Reverse Engineering challenge #4.

What does this code do?

Some versions have the 0x1010101 constant, some do not. Why?

Optimizing GCC 4.8.2:

   0:          mov    edx,edi
   2:          shr    edx,1
   4:          and    edx,0x55555555
   a:          sub    edi,edx
   c:          mov    eax,edi
   e:          shr    edi,0x2
  11:          and    eax,0x33333333
  16:          and    edi,0x33333333
  1c:          add    edi,eax
  1e:          mov    eax,edi
  20:          shr    eax,0x4
  23:          add    eax,edi
  25:          and    eax,0xf0f0f0f
  2a:          imul   eax,eax,0x1010101
  30:          shr    eax,0x18
  33:          ret

Optimizing GCC 4.9.3 for ARM64:

   0:           lsr     w1, w0, #1
   4:           and     w1, w1, #0x55555555
   8:           sub     w0, w0, w1
   c:           and     w1, w0, #0x33333333
  10:           lsr     w0, w0, #2
  14:           and     w0, w0, #0x33333333
  18:           add     w0, w0, w1
  1c:           mov     w1, #0x1010101                  // #16843009
  20:           add     w0, w0, w0, lsr #4
  24:           and     w0, w0, #0xf0f0f0f
  28:           mul     w0, w0, w1
  2c:           lsr     w0, w0, #24
  30:           ret

(ARM) Optimizing Keil 5.05 (ARM mode):

        LDR      r1,|L0.148|
        AND      r1,r1,r0,LSR #1
        SUB      r0,r0,r1
        LDR      r1,|L0.152|
        AND      r2,r0,r1
        AND      r0,r1,r0,LSR #2
        LDR      r1,|L0.156|
        ADD      r0,r0,r2
        ADD      r0,r0,r0,LSR #4
        AND      r0,r0,r1
        ADD      r0,r0,r0,LSL #16
        ADD      r0,r0,r0,LSL #8
        LSR      r0,r0,#24
        BX       lr

        DCD      0x55555555
        DCD      0x33333333
        DCD      0x0f0f0f0f

(ARM) Optimizing Keil 5.05 (Thumb mode):

        LSRS     r1,r0,#1
        LDR      r2,|L0.100|
        ANDS     r1,r1,r2
        SUBS     r0,r0,r1
        LDR      r1,|L0.104|
        MOVS     r2,r0
        LSRS     r0,r0,#2
        ANDS     r2,r2,r1
        ANDS     r0,r0,r1
        ADDS     r0,r2,r0
        LSRS     r1,r0,#4
        ADDS     r0,r1,r0
        LDR      r1,|L0.108|
        ANDS     r0,r0,r1
        LDR      r1,|L0.112|
        MULS     r0,r1,r0
        LSRS     r0,r0,#24
        BX       lr

        DCD      0x55555555
        DCD      0x33333333
        DCD      0x0f0f0f0f
        DCD      0x01010101

Optimizing GCC 4.4.5 for MIPS:

        li      $2,1431633920                   # 0x55550000
        srl     $3,$4,1
        ori     $2,$2,0x5555
        and     $2,$3,$2
        subu    $4,$4,$2
        li      $3,858980352                    # 0x33330000
        ori     $3,$3,0x3333
        srl     $2,$4,2
        and     $2,$2,$3
        and     $3,$4,$3
        addu    $2,$2,$3
        srl     $3,$2,4
        addu    $2,$3,$2
        li      $3,252641280                    # 0xf0f0000
        ori     $3,$3,0xf0f
        and     $2,$2,$3
        sll     $3,$2,8
        addu    $2,$3,$2
        sll     $3,$2,16
        addu    $2,$2,$3
        j       $31
        srl     $2,$2,24 

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