UNIVERSITY OF MANCHESTER

ATLAS AUTOCODEREFERENCE MANUAL

A. BROOKERJ.S. ROHL

1st MARCH 1965

Scanned by The Centre for Computing Historywww.ComputingHistory.org.uk

PREFACE

Tills manual is a reference manual which describes the Atlas

Autocode Compiler currently available (I/3/65) at Manchester

University. It is not a teaching manual though we have tried to

make it fairly readable. Further compilers may in the future

become available both on Atlas and other machines and it is

expected that they will be described with reference to this manual,

Vi'e v.ould like to thank Mr, G. Ri

OJKTF.NTS

1 • IKTm.lDUCTI(jN ,

Example of an Atlas Avitocode Program 1.1

Blocks and Ron Lines

phrase Structure Notation

THE BASIC LANGUAGE

Symbols of the Language ^2. 1

2.2

2.2

2.3

Names

Constants

Delimiters

Typos

Declaration of Variables 2.3

ruuctional D'-poncJonce 2.5

Standard Functions ^'5

Aritliniotic Expressions ' 2.5

Integer Txpre^^yions

Arith)ne tic Ass iemnents

Simple Labels

Vector Labels

Conditional Labels

Co nd i t i o n a1 Ope r a t or s

Cycle Instructions2 11

Miscellaneous Notes

2. 6

2.7

2.8

2.8

2.9

2.9

2.10

3. SitjRAGE AT.LGCATIUH AND Biy)CK STRUCi'URE OF PROGRAMSq 1

The Stack "

Storage Allocation Declarations 3'^Block Structure of Programs

4. noUTIKES

Basic Concepts

Formal Parameters and Actual Parameters 4*3Function Routines 4o

Scope of names

Permanent Routines

3.2

4.1

4.6

4.6

Fmictions find Routines as Parameters 4-7Recursive Use of Routines 4-^own Variables 4*9

5. INPUT AND OUTPUT OF DATA

selection of Data Channels 5*^

Basic Input Routines 5*^

Basic output Routines 5*4

Captions 5'^

Binary Input and output 5*^

6. M-HNITOR PRINTING AND FAULT DlAGNOSIS

Compiler Time Moniioiing 6.1

Run Time Monitoi ing

Fault Trapping

Fault Diagnosis 6*5

Queiy Printing 6.0

Routine Tracing 6.7

Jump Tracing

Array Bound Check 6.7

Other Checking Facilities ^.7

7. PRESENTATION OF gjMPLETE PROGRAMS

Program and Data 011 Same Tape • 7*^

Program and Data Tapes Separate 7*3

Program on Several Tapes 7*4

S. COMPLEX ARITHMHTIC

Declarations 8.1

Standard Functions 8.1

Arithmetic Expressions 8.2

Arithmetic Instructions 8.2

Conditions ^*4

Routines and Functions 8.4

Input and Output of Complex Numbers 8.5

9. STORE MAPPING

The Addi^ess Recovery Function 9*^

Array Functions 9*^

The Renaming of Variables within a Block 9« 3

Store Mapping Routines 9*4

1^• THE USE OF MACHINK INST]

1 INTRODUCTIQN

All ATJJ\S AU'A;a:)DE PROGRAM Consists of a series of STATEMENTS

v.hich describe in algebraic notation the calculation to fee executed.

The statements are of two kinds, declpjrative statements giving the

nature of the quantities involved, and imperative statements which

describe the actual oper.ations to be performed on them, and the sequence

in wliich thoy are to V.e carried out, 'ihe statements are not immediately

recofjnisal: le hy the ccmpvrler .••.ad must first he converted into an

oquivalont :iOqucnce of l a.sic MACHINE INSTRUCTIONS. This is done by

a special translation pro^rairt called a COMPILER which is held

per!!v;.)icntly j.vailalle in the in^chinG. Not until tJe program has l-een

'cc^piltd' t '.n it !.e executed,

Tfte folJov.'irig example i,x\fes a ij;eneral idea of the principles

i iwolvcd in v-ritiiig a proj^ram, Vt'e v/ish to fit a straight line

y •= rx + h to sets of data of the form Xl. ,Y1; X?,,Y2; ; Xn, Yn

wlilch are to le pujiched and presented on a data tt-'pe in this order.

E;iC}i such set is to be terininated by the number 999999 and the final

set Ky two such numbers. For each set the quantities

^ - "f^XiYi - {'XifYi

nfxi^ - (i-Xi)^

1.1

^ = gYi -- afXl

n

c = iYi^ - 2(aiXiYi + bf:Yi) + a^ ixi^ + 2ab^Xi + nls^

are calculated, the last being the sum of the squares of the deviations

HYi - aXi - b)2.

The following is the formal proi^-rs-ra for this calculation. The

statements are to be interpreted in the v/ritten order unless a statement

is encountered which transfers control to another specifically labelled

stateinent. In general each statement is written as a new line, otherwise

it must be separated from the previous statement by a semi-colon.

1.2

begin

real a, b, c, Sx, Sy, Sxx, Sxy, Syy, nextx, nrxty

intc[;er n

read (nextx)

Z: Sx = o; Sy = o; sxx = (3; Sxy = o; Syy - O

n = o

1: repd (nexty) ; n = n -

2.1

the basic L.A.NGUAGli]

SYMBOLS OF THE LANGUAGE

A program is presented to the computer as a length of perforated

pspcr tape, prepp.red on a Flexowrlter keyboard machine, the keys of which

are engraved with the following symbols:-.

A ^ C})K i"G HIJ K LMWn R STU VvV XYZ

: b c d e rgb i j k 1n;nopq r s t u vv/x.y z.

a 0 rf

o'231567'"59

-=>< 1 M )[] ?

A back-spr.cii)g facility allows underlining and also the forniation of

Compound characters. For exarriple : -

c^c^ ^ > < ; ^

The 1 ;3t of these consists of an asterisk superimposed on a vertical bar .

It is usually referred to as a vertical arrow (and would be written

?s such in a manuscript) *nd is used to denote exponentiation,

thus af(n-l) means 'a raised to the power (n-1)'. Such a notation is

necessary because we have no iiieans of effecting superscripts and subscripts

with a Flexowriter; the format is essentially one dimensional. There is

one exception, the superscript ^ for which there is a special symbol:

it is equivalent to [2,

Since the handbook itself is prepared on a Flexowriter the same

conventions for exponents will also be used in the text,

NOTE All SPACES and UNDPJRLINED SPACES in a program are ignored when the

program is read into the machine. Thus they may be used freely to assist

legibility in the written form of the program,

NAMES

These are used to identify the various operands, functions and

routines which appear in the program, A name consists of one or

more Roman letters, possibly followed by one or more decimal digits,

and poh;.;ibly terminated by one or more primes(*). For example:-

X I Alpha alo TEMPI y'* b3'

UndGx"lined names and mixed nj'.uios su«.'h rs IUWST -'re HuT J'llov/ed, C

Tliore are cert3.in nr.mes, e.g. log, sin, exp, print, ror.d, etc.

which have a stajidard meaning (the PERMANENT routines) but s.11 other

n?inos must fee declared before any reference is m€?.de to them (see fcelow),

m future a general name will be denoted by [haMIO.

QJNSTAKTS

Nuir.ericy.l (positive) constants are written in a straight for\v;^rd

notation. For exi^mple:-

2.538 1 .25 J7.28a--1 iay

The last tv.o ex amp lea mean I.728 and 10000000.

The numerical pai t can be written in any number of ways. For example:-

15 015 15. I5.OVOO

are all equivalent. The exponent, where prei-ont, consists of a

follov.ed by an optional sign and decimal dibits.

The symbol ^ is equivalent to the tv;o symbols .5. Thus 2.5

mi?.y be punched as 2^. (

There is a further specialised type of constant consisting

of a symbol (either basic or composite) enclosed in quotes. Its value

is that of the intt'.rnal equivalent of the symbol, a list of which is

given in Appendix 5. Thus

z 33

= 2063

Though this form of constant may be used whenever a constant is relevant

it Is most often used when reading symbols off a data tape (see Section 5),

DELIMITERS

These are a preassigned set of symbols and underlined words. For example:-

+ -*/(» )>>->;sr

cycle repeat integer real then cayjtion comment

Note that -> consists of two symbols, - followed by >

Unlike names whose meaning ca.n be defined by the user, delimiters

have fixed absolute meanings in the language, I

2.3

TYPES

Calculations are performed on tv/o principal types of opersnd,

rep.l fi.Dd integer (later on we sha.ll introduce coiuplex). I^oth are

represented Tsy floating point nur.-.i jrs (in the form where a

is held to a precision of 40 binary digits and fe is an S-l^it integer);

I lit those of integer type are kept in P.n unstnn.d»rdised form

(so that the losist significant 24 bits can be used directly for

B-modification; the precise method of storr.£;e is described in the

section on machine instructions).

The lo

OUO dlmonsion^l arrays of elements may be docar.rcd by statcn.aiits such as(•

array a,b(0:99), cClOllg)

which reserves space for three arrays of real variables a(i), U>(i), c

2.5

FUNCTIUKAL DEPENDENCE

FuiicLlonal dependfince is indicated by writing the n-me of the

function follov/ed by the list of arguii'euts in parentheses (in a sirsilp.r

fashion to array elcineuts). For example:-

sir.(27rx/a) arctan(x,y) TE!.;P(i) a(Jo,lo)

E&.ch ; rgurjicnt can be an arithmetical c-.rprGssion (stie below).

Witliin a block all n?.Hies rn-jyt bo tiistiiiCt, and it is not

possible to liave a function v/ith Lhe srnse nr'Ae as a scalp.r. Thus

a and i-ii) or f and f(x) would JJCJT be nllcwed to rv.ppear in the

same block,

S TAN DARD FUH CF I(.)NS

Certain standard functions s-.x-e p-v'p.il:?ble and may be used

directly in arithivictic expressions (see next section) without formal

declaration:

sin(x) cos(x) tan(x) 1og(x) exp(x) sqrt(x)

arcsin(x) {-n/Z ^ result < 7r/2)

iirccos(x) (O < result < vr)

arctan(x,y) (- o.rctan (y/x), -?r < result < tt)

radius(x,y) (= sqrt (x^fy^) )

niod(x) (- 1x1)

fracpt(x) (= fractional pajrt of x)

intpt(x) (= integral part of x)

int(x) (:= nearest integer to x. i.e. it-' ot(x+.5) )

parity(n) (= (-l){n)

The last three functions are of type integer (see later), the rest of type real.

