Revised report on the algorithmic language Algol-68

h)op - =(L real a) L real : L 0-a;

i)op + =(L real a, b) L real : a - - b;

j)op + =(L real a) L real : a;

k)op abs =(L real a) L real :(a < L 0 j -a j a);

l)op h , i =(L real a, b) L real : C the value of 'a' times f2.1.3.1.eg that of 'b' C;

m)op / = (L real a, b) L real : C the value of 'a' divided by f2.1.3.1.eg that of 'b' C;

n)op leng = (L real a) long L real : C the long L real value lengthened from f2.1.3.1.eg the value of 'a' C;

o)op shorten = (long L real a) L real : C if abs a S leng ` max real, then a L real value 'v' such that, for any L real value 'w', abs (leng v - a) abs (leng w - a) C;

p) op round = (L real a) L int : C a L integral value, if one exists, which is widenable to f2.1.3.1.eg a L real value di ering by not more than one-half from the value of 'a' C;

q)op sign =(L real a) int:(a>L 0 j 1 j: a < L 0 j -1 j 0);

r)op hentier, bi =(L real a) L int:

begin L int j := L 0;

while j < a do j := j + L1 od; while j > a do j := j - L1 od; j

end;

s) op h?, + , + , ii =(L real a, b) L compl :(a, b);

10.2.3.5. Operations on arithmetic operands

a)op P = (L real a, L int b) L real :a P L real (b);

b)op P = (L int a, L real b) L real : L real (a) P b;

c)op R = (L real a, L int b) bool: a R L real (b);

d)op R = (L int a, L real b) bool: L real (a) R b;

e)op h?, + , + , ii = (L real a, L int b) L compl :(a, b);

f)op h?, + , + , ii = (L int a, L real b) L compl : (a, b);

g)op h", , upi = (L real a, int b) L real : (L real p := L 1; to abs b do p

:= p a od; (b 0 j p j L1 / p));

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10.2.3.6. Operations on character operands

a)op R (char a, b) bool: abs a R abs b; f10.2.1.ng

b)op + =(char a, b) string: (a, b);

10.2.3.7.Operations on complex operands

a)op re = (L compl a) L real : re of a;

b)op im = (L compl a) L real : im of a;

c)op abs = (L compl a) L real :` sqrt(re a"2 + im a"2);

d)op arg = (L compl a) L real :

if L real re = re a, im = im a; re /= L 0 _ im /= L 0

then if abs re > abs im

then ` arctan(im / re) + ` pi/ L 2

( im < L 0 j sign re - 1 j 1 - sign re)

else - L arctan (re / im) + ` pi / L 2 sign im

;

e)op conj = (L compl a) L compl : re a i - im a;

f)op h=, eqi = (L compl a, b) bool: re a = re b ^ im a = im b;

g)op h/=, /=, nei = (L compl a, b) bool: : (a = b);

h)op - = (L compl a, b) L compl : (re a - re b) i (im a - im b);

i)op - = (L compl a) L compl : -re a i -im a;

j)op + = (L compl a, b) L compl: (re a + re b) i (im a + im b);

k)op + = (L compl a) L compl: a;

l)op h , i = (L compl a, b) L compl : (re a re b - im a im b) i (re a

im b + im a re b);

m)op / = (L compl a, b) L compl:

( L real d = re(b conj b); L compl n = a conj b; (re n/d) i (im n/d));

n)op leng = (L compl a) long L compl : leng re a i leng im a;

o)op shorten = (long L compl a) L compl : shorten re a i shorten im a;

p)op P = (L compl a, L int b) L compl : a P L compl (b);

q)op P = (L compl a, L real b) L compl : a P L compl (b);

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r)op P = (L int a, L compl b) L compl : L compl (a) P b;

s)op P = (L real a, L compl b) L compl : L compl (a) P b;

t)op h", , upi = (L compl a, int b) L compl : (L compl p := L 1; to abs b do p := p a od; (b 0 j p j L 1/p));

u)op E = (L compl a, L int b) bool: a E L compl (b);

v)op E = (L compl a, L real b) bool: a E L compl (b);

w)op E = (L int a, L compl b) bool: b E a;

x)op E = (L real a, L compl b) bool: b E a;

