Working with ‘bits’
Some observations on using x86
bit-manipulations
Twos-complement extension
• The following are legal statements in C:
char
short
int
c = -5;
s = c;
i = s;
• They illustrate ‘type promotions’ of signed
integers having different storage widths
11111111 11111011
16-bits
‘sign-extension’
11111011
8-bits
The byte’s sign-bit is replicated throughout in the upper portion of the word
Sign-Extensions
• The x86 processor provides some special
instructions for integer type-promotions:
•
•
•
•
•
•
CBW:
CWDE:
CDQE:
CWD:
CDQ:
CQO:
– movsx
– movzx
AX  sign-extension of AL
EAX  sign-extension of AX
RAX  sign-extension of EAX
DX:AX  sign-extension of AX
EDX:EAX  sign-extension of EAX
RDX:RAX  sign-extension of RDX
sign-extends source to destination
zero-extends source to destination
Absolute value (naïve version)
• Here is an amateur’s way of computing |x|
in assembly language (test-and-branch):
#
# Replaces the signed integer in RAX with its absolute value
#
abs:
cmp
$0, %rax
# is the value less than zero?
jge
isok
# no, leave value unchanged
neg
%rax
# otherwise negate the value
isok:
ret
# return absolute value in RAX
• But jumps flush the CPUs prefetch queue!
Absolute value (smart version)
• Here is a professional’s way of computing
|x| in assembly language (no branching):
#
# Replaces the signed integer in RAX with its absolute value
#
abs:
cqo
# sign-extend RAX to RDX:RAX
xor
%rdx, %rax
# maybe flips all the bits in RAX
sub
%rdx, %rax
# maybe subtracts -1 from RAX
ret
# return absolute value in RAX
• No effect on positive integers, but ‘flips the
bits and adds one’ for negative integers
Boolean operations
&
0
1
|
0
1
^
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
AND
OR
XOR
~
0
1
1
0
NOT
Propositional Logic
P && Q
P || Q
!P
Assignment Operators
P &= Q
P |= Q
P ^= Q
Examples
0
1
1
0
1
1
0
0
0
1
1
AND
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
OR
1
0
1
1
1
0
equals
0
0
0
0
equals
1
0
0
1
1
1
0
1
‘squares.s’
• We can compute the ‘square’ of an integer
without using any multiplication operations
(N+1)2 = N2 + N + N + 1