02 Bits Ints

7/18/2019 02 Bits Ints

http://slidepdf.com/reader/full/02-bits-ints 1/79

Carnegie Mellon

1

!"#$% !'#($% )*+ ,*#(-(.$

!"#$!%& ()*+,-./0,) *, 1,23.*4+ 567*427 $)- 84/*.+49 :.;< $=9 $>!>

,*$#./0#1.$2

?@)-6 A+6@)* @)- B@C4 DEF@GG@+,)

7/18/2019 02 Bits Ints


Carnegie Mellon

2

31+)'2 !"#$% !'#($% )*+ ,*#(-(.$

! 4(5.($(*6*- "*71.8)61* )$ 9"#$

! !"#:;(<(; 8)*"5/;)61*$

! ,*#(-(.$

! ?43+474)*@0,)& .)7H;)4- @)- 7H;)4-

!

1,)C4+7H,)9 /@70);

! IJ3@)-H);9 *+.)/@0);

! :--H0,)9 )4;@0,)9 2.G03GH/@0,)9 7KHLH);

! =/88).'

7/18/2019 02 Bits Ints


Carnegie Mellon

3

!"*).' 4(5.($(*#)61*$

0.0V

0.5V

2.8V

3.3V

0 1 0

7/18/2019 02 Bits Ints


Carnegie Mellon

4

>*01+"*- !'#( ?);/($

! !'#( @ A 9"#$

! AH)@+6 >>>>>>>>$ *, !!!!!!!!$

! B4/H2@G& >!> *, $""!>

! F4J@-4/H2@G >>!= *, MM!=

!

A@74 != ).2N4+ +43+474)*@0,)

! O74 /K@+@/*4+7 P>E *, PQE @)- P:E *, PME

! R+H*4 M:!B%SA!= H) 1 @7

T >JM:!B%SA

T >JU@!-%SN

0 0 00001 1 00012 2 00103 3 0011

4 4 01005 5 01016 6 01107 7 01118 8 10009 9 1001A 10 1010B 11 1011

C 12 1100D 13 1101E 14 1110F 15 1111

7/18/2019 02 Bits Ints


Carnegie Mellon

5

!'#(:B."(*#(+ C(81.' B.-)*"D)61*

! E.1-.)8$ 4(7(. #1 ?".#/); F++.($$($! 1,)/43*.@GG6 C4+6 G@+;4 @++@6 ,U N6*47

! :/*.@GG6 H23G424)*4- VH*K KH4+@+/K6 ,U -HW4+4)* 242,+6 *6347

! 567*42 3+,CH-47 @--+477 73@/4 3+HC@*4 *, 3@+0/.G@+ X3+,/477Y

! Z+,;+@2 N4H); 4J4/.*4-

!

Z+,;+@2 /@) /G,NN4+ H*7 ,V) -@*@9 N.* ),* *K@* ,U ,*K4+7

! G185";(. H 4/*:3"8( ='$#(8 G1*#.1; F;;10)61*

! RK4+4 -HW4+4)* 3+,;+@2 ,N[4/*7 7K,.G- N4 7*,+4-

! :GG @GG,/@0,) VH*KH) 7H);G4 CH+*.@G @--+477 73@/4

• • •

7/18/2019 02 Bits Ints


Carnegie Mellon

6

C)0I"*( J1.+$

! C)0I"*( K)$ LJ1.+ ="D(M

! \,2H)@G 7H]4 ,U H)*4;4+#[email protected] -@*@

! ()/G.-H); @--+47747

! ^,7* /.++4)* 2@/KH)47 .74 %$ NH*7 _` N6*47a V,+-7

!

8H2H*7 @--+47747 *, `bA

! A4/,2H); *,, 72@GG U,+ 242,+6#H)*4)7HC4 @33GH/@0,)7

! FH;K#4)- 767*427 .74 =` NH*7 _c N6*47a V,+-7

! Z,*4)0@G @--+477 73@/4 d !<c e !>!Q N6*47

! Jc=#=` 2@/KH)47 7.33,+* `c#NH* @--+47747& $"= f4+@N6*47

!

^@/KH)47 7.33,+* 2.G03G4 -@*@ U,+2@*7

! M+@/0,)7 ,+ 2.G03G47 ,U V,+- 7H]4

! :GV@67 H)*4;+@G ).2N4+ ,U N6*47

7/18/2019 02 Bits Ints


Carnegie Mellon

7

J1.+:B."(*#(+ C(81.' B.-)*"D)61*

! F++.($$($ =5(0"7' !'#(

N10)61*$

! :--+477 ,U g+7* N6*4 H) V,+-

! :--+47747 ,U 7.//477HC4 V,+-7 -HW4+

N6 ` _%$#NH*a ,+ c _=`#NH*a

0000

0001

0002

0003

0004

0005

0006

0007

0008

00090010

0011

32-bit Words

Bytes Addr.

0012

0013

0014

0015

64-bit Words

Addr

=

??

Addr

=

??

Addr

=

??

Addr

=

??

Addr

=

??

Addr

=

??

0000

0004

0008

0012

0000

0008

7/18/2019 02 Bits Ints


Carnegie Mellon

8

O)#) 4(5.($(*#)61*$

C Data Type Typical 32-bit Intel IA32 x86-64

char 1 1 1

short 2 2 2

int 4 4 4

long 4 4 8

long long 8 8 8

float 4 4 4

double 8 8 8

long double 8 10/12 10/16

pointer 4 4 8

7/18/2019 02 Bits Ints


Carnegie Mellon

9

!'#( B.+(."*-

! K1P $I1/;+ 9'#($ P"#I"* ) 8/;6:9'#( P1.+ 9( 1.+(.(+ "*

8(81.'Q

! G1*<(*61*$

! AH; I)-H@)& 5.)9 ZZ1 ^@/9 ()*4+)4*

!

