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14
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Introduction to Programming in F
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24
Some Intrinsic Functions
Introduction to Programming in F
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1.5 Some Intrinsic Functions 25
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26 Introduction to Programming in F
1.5.4
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1.6 Expressions and Assignment 27
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28 Introduction to Programming in F
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2.2
52
The
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Testing an
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72 Control Constructs
1
d 8
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0 c W 1
G
2 2 3 '8 W
G
d ~ &G
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V G) 0 W X X V 8) 0 W
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v r V G) 0 W # V
2.4.5
Loop Control with a
Variable
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Construct
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74 Control Constructs
1+
max
x
m2 m1
m3
m2 m1 + m3
m3
,0
1
r
V
0 W c V c ' '
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( 11 2 + 2 ) / 2
V GW 0
z d ` ` d z { 0 W xxiV G)
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2.4.6
Counting Backward
2.4 The
( 10 2 + 2 ) / 2 )
Construct
75
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I
(
d 2 2 3
v 2 2 3
G V n 0 'q c 1 3 ' 2 v 2 2 3
V G
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G 2q 0 cp 0 2q 0 n G v rV 0 V 0 d 2 2 3 v 2 2 3 G V 'q c 1 ' 2 3 v 2 2 0 3 2 q 0h` 2 q 0h` v v v 0 V G 2q 2 q 0 0 Gt u Gt u G 2q 0 3t 2q 0 n G v rV 0 V 0
2.4.7 Case Study: Approximating a Definite Integral A = (b a) f a +f b 2
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d 2 2 3
v 2 2 3
G V 'q c 1 ' 2
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0
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76 Control Constructs
23 V
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Control Constructs
n1
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F k
T
r
g Yxv3
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x d q x s v p q p A m o sg'vs h hx dq m q g onzupsq m sehsux u pd s p7ng hn u gkuhuku k v r! uxsuupspsuugfghpqgT pghpd r!usee rxp m v m q pfg h5 nxt hrxuuh uhuh uhx uhh v j g n q us h5vtfus q fx prf irxqm dnIqpgqpm gpgm vu wsq dusGrV pg pfd pgdngm exs hpgrxu mustq deq ox pgfIfuwsxdon hdqqex op xpg f qhn uvsupsgougfgs h qdrs xgun5x5 dwsmu qd dxuq sA pgAhprqg uxswsumqukukk pg s gjrpxgupfrrxd q k mp muonuns oug xys rxwmqghd qrdrxx tsu dusgf5pvpgpgh d uAhfgpguxh umnttsq q xukgonogp pggodg rpx gx upvgpf xqv imqmu7ps hnetuqens 5hu hpds er gx uvn rp yg$u upsm s g 4 4$rr $$r v 3 $$ uu $ && $$ $ 4 4$rr $$r v 3 $$ uu $ && $$ $ $X r $ ` `$rr V $$ rr$ $v ur X $$B r$4r $ r T B $$ r u r4r$$ r $$ ff r ur s 4 g u$ r'& uu
0
2.4.8
The
statement
2.4 The
Construct
79
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r$$ $ r $r$ $ r$$ $ r $r$ $ r$$ $ r $r$ $ r$$ $ r $r$ $ $$ T $$ru g rgnusrgrpxgpdrx7nus $epiupswgqu7nr7rpdxmx pxuyponrpxppgux~nv x x s s5 eA r sn r $ B r Br r 4 r u r r $ r r$$$uur B fuwsxqyppxprx~nyvrGhrxphmrusvq q m g i d qm gd dx n r r r T $$ru j pusg mrn u ysAgf pxugsdG ppxnp5qxus n pxguds!ohnx u pd us pfndps gr'vTuugqsev p er r x x ws {f x g
n '
2.4.9
80
Exercises
Control Constructs
`n
r
V
8
` p u z
r
0 V
0 0 0 0 0
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r r r r r 08W) 2n r ' ' ' ' ' w t ` p u z f
pmgfuvuuuvsqdpupsggyxqxquu!hdpwuqsg!nn!pgqrxhrdipghxdhdppmg!gp!ontngpfiqoxrqnrdiggpfwhqf!!suspngThudpsgtmqpmg v (! d n s$ !
@ t3t v v v ` e u w p z
vpgerxpprx~n xr s q m !q pgpsuqAxpu0npdrkuxk np Qsufunsw!xqp!tpqgrnigfhxdzdmdrxpmgfus$uvqushdzwqm d xngwqmTvppgqpm GxgGsufwq tvjrqxq mes !pzg pqgtqGnrvur u" pqg ups!dg hed us n5!"gip pqu"sg pxqusd t"qm tqs peumg s5ypzqgp ufs pq 7v x x o s e r g x
2.4 The
Construct
F
81
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F1
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F v v v pv u z ` v t e u fz V p ' v 9 v t t v t e 3t f v e w f1e 2 ' 1 G ' v v v t t ` e t ` V v
r u $ v g perpxprx~n x jp g ppgVpou phngs pf xtgTv kuhkd rp xqu4ngm pdrpx rwsfuxqtqrxqTqm nm ~hrp 7ruq pxgs hd hx quvr ui sf gf d q s n pg s g m x d d v upwgws qqd 1!rsu} g x e nu wsnn gxeu rpsrhpxxqrdxpghm p hnmzn "n phdmxgrxq$g usm uurhedivyq x n h dkuuonvp xpxqgp!fupvuqssphg gpgtvqph uquplg q 7 f g g d x q m
82 Control Constructs
2.4.10 The
n 1 + 1 n
n 1 + 1 n
Statement
2 2 3 r
r r
R R
R T R
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86
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Subroutines
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Dummy Arguments and Local Variables
