Embed Size (px)
Citation preview
158
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
158
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Plus_1
mov
r4, r0
…
…
…
…
Plus_1:
add
r0, #1
bx
lrlr
Ho
w is
the
par
amet
er x
pas
sed
?
Wh
ere
do
yo
u fi
nd
the
resu
lt a
fter
the
fun
ctio
n r
etu
rns?
Co
uld
it b
e d
on
e d
iffe
ren
tly?
Do
es it
wo
rk?
155
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
155
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
(Gre
atne
ss fr
om …
) Sm
all b
egin
ning
splus_1 :: (Num a) => a -> a
plus_1 x = x + 1
int plus1 (int x) {
return x + 1;
} function Plus_1 (x : Integer) return Integer is (x + 1);
def plus1 (x):
return x + 1;
pure function plus_1 (x)
int, intent (in) :: x
int :: plus_1
plus_1 = x + 1;
end function;
function Plus_1 (x : integer) : integer;
begin
Plus_1 := x + 1;
end;
152
3Fu
nctio
ns
Uw
e R
. Zim
mer
- T
he A
ustr
alia
n N
atio
nal U
nive
rsity
Co
mp
ute
r Org
anis
atio
n &
Pro
gram
Exe
cuti
on
202
1
159
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
159
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
add
r0, #1
mov
r4, r0
…
…
…
…
Can
/sh
ou
ld th
is a
lway
s b
e d
on
e?
Th
is is
cal
led
inlin
ing
156
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
156
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Plus_1
mov
r4, r0
…
…
…
…
Plus_1:
add
r0, #1
bx
lr
153
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
153
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Ref
eren
ces
for
this
cha
pter
[Pat
ters
on1
7]D
avid
A. P
atte
rso
n &
Joh
n L
. Hen
nes
syC
om
pu
ter O
rgan
izat
ion
an
d D
esig
n –
Th
e H
ard
war
e/So
ftw
are
Inte
rfac
eC
hap
ter 2
“In
stru
ctio
ns:
Lan
guag
e o
f th
e C
om
pu
ter”
AR
M e
dit
ion
, Mo
rgan
Kau
fman
n 2
017
160
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
160
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
… … … … … … … … … …
… … … … … … …
… … … … … …
157
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
157
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Plus_1
mov
r4, r0
…
…
…
…
Plus_1:
add
r0,
#1
bx
lrlr
154
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
154
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
… … … … … … … … … …
… … … … … … …
167
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
167
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
sp
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
…
…
…
…
bl
Fib
mov
r4, r0
…
bl
Fact
add
r0, r4
…
…
bx
lr
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr
167
f
bx
lr
… w
her
e d
oes
this
lead
us?
164
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
164
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
add
r0, #2
mov
r3, r0
…
…
…
…
… w
e n
eed
an
exa
mp
le, w
her
e a
com
pile
r
will
no
t ju
st r
emo
ve a
ll o
ur
cod
e!
161
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
161
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
(Gre
atne
ss fr
om …
) Sm
all b
egin
ning
splus_2 :: (Num a) => a -> a
plus_2 x = plus_1 $ plus_1 x
int plus2 (int x) {
return plus1 (plus1 (x));
} function Plus_2 (x : Integer) return Integer is (Plus_1 (Plus_1 (x)));
def plus2 (x):
return plus1 (plus1 (x));
pure function plus_2 (x)
int, intent (in) :: x
int :: plus_2
plus_2 = plus_1 (plus_1 (x));
end function;
function Plus_2 (x : integer) : integer;
begin
Plus_2 := Plus_1 (Plus_1 (x));
end;
168
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
168
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
str
lr, [sp, #-4]!
…
…
…
bl
Fib
mov
r4, r0
…
bl
Fact
add
r0, r4
…
ldr
lr, [sp], #4
bx
lr
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr lrsp
165
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
165
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
(Gre
atne
ss fr
om …
) Sm
all b
egin
ning
sfib_fact :: (Num a) => a -> a
fib_fact x = (fib x) + (fact x)
unsigned int fibFact (unsigned int x) {
return fib (x) + fact (x);
} function Fib_Fact (x : Natural) return Natural is (Fib (x) + Fact (x));
def fibFact (x):
return fib (x) + fact (x);
pure function fib_fact (x)
int, intent (in) :: x
int :: fib_fact
fib_fact = fib (x) + fact (x);
end function;
function Fib_Fact (x : cardinal) : cardinal;
begin
Fib_Fact := Fib (x) + Fact (x);
end;
162
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
162
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Plus_2
mov
r3, r0
…
…
…
…
Plus_2:
…
bl Plus_1
bl Plus_1
…
bx
lr
Plus_1:
add
r0, #1
bx
lr
bx
lr is u
sed
thre
e ti
mes
Wh
at is
the
valu
e o
f lr
in e
ach
cas
e?
169
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
169
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
str
lr, [sp, #
-4]!
…
…
…
bl
Fib
mov
r4, r0
…
bl
Fact
add
r0, r4
…
ldr
lr, [sp], #4
bx
lr
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr lrsp
Npa
ge 1
69N
atio
nal U
nive
rsity
pa
ge 1
y
r4
… w
hat
if th
is w
as h
old
ing
som
e in
form
atio
n
at th
e ti
me
wh
en w
e w
ere
calle
d?
166
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
166
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
sp
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
…
…
…
…
bl
Fib
mov
r4, r0
…
bl
Fact
add
r0, r4
…
…
bx
lr
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr
163
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
163
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Plus_2
mov
r3, r0
…
…
…
…
Plus_2:
str
lr, [sp, #
-4]!
bl Plus_1
bl Plus_1
ldr
lr, [sp], #4
bx
lr
Plus_1:
add
r0, #1
bx
lr
bx
lr is u
sed
thre
e ti
mes
Wh
at is
the
valu
e o
f lr
in e
ach
cas
e?
176
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
176
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fib_FactFact 1Fact 0 Fact 2 Fact 3
fp r4
fp fp
lr fpx (3)
lrfp x (3)
lrx (2)
fplrx (1)
fplrx (0)
fpfpfpsp
Fact:
stmdb
sp!, {fp, lr}
add
fp,
sp, #4
sub
sp,
#4
str
r0, [fp,
#-8]
cmp
r0,
#0
bne
Case_Others
mov
r0,
#1
b End_Fact
Case_Others:
sub
r0,
#1
bl
Fact
mov
r1,
r0
ldr
r0, [fp,
#-8]
mul
r0,
r1End_Fact:
add
sp,
#4
ldmia
sp!, {fp, lr}
bx
lr
Fib_Fact:
stmdb
sp!, {r4, fp, lr
}
add
fp, sp, #8
sub
sp, #4
str
r0, [f
p, #-12]
bl
Fib
mov
r4, r0
ldr
r0, [f
p, #-12]
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {r4, fp, lr
}
bx
lr
}}
Wh
ere
is th
e la
st lr
sto
red
?
Ho
w h
igh
do
w
e st
ack?
Fact
Is Fact
ree
ntra
nt?