The arguraents of all these functions infs.y be general expressions, except

that the argument of the last must be of type integer,

A complete list of standai-d functions is given in Appendix 2,

AR ITID.'iET IC EXPR ESS IONS

A general arithmetical expression is denoted by Cexpr] and consists

of an alternating sequence of operands and operr-.tors possibly prece>ied by a

sign symbol, thus *

[ + • ] [operand] Toperator] Cqperand] [operator] .... [.OPERAKD]

An [operand] is a [VARIABLE], [ CONSTAl\"r], ([EXPR]), KexI'R]!., or [FUNCTION],

and an [OPERATOR] is one of + - / ^ (the asterisk denoting multiplication).

*=H3r, more strictly, (See Appendix 1)

[eXPR] = [+'][EXPR']

[EXPR'] = [operand][op][EXPR'],[operand]

[operand] = [NA?rIE][APP], [const], ([EXPR]), I [EXPR] I

[ + ♦] = +,-,NIL

Ml explicit multiplication sign is not required when ambiguity could not

nri.se from its omission. For example:-

2.5alb means 2.5''al=*b

h'i;TE: When the compiler looks for a name, it finds the longest possible

ns.me. Thus ab is i.iilten as a name rather than a'̂ 'b even if only a and b and not

.-^.b Y>ere declared. In this case a fault (NAME ab NoT SET) would be indici-'.ted.

E>:;v!:.p.les of expressions are:-

A(i~3,j) + A(i+3,j) + A(1,J~1) + A(i,j +1) - 4A(i,j)

Z + logd + cos(27r(x/a + y/b + z/c)))

LENGTH + BREADTH + HKIGHT

1 + sqrt(x(i)^ + y(i)^ + '/-(i)^)

a * b/c + d/e

(x + y + xO/Ca + bH-c)

2.5x1b * (c + d)e

e = Ix-yl + .00001

(l4.x)K(n-3) * (1-^)^3

NOTES

1, MultipliC5».tion and division take proccdence over addition ?.nd

subtraction and division tjikes precedence over multiplication, fhus

the fifth example iner'.ns a ♦ (b/c) * (d/e),

2, i'^'^XPR]! is interpreted as the positive magnitude of the

LkXI.:]. Thus it is equivalent to niod([eXPR] ),

3, An expoaent is denoted by | [oPERAKD] and exponentiation tj'kcsprecedence over the other operations. Thus the last exaiople me«ns

((1 + x) to the (n - 3))*((1 - x) to the 3). In the formation of

a I n, n must be an Integer or integer CfjxPR] (see next section);

then if

(i) n > 0, result = a*a»a (n tiwes)

(ii) n = o, result = 1 '

(iii) n < O, result = l/(a+a^a ^a)

4, To form a ^ b, where b is real we must write it in the formexp(b*log(a)),where a must be positive,

INTEGER EXPRESSinNS

An [EXPR] is an integer [EXPR] if all the [OPERAND]-s ai-e

scalars, array elements etc. declared to be of type integer, or are

integer constants or integer functions (e.g. int, intpt, or parity).

2.7

Thus if we assuiue th^t x is a. CVAHIAnJ.E] ^nd 1, n, j, k(l),k(2)

integer LvaRIAKLE]'s the follov/ing ^-ro intcf;fcr [exPR]'s,

»*(n-l)/2

i + J + k(2) + int(x)

j ^ k

intpt(n (n-l)/3)

The definition given P.bovG docs not ^n.?a"^ntee tlK'.t an inte£;er Cf^XPR]

will ?lw;\ys give j-vn integral result, e.g-. , I0/3 jK-O -Te riot

inlojii'al, Thore is no gu^irp.ntee either thiit expressions like

n-(n-l )/2(v;hich is integral) will always yield the exact finswer (in this

pp.rticul?..r case it does), V.'hen the result of such an operation is in doubt

it is preXc-rr-ble to use 'int' e.g., int(ri +(n-.l)/2) to give r.n ex?.ct integer

result.

Except in certain speciiil eases integer [exPRI's are ev-luated by floating

point P.rithrnetic in exactly the spjne way s.s general (real) expressions, tut

rre dostnndardised on assigm.ient (explicit or in^plicit) to their integer

uGstination. The definition of an integer [EXPR] is a basis for checking

tl:?-t such assignments ai-e sensible. The special cases rncntioned al*'Ove refer to

the subscript expressions in array elcjr.cnts. Such expressions, which i:hould

8.: :\ys be integer [exPR]*s are usually simple linear forms which are de^lt

v.'lth "ore ;;ppropriately by E-JTiodificp.tion, It is mainly to facilitate

siich operations (and the .-associated operation of counting) that integer's

sre used, Being destandardised quantities they can be transferred directly

to B-registers without using the floating point accumulator.

ARITHMETIC,ASSIGNMENTS

The general arithioetic ivvstmctioa is

CVARIABLE] = CEXPR]

Exsjnples are:-

X(p,q) = lH2Cos(2«'(x+y))

a = (b4c)/(d+e)+F

i = i+1

The action of the general arithmetic assignuient is to place

the computed value of the [exPR3 in the location allocated to the l.h.s,

tVARIABLE]. If the l.h.s. is a [VARIABLE], the r.h.s. CeXPR]

may be of type real or integer, but if the l.h.s. is integer then

the r.h.s. must be an integer [exPR]. For exsjuple, if y had been declared

i-eal and i integer then we could vrite y = i feut not i = y even if we knew •

that y had an integral value.

LABELS, JUMPS AKD OJNDITIJJiAI• ' ''̂ ATORS

Normally instructions are obeyed sequentially, but.frequently it

is required to transfer control to some instruction other than the nextin the sequence, or to obey an instruction only if certain conditions aresatisfied. The following facilities are provided:

SIML^LE LABELS Any instruction can be labelled

;y writing an integer Tn] before it, separated

'.y a colon. Irtore than one label is porinltted.

Unconditional juwp instructions are written as

tK]

VECTOR T^^BKLS

These are used to provide for a

multi-4vay switch. With reference to the

accompanying diagram the instruction

-> A(i) will jump to A(l), A(2) or A(3)

according as i = 1, 2 or 3.

A fault is signalled if the value of i

Corresponds in any way to a label not set.

The general form of the label is [nA^ME] ( Cn] ) J

The range must be ' clared a,t the head of

the routine by a statement of the form

svi_tch 1!nAME]([ +']Cn]:[ +'][n]) wh^^re

the C+'] indicates that the intej^e;. s

may be preceded by a sign if necessary.

For example

^itch SEGMFNT (-4-.+4)

A list of switches can be given. For exainple:-

switch A,B,C(1:3),D(o:2)

The [nAK^eI's must not conflict with those

of other operands in the same block.

->10

lo: —

4:5;

-^4

switch A(1 : 3)

A(l):

A(3):

->A(i)

A(2):

QINDITIUNAL LABELS

Another kind of multi-v;a.y switch is test 4, 5, 6

illustrated by the accompanying diagram,

Kere the conditions at the places indicated

are tested in turn and control passes tg the 4 case x

2. 10

Alternatively, conditional operators may appear AFTER unconditional

instructions, in which case they are written

ijf [OJND] or unless [Q^ND]

for example x - u ^ Ixj < ,0000001

-> 1 unless z > R or z = O

CYCLING INSTRUCriONS

These are pairs of statements which allow a ^roup of

instructions to fee obeyed a fixed numfeer of times. For exp-jviplo;-

eyele i = o, 1, n-1

repeat

In the above example the instructions between cycle ».nd repeat are

traversed n times, with i successively taking the values 0,1,

After the final cycle, control goes to the statement following repeat.

The l.h.s. must fee an intei^er name, but the r.h.s. qu?,ntities m?.y he

£;onoral integer [exPR]'s which axe initially evaluated and stored. Thus

within the imiermost cycle of the example kelow, the values of p,q and r

may be altered without affecting the number of times the cycle is traversed.

Tl^e initial value, increment, and final value must la such that

final value - initial value

increment

must be a positive integer or zero otherwise a fault is indicated.

For example

cycle i = 1,1,p

cycle k = 1,1,r

c(i,k) = 0

repeat

cycle j = 1,1,q

cycle k = 1,1,r

c(i,k) = c(i,k) + a(l,j)*b(j,k)

repeat

repeat

repeat

NOTE Statements such as cycle x = .2,. 1,1 are NOT allowed,a.nd

should fee replaced by an equivalent permissible form. For example:-

cycle 1 - 2,1,lO

X . 11

where i has been declared Integer and x real.

2. 11

MISCELLANEOUS NOTES

"snd of program is the formal end of tlie program aud P-ppes-rs after the

Iff.st written instruction; its action is to terminate the reading of the

program and to start obeying it from the first instruction.

2. The instruction stop can appear anywhere in the program s.nd signifies

the dynamic end of the program; its action is to terminate the c^^ lcu3 a.tion,

3. The delimiter comrrient allows written coniyieuts to he inserted in a

program to assist other users in understi;.nding it. The information

f "ilo'ivlng co)"v-ient (which may inclu le coJnposite characters) up to tJ^e

li-.xt newline or serai-colon is igno •'-d by the cotjputer. The delimiters pg.ge

f'u.d I are synonyms for comisent, th gh the first has an obvious special use

in the pagin^ition of programs,

/j.. It has been noted earlier that all spaces and underlined spaces in a

program are ignored and that Autocode statements are terminated by a semi

colon or a newline. If a line is terminated by the delimiter £ then the

following newline character is ignored by the computer. Thus a single

statement may extend over several lines of the printed page, , It is not

anticipated that this facility will be frequently used, excei>t vl.en

writing conmients and possibly long algebraic expressions,

5. If a program)r4er is prepared to exclude upper case letters from names

and captions, then he can effect a saving both in the size of the tape

and the speed of compilation, by using the special instruction

upper case delimiters

f.i)d then writing all following delimiters in upper c?..se without the

underlining. Thus the example of P2.10 could then hs written: -

CYCLE i = 1,1,p

CYCLE k = 1,1,r

c(i,k) = 0

REPEAT

CYCLE j = 1,1,q

CYCLE k = 1,1,r

c(i,k) = c(i,k) + a(i,J)*b(j,k)

REPEAT

REPEAT

REPEAT-

The delimiter causes the con.piler to replace each upper case letter by

the equivalent underlined lower case letter, so that a mixture of

normal and upper case delimiters can be used. If this is required only for

certain parts of a program then the instruction

normal delimiters

can be used to return the compiler to its normal operation.

3«i

3 STORAGE ALIOCATION AKD TOE PTOCK STtiUCfURE OF I'RjGR.-UtS

TKE STACK

In order to illustrate the priiiciiJlas of £tor?g;e allocation, we

assume the following simplified .>icture of the data store (the stack),

fuller description being givej; in the section on tJie use of macliine instructions,

CELI^ IN 1st AVAILABIJS CELLS

USE I

I t i I III

E^^ch cell or acntion repieseut.-j a 1-it -word In tlie co5Tiyuter store

r-.nd can 1-3 used to hold eitlxer a re^.l or jui integer vp.rli'.ble. At Eiiy

•'.mo duriiig the running of a the stack pointer, St, points to the

xt avfilahle location i.e, it contains the c.ddres3 of the next free word.