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y
p x f q s y v l 66 uvnrg!uk u uuq t yukukuuyuik A ngepgpus i hppsuy uggnxuuftsq s pi mrgq dr`wgx pq ohhrmnq sv nq peqg p 6op7gpg 6n dr~ixx q pdh `hd un wsnyyp v n qv p g Xpsurrpxsufpv s n0d gppugtgnqtfm`qq od noeuns smr m y gf` s d q x x x jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj d q g g f m n x f m i g s pswfrx~g n grtrdiv gprdpf gx qvusi pv!hsn s uy rverg rT6x pgus!yxdptug rrpx!ntns poner pIeousuf n rggpmxs ptg !qm rupxf!sd oxq ` n opd uuphususq tuzsq n~ qppg xudisq d!u s7upwgqs Gyvq x s d v q d qi i pduss n tqrwsqx~nptgmusypm ghxrhd hdjq n !rqx phui ppddhyqg s td nxq"r ogh$vdfntq7hq udrsq txqwqx !su phuuhsg os nq utxf up$e qxom usTpgpuhy pTrdg yg xygq ydd ypTruivppi s wgwguqqGgpsv p us g h s i s r
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m m
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3.5 Functions 91
3.4.3
e z e v 131` u xz e z e v 131` u xz e z e v 131` u xz e z e v 131` u xz e z e v 131` u xz u 31` u xz z e v w 31` u xz ` e v t z 1 ` u xz v `3eq u xz f v t v f u p w xz 3xz v
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92 Modules and Procedures
1 f x = 1 + x
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3.5 Functions 93
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Invoking a Function
Modules and Procedures
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96 Modules and Procedures
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3.12 Case Study: Calculating Probabilities 111
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Array Declarations
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138
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140
Array Sections
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4.1 Declaring and Using Arrays in F 141
3fx`d w &p
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Array Assignment
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4.1 Declaring and Using Arrays in F 143
V r {h V r 23 `1{h 3 V r 23 `{h r r 3
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r r
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V r V a ` ` ` ` ` ` ` ` v u xz v w xz v p v xz w xz v t xz v pxz v t xz v p v xz ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `1 `1 ` 1 ` ` ` ` ` ` ` `1 `1 `1 ` `1 `1 `1 ` 1 ` `1 `1 `1 `1 `1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `1 `1 `1 `1 `1 `1 `1 `1
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145
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146
Arrays
Construct
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w Ew as
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4.1 Declaring and Using Arrays in F 147
4.1.11 The
Statement
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4.1.13 Element Renumbering in Expressions
148 Arrays
4.1.14 Using a Function in a Declaration Statement
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4.1 Declaring and Using Arrays in F 149
s x x A g us x i n x ryrud xs fnug pr pxpggdg sppgusg rny7qdrrghdf rxd sdrx pxguuspspgh qumsums `hgp hqn Auv ufpwgs q gs Gqx m rg do npg n q sjouspT !x qugvonusrvustwqqurAqe rxmngpguwsqd p~g pG uqd serxxwuqsnr gs us f us r g grxf gGpxrgv r pxr ppgqn ft v umwgpswgqhq rim qxdVmus uns vuwsq tpiquwgqs hoqwgp pxog xehp wdpxgq gq nm hx m
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(
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154
Program Notes
Arrays
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160 Arrays
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4.3.1
Quick Sort
2
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162 Arrays
3
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4.3 Sorting 163
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4.3.2
164
Sorting Small Lists
Arrays
F
r
X
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X r X r
X 21'8 W X 21'8 W
W X W X
a
X T
9
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4.3 Sorting 165
V r 2VXV 08W)
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4.4
166
Selecting
Arrays
F
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F
F
F
2 3
XY
9h
#01
sV
V rV 3 ) 2 d 2 2 W
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F 1 2 2 3 X T 9
4.5 Case Study: Solving Linear Equations
3
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4.4.1
168
Exercises
Arrays
F
