= t s=s Application Program GH20-0367-3
System/360 Continuous System
Modeling Program
Users Manual
Program Number 360A-CX46X
This is an IBM System/360 program for the simulation
of continuous systems. It provides an application-oriented
input language that accepts problems expressed in the form
of either an analog block diagram or a system of ordinary
differential equations. Data input and output are facilitated
by means of application-oriented control statements.
This manual contains a general description of the program,
detailed programming information, and a description Of
the inputs and outputs.
Fourth Edition (October 1969)
This edition, H20-0367-3, is a reprint of H20-0367-2 incorporating TNL's N20-1938 and N20-2039.
It does not obsolete H20-0367-2 as updated by those TNL's.
This edition applies to version 1, Modification Level 2, of System/360 Continuous System Modeling
Program (360A-CX-16X) and to all subsequent versions and modifications until otherwise indicated
in new editions or Technical Newsletters.
Changes are continually made to the specifications herein. Therefore, before using this publication,
consult the latest System/360 SRL Newsletter (N20-0360) for the editions that are applicable and
current.
Copies of this and other IBM publications can be obtained through IBM branch offices.
A form has been provided at the back of this publication for readers' comments. If this form has
been removed, address comments to: IBM Corporation, Technical Publications Department,
1 12 East Post Road, White Plains, N. Y. 10601.
© Copyright International Business Machines Corporation 1967, 1968, 1969
PageofGH20-0367-3, 2
Revised February 26, 1971
By TNL GN20-2329
CONTENTS
Introduction 1
General Description of the Program .... 2
Elements of the System/360 CSMP
Language 5
Numeric Constants 5
Symbolic Names 5
Operators 6
Functions 6
Labels 6
Structure of the Model 15
Initial, Dynamic, and Terminal
Segments 15
Sections — Parallel or Procedural ... 16
Structure Statements 17
Data Statements 19
Control Statements 21
Translation Control Statements ..... 21
Execution Control Statements 24
Output Control Statements 25
User-Defined Functions 28
MACRO Functions 28
PROCEDURE Functions 30
Subprograms 31
Modeling Techniques . 32.2
Sorting 32.2
NOSORT Option 32. 2
Initialization 33
Termination 33
Integration 34
Arbitrary Functions 35
Implicit Functions 35
Tabular Data 37
Run Control 38. 1
Sequential Runs . . 38. 1
Main Program Control ........ 38.2
Data Output 39
Sample Problem 42
Problem Checkout Facilities 45
Diagnostic Messages 46
Methods 53
Integration Techniques 53
Dynamic Storage Allocation 54
Program Restrictions 54
Reserved Words 55
Statement Ordering 55
System Macros 56
Appendix: Index of S/360 CSMP
Functions and Statements 57
Glossary 60
Bibliography 61
INTRODUCTION
The S/360 Continuous System Modeling Program
(S/360 CSMP) is a problem -oriented program de-
signed to facilitate the digital simulation of contin-
uous processes on large-scale digital machines.
The program provides an application-oriented lan-
guage that allows these problems to be prepared
directly and simply from either a block-diagram
representation or a set of ordinary differential
equations. The program includes a basic set of
functional blocks with which the components of a
continuous system may be represented, and accepts
application -oriented statements for defining the
connections between these functional blocks. S/360
CSMP also accepts FORTRAN statements, thereby
allowing the user to readily handle nonlinear and
time-variant problems of considerable complexity.
-Input and output are simplified by means of user-
oriented control statements. A fixed format is
provided for printing (tabular format) and print-
plotting (graphic format) at selected increments of
the independent variable. Through these features
S/360 CSMP permits the user to concentrate upon
the phenomenon being simulated, rather than the
mechanism for implementing the simulation.
Typical applications might be a control engineer' s
study of the effectiveness of various control system
designs, a physiologist's simulation of the cardio-
vascular system, and a mechanical engineer's inves-
tigation of the effects of damping and backlash in a
proposed mechanical device. This program is based
on the Digital Simulation Language (DSL/90).
The publication System/360 Continuous System
Modeling Program, Application Description (H20-
0240-1) provides an introduction to the material in
this manual and is strongly recommended as pre-
liminary reading.
GENERAL DESCRIPTION OF THE PROGRAM
S/360 CSMP is a "continuous system simulator" that
combines the functional block modeling feature of
"digital analog simulators", such as 1130 CSMP,
with a powerful algebraic and logical modeling capa-
bility. Designed for use specifically by the engineer
or scientist, it requires only a minimum knowledge
of computer programming and operation. The input
language enables a user to prepare structure state-
ments describing a physical system, starting from
either a block diagram or a differential equation
representation of that system. Simplicity and flex-
ibility are salient characteristics of this language.
