By Constants; Shift Factor - AMD Athlon Processor x86 Optimization Manual

22007E/0—November 1999
Derivation of Multiplier Used for Integer Division by
Constants
Unsigned Derivation for Algorithm, Multiplier, and Shift Factor
Derivation of Multiplier Used for Integer Division by Constants
ADD EAX, EDX
MOV EDX, EDX
SHR EAX, 4
ADD EAX, EDX
AND EAX, 00F0F0F0Fh ;y = (x + (x >> 4) & 0x0F0F0F0F)
IMUL EAX, 001010101h ;y * 0x01010101
SHR EAX, 24
MOV retVal, EAX
}
return (retVal);
}
The utility udiv.exe was compiled using the code shown in this
section.
The following code derives the multiplier value used when
performing integer division by constants. The code works for
unsigned integer division and for odd divisors between 1 and
31
2 –1, inclusive. For divisors of the form d = d'*2
is the same as for d' and the shift factor is s + n.
/* Code snippet to determine algorithm (a), multiplier (m),
and shift factor (s) to perform division on unsigned 32-bit
integers by constant
Microsoft Visual C compiler. */
/*
In: d = divisor, 1 <= d < 2^31, d odd
Out: a = algorithm
m = multiplier
s = shift factor
;algorithm 0
MOV EDX, dividend
MOV EAX, m
MUL EDX
SHR EDX, s ;EDX=quotient
AMD Athlon™ Processor x86 Code Optimization
;x = (w & 0x33333333) + ((w >> 2) &
; 0x33333333)
;x
;x >> 4
;x + (x >> 4)
;population count = (y *
; 0x01010101) >> 24
;store result
divisor. Code is
n
, the multiplier
written for the
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