x rxon7$v 8 qr8 xfwqrxp~xnzirursxTsouxpsgTsun dpgnexys xp~gu osndy unsrnmntDgqp~fr xqn r r 8 si uspggfpf gp qusz y vvvy g y 8dpiups wgqud on p ugs ypvpsus hdh vf xgpxg jujhd Qs xg qx xs pus 8 f d ufs ppfpg8 xeo pxgus s ppugd fq n rx q`g uwsn q vdeq uqp "r5d p pmgpg 8 usi y qrs x prx5ggrpxg u rsxd enGh qq x x rpxgup xqdtpriupswgqugngupgfppg8 xrpxgupopugsgf rjjx5umm n ggnnsu Id s usfryx qhgu gs uws7qf rp"sd5 pgqupysg x gxu7s pd gyv vtgpqAg5nprui wgx ps uqps "mgpthpq dggef5o nups tgrxqq m s gh G o qpsxi 5pTrpxguh"w pqen"o un7peun7pnGp7e shumm "uoneypgrx xg s m g g s n s d uuqrxss uux pv s hrgg px upuggg~pffgss p g nurpsgx du5gs pg| rgxupos u nms uwsgpqgqx u n7uqedpwgpgqusgrxf epggpnpxg rrx x ujhns !rd5ux nrps gux ps hgn Spft q uxswApxqr mrtqi uxsomqrspxgpgvgutqi ws xm rp5xrpuxs 7rnqohpi p opx tfr g uq pxxghrpf 7xuqv"tpxg d dg R xn s g s n A s ups g id h g uqd uq i yrpxguh~qusppg!hxeus pxppfgTo pgprxrp pxpd x~ngpfpgggrxf d x s y s d s s d d v d o m g gh ! i q d ogxf pdrxs duonv sr qmBpi r iupsgtqu nds r pdushtf nps pg usjq n i s q s x d pjxguqtg p s u rpd s nqg gufufsp!xqg npg t rd rugsx fuyxx nsvrgp gfppdgrxr0X!xpprtgg vqggsu pmp7gnpoug pfpdrrui xs x s m pg n n v x x f g sqsgpxut hxpxguvrsdi yqnrus`x!erxqAy vgpxg s v jjupghps dd n u oyxq o hgp hp gupsg urx ruypwgq uusg!fs g rx ytpsnp gxgqxq hy pgv vg uTrns pxgquhgdpgTu x s rpd xg gpvuf sm f xh hnj pdpnxg zeVn~px g pxugux gs pgis g d pduxGp ngogguwfs rqrn xuqtqos npvrn p4r7h`Gprgpx gx utspxquyrxm d pxgwsu q qnnVopx hpngpdx$ruv pxprpx xg G g n qus r m4 Gx frs pg ms i x rex g s r ge
w wj h x dw u u i d v@kkkYTr
a n1 a n2 a 11 a 12 ... a 1n x 1 a 21 a 22 ... a 2n x 2 ... ... ... a nn x n = ... bn b2 b1
-
x 1 + c 12 x 2 + c 13 x 3 + ... + c 1n 1 x n 1 + c 1n x n = d 1
x 2 + c 23 x 3 + ... + c 2n 1 x n 1 + c 2n x n = d 2
x 3 + ... + c 3n 1 x n 1 + c 3n x n = d 3
4.5 Case Study: Solving Linear Equations
... = ... x n 1 + c n 1n x n = d n 1
xn = d n
F Fy
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169
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4.5 Case Study: Solving Linear Equations 171
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4.5 Case Study: Solving Linear Equations 173
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4.6 Case Study: Calculating Probabilities
175
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4.7 Date and Time Subroutines 177
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178 Arrays
F "
F
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5.1 5.1.1 Use of Character Data in F Programs Character String Declarations
V X
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a
u X
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Character Data
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5.1.4 5.1.3 5.1.2
180
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he h d k@d rC r
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v rV '8W1 W d 2q 2 1 ' W W V d 3 )~ { 2 2 W V '1G) d b { 22q i V c W ' W dc b ' W 2 V V 3 2 2 W 3 i V ' 3 2 2 X V u d t d w W
Character Parameters
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Character Data
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5.1.5 Length of a Character String
5.1 Use of Character Data in F Programs 181
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5.1.7 5.1.6
182
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Character Data
Character Collating Sequences Input of Character Strings
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The Built-In Functions
5.1 Use of Character Data in F Programs
and
E
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5.1.9
A Testing Technique for Character Output
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184 Character Data
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5.1 Use of Character Data in F Programs 185
V
2VX 2q
w w u z zlp ` 3fz
W
W
h n ussx5rqx$youpswgwquqsmenxpqpdvgtstxmxgdzoqunspqtppgpxAmmdxypgwuqswqhsdprppx1qtphmgsuftufuqrswsrqusxnqm~uospnhyvnhgfpgwg!qs md p f n~ g zpg5 z5 opgwqh uspppgzpgg5 npdo~dwqdwnqzpppgg5 z5 yundwqu y y # s pxg~p mgfusqxvpgwqhpd~ong zpgpdq~n x#ym v s q u rx u 7rs Gn pe n nxush Tu n7p7tqs rpx g p d q x s v gpg uq us#d~hpdunqhy # i uf p7 ps Am uf 7 nphqwg v ~nnrp~np qeyr x frxqtqrghd uqxopxgpgrm x g n j hex g nshnuqsv `gpm tqpgqrhi mdr~px n zgp ow uqg `xs us txqu xs Gn suvrpsGi uwsus uqwgsq m~ q x nuqrs yox s pxggpgr mm xq sntpdun rpxgheq rpedgfps uvwstquqsrt pruix pstguqequs ruqtj gnouv sd q ui dghp gpd hepgv g rr!hxv upgxpqg n x pqwg vuAq u tspuqsg nxrwseqpug wsquqohnns x g s e xgtq dr i x s v q e s r
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5.1.12 Referencing Substrings
Q F
Fs
ql W
r
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rkw vTr T y x e u i u
5.1.11 Substrings
186 Character Data
{ p 21
x) r Y X W X
2
a
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2 3 1
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2
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r W r Y X
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r Y W X r)W 2 X
5.1.13 Trimmed Length of a String
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5.1 Use of Character Data in F Programs 187
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XY
r
01
r W r
3
r W r Y X
2 x`
2 3 21' a
W a XY 2VX" W W r XY 2 W r XY
2 X W V)3