84@7* 7H;)Hg/@)* N6*4 K@7 KH;K47* @--+477

! 8HhG4 I)-H@)& Jc=

! 84@7* 7H;)Hg/@)* N6*4 K@7 G,V47* @--+477

7/18/2019 02 Bits Ints


Carnegie Mellon

10

!'#( B.+(."*- >R)85;(

! !"- >*+")*

! 84@7* 7H;)Hg/@)* N6*4 K@7 KH;K47* @--+477

! N"S;( >*+")*

! 84@7* 7H;)Hg/@)* N6*4 K@7 G,V47* @--+477

! >R)85;(

! i@+H@NG4 J K@7 `#N6*4 +43+474)*@0,) >J>!$%`"=S

! :--+477 ;HC4) N6 jJ H7 >J!>>

0x100 0x101 0x102 0x10301 23 45 67

0x100 0x101 0x102 0x103

67 45 23 01

Big Endian

Little Endian

01 23 45 67

67 45 23 01

7/18/2019 02 Bits Ints


Carnegie Mellon

11

Address Instruction Code Assembly Rendition

8048365: 5b pop %ebx8048366: 81 c3 ab 12 00 00 add $0x12ab,%ebx

804836c: 83 bb 28 00 00 00 00 cmpl $0x0,0x28(%ebx)

4()+"*- !'#(:4(<(.$(+ N"$6*-$

! O"$)$$(89;'

! f4J* +43+474)*@0,) ,U NH)@+6 2@/KH)4 /,-4

! b4)4+@*4- N6 3+,;+@2 *K@* +4@-7 *K4 2@/KH)4 /,-4

!

>R)85;( T.)-8(*#

! O(0"5I(."*- U/89(.$

!

[email protected]& 0x12ab

! Z@- *, %$ NH*7& 0x000012ab

! 53GH* H)*, N6*47& 00 00 12 ab

! ?4C4+74& ab 12 00 00

7/18/2019 02 Bits Ints


Carnegie Mellon

12

>R)8"*"*- O)#) 4(5.($(*#)61*$

! G1+( #1 E."*# !'#( 4(5.($(*#)61* 17 O)#)

! 1@70); 3,H)*4+ *, .)7H;)4- /K@+ k /+4@*47 N6*4 @++@6

Printf directives:

%p: Print pointer

%x: Print Hexadecimal

typedef unsigned char *pointer;

void show_bytes(pointer start, int len){int i;for (i = 0; i < len; i++) printf(”%p\t0x%.2x\n",start+i, start[i]);

printf("\n");}

7/18/2019 02 Bits Ints


Carnegie Mellon

13

show_bytes >R(0/61* >R)85;(

int a = 15213;

printf("int a = 15213;\n");

show_bytes((pointer) &a, sizeof(int));

Result (Linux):

int a = 15213;

0x11ffffcb8 0x6d

0x11ffffcb9 0x3b

0x11ffffcba 0x00

0x11ffffcbb 0x00

7/18/2019 02 Bits Ints


Carnegie Mellon

14

4(5.($(*6*- ,*#(-(.$Decimal: 15213

Binary: 0011 1011 0110 1101

Hex: 3 B 6 D

6D

3B00

00

IA32, x86-64

3B

6D

00

00

Sun

int A = 15213;

93

C4

FF

FF

IA32, x86-64

C4

93

FF

FF

Sun

Two"s complement representation

(Covered later)

int B = -15213;

long int C = 15213;

00

00

0000

6D3B

00

00

x86-64

3B

6D

0000

Sun

6D3B

00

00

IA32

7/18/2019 02 Bits Ints


Carnegie Mellon

15

4(5.($(*6*- E1"*#(.$

BHW4+4)* /,23HG4+7 j 2@/KH)47 @77H;) -HW4+4)* G,/@0,)7 *, ,N[4/*7

int B = -15213;

int *P = &B;

x86-64 Sun IA32

EF

FF

FB

2C

D4

F8

FF

BF

0C

89

EC

FF

FF

7F

00

00

7/18/2019 02 Bits Ints


Carnegie Mellon

16

4(5.($(*6*- =#."*-$

! =#."*-$ "* G

! ?43+474)*4- N6 @++@6 ,U /K@+@/*4+7

! I@/K /K@+@/*4+ 4)/,-4- H) :51(( U,+2@*

! 5*@)-@+- S#NH* 4)/,-H); ,U /K@+@/*4+ 74*

!

1K@+@/*4+ X>Y K@7 /,-4 >J%>

T BH;H* H K@7 /,-4 >J%>lH

! 5*+H); 7K,.G- N4 ).GG#*4+2H)@*4-

! MH)@G /K@+@/*4+ m >

! G185)69";"#'

!

A6*4 ,+-4+H); ),* @) H77.4

Linux/Alpha Sun

31

38

32

34

33

00

31

38

32

34

33

00

7/18/2019 02 Bits Ints


Carnegie Mellon

17

31+)'2 !"#$% !'#($% )*+ ,*#(-(.$

! 4(5.($(*6*- "*71.8)61* )$ 9"#$

! !"#:;(<(; 8)*"5/;)61*$

! ,*#(-(.$

! ?43+474)*@0,)& .)7H;)4- @)- 7H;)4-

!

1,)C4+7H,)9 /@70);

! IJ3@)-H);9 *+.)/@0);

! :--H0,)9 )4;@0,)9 2.G03GH/@0,)9 7KHLH);

! =/88).'

7/18/2019 02 Bits Ints


Carnegie Mellon

18

!11;()* F;-(9.)

! O(<(;15(+ 9' V(1.-( !11;( "* WX#I G(*#/.'

! :G;4N+@H/ +43+474)*@0,) ,U G,;H/

! I)/,-4 Xf+.4Y @7 ! @)- XM@G74Y @7 >

:)-

" :jA m ! VK4) N,*K :m! @)- Am!

D+

" :nA m ! VK4) 4H*K4+ :m! ,+ Am!

\,*" o: m ! VK4) :m>

IJ/G.7HC4#D+ _e,+a" :pA m ! VK4) 4H*K4+ :m! ,+ Am!9 N.* ),* N,*K

7/18/2019 02 Bits Ints


Carnegie Mellon

19

F55;"0)61* 17 !11;()* F;-(9.)

! F55;"(+ #1 O"-"#); ='$#(8$ 9' G;)/+( =I)**1*

! !Q%S ^(f ^@7*4+E7 fK47H7

! ?4@7,) @N,.* )4*V,+q7 ,U +4G@6 7VH*/K47

! I)/,-4 /G,74- 7VH*/K @7 !9 ,34) 7VH*/K @7 >

A

~A

~B

B

Connection when

A&~B | ~A&B

A&~B

~A&B = A^B

7/18/2019 02 Bits Ints


Carnegie Mellon

20

V(*(.); !11;()* F;-(9.)$

! B5(.)#( 1* !"# ?(0#1.$

! D34+@0,)7 @33GH4- NH*VH74

! F;; 17 #I( E.15(.6($ 17 !11;()* F;-(9.) F55;'

01101001

& 01010101

01000001

01101001

| 01010101

01111101

01101001

^ 01010101

00111100

~ 01010101

1010101001000001 01111101 00111100 10101010

7/18/2019 02 Bits Ints


Carnegie Mellon

21

4(5.($(*6*- Y C)*"5/;)6*- =(#$

! 4(5.($(*#)61*

! RH-*K V NH* C4/*,+ +43+474)*7 7.N74*7 ,U r>9 s9 VT!t

! @[ m ! HU [ :

!

