AMD 250 Signed Division by 2n, Signed Division by -2n, Remainder of Signed Division by 2 or, 163

25112 Rev. 3.06 September 2005 Software Optimization Guide for AMD64 Processors

Signed Division by 2n

;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, 80000000h		; CF = 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 –(2n)

;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 Division by 2 or –2

;In: EAX = dividend

;Out: EAX = remainder

cdq	; Sign extend into		EDX.
and eax, 1	; Compute remainder.
xor eax, edx	;	Negate remainder	if
sub eax, edx	;	dividend was < 0.

Remainder of Signed Division by 2n or –(2n)

;In: EAX = dividend

;Out: EAX = remainder

cdq	; Sign extend into EDX.
and edx, (2^n - 1)	; Mask		correction (abs(divisor) - 1)
add eax, edx	; Apply pre-correction.
and eax, (2^n - 1)	;	Mask	out remainder (abs(divisor) - 1)
sub eax, edx	;	Apply pre-correction if necessary.

Chapter 8 Integer Optimizations 163