[PDF]

Chapter 4
Compound Types
4.1 Structs
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int
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HZa" ~ HUa"e0-§e | Oe ~G} a0¨= ~ a =| d9 ~ bc_
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n
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e0Za ~ _
a"9Za =~ Zb ~ ~ ZO £a"zkHZa" ~ HZace0-Sa¢¡ }S~ 6 ~G¯ ~ z¡a"_ -d ~ bZ9 ~ AD!Mac_
dOOeGa" | 9-£a°¡z±1_ ~F~ ~ eGa" | ² D³
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e0- ~
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// input
std :: cout < < " Rational number r :\ n";
rational r ;
std :: cin > > r;
std :: cout < < " Rational number s :\ n";
rational s ;
std :: cin > > s;
// computation and output
std :: cout < < " Sum is " < < r + s < < " .\ n" ;
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e ~f|4 e | ~ Z |mD~
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// Program : userational. C
// Add two rational numbers .
# include < iostream >
Æ
// the new type rational
struct rational {
Â
ÄÅ
\KI8I
int n;
int d ; // INV : d != 0
Á
0Á Á
Á"Â
Á"Ã
Á3ÄÅ
Á
Á"Æ
Á
Á
Á
Â Â4Á
Â0Â
Â0Ã
ÂGÄÅ
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Â
};
// POST : return value is the sum of a and b
rational add ( rational a , rational b)
{
rational result ;
result . n = a.n * b .d + a.d * b.n;
result . d = a.d * b .d;
return result ;
}
int main ()
{
// input
std :: cout < < " Rational number r :\ n";
rational r;
std :: cout < < " numerator =?
" ; std :: cin > > r.n ;
std :: cout < < " denominator =? " ; std :: cin > > r.d ;
Â
std :: cout < < " Rational number s :\ n";
rational s;
std :: cout < < " numerator =?
" ; std :: cin > > s.n ;
std :: cout < < " denominator =? " ; std :: cin > > s.d ;
Â
Ã
Ã Á
4
Ã0Â
Ã0Ã
ÃGÄÅ
// computation
rational t = add (r , s );
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Ã0Æ
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// output
std :: cout < < " Sum is " < < t.n < < "/" < < t.d < < " .\ n ";
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Ã
Ä
return 0;
}
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Program 30:
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int int ~ ~+=~
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// INV:
K£µ ~} b ~ ®SZ9 }6| _3a"e | 9Oac | O_ |4 dOOeGa" | 9_±1_ ~F~ ~ eGa" | (²² ³ U Zb"-ja"_?Zb ~ -v | b"H-
F ¡ |4 | eFdO ~ acO=ac ~¦} b | b-¸Ua" ~ ¡Ub ~ | a»_3a-O9Zb"O ~ K--O | dib F¡ |4 b"£a"O a" ~
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b

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}9}S~ Zb-_ } Ub- ~ a ~ ba¢¡ }6~ Z9{b ~ a"dib"¥a¢¡ }6~ dOOeGa" | O_µ ~ add
A struct defines a type, not variables.
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struct rational {
int n ;
int d ; // INV : d != 0
};
OO ~
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a | ~ "a ~ bf ~G¯
a" ~ 9- ~
9diaZa8acUa }6| ja0 ~ £a" ~ b Zb"Z9 ~|4 ac
Ua ~G a¢¡ }S~ (
rational
|4 a¢¡ }6~ int 9 D~ ~F~ ~G¯ ~ ?V¨= ~ a =| T9O ~ ~ _
int n ;
int d ; // INV : d != 0
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int
n
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} ~ e ~ _ |4 9Za"
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4.1.1 Struct definitions.
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struct
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... ®*a"d } ~

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(t1 , t2 , . . . , tN ) ~ ~ ti

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3
struct rational_vector_3 {
rational x;
rational y;
rational z;
};
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unsigned int =~
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0, 1, . . . , U
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{−U, −U + 1, . . . , −1, 0, 1, . . . , U − 1, U}
- _ | |m _F
struct extended_int {
// represents u if n == false and -u otherwise
unsigned int u ; // absolute value
bool
n ; // sign bit
};
¨
=
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}O} Zb ~ ja"¡ ~ d9-?_3acb"dOeGa"_ ~G¯ ~ |UD~ b- ~ } a¢¡H_ ~ a |4~B· _3acOa¢¡ }S~ _F
struct S {
};
struct T {
};
void foo ( S s ) {}
int main () {
S s;
T t;
foo ( s ); // ok
foo ( t ); // error : type mismatch
return 0;
}
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3
acUa =~
struct rational_vector_3 {
rational v [3];
};
4.1.2 Structs and scope
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a | dOOeGa" | O_ ~ b ~ ¬a" ~ _ce |}S~f|4 h_3acb"dOeGa=_8a" ~ O
d O | |4 "a ~ _3e |}6~ _ |4 -g£a"_+MO,G.0>ADCGAj#1'r24!?)F
~ b ~ _3acb"dOeGa ~ eFUbZa" | o9-_=a" ~+| b"
struct
¨ ~ _3acb"dOeGa§ ~/¯ Oac | +_§ ~ eFZbZa" | -_ =~ 1--Ohd9_3dZ¡ | ~ -eGacdZ¡] ~F~ O_§a" ~ ~/¯ Oac |
=
| b" ~ b»a | dO_ ~ _3acb"dOeGa0¨O_?_ ~ -_r¡fa |~/· } -?¬6 | b" ~ b»a | acb"-O_cZa ~ Zb"Z9 ~ ~ eGZbZac |
|4 _3acbcd9e/aa¢¡ }6~ | b dOOeGa" | a" | b"HZ } ZbZ ~ a ~ b"_ |4 _3acbcd9e/aa¢¡ }6~ a | HZeBO ~ -O4d9- ~
a" ~ e | } ~ b= ~F~ O_a | µ( |U a" ~ - | dOa |4 ~ | bc¡Tb ~ dOb ~ ¡¥- | ~ e/a |4 ac ~ _3acb"dOeGaF
Vdia
a"O_ | b"HZa" | o_ | 9£¡ | Oa-U ~v b | a" ~ ~G¯ Oa" | |4 ac ~ _3acb"dOeGa0¸S-_ | OTZ_a" ~
e | } ~ b9-_ | O¡k_ ~F~ ov ~ eFZbZa" | |4 ja" ~ _3acb"dOeGa _V_c-Na | 9 D~ 'Q!I.G24W¹JK> ,0#c,h#17mJ6,0
4.1.3 Member access
¼y_3acb"dOeGaV_ | b ~ acZka" ~ =Zbca ~ _c- } b | OdOeGa |4 a"_¦d9O ~ b"£¡(O]a°¡ }6~ _£a |ºg~ b"_V_ | ~ -_ce
dOOeGa" | 9-£a°¡ | ^ac_ |m a"9Za =~~/·(} Z ~/· a0 ¨= ~ | _3aH }6| bca-ja±&Z9-_ | | _3a
_c9 ~ ³ dO9e/a" | 9-a¢¡ |4 k_racb"dOeGa_a" ~ -eFe ~ _c_
a | a" ~ Ua¹ ~ ~ bc_v±*ac ~v -d ~ _ t a" ~
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³ 6-O ~ b ~ _ ~ b ~ ac ~ ~ a" ¯9~ bc_ . B0F / e |i ~ K
N } ~ t = (t1 , . . . , tN )
´ _- ~/·(} b ~ _3_c | |4 a¢¡ }6~ a" -d ~
(ac ~
ya" ~ ®1a"{e | }6| ~ a
(t1 , . . . , tN)
tK
K
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Na" ~ ¼ O
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a" ~ 1® a"d } ~
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(n, d)
n/d
4.1.4 Initialization and assignment
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_K9£a"- ~ £a"
t
rational
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add (r, s)
~ ~ b3® _ ~ §1 ~ | b ~ -e 9Za ~ ~ b_ ~G} Zb"Za ~ ¡DO ~ bha" ~ | | Kac ~ ~ eGZbZac |
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rational t = add (r , s );
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³ Z9
add (r, s)
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-_c_34O ~ a] ¡
~ -?
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± aca" ~ _ ~ e | Oze | }6| ~ a ³
´1ja ~ b ~ _ra"O4¡DOa"O_-_ |N=| bcµ(_ a"
t.d
a3b"dOeGa"_Ta" ~ b ~F| b ~} b |m ~ 0¡ |4 Zµ O4ª Zb3bF¡ Oa"-0Za" | -O
©
b }O} Ooa" ~ ZbcbF¡a | H_3acb"dOeGaFN¿ ~ b ~ _v- ~/· - } ~ a | _3 |m¶ 9Za =~
# include < iostream >
struct point {
double coord [2];
};
int main ()
{
point p;
p . coord [0] = 1;
p . coord [1] = 2;
point q = p;
std :: cout < < q. coord [0] < < " "
< < q. coord [1] < < "\n" ;
// 1
// 2
return 0;
}
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b ~ dOb ~ ~ ja"_F (b | a"O_Fia" ~ e | } ~ be0- ¯ 4dib ~v| dOa |U H-j¡H ~ | bc¡He ~ _Ub ~ a | ~
e |} ~ | ba" ~ Oa"Z0Zac | |4

q
point q = p
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a" ~
a
b |4
dOOeGa" | add Zb ~ Oac- ~ b | a" ~k Zd ~ _ |4 r -O s ¸a" ~k -d ~N|4 add (r, s) ac_ ~
-_ | b ~ _cdOa"_ b | -oOa"-0Za" | |4 k±Qa ~ }6| bUbc¡ ³ | ~ eGa ~ Ta" ~
_3aZa ~ ~ a |4
return
a" ~f d9OeGac |
_
eFdia ~ ?
add ~/·(~
´1O_3a ~ - |4 "a ~ Z |UD~ ~ eFZbUa" | f_3aZa ~ ~ a?a"9Za»Oa"Z ~ _ =~ e | dO-_ | 9 D~ b"a3a ~
t
rational t ;
t = add ( r , s );
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t
e0-_ ~ Va" ~ ¡EZb ~{|4 a°¡ }6~
¸
b d9O9- ~ ja-Va¢¡ }6~ _F ~G -dOa3®&9£a"- 0Za" | | ~ _ | a"OOi
int |
_ | a" ~ Zd ~ _ |4 ac ~ 9Za" ~ ~ b"_NUb ~ dO9 ~G¯ ~ a ~ bo ~F -dOar®&Oa"-0Ua" | ±1_ ~F~ -_ |
~ eGac |
² D³ `´1a" ~ ~/· ao ~ =a" ~ Zd ~z|4
_o-_c_c4 ~ a |

-Oac9_
add (r, s)
t
-_c_34O ~ a-DZ¥9 }O}6~ O_ ~ ~ b3® _ ~
| b ~GD~ bc¡ dOO9- ~ a"-a¢¡ }S~ ¦a =|$~/· } b ~ _c_c | 9_ |4 a¢¡ }S~
What about other operations?
-O
z´*a =| dO½a" ~ b ~G| b ~ _ ~F~
e0-$ ~ a ~ _ra ~ | b ~ d9-a¢¡DdO_c9ac ~T|}S~ bZa | bc_
==
!=
9Za"dib-8a | 9 D~ a" ~ _ ~ a =|z|}6~ b"Za | b"_-_ || b_3a3b"dOeGa"_F } ~ ~ ja ~ _cdOep 0¡½acUa
a" ~ ¡oe | } Zb ~ ~ ~ br® _ ~
| b"H-¡DDa"O_ =| dOH ~ e | bcb ~ eGa0¬¦
Z9 (a" ~ =~ 9 D~
t = (t1 , . . . , tN)
t = (t1 , . . . tN )
-O
O

H
¡

|
t = t | K = 1, . . . , N
t=t
K
K -b -i¡p_c
Vdia | dibHa¢¡ }6~
~
|m _Ha"9ZaHa"O_ =| a =| bcµS¬$dOO ~ b¥ ~ ~ b3® _ ~
rational
¨= ~} b | ~ _{a"9Za{a" ~
~ dZa¢¡D =~<=| dO ~ b3b | ~F| dO_c¡e | OeFdO ~ a"9Za 2/3 =
4/6
)G7j!?#3AO.0#1'3.BAj>¹P Aj>q:§, CGAD!SRi,
"
a

¢
a
¡
~
}S~ rational | ~ _ | a¥e | OeF ~ a"^ac ~
int int |4
)-,FWzAD!?#1'3.BAj>P Aj>q:§,¹CGAD!SRi,T Oe =~ ~ ja" ¡ } Zb"_
a"9Za ~/¯ ~ a" ~ _"- ~ bZa" | 9-
(n, d)
dO ~ b

n/d
¨ ~ _"Z ~ 9 }O}6~ O_ a" | diba¢¡ }S~
b Z |mD~ ¬§_c9e ~ | a" } -bc_
extended_int |
(0,
)
-O
ª{<a"O_
Zb ~ a ~ b } b ~ a ~ ½-_ » ~ ~ b3® _ ~h~ dZa¢¡ =| dO<4 D~ dO_
(0, )
0
©0=
0
e0-_ ~
O¡
a" ~ } ~ ~ ja | b |4 <_3acbcd9e/aTµ( |U _ka" ~ _ ~ HZa"eF- -d ~ b"-O ~ -O | bTac9_
b ~ Z_ | ?¦f ~ ac ~ b } b |U ~ _ ~ d9-a¢¡ |}6~ bZa | b"_ | b_3a3b"dOeGa"_FI | b-j¡ | a" ~ b |}S~ bZa" | 9_
~ ¡ | Oza" ~ ~ ~ b]-eFe ~ _c_F?Oa"Z0Zac | ?O-O-_c_34O ~ aO_3eFdO_c_ ~ <Z |mD~ }6~ bZac | O_
a"9Zab ~ _ }6~ e/aha" ~ _ ~ H-ja"e0Z -d ~ b-O ~ eF-½ ~N} b |U ~ ½ ¡ac ~ } ~ ~ ja | b06a" | dO4K
_ ~F~ ~/· a_ ~ eGac | ?
| dhT4a§Zb"4d ~ a"9Za ~GD~ ~ ~ b3® _ ~ Oac-FZa" | ]-O-_c_34O ~ a»e | dO ~ 9e | i®
_c_ra ~ a a"Ha" ~ _ ~ H-ja"eF_ |4 a" ~ a¢¡ }6~ KZa ~ bF =~ O ~F~ ~ Oe | dOa ~ b_cdOeh_c£a"d9Za" | ?
-O =~] S_c |U |m £aeF-¥ ~ ~ -a £a" ~ ~ D-ac¡D
4.1.5 User-defined operators
_F
~G a°¡ }6~ _8b ~ dOb ~ G~ |}S~ bZa" | 9_G9dia ~ oa e | ~ _8a | a" ~ 9-TO 4
| _cdOe |}6~ b"Za" | O
| ~ ~ _c_+Oe ~ -_ }6~ eGa 4
| b | b- {_3 |m _f ~ i ¡z ~G¯ 99Ha" ~ d9OeGac | add =
~
b