A knowledge of basic FORTRAN is helpful but not
necessary.
The program provides a basic set of 34 functional
blocks (also called functions), plus means for the
user to define functions specially suited to his par-
ticular simulation requirements. Included in the
basic set are such conventional analog computer
components as integrators and relays plus many
special purpose functions like delay time, zero-
order hold, dead space, and limiter functions. This
complement is augmented by the FORTRAN library
functions, including, for example, cosine, and ab-
solute value. Special functions can be defined either
through FORTRAN programming or, more simply,
through a macro capability that permits individual
existing functions to be combined into a larger
functional block. The user is thereby given a high
degree of flexibility for different problem areas.
For example, by properly preparing a set of special
blocks, he can restructure S/360 CSMP into a
problem -oriented language for chemical kinetics,
control system analysis, or biochemistry. In effect,
S/360 CSMP does not have to operate within the
framework of a digital analog simulator language,
but can take on the characteristics of a language
oriented to any particular special purpose field in
continuous system simulation.
Application-oriented input statements are used
to describe the connections between the functional
blocks. S/360 CSMP also accepts FORTRAN state-
ments, thereby allowing the user to readily handle
complex nonlinear and time -variant problems. A
translator converts these structure statements into
a FORTRAN subroutine, which is then compiled and
executed alternately with a selected integration rou-
tine to accomplish the simulation.
Figure 1 shows the general form and application of
the S/360 CSMP functions and structure statements.
A specific example of a structure statement is
Y=INTGRL(IC,X)
which states that the output Y is obtained by inte-
grating X, with the initial condition that Y at time
zero is equal to IC. The name INTGRL defines the
particular DEVICE, that is, the particular function
to be performed on the variable X.
INPUTS (X r X 2 )
DEVICE
(Para-
meters
P r P 2 .....)
OUTPUT (Y)
Block Diagram Representation
Y=f(P r P 2 X 1 ,X 2 ....)
Mathematical Representation
OUTPUT=DEVICE (PARAMS, INPUTS)
Equivalent S/360 CSMP Structure Statement
Figure 1. Illustration of S/360 CSMP functional blocks
Input and output are simplified by means of a free
format for data entry and user-oriented input and
output control statements. With few exceptions,
data and control statements may be entered in any
order and may be intermixed with structure state-
ments . Output options include printing of variables
in standard tabular format, print-plotting in graphic
form, and preparation of a data set for user-pre-
pared plotting programs.
Data statements are used to assign numeric values
to variables that are to remain fixed during a run —
for example, IC in the structure statement above. A
representative data statement is
INCON IC=10.0
where INCON is the label identifying the card as an
initial condition card, IC is the variable to be assigned
a numeric value, and 10. is the value assigned .
Control statements are used to control certain
operations associated with the running of the program,
such as run time, printout, and stacking of jobs. An
example is the output control statement
PRINT Y
where PRINT is a card label specifying that a list of
the variable Y is to be printed.
Two important features of S/360 CSMP are state-
ment sequencing and a choice of integration methods.
With few exceptions, structure statements may be
written in any order and, at the user's option, may
be sorted automatically (or not sorted) by the system
to establish the correct information flow. Centralized
integration is used to ensure that all integrator out-
puts are computed simultaneously at the end of the
iteration cycle. A choice may be made between the
fifth-order Milne predictor-corrector, fourth-order
Runge-Kutta, Simpson's, second -order Adams,
trapezoidal, and rectangular integration methods.
The first two methods allow the integration interval
to be adjusted by the system to meet a specified
error criterion.
An entire S/360 CSMP simulation can be conven-
iently controlled by a sequence of FORTRAN state-
ments performed only at the termination of a simu-
lation run. A user-written FORTRAN program can
test run responses, define run control conditions,
and supervise both input and output information. This
provides a simple and efficient method for handling
the type of iterative computation involved, for ex-
ample, in automatic search procedures for para-
meter optimization.
Another feature is the ability to initialize varia-
bles or parameters — that is, to indicate a group of
structure statements to be executed only once at the
start of the simulation. This feature provides effi-
ciency in executing the problem, since the com-
putations will be made only once and not for each
iteration.
FORTRAN rv (Level E) is used as the source
language for approximately 95% of this application
package; those operations not readily performed in
FORTRAN IV (Level E) are coded as subroutines in
System/360 Assembler Language. All routines
operate under Operating System/360. All calcula-
tions are done in single-precision, floating-point
arithmetic.