In the examples that follow, shaded arer-s represent 3oCf.tions

• •lich hold inforrny.tion essentiiil to the pruii;rrin, such rs ai-ray diraensions

..s)d origins, and are not of impoi'tsince in the context of tl.is section. Each

area may in fact consist of several locations. Cells which pxe allocated

to variables are indicated by the presence of the nar.ie given to the v^-rialfle,

'"'"OHAGE ALLOCATION DECL.ARATICDNS

The declarations which allocate storage space f.re

real integer p.rra.y integer array

and to illustrate the stack mechanism we consider the follcv/ing exi-Jiiple:

begin

x-eal a, b, c; integer i, max

array A(l:2,l:2), x(l;3)

After the above declarations the stack picture would be as k-elow

Stl St2

IM\\\\\yi a I b I c I 1 |maxlA\\\\\\\\MA(l.l)IA(l,2)lA(2,l)lA(2,?,)JMMVL^)l^JaIM3Ll

Stl is the position of St teefore feegin and St2 its position after the

dt;clarations. Any further declaration advances St by an appropriate pjnount,

likewise any activity initiated by the instructions in the body of the block

causes St to be advanced(either explicity or iiaplicity) still further,

Finally when end or end of program is reached, then St reverts to Stl,

Variables declared by real and integer are called FIXED VARIAJiLES,

'acause the amount of storage space required can be determined at conpiler time.

Array declarations, however, may have general integer expressions as the parameters

and hence have dynamic significance. For example one wight have a declaration

;-iich as . .

array A,B(l:m, l:n),x(l:n)

In this case the space allocated will depend on the cortiputed values

of m and n and cannot be determined at compiler time. The stack pointer

St is thus advanced in several stages i'ollowing the initial step which

reserves space for all the fixed variables.

. (

BLOCK STRUCrURE OF PHOGRA-MS

This is illustrated by the following exsjiiple:-

boj^.n

re^ a,b,c

a = 1; h 'Z

c - ?-+b

begin

real i?,h,d

a -- 2; d --- 1

h -- c

c - 4

end

a - :b-(-c

end

The .stack picture associated with the above block is given V.-elow:

Stl St2 St3

I imvw a12 3 456

Before the first begin St is at Stl, and moves to St2 on entering the

outer block. After the second begin St is at St3 and reverts to St2

when end is reached. At the second end, corresponding to the first

begin, St assumes its origin^.l position, Stl,

In the diagrajn, positions 1, 2, 3 cox'respond to the declarations

of the outer block, and 4, 5, 6 to those of the inner block. After the

instruction c =: a+b, the value 3 is left in position 3; while the instructions

of the inner block leave the values 2, 1, 3, 4 in the positions 4, 6, 5, 3

respectively. The last instruction of the outer block leaves the value

7 in position 1,

3.3

Tlius the vjiiiables a, fe of tJie I.lock

4.1

4

BASIC CONCEPTS

A large progrfun Is usually inade up of scvc-r?.l rovitines

• ach of \vhlch represents some characteristic part of the calculation.

Such routines may be called in at several different points in the progra-in,

and their design and use is a fundamental feature of the If.nj/uage,

The inti oductory exai^ple consisted of a in^^in block only (delimited by

begin and end of pro;^rr..)n) although it ri.'i'ko;, reference to the routines 'rerd',

'print*, 'newline*, which : o)

where the coefficients >vre selected from sGtrie vector a,

routine pol^'^Creal nairie y, eg-ray n-me a, real x, intec,er m,n)

integer i

y = R(r.Hn) ; return if n = 0

cycle i = m+n -1,-l,m

y =: x*y+a(i)

repeat

return

end

Given the values of x,iii,n and the addresses of y and the s-rray

elements a(i), it evaluates the polynomial and sets y to this value.

The'statement ei^ is the formal or written end of the

routine while return is the dynamic end, i,e. it is the instruction

which returns control to the main routine. Where the formal end is also a

dynamic end as in the present example the return instruction preceding end

can be omitted; in this case ervd serves for both purposes.

NOTES

1: There can be any number of alternp'ive exit points in a routine - i.e.

return can occur more than once,

2; return is a member of the FORMAT CLASStui] - i.e. it can be made conditional,

as above.

4.2

T)^is routine can be EK'.; EDDED and used in a )r.?in routine as illustrated

below,

V^egin

real U, V, z, x ; integer m

array bCo:!^), 0(0:50)

routine spec poly (realname y, prray name a, real x, integer m,n)

poly(U,b,z,o,m)

roly(V,c,x2,20,l0)

stop

routine poly(realn^xie y, .-Array nr-Uie a, real x, integer in,n)

^r^e^r^ i

y = a(r!H-n); return if n = O

cycle i = ni+n-1, -1,m

y = x^yi:r(i)

repeat

return

end

end of program

The routine is called in by the i-aln routine whenever the

name 'poly' appeai-g. The first reference to *poly* would cause the poly

routine to evaluate

U = b(o) + b(l)z + + b(ra)z^m

and the second would cause it to evaluate

V = c(20) + c(21)x2 + . .. + c(30)xj«20

The parr.ineterM in the routine specification and routine

heading are the FOR>«^AL PARA.METERS and the ps^xsmeters in the call statements

axe the ACTUAL PARAMETERS (see next section).

The body of the r0^1 tine may be considered as a felock

.delimited by routine and end, and the concepts of storage allocation, local

and non—local names

4-3

Any nuHiber of routines may be ovibcdded in a mp.in routine

in the above farJiion and they are referred to s.s SUE'l^UTINES of the main

routine. If the body of R subroutine occurs before any reference to it

in the msin routine, the routine spGCific;ation )iiay be omitted, but by

convention it is usual to place all the subroutine specifications among

the declarations at the head of the main routine and the bodies at the end.

l^RMAL PARAMETERS AND ACTUAL PAR^METER^

The p?^r?)iictei^s of the ro-'tine are the iteins of information which

.specj.ry Ihe of the routine V'/henever it is usvid. The foriT'.al paranicters

are t>:e names by wJiich this infoxrnation is ref. raineter, as shown in the following table:-

Forrnal p?n:ametcr type

intGr(5T name

real '?? me

3. 1 •: f.'''-1"

i oal

integer array name

array name

integer array

array

rcuti)i.3 type i.e.

routine

ieaX fa

integer fn

I Corresponding actual parameter

1 name of an integer vpjriable

1 name of a real variable

an integer CexPR]

(similar to an integer assiguioent)

a li -nera1(i. e, real or integei') CEX.PR]

(siinilar to a real assignment)

name of an int cer array

name of a (real) array

name of an integer array

name of a (real) array

(the difference between these and the

previous pair of parameters is

explained l?elow)

SoiiiotiioQs it is required to pass on the

najne of a routine as a parameter.

In this case the actual pejrameter is the

name of a routine which must correspond in

type and specification with the formal

pi^jraraeter, the specification of which will be

found in the routine body

In the expjT.ple of a routJiie to evaluate a polynomial described e^irlior,

the forip.al parameter y is the iiatr.e of the vn.riable to which the result is fissijined,

and the corre.'jpoiiding actual pra'ansuter must be a najiie, in this case the name of (

a real variable. The formal parant:. "er then is of type real naine^

A reference to y inside the routine is essentially a reference to the non-local

variable ny.med by the actual paraineter. The sariie applies to the .t^rra^n-^ne

parameter a, a reference to a inside the routine being a reference to the

non-local am?.y v.-hoso luuns is Kukstituted for a in the calling statement.

The formal para^^ieter rcr.l x on l^he othcu' hand can be replaced' l:y a

^tiuersl aritJur^etic expre^^slon, -..hich is evaluated and y.ssip'nod to the local

variable x which is specially cn^ated in addition to r.ny local real

v.-riables declared in the routine. The same applies to tJ)e fornial parameters

iitteger ni,n. These are essentially local quantities, and expressions are subiitituted

In place of tJicm ai*e evaluated and the resultant values assij/ned to the local

vr'.riablos m and n, v/hich are lost on exit from tlie routine. Consequently

the routine hhould place the information it produces in variables vrhich are

Cf lied by KA?nC (such as x and a),"

The foi'inal parameters x, m, n are said to be called by VALUE in so far

n.s it is only the values of the corresponding actual parameters which are of

ir; Lcrest, This is the essential difference between the formal parameter types

ai^^a^ 1ad f:rray name (or integer array and integer array name). In the former

case the array naiued by the actual parameter is copied into a specially created

local array, and a reference to the nPiae in the routine is taken as referring to {

this local array. As the copying process can be time-^ons\iuiing and space-consuming,

array's should be called by NAMJE if at all possible, especially if they r.re large.

Another example of a routine is the following

routine matmu It ( arrayname A, B, C iutci^-er p, q, r )

integer i,j,k ; real c

cycle i - 1,l,p

cycle j = 1,1,r

c = 0

cycle k = 1,1,q

c = c+A(i,k)=i=E(k, j)

repeat

C(l,j) = c

repeat

repeat

end

This forms the product of a p x q matrix A and a q x r matrix B, The

result, a p X r matrix, is accumulated in C, The routine assu! js that the first

element of each matrix has the suffix (1,1), A typical call sequejice might be !

mat mult(M, x, y, 20, 30, 1)

where H, x, y had been declared by

array H(1;20,1:20), x,y(l:20,1:1)

4o

FUNCTION ROUTINES

When a routine has a single output value it may he writi n as a

function routine and then used in an arithmetic expression in the same way as

the permanent functions (cos, sin etc.). For example, the polynomial routine

described earlier may be recast as a function routine as follows;-

real fn poly (arrayname a, x-eal x, integer m,n)

integer i ; real y

y = a(mHn) ; if n = 0 then result = y

cycle i =

y = y*x+a(i)

repeat

result = y

end

NOTES

1: In general, the e it from a routine is of the form : result - LexPR]

and this causes the EXi SESSION on the right hand side to be evaluated as

the value of the function,

result = CexFR] acts as the dynamic end of a function (i.e. it corresponds

to return in a routine), and may appear any number of times within the function,

3^ result = [EXPR] is a number of the FORJ^iAT CLASSCui] - i.e. it maybe mp.de conditional.