173
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
173
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
stmdb
sp!, {r4,
lr}
…
sub
sp, #4
str
r0, [sp]
bl
Fib
mov
r4, r0
ldr
r0, [sp]
bl
Fact
add
r0, r4
add
sp, #4
ldmia
sp!, {r4
, lr}
bx
lr
Fib_Fact
r4
splrx (3)
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
itypa
ge
y
Wh
ile a
dd
ress
ing
via
the
sp is
po
ssib
le, i
t may
als
o b
e
com
ple
x to
kee
p tr
ack
of,
as th
e sp
may
ch
ange
furt
her
.
170
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
170
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
stmdb
sp!, {r4,
lr}
…
…
…
bl
Fib
mov
r4, r0
…
bl
Fact
add
r0, r4
…
ldmia
sp!, {r4
, lr}
bx
lr
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr
Fib_Fact
r4sp
lr
177
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
177
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
A c
om
pile
r w
ill li
kely
re
pla
ce s
uch
a r
ecu
rsio
n!
177
f487
(h
3“F
i”
27
function Fact (x : Natural) return Positive is
Fac : Positive := 1;
begin
for i in 1 .. x loop
Fac := Fac * i;
end loop;
return Fac;
end Fact;
function Fact (x : Natural) return Positive is
(if x = 0 then 1
else x * Fact (x - 1));
174
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
174
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
stmdb
sp!, {r4,
fp,
lr}
add
fp, sp,
#8
sub
sp, #4
str
r0, [fp, #-12]
bl
Fib
mov
r4, r0
ldr
r0, [fp, #-12]
bl
Fact
add
r0, r4
add
sp, #4
ldmia
sp!, {r4
, fp,
lr}
bx
lr
Fib_Fact
r4fp
fplrx (1)
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr
2021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
174
of
y20
21 U
we
R. Z
imm
er, T
he A
ustr
alia
n N
atio
nal U
nive
rsity
page
174
y
Kee
pin
g a
refe
ren
ce to
the
star
t of t
he
Stac
k Fr
ame
for
this
fun
ctio
n (w
ith
the
fram
e-p
oin
ter
fp) m
akes
thin
gs n
eate
r
and
en
able
s st
ruct
ure
d a
cces
s to
the
dyn
amic
co
nte
xt.
171
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
171
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
stmdb
sp!, {r4,
lr}
…
…
…
bl
Fib
mov
r4, r0
…
bl
Fact
add
r0, r4
…
ldmia
sp!, {r4
, lr}
bx
lr
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr
Fib_Fact
r4sp
lr
nive
rsity
pa
ge 1
7y
iitW
hat
hap
pen
s to
ou
r p
aram
eter
x (1
) d
uri
ng
the
fun
ctio
n?
178
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
178
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
A c
om
pile
r w
ill li
kely
re
pla
ce s
uch
a r
ecu
rsio
n!
unsigned int fact (unsigned int x) {
if (x == 0) return 1;
else return x * fact (x - 1);
}
178
f487
(h
3“F
i”
27
unsigned int fact (unsigned int x) {
int fac = 1;
for (i = 1, i <= x, i++) {
fac = fac * i;
}
return fac;
}
175
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
175
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Rec
ursi
veunsigned int fib (unsigned int x) {
switch (x) {
case 0 : return 0;
case 1 : return 1;
default : return fib (x - 1) + fib (x - 2);
} }
function Fib (x : Natural) return Natural is
(case x is
when 0 => 0,
when 1 => 1,
when others => Fib (x - 1) + Fib (x - 2));
unsigned int fact (unsigned int x) {
if (x == 0) return 1;
else return x * fact (x - 1);
} function Fact (x : Natural) return Positive is
(if x = 0 then 1
else x * Fact (x - 1));
Will
ou
r st
ack
han
dlin
g w
ork
fo
r re
curs
ive
fun
ctio
ns?
172
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
172
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
…
…
…
mov
r0, #1
bl
Fib_Fact
mov
r3, r0
…
…
…
…
Fib_Fact:
stmdb
sp!, {r4, lr
}
…
sub
sp, #4
str
r0, [sp]
bl
Fib
mov
r4, r0
ldr
r0, [sp]
bl
Fact
add
r0, r4
add
sp, #4
ldmia
sp!, {r4, lr
}
bx
lr
Fib_Fact
r4
splrx (3)
Fib:
…
…
…
bx
lr
Fact:
…
…
…
bx
lr
185
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
185
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Pro
logu
e
Epilo
gue
Com
pone
nts
/ ph
ases
of a
func
tion
cal
l:•
Val
ues
(par
amet
ers)
to b
e p
asse
d to
a fu
nct
ion
.
• Lo
cal v
aria
bles
insi
de
a fu
nct
ion
.
• V
alu
es (r
esul
ts) t
o b
e re
turn
ed fr
om
a fu
nct
ion
.
So fa
r w
e: …
pas
sed
para
met
er v
alu
es in
reg
iste
rs ( r
0 - r
3).
… c
alle
d th
e fu
ncti
on (s
tore
the
retu
rn a
dd
ress
an
d ju
mp
to th
e b
egin
nin
g o
f th
e fu
nct
ion
).
… p
ushe
d th
e re
turn
ad
dre
ss, t
he
pre
vio
us
stac
k fr
ame
and
use
d r
egis
ters
( r4
…).
… c
reat
ed a
new
sta
ck fr
ame
(an
d a
dd
ress
ed a
ll lo
cal v
aria
ble
s re
lati
ve to
this
).
… g
rew
the
sta
ck s
uch
that
it c
an h
old
the
loca
l var
iab
les.
… d
one
the
calc
ulat
ions
/ope
rati
ons
bas
ed o
n th
e lo
cal v
aria
ble
s an
d s
crat
ch r
egis
ters
.
… p
asse
d re
turn
val
ues
in r
egis
ters
( r0
- r1)
.
… r
esto
red
the
stac
k po
inte
r (a
nd
thu
s d
e-al
loca
ted
all
loca
l var
iab
les)
.
… p
oppe
d th
e re
turn
ad
dre
ss, t
he
pre
vio
us
stac
k fr
ame
and
use
d r
egis
ters
( r4
…).
… ju
mpe
d ba
ck to
the
nex
t in
stru
ctio
n a
fter
the
ori
gin
al fu
nct
ion
cal
l.
… u
sed
the
retu
rn v
alue
s fo
un
d in
r0
- r1.
Wh
at h
app
ens
if th
e p
aram
eter
s o
r
retu
rn v
alu
es w
on
’t fi
t in
to r
egis
ters
?