Z
9

a
b
"
b

a
"

b
Z

"
a

"
a
i

b
O
d
4

{
"
a

3
_

a
Z

a
=~ ~
~ |¹}S~ |
~ |}S~
v
| t := r + s
|
~
~ ~
rational t = add (r , s );
1´ ~ - £¡D |m=~GD~ b0 =~
=| O
d Hµ ~ a | Z9HbZac | 9-gd9 ~ bc_ µ ~=~ -Ooa ~ ~ b"_ | b «9| Za"O-®
a dO ~ b"_F(¡{_3 } ¡ bca"OT±1 | dObe0-_ ~ ³
}6| j
\KI8I
rational t = r + s ;
¨ ~ ~ ~G¯ a |4 a"O_=T4a | a= ~ T ~ OUa ~ ¡ | | dO_Fi } Zbca"eFdOZb c_ 9e ~ "a ~ 9-TO |4
=
a" ~f d9OGe ac |
_ T_=a | ~ dO a ~ b ~ Z_ | 9Z9 ~ ¸(9
diae | O_c ~ b a" ~f~/·(} b ~ c_ _c |
add ~F~
rational t = subtract ( multiply (p , q ) , multiply (r , s ));
-Oac_
©
9ZacdOb"-ªe | dOa ~ b } Zbca
rational t = p * q - r * s;
a | ~ a
Z ~ 9Za =~ ~ -?
¨ ~ 9ZacdOb"-» | aUa" | e0Zz9 ~F~ ~ -eO ~GD~ K¬µ ~ ¡ ~ ZacdOb ~|4 a" ~ v -O4d9- ~ _
a"9ZaK | _3a |4 a"_ |}6~ b"Za | b"_±1_ ~G~ ¨U ~
va" ~ ¼ }O}6~ OO ·]| bKa" ~¦ dO4_3a ³ e0Z+ ~ 24P(,FCm> 2-AiMO,/M
??
a |=| bcµ | b | a" ~ b=a¢¡ }6~ _-_ =~ 1¦¨O_ ~ Z9_8acUa =~ eF-¥dO_ ~ a" ~ _"- ~|}6~ b"Za | b a | µ ~ oa |
} ~ ~ a Zb" | d9_ |}6~ b"Za | b"_F¬ =~ |UD~ b" | -Oª¹ac ~ a | µ ~ ?
©
´1 } b"9eG } ~ Va"O_k_N | a"OO ~G ¬ =~ -b ~ -i¡µ |U acUaNa" ~ 99Zbc¡ |}6~ bZa | b
_
+
ZZ9 ~| b _ ~GD~ b-ga¢¡ }S~ _F | b ~B· - } ~
-O
¤y9Za _V ~G _Va"9Za =~ e0-H-O
int
double
~GD~ E | b ~¹|UD~ bc | -O_ | | dib |U ?I-O½_c } ¡z ~ ava" ~ e | } ~ b ¯ 4dib ~N| dia b | a" ~ e0-
} Zb- ~ a ~ b a¢¡ }6~ _ Oe | ~ _ ~F~ ~ ¥e ~ bca-¥e | a ~B· a0
´1 |mD~ b" | Z99E- |}6~ bUa | b0 =~ e0Z9 | aHe9-O ~ ac ~|}6~ bZa | b u_HZb"a¢¡D } b ~ e ~ ~ Oe ~| b
-_c_ | eFUa" £a°¡DZdia =~ e0-Ne/b ~ Za ~=D~ b"_3 | O_ |4 a ackZb3£acbZbc¡ | b"H- } ZbZ ~ a ~ b¦-Ob ~ a"dib"
a¢¡ }6~ _F
}S~ bZa | b |mD~ b" | Z99h_ _c } ¡k_ }6~ eF-Se0-_ ~f|4 LG:!I.0#1'324!y24P(,FCm> 2-AiMD'Q!SRD | b ~/· - } ~
-O
-U ~ =~ e | dOT ~ eFUb ~ a" ~
| |U O
9 O+a" ~ _racb"dOeGa"_
rational
extended_int
a =|{ dOOeGa" | 9_a" ~ _"- ~} b | bZ £a" | dOa
eGb ~ ZacO{T9- ~ eF-_c?¬ | b+-¡e0Z§a | a" ~
dOOeGa" | square oac ~
} b | b"-a" ~ e | } ~ b8e0Z ¯ O | dia b | na" ~ e0- } Zb- ~ a ~ b8a¢¡ }6~
Oe |4 a" ~ a =|¹ d9OeGac | O_ =~ ~ -?
// POST : returns a * a
rational square ( rational a );
// POST : returns a * a
extended_int square ( extended_int a );
d9OeGac | |mD~ b" | -OOT ~ ~ b-I_dO_ ~G d9*?9dia] | a]
i
| -OOi`¨ | ~G¯ ~ - |mD~ b" | - ~ |}6~ bUa | b0 =~ 9 D~
!I2D#3Aj#1'324!?´1Ha"O_ | aZa" | ?Da" ~ Z ~
|4 a" ~f|}S~ bZa | b8_
a | a" ~} b ~G¯i·
f´1e0Z_ ~|4 a" ~ 99Zbc¡-O9£a" |
operator
a"O_= || µ(_-_ | |U _-O{b ~G} Ze ~ _ac ~f dOOeGa" |

add
~ Z b"¡-_dO_ ~F dO¦-_ |}6~ bUa | b |UD~ b3®
a | dO_ ~ ac ~ L/:g!I.0#1'r24!Aj>N2FJ6,FCGAj#c24C
| 9a"- ~ T ¡H }9}S~ O99h£a"_8a | µ ~
|}6~ bZa | b | ba" ~ a¢¡ }6~ rational
// POST : return value is the sum of a and b
rational operator + ( rational a , rational b)
{
rational result ;
result .n = a .n * b.d + a.d * b. n;
result .d = a .d * b.d ;
return result ;
}
´1 b | b-
( =~ e0- |m
b ~G} -e ~ ~ ¡
rational t = r + s ; // equivalent to rational t = operator + ( r , s );
¿ ~ b ~ Kac ~ e | T ~ jab ~F~ bc_+a | a" ~k -eGafa"9Zav- |}S~ bZa | bfe0Z½-_ | ~ ./Aj>*> ,/M½ dOOeGa" | 9-
| aZa" | K¸^e | jacb-_3aFa{ }O}6~ Ub"_H 'Q!4tX !I2D#3Aj#1'r24!
¨= ~ eF- d9OeGac | 9-
r + s
| aZa" | he0-h ~ dO_ ~F dO | bO9-eGace } dib }6| _ ~ _F4_cOe ~ a ~ } Z_c ~ _Ka" ~ -eGaIa"9ZaI- |}6~ bZa | b
__c } ¡o_ }6~ eG- d9OeGac | ?¸9- }O} eFZa" | ? |m=~GD~ b09a" ~v}6| a_=a | D| dOOeGa" | 9-
| aZa" | ¥-OdO_ ~ a" ~ ¯i· | aZac | ?
¨ ~h| a" ~ ba"ib ~F~ -_cehZb"ac9 ~ a"e |}6~ bUa" | O_
Zb ~ _cTZb0O-O ~ b ~=~h| O¡{4 D~ a" ~ £b
~ eFUbZa" | O_F
// POST : return value is the difference of a and b
rational operator - ( rational a , rational b );
// POST : return value is the product of a and b
rational operator * ( rational a , rational b );
// POST : return value is the quotient of a and b
// PRE : b != 0
rational operator / ( rational a , rational b );
¤ ~ e0ZZ_ ||mD~ b" | - ½a" ~ dO9Zbc¡
bZa | b0¸ d9OeGac | 9- |}S~ b Za | b | a"Za" | ?
§£a9-_
- |}6~
"a ~ _c- ~ Z ~ Z_a" ~
Ubc¡ D~ b"_c | ?i9diaa9-_ | 9£¡ | ~ O_3a ~ - |4 a =|¹} ZbZ ~ a ~ b"_GV´1
"a ~h| |m 9 } ~ ~ a Zac | ? =~ dO_ ~ a" ~ ±1 | 9 ¯~ ³ | e0-»e |} ¡ ª |4 ca ~ eF- } Z"b - ~ a ~ b
©
Z_a" ~ b ~ a"dib" -d ~
a
// POST : return value is -a
rational operator - ( rational a)
{
a .n = - a .n;
return a ;
}
´1 | cb ~ b8a | e | } Zb ~ bZa" | 9-9 dO ~ b"_G =~ ~F~ Ha" ~ b ~ Za" | 9- |}6~ bUa | b"_ -_ =~ 1¿ ~ b ~
_=a" v
d -a¢¡ |}6~ bZ a | b-_- ~/· - } ~
~ ~ 9
// POST : return value is true if and only if a == b
bool operator == ( rational a , rational b)
{
return a .n * b.d == a.d * b .n;
}
4.1.6 Details
´ ac ~ b ~ Zb ~ _ ~GD~ b- dOOeGa" | O_ | b |}6~ bZa | b"_ |4 a" ~ _c- ~ 9- ~
Overloading resolution.
b

"
a

f
b
_ ~ -av½oe ~ bca"- dOOeGa" | ½eF-1
} |
~ | } ~ 9-_va |¥¯ 4dOb ~k| dia Oe | ~ f
¨=9_ } b | e ~ _c__=e0- ~ $24P(,FCm> 2-AiMD'*!SR{CF,0)-2D>q:S#1'r24!p-O | 9£ ¡T ~G}6~ OO_ | oa" ~ a¢¡ }6~ _ |4 a" ~ e0-
\KI8I
} Z b- ~ a ~ b"_F e0-_ ~ _¹a"9Za =~

add (r, s)
b
e
c
_
_
Z

O
d

} | ~
D~ b" | -OOb ~ _ | dia" | $_ac ~ b ~F| b ~ | ~ Zae | } ~ a" ~ ¨= ~ b ~ Zb ~ a =|
~F~ a | e | O_c ~ bF¬ =~ e0Z ~ a" ~ b9 D~ - y:g!0:KAj>w'ut,/M dO9e/a" | eF-±1£µ ~
b | b"- ³ | b{0:KAj>w'ut,/M d9OeGac | Fe -h±1£µ ~ std::sqrt(2.0) ³ ¨ |
d9- ¯9~ dO9e/a" | ¥eF- |4 a" ~f| b"
C
K££ ³
a" ~ e | } ~ b Z_fa |H¯ OTHZa"eOO dO9e/a" | < ~ eGZbZac | ?=-OO9Za ~ _]Zb ~ - dO9e/a" | O_
Z ~ _3d9e\a"9Zahac ~o dOOeGa" | e0- _$a" ~ _ce |}6~o|4 _ | ~ ~ eGZbZac | |4
f |4
f
´1½-OOa" | Ka" ~ d9 ~ b |4| b"H- } Zb- ~ a ~ b"_]d9_ravHUa"eza" ~ dO ~ b |4 e0Z } Ub- ~ ®
a ~ bc_FI-O ~ -e½e0Z } Zb"- ~ a ~ bfdO_3av ~N|4 oa¢¡ }6~¹ | _ ~k Zd ~ _+e0Z ~ e | D~ bca ~ $a | a" ~
e | bcb ~ _ }6| OOO | bcH- } Zb- ~ a ~ b=a°¡ }6~ _F
´1 d9- ¯9~ dOOeGa" | eF- |4 a" ~f| b"
± ¬£¬ ~ b~ £ ³
C ?
_9- ~ _ } Ze ~ | O¡Ha"O_=9- ~ _ } -e ~ __ ~ Zb"e ~ | b
e0Z9O9Za ~ _F
± ¨ ~ b ~ _ | ~ _ }6~ eFZ8b"dO ~ a"9Za_ | ~ ®
Argument-dependent name lookup (Koenig lookup).
a" ~ _HZµ ~ _a" ~ _3a |4 eF-O9Ua ~ _Zb" ~ b0´ _ | ~ e0- } Zb- ~ a ~ ba°¡ }6~|4 -dO d9- ¯9~
dOOeGa" | Ee0-_h ~G¯ ~ E9- ~ _ } Ze ~ ± | b ~/· - } ~ a" ~ 9- ~ _ } -e ~ std ³ ac ~ Ea" ~
e | } ~ b¦-_ | _ ~ Zb"e ~ _ | bVe0-OO9Za ~ _¦+¨=O_¦_dO_ ~G d9H-O¡ | b |}6~ bUa | b"_-OT- |m _
a" ~ a | ~ e0- ~ $dO d9- ¯9~ $E ¯i· | aZa" | ?¨= ~H}S| a |4 dO_cO |}6~ bZa | b"_hE ¯O·
| aZa" | =| d9H ~ _ }6| ~ o ?=~ 9-Ha | ~ ja" | Hh9- ~ _ } -e ~ _ | ~G ~ b ~ Ha" ~|}6~ bZa | b
e0-1
| b ~ -eeF-O9Ua ~I O
d 9e/a" | Z9 ~ -ee0Z } Zb- ~ a ~ 0b ma
Resolution: Finding the best match.
_e ~ e"µ ~ H |mp=~ (ac ~ e0- } Ub- ~ a ~ bIa°¡ }6~ HZa"e ~ _Ia" ~ e | bcb ~ _ }S| 9OO | b"H- } Zb"- ~ a ~ b
a¢¡ }6~ H¨ ~ b ~ Zb ~k| dib d9-a¢¡ ~GD~ F_ | O b | ~ aca ~ bva ¥

