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Replace Divides with Multiplies 79
22007E/0—November 1999 AMD Athlon™ Processor x86 Code Optimization
Example 1:
;In: EDX = dividend
;Out: EDX = quotient
XOR EDX, EDX;0
CMP EAX, d ;CF = (dividend < divisor) ? 1 : 0
SBB EDX, -1 ;quotient = 0+1-CF = (dividend < divisor) ? 0 : 1
In cases where the dividend does not need to be preserved, the
division can be accomplished without the use of an additional
register, thus reducing register pressure. This is shown in
example 2 below:
Example 2
:
;In: EDX = dividend
;Out: EAX = quotient
CMP EDX, d ;CF = (dividend < divisor) ? 1 : 0
MOV EAX, 0 ;0
SBB EAX, -1 ;quotient = 0+1-CF = (dividend < divisor) ? 0 : 1
Simpler Code for
Restricted Dividend
Integer division by a constant can be made faster if the range of
the dividend is limited, which removes a shift associated with
most divisors. For example, for a divide by 10 operation, use the
following code if the dividend is less than 40000005h:
MOV EAX, dividend
MOV EDX, 01999999Ah
MUL EDX
MOV quotient, EDX
Signed Division by Multiplication of Constant
Algorithm: Divisors
2 <= d < 2
31
These algorithms work if the divisor is positive. If the divisor is
negative, use abs(d) instead of d, and append a ‘NEG EDX’ to
the code. The code makes use of the fact that n/–d = –(n/d).
;IN: d = divisor, 2 <= d < 2^31
;OUT: a = algorithm
; m = multiplier
; s = shift count
;algorithm 0
MOV EAX, m
MOV EDX, dividend
MOV ECX, EDX
IMUL EDX
SHR ECX, 31
SAR EDX, s
ADD EDX, ECX ;quotient in EDX