182
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
182
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fib_Fact:
stmdb
sp!, {r4, fp, lr
}
add
fp, sp, #8
sub
sp, #4
str
r0, [f
p, #-12]
bl
Fib
mov
r4, r0
ldr
r0, [f
p, #-12]
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {r4, fp, lr
}
bx
lr
tytytytyy
Fib:
stmdb sp!, {r4, fp, lr}
add fp, sp
, #8
sub sp, #4
str r0, [fp, #
-12]
cmp r0, #0
beq End_Fib
cmp r0, #1
beq End_Fib
sub r0, r0
, #1
bl Fib
mov r4, r0
ldr r0, [fp, #
-12]
sub r0, r0
, #2
bl Fib
add r0, r4
, r0
End_Fib:
add sp, #4
ldmia sp!, {r4, fp, lr}
bx lr
Fib_Fact
r4fp
fplrx (3)
179
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
179
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fact:
adds
r3, r0, #0
mov
r0,
#1
beq
End_Fact
Fact_Loop:
mul
r0,
r3
subs
r3,
#1
bne
Fact_Loop
End_Fact:
bx
lr
Fib_Fact:
stmdb
sp!, {r4, fp, lr
}
add
fp, sp, #8
sub
sp, #4
str
r0, [f
p, #-12]
bl
Fib
mov
r4, r0
ldr
r0, [f
p, #-12]
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {r4, fp, lr
}
bx
lr
}}
Fib:
…
…
…
bx
lr
mm
er, T
he A
ustr
alia
n N
atio
nal U
nive
rsity
pa
ge
y20
21 U
we
R. Z
imm
er, T
he A
ustr
alia
n N
atio
nal U
nive
rsity
pay
Bes
ides
all
the
inlin
ing,
un
rolli
ng,
fl at
ten
ing,
etc
. :
Sta
ck o
per
atio
ns
are
still
vit
al fo
r an
y n
on
-tri
vial
pro
gram
.
Co
mp
lexi
ty?
Ru
nti
mes
?
Is Fact
ree
ntra
nt?
Fib_Fact
r4fp
fplrx (3)
186
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
186
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Con
vent
ions
AR
M a
rchi
tect
ure
calli
ng p
ract
ice
• r0
-r3
are
use
d fo
r p
aram
eter
s.
• r0
-r1
are
use
d fo
r re
turn
val
ues
.
• r0
-r3
are
no
t exp
ecte
d to
be
inta
ct a
fter
a fu
nct
ion
cal
l…
all
oth
er r
egis
ters
are
exp
ecte
d to
be
inta
ct!
If th
ose
reg
iste
rs d
o n
ot s
uffi
ce,
ad
dit
ion
al p
aram
eter
s an
d r
esu
lts
are
pas
sed
via
the
stac
k. Co
nve
nti
on
s ar
e d
iffe
ren
t in
oth
er
arch
ite
ctu
res
(e.g
. x86
, wh
ere
par
ame
ters
are
ge
ne
rall
y p
asse
d v
ia t
he
sta
ck).
fh
Wh
y ar
e t
he
se c
on
ven
tio
ns
arch
ite
ctu
re r
ela
ted
at
all?
Th
ere
are
als
o m
em
ory
al
ign
me
nt
con
stra
ints
.
(Mo
stly
du
e t
o m
em
ory
b
us
con
stra
ints
)
183
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
183
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fib_Fact:
stmdb
sp!, {
r4,
fp,
lr}
add
fp, sp, #8
sub
sp, #4
str
r0, [fp,
#-12]
bl
Fib
mov
r4, r0
ldr
r0, [fp,
#-12]
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {
r4,
fp,
lr}
bx
lr
tytytytyy
Fib:
stmdb
sp!, {
r4,
fp, lr
} add fp, sp, #8
sub sp, #4
str r0, [fp, #
-12]
cmp
r0
, #0
beq
End_Fib
cmp
r0
, #1
beq
End_Fib
sub
r0
, r0, #1
bl
Fib
mov
r4
, r0
ldr
r0
, [fp, #
-12]
sub
r0
, r0, #2
bl
Fib
add
r0
, r4, r0
End_Fib:
add
sp
, #4
ldmia
sp!, {r4, fp
, lr}
bx
lr
Fib_Fact
r4fp
fplrx (3)
p p r4,r0
4, r0
0, [fp
, #-12
]act
0, r0, r4
p, #4
p!, {r4, fp, lr}
r
Th
ere
cou
ld b
e tw
o fu
rth
er F
ib-c
alls
fo
r ea
ch c
all
to F
ib …
Wh
at w
ou
ld th
e st
ack
loo
k lik
e?
Wh
at w
ou
ld b
e th
e m
axim
al d
epth
fo
r th
e st
ack?
180
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
180
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fact:
adds
r3, r0
, #0
mov
r0, #1
beq
End_Fact
Fact_Loop:
mul
r0, r3
subs
r3, #1
bne
Fact_Loop
End_Fact:
bx
lr
Fib_Fact:
stmdb
sp!, {
r4,
fp,
lr}
add
fp, sp, #8
sub
sp, #4
str
r0, [fp,
#-12]
bl
Fib
mov
r4, r0
ldr
r0, [fp,
#-12]
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {
r4,
fp,
lr}
bx
lr
}}
Fib:
…
…
…
bx
lr
… … bxlr
Wh
y d
o w
e sa
ve r
4?
Bu
t we
do
n’t
save
r3?
Fib_Fact
r4fp
fplrx (3)
187
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
187
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Para
met
er p
assi
ng
Cal
l by
…
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
184
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
184
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Com
pone
nts
/ ph
ases
of a
func
tion
cal
l:•
Val
ues
(par
amet
ers)
to b
e p
asse
d to
a fu
nct
ion
.
• Lo
cal v
aria
bles
insi
de
a fu
nct
ion
.
• V
alu
es (r
esul
ts) t
o b
e re
turn
ed fr
om
a fu
nct
ion
.
So fa
r w
e: …
pas
sed
para
met
er v
alu
es in
reg
iste
rs ( r
0 - r
3).
… c
alle
d th
e fu
ncti
on (s
tore
the
retu
rn a
dd
ress
an
d ju
mp
to th
e b
egin
nin
g o
f th
e fu
nct
ion
).
… p
ushe
d th
e re
turn
ad
dre
ss, t
he
pre
vio
us
stac
k fr
ame
and
use
d r
egis
ters
( r4
…).
… c
reat
ed a
new
sta
ck fr
ame
(an
d a
dd
ress
ed a
ll lo
cal v
aria
ble
s re
lati
ve to
this
).
… g
rew
the
sta
ck s
uch
that
it c
an h
old
the
loca
l var
iab
les.
… d
one
the
calc
ulat
ions
/ope
rati
ons
bas
ed o
n th
e lo
cal v
aria
ble
s an
d s
crat
ch r
egis
ters
.
… p
asse
d re
turn
val
ues
in r
egis
ters
( r0
- r1)
.
… r
esto
red
the
stac
k po
inte
r (a
nd
thu
s d
e-al
loca
ted
all
loca
l var
iab
les)
.
… p
oppe
d th
e re
turn
ad
dre
ss, t
he
pre
vio
us
stac
k fr
ame
and
use
d r
egis
ters
( r4
…).
… ju
mpe
d ba
ck to
the
nex
t in
stru
ctio
n a
fter
the
ori
gin
al fu
nct
ion
cal
l.
… u
sed
the
retu
rn v
alue
s fo
un
d in
r0
- r1.