>!!>!>>! r >9 %9 "9 = t! ! "#$%&'(

! >!>!>!>! r >9 $9 ̀ 9 = t

! ! "#$%&'(

! B5(.)61*$! j ()*4+74/0,) >!>>>>>! r >9 = t

! n O)H,) >!!!!!>! r >9 $9 %9 ̀ 9 "9 = t

! p 56224*+H/ -HW4+4)/4 >>!!!!>> r $9 %9 ̀ 9 " t

! o 1,23G424)* !>!>!>!> r !9 %9 "9 S t

7/18/2019 02 Bits Ints


Carnegie Mellon

22

!"#:N(<(; B5(.)61*$ "* G

! B5(.)61*$ % |% ~% ^ F<)";)9;( "* G

! :33G6 *, @)6 XH)*4;+@GY -@*@ *634

! long, int, short, char, unsigned

! iH4V @+;.24)*7 @7 NH* C4/*,+7

!

:+;.24)*7 @33GH4- NH*#VH74! >R)85;($ ZGI). +)#) #'5([

! ~0x41 ! 0xBE

! ~010000012 ! 101111102

! ~0x00 ! 0xFF

!

~000000002 !

111111112

! 0x69 & 0x55 ! 0x41

! 011010012 & 010101012 ! 010000012

! 0x69 | 0x55 ! 0x7D

! 011010012 | 010101012 ! 011111012

7/18/2019 02 Bits Ints


Carnegie Mellon

23

G1*#.)$#2 N1-"0 B5(.)61*$ "* G

! G1*#.)$# #1 N1-"0); B5(.)#1.$

! &&, ||, !

! iH4V > @7 XM@G74Y

! :)6*KH); ),)]4+, @7 Xf+.4Y

!

:GV@67 +4*.+) > ,+ !! I@+G6 *4+2H)@0,)

!

>R)85;($ Z0I). +)#) #'5([! !0x41 ! 0x00

! !0x00 ! 0x01

!

!!0x41 ! 0x01

! 0x69 && 0x55 ! 0x01

! 0x69 || 0x55 ! 0x01

! p && *p _@C,H-7 ).GG 3,H)*4+ @//477a

7/18/2019 02 Bits Ints


Carnegie Mellon

24

=I"\ B5(.)61*$

! N(\ =I"\2 x << y

! 5KHL NH*#C4/*,+ x G4L y 3,7H0,)7

T fK+,V @V@6 4J*+@ NH*7 ,) G4L

! MHGG VH*K 0E7 ,) +H;K*

! 4"-I# =I"\2

x >> y

! 5KHL NH*#C4/*,+ x +H;K* y 3,7H0,)7

! fK+,V @V@6 4J*+@ NH*7 ,) +H;K*

! 8,;H/@G 7KHL

! MHGG VH*K 0E7 ,) G4L

!

:+H*K240/ 7KHL

! ?43GH/@*4 2,7* 7H;)Hg/@)* NH* ,) +H;K*

! ]*+(^*(+ !(I)<"1.

! 5KHL @2,.)* u > ,+ v V,+- 7H]4

01100010Argument x

00010000<< 3

00011000Log. >> 2

00011000Arith.

>> 2

10100010Argument x

00010000<< 3

00101000Log. >> 2

11101000Arith. >> 2

0001000000010000

0001100000011000

0001100000011000

00010000

00101000

11101000

00010000

00101000

11101000

7/18/2019 02 Bits Ints


Carnegie Mellon

25

31+)'2 !"#$% !'#($% )*+ ,*#(-(.$

! 4(5.($(*6*- "*71.8)61* )$ 9"#$

! !"#:;(<(; 8)*"5/;)61*$

! ,*#(-(.$

! 4(5.($(*#)61*2 /*$"-*(+ )*+ $"-*(+

!

1,)C4+7H,)9 /@70);

! IJ3@)-H);9 *+.)/@0);

! :--H0,)9 )4;@0,)9 2.G03GH/@0,)9 7KHLH);

! =/88).'

7/18/2019 02 Bits Ints


Carnegie Mellon

26

>*01+"*- ,*#(-(.$

short int x = 15213;short int y = -15213;

! G short _ 9'#($ ;1*-

! ="-* !"#

!

M,+ $E7 /,23G424)*9 2,7* 7H;)Hg/@)* NH* H)-H/@*47 7H;)

! > U,+ ),))4;@0C4

! ! U,+ )4;@0C4

]*$"-*(+ 3P1 $̀ G185;(8(*#

="-*

!"#

7/18/2019 02 Bits Ints


Carnegie Mellon

27

>*01+"*- >R)85;( ZG1*#a[x = 15213: 00111011 01101101y = -15213: 11000100 10010011

7/18/2019 02 Bits Ints


Carnegie Mellon

28

U/8(."0 4)*-($

! ]*$"-*(+ ?);/($

! *+,- m >

>>>s>

! *+./ m $0 T !

!!!s!

! 3P1`$ G185;(8(*# ?);/($

! 1+,- m T$0 T!

!>>s>

! 1+./ m $0 T! T !

>!!s!

! B#I(. ?);/($

! ^H).7 !

!!!s!

?);/($ 71. ! @ Wb

7/18/2019 02 Bits Ints


Carnegie Mellon

29

?);/($ 71. O"c(.(*# J1.+ ="D($

! B9$(.<)61*$

! n1+,- n m 1+./ l !

! :76224*+H/ +@);4

! *+./ m $ k 1+./ l !

! G E.1-.)88"*-

! wH)/G.-4 uGH2H*7<Kx

! B4/G@+47 /,)7*@)*79 4<;<9

! O8D\by^:e

! 8D\by^:e

! 8D\by^(\

! [email protected] 3G@z,+2 734/Hg/

7/18/2019 02 Bits Ints


Carnegie Mellon

30

]*$"-*(+ Y ="-*(+ U/8(."0 ?);/($

! >d/"<);(*0(! 5@24 4)/,-H);7 U,+ ),))4;@0C4

[email protected]

! ]*"d/(*($$

! IC4+6 NH* 3@h4+) +43+474)*7

.)H{.4 H)*4;4+ [email protected]! I@/K +43+474)*@NG4 H)*4;4+ K@7

.)H{.4 NH* 4)/,-H);

! G)* ,*<(.# C)55"*-$

! O$A_ / a m A$O#!_ / a

!