10.2.3.8.Bits and associated operations

a)op h=, eqi =(L bits a, b) bool:

begin bool c;

for i to ` bits width

while c := (` F) [i ]=(` F) [i ] do skip od;

c end;

b)op h/=, /=, nei =(L bits a, b) bool: (a=b);

c)op h_, ori =(L bits a, b) L bits :

begin L bits c;

for i to ` bits width

do (` F) [i ] = (` F) [i ] or (` F) [i ] od; c

end;

d)op h^, andi = (L bits a, b) L bits : begin L bits c;

for i to ` bits width

do (` F) [i ]:= (` F) [i ] ^ (` F)[i ] od; c

end;

e)op h , <=, lei =(L bits a, b)bool:(a or b) = b;

f)op h , >=, gei =(L bits a, b)bool: b a;

g)op h" , up, shli=(L bits a, int b)L bits :

if abs b ` bits width then L bits c := a;

to abs b

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c end;

n)op leng = (L bits a) long L bits : long ` bits pack (a);

o)op shorten = (long L bits a) L bits : ` bits pack ([ ] bool (a) [long ` bits width - ` bits width + 1: ]);

10.2.3.9.Bytes and associated operations

a)op R = (L bytes a, b) bool: string (a) R string (b);

b)op helem, []i =(int a, L bytes b)char:(` F)[a];

c)proc ` bytes pack = (string a) L bytes:

if int n= upb a [@1]; n ` bytes width

then L bytes c;

for i to ` bytes width

do (` F)[i ]:= (i n j a[@1] [i ] j nullcharacter) od; c

;

d)op leng = (L bytes a) long L bytes: long ` bytes pack (a);

e)op shorten = (long L bytes a) L bytes: ` bytes pack (string (a) [ : ` bytes width ]);

10.2.3.10.Strings and associated operations

a)op h<, lti =(string a, b)bool:

begin int m = upb a[@1], n = upb b[@1]; int c := 0; for i to (m < n j m j n)

while (c := abs a [@1] [i ] - abs b[@1] [i ])=0 do skip od;

( c = 0 j m < n ^ n > 0 or c < 0) end;

b)op h , <=, lei =(string a, b)bool: :(b < a);

c)op h=, eqi =(string a, b)bool: a b ^ b a;

d)op h/=, /=, nei =(string a, b)bool: :(a = b);

e)op h , >=, gei =(string a, b)bool: b a;

f)op h>, gti =(string a, b) bool: b<a;

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g)op R = (string a, char b) bool: a R string (b);

h)op R = (char a, string b) bool: string (a) R b;

i)op + = (string a, b) string:

( int m=(int la = upb a[@1]; la< 0 j 0 j la), n=(int lb = upb b[@1]; lb<0 j 0 j lb);

[ 1: m+n]char c;

c[1 : m] := a[@1]; c[m + 1 : m + n] := b[@1]; c);

j)op + = (string a, char b) string: a + string (b);

k)op + = (char a, string b) string: string (a) + b;

l)op h , i =(string a, int b) string: (string c; to b do c := c + a od; c);

m)op h , i =(int a, string b) string: b a;

n)op h , i = (char a, int b) string: string (a) b;

o)op h , i =(int a, char b) string: b a;

fthe operations de ned in a, g and h imply that if abs }a} < abs }b}, then }}< }a}; }a}< }b}; }aa}< }ab}; }aa}< }ba}; }ab}< }b} and }ab}< }ba}.g