Pro
logu
e
Epilo
gue
181
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
181
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fact:
adds
r3, r0, #0
mov
r0, #1
beq
End_Fact
Fact_Loop:
mul
r0, r3
subs
r3, #1
bne
Fact_Loop
End_Fact:
bx
lr
Fib_Fact:
stmdb
sp!, {r4, fp
, lr}
add
fp,
sp, #8
sub
sp,
#4
str
r0, [fp, #
-12]
bl
Fib
mov
r4,
r0
ldr
r0, [fp, #
-12]
bl
Fact
add
r0,
r0, r4
add
sp, #4
ldmia
sp!, {r4, fp
, lr}
bx
lr
}}
Fib:
…
…
…
bx
lr
Fact:
b}}
bxlr
We
keep
a c
op
y o
f r0
her
e.
Bu
t we
do
n’t
keep
a
cop
y o
f r0
her
e!
Fib_Fact
r4fp
fplrx (3)
194
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
194
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fib_FactFact 1Fact 0 Fact 2 Fact 3
Fact:
stmdb
sp!, {fp, lr}
add
fp,
sp, #4
sub
sp,
#4
str
r0, [fp,
#-8]
cmp
r0,
#0
bne
Case_Others
mov
r0,
#1
b End_Fact
Case_Others:
sub
r0,
#1
bl
Fact
mov
r1,
r0
ldr
r0, [fp,
#-8]
mul
r0,
r1End_Fact:
add sp
, #4
ldmia
sp!, {fp, lr}
bx
lr
Fib_Fact:
stmdb
sp!, {r4, fp, lr
}
add
fp, sp, #8
sub
sp, #4
str
r0, [f
p, #-12]
bl
Fib
mov
r4, r0
ldr
r0, [f
p, #-12]
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {r4, fp, lr
}
bx
lr
}}
fp r4
fp fp
lr fpx (3)
lrfp x (3)
lrx (2)
fplrx (1)
fplrx (0)
fpfpfpsp
Ho
w a
bo
ut u
sin
g ca
ll b
y re
fere
nce
her
e?
191
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
191
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
Acc
ess
Ad
aLi
mit
ed c
on
tro
l ove
r “b
y va
lue
resu
lt”.
“by
valu
e” p
aram
eter
s ar
e co
nst
ants
.
188
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
188
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
by
cop
yy
py
yp
yy
py
by
refe
ren
ceyyy
Acc
ess
by
cop
yb
yre
fere
nce
CFu
ll co
ntr
ol o
ver
tho
se th
ree
mo
des
.
“by
valu
e” p
aram
eter
s ar
e lo
cal v
aria
ble
s.
“in
& o
ut,
by
refe
ren
ce”
syn
tact
ical
ly a
s “b
y p
oin
ter
valu
e” p
aram
eter
s.
195
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
195
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fact:
stmdb
sp!, {
r5, fp, lr}
add
fp, sp,
#4
mov
r5, r0
ldr
r0, [r5]
cmp
r0, #0
bne
Case_Others
mov
r0, #1
b
End_Fact
Case_Others:
sub
r0, #1
str
r0, [r5]
mov
r0, r5
bl
Fact
mov
r1, r0
ldr
r0, [r5]
mul
r0, r1
End_Fact:
mov
sp, fp
ldmia
sp!, {
r5, fp, lr}
bx
lr
Fib_Fact:
stmdb
sp!, {
r4,
fp,
lr}
add
fp, sp, #8
sub
sp, #4
str
r0, [fp,
#-12]
bl
Fib
mov
r4, r0
sub
r0, fp, #12
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {
r4,
fp,
lr}
bx
lr
}}
tytyy
r5 h
as b
een
no
min
ated
to h
old
th
e re
fere
nce
to x
insi
de Fact
Fib_FactFact 1Fact 0 Fact 2 Fact 3
r5 r4
fp fp
fp fplr lrr5 x (0)
fplrr5fplrr5fplr
fpfpfpsp
Fact Fact Fact FFac
r5
Fact Fact Fact Fact Fact FFact Fact
r5
Fact Fact Fact Fact Fac FFac Fact
r5
Fact Fact Fact Fact Fact FFact Fact
r5
192
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
192
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
Ass
emb
ly“B
y re
fere
nce
” se
man
tics
by
con
ven
tio
n o
nly
.
189
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
189
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
Has
kell
On
ly c
on
tro
l ove
r in
form
atio
n fl
ow
– n
ot o
ver
acce
ss. ttteteteteteteettee
sity
page
189
of
y48
7(c
hapt
er 3
: “Fu
nctio
ns7
nooooooooo
ris
cop
ied
toa
loca
lF
tir
is c
op
ied
to a
loca
l an
d c
op
ied
bac
k at
ret
urn
.Fu
nct
ion
can
rea
d a
nd
wri
tti
me.
Ou
tsid
e co
de
shal
l n“i
n &
ou
t” p
aram
eter
s ar
e si
de-
effe
ctin
g an
d c
an
ther
efo
re n
ot e
xist
in a
pu
re fu
nct
ion
al la
ngu
age.
196
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
196
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fact:
stmdb
sp!, {r5, fp
, lr}
add
fp,
sp, #4
mov
r5,
r0
ldr
r0, [r5]
cmp
r0,
#0
bne
Case_Others
mov
r0,
#1
b End_Fact
Case_Others:
sub
r0,
#1
str
r0, [r5]
mov
r0,
r5
bl
Fact
mov
r1,
r0
ldr
r0, [r5]
mul
r0,
r1End_Fact:
mov
sp,
fp
ldmia
sp!, {r5, fp
, lr}
bx
lr
Fib_Fact:
stmdb
sp!, {r4, fp
, lr}
add
fp,
sp, #8
sub
sp,
#4
str
r0, [fp, #
-12]
bl
Fib
mov
r4,
r0
sub
r0,
fp, #12
bl
Fact
add
r0,
r0, r4
add
sp, #4
ldmia
sp!, {r4, fp
, lr}
bx
lr
}}
tytyy
We
turn
ed Fact
into
th
e co
nst
ant 0
.
Fib_FactFact 1Fact 0 Fact 2 Fact 3
r5 r4fp fplr lrr5 x (0)
fplrr5fplrr5fplr
fpsp
Fact Fact Fact FFac
r5
Fact Fact Fact Fact Fact FFact Fact
r5
Fact Fact Fact Fact Fac FFac Fact
r5
Fact Fact Fact Fact Fact FFact Fact
r5r5 r4
fpfp fplr lrr5 x (0
fplrr5fplrr5fplr
fpfpfpfpfpfpfpfffpfpfpfp
fp,
sp, #4
r5,
r0r0, [r5]
r0,
#0Case_Others
r0,
#1End_Fa
thers
r000,
##1#r0, [r555]
r0,
r5Fact
r1,
r0r0, [r5]
r0,
r1ct:
s
s
_Fa
ssssssssssssss
s
iiiiiiii
s
_Fa
_FaFaFac
FFFac
Fac
Facacac
_Fa
_FacacFac
FacaFac
_Fa
_FacacFacacFaFacaFac
Faacttt
s:ss:s:s:s:s:ssssss:s:s:ss:sss:sss:ss:ss:s:: 0#1
55]]]]]]]]]]]]]]]]]]]]]r1r1r1r1r1111111111r111r1r11r1r111111
fpspspspspspspspssspspspspsspsspspspspspspsspspspppp
lrp!, {r5, fpp,
lr}
lll
ct:
c iiiiiisp,
fpfpfffiiiaaaa
spspsssp!, {r5,fp
,lr}
fpct:
ispspsss
iiiiiaa W
hat
did
we
ove
rlo
ok?