AH* 3@h4+) U,+ .)7H;)4-H)*4;4+

! f$A_ / a m A$f#!_ / a

! AH* 3@h4+) U,+ *V,E7 /,23

H)*4;4+

2 !_3Z # [!_]Z # [>>>> >

>>>! !

>>!> $

>>!! %

>!>> `

>!>! "

>!!> =

>!!! S

Tcc

TSQ

T=!>

T"!!

T`!$

T%!%

T$!`

T!!"

!>>>

!>>!

!>!>

!>!!

!!>>

!!>!

!!!>

!!!!

>

!

$

%

`

"

=

S

7/18/2019 02 Bits Ints


Carnegie Mellon

31

31+)'2 !"#$% !'#($% )*+ ,*#(-(.$

! 4(5.($(*6*- "*71.8)61* )$ 9"#$

! !"#:;(<(; 8)*"5/;)61*$

! ,*#(-(.$

! ?43+474)*@0,)& .)7H;)4- @)- 7H;)4-

!

G1*<(.$"1*% 0)$6*-

! IJ3@)-H);9 *+.)/@0);

! :--H0,)9 )4;@0,)9 2.G03GH/@0,)9 7KHLH);

! =/88).'

7/18/2019 02 Bits Ints


Carnegie Mellon

32

f$O

f$A A$O

3P1 $̀ G185;(8(*# ]*$"-*(+

^@H)*@H) 5@24 AH* Z@h4+)

x

ux

X

C)55"*- !(#P((* ="-*(+ Y ]*$"-*(+

O$f

O$A A$f

3P1 $̀ G185;(8(*#]*$"-*(+

^@H)*@H) 5@24 AH* Z@h4+)

ux

x

X

! C)55"*-$ 9(#P((* /*$"-*(+ )*+ #P1`$ 0185;(8(*# */89(.$2

e((5 9"# .(5.($(*#)61*$ )*+ .("*#(.5.(#

7/18/2019 02 Bits Ints


Carnegie Mellon

33

C)55"*- ="-*(+ ]*$"-*(+

0

1

2

3

4

5

6

7

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111

]_3

3_]

7/18/2019 02 Bits Ints


Carnegie Mellon

34

C)55"*- ="-*(+ ]*$"-*(+

0

1

2

3

4

5

6

7

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111

@

Hf: Wb

7/18/2019 02 Bits Ints


Carnegie Mellon

35

+ + + + + +• • •

- + + + + +• • •

ux

x

w –1 0

4(;)61* 9(#P((* ="-*(+ Y ]*$"-*(+

N).-( *(-)6<( P("-I#

3456748

N).-( 51$"6<( P("-I#

f$O

f$A A$O

3P1 $̀ G185;(8(*# ]*$"-*(+

^@H)*@H) 5@24 AH* Z@h4+)

x

ux

X

7/18/2019 02 Bits Ints


Carnegie Mellon

36

>

1+./

1+,-

T! T$

>

*+./*+./ T !

1+./1+./ l !

$E7 1,23G424)*

?@);4

O)7H;)4-?@);4

G1*<(.$"1* ?"$/);"D(+

! _`$ G185a#

]*$"-*(+

! D+-4+H); ()C4+7H,)

! \4;@0C4 # AH; Z,7H0C4

7/18/2019 02 Bits Ints


Carnegie Mellon

37

="-*(+ <$a ]*$"-*(+ "* G

! G1*$#)*#$

! A6 [email protected]* @+4 /,)7H-4+4- *, N4 7H;)4- H)*4;4+7

! O)7H;)4- HU K@C4 XOY @7 7.|J

0U, 4294967259U

!

G)$6*-! IJ3GH/H* /@70); N4*V44) 7H;)4- j .)7H;)4- 7@24 @7 O$f @)- f$O

int tx, ty;

unsigned ux, uy;

tx = (int) ux;

uy = (unsigned) ty;

! (23GH/H* /@70); @G7, ,//.+7 CH@ @77H;)24)*7 @)- 3+,/4-.+4 /@GG7

tx = ux;

uy = ty;

7/18/2019 02 Bits Ints


Carnegie Mellon

38

0 0U == /*$"-*(+

-1 0 < $"-*(+

-1 0U > /*$"-*(+

2147483647 -2147483648 > $"-*(+

2147483647U -2147483648 < /*$"-*(+

-1 -2 > $"-*(+

(unsigned) -1 -2 > /*$"-*(+

2147483647 2147483648U < /*$"-*(+

2147483647 (int) 2147483648U > $"-*(+

G)$6*- =/.5."$($!

>R5.($$"1* ><);/)61*

!

(U *K4+4 H7 @ 2HJ ,U .)7H;)4- @)- 7H;)4- H) 7H);G4 4J3+477H,)9

$%&'() *+,-($ %./,%0%1,2 0+$1 13 -'$%&'()

! ()/G.-H); /,23@+H7,) ,34+@0,)7 <% > % ==% <=% >=

! IJ@23G47 U,+9 m %$& 3C,U @ :_%Wgh%gAi%bgA % 3CFj @ _%Wgh%gAi%bgh

!

G1*$#)*#W G1*$#)*#_ 4(;)61* ><);/)61*> >O

#! >

#! >O

$!`S`c%=`S #$!`S`c%=`S#!

$!`S`c%=`SO #$!`S`c%=`S#!#! #$

_.)7H;)4-a#! #$

$!`S`c%=`S $!`S`c%=`cO

$!`S`c%=`S _H)*a $!`S`c%=`cO

7/18/2019 02 Bits Ints


Carnegie Mellon

39

G1+( =(0/."#' >R)85;(

! ="8";). #1 01+( 71/*+ "* T.((!=O`$ "85;(8(*#)61* 17

-(#5((.*)8(

! 3I(.( ).( ;(-"1*$ 17 $8).# 5(15;( #.'"*- #1 ^*+

</;*(.)9";"6($ "* 5.1-.)8$

/* Kernel memory region holding user-accessible data */#define KSIZE 1024char kbuf[KSIZE];

/* Copy at most maxlen bytes from kernel region to user buffer */int copy_from_kernel(void *user_dest, int maxlen) {

/* Byte count len is minimum of buffer size and maxlen */int len = KSIZE < maxlen ? KSIZE : maxlen; memcpy(user_dest, kbuf, len);return len;

}

7/18/2019 02 Bits Ints


Carnegie Mellon

40

3'5"0); ]$)-(




}

#define MSIZE 528

void getstuff() {char mybuf[MSIZE];copy_from_kernel(mybuf, MSIZE); printf(“%s\n”, mybuf);

}

7/18/2019 02 Bits Ints


Carnegie Mellon

41

C);"0"1/$ ]$)-(




}

#define MSIZE 528

void getstuff() {char mybuf[MSIZE];copy_from_kernel(mybuf, -MSIZE);. . .

