    printf("tmp_div2     ");print_sse_128_bin(tmp_div2     );       
    printf("average      ");print_sse_128_bin(average      );       
    printf("MASK_div2    ");print_sse_128_bin(MASK_div2    );       
    printf("leading_bits ");print_sse_128_bin(leading_bits );       
    printf("rev_added    ");print_sse_128_bin(rev_added    );       
    printf("OUT          ");print_sse_128_bin(OUT          );       
    printf("\n");*/
    return OUT;       
}


int main(){
    __m128i IN   = _mm_set_epi64x(0b11111110011010110, 0b1100010010010100);
    __m128i MASK = _mm_set_epi64x(0b01011011001111110, 0b0001111010111011);
    __m128i OUT;    

    printf("Example 1 \n");
    OUT = mm_select_bits_epi64(IN, MASK);
    printf("IN           ");print_sse_128_bin(IN);
    printf("MASK         ");print_sse_128_bin(MASK);
    printf("OUT          ");print_sse_128_bin(OUT);
    printf("\n\n");

                      /*  0b7654321076543210765432107654321076543210765432107654321076543210  */
    IN   = _mm_set_epi64x(0b1000001001001010000010000000100000010000000000100000000111100011, 
                          0b11111110011010111);
    MASK = _mm_set_epi64x(0b1110011110101110111111000000000111011111101101111100011111000001, 
                          0b01011011001111111);

    printf("Example 2 \n");
    OUT = mm_select_bits_epi64(IN, MASK);
    printf("IN           ");print_sse_128_bin(IN);
    printf("MASK         ");print_sse_128_bin(MASK);
    printf("OUT          ");print_sse_128_bin(OUT);
    printf("\n\n");

    return 0;
}


int print_sse_128_bin(__m128i x){
    for (int i = 127; i >= 0; i--){
        printf("%1u", _mm_testnzc_si128(bit_128_k(i), x));
        if (((i & 7) == 0) && (i > 0)) printf(" ");
    }
    printf("\n");
    return 0;
}


/* From my answer here https://stackoverflow.com/a/39595704/2439725, adapted to 128-bit */
inline __m128i bit_128_k(unsigned int k){
  __m128i  indices     = _mm_set_epi32(96, 64, 32, 0);
  __m128i  one         = _mm_set1_epi32(1);

  __m128i  kvec        = _mm_set1_epi32(k);  
  __m128i  shiftcounts = _mm_sub_epi32(kvec, indices);
  __m128i  kbit        = _mm_sllv_epi32(one, shiftcounts);   
  return kbit;                             
}


/* Copied from Harold's answer https://stackoverflow.com/a/46318399/2439725         */
/* Adapted to epi64 and __m128i: bit reverse two 64 bit elements                    */
inline __m128i mm_bitreverse_epi64(__m128i x){
    __m128i shufbytes = _mm_setr_epi8(7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8); 
    __m128i luthigh = _mm_setr_epi8(0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15);
    __m128i lutlow = _mm_slli_epi16(luthigh, 4);
    __m128i lowmask = _mm_set1_epi8(15);
    __m128i rbytes = _mm_shuffle_epi8(x, shufbytes);
    __m128i high = _mm_shuffle_epi8(lutlow, _mm_and_si128(rbytes, lowmask));
    __m128i low = _mm_shuffle_epi8(luthigh, _mm_and_si128(_mm_srli_epi16(rbytes, 4), lowmask));
    return _mm_or_si128(low, high);
}


/* Add in the reverse direction: With a carry from left to */
/* right, instead of right to left                         */
inline __m128i mm_revadd_epi64(__m128i x, __m128i y){
    x = mm_bitreverse_epi64(x);
    y = mm_bitreverse_epi64(y);
    __m128i sum = _mm_add_epi64(x, y);
    return mm_bitreverse_epi64(sum);
}
/* End of SSE code */


/************* AVX2 code starts here ********************************************/

/*  gcc -O3 -m64 -Wall -march=skylake select_bits256.c    */
#include <immintrin.h>
#include <stdio.h>
#include <stdint.h>

int print_avx_256_bin(__m256i x);
__m256i bit_256_k(unsigned int k);
__m256i mm256_bitreverse_epi64(__m256i x);
__m256i mm256_revadd_epi64(__m256i x, __m256i y);