193
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
193
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Para
met
er p
assi
ng
Cal
l by
nam
e…
is c
on
cep
tual
ly a
cal
l-b
y-va
lue,
wh
ere
the
valu
e h
as n
ot b
een
cal
cula
ted
yet
.
Tech
nic
ally
a r
efer
ence
to a
fun
ctio
n is
pas
sed
an
d th
e ev
alu
atio
n
of t
his
par
amet
er (f
un
ctio
n) i
s le
ft to
the
calle
d fu
nct
ion
.
Feat
ure
s:•
Val
ues
are
on
ly e
valu
ated
if a
nd
wh
en th
ey a
re n
eed
ed.
• V
alu
es c
an c
han
ge d
uri
ng
the
life-
tim
e o
f a fu
nct
ion
(in
cas
e o
f sid
e-ef
fect
ing
fun
ctio
ns)
.
• V
alu
es c
an b
e st
ore
d o
nce
cal
cula
ted
(in
cas
e o
f sid
e-ef
fect
-fre
e fu
nct
ion
s).
Wh
ile th
is is
po
ssib
le to
a d
egre
e in
mo
st p
rogr
amm
ing
lan
guag
es …
(eve
n if
ther
e is
no
sp
ecifi
c p
assi
ng
mo
de,
yo
u c
an s
till
pas
s a
refe
ren
ce to
a fu
nct
ion
)
… it
is a
co
re c
on
cep
t fo
r fu
nct
ion
al, l
azy
eval
uat
ion
lan
guag
es, l
ike
e.g.
Has
kell,
and
it d
oes
fi n
d it
s w
ay b
ack
into
mai
nst
ream
lan
guag
es li
ke C
++
, .N
ET la
ngu
ages
or
Pyth
on
as
ano
nym
ous
func
tion
s (s
om
etim
es r
efer
red
to a
s m
-fu
nct
ion
s o
r m
-exp
ress
ion
s).
Pop
s u
p in
pro
gram
min
g la
ngu
ages
sin
ce th
e 60
’s.
190
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
190
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
Pyth
on
All
par
amet
er a
cces
s is
do
ub
le-i
nd
irec
t ( h
andl
es).
by
refe
ren
ceA
cces
sb
… th
is h
as a
n im
pac
t on
per
form
ance
.
203
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
203
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
A
Fun
ctio
ns
One
-way
-Out
and
by-
refe
renc
eSi
de-
effe
ct-f
ree,
if n
ew m
emo
ry is
allo
cate
d o
n r
etu
rn
– ca
nn
ot b
e en
forc
ed o
n a
ssem
bly
leve
l (re
qu
ires
co
mp
iler)
.
Val
ues
hav
e to
be
pas
sed
in m
emo
ry.
200
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
200
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
A
Fun
ctio
ns
One
-way
and
by-
copy
Tho
se a
re s
ide-
effe
ct-f
ree
and
hen
ce th
e re
sult
ing
scen
ario
s ar
e ea
sy to
an
alys
e.
Co
pyi
ng
larg
e d
ata
stru
ctu
res
mig
ht b
e ti
me
con
sum
ing
or
infe
asib
le.
Val
ues
can
be
pas
sed
in r
egis
ters
.
197
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
197
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Fact:
stmdb
sp!, {r5,
fp, lr}
add
fp,
sp, #4
mov
r5,
r0
ldr
r0, [r5]
cmp
r0,
#0
bne
Case_Others
mov
r0,
#1
b End_Fact
Case_Others:
sub
r0,
#1
str
r0, [r5]
mov
r0,
r5
bl
Fact
mov
r1,
r0
ldr
r0, [r5]
mul
r0,
r1End_Fact:
mov
sp,
fp
ldmia
sp!, {r5,
fp, lr}
bx
lr
Fib_Fact:
stmdb
sp!, {r4, fp, lr
}
add
fp, sp, #8
sub
sp, #4
str
r0, [f
p, #-12]
bl
Fib
mov
r4, r0
sub
r0, fp, #12
bl
Fact
add
r0, r0, r4
add sp, #4
ldmia
sp!, {r4, fp, lr
}
bx
lr
tytyy
p,Fib
db!
{4
fmdb
sp!, {r4, fp,lr
dfp,sp, #8
bsp,#4
rr0, [fp, #-12]
}}
Wh
at is
the
valu
e o
f x d
uri
ng
on
e ex
ecu
tio
n o
f Fact?
Fib_FactFact 1Fact 0 Fact 2 Fact 3
r5 r4
fp fp
fp fplr lrr5 x (0)
fplrr5fplrr5fplr
fpfpfpsp
Fact Fact Fact Fac Facc
r5
Fact Fact Fact Fact Fact Fac Fact Fact
r5
Fact Fact Fact Fact Fac Fac Fact Fac
r5
Fact Fact Fact Fact Fact Fac Fact Ft
r5
204
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
204
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
A
Fun
ctio
ns
One
-way
-In
and
by-
refe
renc
e
Sid
e-ef
fect
-fre
e –
can
no
t be
enfo
rced
on
ass
emb
ly le
vel (
req
uir
es c
om
pile
r).
No
dat
a h
as to
be
rep
licat
ed.
Val
ues
hav
e to
be
pas
sed
in m
emo
ry.
201
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
201
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
A
Fun
ctio
ns
Two
-way
and
by-
copy
Still
sid
e-ef
fect
-fre
e w
ith
in th
e fu
nct
ion
(bu
t no
t on
the
ou
tsid
e).
Pote
nti
ally
mo
re c
on
ven
ien
t as
mem
ory
sp
ace
can
be
reu
sed
.
Val
ues
can
be
pas
sed
in r
egis
ters
.
198
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
198
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Para
met
er p
assi
ng
Cal
l by
…
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)7
f487
(h
3
Yet w
e u
sed
this
mo
de
eN
o r
ead
acce
ss fr
om
insi
de
the
))
eby
ref
eren
ce (
mut
able
, no
read
)N
df
iid
thW
e sh
ou
ld h
ave
use
d e
ith
er o
f th
ose
mo
des
205
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
205
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eLe
t th
ere
be
som
e (g
lob
al) d
ata
on
the
stac
k.
Stac
k-B
ase
(SB
) is
a st
atic
ad
dre
ss,
alw
ays
po
inti
ng
to th
e …
wel
l.