}

/* Declaration of library function memcpy */void *memcpy(void *dest, void *src, size_t n);

7/18/2019 02 Bits Ints


Carnegie Mellon

42

=/88).'

G)$6*- ="-*(+ k ]*$"-*(+2 !)$"0 4/;($! !"# 5)S(.* "$ 8)"*#)"*(+

! !/# .("*#(.5.(#(+

!

G)* I)<( /*(R5(0#(+ (c(0#$2 )++"*- 1. $/9#.)06*- _P

! >R5.($$"1* 01*#)"*"*- $"-*(+ )*+ /*$"-*(+ "*#

! int H7 /@7* *, unsigned}}

7/18/2019 02 Bits Ints


Carnegie Mellon

43

31+)'2 !"#$% !'#($% )*+ ,*#(-(.$

! 4(5.($(*6*- "*71.8)61* )$ 9"#$

! !"#:;(<(; 8)*"5/;)61*$

! ,*#(-(.$

! ?43+474)*@0,)& .)7H;)4- @)- 7H;)4-

!

1,)C4+7H,)9 /@70);

! >R5)*+"*-% #./*0)6*-

! :--H0,)9 )4;@0,)9 2.G03GH/@0,)9 7KHLH);

! =/88).'

7/18/2019 02 Bits Ints


Carnegie Mellon

44

="-* >R#(*$"1*

! 3)$e2

! bHC4) 0 #NH* 7H;)4- H)*4;4+ /

! 1,)C4+* H* *, 0 l: #NH* H)*4;4+ VH*K 7@24 [email protected]

! 4/;(2

! ^@q4 : /,3H47 ,U 7H;) NH*&

! 2 $ m / 0 T! 9s9 / 0 T! 9 / 0 T! 9 / 0 T$ 9s9 / >

4 015"($ 17 C=!

• • • X

X $ • • • • • •

• • •

0

0:

7/18/2019 02 Bits Ints


Carnegie Mellon

45

="-* >R#(*$"1* >R)85;(

! G1*<(.6*- 7.18 $8);;(. #1 ;).-(. "*#(-(. +)#) #'5(

! G )/#18)60);;' 5(.71.8$ $"-* (R#(*$"1*

short int x = 15213;int ix = (int) x;short int y = -15213;int iy = (int) y;

Decimal Hex Binary

x 15213 3B 6D 00111011 01101101

ix 15213 00 00 3B 6D 00000000 00000000 00111011 01101101

y -15213 C4 93 11000100 10010011

iy -15213 FF FF C4 93 11111111 11111111 11000100 10010011

7/18/2019 02 Bits Ints


Carnegie Mellon

46

=/88).'2

>R5)*+"*-% 3./*0)6*-2 !)$"0 4/;($

! >R5)*+"*- Z(a-a% $I1.# "*# #1 "*#[

! O)7H;)4-& ]4+,7 @--4-

! 5H;)4-& 7H;) 4J*4)7H,)

!

A,*K 6H4G- 4J34/*4- +47.G*

!

3./*0)6*- Z(a-a% /*$"-*(+ #1 /*$"-*(+ $I1.#[

! O)7H;)4-~7H;)4-& NH*7 @+4 *+.)/@*4-

! ?47.G* +4H)*4+3+4*4-

! O)7H;)4-& 2,- ,34+@0,)

! 5H;)4-& 7H2HG@+ *, 2,-

! M,+ 72@GG ).2N4+7 6H4G-7 4J34/*4- N4K@CH,.+

7/18/2019 02 Bits Ints


Carnegie Mellon

47

31+)'2 !"#$% !'#($% )*+ ,*#(-(.$

! 4(5.($(*6*- "*71.8)61* )$ 9"#$

! !"#:;(<(; 8)*"5/;)61*$

! ,*#(-(.$

! ?43+474)*@0,)& .)7H;)4- @)- 7H;)4-

!

1,)C4+7H,)9 /@70);

! IJ3@)-H);9 *+.)/@0);

! F++"61*% *(-)61*% 8/;65;"0)61*% $I"\"*-

! =/88).'

7/18/2019 02 Bits Ints


Carnegie Mellon

48

U(-)61*2 G185;(8(*# Y ,*0.(8(*#

! G;)"82 T1;;1P"*- K1;+$ 71. _`$ G185;(8(*#

~x + 1 == -x

! G185;(8(*#

! DN74+C@0,)& ~x + x == 1111…111 == -1

! G185;(#( E.117Q

! > > ! > !! !J> ! ! > ! >> >oJl

! ! ! ! ! !! !#!

7/18/2019 02 Bits Ints


Carnegie Mellon

49

G185;(8(*# Y ,*0.(8(*# >R)85;($

R @ Wl_Wi

R @ m

7/18/2019 02 Bits Ints


Carnegie Mellon

50

]*$"-*(+ F++"61*

! =#)*+).+ F++"61* T/*061*

! (;),+47 /@++6 ,.*3.*

! ,85;(8(*#$ C1+/;). F."#I8(60

8 m O:--0 _; 9 < a m ; l < 2,- $0

• • •

• • •

u

v +

• • •u + v

• • •

f+.4 5.2& 0 l! NH*7

D34+@)-7&0 NH*7

BH7/@+- 1@++6& 0 NH*7 UAddw(u , v)

7/18/2019 02 Bits Ints


Carnegie Mellon

51

?"$/);"D"*- ZC)#I(8)60);[ ,*#(-(. F++"61*

! ,*#(-(. F++"61*

! `#NH* H)*4;4+7 ;9 <

! 1,23.*4 *+.4 7.2

:--`_; 9 < a

!

[email protected] H)/+4@74 GH)4@+G6VH*K ; @)- <

! M,+27 3G@)@+ 7.+U@/4

F++gZ- % * [

-

*

7/18/2019 02 Bits Ints


Carnegie Mellon

52

?"$/);"D"*- ]*$"-*(+ F++"61*

!

J.)5$ F.1/*+

! (U *+.4 7.2 v $0

! :* 2,7* ,)/4

>

$0

$0 l!

]F++gZ- % * [

-

*

3./( =/8

C1+/;). =/8

DC4+•,V

B<(.n1P

7/18/2019 02 Bits Ints


Carnegie Mellon

53

C)#I(8)60); E.15(.6($

! C1+/;). F++"61* T1.8$ )* 56(,%+' 783-/

! G;1$(+ .)-4+ @--H0,)

> & O:--0 _; 9 < a & $0 T!