| =| b"_ ~ §4 D~ ½a" ~k| |m 9
_ra0
±c² ³
¨= ~ ¢a ¡ S
} ~ _ |4 "a ~ e0- } Zb"- ~ a ~ b -O{a" ~]| b"H- } Zb"- ~ a ~ b Z b ~ "a ~
_"Z ~
± 4³!"
¨= ~ b ~ _ } b | | a" | b | a" ~ e0- } Zb"- ~ a ~ b+a°¡ }6~ a | a" ~
| b"HZ } Ub- ~ a ~ ba¢¡ 6
} ~ ¤ ~ 9 D~ _ ~F~ p_ | ~{~/· - } ~ _ | b } b | | ac | O_Fµ ~o b |
a
-O b |
a

bool | int
float | double
± ³$#%&&')(+*,-.!/0!1 ¨= ~ b ~ _H½_3aZ99Zbce | D~ b"_c | b | a" ~ e0-
} ZbZ ~ a ~ ba¢¡ }6~ a | a" ~+| b"HZ } ZbZ ~ a ~ b=a¢¡ }6~ ¤ ~ 9 D~ _ ~F~ a"9Za
- dO99- ~ a-
Zbca"O ~ a"ea°¡ }6~ _e0-¥ ~ e | D~ bca ~ a |~ -e | a" ~ b ¡{_3aZ99Zbc¥e | D~ b"_c | O_F
± ³23-4*,)56&*,7%8*,&9!)(+*,-.9!1 ¨= ~ b ~ _kdO_ ~ 3b ®& ~G¯ ~ <e | D~ "b _3 | b | Àa" ~
e0Z } ZbZ ~ a ~ bNa¢¡ }6~ a | a" ~| b"H- } Zb- ~ a ~ k
b a¢¡ }S~ ¤ a a | dO_ ~ b31® /~ ¯ ~
~ ~ T
e | D~ b"_c | 9_ | O¡HZa ~ b{a"O_= | | µg
¼ dOOeGa" |
_=e0- ~ ElG,0#&#c,FCHa"9-
a"ob ~ _ }S~ eGaa | } Zb- ~ a ~ b0( a" ~ HZa"eoacUa
f
g
f
OOdOe ~ _ | a"9Za } Zb"- ~ a ~ b_Za
~ -_3a-_
| | -_
a" ~ HZaceB9OdOe ~ ¡
´ a" ~ HZa"e
g
_=b ~ -¡T ~ aca ~ b0 _e0- ~ <)F#1C0'r.0#&>q7$lG,0#&#c,FC | bac ~]} Zb- ~ a ~ b0
f
¼ d9OeGac |
_e0- ~ <lG,0)F#fWAj#c.0%E a]_ ~ a3a ~ ba"9--¡ | ac ~ bveF-O9Ua ~
-
f
g
Z

a
"
b
F
_
(

3
_
c
a
"
b

G
e
"
a

T
¡

c
a
a
b
"
a
9

r
_
a

a
0
b

}
~ ~
~ ~
~
| ~]}
~ ~
g
O ~ b a"O_8 ~G¯ Oa" | ?Da" ~ b ~ _ Ua= | _3a | ~ ~ _3a=HUa"eKD9dia=a HF¡N9 }O}6~ Ha"9Za8ac ~ b ~
_ | ~ _3aHZa"e?O OeeF-_ ~ ac ~v dO9e/a" | e0Z»_ADWzl0'QR4:»24:S)F9-O¥ac ~ e | } ~ b_3_cd ~ _
- ~ bcb | b ~ _c_"- ~
¿ ~ b ~ _- ~/· - } ~ ¦ | O_c ~ ba" ~ a =|k|mD~ b" | - ~ dOOeGa" | { ~ eFZbUa" | O_
void foo ( double d );
void foo ( unsigned int u );
´1¥a" ~ e | ~+ b"-4 ~ a
float f = 1.0 f ;
foo (f );
a" ~ ¯ b"_3a U| D~ b" | -{_=eB | _ ~ KO_c9e ~ float e0Z¥ ~} b | | a ~ Ta | double (9dOa | O¡H_3a"-OUb"(®
e | D
~ bca ~ a | unsigned int ´1
int i = 1;
foo (i );
a" ~ e0-4_?-94d | dO_F0_c9e ~
e0-v ~ _ra-O9Zb"(®&e | D~ bca ~ va | | a"
Z9

int
double
unsigned int
4.1.7 Goals
Dispositional.
² ³ µ( |m
|m
¼=a=a"O_ }6| ja0 ¡ | d_3 | dO<FF
_3acb"dOeGac_e0Zk ~ d9_ ~ ka | -4b ~ DZa ~ _ ~GD~ b-9O ºS~ b ~ a¦a¢¡ }6~ _ja |f| ~ ~G
a¢¡ }6~ ¸
d 9 ~ bc_3a-Oa" ~ O
g
4³ O
º ~ b ~ Oe ~ ~ a =~F~ ac ~ _3¡(ja-eGace0--O_ ~ HZa"eF- Zd ~ b-O ~¹|4
_3acb"dOeGa0¸
³ µ( |m
acUa
f
Operational.
dOOeGa" | 9_-O |}6~ bZa | b"_=e0Z¥ ~+|mD~ "b | - ~ ?
´1 } Zbca"eFdOZb0j¡ | d_c | d9{ ~ Z9 ~ a | G0
± ² ³ G~ ¯ ~ _3a3b"dOeGa"_ | _ ~ _ ~ H-ja"e0- -d ~ b-O ~ _e | cb b ~ _ }S| 9a | acUa |4 4
D
~ HZa" ~ ®
HZace0-S_ ~ a"_F¸
± 4³ } b |m ~ ~/¯ O
ac | O_ |46 dOOeGa" | O_ Z9 |mD~ "b | Z ~ |}S~ bZa | bc_ | H_3acb"dOeGac_Fi-eFe | b"OO+a |
4 D~ dO9
e/a" | 9
-a¢¡g¸
± ³ b"a ~} b | bZT_8a"9Za ~/¯ ~ -O¥dO_ ~ _racb"dOeGa"_-eFe | bc99a | 4
D
~ dOOeGa" | 9-a¢¡D
\KI8I
4.1.8 Exercises
,1t !I, Ay#17mJ6,
L-24C½#&%(CG,G,0s°P Aj>w:»,/M >@2GR'3.'Q!
Exercise 93
Tribool
%gADP(,¹#&%S,N#1C0:g#&%P Aj>q:§,0)#1C0:§,G5»LUAj>£)-,G5
AD!M:g!?Z!I24;!Y
I24CT#&%S,k#17mJ6,
5'QW¹JK> ,FW<,G!?#
#&%S,N> 2GR4'r./Aj> 2FJ6,FCGAj#c24Cm)
Tribool
#&%(CF,G,FsrP Aj>q:§,BM
> 2GR4'r.F5H;f,
// POST : returns x AND y
Tribool operator && ( Tribool x , Tribool y );
// POST : returns x OR y
Tribool operator || ( Tribool x , Tribool y );
;%S,FCF,
AD!M
ADCF,{MO,*t !I,/MAO./.G24CGMD'Q!SR#c2#&%S,L-2D>*> 24;='*!SR{#1;]2#3Ailm> ,0)ZY
∧
∨
± ¹² ³ ± 4³
LZAj>w)-,
LUAj>£)Z,
LUAj>£)Z,
LUAj>£)Z,
∧
LUAj>£)Z,
:g!?Z!I24;!
#1C0:»,
:!?-!I24;=!
LUAj>£)Z,
:!?-!I24;=!
:!?-!I24;=!
1# C0:§,
LZAj>w)-,
:g!?-!I24;=!
#1C0:§,
¨ ~ _3a¡ | diba¢¡ }6~ ¡ b"acO } b | b"-
¡
|4 | dibeB | e ~
∨
LZAj>w)-,
:!?-!I24;=!
#1C0:§,
LUAj>£)-,
LZAj>w)-,
:g!?-!I24;=!
#1C0:§,
:!?-!I24;=!
:g!?Z!I24;!
:g!?Z!I24;!
#1C0:»,
#1C0:§,
#1C0:»,
#1C0:»,
#1C0:»,
a"9Za | dOa } dia"_ a" ~ _ ~ acbcdOac{aZ9 ~ _¥_ | ~]| b"HZa
,1t !I,+A#17mJ6,
LZ24Ch.G24WJ?:S#1'*!SR;'*#&%N'*!?#c,°Ri,FCm)W<2-MD:g>@2 Y Aj#&%S,FWAj#1'r./Aj>Q>w7j5
Exercise 94
Z_7
7
#&%('1)H.G24C0CG,0)rJ624!Mj)¹#c2#&%S,t !6'*#c,kC0'Q!SR
À2"LCF,0)G'°MD:§,o.0>Aj)F)-,0)W<2-MD:g>@2
Y
= /7
7
I24CT#&%S,k#17mJ6,
5='*WJK>@,GW<,F!?#vAiMiMD7'*#1'324!yAD!M)G:Klm#1CGAO.0#1'r24! 2FJ6,FCGAj#c24Cm)
Z_7
// POST : return value is the sum of a and b
Z_7 operator + ( Z_7 a , Z_7 b );
// POST : return value is the difference of a and b
Z_7 operator - ( Z_7 a , Z_7 b );
AO.G./24CGMD'*!SR#c2¥#&%S,LZ2D>*> 24;'Q!SR#3Ail0>@, #&%('1)#3Ailm> ,{Aj>w)-2MO,1t !I,0)k)/:»lm#1CGAO.F#1'324!
'1)#&%S,
x−y
:g!6' 0:§,!6:gWzlF,FC
)G:§.0%z#&%gAj#
Y
± ¹² ³ ± 4³
z {0, . . . , 6}
x = y + z
+
0
1
2
3
4
5
6
0
0
1
2
3
4
5
6
1
1
2
3
4
5
6
0
2
2
3
4
5
6
0
1
3
3
4
5
6
0
1
2
4
4
5
6
0
1
2
3
5
5
6
0
1
2
3
4
6
6
0
1
2
3
4
5
CG24P'rMO,¥MO,*t !6'1#1'324!?)L-24CT#&%S,L-2D>*> 24;='*!SRl0'*!ADC07½ADC0'1#&%(W,0#1'3.¥2FJ6,FCGAj#c24Cm)¥24! &# %S,
Exercise 95 #17mJ6,
Y
± 4³ ± ³
rational
// POST : return value is the difference of a and b
rational operator - ( rational a , rational b );
// POST : return value is the product of a and b
rational operator * ( rational a , rational b );
// POST : return value is the quotient of a and b
// PRE : b != 0
rational operator / ( rational a , rational b );
CG24P'rMO,zMO,1t !6'1#1'r24!?)vL-24C#&%S,+L-2D>Q>@24;='Q!SR l0'Q!ADC07ECG,0> Aj#1'r24!Aj>f2FJS,FCGAj#c24Cm)24!#&%S,
Exercise 96 Y "! MO24'Q!SR #&%('*)G5$#1C07 #c2`CF,G:S)-,2FJ6,FCGAj#c24Cm)y#&%gAj#EADCF, Aj>wCG,/AiMD7 MO,1t !I,/MiY
#17mJ6,
rational
± 4³ ± ³
// POST : return value is true if and only if a != b
bool operator != ( rational a , rational b );
// POST : return value is true if and only if a < b
bool operator < ( rational a , rational b );
// POST : return value is true if and only if a <= b
bool operator <= ( rational a , rational b );
// POST : return value is true if and only if a > b
bool operator > ( rational a , rational b );
// POST : return value is true if and only if a >= b
bool operator >= ( rational a , rational b );
CG24P'rMO,¥MO,*t !6'1#1'324!?)L-24CT#&%S,L-2D>*> 24;='*!SRl0'*!ADC07½ADC0'1#&%(W,0#1'3.¥2FJ6,FCGAj#c24Cm)¥24! #&%S,
Exercise 97 #17mJ6,
A4Ri, 5oAD!M\#c,0)F#N#&%S,GW 'Q!¶AJ?CF2GR4CGADW
LZ24C#&%gAj#¹'*#{./24:S>M^lF,
extended_int %S,0> JDLG:g>#c2<J?CF24P'°MO,AD!n24:g#J?:S#¥2FJ6,GCGAj#c24CTL-24C<#&%S,#17mJ6,
5AD!MALG:!I.0#1'324!
extended_int
#&%gAj#¥Aj)F)G'@R4!?)z#c2 AD!
P Aj>q:§,ApP Aj>q:§, 2"L#17mJ6,
Y )'Q! #&%S,{J?CF,FP-'324:S)
extended_int
int
,BX9,GCF.F'1)Z,F5#1C07z#c2{CF,F:S)Z,¥.G2ZMO,-Y
± 4³ ± ³
// POST : return value is the sum of a and b
extended_int operator + ( extended_int a , extended_int b );
// POST : return value is the difference of a and b
extended_int operator - ( extended_int a , extended_int b );
// POST : return value is the product of a and b
extended_int operator * ( extended_int a , extended_int b );
// POST : return value is -a
extended_int operator - ( extended_int a );
\KI8I
Exercise 98
]24!?)/'rMO,FCk#&%S,LZ2D>*> 24;'Q!SR)Z,0#+2"L#&%(CF,/,
LG:!I.0#1'324!?)ZY
void foo ( double , double )
{ ... }
void foo ( unsigned int , int )
{ ... }
void foo ( float , unsigned int ) { ... }
I24C,/AO.0%p2"L¹#&%S,L-2D>Q>@24;='*!SR+LG:!I.0#1'324!
// function A
// function B
// function C
B. Aj>*>w)G5vMO,/.F'rMO,H#c2;%('3.F%\2"LN#&%S,
L/:g!I.0#1'r24!?)
A, B, C
'1#fCF,0)-2D>qP(,0){#c245¹24CzMO,G.F'°MO,¥#&%gAj#v#&%S,<.BAj>*>8'1)ADWlF'QR4:»24:S)ZY VXmJK>AD'*! 7924:gCMO,G.G'1)G'r24!?)
V%('*)
,BX9,GCF.F'1)Z,hCF, 0:'*CF,F)724:#c2TCF,/AiMo#&%S,JSADCGA4R4CGA0JK%½24!p24P(,GCm>@2-AiMD'Q!SRTCF,0)Z2D>w:g#1'324!½'*!#&%S,
,0#3AD'1>w)
)-,/.0#1'324!Y
A
l
foo(1, 1)
foo(1u, 1.0f)
.
foo(1.0, 1)
foo(1, 1u)
foo(1, 1.0f)
M
L
,
foo(1.0f, 1.0)
4.2 Type Variants
%('1)f)-,G.F#1'324!p,BXmJK>AD'*!?)+#1;f2T;AD7)¹2"L2(lm#3AD'Q!6'*!SRTP ADC0'°AD!?#&)k2"LhANR4'QP(,F!$#17mJ6,#&%gAj#
%gADP(,E#&%S,)ZADW<,$P Aj>q:§,$CGAD!SR(,yl0:g#zMD' h,FC'Q!./,FCm#3AD'*!LG:!I.0#1'324!Aj>q'1#17 Aj)rJS,G.0#&)ZY
F~ ~ b ~ Oe ~ a¢¡ }S~ _k,F!Ailm> , LG:!I.0#1'324!?)+#c2AO.G.G,rJK#]AD!MHCF,F#1:gC0!>wP Aj>q:§,F)¹AD!MH'*!JSADCms
#1'r.F:S>ADC.0%gAD!SRi,o#&%S,TP Aj>q:§,0)2"Lk#&%S,F'*CfL-24C0WzAj>?JSADC/ADW<,0#c,FCm)UYH | O_3a3®1a¢¡ }6~ _¥Aj>*> 24;
:g)#c2zMO,*t !I,hP Aj>w:»,0)kAj)klF,G'*!SRo!I24!?srW2-MD' t
Ailm> ,F5 'Q!)/:§.0%<Ao;AD7#&%gAj##&%S,T.G24W¥s
J?'*>@,FCp.BAD! MO,F#c,G.0#H'1>Q>@,°R(Aj>vW2-MD' t.BAj#1'324!?)ZY ],1LZ,FCF,F!I./, #17mJ6,0)\AD!M.G24!?)G#&s3#17mJ6,0)
.BAD!¶lG,./24Wl0'Q!I,/M^AD!M!Aj#1:gC/Aj>*>q7 .G24W,z:jJ`'Q!'*W¹JK> ,FW,F!?#1'*!SR{LG:!I.0#1'324!Aj>q'1#17
LZ24CN)F#1C0:».0#&)ZY
4.2.1 Reference types
~ I
a dO_I U| acbc¡va | } ~ ~ ja6a" ~ - OOa" | +-_c_c4O ~ ja |}6~ bZa | b
bac ~ _racb"dOeGa
+= |
rational
b | b | b- (V¿ ~ b ~ _Z Zaca ~ } aF¬
rational operator += ( rational a , rational b ) {
a .n = a. n * b.d + a. d * b.n ;
a .d *= b .d;
return a ;
}
¤ya"oa"O_F =~ eF- bca ~
rational r ;
r.n = 1; r .d = 2;
// 1/2
rational s ;
s.n = 1; s .d = 3;
// 1/3
r += s;
std :: cout < < r .n < < "/ " < < r. d < < "\ n";
d HF¡ -b ~ -i¡\_ ~F~ a"9Zaka" ~| dia } dOa |4 ac9_ | aN ~ ac ~ ~ _cb ~
~ eF-
| y
5/6