f f $$ u$ & r r u $ u r 4r # # u ur T r uu$urr&' u# $ $ $ $ $ur r r#0 uur T r$ $ vuspriypgppgustqspgusrxrxhusnxnp px xypgtqrid usp hn rxpgrxmd tpgwqusendpg7#Ariurspgwm$q us nrx u m r g m s r xsrwgixd qqrhhdmim 7op h0'vsnu d pqmgtpzuppg m hdyp wgq p q p wsuuq o$ns yufv uwsrrxqxqs x Xhnn p p m g ~ n v xv i v qv o px g$pg5 s s4ufws i u q xrj npqtqwg!pm guf s !unpTg rdpgdus uurgftrupssop p g pugwsuq7uu!pn ufges x s g hosuqwsuq 0pGongpG7pdugs Gox egfwgq0xgq d dspgjpprsgpg s n gr g gdri n y g d i s qoxfymd n pxg phsug nu xgv dsix ugpjpgpspd r r urxpxs gpd h dnuf$syp pv uns yd v7 u o r $r r 4r Br r $ r # # ` # $Vr #u# rur$ru f
8 { p 1 2 x) a Y 2 X W X n~ 3E l ~ { r 1 2 0 2 r ` d ` d 1x3 r i{7 2
188 Character Data
V
2
~ V W
~ 2 q
{ ` q Wh V
W
q } G
'c
sr 2 aV 2 W {p8TV ` g 2 x`8YV g 2 W ` d ` 1d iV ` { c 2 n 2 0 W 2 n ~ 8 c21 G ~ 2 0 { W
W
W
W 1 3 X 2 W8 X { 1 ` ` W ~V Y~ { X 3 W 2 W83 X 1 V ~ 2 0 G ~ { W
W
2 3
p x pp g jppdg Gtuopsxur psdi nonnyreq xu s yqv pqp regpxirgxpph{ emxvd x xpqg h$ rp gud~nxsf r rzppd upsgt7o g nn rrpm x pxpxgp ~g pnmx prmypxguupswsq pm i x gx i rd e y r x g ( 7 A x hpnn ex p y p pxgpgrxe xk tjrpxq xgp grh7Guipgxmdx p upswgpsrqui7n rn7f us tnpxgpq h d ~mxqx qt rxrrui px osx pridv ex pykusn~rf xrq uqse s x g g B $ $& f r $$ $$ r r u 4su 0#r$$ r4rrX$u r$ f u $ wqus v p s ptjj uqgnmi s d"uf ol s gfu spupum Aspxpqdqg xhApxnognqrrxsptxf rxeqq ups ug5ox rum pxn efs dd xu hoxg n5v s wgoqx n g ps rr v x s D s hf nx x s pdu pgtqridXprnerx npog n~ud jpvufuss hx pdrix upgtsq rnid p~uGon xn spnun tvuqsd 7ppgypm us r g s o s qwgps idy~ rxpdu !nG d i pm or pf gpgus d s o gh q z f s rxqr Bpruipswgqunv rxgpripdduyopv ngo uxsn n}u4xxtqpgrxquos nrn pqxhu}g r h ) $$o h $ $ ) $ n f rxu}Drxqr Gp ppg ~psiu wgqunsq en ny rpveqx tuhp s ppdgpfsg u $unv epg ruhsd nxv rnqxhmgxrf xprpg hni v z g i d u} dx r$X $ $ r x sdx g ntpguhnpetwgqrhpgi p d~ nqs ednuys e unsGop pgg ruq sx oxqv peqwgpr~pi go nrxmx 5pg"q x ~
~ 8 01 2 v p { W rY}E3 ~ ~ { 2 G ~ { W
5.1.14 Reassigning the Value of a Substring
v g x s g q m r pxgzpn xx G ~rn us i pg sqtjAuthprxh5quq 5ms s n5q ppgAus vunro5pr pigi d rsm susrxA5vwgqrhd upyg pp g dus n x ufs tqrrxhGpwg pq drxe m rymrrxrpxtprhnx Tpq gh h n p v s yprGru rpg tq rhi udr$ npfuustsxqd x5pm wgnqxx1fx untsg7mqfq x y ppgwgumuprhxvd w e s s
z X rsG 2 X r X Y r 0 1
5.1 Use of Character Data in F Programs 189
0 0s
X W )
# ~
~C&V d ~
s~ W
# ~
~C& d ~
0 )~
r ~
~C&V d ~
s~ W
~ )G
~C&V d ~
s~ W
gA q y# g # e n rn g n0xp pgg n uqs f7 gnm rpf5gyrwdx q p5A5fdrrqy urgpxs tpqqong zupgrps wgpxgqrpm 7unguonvs pxgt q z g 0 r x s pxrg s hd~g p rofg pq wgqped rhin erpxpxe $h pgdrppzss ug Gn r px gxrhden"rxGrpxgtq g m v x jpgi ~hj qgxgytsufm xqrxrxqrs ypg qwrregpxx rpxdgp gjdpoin1pr$rprhpxg g usht dqh hn dq pjuoupg7nqrxgus7 $rpxgd5nApusunvs pqufgwshxq pmgq xquv~k Ap gd s s $ uV # m gyq x vuo s s d s x s s y s s q ypufss rpg!uGzpsg gqx uxr~pdurpxgd!pgunurxtqq up7 pg jpjusdu nhns qv us n uuwssuq y quexhpf udr7qs uusxs utps q gusri unh xr7gxixx p5qg t rtiqdwsuuqs rnxs prhgn d xn rd uq sGrpq gx f r r ussnxyq n x utj nq ds n dghgrfdxfxxq r tuq7sqpd tpq xTrgn fudrpog4squpgrppgomixmdVp rnxqgtruGBss pxg unr~pg pxnmmVod wgp 0pqrg wg hqi pdduVnu px Tgs hrd x n x sy y f g s jx x ogufdrqpVntqdrxnusprGrvuptgqrdnudsv ipv g g i i u uV # # x s i i pwgqnxqpGox~onuzopgrrrxuywgqrhdo!hrudsun vs rri xgufpg q z uV # i h ! s ! rx ~ y ptpgpqj gpghufgm!rs d n orpqi Ghgrhgvx tvxq! nqroesnx uxp s pyx xpg pgtg q rndxtuzss unypq wgqx ftq uuqws ppos n~$rr pxgushdpg p n x us ! g T `sppgqre`pguswqTs5pGs`pgyps geqp g qq x q x jopsuqx d7p gpto~wgmsuqg p sq oxx p gxorutnrp pg7edvr tqrqx~n xuugss pptgd xqqrhdfi d~uuqtqugphsn xo ex o g g f us t xr g 7h g sA s r ~ o qr r x reguf"upsen5pg"f uogns tf ursppxprepi gp~n ensu np mg oxq retgpn p~pignxx pxgpgrm x s x m5pg " m x x nhuv r m g g ipsr rpx!nrusrxv l!x pq n rpxgpgoxpxypgm xgGx!ruf Ghmxddi x~pq riGpxpgp grrxd em n d x x
5.1.15 Finding the Position of One String in Another
``
W
{ u x`` `
W
190
Character Data
r
2 {
8 3nE | ~V1 G{1 d ~ { W d b r 2 a 1e1`8) {
}r 2 V V 3
2 2 ' W 3 i V '
2 3 21'
xqvkerxkedYrqY w d h r x r
1
X W )3
X 2cp 1 { 2 x X G r { { q Y X X 2 ` hc r 2cp g X 2c { X G ` g i3 r 2 pc3 1 2 d x`ip { X 2 n{p 21 ) X q X
r
d 1
d X 2 }r 2 1 X ) }r 1G) 2 V d b { V 3
G
nh1 { r
2 3 1
r # v X x)
2
0 1
a
d v W1 2 G V V 3 'c G d r a 3 V d 1 X W )E 0 )~
d ~ |#
191
Br b $4T r f r rb4u$$ru$f u4 G rT $u $ $ r jug soxq nxrg d ng ui wsqhpd ppghxpgxhdr yhusxputvhrhuqs x dtsqdmgtvx qp x gxu rsx x v x i g ufvtsq xdxm pn ypvhsd pxr~uo nue uqp mr!onsu popgd m rTrxqdyngf s i n g` s x nn v ri rh G h0npq pgp pgru!rdyssqx u utq p d pgtqm nduftsq xr`xi5gfgg f5G uonrzdufws xpq m qg x r gi q x s n n m m `rpx erxu wsq n rm `pxngrux u srxv y nups evx i p g`rpxg us usq rx gx7vf eh'vqos nzqu sv i pgtq rs x pgusrpvgfgwfrx5hpnd g jrx q ptg"qm unep tggqx Ggx urus qwfrrxxt7q r"Tus"unTpxguwspqgp rTdxm pgpq j pg rwd g qt~osi pv A x h s x mh $ $r r 4r Br o $ r r u rou$ r $r $ $o r ru ror rrru$$$ o o u $ o $ $$u r $ $ T t r$uT $rT $u 4 $ uu $ B$ $$& u uX$rsr4T$rXuBrG rs ff s r 4& f r T $ $ $r 4$ ur $Bur4 r u`$ r r$$rf v qr g rp 7 $ypgfm urs d$x rpv wg qid Anruyp7wqg hd rrxgfrrpn tgq q d x i q x
