AMD Athlon Processor x86 Optimization Manual page 96

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