b |
~ eGac | (² 9ZaH9 }O}6~ O_ ~ r += s ± ~ dO Z ~ ac¡D operator+= (r, s) ³ _

9
d
Z

a
~G
~ K¬ r Z9 s Ub ~~G -d9Za ~ ?-Oyac ~ b ~ _cdOa"O -d ~ _oZb ~ dO_ ~ a | Oa"- ~ a" ~
| b"H- } Zb"- ~ a ~ bc_ a -O b |4 a" ~¹ dOOeGa" | operator+= ¨ ~ -d ~ _ |4 r -O s Ub ~ | a
e9-O ~ ¥ ¡oa" ~f d9OeGac | ¥e0Z1
¿ ~ Oe ~ a"a" ~ Z |UD~ } ~ ~ aUa" | |4
a" ~ PAj>w:», |4 a" ~T~/· } b ~ _c_c |
operator+=
_IO ~G~
D9diaIa" ~ ~ _cb ~ , h,/.0#&a" ~ OeGb ~ ~ a |4 D | ~ _¦ | a9 }O}6~ ?¨=9Za _
r += s
5/6
r
j

_
i
d

=~ ~ 1/2
| a } dOaoa" ~ Z |UD~]} ~ e ~v|4 e | ~
´1 | b" ~ b=a | } ~ ~ a
b
b"£¡D =~ ¹dO_3a ~ U ~ d9OeGac | O_=a | eB9-O ~ a" ~
operator+= } |}6~
-d ~ _ |4 a" ~ be0- } Zb- ~ a ~ b"_F dib } b"_c94£¡D =~ | | a ~G~ <¹ ~/ e | Oe ~/} a | ba"9Za |
a" ~f d9OeGac | _c ~ ¸ =~ _c } ¡N ~G~ h ~/ eFZa ~ | bc¡ |4 a¢¡ }6~ _F
(1]I
O²
(¦
Definition.
´ _Z¡Ha¢¡ }6~ ia" ~
_=a" ~ e | bcb ~ _ }S| 9OOHCF,1LZ,FCF,F!I./,T#17UJS,¥±*b ~ - -_ b ~F~ b ~ Oe ~ ª | b b ~F~ b ~ Oe ~ a | ª ³ O´1
©
©
_V ~ ja"e0Z9a | ¨ ~ O ºS~ b ~ Oe ~ _VNa" ~ Oa"-0Ua" |
-d ~ b-O ~ Z9 dOOeGa" | Za¢¡D -O-_3_c4O ~ a=_ ~ H-aceF_F
¼ Zb"Z9 ~|4 b ~F~ b ~ Oe ~ a¢¡ }6~ ±&-_ | e0- ~ T¹CF,1LZ,FCF,F!I./, ³ e0-T ~ Oa"Z ~ | O¡ b |
->qP Aj>q:§, |4 a¢¡ }6~ | b
Z¡Ha¢¡ }6~f | _ ~] -d ~ _e0Z¥ ~ e | D~ b3a ~ a | O¨= ~ Oa"-0Ua" |
HZµ ~ _=a-EAj>w'°Aj) |4 a" ~ Zd ~ ¬¦- | a" ~ bZ ~f| ba" ~f| ~ eGa ~ OOoa" ~ -d ~ I¤ ~ -_ |
_"F¡oa"9Za=a" ~ b ~G~ b ~ Oe ~ CG,1L-,FCm)ha | a"9Za | ~ eGaF¨= ~v| |U O ~/· - } ~ _3 |m _=a"O_F
int i = 5;
int & j = i ;
// j becomes an alias of i
j = 6;
std :: cout < < i < < "\n" ;
// changes the value of
// outputs 6
¼¾b ~G~ b ~ Oe ~ e0-O | af ~
Za ~ b-_3_c4_ | ~ a"OOa |
´1 b"a"O
¹ac ~ Z
j = 6
_---_ |4
j
i
´1a ~ b"9-¡D§ Zd ~T|4
a | ¨O_ ~/· } -O_ ¡ =~
a"OO4_=µ ~
e 9-O ~ a |
a" ~ b ~F~ b ~ Oe
|mD~ } ~ e ~|4
b G~ ~ bha | - | a" ~ b | ~ e/ah
~ =~ - e/a]-_c_c4a | a" ~
e | ~ =~ a" ~ b ~G| b ~ e9-O ~
i
b Oa"-0Ua" | ?´ 8=~
a ~
2(l
,/.0#]b ~F~ b ~ a | ¡a0
a" ~ -d ~=|4 a | D_cOe ~
i 6
a°¡ 6
_+b ~G} b ~ _ ~ ja ~ E ¡a" ~ Z9ib ~ c_ _ |4 a" N
} ~ ~ | ~ e/ahab G~ ~ b"_
~G~
- -d ~ a | Oa"- ~ hb ~F~ b ~ Oe ~ ¢a ¡ 6
¡
} ~] Z b"Z9 ~ O-O j
int & j ;
int & k = 5;
// error : j must be an alias of something
// error : the literal 5 has no address
int i = 5;
int & j = i ;
int & k = j ;
// j becomes an alias of i
// k becomes another alias of i
| u a =
| b3µS=¼
¡ ~/· } b ~ c_ _c | |4 b ~G~ b ~ Oe ~ ¢a ¡ 6
} ~ _- - d ~ a"_ ~ 8¤ ~ eF-a" ~ b F~ | b ~ d9_ ~
b ~F~ b ~ Oe ~
a Oac- ~ - | a" ~ b b ~F~ b ~ Oe ~
9dOa ac ~ =
b ~G~ b ~ Oe ~ a | dia
~ | ua= ~ a+
r |
rr
r
- | a" ~ bb F~ ~ b ~ Oe ~ a | a" ~v| ~ eGab ~F~ b3b ~ a | ¡ ¬
r
4.2.2 Call by value and call by reference
¤y ~ E dO9e/a" | $9-_h | bcH- } Zb"- ~ a ~ b |4 b ~F~ b ~ Oe ~ a°¡ }6~ a" ~ e | bcb ~ _ }S| 9OOeF- } m®
b- ~ a ~ b
dO_3a ~ - -d ~ ¸ ~ a" ~ dOOeGa" | e0Z»_ ~G -d9Za ~ ?Oa" ~ Oa"-0Ua" | |4 a" ~
| b"H- } Zb- ~ a ~ b8HUµ ~ _Va -o--_ |4 a" ~ e0- } Zb- ~ a ~ b0I´1Ha"O_ 0¡D =~ e0-H } ~ ~ a
dOOeGa" | O_=a"9ZaeB9-O ~ a" ~f -d ~ _ |4 a" ~ £be0Z } Zb- ~ a ~ b"_F¦¿ ~ b ~ _- ~B· - } ~
void increment ( int & i )
{
++ i;
}
int main ()
{
int j = 5;
increment ( j );
std :: cout < < j < < "\ n" ; // outputs 6
return 0;
}
´ | b"H- } Ub- ~ a ~ b |4 dOOeGa" | {Z_=b ~F~ b ~ Oe ~ a¢¡ }6~ =~ 9 D~ .BAj>*>wsBl07srCG,1L-,FCG,F!I.G,T_ ~ ®
H-ja"eF_ acb ~ _ }6~ eGaIa | a"9Za } Zb"- ~ a ~ bF dO - ~ ja"¡D =~ _"F¡a"9Za =~ JgAj)F)ac ~8} Zb"- ~ a ~ b
¡Hb ~G~ b ~ Oe ~
´ a" ~o| b"H- } Zb"- ~ a ~ b_ | a |4 b ~F~ b ~ Oe ~ a°¡ }6~ =~ 9 D~ ./Aj>*>wsBlF7 s°P Aj>w:»,<_ ~ H-aceF_F¬
=~+} -_c_
ac ~v} Ub- ~ a ~ b ¡ Zd ~ O ~ be0Z»¡¥b ~F~ b ~ Oe ~ 6a" ~ -Oib ~ _3_ |4 ± | b]¹b ~G~ b ~ Oe ~
a | ³ ac ~ eF- } Zb"- ~ a ~ bk_NdO_ ~ ya | Oa"- ~ a" ~| b"HZ } ZbZ ~ a ~ b0¸dO9 ~ bHeF-£®* ¡® Zd ~
_ ~ HZa"eG_F(a_ a" ~f -d ~f|4 a" ~ e0- } Zb- ~ a ~ b a"9Za_dO_ ~ | bOa"-0Za" | K
¨ ~ -_cekb"dO ~ _va |} -_c_h } ZbZ ~ a ~ bf ¡b ~F~ b ~ Oe ~H| O¡< a" ~N dOOeGa" | $ d ~ _ra" |
-eGacdZ¡ ~F~ O_Va | e9-O ~ a" ~ eF- } Zb"- ~ a ~ b -d ~ ´ a"9ZaV_8 | aVa" ~ eF-_ ~ (eF-O ¡ -d ~ _
| b ~ «9~/· £ ~ 4_cOe ~ a- |m _¦Zbc ~ bVeG-_c_ |4 e0Z } Zb- ~ a ~ b"_=±1 -d ~ _
AD!MNb -d ~ _O_3a ~ -
|4 -d ~ _ | O¡ ³
4.2.3 Return by value and return by reference
¨= ~ b ~ a"dib"Ea¢¡ }6~H|4 dOOeGa" | Ee0-E ~ b ~F~ b ~ Oe ~ a¢¡ }6~ -_ =~ 1I 9eBEe0-_ ~H=~ 9 D~
CF,0#1:C0!?sBl07srCG,1L-,FCG,F!I.G,H_ ~ H-a"eF_]± | a" ~ b _ ~ =~ CF,0#1:C0!^l07P Aj>q:§, ³ ¦´ a" ~f dO9e/a" | {b ~ a"dib"O_
Tb ~F~ b ~ 9e ~ a" ~k dOOeGa" | <e0- ~/· } b ~ _c_c | ½_+-½ -d ~ ac_ ~ §-O =~ e0ZdO_ ~ a ~ b ~GD~ b
-d ~ _Zb ~v~/·(}S~ eGa ~ ?
¨O_ ~ -O_acUaVa" ~ dOOeGa" | Ta"_ ~ e || _ ~ _
±Q ¡NdO_c9vb ~F~ b ~ 9e ~ a°¡ }6~ _ | b8 | a ³ ~ a" ~ b
a"_?e0Z } Zb- ~ a ~ b"_?-Ovb ~ a"dib" -d ~ Zb ~ -d ~ _ | bKb -d ~ _F ~ eGa" | ²² Z9 ~ eGa" |
| eFdO ~ jaa" ~ _ ~ e | e ~ _ | b+_ | ~h|4 a" ~|}6~ bUa | b"_ | dOO9- ~ a"-§a¢¡ }6~ _F6dia | O¡ |U
=~ d9O ~ b"_ra-O¥a" ~ ~ eZ9_cna"9ZaHZµ ~ _=_cdOeeB | e ~ _ }S| _c_c9 ~
¼
_e | OeGb ~ a ~ ~/· - } ~ U ~ aIdO_Ie | O_c ~ b§a" ~8| |m O D~ b"_c | |4 a" ~8 dOOeGa" |
increment
a"9Za ~/· ZeGa"¡ | ~ _ac ~ ~ 9 | b |4 a" ~o} b ~ ®&OeGb ~ ~ a |}6~ b"Za | b
¬{ak9e/b ~ ~ ja"_¹£a"_
++
-d ~} Zb- ~ a ~ b-O{b ~ acdObc9_a-_- -d ~
int & increment ( int & i )
{
return ++ i;
}
´1½ ~ ~ b-* =~ dO_3a+HUµ ~ c_ dib ~ a"9Zah- /~ ·(} b ~ _3_c | 4
| b ~F~ b ~ Oe ~ ¢a ¡ }6~ "a 9Za =~ b ~ a"dib"
b F~ ~ b"_a | <
!I24!?sr#c,FW¹JS24CGADC07 | ~ e/a0z¨ | d9O ~ "b _ra-O 9Z a¥a ~ 6
~ eGa_F ~ adO_
} | b"Z bc¡ | e | O_c ~ ba" f
~ | |m O dOOeGa" | ?
(1]I
(¦
int & foo ( int i)
{
return i ;
}
¨=9_N_T-_rµ(O | bTacb | dO9 ~ _cOe ~ "a ~| b"HZ } ZbZ ~ a
9Za ~ _G§¨=O_§ ~ Z9
_Ka"9Zaa" ~ Zc_ _ | eGZa ~
dOOeGa" | he0Za ~ b"T
~/· } £b ~ _f±1_ ~F~ ~ eGa" | i ³ ´ §=~ m| b"a ~f| b ~/· - }
~ b i cb d9O_ | dia 4
| _ce |}6~ ~ pa" ~
h ~ | bc¡]_ b ~G~ k
Z9ha" ~ Z9ib ~ _c_
~
int i = 3;
int & j = foo (i );
// j refers to expired object
std :: cout < < j < < "\n" ; // undefined behavior
a" ~ b F~ ~ b ~ 9e ~
b
b"_a | - ~B·(} b ~ | ~ e/a09-O{a" ~ b ~ _cdOa"9h ~ | b |4 "a f
~ } b | b"-
j ~G~
dOO ~/¯ ~ ?
_
¤y ~ ~GD~ b
¡ | de/b ~ Z a ~ -Z-_ | b- | ~ eGa0 ~ O_cdib ~ a"9Zaac ~f| ~ eGa
Reference Guideline:
| ~ _ | a ~B·(} b ~ ~F| b ~ a" ~ Z-_B
Oi
¨ ~ e | } ~ bdO_cd9-£¡ | ace ~ _ | Za" | O_ |4 "a ~ ~F~ b ~ Oe ~ fdO ~ ~ -ON_c_cd ~ _V Ub"(®
4.2.4 More user-defined operators
~ a u_¦ ~ a¦-e"µha | a" ~ -OOa" |
Rational numbers: addition assignment.
b
i
d
v
b