The specification of the above routine would be written

real fn spec poly(arrayn3jne a, real x, integer ',n)

and the routine can be called in an arithmetic statement, for example

y = a-b + 2h*poly(c,l/x,0,l6)

An example of an integer function is given next. It selects the index of the

maximum element x(k) in a set of array elements x(m), x(m+l),.,,.,x(n) (n> m)

integer fn max(arraynaine x, integer in,n)

integer i,k

k = m

->1 ^ n = m

cycle i = m+l,l,n

k = i ^ x(i) > x(k)

repeat

1: result = k

end

A call sequence for this function routine might be

y = 1 + x(max(x,1,100))

(•

SCOPE OF NAMES

In general all names are declared at the head of a routine

ither in the routine heading or l^y the declarations integer, r

4.7

FUNCiaoNS AND RiJUTINKS AS PAJiAHETERS

This Is illiiatrated by the following e>raiBpl0 involving an

integration routine

routine spec integr; : e(real name y, real a, b. intes-^r n, real fn f )

v.'hich integrates a function i'(x) over tJie ronrje (a, b) by ev?.lu.vting

y =

b :-gi_n

routine integrate (real name y.real a,b,^lciger n,real_fn f)real £n sj)ec mix (r^t^al y)

real z, b

coinment Simpson rule integration

1;read (b)

b = lOUO then stop

integrate (z, O, 1, int(lOb), aux)

new l ine

print (b, 1, 2);spaces(2);print (z, 1, 4)1

real fn auy)

result - expC -y) cos(b-y)

.jfid

I routine integrs-te 1

end of progr

NiiTRS

1: That the nain^s given to the auxiliary I'outine and its

parameters need not be the same in the integration routine as in themain program, but they must c-orrospond in type.

2; Since 1he result of the intergration is a single quantity, the routinecould be rec st as a real fn : -

2al fn spec integrate (real a,b, integer n, real fn. f)re

nnd called by, for example:-

print (integrate (0,1nt (lob), 8.ux) ,1,6)

RECURSIVE USE OF RtjUTINES

The name of a routine is local to the routine or block in which

its specification appears, and so the body of the routine is within thescope of its own name. Hence it may call itself. It may also call itselfindirectly by invoking other routines which make use of it. on each activationof the routine a fresh copy of the local working space is set up in the stack,so that there will be no confusion between variables on successive calls.(This does not apply however to own variables. See next section.) Some criterionwithin the body of the routine must eventually inhibit the calling statementand allow the process to unwind. Functions defined recursively, for exaiiiple;-

n: = n(n-l): , n > 1

- 1 , n = 1

can be implejnenled in this way, but it is always more efficient to userecurrence rather than recursive techniques.

4-9

OV/N VARIABLES

Wlien a routine is left s.ny infojrroatton stored in vai'iables coi'reypoGoJ

to local declarations in th:?t routine is lost, and no furthur reference rc-y

be ruade to it. In some cases it may be desirable to retHin soivjo of this

iuforination and be able, to refer to it on a sub

5.1

5. INPUT AMD OUTPUT OF DATAThe input and ou1;pu1; of data v^ill generally ho accomplished by

means of permanent routines. In this suction these permanent routines aredescribed and the precise form of data is given.

SELKCT ION GF DATA CHAJ'iHELS

The selection of an input channel is performed by the routine:-

• routine spec select input (intetor i)

This selects the input chajHiel corroyponding to the value of i, andthis channel, tceether with the particular input device assigned to itin the Job Description

It should be noted that a siJiijle Hinice is sufficient to terminate a

number, and that no spaces are allowed within .lie u'antissa or within tne numericalpart of the exponent (unlike constants appearing in a program where all spaces

arc irrelevant and the number is terminated by the following name or delimiter).Further since 'tabs' are converted to a number of spaces, numbers may

be scparnted by 'tabs'. Several numbers in a sequence way be read by the routine:-

routine ^>pGjC read([VARIABLE LIST])

For exarnpTo, read(a, i , x(i ) )

This is treated if it wore a series of instructions

read (a) ; > iad(i) ; read(x(i))

htnce the subscript of X(i) takes the value just assigned to 1.

The read routine is an exception to the general form of a routine, as

it )T)ay have an indefinite number of real n^ie and int'::ger name p&rarneters.

Successive numbers on a data tape may be read so ss to fill

an array by means of the routine

routine spec read array(arrayname A)

For example:- A(1:20, 1:20) ^read array (A)

would cause the next 4OO numbers on the data tape to be read so to fill

the array A, row by row. It is thus equivalent to

array A^(l:20, 1:20)

integer i,j

cycle i - 1,1,20

cycle j = 1,1,20

read (A(i,J))

repeat

repeat

Thi"ee permanent routines ai-e provided for manipulating alpba-nuvaeric

data. The first:-

routine spec read symbol (integername i)

reads the next symbol (simple or compound) from the selected channel,

converts it into a numerical equivalent and places the result in the ^specified integer location.

For example, if the next character on the data tape were an

asterisk (numerical equivalent I4) the instruction 'read symbol (p)'would set the value of the integer variable p to I4 and move to the next

character on t^pe.

5.3

T^e second allows the next symbol on the data tape to be inspected without

mc .'ing on to the following one. It is

integer fn spec next .sysiibol

Tie third:-

routine spec skip

pj^-.'-ses over the next syiribol without reading it.

A table of numerical equivalaixts and a description of the formation

of compound symbols is given in Appendix 5,

It is in testing syj.ibols that the alternative form of a constant

is useful. For exa/r.ple, we coxild test if the not symbol on a t?.pe were rvi

asterisk by

->1 jl^f next symbol = I4

or ->1 i^ next symbol =

Since spaces and underlined spaces are ignored in a program, and nov.-line

pnd :;emirolou are used as terwdnaters, special symbols sxe provided to

r present thera. Thus a space can be tested for by

~>1 ^ next symbol ~ ^

The symbols ave:-

^ i representing a space

^ ^ '' an underlined space

;1 ' * a nev;line

/I '* a seiai-colon

If the data itself contains these special symbols, then they can be tested only

by using the internal equivalent.

Finally there is a permanent input routine which permits the reading

of an indefinite number of decimal nun'bers into successive storage locations,

stopping v.'hen a particular s^'inbol on the data tape is reached. This routine is

routine spec read sequence (addr s, integer p, integer name n)

The formal parameter type addr is explained in Section 9; for the

present purpose it is sufficient to say that the actual parameter will be the

n?.me of a variable, representing the first location into which the numbers are

to go, p is the numerical equivalent of the terminating character, and on

exit from the routine, n contains the number of numbers that have been read.

As an example of the use of the nbuve rout e, suppose a data tape

contains an unknown number of juiinbers, but less than lOOO, and tliat the

last number is follov.'ed by an asterisk. Then the instructions

array X (.l:loOu)

in t :gor n

road sequf,Mice (X(l), 34, n) [or : read sequoncc(x(l) , * , n) ]

v.ould cause the successive numbers to be read into X(l), X(2), etc.

If there were 800 numbers in the sequence, then n would be.set to 800

when the routine was left,

NOTE

on input, each line of data is reconstructed to give an image of the

print-out produced by the Flexowriter. Thus 'backspacetab','upper case'

rnd 'lower case* do not appear as characters in the reconstructed line,

since they do not appear on the print-out. 'Tab* produces an equiv.;lent

-^ubei* of spaces, 'backspace' helps form a composite r-iiaractor, asid

non-significant cases are iii'jjored. Those positions containing an erase

are then deleted from this line. The line image is normally 16

5-5

It sliould be noted that nc termintiting characters are included

by the above routines. They may be .included by the user by means

of the routines;-

£.^1' ^ ® spe c ncw1 i ne

routine spo*; pa.ce

routine spec newlines(iiUerer n)

routine spec sp^ices (inte^-er n)

routine spec tab

routine spec print syinbol (intc£,er i)

The first of these resets the carri?-.ge of the approprii^te printer

(or pu)\ches the ncwline cliuracter), and the .'-econd causes the print r to

::];ttings are at positioris 8, 16, 24, 32, 48, 84, 80,

96, 112, 128, l44» ^59* 1'̂ ® sixth" prints the syjiiboi corresponling to the

value i.

The routiu^^:-

He? 1' .•.'pago

causes the lineprlnter to comncnce a new page, if the output

device is a line printer, or punches 30 newline characters if it is a puisch.

The routine:-

routine spec runout (integer n)

punches n runout characters (used to seperate sets of results, for example)

on the punch. It has no effect if the output is on a line printer.

Arrays of numbers may be output by means of the routines

routine spec print array fl (array name A, integer m)

routine spec print array (array name A, integer m,n)

For a one-dimensional array, the elements of the array ai-e printed

across tJie page, each number being terminated by two spaces, or a newline

if the right hand edge of the page has been reached. The successive rows of

a two dimensional array are printed as above, successive planes of a three

dimensional array are printed as two dimensional arrays, and so on. Each

array is started on a newline and the printing style for the Individual

numbers is the same as that of the *print fl' and 'print* routines.

CAPTIONS

Tli'TG is a special facility for lu-liMng captions. For exi^'inple

caption TAJ31.E ^ UF TKMP AGAINST fi VOL

This prints the information after cr^-ption up (o, but not including, the ^terminating symbol 'newlina' or ' semi-colon *. Since spr.c 3 and underlined spaces

are Ignored and *new line* f!.nd 'semi-colon' nre used as terir.inators, we also use

the special characters:-

^ or

;l " A

A " ^

Thus

newline

~ r pj-'int (y,l,3); ncv.lJno

caption B p -- ; print (2,1,3);

v/Quld be printed as

A = 1.7.12

B = -2,380

In general c_ can be used (in its usual S'-i;;-. ) in a Cf.ption if the inforr^iation

is too long to fit on one line across the pi"-.2e. In view of this if i-.a

underlined word ending in _c is used at the end of a caption, it mvist 'oe

terminated by 'semi-colon' not 'newline',

BINARY INPUT AND OUTPUT

Binary tape may be read and punched by means of the routines

routine spec read b':iajL-y (integername i)

routine spec punch b-inp.ry (integer i)

The first reads the next row of holes on the tp.pe as a binary mmber

(in the rauge 0~127, with the tape so oriented that the sprocket hole comes

:2tv.'eeu the digits of value 4 and 8), and places it in the nayned Vtf

6.1

6 MONIT ,R PRINTING AND FAULT DIAGNOSIS

F/>ULT NtlNITtMUNG

Thei^e are two types of fault which can be detected by the compiler,

those which can be found during compiling and tho:je which become evident during

the running of the cojupiled program. To J-id the programrtier in correcting

Ihetje faults information is .?.utor. • tically printed out where a fault occurs,

QDMPILER TIME MUNI^njRING

During compiling an outline of the program is produced as an aid to the

finding of faulty instructions. It also associates each block and routine with

its serial number, for use in tracing faults found at run time (see later).

/ .11 faults during compiling are monitored. Those to which a line

•rabor can be attached, such as NAME NUT SET, are preceded by it, while

• o;.e whicli can only be found at the end of a routine such as TuO TEW

. KATS are monitored after the END. In calcu'^ating the li-io ninr.ber, blank

liniis are ignored, .-ind lines joined >,\y the continuation symbol c count as one.

