AMD x86 manual Bit field. Thus the following computation is performed

AMD Athlon™ Processor x86 Code Optimization 22007E/0 — November 1999

Step 3	For the first time, the value in each k-bit field is small enough
	that adding two k-bit fields results in a value that still fits in the
	k-bit field. Thus the following computation is performed:
	y = (x + (x >> 4)) & 0x0F0F0F0F
	The result is four 8-bit fields whose lower half has the desired
	sum and whose upper half contains "junk" that has to be
	masked out. In a symbolic form:
	x	= 0aaa0bbb0ccc0ddd0eee0fff0ggg0hhh
	x >> 4 = 00000aaa0bbb0ccc0ddd0eee0fff0ggg
	sum	= 0aaaWWWWiiiiXXXXjjjjYYYYkkkkZZZZ
	The WWWW, XXXX, YYYY, and ZZZZ values are the
	interesting sums with each at most 1000b, or 8 decimal.
Step 4	The four 4-bit sums can now be rapidly accumulated by means

of a multiply with a "magic" multiplier. This can be derived from looking at the following chart of partial products:

0p0q0r0s * 01010101 =

:0p0q0r0s

0p:0q0r0s

0p0q:0r0s

0p0q0r:0s

000pxxww:vvuutt0s

Here p, q, r, and s are the 4-bit sums from the previous step, and

vvis the final result in which we are interested. Thus, the final result:

z = (y * 0x01010101) >> 24

Example:

unsigned int popcount(unsigned int v)

{

unsigned int retVal;
__asm	{
MOV	EAX, [v]	;v
MOV	EDX, EAX	;v
SHR	EAX, 1	;v >> 1
AND	EAX, 055555555h	;(v >> 1) & 0x55555555
SUB	EDX, EAX	;w = v - ((v >> 1) & 0x55555555)
MOV	EAX, EDX	;w
SHR	EDX, 2	;w >> 2
AND	EAX, 033333333h	;w & 0x33333333
AND	EDX, 033333333h	;(w >> 2) & 0x33333333

92 Efficient Implementation of Population Count Function