Stac
k-Po
inte
r (S
P) p
oin
ts to
the
curr
ent t
op
of t
he
stac
k.
page
205
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Glo
bal
var
iab
les
can
als
o
be
sto
red
so
mep
lace
els
e.
202
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
202
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
A
Fun
ctio
ns
Two
-way
and
by-
refe
renc
e
Sid
e-ef
fect
ing
and
par
ticu
lar
care
is r
equ
ired
as
mu
ltip
le e
nti
ties
co
uld
wri
te o
n th
is.
No
dat
a h
as to
be
rep
licat
ed.
Val
ues
hav
e to
be
pas
sed
in m
emo
ry.
199
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
199
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Acc
ess
by
cop
yb
y re
fere
nce
Info
rmat
ion
fl
ow
in
by v
alue
Para
met
er b
eco
mes
a c
on
stan
t in
sid
e th
e fu
nct
ion
or
is
cop
ied
into
a lo
cal v
aria
ble
.
by r
efer
ence
(im
mut
able
)N
o w
rite
acc
ess
is a
llow
ed
wh
ile th
e fu
nct
ion
ru
ns
(als
o
fro
m o
uts
ide
the
fun
ctio
n).
ou
t
by r
esul
tC
allin
g fu
nct
ion
exp
ects
the
par
amet
er v
alu
e to
ap
pea
r in
a
spec
ifi c
spac
e at
ret
urn
.
by r
efer
ence
(m
utab
le, n
o re
ad)
No
rea
d a
cces
s fr
om
insi
de
the
fun
ctio
n, w
rite
acc
ess
on
ret
urn
.
in
&
ou
t
by v
alue
res
ult
Para
met
er is
co
pie
d to
a lo
cal
vari
able
an
d c
op
ied
bac
k at
ret
urn
.
by r
efer
ence
(m
utab
le)
Fun
ctio
n c
an r
ead
an
d w
rite
at a
ny
tim
e. O
uts
ide
cod
e sh
all n
ot w
rite
.
A
Whe
n to
use
wha
t?
212
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
212
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Stat
ic v
s. d
ynam
ic li
nks
function a (x : Integer) return Integer is
function b (y : Integer) return Integer is (x + y);
function c (z : Integer) return Integer is (b (z));
begin
return c (x);
end a;
a :: Integer -> Integer
a x = c x
where
b :: Integer -> Integer
b y = x + y
c :: Integer -> Integer
c z = b z
Th
e dy
nam
ic a
nd
sta
tic
link
for
function
c a
re b
oth
function a.
209
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
209
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eFu
nct
ion
s (i
n p
rogr
amm
ing
lan
guag
es) h
ave
a co
nte
xt.
E.g
. th
e su
rro
un
din
g fu
nct
ion
or
the
ho
stin
g o
bje
ct.
The
calle
r kn
ow
s th
is c
on
text
an
d p
rovi
des
it.
page
209
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
So
me
lan
guag
es w
ill n
ot h
ave
a co
nte
xt
by
def
ault
, lik
e C
or
Ass
emb
ly.
(gn
u C
exp
and
s th
e C
sta
nd
ard
an
d p
rovi
des
it th
ou
gh)
206
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
206
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e cu
rren
t co
de
pre
par
ed to
cal
l a fu
nct
ion
: P
ush
par
amet
ers
on
the
stac
k.
Wo
rks
for
any
dat
a si
ze (u
nle
ss th
e st
ack
ove
rfl o
ws)
an
d p
aram
eter
pas
sin
g m
od
e.
page
206
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
a
Typ
es, s
tora
ge s
tru
ctu
res
and
p
assi
ng
mo
des
hav
e to
be
agre
ed
up
on
bet
wee
n c
alle
r an
d c
alle
e.
213
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
213
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Stat
ic v
s. d
ynam
ic li
nks
function a (x : Integer) return Integer is
function b (y : Integer) return Integer is (x + y);
function c (z : Integer) return Integer is (b (z));
begin
return c (x);
end a;
a :: Integer -> Integer
a x = c x
where
b :: Integer -> Integer
b y = x + y
c :: Integer -> Integer
c z = b z
Dyn
amic
link
(pri
or
fram
e)
Th
e ca
ller
of f
unction b
is function c.
Hen
ce e
xcep
tio
ns
rais
ed in
b a
re
han
dle
d fi
rst i
n b
, th
en in
c, a
nd
then
a.
Th
e dy
nam
ic a
nd
sta
tic
link
for
function
c a
re b
oth
function a.
210
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
210
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e ca
ller
also
pro
vid
es a
ref
eren
ce to
its
ow
n s
tack
fram
e.
Th
is b
uild
s a
linea
r ch
ain
of c
alls
thro
ugh
the
stac
k.
Will
be
use
d e
.g. f
or
deb
ugg
ing
(sta
ck tr
ace)
an
d e
xcep
tio
n p
rop
agat
ion
.
page
210
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
k
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
k
Th
e st
atic
an
d d
ynam
ic li
nk
mig
ht
be
iden
tica
l in
so
me
case
s.
207
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
207
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e cu
rren
t co
de
pre
par
ed to
cal
l a fu
nct
ion
: P
ush
par
amet
ers
on
the
stac
k.
Wo
rks
for
any
dat
a si
ze (u
nle
ss th
e st
ack
ove
rfl o
ws)
an
d p
aram
eter
pas
sin
g m
od
e.
page
207
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Typ
es, s
tora
ge s
tru
ctu
res
and
p
assi
ng
mo
des
hav
e to
be
agre
ed
up
on
bet
wee
n c
alle
r an
d c
alle
e.
So
lved
if it
’s th
e sa
me
lan
guag
e, c
om
pile
r an
d p
rogr
am.
If t
he
lan
guag
es o
r th
e co
mp
ilers
are
dif
fere
nt,
then
sta
nd
ard
s w
ill b
e re
qu
ired
.
214
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
214
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Stat
ic v
s. d
ynam
ic li
nks
function a (x : Integer) return Integer is
function b (y : Integer) return Integer is (x + y);
function c (z : Integer) return Integer is (b (z));
begin
return c (x);
end a;
a :: Integer -> Integer
a x = c x
where
b :: Integer -> Integer
b y = x + y
c :: Integer -> Integer
c z = b z
Dyn
amic
link
(pri
or
fram
e)
Th
e ca
ller
of f
unction b
is function c.
Stat
ic li
nk (c
on
text
)
Th
e co
nte
xt fo
r function
b is
function a.
page
214
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)7
page
214
of48
7(c
hapt
er3:
“Fun
ctio
ns”
upto
page
232)
7
Hen
ce b
can
acc
ess x
(bu
t no
t z).
Hen
ce e
xcep
tio
ns
rais
ed in
b a
re
han
dle
d fi
rst i
n b
, th
en in
c, a
nd
then
a.
Th
e dy
nam
ic a
nd
sta
tic
link
for
function
c a
re b
oth
function a.