FiT)ally at the end of each routine all the non-local variables except the

permatient routines and functions are printed out. Although these do not

necessarily indicate a fault, they may indicate a name which should have been

c-clared locally. A typi-cal program monitor might be

O BKGIN BUICK ; SERIAL NO = 89, M/C ADDRESS = >^721

26* NAME TEMP NOT SET

55+ LABEL 7 SET TWICE

70 BEGIN R(3UTINE POLY: SERIAL NO = 9O, M/C ADDRESS = 32IO115* NAME TEMP NDT SET

115* REAL NAME X IN EXPRESS KJN

120 END R0UTINT3 Pf)LY ; OCCUPIES 256 M/C INSTRUCTIONS

* Li\BEL 18 NOT SET

NON-LOCAL VARIABLES A TEMPI Si

182 END OF PRi:}aRAM: OCCUPIES 800 M/C INSTRUCTIONS

The above should be self-explanatory. It indicates that the program

started at line o and finished on line 182. These are physical lines

and exclude all blank lines on the print-out. The cuter block is given

the serial number 8g. The routine PoLY started on line 70 and was given

the serial number 90, There were mistakes in lines 26 and 55 line115. Finally label 18 was not set in the routine POLY,

6.2

since there jnay be jriore than one statement on a line, it is not possible

to tell specifically which statement is involved but the faults are printed

in the order in which they are discovered, A full list of faults is given

in Appendix 4 tosether with a brie>: description of th#iir nature,

RUN TIME MnNI'miUKG

During the running of a program certain faults may bo detected

Ijoth by the coiripiler r-ad by the machine and its supervisor progr^jn.

For exaniple, the supervisor program detects the case where the square

root of a i ogative argur.5(-,ut is being requested and the compiler detects

faults connet:ted with s'.'itch and tost instructions,

TJie standard procedure is to print out 2 lines of information

specifying the frailt and the line on which it occurs folluwed by a list

of useful informntion found in the FIXED part of the sta«.'k. For exejiiple: -

LINE 117 ROUTINE 90

EXP QVERFIJJW

R{)UTINE 90

arrayCi;10,1:5)

ARRAY(1:10,1:5)

10 5

333333334^0 ^ • J^^'49999997« o.ooooooooooa-99

64

CYCLICCURRENT VALUE = 6, FINAL VALUE = 10, INCREMENT ==1)

CYCLE(CURRENT VALUE = 4, FINAL VALUE = 5, INCREMENT = 1)

BLOCK 89

0.0000000000a-99 3.7152463802a 3

10 5 3 6

ARRAYd: 10,1:5)

ARRAYd; 10, 1:5)

NOTES

1: This fault print out must be interpreted with care. V.hen the ffiult occurs,

the fault print out routine looks in the STACK to find the fixed variables ?.nd

interpret them (see Section 10). Now every location in the store initially looks

as if it contains a real qua)itity. Thu.s:-

(i) until an integer is a.ssigned a value, it will appear as (and be printed

as) a floating point quantity (probably zero),

(ii) until an array declaration is obeyed, it will appear as 2 floating

point quantities.

(iii) until a cycle has been entered, it will appear as 3 floating-point

quantities.

Conversely, since all sub-routines of a program share the same spac-,

ll\en on entry to the sccond and subsequent routines, the stack will contain

the valur*s l(>ft by t! ; previous routine and these will be interpreted accordingly,

if the current routine does not alter them.

2: The 'CURRENT VALUK' attributed to a cycle is the value o" the inj^eg^

n.*?.rne used on the left hand side of the instruction at the tih.e of the fault.

Thus if a program consisted of a number of cycles one after other, controlled

by i, and the fault were inside tl\e last cycle, then all cycles would have the

same 'CURRliKT VALUE* - the current value of i.

3: only cycles, arrays, integers and reals are distinguished.

(i) for integer name's and real name's the address of the actual paramter

is printed (as an integer) .

(ii) for array fn's (see Section 9) its parameters are printed (as integers).

(iii) for routines and function's used as parameters, six real quantities

are printed,

(iv) for complex quantities, the real and imaginery parts are printed in

floating point style.

6.5

t\^UT;r TRAPPING

The above stpjulard monitoring procedure involving the termination of

the program, is not always convenient. For exrinple if a program is dealing

with a series of data sets, it may be preferable to restart on the next

'case' in the event of (say) EXP OVFm;^IX)W rather than terminate the entire job.

An instruct;", n is provided which enables the usex* to trap certain

faults and ti'ajisfer control to some preassigncd point in the program. It

takes the form:-

fault [fault list]

where I FAULT LIST] = LK-LIST]-> [n] [H)5ST OF FAULT LIST]

Foi' example:-

fault 1,2,5 3,4 ->10

mor.ns 'if a fault of type l.,2 or 5 subsequently occurs then jump to label 18 ; aadif a faulL of type 3 or 4 occurs then jump to label 10,

The effe^.-t is to preserve all the necessary control data to enable control

to revert to this point in the program (and then jump to label 18 or lo) should

ona of the specified types of faults occur at some lower (or the same) level.

Tlie l:'bel must be in the same block as the trapping statement, whi

6.6

The first pair of statements are DECLAilATIVKS V:))ich di.Oimlt the -rePs 'f

the program in which provision is to bo in?~de for the pp.rticulp.r checking facility.

The second pair are INSTRUCTION'S v.Iiich turn the facility oji or off (initially they

sjt-e on). They do this by setting a cert».in switch V:hich is oxf^mined whenever

the facility is about to be executed. If tlie relevant sv/itch is on then tKe

facility is executed, if off it is skipped. If the facility hr.s not been

co'-piled in the first place then the instructions have no effect. This sv.-itch

;:ui. ( irjg is oxtrytnely f?.st so that there is nothing to be !;r,i;.£.-d from recorv.ing

tlie current sts>.te of the switch (in some integer, say), p.nd testing this before

each settijig order. For example, the following sequence causes queries to be

printed every tenth time round the cycle,

cycle i = 1,1

queries off

if fr2cpt(i/lo) = 0 then queries o^

repeat

The switch sensing on the other h«nd is a tir.ie consuming opor?.tjon and it

is for this reason that the declaratives are provided to delimit the areas of the

progTam in v-hich tliis takes place. In most cases, however, the check is compiled

over the entire program.

The checking facilities in question ^re described by the phrase:-

[check] = queries, routine trace, jump trace, array bou?\d check

They will be described in turn.

QUERY .vUNTING

Any arithmetic instruction (including complex) can be followed by a ?,

for example:-

a =: b(i) + c?

When the facility is operative the new value oji the l.h.s. is printed every

time the instruction is obeyed. The style of printing will be fixed, floating,

or complex floating according as the l.h.s. is of integer, real, or complex

type.

[Unlike the other facilities, ?'s are normally compiled so that a

compile queries at the head of a program is redundant. Also ignore queries

is equivalent to stop queries.]

(

6.7

ROUTINB TRACING

Vi'hen the routine trace is op«;rntive It • r.u^oa the routine Jiuir.bca- to

be printed each time a routine or block is e)(t« ..-d p.nd left. The corref?poj;de)ice

between the routine number and the nr/Uio cyn he ound from the pro^rj^un out 1.1 -e

produced during compilation, TJie printout of m. i'outiue trr.c© hiight appear

R95 Rgy RF96 EKO96 KMD97 R90

]i3 Ti ->4 ->6 S3 ">7 '>S ->9

Hera T and S refer to test and switrh rc:;pectively. If the labol and

routine trace are both oper;--tive the print out i>iiiht aijpepr:-

F^95 -^3 Ti -^4 ">'3 R97 S3,

ARRAY BOUND CHECK

If this facility is operative the values of the subscript

expressions in all array eleir.ents are checked to see if they lie in the

range s*/ecifiod by the bound pairs in the array (declarations. If not, the

progrfiju is terminated with the approt>riate monitoring.

OTHER CHECKING FACIIJTXES

Certain checks are luilt into the object program e.g., whether

a cycle instruction calls for an integx*al nuwber of cycles and whether a

switch index is out of re-rAf^e or corresponds to a label not set. All

are time and space consuming operations. They can be removed from an

object program v/hich is otherwise ready for production by means of the

declaration

production run

7 r-Hi^SKKrATIUN t.;F QjMPLETE rR(;GH/VMS

J(';B DKS CHI FT IONS

The running of programs on the computer is controlled by a

supervisor proijram Jield permanently in the • nchine. The supervisor

accepts coir-plete programs as a series of t; ..es (program and data) and

a J{j!5 i)ESCJUPTIi3N which may be on a separate tape or included with the

pi-o^i ; !ii or data. A full description of the system is given elsewhere

fj], ;!nd in tliis section we give examples to illustiate the general

principles of job descriptj.ons.

PH.OGHAM AND DATA (3N SA?>1K TAPK

The simplest form of job consists of job decription, program and

dat;a on the one tape. For example;-

J(jB

UMA, J(jNES.5/2

OUTPUT

O LlNKPRIiNTER 100 LINES

STORK 32 BTXlCKS

COMPUTING JOOOO INSTRUCTIONS

OjMPILER AA

begin

I PRGGR/\M 1

1 1I I

end of program

I II DATA I

I II I

NOTES

1. The title f'^nd line) identifies the job. The first few characters

will be a ». ode lo idcntily the particular organisation and the rest wj,H

be information of an arbitrary form to identify the progranimer and the

program within the organisation.

Reference

Cl] 'Documents and Job Description* I,C,T. Ltd., October 191)3.

This gives a full description of the possible arrangements of program

and data tapes and the utilisation of the multi-channel input/output

facilities on Atlas.

7.1

2, The 13UTPUT inXoi tiiation aays that reference to channel o in the

pio2r?-m moans the iinepriiiLcx* (if no c iput channel is selected in the

proj^x 1 channel 0 is used), Tlie ninriber of LINES gives an upper limit

to i:he amount of output that is to be permit Led.

2, STORK gives an uppex* limit on the number of 5^^ word main store

blocks used by the program and data.

3. ajMPUTING gives a limit on the running time of the program. An'INSTRUCTION' is equivalent to 2048 machine instructions.

The (HJTPUT, .'-mRE, and mMPUTING sections are optional, both

individually and collectively. If they are omitted the allowances given

in the above example are r.,; sumed, i.e., 100 LINES, 3^ BIj(JCKS, 10000

INSTRUCTIONS, These should in fact be adequate for most small probl

;.3

PROGRAM AND DATA TAPES SEPARATE

OXten \ • en a lirogram is being used for productioa runs, it is

convenient to keep the program on a separate tape which is never changed.