3
_
c
a
"
b
O
d
G
e
a
k

1
´

"
b

| |
~G
| ~ bfa |{¯i·<| dOb - ~ Za3a ~ } a
rational
a"O_=_ ~ e/a" | ? =~ ~F~ a | -O¥a =| eB9Zb"-eGa ~ bc_ | O¡D
¼
_a" ~v} b ~G | dO_ dOOeGa" |
9a" ~+| b"H- } ZbZ ~ a ~ b
increment
b ~F~ b ~ Oe ~ g-O¥a | ~ e | } -a a"Ha" ~ dO_cd9-K_ ~ HZa"eG_ |4

+= =~
-_b ~F~ b ~ Oe ~ ¬
-_c_34O ~ a |}S~ bZa | b
9OO |4
b | ac ~ ~ 4
dO_3a ~+} -_c_ ~
Z_

a
-_ | b ~ acdObc¥a" ~ b ~ _cdOa
// POST : b has been added to a ; return value is the new value of a
rational & operator += ( rational & a , rational b)
{
a .n = a. n * b.d + a. d * b.n ;
a .d *= b .d;
return a ;
}
¨ ~| a" ~ bIZbca"O ~ a"eZ_c_c4O ~ ja |}6~ bZa | b"_Zb ~ _cTZb0mZ9 =~ | ua»_3aKa" ~ ~ b V
~ ~/· ®
ac ~ Zbca"O ~ a"eV-O¹b ~ Za" | 9- |}6~ bZa | b"_9_ceFdO_c_ ~ k ~ eG"a | i²
} eF£a"¡D»¨ | ~ a" ~ b £a"
=~ |m 9 D~ hd9_ ~F dO§_ ~ a |4|}6~ bZa" | O_ | ¥b"Za" | 9-6d9 ~ bc_F
~ a¥dO_{ | | µZa b | b- | Oe ~ | b ~ a"ac ~
Rational numbers: input and output.
d OOeGa" | H9- ~
b ~/} -e ~ T ¡
-ONa" ~ dOOeGa" | TeF-
b -e ~ H¡
add
operator+
add (r, s) G~ }
a"* =~ eF-_ }6| a }6| a ~ a"Z6 } b |UD~ ~ a"_G¬O_3a ~ Z |4§ b"a"O
r + s
std :: cout < < " Sum is " < < t.n < < "/" < < t.d < < "\n" ;
{ ~ =~ {b"Za" ~ b b"a ~
std :: cout < < " Sum is " < < t < < "\ n";
°dO_3aµ ~=~ Ub ~ | 9a | b dO99- ~ a-a°¡ }6~ _F¦¼ a ~ bZ1 =~ -jaa | a"Oiµ |4 b"Za" | 9-
dO ~ b-__3O4 ~ -d ~f b | a" ~ _ ~ a]`Z9¥ | a-_=a =|¹ -d ~ _ b | a" ~ _ ~ a f
(b | 9Za =~ 9 D~ | ~ Z |mD~ g¡ | de0-4d ~ _c_acUa- =~ 9 D~ a | | _a |T|UD~ bc | -
a" ~o| dOa } dia |}6~ bUa | b
´1p9_ceFdO_c_cOa" ~¥| dia } dia |}6~ bZa | bk ~ eGa" |
²² =~ 9 D~
<<
Zb"4d ~ a"9Zaa" ~| dia } dia
_3acb ~ - } -_3_ ~ a | -Ob ~ a"dib" ~ ¡¥a" ~| dia } dia |}6~ bZa | b¹dO_3a ~
- -d ~ 9_3Oe ~ ac ~v| dia } dOa |}6~ b"Za | b | O ¯9~ _ a" ~ _3acb ~ ZV¿
O¹b ~F~ b ~ Oe ~ a¢¡ }S~ _
Za | dib
O_ }6| _c-1Oa"O_
e0- ~ Z_c¡{ ~ | ~ ¬ =~ _3 } ¡ } Z_c_-Ob ~ a"dib"a" ~h| dia } dia
_3acb ~ - ± | _ ~
a¢¡ }6~ _
³ -_b ~G~ b ~ Oe ~ ¬
std::ostream
// POST : a has been written to o
std :: ostream & operator < < ( std :: ostream & o , rational r)
{
return o < < r.n < < " /" < < r .d;
}
¨ ~ b ~ _ | b ~ - _ | Ea | _3a |} ~ b ~ ¬ | ba" ~ } dia0 =~T=| dOEa" ~ _"- ~T Z_cO | £µ ~
a | b ~G} - e ~ "a ~ a =
ac_
-O
¡za" ~
| } diaf_3aZa ~ ~ std::cin >> r.n;
std::cin >> r.d;
_cO4 ~ _3a"Za ~ ~ ja
std :: cin > > r;
±&-Oa" ~ _c- ~+| b
ac ~ } dia |4 ³ ¼D-? =~ ~G~ a |k} -_c_]-Ob ~ a"dib"a" ~ } dOa_3acb ~ -
s
± |4 a°¡ }6~
³ -_fHb ~F~ b ~ Oe ~ k´1<-O9£a" | ? =~ ¹dO_3a } -_c_]a" ~ bZa" | Z dO ~ b
std::istream
a"9Za =~v Za=a | b ~ --_hb ~F~ b ~ 9e ~ g_c9e ~ a" ~ } dOa |}6~ bZa | b9-_=a | | 9 ¡Ta"_ Zd ~
¨ ~{|}6~ bZa | b ¯ b"_3ab ~ Z9_a" ~ d9 ~ bZa | b b | a" ~ _3a3b ~ - | |m=~ ¡\_ ~G} ZbUa"O
e9Zb-eGa ~ b0SZ9 ¯ 9-£¡oac ~ ~ | T9Za | b0V¨d9_G =~ e0Zb ~ -b"Za" | 9-? dO ~ b | ~ |
¡ ~ ja ~ b"9 | b ~/· - } ~

1/2
// POST : r has been read from i
// PRE : i starts with a rational number of the form " n /d"
std :: istream & operator > > ( std :: istream & i , rational & r)
{
char c ; // separating character , e .g . ’/ ’
return i > > r.n > > c > > r.d ;
}
´1¥e | jacb-_ra a |
(a"OO4_ e0-o | b | Oi ~ i ac ~ dO_ ~ b ~ ja ~ bc_=ac ~ e9Zb-e/a ~ b
operator<<
_ ~ d ~ Oe ~
ª
b a
b
+bUa" | 9-gdO ~ b0¼
_ | =~} b | Z9¡k | a -a a |
© A/B ~ } | } ~ |
-eFe ~G} a
-_fTb"Za" | 9-» dO ~ bf-_ | dibv } dia |}6~ b"Za | b] | ~ _Gh¨ ~ b ~ Ub ~ ~ eZ9_cT_a |
3.4
~ - £a"¥_cdOe_c_3d ~ _Fidia =~f=| aO_3eFdO_c_ac ~ ~ b ~
~ a+dO_+e | 9eGdO ~ a"O_f_ ~ eGac | £a"<T ~ ZdOac ¯9~ D~ bc_c | |4 b | bZ (¤yUa+HZµ ~ _
a"O_ D~ b"_c | ~GD~ oOe ~ b _¦a" ~
-eGa8acUaVNac ~
dOOeGa" | ?Da" ~ ~G a¢¡ }6~ _d9_ ~ ~/· -e/a"¡
main
µ ~ - Za | TeFª dOO9- ~ ja-Sa¢¡ }6~ _cdOe-_