! G188/#)6<(

O:--0 _; 9 < a m O:--0 _< 9 ;a! F$$10")6<(

O:--0 _= 9 O:--0 _; 9 < aa m O:--0 _O:--0 _= 9 ; a9 < a

! m H7 @--H0C4 H-4)0*6

O:--0 _; 9 >a m ;

!

IC4+6 4G424)* K@7 @--H0C4 "*<(.$(! 84* O1,230 _; a m $0 T ;

O:--0 _; 9 O1,230 _; aa m >

7/18/2019 02 Bits Ints


Carnegie Mellon

54

3P1`$ G185;(8(*# F++"61*

! 3F++ )*+ ]F++ I)<( ,+(*60); !"#:N(<(; !(I)<"1.

! 5H;)4- C7< .)7H;)4- @--H0,) H) 1&

int s, t, u, v;

s = (int) ((unsigned) u + (unsigned) v);t = u + v

! RHGG ;HC4 s == t

• • •

• • •

u

v

+

• • •u + v

• • •

f+.4 5.2& 0 l! NH*7

D34+@)-7&0 NH*7

BH7/@+- 1@++6& 0 NH*7 TAddw(u , v)

7/18/2019 02 Bits Ints


Carnegie Mellon

55

3F++ B<(.n1P

! T/*061*);"#'

! f+.4 7.2 +4{.H+47 0 l!

NH*7

! B+,3 ,W ^5A

!

f+4@* +42@H)H); NH*7 @7$E7 /,23< H)*4;4+

T$0 T! T!

T$0

>

$0 T!

$0 T!

3./( =/8

3F++ 4($/;#

W >>>s>

W >!!s!

m >>>s>

m !>>s>

m !!!s!

!>>s>

>>>s>

>!!s!

Z,7DC4+

\4;DC4+

7/18/2019 02 Bits Ints


Carnegie Mellon

56

?"$/);"D"*- _`$ G185;(8(*# F++"61*

! ?);/($

! `#NH* *V,E7 /,23<

! ?@);4 U+,2 #c *, lS

! J.)5$ F.1/*+! (U 7.2 ' $0 T!

! A4/,247 )4;@0C4

! :* 2,7* ,)/4

! (U 7.2 u T$0 T!

!

A4/,247 3,7H0C4

! :* 2,7* ,)/4

3F++gZ- % * [

-

*

E1$B<(.

U(-B<(.

7/18/2019 02 Bits Ints


Carnegie Mellon

57

GI).)0#(."D"*- 3F++

!

T/*061*);"#'

! f+.4 7.2 +4{.H+47 0 l! NH*7

! B+,3 ,W ^5A

! f+4@* +42@H)H); NH*7 @7 $E7

/,23< H)*4;4+

ZU(-B<(.[

ZE1$B<(.[

u

v

u > x >u >

x >

\4;@0C4 DC4+•,V

Z,7H0C4 DC4+•,V

3F++Z- % * [

2w

2w

7/18/2019 02 Bits Ints


Carnegie Mellon

58

C)#I(8)60); E.15(.6($ 17 3F++

! ,$181.5I"0 V.1/5 #1 /*$"-*(+$ P"#I ]F++

! f:--0 _; 9 < a m O$f_O:--0 _f$O_; a9 f$O_< aaa

! 5H)/4 N,*K K@C4 H-4)0/@G NH* 3@h4+)7

! 3P1`$ G185;(8(*# ]*+(. 3F++ T1.8$ ) V.1/5

! 1G,74-9 1,22.*@0C49 :77,/H@0C49 > H7 @--H0C4 H-4)0*6

! IC4+6 4G424)* K@7 @--H0C4 H)C4+74

7/18/2019 02 Bits Ints


Carnegie Mellon

59

C/;65;"0)61*

! G185/6*- >R)0# E.1+/0# 17 0 :9"# */89(.$ / % >

! IH*K4+ 7H;)4- ,+ .)7H;)4-

! 4)*-($

! O)7H;)4-& > € / k > € _$0 T !a $ m $$0 T $0 l! l !

!

O3 *, $0 NH*7! fV,E7 /,23G424)* 2H)& / k > v _T$0 T!ak_$0 T! T!a m T$$0 T$ l $0 T!

! O3 *, $0 T! NH*7

! fV,E7 /,23G424)* 2@J& / k > € _T$0 T!a $ m $$0 T$

! O3 *, $0 NH*79 N.* ,)G6 U,+ _1+,-0 a$

! C)"*#)"*"*- >R)0# 4($/;#$! R,.G- )44- *, q443 4J3@)-H); V,+- 7H]4 VH*K 4@/K 3+,-./* /,23.*4-

! B,)4 H) 7,LV@+4 N6 X@+NH*+@+6 3+4/H7H,)Y @+H*K240/ 3@/q@;47

C i

7/18/2019 02 Bits Ints


Carnegie Mellon

60

]*$"-*(+ C/;65;"0)61* "* G

! =#)*+).+ C/;65;"0)61* T/*061*

! (;),+47 KH;K ,+-4+ 0 NH*7

! ,85;(8(*#$ C1+/;). F."#I8(60

O^.G*0 _; 9 < a m ; < 2,- $0

• • •

• • •

u

v

*

• • •u · v

• • •

f+.4 Z+,-./*& $k0 NH*7

D34+@)-7&0 NH*7

BH7/@+-0 NH*7& 0 NH*7

UMultw(u , v)

• • •

C i M ll

7/18/2019 02 Bits Ints


Carnegie Mellon

61

G1+( =(0/."#' >R)85;( o_

! =]U jO4 ;"9.).'! RH-4G6 .74- GHN+@+6 U,+ *+@)7U4++H); -@*@ N4*V44) 2@/KH)47

void* copy_elements(void *ele_src[], int ele_cnt, size_t ele_size);

ele_src

8);;10Z(;(p0*# q (;(p$"D([

C i M ll

7/18/2019 02 Bits Ints


Carnegie Mellon

62

jO4 G1+(

void* copy_elements(void *ele_src[], int ele_cnt, size_t ele_size) {/** Allocate buffer for ele_cnt objects, each of ele_size bytes* and copy from locations designated by ele_src*/void *result = malloc(ele_cnt * ele_size);if (result == NULL)

/* malloc failed */return NULL;

void *next = result;int i;for (i = 0; i < ele_cnt; i++) {

/* Copy object i to destination */ memcpy(next, ele_src[i], ele_size);

/* Move pointer to next memory region */next += ele_size;

}return result;

}

C i M ll

7/18/2019 02 Bits Ints


Carnegie Mellon

63

jO4 ?/;*(.)9";"#'

! JI)# "72

! ele_cnt m $$> l !

