user manual

80 Replace Divides with Multiplies
AMD Athlon™ Processor x86 Code Optimization
22007E/0—November 1999
;algorithm 1
MOV EAX, m
MOV EDX, dividend
MOV ECX, EDX
IMUL EDX
ADD EDX, ECX
SHR ECX, 31
SAR EDX, s
ADD EDX, ECX ;quotient in EDX
Derivation for a, m, s The derivation for the algorithm (a), multiplier (m), and shift
count (s), is found in the section “Signed Derivation for
Algorithm, Multiplier, and Shift Factor” on page 95.
Signed Division By 2
;IN: EAX = dividend
;OUT:EAX = quotient
CMP EAX, 800000000h ;CY = 1, if dividend >=0
SBB EAX, –1 ;Increment dividend if it is < 0
SAR EAX, 1 ;Perform a right shift
Signed Division By 2
n
;IN:EAX = dividend
;OUT:EAX = quotient
CDQ ;Sign extend into EDX
AND EDX, (2^n–1) ;Mask correction (use divisor –1)
ADD EAX, EDX ;Apply correction if necessary
SAR EAX, (n) ;Perform right shift by
; log2 (divisor)
Signed Division By –2 ;IN:EAX = dividend
;OUT:EAX = quotient
CMP EAX, 800000000h ;CY = 1, if dividend >= 0
SBB EAX, –1 ;Increment dividend if it is < 0
SAR EAX, 1 ;Perform right shift
NEG EAX ;Use (x/–2) == –(x/2)
Signed Division By
–(2
n
)
;IN:EAX = dividend
;OUT:EAX = quotient
CDQ ;Sign extend into EDX
AND EDX, (2^n–1) ;Mask correction (–divisor –1)
ADD EAX, EDX ;Apply correction if necessary
SAR EAX, (n) ;Right shift by log2(–divisor)
NEG EAX ;Use (x/–(2^n)) == (–(x/2^n))
Remainder of Signed
Integer 2 or –2
;IN:EAX = dividend
;OUT:EAX = remainder
CDQ ;Sign extend into EDX
AND EDX, 1 ;Compute remainder
XOR EAX, EDX ;Negate remainder if
SUB EAX, EDX ;Dividend was < 0
MOV [remainder], EAX