v 3 |# 2 v d ~ 0 ~ ~ d ~ &
5.1.16 Concatenation
v a d|~ v
~
5.1 Use of Character Data in F Programs
~ v 2 x
Tr
G
W
G
V
V~
~
8
' r9G
2 2 2 2
~ z )GGf~ W 2 q 0 3 ~ ~ V 3 333 ~ 0 ' 2 w ~ ~ #
u` rr r4 4r us g nj vopsu r xTdgpfnug gusf rGdx ropwgv qr5q nus tq ups gsxshhpushg tqdqrm upodsi znu~ps uuftss hrqd ry qpxtgqq mgrupsgqwgpGukgnv g v sm iy r r f p s xr n r v sn x x i gf ruihpmusuopwgq~onx!npxzpwgqd~onhpusphvq r v 4 u 5p$ # $$$$ r $$ r r m g x x s g n r pxgqyerpxpx~nrnusxpdunzpusv p
r { | ~V{1 dG{1 d ~ W b
5.1.17 Exercises
2 2 3 # 1'
2 3 2 2 3 2 2 3 2 2 3 2 2 3 2
' 3 ' 3 ' 3 ' 3 ' 3
V 3 W W V W3W W W
r r r ' W 81 r ' W 81 r W r W V # ' V # ' V # ' V # '
r r r r r r r r r r
2 3 21i V c ' W '
g g h xd m s x x vxurhedusrdrxv gptpqgu hwfd rpqm x~nd hpgp hxd uduqszhs h i s m rn b uG G $ $ 7 d gp tgq e jjus pqxhu q ypumg nds m pg ps duwfsqr xnh0~ rn7pxs dAxn y d usn vrpps pgg ~en yrq xersx e{nBv pqv q Vg! xd i m su xop gf ugpdup gusrtTxprs uipstguqqr pg us g~wfn rq xsnsu nrrx dh usGhmdr$thdfm upwsgq r x qnmu sp xrmgg ufsus o u urs pxgsuq pghpn g m i d x xg $r o r o $$ u$ & u$ G o o u$ G o$$ u $ & r o $$ u$ & o r o o$$ uu $ && o $$ $ r r 4r r$ r$ '& uur r
~ ~ 8 } r W r |C r d ~ r W r |C r d ~
u
2 3 2
'
~d b ~ d b
' '
192
Character Data
r
'c
r h r
7 ' p 7 '
W
2 1 W
2 3
'
r V '
7 ' 8
2h V 2 V Tx V 0 V W1 3 2
A e xw rkg
# C$r r 4u3 U V oC$r 4 $ C$r r $ r$$Bu 3 $ C$ 4 u B$$ B $r ` $Br4$rr $uo3 'dmdrx g q m q os perpxp rx ~s n~ h hxd x xn pggf sr { m x x Tpxgm dA ' ~gfusXvuhm qreus mxr x n p pgzuhs peuz rmxrppg v qreg usqtq xse$pgrxdppguszqds ngpfgnus qu ds gqf n pdggp o| pu'vms `pv pdzgzg pg pdgusunwv`uo`gp rp v zsum pq pgyp owg qnupop pxg`pg hg r rhxq eVsu xesu gm x s pg q g nppug tgspsugqGuxv g hr rq egtnq0usumpox pguqrnexs furuws~qx spm xgqtmqsqust uhpn ons gusv ohp jugxsguq us f u fmhs 0um vphus pguqsnIufxmgwsrgf qp xx 1pvi s r x s s d q m v i r st i h s h rpgfg g rryprd oruifxs s x n r d x v g pjpxng gd gfxx v qpu ons Tgpy uus uspppmrgvdpvpm upsgohgp n pgusrpgdp rdpvx n7ohummx hsx rn "ux ned g n v pu psgs jr wgtmdrvugsdrx " suhddopgdrphustupwfqxd q q i s f v ss m x g q s g gxhj ynys 7pq g p Adpyo npysg xpgpyrxAr!opxgpgrmAm srxgfhps r m t v m g s x x x uvn p tgqpqdru uqtsx os unk urkupxwq x usf tuquznr~kuhpg p tehf tuqrgxs ponsu pqwgtsuf qrq ru xwsuqq ns ypnwguqGv p nrop gpfugrGopwgq5qustquvuns gp wgsqh uisdzupnr puufzrqs st rxpwgmqq gs upwg!qs Gk v fd g s f x q gso x o mG r r
x 2 v 2 v v v r
r r u $ $ i x m g m g f d dx n pdrnhdp~pfuszpn rxqmh
|s p X a 01
5.1 Use of Character Data in F Programs 193
TV
0V X
X )
~
G ~
X
XV 3
~ # ~
X
r 3 X
X
V 3 X
W
X
' r G
2 2 G a
r 'q
2q a 2
2q
'
r q '
2 2 q |
2
r
'
2
V X
2
3
r
V
x nq g pehrndg xm pv ukudrzqx n uqsk tuqns e op rgn ut5s uns tpsu mi pu"etxyx pqguptg u xsg ppgwg qpg q s jj d nx pugssom xthps npgt q7roupsrnpptgq7g nk qhoppugsgf q d x x n v i g q x ouug pgtq dnyrpxgtqrxuoss nj$n r p gtdo gnypuuds s nrs qm tjuqs d En( 7$y'vs qxAqr ppg sn uxtqrp x g ursx xus nqmv tq upgrinu~p urpxs gnpdtg!q qpwgqGuzv pp uyy p ' v s k 'v$uiq s x u $o uV$' ur $ ypgus gqm uf px~TX uvrsqpemqt msnd ruqyqx nupgcprig p qpuwsdrqunncon ~u pd ps~crsuig nIpmutqTs np m q q x g x s g x G s n pv u pwgpxqsr gGtgg pp r q xn `q ysug n qt qupusgwsnquGn`s yunmuiuszxsq un udrox s oq n nrxy wrq$porpd nx77hrpqx B d uxpxgs hd q sypt~pgq wgdqGhvk p sp q q i g s n rq v xr q x n g s x s pg g T s rAqnopgftgq fuhyh usus rn~p r!zpxgfod qudsy pwg qpduqpjusuptsruqg rs pxnezs ppg wgrq Gvh EEEEEVEEEEVEEEEEVf fffffffffffffffff f u f a EEEEEVEEEEVEEEEEVf fffffffffffffffff u r u$ r& a i dx d dx rGprnhmh~n u a g mg g g s s i s s pd p~oq nxi vvu spmpi h~ x n pq uwsuqon u ps g n5 qu u5qustqrqux ng y tpqgg nsvu xs rf upss r ushf tvhq xd mpqi g inpzupsryop pgpg gufwsq~x m!rppgums 5g wqurpxgugoufs ps xgx q h!s jrrxv !hsm p tgrtqxqd rtvq do ppdgtrqhss ux hd usm pgpfuGh upgtzqs rq pguuswsouq nn~psuvs u msphyx vufpwsgev q u$ u $u $r& ur$ i dx d dx rGprnhmh~n u$ m g v i s dsg hdp~n d T rpxghdpdus pjqg putgwsuqq tngssu dmd pAguggdkfu rnx r" ov u psu frgfpg upgggs puqfst rx pxq wgq tv qqh urwq s uqsx nw~q ts usq pg vl mo
@
194 Character Data
rT ' X
2 0
2 301 '
21
W8T X
2 0 n 21
W
rT ' X
2 0 ' 0 X 3V
' X rT
g 2 0
$ # $$ r $$ $ rr Vr$ # x g g s m vh x # d i m rnxhpprpxguhddrd tu7s r$i $ $ r s grxrq d~nrxn qx u q 1ufws nq xq ~s hqn f x d jp5hgr 'vdrs v us psr~rs x! w qu gf# r px gushd dd um!i zu syupsrirq s i x i i s uqtsuqn eouhquq $$$ V s opghxrhd oh'vghruqs g ppg pwfhqm dv tdpq gus !nn $Gpgtrqpxgr ygsd d rn ~pusgsggxfqd u!uq dups pgmmf x gdd q x un Toun psnf g m x i xd f g s s gg j pm rpxghdpgpgtq~nG uyvppg pgus d g p guq si ~gepduswgq j m rxdqi `orn px5u g psh"ugdd pm rggpxs 5suf d pdhghpfmm gd wf uqrpsx tiq!d$m u$o$ns y# rpgxq grxfd xr0dn5hwn uquvst r x