! ele_size m `>Q= m $

!$

! :GG,/@0,) m ‚‚

! K1P 0)* , 8)e( #I"$ 7/*061* $(0/.(Q

8);;10Z(;(p0*# q (;(p$"D([

Carnegie Mellon

7/18/2019 02 Bits Ints


Carnegie Mellon

64

="-*(+ C/;65;"0)61* "* G

! =#)*+).+ C/;65;"0)61* T/*061*

! (;),+47 KH;K ,+-4+ 0 NH*7

! 5,24 ,U VKH/K @+4 -HW4+4)* U,+ 7H;)4-

C7< .)7H;)4- 2.G03GH/@0,)! 8,V4+ NH*7 @+4 *K4 7@24

• • •

• • •

u

v

*

• • •u · v

• • •

f+.4 Z+,-./*& $k0 NH*7

D34+@)-7&0 NH*7

BH7/@+-0 NH*7& 0 NH*7

TMultw(u , v)

• • •

Carnegie Mellon

7/18/2019 02 Bits Ints


Carnegie Mellon

65

E1P(.:17:_ C/;65;' P"#I =I"\

! B5(.)61*

! u << k ;HC47 u * 94

! A,*K 7H;)4- @)- .)7H;)4-

! >R)85;($

!

u << 3 == u * 8! u << 5 - u << 3 == u * 24

! ^,7* 2@/KH)47 7KHL @)- @-- U@7*4+ *K@) 2.G03G6

! 1,23HG4+ ;4)4+@*47 *KH7 /,-4 @.*,2@0/@GG6

• • •

0 0 1 0 0 0•••

u

2k

*u · 2k

f+.4 Z+,-./*&0 l: NH*7

D34+@)-7&0 NH*7

BH7/@+- : NH*7& 0 NH*7 UMultw(u , 2k )

•••

k

• • • 0 0 0•••

TMultw(u , 2k )

0 0 0••••••

Carnegie Mellon

7/18/2019 02 Bits Ints


Carnegie Mellon

66

leal (%eax,%eax,2), %eaxsall $2, %eax

G185";(+ C/;65;"0)61* G1+(

! G 0185";(. )/#18)60);;' -(*(.)#($ $I"\f)++ 01+( PI(*

8/;65;'"*- 9' 01*$#)*#

int mul12(int x){return x*12;

}

t <- x+x*2return t << 2;

G T/*061*

G185";(+ F."#I8(60 B5(.)61*$ >R5;)*)61*

Carnegie Mellon

7/18/2019 02 Bits Ints


Carnegie Mellon

67

]*$"-*(+ E1P(.:17:_ O"<"+( P"#I =I"\

! r/16(*# 17 ]*$"-*(+ 9' E1P(. 17 _! u >> k ;HC47

(

u / 94)

! O747 G,;H/@G 7KHL

0 0 1 0 0 0•••

u

2k

/

u / 2k BHCH7H,)&

D34+@)-7& •••

k

••• •••

•••0 0 0••• •••

( u / 2k ) •••?47.G*&

<

AH)@+6 Z,H)*

0

0 0 0•••0

Carnegie Mellon

7/18/2019 02 Bits Ints


Carnegie Mellon

68

shrl $3, %eax

G185";(+ ]*$"-*(+ O"<"$"1* G1+(

! ]$($ ;1-"0); $I"\ 71. /*$"-*(+

! T1. s)<) ]$(.$

! 8,;H/@G 7KHL V+Hh4) @7 >>>

unsigned udiv8(unsigned x){return x/8;

}

# Logical shiftreturn x >> 3;

G T/*061*

G185";(+ F."#I8(60 B5(.)61*$ >R5;)*)61*

Carnegie Mellon

7/18/2019 02 Bits Ints


Carnegie Mellon

69

="-*(+ E1P(.:17:_ O"<"+( P"#I =I"\

! r/16(*# 17 ="-*(+ 9' E1P(. 17 _! x >> k ;HC47

(

x / 94)

! O747 @+H*K240/ 7KHL

! ?,.)-7 V+,); -H+4/0,) VK4) u < 0

0 0 1 0 0 0••• x

2k

/

x / 2k

BHCH7H,)&

D34+@)-7&•••

k

••• •••

•••0 ••• •••

RoundDown( x / 2k ) •••?47.G*&

<

AH)@+6 Z,H)*

0 •••

Carnegie Mellon

7/18/2019 02 Bits Ints


Carnegie Mellon

70

G1..(0# E1P(.:17:_ O"<"+(

! r/16(*# 17 U(-)6<( U/89(. 9' E1P(. 17 _! R@)*

*

x / _4+

_?,.)- f,V@+- >a

! 1,23.*4 @7( (x+_4 -1)/ _4

)

! () 1& (x + (1<<k)-1) >> k

! AH@747 -HCH-4)- *,V@+- >

G)$( W2 U1 .1/*+"*-

BHCH7,+&

BHCH-4)-&

0 0 1 0 0 0•••

u

2k

/

* u / 2k +

•••

k

1 ••• 0 0 0•••

1 •••0 1 1••• <

AH)@+6 Z,H)*

1

0 0 0 1 1 1•••+2k –1

•••

1 1 1•••

1 ••• 1 1 1•••

:%+$%'& ;+$ '3 (<(01

Carnegie Mellon

7/18/2019 02 Bits Ints


g

71

G1..(0# E1P(.:17:_ O"<"+( ZG1*#a[

BHCH7,+&

BHCH-4)-&

G)$( _2 41/*+"*-

0 0 1 0 0 0•••

x

2k

/

* x / 2k +

•••

k

1 ••• •••

1 •••0 1 1••• <

AH)@+6 Z,H)*

1

0 0 0 1 1 1•••+2k –1

•••

1 ••• •••

:%+$%'& +))$ = 13 >'+, 8($-,1

•••

()/+424)*4- N6 !

()/+424)*4- N6 !

Carnegie Mellon

7/18/2019 02 Bits Ints


g

72

testl %eax, %eaxjs L4

L3:sarl $3, %eaxret

L4:addl $7, %eaxjmp L3

G185";(+ ="-*(+ O"<"$"1* G1+(

! ]$($ )."#I8(60 $I"\ 71. "*#

! T1. s)<) ]$(.$

! :+H*K< 7KHL V+Hh4) @7 >>

int idiv8(int x){return x/8;

}

if x < 0x += 7;

# Arithmetic shiftreturn x >> 3;

G T/*061*

G185";(+ F."#I8(60 B5(.)61*$ >R5;)*)61*

Carnegie Mellon

7/18/2019 02 Bits Ints


g

73

F."#I8(602 !)$"0 4/;($

! F++"61*2

! O)7H;)4-~7H;)4-& \,+2@G @--H0,) U,GG,V4- N6 *+.)/@*49

7@24 ,34+@0,) ,) NH* G4C4G

! O)7H;)4-& @--H0,) 2,- $V

! ^@*K42@0/@G @--H0,) l 3,77HNG4 7.N*+@/0,) ,U $V

!