©
int
(1]I
(¦
1´ a" ~ _ } £b"a |4 ~ eGac | (² | < | OdOZb"FZa" | ? =~ -eGacdZ¡_ } £afac ~} b | b- ja |
a"ib ~F~¯ ~ _F¬ ¯ ~
a"9Zae | a-9_a" ~ ~/¯ Oac | |4 a" ~ _3acb"dOe/a
?Z O
rational.h
rational |
£a"k ~ eFZbZa" | 9_ |4 a" ~|UD~ bc | - ~ |}6~ bZa | b"_G¸ ¯ ~ rational.C a"9Zae | a"-O_¦ac ~ ~G¯ 9w®
a" | O_ |4 a" ~ _ ~+|}6~ b"Za | b"_F¸ ¯ 9-¡D( ¯ ~
a"9Zae | ja-O_=a" ~ H- } b | b"-
userational2.C
¼ a§a" ~ _c- ~ ac ~ =~} dia | dibI ~G a°¡ }6~
-Oa" ~8|}S~ bZa" | 9_ | ha§a | 9- ~ _ } -e ~
rational
| bc ~ ba | D| }6| _c_c£ ~ 9- ~ eF-_c ~ _F
b"eF_ ~
-_3µ _¡ | d¥a | -eGa"d9-¡Tja ~ bZa ~
·i~
ifm
a" ~ ~G bZac | 9-6 dO ~ ba°¡ }6~ a | a" ~ HZa"{ObZb3¡oacUa¡ | d9 D~ 9dOa
bceF_ ~
·i~
_ | a"9Za b | bZ i²] ~ |m e0-{ ~ e | } ~ HdO_cO¹a"O_=£9b"Zbc¡D
Á
// Program : userational2.C
// Add two rational numbers .
# include < iostream >
# include < IFM / rational .h >
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Ã
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Æ
int main ()
{
// input
std :: cout < < " Rational number r :\ n";
ifm :: rational r ;
std :: cin > > r;
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Á"Ã
Á3ÄÅ
std :: cout < < " Rational number s :\ n";
ifm :: rational s ;
std :: cin > > s;
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// computation and output
std :: cout < < " Sum is " < < r + s < < " .\ n" ;
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return 0;
}
Program 31:
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J?CF2GRD)4?:S)-,FC/Aj#1'324!Aj> Y
// Program : rational .h
// Define a type for rational numbers , and declare
// operations on it .
# include < iostream >
namespace ifm {
// the new type rational
A%
3><HF"-+%5#(H!5970)LB
#&3)+
"
-
#E%.CHI>:;G4
,1)+.
<,%7=,AKG
6$,%
3G?%!#&%.
#&%.3>A6$#E%.C; N-+N;%!)L
operator+
,AE6#?9#E%.M5;
4>E>&")+
"0B4>J#&3)L
r + s
"
?)+-LH+/, #E%.)+B #CHI4
">A.
4 OA%(#"*">1)'4G#&3)L
O(0;*8".>
N?-+B.HI5#.; 5# HI<*")5)5B
; O
struct rational {
int n ;
int d ; // INV : d != 0
};
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Á"Â
Á"Ã
Á3ÄÅ
// POST : return value is the sum of a and b
rational operator + ( rational a , rational b );
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Á"Æ
Á
// POST : a has been written to o
std :: ostream & operator < < ( std :: ostream & o , rational a );
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Â0Â
Â0Ã
ÂGÄ
// POST : a has been read from i
// PRE : i starts with a rational number of the form " n /d"
std :: istream & operator > > ( std :: istream & i , rational & a );
}
Program 32:
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// Program : rational .C
// Define operations on the type rational
# include < IFM / rational .h >
Æ
namespace ifm {
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J?CF2GR4)?CGAj#1'324!Aj>Y%
// POST : return value is the sum of a and b
rational operator + ( rational a , rational b)
{
rational result ;
result .n = a. n * b.d + a .d * b. n;
result .d = a. d * b.d ;
return result ;
}
// POST : a has been written to o
std :: ostream & operator < < ( std :: ostream & o , rational a)
{
return o < < a .n < < " /" < < a .d;
}
// POST : a has been read from i
// PRE : i starts with a rational number of the form " n /d"
std :: istream & operator > > ( std :: istream & i , rational & a)
{
char c ; // separating character , e. g . ’/ ’
(1]I
(¦
Â
return i > > a .n > > c > > a.d ;
Â
}
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}
J?CF2/RD)?CGAj#1'r24!Aj> Y
Program 33:
¿ ~ b ~ _- /~ · - } ~ b"dO |4 ac ~]} b | b-
Rational number r:
1/2
Rational number s:
1/3
Sum is 5/6.
4.2.5 Const-types
~ afd9_]e | ~ -e"µa | a" ~ -OOa" |
a" | dO4Eac9_ |}6~ bZa | b |~ _T!I2D#¹a
~ eF ~ OeG¡ -9Za"e=¹¡ | dNT4a_3d94
-j¡ F¡S¬
|}6~ bZa
~ O$a |
~ _3aa |
| b | b]bZac | 9- dO
eB9-O ~ a" ~N -d ~ _
_ }6~G~ Td } a"O_ |}6~ bUa
~ b"_ b | b | bZ (+¼
£®
|4 £a"_e0- } Zb"- ~ a ~ bc_Fa" ~
| b¡d9_3Ovb ~F~ b ~ Oe ~ a¢¡ }S~ _
// POST : return value is the sum of a and b
rational operator + ( rational & a , rational & b )
{
rational result ;
result .n = a .n * b.d + a.d * b. n;
result .d = a .d * b.d ;
return result ;
}
´1O ~F~ ?Va"O_ D~ b"_3 | \_e | bcb ~ eGaNZ9 }6| a ~ ja"-£¡ -_3a ~ bka"9-a" ~o} b ~G | dO_ | ~ 8_cOe ~ a" ~
Oa"-0Ua" | |4 | b"HZ } Ub- ~ a ~ b_ | ~ ¡e |} ¡ O °dO_3av24!I,+Z9ib ~ _c_FDbZa" ~ b¦a"9-¥#1;]2
Zd ~ _I-_»a" ~ ~ ~ br® _ ~ e |} ¡va"9Za§aUµ ~ _ } -e ~ dOO ~ ba" ~ e0Z£®1¡® -d ~ _ ~ H-ja"eF_G
int
z a" ~ _" Ok__cHZ6{ac9_ ~/· - } ~ ¡ | deF-H-4 ~ a"9Za ~ ~ b3® _ ~ e |} ¡
D~
e0- ~h} b ~ aca¢¡ ~B·(}6~ O_c D~ _3a3b"dOeGa"_a"9Za]Zb ~ | b ~~ Z | bZa ~ acZ
¸?ze | acb"-_3a0
rational
e0-?¡Hb ~F~ b ~ 9e ~ _ -_3a | b¹Aj>*>»a°¡ }6~ _F ~GD~ a" ~ | _3ae | } e0Za ~ | ~ _F
| bca"dO9Za ~ £¡DVa" ~ e0- } ZbZ ~ a ~ b"_d9_rak ~ -d ~ _kdOO ~ bNe0- ¡b ~F~ b ~ Oe ~ _ |=~
e0- a b"a ~ a" ~~/·(} b ~ _c_c |
b
- } ~ ~GD~
Zb
Zb"U ~ _ |4 a°¡ }6~
a + b + c | ~/·
a, b, c ~

±
¡ ³ ac1Sa" ~ -_3a ~ b D~ bc_c | T4ja =| bcµz | dOb+ }O} e0Ua" | ?¸Saf | ~ _f_ |
rational
b

i
²

|
| b ~/· Z } ~ _3Oe ~ Ta"O_ } b | b"- =~ e0- operator+ a"T -d ~|}S~ b-OO_
| O¡D
~ ~ _c_ | | dO_±1-O¹dOe< | b ~ Z9 ~ b | dO_ ³ } b | 9 ~
b ~ H-O_FSac | dO4?¬] } -_3_cO
a" ~} Zb- ~ a ~ b"_H-_Hb ~F~ b ~ Oe ~ _F =~ Aj>*> 24; a" ~z|}6~ bZa | bTa | e9-O ~ a" ~ -d ~ _ |4 a"_He0-
} Zb- ~ a ~ b"_8oa" ~
¯ b"_3a } Ze ~ ~GD~ ¥ a"9Za=9 }O}6~ O_ dOOa ~ a" | Z¡D»´1 dOOeGa" | O_Va"9ZaUb ~
Zbc ~ b
a"9-a" ~ Z |mD~
SaeF- ~ -_c£¡9 }O}6~ a"9Za =~ | O ¡o_ | ~|4 a" ~ e0-
operator+
} Zb- ~ a ~ b"_=_c } ¡¹ ¡{T_3aUµ ~
| aHZµ Ok_cdOe<T_3aZµ ~ __
a" ~+} b" ~ b ~ _ }S| 9_39a¢¡ |4 a" ~} b | b-T ~ b0 |4 e | dib"_ ~
9diaa" ~ eG ~GD~ b } b | b"-T ~ b=e0-_ac ~v} b | b-TTOh-O4d9- ~]| b ~ } ~ ~GD~ b }6| _3_c9 ~
_=h-{ |UD~ (_cOe ~ a=jacb | 9dOe ~ _
´1{ac9_ _ } b"a0ja" ~ Z |mD~ ~ eF ~ 9e/¡ ¯i· ª | b
operator+
©
~/ }S| _c_c9 ~ _ | dib"e ~v|4§~ b3b | b"_F
´ a"O_]_ | dOOO_fa || U_racb-eGa | bv¡ | dKK ~ b ~ _v- ~/· - } ~ ~ b ~ af_f_c } ¡ b | OHa |
|mD~ a | e0Z£®1¡®*b ~F~ b ~ 9e ~ _ ~ HZa"eG_F¸4a" ~ e | } ~ bI9-_¦ | e9-Oe ~ a | ~ a ~ e/aa"O_ ~ b3b | bV_3Oe ~
a_ } dib ~ ¡{_ ~ HZa"eF-1= | O_c ~ bac ~ dOUbc¡_cdiOacbZeGa" | |}S~ bZa | b | b
a" ~ a¢¡ }6~
rational
b | ~ eGa" | i²
// POST : return value is -a
rational operator - ( rational a)
{
a .n = - a .n;
return a ;
}
Z949ha"O_=a |
rational operator - ( rational & a)
{
a .n = - a .n;
return a ;
}
9-_ib-_3a"e±&-OdOO ~ _cb ~ ³ e | O_ ~ d ~ Oe ~ ¬Na" ~T~/·(} b ~ _3_c |
V_3a"V9 D~ ac ~ _c- ~
-a
-d ~ -_ ~F| b ~ j9dOa8a O9 D~ a" ~ -OOa" | Z ~GºS~ e/a |4 eB9-O4Ofa" ~ -d ~
|4 I¤ ~ 9 D~
a
-eFeG ~ aZ¡(ªeGb ~ Za ~ e | } ~ a ~ ¡TO ºg~ b ~ ja |}S~ bZa | bF
©
¼
_fH-¡ | a" ~ bfO4(®& ~GD~ } b | b-TTO¹-O4d9- ~ _FKv |ºg~ b"_T ~ e9-O_c acUa } b |}6~ b"¡$dO_ ~ ^Z |m _ha" ~ e | } ~ ba | ~ a ~ eGakdO9 ~ _3b ~ \e9-O ~ _ |4 -d ~ _¹-_kEa" ~
} b ~G | dO_ ~B· - } ~ ¨= ~ ~ h_ a | J?CF24W¥'*)-,ha"9Zahe ~ bcaZ -d ~ g | a= ~ eB9-O ~ ?O-O
a" ~ ~ aac ~ e | } ~ b»eB ~ e"µ ~ ac ~ b =~ µ ~F~G}k| dOb } b | T_ ~ ´1ha" ~ e0Z£®1¡®*b ~F~ b ~ 9e ~=D~ b"_c |
|4 ac ~ dO9Zbc¡H_cdiOacbZeGa" | |}6~ bUa | b0(a" ~ ± -_ ~ ³ } b | T_ ~ e0-o ~ 4 D~ Z_ | |U _F dO_cOa" ~
µ ~ ¡ =| b"

const
rational operator - ( const rational & a)
{
a .n = - a .n ; // error : a was promised to be constant
return a ;
}
´1Ne | } Oa"O_ Zbc-a |4 ac ~|}6~ b"Za | b04a" ~ e | } ~ b (_3_cd
O | diaa" ~ T_3aZµ ~ ¤ ~ e0-a" ~ ¯O· a ¡ ~ a" ~ b | OgZeµoa
| b ¡{acb | OdOeFOb ~ _cdOa ZbcZ9 ~ µ ~ operator+ Z |mD~
(b | a" ~ _3acb"e/a"¡ dOOeGa" | Z }6| ja |4 ~G Ia"O_ } b | T_ ~
-O$a" ~ b ~ Zb ~N} b | b-TT9{-O4d9- ~ _dO_ ~ a"9Za | uah9 D~
~ - ~ bcb | b ~ c_ _"- ~ }S| a3®
| e0-£®* ¡j® -d ~ _ ~ H- aceF_F
~ e Z9_c _h_cd 6
} ~ b « d | dO_F
£aH±¢¶dO_ ~
a | ~ _cdOeB
(1]I
(¦
-O4d9- ~ 4dOja"(a" ~
µ ¡
b" Z_V-O ~ ¹²
D | a" Za ~ ¡¹£a"__cdOeFe ~ _c_VTv ³
const ~ =|
¼
_ | i | | i¡ | b"e ~ _d9_a | HUµ ~ dO_ ~v|4 a" ~f} b | T_ ~ ~ e9-O_c Vdiaa" ~v | ~]}S| a |4
O4(®& ~/D~ } b | b"-TTO -O4d9- ~ _K_§a | HZµ ~ ac ~} b | b-T ~ b u_6 ~~ -_c ~ b0¸a" ~ e | } ~ b?_
| dib b" ~ 9HZ9He0ZT ~ } d9_a | D| TH-j¡¹a" ~ ®&e | O_cdOTO ~ b3b | b"_F¨ ~ const ~ e9-O_c
_fµ ~ oe ~ e"µO4£a0¬
¡ } b |U OO¥Z9Oac | 9-§b ~ OdOO9-av9Za±*a" ~
µ ¡
b" ³ =~
const ~ =|
HZµ ~ _cdib ~ a"9ZaOe | O_c_3a ~ OeF ~ _hEac ~T | ~ 9Za_ ~ a{±*a" ~N} b | bZ ³ Zb ~ -dia | HZace0-£¡
~ a ~ e/a ~ ?
Definition.
const
´ _Z¡Ha¢¡ }6~ ia" ~
_+ac ~ .G24!?)F#&s 0:»Aj>q' t,BMa¢¡ }6~ ±1e | O_3ar®1a¢¡ }6~T| b_c | bca ³ |4
#17mJ6,0I¨= ~ e | O_3ar® d9- ¯9~ D~ b"_c | |4 Z_ ~B· e0-e/a"¡]a" ~
-_ ¨= ~N| O¡O ºg~ b ~ Oe ~ _va"9Za- ~/· } b ~ _c_c | |4 e |
a"_ Zd ~ ±1 | ac ~ b =| b"O_F£a_ve | O_3a-ja ³ ¸a"O_v_ | dib
~ ac ~ b =~ µ ~F~G} a"9Za } b | T_ ~
´ §=~] b"a ~f| b ~/· Z } ~
-O a"_ ~ _va" ~
"_ - ~I Zd ~ b"-O ~ Z9
O_3a3®*a¢¡ }6~ _+ | ah- |m=~
} b | T_ ~ Z9ac ~ e |
: !MO,FCm>q7'Q!SR
g
d9OeGac | 9-a¢¡
a | e9-O ~
} ~ bfe ~ e"µ(_
const int n = 5;
n = 6;
"a ~ e | } ~ b I_c_cd ~ - ~ bcb | b ~ _c_c- ~ e | 9e ~ b"OO{a" ~ -_c_c49 ~ a
»_3Oe ~
9-_
n = 6
n
a" ~ e | O_3a3®1a¢¡ }6~