211
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
211
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Stat
ic v
s. d
ynam
ic li
nks
function a (x : Integer) return Integer is
function b (y : Integer) return Integer is (x + y);
function c (z : Integer) return Integer is (b (z));
begin
return c (x);
end a;
a :: Integer -> Integer
a x = c x
where
b :: Integer -> Integer
b y = x + y
c :: Integer -> Integer
c z = b z
208
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
208
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eFu
nct
ion
s (i
n p
rogr
amm
ing
lan
guag
es) h
ave
a co
nte
xt.
E.g
. th
e su
rro
un
din
g fu
nct
ion
or
the
ho
stin
g o
bje
ct.
The
calle
r kn
ow
s th
is c
on
text
an
d p
rovi
des
it.
page
208
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
221
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
221
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e n
ext f
un
ctio
n c
all w
ill p
rod
uce
the
nex
t sta
ck fr
ame.
Var
iab
les
and
par
amet
ers
fro
m th
e co
nte
xt s
tay
visi
ble
(v
ia th
e ch
ain
of s
tati
c lin
ks).
page
221
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FPSPLo
cal v
aria
bles
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
FP
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Cal
ler
Cal
lee
218
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
218
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eA
Fra
me
Poin
ter
(FP)
is e
stab
lish
ed a
t th
e b
ou
nd
-ar
y b
etw
een
the
calle
r an
d th
e ca
llee.
Up
war
ds
fro
m th
e FP
: dat
a fr
om
this
fun
ctio
n.
Do
wn
war
ds
fro
m th
e FP
: d
ata
pro
vid
ed b
y th
e p
revi
ou
s fu
nct
ion
.
page
218
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
SPSa
ved
reso
urce
sFP
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FP
Save
d r
eso
urc
es a
re fo
r in
stan
ce r
egis
ters
wh
ich
the
calle
e is
pla
nn
ing
to u
se.
215
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
215
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e ca
ller
also
pro
vid
es a
ref
eren
ce to
its
ow
n s
tack
fram
e.
Th
is b
uild
s a
linea
r ch
ain
of c
alls
thro
ugh
the
stac
k.
Will
be
use
d e
.g. f
or
deb
ugg
ing
(sta
ck tr
ace)
an
d e
xcep
tio
n p
rop
agat
ion
.
page
215
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
k
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
k
222
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
222
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e n
ext f
un
ctio
n c
all w
ill p
rod
uce
the
nex
t sta
ck fr
ame.
Var
iab
les
and
par
amet
ers
fro
m th
e co
nte
xt s
tay
visi
ble
(v
ia th
e ch
ain
of s
tati
c lin
ks).
page
222
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FPSPLo
cal v
aria
bles
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Ret
urn
addr
ess
Save
d re
sour
ces
FP
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Ret
urn
addr
ess
SaSaSavvve
dre
sour
ed r
esou
red
reso
urce
sce
sce
s
Cal
ler
Cal
lee
Loca
l var
iab
les
can
on
ly
be
add
ed to
the
curr
entl
y ex
ecu
tin
g fu
nct
ion
.
219
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
219
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eLo
cal v
aria
ble
s ar
e al
loca
ted
(by
mo
vin
g th
e st
ack
po
inte
r).
Loca
l var
iab
les
can
be
of a
ny
size
or
stru
ctu
re,
un
less
the
stac
k o
verfl
ow
s.
Th
e co
mp
lete
s a
new
sta
ck fr
ame.
page
219
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FPSPLo
cal v
aria
bles
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FP
Loca
l var
iabl
es
216
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
216
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e la
st it
em to
be
sto
red
bef
ore
han
din
g o
ver
con
tro
lis
the
add
ress
of t
he
follo
win
g in
stru
ctio
n.
Th
e co
ntr
ol fl
ow
can
late
r re
turn
to th
is a
dd
ress
.
page
216
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
223
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
223
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e n
ext f
un
ctio
n c
all w
ill p
rod
uce
the
nex
t sta
ck fr
ame.
No
te w
hic
h v
aria
ble
s an
d p
aram
eter
s ar
e vi
sib
le.
page
223
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FPSPLo
cal v
aria
bles
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
s
Para
met
ers
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
FPSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
ynam
ic) l
ink
Ret
urn
addr
ess
Loca
l var
iabl
es
Save
d re
sour
ces
Cal
ler
Cal
lee
Save
d re
sour
ces
Par
PPam
eter
s
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l vLo
calv
Loca
lvar
iabl
esar
iabl
esar
iabl
es
ynam
ic) l
ink
Ret
urn
addr
ess
SaSaSaSavvvve
dre
sour
ed r
esou
red
reso
ured
reso
urce
sce
sce
sce
s
Con
text
(sta
tic) l
ink
SB220
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
220
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eLo
cal v
aria
ble
s ar
e al
loca
ted
(by
mo
vin
g th
e st
ack
po
inte
r).
Loca
l var
iab
les
can
be
of a
ny
size
or
stru
ctu
re,
un
less
the
stac
k o
verfl
ow
s.
Th
e co
mp
lete
s a
new
sta
ck fr
ame.
page
220
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FPSPLo
cal v
aria
bles
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FP
Loca
l var
iabl
es
Wh
ile th
is fu
nct
ion
is
exec
uti
ng,
loca
l var
iab
les
can
sti
ll b
e ad
ded
.
Han
dy,
if e
.g. t
he
size
of a
loca
l va
riab
le is
no
t yet
det
erm
ined
w
hen
the
fun
ctio
n s
tart
s.
217
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
217
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eC
on
tro
l is
han
ded
ove
r to
the
calle
e.
Th
e In
stru
ctio
n P
oin
ter
(IP)
, so
met
imes
als
o c
alle
d
Pro
gram
Co
un
ter
(PC
) is
chan
ged
to a
new
ad
dre
ss.
Op
erat
ion
s fr
om
her
e ar
e in
the
con
tro
l of t
he
calle
e.
page
217
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
230
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
230
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
e –
Hea
p
By
usi
ng
an o
ut,
by-
refe
ren
ce p
aram
eter
, th
e lin
k to
the
new
ly a
lloca
ted
m
emo
ry a
rea
is k
ept.
… a
nd
a lo
cal v
aria
ble
in th
e ca
llin
g fu
nct
ion
can
kee
p th
is li
nk.
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
FP
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Heap
memory
Ho
w to
kee
p a
ny
mem
ory
al
loca
tio
n a
fter
fun
ctio
n r
etu
rn?
227
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
227
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
e –
Cal
lee
Prologue:
…
; Save all registers which are needed
…
; inside this function to the stack
…
; Establish a new frame pointer
…
; while potentially saving the previous fp
…
; Allocate/identify space for local variables
…
; Potentially initialize local variables
Op
erat
ion
s, w
hic
h w
ill u
se
loca
l an
d c
on
text
var
iab
les
and
par
amet
ers
(via
the
FP(s
))
Epilogue:
…
; Potentially restore the prior frame pointer
…
; Restore the stack to its state at entry
Ret
urn
fro
m fu
nct
ion
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
(Glo
bal)
vari
able
s
Para
met
ers
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
FPSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Save
d re
sour
ces
Cal
ler
Cal
lee
Save
d re
sour
ces
Par
PPam
eter
s
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l vLo
calv
Loca
lvar
iabl
esar
iabl
esar
iabl
es
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
SaSaSaSavvvve
dre
sour
ed r
esou
red
reso
ured
reso
urce
sce
sce
sce
s
Con
text
(sta
tic) l
ink
SB224
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
224
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
eTh
e n
ext f
un
ctio
n c
all w
ill p
rod
uce
the
nex
t sta
ck fr
ame.