A 1 ' X rT 2 0
m vushzutvsow prgpfpg rzp g uns wfrqxqp g o pysg u d tqpg hrduphsg dzdr xvd uqzn wnq! x`rxfqmn e rxpd n q g x x m g i vz x r ri s d d q x puwsqugsg nhf uspgpg ustn$d utgwvuqtsqp xusptgq x gs uhx v q x pgq s s nr rwnigvpm rrenxxqq udpyp5sugs o n7 pfd tpqg Txg A pA rpxg usgg 5sfq u ndqr7~xx ~r xtvuqs~pq rxvd gqqi fdptuquqrq xe
0
5.2 Text Analysis
1
0 X)3W
xonrpgtq fxqquseusidh r v'p xqgmnqusnoyhdqdpg5# stnv jrmrxpgxusdzpugsoonqgpwxpg7p np vxouxpgspgo$uppgpgopgrgprsug$fry#5 ogxpfodqduqpngnovpughsxgxpvq p v vrxpgndp5nngpgApgrosusunxnouusosngxpvugpsustnxdtpqpgtdrxpgqi p d!xpndpgwqgrxxpghdgfGdx n" r ghh s gh rxt ! q d5 ku|Yk |Yp |Y|Y|ppg5 r$ $ u g 5 r$ $ 5 r$ $ u p kk p pp5 r$ $ uu gg s s x d x g q vupgt quhpurpg x phnpydn ~npugs rx jxxydggprhxdgn pghr uqps dpxhp gresfx ppg rT0iinrropdrpdrnAx nquqps quhs tquudns wsqunsnupiv psrus nrrxpxxiro 5wzpq gpquwgs n exy hn pp ygdu ps gqyppxgrgx pgm n p g v p x
-
uu 3) f sYY 3 Y w
TV TV TV TV
0VX 0V X 0V X 0 X V
X) X) X) X )
5.2.1
Blanking Out Punctuation
5.2 Text Analysis
195
d ~ |#
0 ~
V
83 ~ 0
~ d ~ I|#
~3 ~ 0 0 )~ V
' X rT
0s 2
r '
V
23 V 3 '
3' '
' X 30V
V c W '
~ v Tx
' b pV)1
1 dc b ' 3 'aT X 2 30h23 2 23 r dl w ' ' ' ~ { 3 )}p q`8) 2 V { V 3 21 W8T X 2 0 n ' 0 X qV
V ' W p W
2 1
W8XT
2 0 n 21
' rXY
2 0
#01
G
{ 3{ 2 0 3n
1
G V
~ h~}{1 drXr XV 0 2 1 q r XY Ix`E W 2 d { n G 2 0 V r 2 r 3 ) 21q '
~ 8 ) 9 ' rG W 2 q ~V #1 V 3 G { 0 X EVa XV I V 2 W V '1G) d b { 3 3 1G) d b { 2 0 V
}r 0 3 ~ ~ 2 V V 3 2 V V 3
q uus s s x vguirx q np gpg un q x ptpqs g7n x uuosk usrg iugpgg r pxggrm5onruyApd rr m s q x pdu nousGp g x r r$ jrxr hxusuq pd ws ogpq n g gfusvtx fdr k qusXrxn4p!rtpgusngf d ntp qustqunxrgfp!ntrpxgpgrx quwsuqon!ndptpxg x mA s g jn d7xgp npu ~~pxs upd fd rnrq uyps epqwg tgqn ~Tgvn qpg urstpxqugns d 7un s n$~'vx pdugs hf 7rd nuqrs ygxx T g s ~ ynngpfg duqddus n $w $pq wggq75n# rn yupsoxg gp pguh rApxs d gxpiodpd5q wg~5 n rnyrppg x g qwhn quv ruqws opx gs nqy ndpugsh upvjpsrpgp nn d gi74r on s gqr xy g p $$$ $ur $ $r ppd~oh g q n u r t u # r$ $u $$ Vr r # rt $t $rrr$ Vr$ $ urr r # V $ r r # X $$ Vr ru4$r r w Br r w t r$ $ r$ B #Vr u4X X 4$ a f #r T $$ f v 4 u u % $$T$ $$u a # c p & u 5V W )5E V C 3 g 9 6 r$ rt uruT r$ $Vr r $ a f # $ # 0 $$V$ urVu# r $f
3 1 rXT ' i21 2 ' c 2 0 n 2 V01
196 Character Data
a
r
0 30VXY W
#'8W1
x8g `
W
W
x`8g W
W
p {
vx s g g q j r q m s q rpxg id ~npGg hdq hqpdrv ufws vxon$ ropwgq7pghs npusx ppghunA r ufwsxm7qseigppuspg puuAo gfn pwg!qq n uupsrA7hpqis drhhxxdi uAnqgnfrx zm gro pgwqes pf xgqdrxd hpsiu d 7!i phrh s x o m o $ r nri d x unyqtrnyquwsquonrxpG r sudsi hhupgv 0 usr1 s qx s g s i s x v i i g i x m g s n gfus~ nqpgs ~ us5r z x5rpx gpg r pqg uwsuqson htvq u tsuqndrgfnrwgtnu shuspusrGsxsousVptruuson x gu osf usqh5tgp qp~opg nwg q enx n" rpx o urso uxpstiq uppspgguhws q7 on rphyg w pdrpdq xgr7x oryv op gu xsnusGpnrpv i r mwgpfquds n$pwg dqx ~fi h frs rxqgp"q uwsquon7rs yoe$ydhtvpdnx y y s g s n n rn px~pg grrpxx !Vrx Tux p ~s !qugqx fuqqstuqs nTs utqups ngTn npg `rr7xnxpv ptgr!onxq y gxpdqtg wq uqwsus roxsf nq r wpx gn r8 d tx q pgdgip`q no0tsu nXq uuvs russu~rytndvr rv` u upsup s minogpXtpg tqpqguswsgfsysTuqptgqsnutsgyuqqs $n$uuq $ snV# nr s ni s ih i s dpg s u uqs q rn x z ws s n s q x
) rT ' X 20 rT ' X 2 0 I ' rXY 2 0 #01
5.2.2 Excising a Character from a String
10VXa XV
n~ ~ { 3E { { I V hE 2 d { n G 2 0 r 3 ) V
2 0 3n
G V
r 2 21q '
~ 8 ) 9 ' rG W 2 q ~V #1 V 3 G { 0 X EVa XV I V 2 W V '1G) d b { 3 3 1G) d b { 2 0 V
}r 0 3 ~ ~ 2 V V 3 2 V V 3
d uq xwsunqr orm rpxux g wgqus5q rxsutq uhg~ps pgh xr$$pvx $ #prvppgn x pypgg usrx rrxq q dii ~xGrhx hn u znpg x p nn g s s v d s # $$ Vr ru $Xr w r r 4 $ r 4 #Vr u4X X 4$ a f #r T $$ f v 4 u u % $$T$ $$u a # c p & u 5V W )5E V C 3 g 9 6 r$ rt uruT r$ $#Vr r $ f r $$V$ urVu# $f $ # 0 r
3 rXT ' i21 2 ' c 2 0 n 2 30 V01
5.2 Text Analysis 197
r
p 2 0
V
r 3
2q
2 0 c
2 3
h 0VXY 2
V V q 3 2 23 9 2 30VXY sq X 2 V V 3 3 2 r G ' `ih2q 0 V W r V 3 3 2 r a 2q Vs s3 2 0 X X 2 1 G 2 `E3 { 2 r 3 V Cr 2 0 G 3 V q 2 0 2 2 n G 2 3 X 2 s3
0 30VXY
#'8W1
3q
0VXY 0
'8W1
#01
~
x8g ` p { 3E { { ~ d C3 W r 1 { E
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Character Data
5.2.4 5.2.3
198
Listing All the Words Efficiency of
2 32
v
d b 1
2 2
d x
r
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a
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5.2 Text Analysis 199
V @ ` rXY
2V a X
X
r
G
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a
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G
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5.2.5
200
Average Word Length
Character Data
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2 X V a