For each run the job description and data form a separate tape. For example

ajMPILER AA

(title 1)

begin

PR(3(iRy^J4

of program

The data tape including the job description, would be

JOB

(title 2)

INPUT

O (title 1)

SELF ^ 1

DATA

I

IDATA I

+ *Z

The input section gives the relevant program as being channel 0 (the programci'nnnel) and SELF = 1 indicates that the data tape is to be read as channel 1.

Tlius an instruction 'select input (1)' is required in the program. Thiscould, if necessary, include any OUTPUT, STORE, and COMPUTING information

since this is the part of the job description.

Possible titles for the above exajiiple might be

(title 1) MA, PIO

(title 2) UMA, PIO/RUN 26

7-4

PROGR/Ul ON SEVERAL TAPES

It is often convenient to Jiave the program itseli on tv;o or more distinct

tapes, where,, for example, the program may be so long t))iiL it would be pliysically

uiunanageable to keep it on one tape.

Alternatively the program may contain a large section (declarations and

routines perhaps) which is common to many programs and which can conveniently

be kci:)t on a separate tape.

The instruction

i^w coiTipile from inputLn3

is n^ed to switch the compiler from one input stream to anot)ier. For example: -

Jt3B

(t i 11 e 1)

INP-.T

1 (title 2)

2 (title 3)

QDMPILER AA

begin

I FIRST PART I

I OF II PROGRAM !

now compile from input 1

+ - z

QJMPILEK .VA

(title 2)

1 SECXDND PART

1 OF1 PROGRAM

I

end of program

* v»Z

DATA

(title 3)

I DATA 1

I iI

***Z

8.1

S CX)MPLEX ARITH}.€STIC

As indicated previously, facilities c-xist for the wAnipultitloa

of coinpl&x as well as r&Pl and ' qur.atities, co^nplgx quantities

iire stored as a pair of res-l m

AKIT.' :';ETIC EXPRESS IONS

The arithmetic expression [EXPR] is still of the form

[ +' ] iOPERAND] CciPERATQR] l OPERANP] IlOPERATfjR] [OPERAND]

but UjPKRAKD] is now expanded to be

LVAR lAliLE] , [ ajNS'IVvNT] , ( LEXPR] ) , 1LEXPR] I , IFUNCTION] or x

Ilcie ^ is a delimiter denoting the i (or j) of complex algebra notation.

Kxai.iples of tliis r ore general expression are: -

(V'Conj(l) - I

KIJTES

1, Just as real quantities may not appear on the r.h.s. of an integer

assignment (except as arguments ox integer Xunctions), so complex

quantities may r jt appear in real or integer expressions.

Hov/evur, the functions

re(z), i!ii(x.), magCz), arg(z)

convert from complex to ri^al quant it •:< s and may therefore appear on

the r.h.s, of a reai assignment. In fact any function wJiose

value is real regardless of its arguments may be used in a real

expression (just as any ini eger function, regardless of its argument,

may appear in an integer expression). Thus if K and B are real and Y

complex then:-

X = B + im(Y)

is valid,

2. re(^) and im(z) are actual locations in the store and can therefore

be used on the l.h,s. of an instruction (whose mode is then real).

For example:-

re(z) = sqrt(2)

ira

8.4qiNDITIOKS

in conditional operators, [EXPR]*s must be real (in the sense

of. note 1 of the previous section ). Hence the following arc legitimate:-

if^ arg (z) > TT/Z Ihcn -> 3

3 case mag 1 s

PJ)l.iTIKES AND FUNCTIONS

Since routines and functions f^re allowed to operate on

Liui.ntitieg, the par; meter types have been expanded to include

Formal paranieter type

c nair.e

nnlox

coniplex array name

c Ginp lex _ai- :• y

1 rorresponding aclual parameter

name of a complex variable

any expression (which will be

evaluated as if for a complex

ossigment)

name of a complex arr^

name of a complex array

The rout'ne types Crt] have also been expanded to include complex fn.

As an example we will rewrite the function routine for the polynomial

a(m) + a(mH-l)x+ + a(in-i-n)xfn

assuming x and the coefficients a(i) to be co)nplex.

complexf^ poly (complex arrayname a, complex x, integer m,n)integer i.; complex y

y = a(m-j-n) ; result - y ^ n. = O

cycle i = m+n-1, -1, ra

y = y*x + a(i)

repeat

result = y

end

8.5

IKPUT-OUTPUT OF COI.iPl.,liX liUMBERS

Data Is punched In the .foi'm

[real PAJiT] + i [IMAGINARY PART]

but the j,miivicJup.l parts can l>e ijun.cJied 3.n r.viy j^cccpt??bl

9.1

9 STORE MAPPING

THE ADDRKSS RECOVERY FUHCTIOK

The absolute p.ddress of Any varj.?.ble is not generally knov/n ia

:?.n Autocode progrfUiiine, but it way l e obt?.inod by rr:c?.ns of a stund-'-rd

function. For pie;-

s = rddr(A(0,0))

TJiis pl>'.< it

ii'itvy bs F.uy vRrir'blo, rsff.l, iivtr, or co:";.>lox ;i.n.d tk@ rt/suj-t is v.h intcgiving the ;'.!;-j:oluto ; ddreps of the storr.re loCi^.tioR ?.llocst6d to thatvrriable.

Absolute addresses used in conJu;-.ctioii vith y^ci'iiy iTuK.ctiois

(i2te below) :^^.a with tho 'storage' functions

i j:at Q;t; r ( ir.t'^ c:'̂ ^ n )

reftl (i}'.tc£;ca- n)

coiijplex (integer n)

Those give the contents of the nddr«s»3 in questiou ixs ar. iKtci:,j;r,

rej?l, or complex nui^ber. Xm the last c-.se the real ?rid iu^s:inPTy pax-tsof the . awbor are ^^ssuFicd to be in n r--.ud n-fl. The P.ctuAl

may of course be an integer expression e.g., s-j-k-1, functionsptpy be employed on the left hfnd side of p.tx sssi£;?x>:-3nt statcv.eat asw-ll PS in an expression. Thus the p-ir of instructions

s = addr(a.)

real(s) = b

are equivalent to

a = b

ARRAY FUNCTION'S

T^e declsxrations of Section 2 defiiie variables and allocate

storage space for tkc;m. In this section we introduce a declarsitioa\ -ich defines variables as the mmbers coiitained ia storage locations

that have already be« t allocated. This is of ir.-.portaRce in coKinuaicatingbetween routines with the addr type of formal par^jr^eter and in reixaiaiEg

variables (see below).

An example is

array fn X(s,p)

which defines X(i) as the real number in the storage location whose

address is given by s+i*p. Thus it defines a vector X(i) interms of an origin s and a dimension parameter p.

Array functions Ji;ay define rectangular J.rrays with any nuniber

of subscripts. For exaruple;-

prra-y fn Yis r^s a.

vector x(i), one could wx'ite

Array fa x(sl,i)

x(0) would theJA corrv^-spoi'd to tbe ia address si, x(l) to that

ia sl+1 etc. If it is degfirod that tke first location sLould

corrctspoi'-d to x(l), tKe declarMtion v/ould k-a written

g.rx'g.y fn x(sl~l,l)

If T/e had wy.K'ted to define a lo x lO Matrix, stored row by row

rstkcx- thr.a a vectco.', wo could kr^'e writ tea

array fa A(si,10,1)

piid a(0,0) v,'ould co-rrdspo>id to Rf.ldress si,

array fK A(sl-11,lo,1)

would defiio a E.atrix ia the avAilal^le space wJr.ose first elcKcat

Y/a.s A(l,l).

NOTES

1, If tlio suffices of arrays &r© to start fro» (1,1, 1) rather tkaa

(0,0, o), approprisvto adjustMent ssust fee mad® to the expressioa giving

tke origia ia tke array fuECtioa declsuratioa,

Z SpriCe redefiucd fey array fH*s may still ¥© referred to by its origiaal

. laaKOo

of VAK:ABLES WITIiIN a BIX)CK

v;e illustrate this with p.a ex^s.^ple. Suppose we wpitt to define arid

allocate storage for pairs of variables x(i), y(i) so that they

Rre ia succesive loca.tions, T-o irr^vy dcClar?tioia will only define

a vector or matrix arrn.y stoiod in the conveutioE.?^! i-'r,iu'er, so "s/e

."ucpt lJlC followinjij d(,vice

b e ;:,i>l

avrg-y (1:2(J00)

s = fiddr(p.(l))

p.rray fa x(s-2,2), y(s-l,2>

9^^

Tl\e first pair of jair;.l>crs could thca lo referred to either sls

x(l), y 1: lo)

:r: d we wisk to dofir.e ti e first colu"n of A :-s a vector, thea v.-e could

write

p-rray fa y(r.cidr(A(l, 1) ) - 10,10)

which defiuc-s y(i) = real (adar(A(l,l)) - 10 + lO+i)

i.e. as the first coluir.n of A. Tlus y(l) is equivaleHt to A(1,1), y(2)to A(2,l), ,y(10) to A(10,1).

la the cs.se of cotxplex pxray fuMCtioRS the user Kust t?Jie i&to account

tl^.r.t a complex Kuv-ber occupies 2 consecutive locations. TKus if si is

tke ?-ddress of Q(1,1) of a coKtplex array Q(1:10,1:10 ) , then

.Complex t^rray R(si-20,20)

defiuos a vector R(i) whose ele)' \ts are tke first colunn of Q, i.e.,

R(l) - y(i» 1)

9-4

STORE MAPPING ROUTINES

Stoi^age JfuEictioK.3 of arbitrary cor.plexity c?.n ofets>.iked T.y l eai s of store ^p.-appiifig: routines, Tfe.ese sore esscRtially rvjAcl^on routiK.es v.hick

cov-pute aa address. For expxiple: -

real x-ap X (t)?.teter i, j)

rci.su^;^ = s+^i*(i-1 i+j-1

« Kd

o";putoa tl.o i'.e'.tbrcss of tLe (i,J)tfe eleK3eKt of a real love-r trira:.£;ulsa' r.r.c'irAg actual p atcr

1

ac.c-r I the of mc.y iKtc^;er, real or cor, piex

I variable (includir.g aa aaray eleueut), Tlie

I a^.dres'- of tl:e vpjri?.ble is Jiauded oki as tke

I ps.raLiCler proper. It is equivs."" ut to rta

1 integer paryj-seter ia tke >:ody of tk©

I routine, la fact aa ac^.f^r parPAJoter

1 replaced by x is equivalent to

I aa iatcrer parRSieter replf'-Ced

1 Ity addr (x)

real n:a.p | tko actual pjiraip.eter is the iti^usa

ii>te£;fcr y.:tip 1 of a niapiviiag routiRs of tl&e

coiaplox t.p>p \ specified type

I

10:THEUSEOFMACHINEINSTHUCriGNS

STACKvSTRUCriJRE

MachineinstructionsCf.nbeusedinroutineseitherto)inp.kep.n

inn^rloopnoie.efficientortoeffectsomeopc-rp.tioav.'hichcannot

easilybedoneotherwise.Itisassuniedthattherordc-risreason?.bly

f;uriiliarwithtJieloi^icalstructureofthemp.chine,t.hj>tiswithth.e

l>asicorderrede.ItpJsoessentialtoknowl^owdatp.isstorediuthe

stack.Vi'eilJustraLethiswithreferencetotliefolliytvinrjroutine.