No
te w
hic
h v
aria
ble
s an
d p
aram
eter
s ar
e vi
sib
le.
page
224
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FPSPLo
cal v
aria
bles
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
(Glo
bal)
vari
able
s
Para
met
ers
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
FPSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Save
d re
sour
ces
Cal
ler
Cal
lee
Save
d re
sour
ces
Par
PPam
eter
s
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l vLo
calv
Loca
lvar
iabl
esar
iabl
esar
iabl
es
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
SaSaSaSavvvve
dre
sour
ed r
esou
red
reso
ured
reso
urce
sce
sce
sce
s
Con
text
(sta
tic) l
ink
SB
Acc
essi
ng
the
con
text
like
th
at c
an b
e in
effi
cien
t! C
om
pile
rs m
ay c
ho
se o
ther
m
ech
anis
m (e
.g. d
ispl
ays,
w
hic
h m
ake
all c
on
text
le
vels
acc
essi
ble
at o
nce
).
231
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
231
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
e –
Hea
p
By
usi
ng
an o
ut,
by-
refe
ren
ce p
aram
eter
, th
e lin
k to
the
new
ly a
lloca
ted
m
emo
ry a
rea
is k
ept.
… a
nd
a lo
cal v
aria
ble
in th
e ca
llin
g fu
nct
ion
can
kee
p th
is li
nk.
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
(Glo
bal)
vari
able
sSBSP
Para
met
ers
Con
text
(sta
tic) l
ink
Ret
urn
addr
ess
Save
d re
sour
ces
FP
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Ret
urn
addr
ess
SaSaSavvve
dre
sour
ed r
esou
red
reso
urce
sce
sce
s
Heap
memory
Ho
w to
kee
p a
ny
mem
ory
al
loca
tio
n a
fter
fun
ctio
n r
etu
rn?
pag
page
231
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
p7
Wh
en to
dea
lloca
te th
ou
gh?
• G
arb
age
colle
ctio
n (J
ava)
?
• Sm
art p
oin
ters
(C+
+)?
• R
efer
ence
ow
ner
ship
s (R
ust
)?
• Sc
op
ed p
oin
ters
/ st
ora
ge p
oo
ls (A
da)
?
228
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
228
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
e –
Hea
p
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
s
Para
met
ers
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
FPSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Save
d re
sour
ces
Cal
ler
Cal
lee
Save
d re
sour
ces
Par
PPam
eter
s
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l vLo
calv
Loca
lvar
iabl
esar
iabl
esar
iabl
es
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
SaSaSaSavvvve
dre
sour
ed r
esou
red
reso
ured
reso
urce
sce
sce
sce
s
Con
text
(sta
tic) l
ink
SB
Ho
w to
kee
p a
ny
mem
ory
al
loca
tio
n a
fter
fun
ctio
n r
etu
rn?
225
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
225
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
e
page
225
of 4
87(c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
7f
hf
h
(Glo
bal)
vari
able
sSB
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Cal
ler
Cal
lee
Save
d re
sour
ces
FPSPLo
cal v
aria
bles
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
s
Para
met
ers
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
FPSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Save
d re
sour
ces
Cal
ler
Cal
lee
Save
d re
sour
ces
Par
PPam
eter
s
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l vLo
calv
Loca
lvar
iabl
esar
iabl
esar
iabl
es
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
SaSaSaSavvvve
dre
sour
ed r
esou
red
reso
ured
reso
urce
sce
sce
sce
s
Con
text
(sta
tic) l
ink
SB
Ho
w fa
st /
com
ple
x is
the
allo
cati
on a
nd
dea
lloca
tion
of l
oca
l var
iab
les
and
par
amet
ers
on
the
stac
k?
232
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
232
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Func
tio
ns•
Fram
ewor
k
• R
etu
rn a
dd
ress
• R
elat
ive
add
ress
ing
• Pa
ram
eter
pas
sing
mod
es a
nd m
echa
nism
s
• C
op
y ve
rsu
s re
fere
nce
• In
form
atio
n fl
ow
dir
ecti
on
s
• La
te e
valu
atio
n
• St
ackf
ram
es
• St
atic
an
d d
ynam
ic li
nks
• Pa
ram
eter
s
• Lo
cal v
aria
ble
s
Sum
mar
y
229
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
229
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
e –
Hea
p
By
usi
ng
an o
ut,
by-
refe
ren
ce p
aram
eter
, th
e lin
k to
the
new
ly a
lloca
ted
m
emo
ry a
rea
is k
ept.
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
s
Para
met
ers
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
FPSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Save
d re
sour
ces
Save
d re
sour
ces
Par
PPam
eter
s
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l vLo
calv
Loca
lvar
iabl
esar
iabl
esar
iabl
es
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
SaSaSaSavvvve
dre
sour
ed r
esou
red
reso
ured
reso
urce
sce
sce
sce
s
Con
text
(sta
tic) l
ink
SB
Heap
memory
Ho
w to
kee
p a
ny
mem
ory
al
loca
tio
n a
fter
fun
ctio
n r
etu
rn?
226
Fun
ctio
ns
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
226
of 4
87 (c
hapt
er 3
: “Fu
nctio
ns”
up to
pag
e 23
2)
Gen
eric
Sta
ck-F
ram
e –
Cal
ler
Pre_Call:
…
; Allocate/identify space for the parameters
…
; Copy the in and in-out
…
; parameters to this space
…
; Potentially provide links
…
; Provide a return address (“Post_Call”)
…
; (usually implicit with the call itself)
Cal
l th
e fu
nct
ion
Post_Call:
…
; Copy the out and in-out parameters
…
; to local variables or registers
…
; Potentially restore the frame pointer
…
; Restore the stack to its previous state
…
; (if the stack has been used)
©20
21U
we
RZ
imm
erTh
eA
ustr
alia
nN
atio
nalU
nive
rsityy
©20
21
(Glo
bal)
vari
able
s
Para
met
ers
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
FPSP
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Para
met
ers
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l var
iabl
es
Save
d re
sour
ces
Cal
ler
Cal
lee
Save
d re
sour
ces
Par
PPam
eter
s
Con
text
(sta
tic) l
ink
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
Loca
l vLo
calv
Loca
lvar
iabl
esar
iabl
esar
iabl
es
Prio
r fr
ame
(dyn
amic
) lin
kR
etur
n ad
dres
s
SaSaSaSavvvve
dre
sour
ed r
esou
red
reso
ured
reso
urce
sce
sce
sce
s
Con
text
(sta
tic) l
ink
SB