5H;)4-& 2,-Hg4- @--H0,) 2,- $V _+47.G* H) 3+,34+ +@);4a

! ^@*K42@0/@G @--H0,) l 3,77HNG4 @--H0,) ,+ 7.N*+@/0,) ,U $V

! C/;65;"0)61*2

!

O)7H;)4-~7H;)4-& \,+2@G 2.G03GH/@0,) U,GG,V4- N6 *+.)/@*497@24 ,34+@0,) ,) NH* G4C4G

! O)7H;)4-& 2.G03GH/@0,) 2,- $V

! 5H;)4-& 2,-Hg4- 2.G03GH/@0,) 2,- $V _+47.G* H) 3+,34+ +@);4a

Carnegie Mellon

7/18/2019 02 Bits Ints


74

F."#I8(602 !)$"0 4/;($

! ]*$"-*(+ "*#$% _`$ 0185;(8(*# "*#$ ).( "$181.5I"0 ."*-$2

"$181.5I"$8 @ 0)$6*-

! N(\ $I"\

!

O)7H;)4-~7H;)4-& 2.G03GH/@0,) N6 $q

! :GV@67 G,;H/@G 7KHL

! 4"-I# $I"\

! O)7H;)4-& G,;H/@G 7KHL9 -HC _-HCH7H,) l +,.)- *, ]4+,a N6 $q

!

5H;)4-& @+H*K240/ 7KHL

! Z,7H0C4 ).2N4+7& -HC _-HCH7H,) l +,.)- *, ]4+,a N6 $q

! \4;@0C4 ).2N4+7& -HC _-HCH7H,) l +,.)- @V@6 U+,2 ]4+,a N6 $q

O74 NH@7H); *, gJ

Carnegie Mellon

7/18/2019 02 Bits Ints


75

31+)'2 ,*#(-(.$

! 4(5.($(*#)61*2 /*$"-*(+ )*+ $"-*(+

! G1*<(.$"1*% 0)$6*-

! >R5)*+"*-% #./*0)6*-

! F++"61*% *(-)61*% 8/;65;"0)61*% $I"\"*-

! =/88).'

Carnegie Mellon

7/18/2019 02 Bits Ints


76

E.15(.6($ 17 ]*$"-*(+ F."#I8(60

! ]*$"-*(+ C/;65;"0)61* P"#I F++"61* T1.8$

G188/#)6<( 4"*-

! :--H0,) H7 /,22.*@0C4 ;+,.3

! 1G,74- .)-4+ 2.G03GH/@0,)

>&

O^.G*0

_; 9 < a&

$0 T!

! ^.G03GH/@0,) 1,22.*@0C4

O^.G*0 _; 9 < a m O^.G*0 _< 9 ;a

! ^.G03GH/@0,) H7 :77,/H@0C4

O^.G*0 _= 9 O^.G*0 _; 9 < aa m O^.G*0 _O^.G*0 _= 9 ; a9 < a

! ! H7 2.G03GH/@0C4 H-4)0*6

O^.G*0 _; 9 !a m ;

! ^.G03GH/@0,) -H7*+HN.*47 ,C4+ @--0,)

O^.G*0 _= 9 O:--0 _; 9 < aa m O:--0 _O^.G*0 _= 9 ; a9 O^.G*0 _= 9 < aa

Carnegie Mellon

7/18/2019 02 Bits Ints


77

E.15(.6($ 17 3P1`$ G185a F."#I8(60!

,$181.5I"0 F;-(9.)$! O)7H;)4- 2.G03GH/@0,) @)- @--H0,)

! f+.)/@0); *, 0 NH*7

! fV,E7 /,23G424)* 2.G03GH/@0,) @)- @--H0,)

! f+.)/@0); *, 0 NH*7

! !1#I T1.8 4"*-$! (7,2,+3KH/ *, +H); ,U H)*4;4+7 2,- $0

!

G185)."$1* #1 ZC)#I(8)60);[ ,*#(-(. F."#I8(60

! A,*K @+4 +H);7

! ()*4;4+7 ,N46 ,+-4+H); 3+,34+0479 4<;<9

; x > ! ; l < x <

; x >9 < x > ! ; < x >

! fK474 3+,34+047 @+4 ),* ,N464- N6 *V,E7 /,23< @+H*K240/

1+./ + 1 == 1+,-

15213 * 30426 == -10030 _!=#NH* V,+-7a

Carnegie Mellon

7/18/2019 02 Bits Ints


78

JI' =I1/;+ , ]$( ]*$"-*(+Q

!

?3'@1 ]$( s/$# !(0)/$( U/89(. U1**(-)6<(

! I@76 *, 2@q4 2H7*@q47

unsigned i;

for (i = cnt-2; i >= 0; i--)

a[i] += a[i+1];

!

1@) N4 C4+6 7.N*G4

#define DELTA sizeof(int)

int i;

for (i = CNT; i-DELTA >= 0; i-= DELTA)

. . .

! ?3 ]$( JI(* E(.71.8"*- C1+/;). F."#I8(60

! ^.G03+4/H7H,) @+H*K240/

! ?3 ]$( JI(* ]$"*- !"#$ #1 4(5.($(*# =(#$

! 8,;H/@G +H;K* 7KHL9 ), 7H;) 4J*4)7H,)

Carnegie Mellon

7/18/2019 02 Bits Ints


,*#(-(. G E/DD;($

• x < 0 ((x*2) < 0)

• ux >= 0

•

x & 7 == 7 (x<<30) < 0

• ux > -1

•

x > y -x < -y• x * x >= 0

• x > 0 && y > 0 x + y > 0

•

x >= 0 -x <= 0

• x <= 0 -x >= 0

•

(x|-x)>>31 == -1• ux >> 3 == ux/8

• x >> 3 == x/8

•

x & (x-1) != 0

"*# R @ 711Z[t

"*# ' @ 9).Z[t

/*$"-*(+ /R @ Rt

/*$"-*(+ /' @ 't

,*"6);"D)61*

Date post:	14-Jan-2016
Category:	Documents
Upload:	vikas-pandey
View:	222 times
Download:	0 times

02 Bits Ints

Documents