&

routi^matrixfn(arraynan-eA,Bintogorni,nrj^al_fn_F)

re?aa,b,c;intcaeri^J

arrr:^C(1:m,1:n),E(1:m)

r£aifnspe£F

cyclei=1,1,m

cyclej=1,1,n

repeat

rej^ef^

end

NUTES

1,Thefirstwordofthelocalstacksectioncontainsthecontrolnuieber

forreturningtothecalli;routine(thefirsthalfword)andtheprevious

contentsofI5d,thecurrentlevelE-line(thesecondhalfword).The1st

halfwordofthesecondwordcontainsthetestlink(whichrecordstheposition

withinthelabellistofatestinstruction),andthe2ndhalfwordcontains

iiiforination(thenumberandtypeoftheroutineandthenumberoffixed

vrriablos)requiredbytherun-tirnefaultmonitorroutine.HereBdrefers

totheB-lineassociatedwiththeroutine,andcorrespondstothetextual

(Jeithoftheroutineintheprograminwhichitisembedded.If(say)

tillsisathenEd=B2.TherelativelocationsofthefixedvariablesA,

B,m,netc.,areassignedatcompiletime.ImmediatelyonentrytotheroutinethecurrentvalueofB90,whichalwayspointstothenextavailablelocationinthestack,isrecordedinBdandthepreviouscontentsofBdrecordedin

thestack(asalreadynoted).B90isthenadvancedtotheendofthefixedstorageallocation.WhenthedeclarationsforCandDare'obeyed'itis

advancedagaintothefinalvalueshown.

^YOUTOFTH5STACKFORTH2DSCLAHA^l'IOXS27V,atr:.xfn'

Everythingexcer'treala,"b,candthe(real)arra;>'-sthemselvesaredestandardisedandheldin'lon^ord'units.InsonecasestheIsu(orm.s.)halfv.'ordofthedestandardisedquantityis'flagged'toidentifyitsfunctionfortheT)'cirposeof'stack-orint'(seetheshadedh.w's.)TheolarJcsectionsindicateanindefinitenurcberofwords.

«•fixedvsz'ia.'blep,llocation'

i3,(initialvalueof3^^)i

idestandardisedI

isimilartonaT.oers

iC,3butrefer"backstandardisedtonon-local{fl.ptarrrys!n^omoers

i

dynajnicallocation-

;st:"(finalvalue'o"^3i^90'

cvclecycle-•

Ipoints

30.3

2, Dcstsiiidiirdlsed quantities are foDned by adciing 0 3K-12) to tlie sti iiJj.rdlsed

form. This const:;Mit will be found in loc^^1;ioa *1000001. This octal form

of tlio address can ba used in rru-'-chine iustruction fori--ats(see lct«r).

Thero rre no integer r-nme or real nrjne purarrieters in this e>:a;nple; if

piv.f^cnt they v/ould ke represented (s.t tba appropriate place nrnong the fixed

v.-.rir ' les) hy si.nt^lQ v/ords, nau.ely he5\- addresses, in a dest^iad-^rdiscd form.

vhey i\e at present in distir.£;aisl)f.fele from inte^'^r' s, sii-il-rly for

coviiplcx narrie pra'TJiietcrs, A complex cnjr?.utily requires tv.'o consecutive

words, representing the real .-rrid irnRi^iAf-.ry pi-rts,

3» arrays. The primary reference to ? • arr?.y c< nsists of a pjiir of vords. Thesecond half of the 1st word points lo the (1st v;ord of the) 'dope vector^

that of the second word to the 'Iliffe vector'. The dope vector cont?d.ns

the vn.lr.cs of the bound--pp.ir list to^^thor v/ith the nu'Jiher of p?.irs, i.e.

the dimensionality of the array. If th

4- the P/vB-AMETRIC function F. six words of information are kept here,lu F.ddition to the control number for entering the routine it is

nc-cesi2>'.ry to keep a record of the display of the relevant E-lines

when the routine is first substituted p.s an actual parameter. For

fvirthor details see the Compiler,

5' in the text the initial and final values j?.udii^creinent iu a cycle ?-re evpluo.ted and checked for compatibility before

the cycle is cc,.U:.onced. The increment ford final vjilues, together with

the ;.ddre:^s of the controlled in ^.-ger variable are recorded for use in

the execution of the cycle. The dis,2;ra)n illustrates how they are stored,

stack: IfTSTRaCTlOKS

The following autocode for/rats i nvolvinj^ t.he stack pointer (EQO)

;- .i e available ^

.'iL == si ±

St = Cexi^r]

Ckaiae] = £t

st represents the contents of rgo. In the last instruction the [NAiuE]

innst 1:3 local to the routine -xwitaining the instruction, otherwise a

fKult is indicated,

MAaiIKE CODE FORMATS

Scviie 'machine code' formats are now described,

1, Where there is no h^wbolic address involved ;.n instruction is written in

the form

Cra],[n],Cn],[address part]

(a.nd terminated ag usual by ; or nevline). Here Cfd] refers to the

function digits, Cn] to the Ea and Bm -Jigits, and [ADDRESS PART] to the

address part, which may take a nuKber of forms. It may be v/ritten as a

Constant in the usual v.-ay (preceded possibly by a sign) bearing in mind

that the binary point is located 3 places from th . right hand und. Thus

0121, 80, O, 2,5 is equivalent to

05064000 00000024

10.5

It iiiJiy aliso consist of an octal numbei which consists of an * follov>ed

by up to 8 octal digits, including any significant aeros. Thus

0101, 91, 0, 'lOOl is equivalent to

04066600 100]0000

in oc?;:.l notation,

i'inr"'/ .it may consist of a label or a (possibly signed) const tint plus

a 1: 1. The label is replaced by the control nuvibcr corresponding to it. We

iiK^y X for to lab^illed constaxits (see next section) in tJiis v/ay. For exaraple

0334, O, o, 14:

0101, 99, o, ^ + 14;

14; ^i'O 3, 00000 \2.

pu:,;s"an r.^standardised 10 in the accuinulator, and a halfword lO in ^399

NOTE : The formal definition of [ADDRESS FART] is

[ADDRESS PART] = [+']faDNSTl+TN]:,[n3:,[+'3[CONST],CoW]

2. The format

[+'][const]

is used to plant a standivrdised 48-bit floating point number in the current

location of i'e program,

3. pairs of 24-bit words may be planted in the object pr.'.a'rgjn by means of the format

[ADDRESS PART]C,][ADDRESS PART]

Thus v..: may plant tables of integers or labels, for example:-

3.4

7:.8:

/», We now have an instruction format which uses a symbolic address,

Efd] , Cn], [ka}:^h;] [j^odhst* ]

where C+CONST']=[+]C QDNST], NIL

Here the [NAIIE] can refer to anything which is represented in the fixed storage

sections of the stack. The resulting instruction is

[FD3,[n3, d, p [+ CONST']

whei'e (Bd, p) is the 'address* of the npjne, Ed beiug the B-iine pointing

to the appropriate section of the stack, and p being the Rddress relative ^

to the origin of that section. Thus an instruction

032^, O, a

appearing in the routine under discussion would be translated as

0324, O, 2, 14

assuming yld ~ V:-2t that F occupies 6 v»'ords.

The effect would be to put a in the accumulator.

If the [r ;E3 refers to an unstaiidardised floating point intej, r then we

T;iRy v.ish to select the intet^iral half for use in a.E-line, For exair.ple

OlOl, 80,

is equivalent to

0101, 80, 2, 6.5

If a and rn h^d been real and integer name' s then 2 instructions would f

be n'vcessary in each case, thus

oiol, 99, a + ^

0324, 0, 99, o

and

0101, 99, m + ^

OlOl, 80, 99, i

If a is complex then

0324, O, a

\vcv»ld put the real part into the accur-.jlator, and

0324, O, a+1

v/ould load the imaginary part,

in the case of arrays vie can select by similar sieans the tv.'o priiaiary

reference v.'ords, and with their aid obtain access to the dope vector and/or (

the array itself.

.10.7

•EXvU^PLE ON THE USE OF MACiilh'E ORDERS

The following ex; :ple forms tJo sum of t;;rcG routir.c.s B, C of

; •••-ilar divricnsions. (It ihi in f».ct tie p«.-?rTn.:-!:e vector of A;cor^n&iit ^364 " no of clciv^cnts in r e.trix

;co:ni.>cnt set /56l = address of Ist oleinnit of A

;co;riraen^ S';;t ,662 - c-ddress of 1st ele;.icut oi B

;cojpj'ieut set ^563 =? fddrcss of 1st elerneiit of C

; coinv.ic-iit perform addition

; Coir.;r:ent DIHENSION FAULT

11.1

11. THK PKHM/Ux'ENT HOUTINKS

Id Soci-ion 5/ deci'ibcd the j.nput and output routines,

•The permanent matei-ial also inc.!udes routines Xoi* the solution of linearequations, the solution of systems of ordinary differential equations andoperations on iiiaurices. Further rovitin' s may be addud from tj.nie to

time.

I-

routine spec eqn so1ve(ax'rayname

'L'.'iis /'outii'.e solves the equations

A(l,l)x(l) -}• A(3,Z)x(2) + + A(l,n)x(n) = b(l)y\(2,l)x(l) + A(2,2)x(2) + + A(2,n)x(n) = b(2)

A(n,l)x(l) + A(n,2)x(2) + + A(n,i50x(n) = b(n)

(i.e. A.X = b), where the coefficients A(i,j) are stored in thematrix A, and b(i) in the vector b. v is destr yed and the solutionis placed in b. If during the el imiiiat ion process, ilie equations arefoi-nd to be linearly dependant, then 'det' is set to iiero and theroutine is left, with both A and b upset, otherwise 'det' is set to

th- determinant of A. Consequently 'det' should be tested after each

Ccill of the routine.

