Re^7: [OT] The interesting problem of comparing bit-strings.

[salva]

The idea is that for long needles, you can discard their borders (the unaligned bits), search for the middle string using some efficient algorithm and only when it matches, check the borders.

update: oh, and BTW, I was not endorsing sundialsvc4 response, just stating that this time, besides all his typical non-sense there may actually be also some insight.

[BrowserUk]

The idea is that for long needles, you can discard their borders (the unaligned bits), search for the middle string using some efficient algorithm and only when it matches, check the borders

I get that. But even then, there is not "the middle bit", but rather 'eight middle bits' (and upto 7 different unaligned bits, at either end):

haystack:                                                             
+                            *      *       *      *
          1         2         3         4         5         6         
+7         8         9         0         1         2
0123456789012345678901234567890123456789012345678901234567890123456789
+0123456789012345678901234567890123456789012345678901234567
1111000101001010110110101100101011101001010100010111100010011001010100
+0111111111001000000011100100100111011100100100111000110111
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
 bbbbbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmme
  bbbbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmee
   bbbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmeee
    bbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmeeee
     bbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmeeeee
      bbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmeeeeee
       bmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmeeeeee
+e
        mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+m
         bbbbbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+me
          bbbbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+mee
           bbbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+meee
            bbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+meeee
             bbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+meeeee
              bbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+meeeeee
               bmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+meeeeeee
                mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
+mmmmmmmmm
...

Note that the "aligned middle bits" are different every bit offset, cycling every 8 bits.

Of course the same problem occurs with 64-bit units, but rotating the 64-bit units using 64, single instruction, 128-bit shiftlefts, is far more efficient than doing 64 x 8 x 16-bit shifts to achieve the same thing.