The program requires a minimum of 102K bytes
of storage (excluding that required by OS/360), the
Standard Instruction Set, and the Floating-Point
Option. In addition to the I/O units needed by the
Operating System/360 for FORTRAN IV (Level E)
compiling, the program will require three logical
utility units. One of these must be a direct access
storage device (DASD), while the other two may be
portions of the required DASD, or may be portions
of other DASD's or magnetic tape drives.
The problem deck must be preceded and followed
by appropriate OS/360 control cards. Each installa-
tion will have its own procedures for making these
available to the user. A sample set is shown in the
Operator's Manual.
To the user and operator of the system, the
entire run will appear as a single job, even though
it is a multiple-step program. The general systems
chart is shown in Figure 2.
System
Library
System/360
Processor
Problem input data,
run parameter cards,
and FORTRAN state-
ments.
Printed
Output
Values of the
variables requested
via parameter cards,
including graphic
format.
Figure 2. General systems chart
A simple illustration of the program is the set of
structure statements that can be prepared from a
block diagram representation of the system shown in
Figure 3. This system consists of a spring, a mass,
and a damper suspended from a fixed reference posi-
tion. If the mass is displaced from its rest position
and then released, it will oscillate until the energy
is dissipated by the damper. The purpose of a simu-
lation might be to analyze the effect of different spring
constants on the motion of the mass. One possible
simulation diagram for representing this simple
mechanical system is shown in Figure 4. The cor-
responding structure statements are shown in Figure
5. Note that operators are used to indicate the basic
arithmetic relationships and that the INTGRL function
block is used to obtain the variables X and XDOT.
The order of statements is of no consequence, since
S/360 CSMP will automatically sort them to achieve
a proper representation of the parallel physical
system. A similar set of statements could, of
course, have been developed directly from the sys-
tem differential equation.
Spring
k = Spring Constant
Mass
m
Damper
C = Damper
Constant
Displacement X
rest position
Model Equation: X = — (cX + kX)
2
MULTl
X
1 »
z
MX
»
X
»
/
X
;
X
— T*"
®00
X
MULT2
MX +CX + KX = (_ K ) X(0) = 0.0 X(0) = A
Figure 4. Block diagram for solution of
spring, mass, damper problem
Figure 3. Model of a spring, mass
damper system
MX2D0T=MULT1+MULT2
X2DOT=MX2DOT/M
XDOT=INTGRL(0. 0, X2DOT)
MULTl=-C*XDOT
X=INTGRL(A, XDOT)
MULT2=-K*X
Figure 5. Structure statement development from the
block diagram
ELEMENTS OF THE SYSTEM/360 CSMP
LANGUAGE
Page of GH 20-0367-3, -2
Revised February 26, 1971
ByTNLGN20-2329
A system to be simulated is described to the pro-
gram by a series of structure, data, and control
statements. Structure statements describe the func-
tional relationships between the variables of the
model, and, taken together, define the network to be
simulated. Data statements assign numeric values
to the parameters, constants, initial conditions, and
table entries associated with the problem. Control
statements specify options relating to the transla-
tion, execution, and output phases of the S/360 CSMP
program, such as run time, integration interval,
and type of output. The basic elements in the pre-
paration of these three types of statements are nu-
meric constants, symbolic names, operators,
functions, and labels.
NUMERIC CONSTANTS
Constants are unchanging quantities used in their
numeric form in the input statements. Note that the
word "constant" is used in two different ways in this
manual. When describing a language element, it
refers to a series of characters (digits) written in
numeric form. The word is also used as a label in
a Data statement ~ that is, to describe a type of
variable. Context will adequately differentiate be-
tween these meanings.
There are two types of constants: integer and real.
An integer constant is a whole number written with
from one to ten decimal digits without a decimal point,
and cannot contain embedded commas or blanks. An
integer constant may be positive, zero, or negative;
if unsigned, it is assumed to be positive. Its magni-
tude must not be greater than 2147483647 (2 31 -1).
The following are valid integer constants:
.+91
-3468
24691
A real (floating-point) constant is a number written
with from one to seven significant decimal digits
with a decimal point. It may be positive or negative;
if unsigned, it is assumed to be positive. A real
constant optionally may be followed by a decimal
exponent written as the letter E, followed by a
signed or unsigned one- or two-digit integer con-
stant. The decimal exponent E format forms a real
constant that is the product of the real constant
portion times ten raised to the desired power. It
may not contain embedded commas or blanks. The
magnitude of a real number, if followed by an E
decimal exponent, can be or any value from 16 "63
through 16 63 (that is, approximately 10 75 ); other-
wise, it may consist of one through seven decimal
digits. The following are valid real constants:
0.