10.2.3.11.Operations combined with assignations

a)op hminusab, -:=i =(ref L int a, L int b)ref L int : a := a-b;

b)op hminusab, -:=i =(ref L real a, L real b)ref L real : a := a-b;

c)op hminusab, -:=i = (ref L compl a, L compl b) ref L compl : a := a -b;

d)op hplusab, +:=i =(ref L int a, L int b)ref L int :a := a + b;

e)op hplusab, +:=i =(ref L real a, L real b)ref L real : a := a + b;

f)op hplusab, +:=i =(ref L compl a, L compl b)ref L compl : a := a + b;

g)op htimesab, :=, :=i = (ref L int a, L int b)ref L int :a := a b;

h)op htimesab, :=, :=i = (ref L real a, L real b) ref L real : a := a b;

i)op htimesab, :=, :=i = (ref L compl a, L compl b) ref L compl : a := a

b;

j)op hoverab, %:= , %:=i =(ref L int a, L int b)ref L int :a := a % b;

k)op hmodab, + :=, :=, % :=i = (ref L int a, L int b)ref L int : a := a

% b;

l)op hdivab, /:=i =(ref L real a, L real b)ref L real :a := a/b;

m)op hdivab, /:=i =(ref L compl a, L compl b)ref L compl : a := a /b;

n)op Q = (ref L real a, L int b)ref L real : a Q L real (b);

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o)op Q = (ref L compl a, L int b)ref L compl : a Q L compl (b);

p)op Q = (ref L compl a, L real b) ref L compl : a Q L compl (b);

q)op hplusab, +:=i = (ref string a, string b) ref string: a := a + b;

r)op hplusto , +=:i = (string a, ref string b) ref string: b := a + b;

s)op hplusab, +:=i =(ref string a, char b) ref string: a +:= string(b);

t)op hplusto , +=:i = (char a, ref string b) ref string: string (a) +=: b;

u)op htimesab, :=i =(ref string a, int b)ref string: a := a b;

10.2.3.12.Standard mathematical constants and functions

a)L real ` pi = C a L real value close to ; see Math.of Comp.V. 16, 1962, pp.80-99 C;

b)proc ` sqrt=(L real x)L real : C if x > L 0 , a L real value close to the square root of 'x' C;

c)proc ` exp = (L real x) L real : C a L real value, if one exists, close to the exponential function of 'x' C;

d)proc ` ln = (L real x) L real : C a L real value, if one exists, close to the natural logarithm of x C;

e)proc ` cos = (L real x) L real : C a L real value close to the cosine of 'x'

C;

f)proc ` arccos=(L real x)L real : C if -ABS x <= L 1, a L real value close to the inverse cosine of 'x', L 0 ` arccos (x) ` pi C;

g)proc ` sin = (L real x) L real : C a L real value close to the sine of x C;

h)proc ` arcsin=(L real x)L real : C if abs x L 1, a L real value close to the inverse sine of 'x', abs ` arcsin(x) ` pi /L 2 C;

i)proc ` tan = (L real x) L real : C a L real value, if one exists, close to the tangent of 'x' C;

j)proc ` arctan=(L real x)L real : C a L real value close to the inverse tangent of 'x', abs ` arctan(x) ` pi/L 2 C;

k)proc ` next random = (ref L int a) L real : ( a := C the next pseudorandom L integral value after 'a' from a uniformly distributed sequence on the interval [L 0,` maxint] C;

C the real value corresponding to 'a' according to some mapping of integral values [L 0, ` max int] into real values [L 0, L 1) fi.e., such that 0 x < 1g such that the sequence of real values so produced preserves the properties of pseudo-randomness and uniform distribution of the sequence of integral values C);

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10.2.4. Synchronization operations

The elaboration of a parallel-clause P f3.3.1.cg in an environ E is termed a \parallel action". The elaboration of a constituent unit of P in E is termed a \process" of that parallel action.

Any elaboration A fin some environg of either of the ENCLOSED-clauses delineated by the pragmats f9.2.1.bg pr start of incompatible part pr and prnish of incompatible part pr in the forms 10.2.4.d and 10.2.4.e is incompatible with f2.1.4.2.eg any elaboration B of either of those ENCLOSED-clauses if A and B are descendent actions f2.1.4.2.bg of di erent processes of some same parallel action.