MATRIX RX3UT ' :«S

The h-.atrix routines operate on tv/q dimensional arrays(i.e. i.iatrices

not vectors). The dimensions of the arrays are not required as parametersas the routines automatically find these from the declarations, and checkthem for compatibility. The programmer may insert similar testsin his own routines by means of the functions

integer fn spec dim (arrayns-me A)

3nteger fn spec bound (arrayname A, integei n)

The first gives the dimensionality of the array(1 for a vector, 2 for amatrix etc.), and the second the nth bound (upper or lower) of the arraycounting from left to right. For example, if A were declared by:-

array A(-5: j-5, l:p) wliere p = lo then

dim(A) would have the value 2

bound(A,l) ' * ' ' ~5

bound(A,2) * ' * ' +5

bouud(A,3) ' ' * * 1

bound(A,4) ' * * '10

n

Tilt-' routines

routine sp^^c unit (5££f^;j' ;lpe_o matrix add (arrayname A,B,C)

rjoui:ine_ spoc matrix sub (arrayname; A,B,C)

routine spec matrix copy (arrayname A,B>

set A to Bi-C, B-C and B respectively. Although the parajiiotcrs are oI .

type arrayna-nio, the operation of r.)ie routines is sucn taat tne san,e array

can be substituted for more tlian one of the para)notc;rs. For example:-

matrix add(A,A,A)

doubles A. The same is not true of the follo\vj.ng routiney:-

1- ou t i ne spec ma t r i x )nu11 ( array name A, B, C)

routine spec matrix mult'(arrayname A,B,C)

routine sp

11.3

Tlie routines

jroutine spec matrix div(arrayr.aKie A,B, roalnaine del)

routino pec invert (arrayname A,B, rc-alname dec)

sec A Co inv(lO A and inv(B) re.spoctively. In the process B is destroyed

and tlie value of iis determinant placed In det. Should the matrix be

fecund to be singular, ' d< i; ' is set i:o zei-o. Consequently 'det* should be

tested aXti^r every call Tor these routines, IjC B is required at the end

oi tjje routine, then the tei-Iiniquos desoj'ibed above sliould be used. The

Xunc tion

real J^n det (urraynai.)e B)

sets 'det' to the determinanc ox B and destroys B,

^L!:^yi:ION ::f diffkiihntial fx^uations

There are two routines available lor advancing the solution ol

a system oX Xirst order oidi- :u-y diXXerential equations

dy(i)/dx - X(i)(x,y(l),y(^), ,. . . ,y(n)) i=U,2,...,n

froin x to x-j-h, using the Kutta-I.'erson Xourth-order integration inethodl.2j.

The system is defined by means of an auxiliary routine, which must bu

s^ipplied by the user, ox the form : -

3

11.4

The parameters are : -

y name of a (real) array. On input y(1) , y . . . y (n) .-jhould

contain the solution at x. on output they will

contain the solution at x+h.

X the initial value of the independent variQ.ble

h the increment of the independent variable.

n the number of equations in the system,

e the name of a real variable, which on c'.M.put will contain

an estiniate of the maxiinum truncation ori'or over the step,

aux the name of the routine which evaluates the derivatives at a

general point (see above).

The second routine

rcucine spec kutta nierson(njt-raynj^me y,£e^l xO,xl, roaJ name e £

inJLegor n,k, yux)

advances the solution, by means of a series of calls for 'intstep*, from

xo to xl, keeping, if possible the estimate of tlie m«xiinum truncation

error less than e. An initial step length of (xl-xo)/2{'m wliere 2l(nMi)

>k > 2fm, is taken. If over a step the local truncation error (given

by 'int step') is greater than e, then the step length is halved; if

the error is loss than .ole thon the step length is doubled.

If three successive reductions in st(ip length give no improvement in the

estimated truncation error, then e is replaced by tv/ice iht: smallest error

achieved, and the iritegration process continued. The parameters are : -

y tiie name of a (real)array, on input y (1), y (2), . .. y (n)

should contain the solution ac xo. ijn output tliey will

contain the solution at xl,

xO the inital value of the independent variable.

xl the final value of the independent variable,

e the name of a real variable, on input tJiis should com ain

the accuracy criterion, on output it will be unchanged if this

accuracy has been acJiieved ; if not, it will be replaced by a

more- realistic value(see above).

n the number of equations in the system

k an estimate of the niuiiber of steps required to cover the

iange(see above)

aux the name of the routine which evaluates the derivatives

at a general point(see above).

Al. 1

APPh'KDIX 1. PHRASE STRUCTUHE NOTATION

In describing Atlas Autocode we uso square brackets round an

entity to denote that it represents a class of entities and may be replaced

by any member of the class. Wo call an entity in square brackets a PilRASE.

For example we could define a decimal digit by

PHRASELDIGIT] ^ 0,1,2,3,4,5,6,7,8,9

where the coiimas r-re interpreted as meaiiiiig 'or'. Thus there are ten

dilforont iJiivigs wliich can be cf.lled I.D1(tIT3, f=-nd wlien we refer to f.niGIT]

elsowliere we menn that any of the ten will bo .lejjitiifate.

We can then buila up from this basis and di.-scribe, for example,

a sij^ned digit as

PJiRASEI SIGNED DIGIT] -- -i-CDIGlT], -LdIGIT]

There are also pl:5ces where a phrr-.se Hiay or may not appear and to

sigi»ify this a special pha ase 'MIL* )nay be written as the last alternative

in a phrase definition. For example Llio swiLt;li .limits in a sv.'itch

declaration can be preceedod by a + or - .sign if desired, (Absence of

a sign corresponds to +,) The relevant definition is

iNAME list] ( [+' 3[N] : [ + ' J r.N] )

whore P}iRASE[ + '] = +,-,NIL

Thus "I *+4

-4: 4

3

are exarriples of switch lini s.

Alternatively we c a use the special ? qualifier as follows,

PHRASEL +3 +, ~

PHRASE [+?] = {.±1yiah

The last is implicit and we can use Lj;. ] (e.g., in place of 1- +']) without

expilicity giving the latter definition.

In the interest of efficiency however, it is preferable to

keep the depth of analysis as snail as possible and fox* this reason we

use the former scltsr.ie.

The phrase structure notation can be used I'ecui-sively, i,e., phrase

definitioiis may,directly or indi.-^ctly, use themselves. For example we

ri;ay define a 'list of names separated by conuiias' by

PKRASElNAh^E LIST] = CNAi^5E] LREST OF NAME LIST]

PERASE[REST of HA.ME LIST] = [, ] LnAME] LrEST OF NAME LIST], NIL

fil.i

i

[since a is used to separate the altcDi;"lives of a phrase definition ^

it cannot stand for itself like the other basic syinbols. Instead v/e

mij.-vt write [,]. similarly Ceol] and CSP] are used to denote 'end of line'

and 'space' in the source language.]

The qua]iXior * also indicates recursiveness and a CkaNIE LIST]

ronld bo tJefined as

Pi-:nASErNAh'.E list] " CNAME]r. ,MAHE^?]

P}IRASE[,NA-ME] = [,][NAAiE]

the definitions

PimASEC,KAJ/.E *? ] = [ , KAJ.l E 0 , KIL

PiiRASE [ , Ky^J.IE ^] = C, NAME 3[ , NAJME *] , C, NAME ]

being ii:iplicit. Again, however, for reasons of efficiency we use tl.e forner definii ion.

Given the phrases of the language it is tJicu possible to describe all t])e .formats

allowed in a program. For example, if we introduce the phraseCTYPE] as

PIIRASECtyPE] " integer, real, corriplex

. . ("we ca) define the format for the scalar declarations as

FORMATfSS] = [TYPS]INA}/.E LIST-Jts]

The tss] iiidicates that it is a source statement, -.vhich means it appears on

its own in an Autocode program.

In Atlas Autocode there is a furtlier type or CLASS of format,

the unconditional instructions [Ul], which have the special property that

they niay be preceded by the conditional operators LcoND]

unless CaJND] then.

A list of the phrases and formats of A.tlas Autocode follows.

Note that some phrases (Cs],tcONST],LNAME] and CtEXT]) are not formally defined.

These are defiued by special built-in routines which we will not consider here,

but those interested may refer to the references given below.

c

At, 3

Finally we should point out that jjonie of the definitions oxe not

completely rigid. For example, the aritbrrietic assignment statement is

defiiied as

FuRMA-TEui] = [NAJIWlfAPP] [EXPR]

In the routine which deals uith titis format, tests ai-e «iade to ensure that

the fNA.ME3[APP] does in fact describe a variable, snd is not, for example,

a function, •

References

[3]. Brooker,R,A., Morris,D. and Rohl,J.S. ''Trees and Routines'',

Computer Journal, Vol. 5, No, 1.

[/jJo Brooker,R. A. , ?viacCsll\nn, I.H. , Morris,D, and Rohl, J, S.

''The Coinpilei' Conipiler'' 3i*d Axinual Review of Automatic Programming

(ed, Goodman), porgamon Press,

[expr]

[+1

lEXPR'] .

[operand]

Eapp]

rexpr-list]

= L+'][expr']

= +, -

== +, NIL

= [operand] l.OP] [}• .-IPR ' ] , [oPKliAND]

= [NAME]LAPP],LCuNST],(CEXPR]),1L}';XPR]!, BUT NOT il

([ EXPR-LIST] ), NIL

= [expr][rest of EXPR-JJST]

Ai.4PHRASE

PHRASE

PHRASE

PHRASE

PHRASE

PHRASE

PHRASE

PHHASE

PHRASE

PjiRASE

PHRASE

PHRASE

PjiRASE,

PHRASE

PHRASE

• PHRASE

[REST f)F KXPR-LIST]=[,][EXPR][REST OF EXPR-LIST], NIL

i"op]

Cc:0

[AO]

[qUEIiY' ]

(CR) [pr^£ii|£]

t,']

Ci V1_]

Cacc']

- +, , I, . I NIL

c5;ia, aco, ca, sac

~ ncc +, acc-, acc /, '!££[ »

= ?, NIL

" ill

i.J, NIL

- if,

- acc, i:a, fiuc

PiiHASE [type] = integer, renl, £o3)\ex

PH SE LTYPE'] -

PHRASE [NAME LIST] = [NAME] [REST OF NAME 1,1ST]

PHRASE [REST OF NAME LIST]=4 , ] INAME] LREST OF NAJrlE LIST], NIL

PHRASE [ARRAY LIST] = [N;U/.E LIST]([B0UND PAIR TJ.ST J)[ REST OF ARRAY 1,1ST]

PHilA.SE [REST OF AJ^RAY LAST]--[,][NAME LIST] ( [B-OUND PAIR LIST] )[jr^ST OF ARRAY LIST], NIL

PHRASE lBDUND pair JJST] •- [}^:.]UKD PAIR] [REST OF )30UND PAIR LIST]

PHRASE [REST OF BOUND PAIR LIST]=[,][B'jUND PAIR][REST OF BOUND PAIR LIST], NIL

PHRASE (.BOUND PAIR] -= [EXPR] ; LKXPR]

PiiHASE [ARRAY FN LIST] = [NAME] ( [EXPR-LI