/* Select specific pieces of contiguous bits from `MASK` based on selector `IN`  */
__m256i mm256_select_bits_epi64(__m256i IN, __m256i MASK){
    __m256i IN_reduced   = _mm256_and_si256(IN, MASK);
    /* Compute the average of IN_reduced and MASK with avg(a,b)=(a&b)+((a^b)>>1)  */
    /* (IN_reduced & MASK) + ((IN_reduced ^ MASK) >>1) =                          */
    /* ((IN & MASK) & MASK) + ((IN_reduced ^ MASK) >>1) =                         */
    /* IN_reduced + ((IN_reduced ^ MASK) >>1)                                     */
    __m256i tmp          = _mm256_xor_si256(IN_reduced, MASK);
    __m256i tmp_div2     = _mm256_srli_epi64(tmp, 1);
    __m256i average      = _mm256_add_epi64(IN_reduced, tmp_div2);   /* average is the average */
    __m256i MASK_div2    = _mm256_srli_epi64(MASK, 1);
    __m256i leading_bits = _mm256_andnot_si256(MASK_div2, average);
    __m256i rev_added    = mm256_revadd_epi64(MASK, leading_bits);
    __m256i OUT          = _mm256_andnot_si256(rev_added, MASK);
    /* Uncomment the next lines to check the arithmetic */ /*   
    printf("IN           ");print_avx_256_bin(IN           );       
    printf("MASK         ");print_avx_256_bin(MASK         ); 
    printf("IN_reduced   ");print_avx_256_bin(IN_reduced   );       
    printf("tmp          ");print_avx_256_bin(tmp          );       
    printf("tmp_div2     ");print_avx_256_bin(tmp_div2     );       
    printf("average      ");print_avx_256_bin(average      );       
    printf("MASK_div2    ");print_avx_256_bin(MASK_div2    );       
    printf("leading_bits ");print_avx_256_bin(leading_bits );       
    printf("rev_added    ");print_avx_256_bin(rev_added    );       
    printf("OUT          ");print_avx_256_bin(OUT          );       
    printf("\n");*/
    return OUT;       
}


int main(){
    __m256i IN   = _mm256_set_epi64x(0b11111110011010110, 
                                     0b1100010010010100,
                                     0b1000001001001010000010000000100000010000000000100000000111100011, 
                                     0b11111110011010111
    );
    __m256i MASK = _mm256_set_epi64x(0b01011011001111110, 
                                     0b0001111010111011,
                                     0b1110011110101110111111000000000111011111101101111100011111000001, 
                                     0b01011011001111111);
    __m256i OUT;    

    printf("Example \n");
    OUT = mm256_select_bits_epi64(IN, MASK);
    printf("IN           ");print_avx_256_bin(IN);
    printf("MASK         ");print_avx_256_bin(MASK);
    printf("OUT          ");print_avx_256_bin(OUT);
    printf("\n");

    return 0;
}


int print_avx_256_bin(__m256i x){
    for (int i=255;i>=0;i--){
        printf("%1u",_mm256_testnzc_si256(bit_256_k(i),x));
        if (((i&7) ==0)&&(i>0)) printf(" ");
    }
    printf("\n");
    return 0;
}


/* From my answer here https://stackoverflow.com/a/39595704/2439725 */
inline __m256i bit_256_k(unsigned int k){
  __m256i  indices     = _mm256_set_epi32(224,192,160,128,96,64,32,0);
  __m256i  one         = _mm256_set1_epi32(1);

  __m256i  kvec        = _mm256_set1_epi32(k);  
  __m256i  shiftcounts = _mm256_sub_epi32(kvec, indices);
  __m256i  kbit        = _mm256_sllv_epi32(one, shiftcounts);   
  return kbit;                             
}


/* Copied from Harold's answer https://stackoverflow.com/a/46318399/2439725         */
/* Adapted to epi64: bit reverse four 64 bit elements                    */
inline __m256i mm256_bitreverse_epi64(__m256i x){
    __m256i shufbytes = _mm256_setr_epi8(7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8);
    __m256i luthigh = _mm256_setr_epi8(0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15, 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15);
    __m256i lutlow = _mm256_slli_epi16(luthigh, 4);
    __m256i lowmask = _mm256_set1_epi8(15);
    __m256i rbytes = _mm256_shuffle_epi8(x, shufbytes);
    __m256i high = _mm256_shuffle_epi8(lutlow, _mm256_and_si256(rbytes, lowmask));
    __m256i low = _mm256_shuffle_epi8(luthigh, _mm256_and_si256(_mm256_srli_epi16(rbytes, 4), lowmask));
    return _mm256_or_si256(low, high);
}