const int
-d ~ _
_3a3®*a¢¡ }6~ ¹dO_3a- 0¡ _ ~ Oac- ~ ?»¤<bca"O
|4 e | O
const int n ; // error : uninitialized constant
_ ~ D-±&-O{HZµ ~ _ | _ ~ O_ ~ _c9e ~v=~ e0- ~GD~ b
-_c_c4 -d ~ a |
Za ~ b ³
n
4.2.6 What exactly is constant?
~ ad9_=e
a¢¡ }6~ a"
_c ~ b=_ | ~ -d ~|4 a¢¡ }6~
O´ a" ~ d9O ~ b"£¡(Oa¢¡ }6~ | O
const
~ Ha" ~ -d ~ _=-_3_ | eFZa ~ £a"H+e | O_3aZah2(l
-,G.0#& | b ~/· Z }
b T_ ~ _]a"9Zafa" ~k Zd ~k|4 a" ~¹| ~ eGav ~ OO<a" ~k
const int n = 5 } |
~ | 9 ¯~ K ¤ ~ H0¡<±&-eFeG ~ aZ¡ ³ acbc¡¥a | e ~ ZafZb | dOOa"O_ } b | T_ ~
9- ~]| bac ~f| ~ eGa0i9dOa=a" ~ e | } ~ b 6e0Ua"edO_F¬
_ | a+b ~F~ b ~ Oe ~
~ jac ~ ~ eGZbZac |
Zb"Z9 ~
| a
n
¡dO_c9HZ | ac ~ b
const int n = 5;
int i & = n ; // error : const - qualification is discarded
i = 6;
4
.
4 /
A* ;.?)+-LHFHI> L><.4>EG?="
065871,A)LB
*3
<=
*3@DC6##E)
#&%%:9CB
3G?%(#E>;#?)
#E%.MG*8>E>J3G9NE#&3G4*"!"#%$&('*) +,-#.%/0213
B>&2>&B.G?%=
?@*6BC)L' #E%.C#:70; > )()L' 7F#:70;+/5')#E%N#
HI4G?%
3>JH=O
H!N#&#E
7/%>G)L.>J#?5#1@L*"B.275,47DO
¤ ~ e0-O | a dO_ ~ - ~/· } b ~ _c_c | |4 a¢¡ }6~
a | 9£a"- ~ ± | b=-_3_c4Na | ³ Z ~B·(} b ~ _c_3 | |4
const
¢a ¡ }6~ S_cOe ~ acUa =| dOeGb ~ Za ~ k | 9 ¯ U ~ --_ | bf- | ~ eGa
a"9Za -_ } b | T_ ~ ¥a |
~ e | O_3a-ja0
Ta" ~
| ac ~ b 9-OK-T -d ~ ±&-eGa"d9-¡DD-¡ ~/·(} b ~ _c_c | ³ |4 a¢¡ }S~
_a" ~ --_
const
|4 Z | ~ eGa069dOafa"9Za | ~ eGav_h!I2D#+ ~ e ~ _3_"Zb"£¡e | O_3a-ja+ac_ ~ h¨= ~ e | 9_ra3® dZ ¯ e0Za" |
Ta"O_8eF-_ ~ _8 ~ b ~ ¡T } b | T_ ~ a"9ZaVa" ~| ~ eGa _ -d ~
| a8 ~ | O ¯9~ #&%(CF24:9RD%a" ~
--_ d ~ _3a" | ?¦¿ ~ b ~ _- ~/· - } ~ a"9ZadO_3a3bZa ~ _a"O_ }S| a0
int n = 5;
const int & i = n ;
int & j = n ;
i = 6;
j = 6;
//
//
//
//
i becomes a non - modifiable alias of n
j becomes a modifiable alias of n
error : n is modified through const - reference
ok : n receives value 6
¿ ~ b ~ =~ | | ak9 D~ ze | O
_3a-ja2(l
-,G.0#&=9dOaN<e | O_3aZa,BX0J?CF,0)F)G'r24!
b
_
c
c
_

a
¢
¡
_-_ | e0- ~ ¥.G24!?)G#&srCF,1LZ,FCF,F!I./,0
/~ · } ~
| 4
|
} ~ const 6
4.2.7 Const-references
±19- ~ ¡
³ ¼

i
§bc_3a |4 Z1-a" ~ a¢¡ }S~ 9- ~
_ } Zb-ja" ~ _c ~ kZ_
± ³ 41 ~ =~ ~ ae |
const
const
}O}6~ Zb+b
-d ~ _ |4 b ~G~ b ~ Oe ~ a¢¡ }6~ | O_3a3®1b ~F~ b ~ Oe ~ _¹Ub ~kD~ bc¡d9_ ~F dO -O |4 a ~ E
e | ~ ~ a¹dO_e | ~ -e"µ$a || dib Z_3a ~ b D~ b"_c | |4
b¹b"Z"a | 9- dO ~
operator+ |
_" ~ ª D~ b"_c | _ a"O_F¬
©
O_3aZa
~ Z£®& ~
b"_F<´*a"_
// POST : return value is the sum of a and b
rational operator + ( const rational & a , const rational & b ) {
rational result ;
result .n = a .n * b.d + a.d * b. n;
result .d = a .d * b.d ;
return result ;
}
¨= ~h ZeGa]a"9Za
a"O_e | } ~ _e | ¯ b"T_acUa =~ Zb ~ | a]eZ949Nac ~ -d ~ _ |4 a" ~h| b"H-
} Zb- ~ a ~ b"_ a | b b a"Okac ~ | i¡ |4 a"O_ dO9e/a" | ?Vdia8a" ~ b ~
-_8- | a" ~ b } b | 9 ~ ¶a"9Za
=~ }O} Zb ~ ja"¡¥99 a
_ | D~ ¡ ~ a0¬ } -_c_3O } Ub- ~ a ~ b"_ ¡¥b ~F~ b ~ 9e ~ b ~ dOb ~ _ -d ~ _]-_e0-
} Zb- ~ a ~ b"_FDZ9a"O_I_ ~/D~ b ~ ¡b ~ _3acb"e/a"_Ia" ~ }9} e0Z9a¢¡ |4 a" ~|}6~ bZa | b0 | bca"dO9Za ~ ¡Dac9_
_¦ | i®1_c_cd ~ ¬§e | O_3a3®1b ~F~ b ~ Oe ~ _
±1 } Ubca"eFdOUb0 | b"H- } Ub- ~ a ~ b"_ |4 e | O_3ar®1b ~F~ b ~ Oe ~ ®*a°¡ }6~ ³
e0-{ ~ 9£a"- ~ b | b Zd ~ _Z_ =~ 1¨O_ ~ -O_ a"9Za =~ eF- bca ~
const int & i = 3;
~ OOvac ~ _ce ~ ~ _FZa" ~ e | } ~ bSeGb ~ Za ~ _§ a ~ }S| bZbc¡ | ~
-Oib ~ _c_ |4 a"O_a ~ }6| bZbc¡ | ~ eGa8_8dO_ ~ Ta | Oac- ~ a" ~
HZµ ~ _h_3dOb ~ acUaha" ~ a ~ }6| bUbc¡ | ~ eGa | ~ _h | a ~/· } b ~
b ~F~ b"_a | af±1_ ~F~ a" ~ ~F~ b ~ 9e ~ fdO ~ ~| - ~
³
¨ ~ _"- ~ 9 }O}6~ 9_ ~ | b"H- dOOeGa" | } ZbZ ~ a
a"Z ~ b | -¥b -d ~
eGa?a"9ZaK | O_Sa" ~¦ -d ~
e | O_3a3®*b ~F~ b ~ 9e ~ ¦¨=
i
~F| b ~ a" ~ e | O_3ar®1b ~F~
Z-Ova" ~
~ e | } ~ b
b ~ Oe ~ acUa
3
~ b |4 e | O_3a3®*b ~F~ b ~ Oe ~ ®1a¢¡ }6~ _O£®
(1]I
²
(¦
¼
_+a" ~ b ~F| b ~ a" ~ -£®1(® | ~ ~/ e ~ _cdOaZ9 ~¹| b ~GD~ bc¡
} Z b- ~ a ~ b |4 a¢¡ }6~ const } dib }6| _ ~ ¬¹' L\a" ~ e0- } Zb- ~ a ~ b+_-½ -d ~ Ka" ~ Oac-FZa" | _ D~ bc¡ ~ eF ~ aN± | 9£¡<ac_
-Oib ~ _c_{ ~F~ O_¥a | ~ e |} ~ ³ ]Z9 | a" ~ b _ ~ =~<~ _c_ ~ ja"-£¡ ZgZeµa | eF-£®* ¡® Zd ~
_ ~ HZa"eG_F
-_N
~ _ } a ~ a"O_FVa" ~ b ~ Zb ~ _3a"_3a"d9Za" | O_ ~ b ~ _ } b ~F~ bcb"Z9 ~¥|mD~ b const } Zb- ~ a ~ bIa¢¡ }6~ ´ _ dOOZ ~ aZ a¢¡ }6~| b8]_3acbcd9e/a a"_cH-( ~ | bc¡+b ~ dOb ~ ~ a"_F
a |~ _= | a } F¡ |º a | |mD~ a |
(_3Oe ~ a" ~ _" OH9-O9O -d ~} Zb- ~ a ~ b"_
const
_=_ | _cH-»± | b ~GD~ | ~/· _3a ~ ja ³ a"9Zaa =| ua=e | }6~ 9_cZa ~| ba" ~ ±1_34ac¡ ³ | b ~ e | _3a"¡
-eFe ~ _c_
a | a" ~| bcH- dOOeGa" | } Zb"- ~ a ~ ba" ~ dOOeGa" | | i¡D´1O ~F~ ?SeF-»¡¥b ~G~ b ~ Oe ~
-OO_ | ~ O9£b ~ eGa" | K¬Ka | | | µkd } a" ~
-d ~|4 | b"H- d9OeGac | } Ub- ~ a ~ b dO9 ~ b=eF-£®* ¡®
b ~F~ b ~ Oe ~ _ ~ HZa"eG_F =~ t Cm)G#9 D~ a | | | µfd } a"_§-Oib ~ _c_IZ9ac ~ | | µfd } ac ~ -eGa"d9- -d ~
Zaa"9Za-Oib ~ _3_F 9 ~ be0-w®1 ¡j® -d ~ _ ~ H-aceF_Fia" ~ -Oib ~ _3_ |4 a" ~v -d ~ _ 9Zb" b ~ Oª
©
±&-Oob ~F~ b"_a | _ | ~]| ~ eGa | ¥a" ~ eF-6_3aZeµg_ ~F~ ~ e/a" | ( 4³
¼
_ | 4£a_ |4 a ~ ke | D~ O ~ jaa | dO_ ~ a" ~| bcH- } Zb- ~ a ~ b-_ | eF- Zb"Z9 ~ Z9¹ | O ¡
a"_ -d ~ ±1_ ~F~
Z
³ ¸ bacUa0ia"_ a¢¡ }6~ ¹dO_3a | a= ~ e | O_3ar®1a¢¡ }6~
operator- |mD~ |
4.2.8 Const-types as return types.
| 9_ra3®1a¢¡ }S~ _HF¡-_ | }O}6~ Zb
-_
b ~ acdObca¢¡ }6~ _ |4 dO9e/a" | O_F °dO_3a]£µ ~ -j¡ | a" ~ b
a¢¡ }S~ _F´1
a"9Zae0-_ ~ 9ac ~
b T_ ~ _ a"9Za=a" ~f dO9e/a" | e0Z ~/·(} b ~ _3_c | ac_ ~ _e | O_3a-ja0
const } |
´ a" ~ b ~ a"dib"ka¢¡ }6~ _¦ | aV]b ~F~ b ~ Oe ~ a°¡ }6~ 4a" ~ d9OeGac | Ne0- ~/·(} b ~ _3_c | N_-kb -d ~ -O
~ Oe ~ | a | 9 ¯ U ~ -j¡ F¡D¦´1¥a"O_ e0-_ ~ ia" ~
µ ¡
b"_= ~ DZSdia9-_= |k~Gºg~ eGa0
const ~ =|
| 9_ra3®1a¢¡ }S~ _ac ~ b ~F| b ~v| 9£¡{HUµ ~ O ºS~ b ~ Oe ~ a" ~f dOa" | {b ~ a"dib"O_b ~G~ b ~ Oe ~
| a ~
acUaNak_¥!I2D#H ~ ~ b-¡ -\a | b ~G} Ze ~ b ~ acdObc a¢¡ }6~ ¡
¸ O ~
const
a"O__" ~ £¡ =| bcµ _ | b¹a" ~¥| b"H- } Zb"- ~ a ~ ba¢¡ }S~ _F ae0- | b¹a" ~ b ~ a"dib"\a¢¡ }6~ b ~ _cdOa¹
_3¡ a-e/a"e0-¡Te | bcb ~ eGa9dia_ ~ H-ja"e0Z¡ b | O¹e | ~
¡
Z_ka" ~ b ~ a"dib"\a¢¡ }6~|4
¼
_T- ~B· - } ~ ¦ ~ a _¹b ~G} -e ~
rational
const rational&
¬
operator+
const rational & operator + ( const rational & a , const rational & b ) {
rational result ;
result .n = a .n * b.d + a.d * b. n;
result .d = a .d * b.d ;
return result ;
}
´1 ~/·(~ eFdia"OHa" ~
_3aZa ~ ~ aFSa" ~ b ~ a"dib" -d ~ ±*zac9_feF-_ ~ He | O_3a3®*b ~F~ b ~ Oe ~ ³ a |
return
k