a)mode sema = struct(ref int F);

b)op level =(int a)sema: (sema s; F of s := heap int := a; s);

c)op level =(sema a)int: F of a;

d)op down = (sema edsger)void:

begin ref int dijkstra = F of edsger; while

pr start of incompatible part pr

if dijkstra 1 then dijkstra -:= 1; false else

C let P be the process such that the elaboration of this pseudo-comment f10.1.3.Step 7g is a descendent action of P, but not of any other process descended from P; the process P is halted f2.1.4.3.fg C;

true

pr nish of incompatible part pr do skip od

end;

e)op up = (sema edsger)void:

pr start of incompatible part pr

if ref int dijkstra = F of edsger; (dijkstra +:= 1) 1 then

C all processes are resumed f2.1.4.3.gg which are halted because the integer referred to by the name yielded by 'dijkstra' was smaller than one C

pr nish of incompatible part pr;

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fFor the use of down and up, see E.W. Dijkstra, Cooperating Sequential Processes, contained in Programming Languages, Genuys, F. (ed.), London etc., Academic Press, 1968; see also 11.12.g

10.3. Transput declarations

f \So it does!" said Pooh, \It goes in!"

\So it does!" said Piglet, \And it comes out!" \Doesn't it?" said Eeyore, \It goes in and out like anything,"

Winnie-the-Pooh, A.A. Milne.g

fThree ways of \transput" (i.e., input and output) are provided by the standard-prelude, viz., formatless transput (10.3.3), formatted transput (10.3.5) and binary transput (10.3.6).g

10.3.1. Books, channels and les

f\Books", \channels" and \ les" model the transput devices of the physical machine used in the implementation.g

10.3.1.1. Books and back les

f aa) All information within the system is to be found in a number of \books". A book (a) is a structured value including a eld text of the mode speci ed by extext (b) which refers to information in the form of characters. The text has a variable number of pages, each of which may have a variable number of lines, each of which may have a variable number of characters. Positions within the text are indicated by a page number, a line number and a character number. The book includes a eld lpos which indicates the \logical end" of the book, i.e., the position up to which it has been lled with information, a string idf, which identi es the book and which may possibly include other information, e.g., ownership, and elds putting and users which permit the book to be opened (10.3.1.4.d) on more than onele simultaneously only if putting is not possible on any of them.

bb) The books in the system are accessed via a chain of back les. The chain of books available for opening (10.3.1.4.dd) is referenced by chainb le. A given book may be referenced by more than one back le on this chain, thus allowing simultaneous access to a single book by more than one process (10.2.4). However such access can only be for reading a book, since only one process may access a book such that it may be written to faag. The chain of books which have been locked (10.3.1.4.o) is referenced by lockedb le.

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cc)Simultaneous access by more than one process to the chain of back les is prevented by use of the semaphore b leprotect, which provides mutual exclusion between such processes.

dd)Books may be created (e.g., by input) or destroyed (e.g., after output) by tasks (e.g., the operating system) in the system-task-list (10.4.2), such books being then added to or removed from the chain of back les.g

a)mode @book=

struct( extext text,

pos lpos /c logical end of book /c, string idf /c identi cation /c,

bool putting /c true if the book may be written to /c, int users /c the number of times the book is opened /c);

b)mode @text = ref [ ] [ ] [ ] char,

mode @ extext = ref ex [ ] ex [ ] ex [ ] char;

c)mode @pos = struct(int p, l, c);

d)prio @beyond=5,

op beyond = (pos a, b)bool:

if p of a < p of b then false elif p of a > p of b then true elif l of a < l of b then false elif l of a > l of b then true else c of a > c of b

;

e)mode @b le = struct(ref book book, ref b le next);

f)ref b le @chainb le := nil;

g)ref b le @lockedb le := nil;

h)sema @b leprotect = (sema s; F of s := CPRIMC int := 1; s);

10.3.1.2. Channnels

f aa) A \channel" corresponds to one or more physical devices (e.g., a card reader, a card punch or a line printer, or even to a set up in nuclear physics the resuls of which are collected by the computer), or to a lestore maintained by the operating system. A channel is a structured value whoseelds are routines returning truth values which determine the available methods of access to a book linked via that channel, Since the methods of access to a book may well depend on the book as well as on the channel (e.g., a certain book may have been trapped so that it may be read, but not written to), most of these properties depend on both the channel and the

150