/* Add in the reverse direction: With a carry from left to */
/* right, instead of right to left                         */
inline __m256i mm256_revadd_epi64(__m256i x, __m256i y){
    x = mm256_bitreverse_epi64(x);
    y = mm256_bitreverse_epi64(y);
    __m256i sum = _mm256_add_epi64(x, y);
    return mm256_bitreverse_epi64(sum);
}

具有未注释的调试部分的 SSE 代码的输出：

Example 1 
IN           00000000 00000000 00000000 00000000 00000000 00000001 11111100 11010110 00000000 00000000 00000000 00000000 00000000 00000000 11000100 10010100
MASK         00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111110 00000000 00000000 00000000 00000000 00000000 00000000 00011110 10111011
IN_reduced   00000000 00000000 00000000 00000000 00000000 00000000 10110100 01010110 00000000 00000000 00000000 00000000 00000000 00000000 00000100 10010000
tmp          00000000 00000000 00000000 00000000 00000000 00000000 00000010 00101000 00000000 00000000 00000000 00000000 00000000 00000000 00011010 00101011
tmp_div2     00000000 00000000 00000000 00000000 00000000 00000000 00000001 00010100 00000000 00000000 00000000 00000000 00000000 00000000 00001101 00010101
average      00000000 00000000 00000000 00000000 00000000 00000000 10110101 01101010 00000000 00000000 00000000 00000000 00000000 00000000 00010001 10100101
MASK_div2    00000000 00000000 00000000 00000000 00000000 00000000 01011011 00111111 00000000 00000000 00000000 00000000 00000000 00000000 00001111 01011101
leading_bits 00000000 00000000 00000000 00000000 00000000 00000000 10100100 01000000 00000000 00000000 00000000 00000000 00000000 00000000 00010000 10100000
rev_added    00000000 00000000 00000000 00000000 00000000 00000000 01001001 00000001 00000000 00000000 00000000 00000000 00000000 00000000 00000001 01000111
OUT          00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111110 00000000 00000000 00000000 00000000 00000000 00000000 00011110 10111000

IN           00000000 00000000 00000000 00000000 00000000 00000001 11111100 11010110 00000000 00000000 00000000 00000000 00000000 00000000 11000100 10010100
MASK         00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111110 00000000 00000000 00000000 00000000 00000000 00000000 00011110 10111011
OUT          00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111110 00000000 00000000 00000000 00000000 00000000 00000000 00011110 10111000


Example 2 
IN           10000010 01001010 00001000 00001000 00010000 00000010 00000001 11100011 00000000 00000000 00000000 00000000 00000000 00000001 11111100 11010111
MASK         11100111 10101110 11111100 00000001 11011111 10110111 11000111 11000001 00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111111
IN_reduced   10000010 00001010 00001000 00000000 00010000 00000010 00000001 11000001 00000000 00000000 00000000 00000000 00000000 00000000 10110100 01010111
tmp          01100101 10100100 11110100 00000001 11001111 10110101 11000110 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000010 00101000
tmp_div2     00110010 11010010 01111010 00000000 11100111 11011010 11100011 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000001 00010100
average      10110100 11011100 10000010 00000000 11110111 11011100 11100100 11000001 00000000 00000000 00000000 00000000 00000000 00000000 10110101 01101011
MASK_div2    01110011 11010111 01111110 00000000 11101111 11011011 11100011 11100000 00000000 00000000 00000000 00000000 00000000 00000000 01011011 00111111
leading_bits 10000100 00001000 10000000 00000000 00010000 00000100 00000100 00000001 00000000 00000000 00000000 00000000 00000000 00000000 10100100 01000000
rev_added    00010000 01100001 00000010 00000001 11000000 01110000 00100000 00100000 00000000 00000000 00000000 00000000 00000000 00000000 01001001 00000000
OUT          11100111 10001110 11111100 00000000 00011111 10000111 11000111 11000001 00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111111

IN           10000010 01001010 00001000 00001000 00010000 00000010 00000001 11100011 00000000 00000000 00000000 00000000 00000000 00000001 11111100 11010111
MASK         11100111 10101110 11111100 00000001 11011111 10110111 11000111 11000001 00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111111
OUT          11100111 10001110 11111100 00000000 00011111 10000111 11000111 11000001 00000000 00000000 00000000 00000000 00000000 00000000 10110110 01111111