3
_
_
$

a
"
a

0
e

b
~ }
~
|
~
~ |4 a" ~T dOOeGa" | ½_Oa"Z ~ aca" ~N~/·(} b ~ _c_c | result |m
b ~ eF-=a"9Zaka" ~ 9£a"- 0Za" | |4 E±1e | O_3a3® ³ b ~F~ b ~ Oe ~ b | Zp Zd ~ _c } ¡$HUµ ~ _kak-
--_ |4 a" ~ -d ~ Vdiaa" ~ -d ~ d ~ _3a" | ±19- ~ ¡
³ _h | eF- ZbcZ9 ~
| _ ~
result
~ | bc¡¥_ b ~F~ ½Z9 | _ ~ -Oib ~ _c_f ~ e | ~ _] Z ~ ac ~ dOOeGa" | e0-a ~ b"T9Za ~ _
±1_ ~G~ ~ eGac | i ]-O ~ eGa" | i ² ³ I¨= ~ e | O_ ~ d ~ Oe ~ _Ia"9Za¦a" ~ b ~ a"dib" ~ kb ~G~ b ~ Oe ~
~ a" ~ -Z_ |4 Z ~/·(} b ~ | ~ eGaFg-OdO_cOa"O_b ~G~ b ~ Oe ~ b ~ _cdOa"_d9O ~G¯ ~ ~ 9 | b
|4 ac ~f} b | b-
b3b b"_oµ ~ a"O_HZb ~D~ bc¡y9Zb"ya |$¯ O±&-O =~ e0-O | aHb ~ Z9¡\e | dOja | e | } ~ b
|
Zb"OO4_ ~ b ~ ³ I_cOe ~ ac ~N} b | b"- WAD7 =| bcµ-_ha ~ O ~ K | b ~B· - } ~ a" ~ ~ | bc¡
a"9Za -_Z_c_ | eGZa ~ $a | a" ~H~/·(} b ~ | ~ eGa_h | aT ~ 9Za ~ ¡b ~ dO_ ~ ? Vdia | \Z | ac ~ b
} Za | bca" ~]} b | b- H0¡k ~ 9 D~ O ºS~ b ~ ac¡ | b ~/D~ eGb-_3K
4.2.9 When to use const?
¤y ~ ~GD~ b¡ | doa"OiµHZ | dia a" ~ }O} b |} b"Za ~ a°¡ }6~f|4 Zb"Z9 ~ i | b"H- dOOeGa" | } Zb-k®
~ a ~ b0 | b+ dOOeGa" | u_
b ~ a"dib" -d ~ 6af_ | | } b-e/a"e ~ a | a"OiµZ | dOa]e | 9_ra3® dZ ¯ e0Za" |
Zava" ~ _"- ~ a" ~ k¼ a ~ bh-*K¡ | d½_c | dO<µ |U¶ 9Zaf¡ | d -afa | |¥ a"ac ~¹ ZbcZ9 ~
} Zb- ~ a ~ b0 | b8b ~ acdObc -d ~ ±* ¡ | dH | a0a"O_ } Zb-b } T_ ~GD~ { | b ~ }S| bca-ja ³ _ | ¡ | d
-_ | µ |m ~ a" ~ ba" ~]} b | b- ~F~ O_a | eZ9 ~ a"_ -d ~ Za_ | ~]}S| a0
¨ ~ gZ_ceb"dO ~ a |k| |U _a"O_G¬
_ ~ e | O_3a a¢¡ 6
_
b a"O__ S
} | c_ _c9 ~ - OHZµ ~ _O ºS~ b ~ Oe ~ 9´*a
Const Guideline:
− } ~ ~ G~ D~
- F¡ _HUµ ~ _O ºS~ b ~ O
e ~ ¥e | O ~ Ge ac | £"a ob ~F~ b ~ O
e ~ a°¡ }6~ 0_
´1O ~G~ ?£aN_¹ | b ~ acZ\a" ~¥} b | T_ ~o|4 e | O_3a-ja -d ~ a"9Za¹O_3a"94dO_3 ~ _a" ~ a¢¡ }6~
¬ O ~k=~ ~F~ -d ~ _+a | Oac- ~ -O-_c_c4$a |z| ~ eGa"_ |4 a¢¡ }6~
b | const
_ } b ~F~ b"Z9 ~ a |
gb -d ~ __cd e ~| b
¤ ~ 9 D~ Z_ | Zb"4d ~ a"9Za
const
const
¥H-j¡H_ca"d9Za" | 9_G(_c } ¡ | b ~ eF ~ OeG¡ob ~ -_ | 9_G | de0-O | a4 | b ~ a" ~ _ ~+ ZeGa"_F ~GD~
¡ | d | ae0Zb ~ Z | dia=a" ~f} b | T_ ~ ~ eZ9_c | a" ~ b _ ~
´ _] | afNb ~F~ b ~ Oe ~ a¢¡ }6~ 6a" ~ ac ~ d ~ _3a" | ~ ac ~ b
HZµ ~ _]HO ºg~ b ~ Oe ~
const
b | 9-_TdO_cd9-£¡\ | aT_cdOe eF ~ ZbH-O_ =~ b0 a" | ~~/· e ~G} a" | ?¬ b ~ a"dib" a°¡ }6~ _ |4
dOOeGa" | O_+a"9Za+ | | avb ~ a"dib"½b ~G~ b ~ Oe ~ _G¦a" ~ const µ ~ ¡ =| bcEb ~ -¡HZµ ~ _v | O ºg~ b ~ Oe ~
-O_c | dOoa" ~ b ~F| b ~ ~f| Taca ~ ?
´1Eac ~ _"Z ~ _ } b"aF§a" ~
µ ¡
bc _a¢¡ } eF-¡ | Taca ~ | b | b"H- dOOeGa" | } U®
const ~ =|
b- ~ a ~ b"_
a"9ZavZb ~ | ab ~G~ b ~ Oe ~ _Gk´1za"O__ca"d9Zac | ?
_h!I2D#vb ~ 9dOO9-aFSa" | d94?¬

const
| b"HZ } Zb"- ~ a ~ b+_ |4 e | 9_ra3®1a¢¡ }S~ =~k} b | T_ ~ | a+a | dO_ ~ a" ~N| b"H- } Zb- ~ a ~ bZ_h
| O ¯ Z9 ~ | eF- Ub"Z9 ~ Vdiaa"O_ } b | T_ ~ _ ~ a" ~ b ~ e ~ _c_"Zbc¡Ea |z} b ~GD~ aN-eFeF ~ a-
| O ¯ e0Ua" | |4 a" ~ e0- } Zb- ~ a ~ bv±1e0-? ¡ -d ~ -b ~ -i¡{aUµ ~ _e0Zb ~+|4 a"O_ ³ 9 | b | ~ _
£a
« d ~ Oe ~ a" ~]| dOac_c ~ ~ 9 | b |4 a" ~] d9OeGac | {¥-j¡ F¡D´1 -eGa0i ¡ | d b"a ~
dO9e/a" | O_
| bH<ObZbc¡y±1_ ~G~ ~ eGa" | (² D³ ¡ | d ~ aca ~ bkb ~F b- b | _cdOeye | 9_ra3®1a¢¡ }S~ dO_"- ~ -_N£a
dOO ~ e ~ _c_"Ub"¡¹b ~ _3acbceGa"_8¡ | d?¬ ¡ | d{Za ~ b ~ eG ~ a | eB9-O ~ a" ~ dOOeGa" | H ~G¯ Oa" | ?D¡ | d¥Ub ~
e | TTa3a ~ ¹a | a" ~ e | O_3a3®*a°¡ }6~
} Zb- ~ a ~ b
± ~GD~ o a"O_a"dib"O_ | dia8a | ~ } b-eGa"e0- ³ -d9O ~ _c_
¡ | d-_ | e9-O ~ ac ~ ~ - ~ b ¯ ~ acUae | a-9_ a" ~f dO9e/a" | ~ eFZbZa" | K
¼
_ | 9 | a- Zb"Z9 ~ _=a"9Za
e | dO{ ~ ~ eFUb ~
} b | bZÀZb ~ a¢¡ } e0-¡H | ~
const
_ | _c } ¡ ~ e0-dO_ ~ £a¹HUµ ~ _H± | bN }9}S~ Zb"_a | HUµ ~ ³ | O ºS~ b ~ Oe ~ a" ~ e | a ~B· a |4 a" ~
~ eFUbZa" | ?¼_ - ~/· Z } ~ e | 9_3 ~ b ~ h b | b"- (¬Ia'1) }S| _c_c9 ~ a | ~ eFZb ~ a" ~
Zb"Z9 ~ t -_¦ ~ O |4 e | O_3a3®1a¢¡ }6~ const rational D9dOa¦a | ~ _3 a¦HZµ ~ fO ºg~ b ~ Oe ~ j_cOe ~
a"O_ Zb"Z9 ~]| eFeFdib"_ | Oe ~f| O¡{ a ~ b Zb"O_FO-O¥a"O_ | eFeFdib ~ Oe ~ _ °dO_3aa"ib ~F~ ~ _ ~ |m
| b e | OeGb ~ a ~ ~ _c_F( ~ a8dO_8_3ac } d9Za ~ a"9Za Ub"Z9 ~ a"9Za8_V ~ -jaa | 9 D~ e | O_3a-ja -d ~
_c | dO¥ ~G¯ Oa ~ ¡H ~ ae | O_3a3®1a¢¡ }6~ a"__ce |}S~ _ } -O_ | b ~ a"9-½² ~ _ |4 e | ~
(1]I
(¦
4.2.10 Goals
¼=a=a"O_ }6| ja0 ¡ | d_3 | dO<FF
Dispositional.
² ³ dO9 ~ bc_3a-O¥a" ~ -Z_ e | Oe ~G} a ~ 99ob ~F~ b ~ Oe ~ a¢¡ }6~ _-O¥ac ~ ~G~ b ~ Oe ~ ]
dO ~ ~ ¸
-aceF_ | b
4³ dO9 ~ bc_3a-Oka" ~ O ºS~ b ~ Oe ~ ~ a =~F~ <.BAj>*>§l07HP Aj>q:§,f-O<.BAj>*>§l07TCG,1L-,FCG,F!I.G,h_ ~ H
d9OeGac | } Zb- ~ a ~ b"_F¸
³ dO9 ~ bc_3a-Oe | O_3ar®1a¢¡ }6~ _
-O{ac ~ | O_3a ]d9 ~ ~
´1 } Zbca"eFdOZb0j¡ | d_c | d9{ ~ Z9 ~ a | G0
Operational.
± ² ³ _raZa ~=~/· -eGa } b ~ ®¢-O }S| _3a"e | OOa" | O_ | b dOOeGa" | O_¦ D
| O | b"H- } ZbZ ~ a ~ bIa¢¡ }S~ _
b
b
"
a
i
d
"
b
{

°
a
¡
_
b
b
O

b
e
O

3
_
3
a
*
®
°
a
¡
¸
|
~
}6~ |4 ~F~ ~ ~
|
|
}6~
± 4³ b"a ~] dOOeGa" | O_ a"9Za | O ¡±*_ | ~]|4 ³ a" ~ be0- } Z"b - ~ a ~ cb _F¸
± ³ ¯ Oo_3¡(ja-eGa"e0-6-Oo_ ~ H-ja"e0Z ~ bcb | b"_ } b | b"-T_Va"9ZaZb ~ O
d ~ a | } b | }6~ bV9-(®
OO |4 b ~G~ b ~ Oe ~ a¢¡ }6~ _F¸
±
³ ¯ Oo_3¡(ja-eGa"e0-6-Oo_ ~ H-ja"e0Z ~ bcb | b"_ } b | b"-T_Va"9ZaZb ~ Od ~ a | } b |}6~ bV9-(®
OO |4 e | O_3ar®1a¢¡ }6~ _F¸
± 4³ ¯ O
a" ~ ~ eFZbZa" | 9
_<T4 D~ } b | b-
a | "a ~ | O_3a fdO ~ ~
| _ ~ °a ¡ 6
} ~ _]_c | dO ~ e | 9_ra3®¢-eGe | b"OO
4.2.11 Exercises
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return ++ i;
}
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³
± 4³
int a = 5;
int b = 6;
// here comes your function call
std :: cout < < a < < "\n" ; // outputs 6
std :: cout < < b < < "\n" ; // outputs 5
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Exercise 102
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// POST : r is normalized
void normalize ( rational & r );
// POST : return value is the normalization of r
rational normalize ( const rational & r );
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Exercise 103 // POST : return value indicates whether the linear equation
//
a * x + b = 0 has a real solution x ; if true is
//
returned , the value s satisfies a * s + b = 0
bool solve ( double a , double b , double & s );
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Exercise 104
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int main ()
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4.2.12 Challenges
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