X
v G
2 n r
r
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5.2 Text Analysis 201
2 1
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5.2.6
202
Modification for a Large Quantity of Text
Character Data
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2
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a p W 2 n V X
2 q 2 W c V ' X V 2
r ` X
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5.2.7 Frequency of Occurrence of Letters
5.2 Text Analysis
203
z X r
V X
2
z X r
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2
` X r
XV
2 m
z X r
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2 W c V c ' G G
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5.2 Text Analysis
205
w z z
a
e e
p z ` w u
c &
g
W
p w ` p `
3
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5.2.8
Palindromes
5.2 Text Analysis
207
G
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208 Character Data
W
q qc qn q
V V
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r
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5.2.9 Exercises
r
q 2 ' 3
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5.2 Text Analysis
209
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7.1 Generic Procedures
233
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2 301 '
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234 Extending F
7.2
The
and
Statements
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7.3 Extending Assignment 235
p pjtgj uqugpzq us n sprg rp nipxg pxxuptwg s qq wdq pgpx00sg zuVs ou rs0qip phdg d uoqnsxrp pm xiuuwgpss snuqpxseug5tspgrhorrrpd g f x ggxfnusyohporqpwg Guiv p s s u g x p s v rs vApg d s g g d i pv ru xs u non uufoy rqf rgx p uus uds p pggh rxfd qt wp q gus n n go rd grddifqx suq xe s d
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236
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Extending F
Exercise
2 1
XY W
21rX3 ' 2
2 n
2 ' X 2 1r3
2 X V
V ' W p W
2 1
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rs3 2 ' X 2
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b v a rr vs g v v v v
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7.4 Extending Operators 237
7.4
Extending Operators
1 ' 2
W
v v
v W ' v vs v1 2 2 v v 9 v v v v v v 2 3 v v rv
x d tvq x g o gfus7 d r$f $rg n rr p fuspgyg g uqAg s pg s g s f d s eh7pdr7susufx pnhg gx npeg $y pxugs hdg dn uhgg fu suswqpupg x grqpmgpgo to hp hx s o txd uq n pspgf g7rq ugx tsqm e rt5opxsq qgwd ps g o wtvqq dq q us neqxupfwgwsqqmr7dpxs n urstdqx fm u7dp gnq"rqn xerTrtqx vphpg ohmm mhpn ggf5pq uesx " yp gm ufx v 7srrx $x w dx y f x s y gt y q y q y g n w rxutsqg xutsqt yn5rqurdi rm d gxpu 5pyrq xxususpgtxpq x $up'rq x" y r txuts qhxntqre r $ e y sux ox!ussgfpxonm 7x ropniqv gerpxpi rrx osu uhf us qrqxudsm ttqqmr epx oi np uxs np mf s x q "hq h hgp mdpgrx i uv xggd ufi sxwgvq s r x s rv hxyd psg n x srxm Gpriu spgdrm pg drex r5u onrxutsq0pgf jrp xphrtvuqsd x m px !xyvrm uiirxhq gd ~vg i qqrnygpfm gtq zpqgp guxgs gp y pgxTpxguwsqrrx ng yhw uruxsq xwsgq qreggp jep pTwyoxunstq xxoxgqp su yosff u n hhm dyTgxsu rx ypgpx phrhg i gusx m g x
v v v v var v v 9 v 1 v 9 v 1 g { {
7.5 7.4.1
238
rtmm v x qd q r m uvhj g nf u xpd xru pxpsuprx7pxzuq trexqxuws qvuwsq tmrq'u7 uuss u~hpdwus ntqruAx suhp stoqg px!px qus puugsjps pnnd77rguxrnixh nrs7x~pptgrwg uqqGv p gd s x ` s s g id x xerm s s s sr r f
{q
Exercise
vAp~rhdgf g i x ~ f jhnrpd g uqeerxsn nq rroyix xh uhns gq rpxgurstiqqrxm xwsu uqmr0x nx h mh gf x d s g x d s rpx ghdB qx q s n i s n d v ug n~hs m x ud dusr5fupsg m tn ~ ntqrxn`pwvuqds5rx e juquss vh v us pqnnh` n pVqg rmpxgq n q!us n `pg udso nri tvuquqss mn~ouqsu nrgf n g~
v rr v ' ' g rs3 2 ' X 2 2V X V c W '
`v` vlp vra v w v w p `vx` pv&p g w v w v r v g v 2 v g v 3 v
$ $r u r uu r$ uu
zvz zvz a 2 3 b dc b dc vhdc b vhdc b ' ' ' '
Extending F
User-Defined Operators
r9 X
V # ' # 21 r 9 r X 9 r 9 r9 3 r V W X 9 X
W V ) ' 201 ' r
2 1
21
W
a 9
31 3 2
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1 3 2
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k
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r9
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W y v ' v v v
Exercise
v W vQ '
0 d b
33` '
0 v
v
0 v W I v '
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W #'v r v V G ' V W 'c ' c 21 W 'v r v ' V G V W
7.6 Extending Intrinsic Functions 239
7.6
7.5.1
Extending Intrinsic Functions
f f f f f p p p p p p p z z z z z ` ` ` 9 r XV X w f
`z z t ` e1` u ` ` w ` ` f q` p z` `` ` u f p z ` e t
V c W '
1
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2 1
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V ' W p W
2 1
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v g w np1 3 2
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x X
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X x
r }r X 9 rr d
h $$ru u r T T ur4r B $ $ r hT $$$u h $$ur urr r rr h $$ru $ r r 4$r r $ u $ ur r ur urG $$uu T r $$ $r uh rr$$r $
2 3 X x r 21 X 9 1 X 9 r
240 Extending F
V
X
0}
g i fd s m i x xm s xg!qrqupsusdxtr0pdrevppgpgrpigr~ovuvtswquqnrx pgpfugpTnq usxp"hdmxqoptpgrTn gf r7pepghxtx pgn s g g i s x d x n g fq 0qgrxhwq`0vtmph!0ruv wstququd`xBuqwrhxnq xpv n v g qus g q x x " s y s s o vj n p ugwsqemrq !r7hgppif fg z" tqpgryvpg ppgrgpig q uhxps5ps 7pg n grp gx n!hxgpphp g xzp gpgg p u Txrnss ht pqgd !np7 q jrpgGmVuvspusgf`ihvrppi4zphgdGnxrrispu7s7vpg~mruvsznpVnxxxz$dpusurxz$rxpgupswpqusTxpdhvrgxgufswfs xq mr g xh g r mr gnfwqrx jjthqfgpmhpogey $u$snAqh$rxqpmsup oopygpgtmrqevtsuussIpys7opqugssuoqgxpuvrswiqmrxgprnxpniuspg dh ixqm7pgnh$vlu ug iyuu u yulu x yuq7pgT npg n y C7p"p g pfpgf xv uss p rm vx $ $ s q q g g g v rr`gi px d pg ptgg q`ngr ` pdu0nus fg vXi Xdu opggtfq x h us eqrpdrqupsnqm`usdptqrgh5xupgton`rdpg jutsj pfrpgq rxArqsum tv 7vqm gpgtqopg5pxgusgx5d ouvm ~s n m g n v g d f f q s n xhggp uswqrg yrn pfTwvqGd fsx u gytqrd pguqps7xusx hx ropg xg g s q m wvvpqpgroumsuig phgsg p t`pg uAps ohpvg upvpgrpmgphg hy phhhoqg usg`pngn p eg pvrq pig prxg ruqm yqts rp g7uqm d$psu
0 W V 8) q E X W )1 } 2s X )W1 s
7.7 Computing with Big Integers -
V
X
0
3
v p u g s se s uns rpxgr uqv q 7$$px$g r$ur!~g od rpgxgiqqrf dhq d uppgos 7upgtnrq upnh x !pgq xV 5hnx zrd v uppxhz ux vq x x s v h s x g m g q g q m fd uvwstquqs s g m s s uvf gs hruqs uduq psus s n rxr ix pg 5vtqrpvquun7gsd uq Tnpge nppysu uV5n p5eung tngp xqdr$px hqtm rnVop pghg ud rxqridprg wgrq gpx pv pgou nopxghhd v p s
V GW 0 X W )1 p X )W1 k
Exercises
s g g gqtvumonzpnpqgpgggupsuG xv hdq hs tdqrj rpypgrgpnmi ~xhgrxxrp hrxgf n g g g d m f d jp ygnpeg uAws pqhqg pdrp pepg prxrx x5nqumus7xen 7eh ud`rpf xpus uv psd goq npguwsq g n usp` s i4 s g gphogfus$$ v urpxg uyps tgus pgr5x rrpxi ghgqwgdpm yf rhpx g!s yhd zopgp pgugspotg q ox gpyphd rxgf 7
r w f f f
7.7 Computing with Big Integers 241
w z z f qz p zz
7.7.1
7.6.1
The Type Definition for Big Integers
X I 0
W Ta
1
3`8) 2 V { V 3 # x }r X d d sV X 0 '81 10 0V X '
V01
0V X
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V
X
0
k
) '
T F F P V
V
X
s 0
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X
0
G
3
z
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X
X
V
r
X
I3 0
X '81 0 rr W d ) ' 2 301 d '81 ' V rV W ' d X
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X
X
X
$r uh $ $ $o ur$uGu $$r $u $ ur ru $ np hrp ghhndqf rh x hpq gpg uygps suhonup utx~ pgdrux~qs ruodsi txphn !p'vsu rph$Buvuphpds f gr xgf g m s s n g g $ d x ~ g h pu psgtvs qp ptg rgprvuistwq"qs uryexs nApdurxs xo ngfop pwgnem us goxni udg ersgni rpx xxesu hsn ushus g r e 7 q usr r sg xp d q q 'vwpqgypgpwgqmnxr~qus~rusz hftvq opr!x~hpdu~n vut pqwgrpm udpsg qrig rq 7rppg x gwsi u tqs x~ex pd uxsf pggh~x 7pxpggtsuhqx txm xtvuq psg n"vvq t vhpxhgn h x pg mr er us r pqng m5 x g x xjwv suqu pTg Ad phxg gd u pstqg f nus rpdsuprxqohpnm pevg u5eud ws n d utn hp gehmmd gvrrxf x $ $ upruis ntuqtg ps "uvsi "osx u$eAr rhee unn7uspuhpxp ruigefs rusi xp hr xgg fe nhdn d v s r s " x t s 5 g s ge x d i x g s ss tvq opggypr~prig rm jruqpsB nxG0 puBpdu o n y $$ rpxghd pgpwgqpB n ho j x us g e o7r7pnp u qs nus rhyy g7pdu $$ $ uq ps5ont sxtx qp g i fpe rqupsonxpghdmxquuonqnrpdv us xpsuv $ u2pp"gpg hrgg rppx w5q pg hr5"qqxd rn x hpeonxn rn5xhp r x rp$vg uvus t wqq ug5ps f pnrgy phhkg pg 5op u epfd n7 5tsrhtuv qdwsx!uqtqn ns5hrx n d s g d n ! sn n $$u $ 4 r ro t $rrr$ $u r $$uh $ $$r$ r $$ru v d phhx d s i ~f nhpgrxur xous hongp usv gf fnnpgp endy gpd piqd wg pu qmdrenxuogs rT7uk rk p xogodms ynqwqgtsufi m n o s q i n ph ge r f uqsd g g qugs fgg ufhts uqePs Vrs pxpu5 ndp g 9VB uBCIkkvu irQxxAQQnIT yhrXGrp v pxp"p ggtqu5ws pqgpgrhi t uqu m vs uerpxp rxro hn oy m s @ ( x i g s n y png r H A U~r 5 t 5 7~ ~""p " T e (grH s " s rx x g ot rt j pfgrHn5e'vB~g p eu gupg fps dgm nus rgx xgp pqhpg g uusgpfegg h u5gfs 5$ vq xprop i gppeh77eumx "ys p gmgfufpsT 5unps m
U
F F F P Rq R P ) k F F a F F S T R RR T F S T F P k FS Pl ) P F a RS FS Ra T k
242 Extending F
0 "
10
0V X
0
X Y
X
0
d0 r 3
~ #
~V {
x
'
x
X
X
`q
0V) X
c '
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0
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x x
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7.7 Computing with Big Integers
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256
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The
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8.2 Case Study: Solving a Heat Transfer Problem 265
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Pointer Variables
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8.4
Trees
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Unformatted Records Formatted Records
9.1 Records
287
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