-97.345
5934.75
+24. 951E9
-83.625E-05
Real constants are restricted to twelve characters
total.
SYMBOLIC NAMES
Symbolic names represent quantities that may
either change during a run or be changed, by the
program, between successive runs of the same
model structure.
A symbolic variable name contains from one to
six alphameric characters ~ that is, numeric
through 9, or alphabetic A through Z. The first
character must be alphabetic. A symbolic name
must not contain embedded blanks or any of the
special characters
/
(
and may not be a word reserved either by S/360
CSMP or FORTRAN IV. These reserved words are
listed under "Methods" in this manual. The follow-
ing are valid variable names:
RATE
SQ915
A41B
All variables and functions that are represented by
symbolic names are normally treated within the simu-
lation as being real — that is , as having floating-
point values. Integer variables and functions must be
specified with a FLXED translation control statement.
Note that this convention differs from FORTRAN,
which automatically treats as an integer any variable
that has as the first character of its name the letter
I, J, K, L, M, or N.
Subject to certain restrictions, symbolic names
may be subscripted to reference arrays and ma-
trices. Note, however, that the symbolic name for
an array comprised of real variables should not
start with the letter I, J, K, L, M, or N. Except
for this, the normal rules of FORTRAN apply: the
subscript must be an integer, or an integer varia-
ble, enclosed in parentheses following the symbolic
name. No special restrictions are imposed by
S/360 CSMP when subscripted quantities are used
within procedural structure — that is, within
NOSORT sections or PROCEDURE functions.
Within parallel, or sorted sections, however, sub-
scripted quantities may appear only on the right-
hand side of equations; the sorting algorithm proc-
esses them as data rather than as output variables.
Single- dimensional arrays are best declared by use
of the STORAGE label. The associated TABLE
PageofGH20-0367-3,-2
Revised February 26, 1971
By TNL GN20-2329
feature permits simple data entry for symbols de-
clared in this way. Matrices must be declared by
use of a FORTRAN DIMENSION statement with a
virgule (/) in cc 1.
OPERATORS
Operators are used, instead of functional blocks,
to indicate the basic arithmetical functions or
relationships. As in FORTRAN, these operators
are:
Symbol Function
+ addition
subtraction
* multiplication
/ division
Symbol Function
**
()
exponentiation
replacement
grouping of
variables and/
or constants
Note that, as in FORTRAN, the equal sign means
"is to be replaced by", rather than "is equal to".
This means that the usual arithmetic usage of the
equal sign is valid, but so too is a FORTRAN state-
ment of the type A=A+1. 0, when used in an unsorted
sequence of statements. If A initially had a value of
2. 0, this statement would give it a value of 3. 0.
As in algebra and FORTRAN, parentheses maybe
used in arithmetic expressions to specify the order
in which the arithmetic operations are to be per-
formed. Expressions within parentheses are always
evaluated first. When parentheses are omitted, or
when an entire arithmetic or functional expression
is enclosed within a single pair of parentheses, the
order in which the operations are performed is as
follows:
Operation
Evaluation of functions
Exponentiation (**)
Multiplication and
division (* and/)
Addition and sub-
traction (+ and -)
Hierarchy
1st (highest)
2nd
3rd
4th (lowest)
Some illustrations of the use of operators to
build structure statements are:
RATE=DIST/TIME
Y=A*X**2+B
A=(B*C)+(D*E)
FUNCTIONS
Finally, there are the functional blocks (functions),
which perform the more complex mathematical op-
erations such as integration, time delay, quantiza-
tion, and limiting. Figure 1 has already illustrated
the basic form and nature of these functions.
The basic S/360 CSMP library includes the stan-
dard functions found in analog computers plus a number
of additional special-purpose functions often encoun-
tered in simulation* problems. Table 1 illustrates this
basic library. The general, canonical form of each
function is shown with inputs indicated by the letter
X, outputs by Y, initial conditions by IC, and param-
eters by P. For the basic S/360 CSMP functions,
all of these are real variables or constants. If
computed rather than specified by data statements,
initial conditions and parameters should be computed
in the INITIAL segment of the model. The DELAY
function deserves special mention since its first
argument, N, must be a literal integer constant;
this tells the translator how many storage locations
should be allocated for its "memory" and cannot be
varied as a parameter. (Details of the internal
coding of these functions are provided in the System
Manual, Y20-0111.)
The functions available in the standard FORTRAN
IV library in the userjs system can also be treated
as functional blocks, supplementing the basic S/360
CSMP library. Illustrations of the most useful
FORTRAN functions are shown in Table 2. Note that,
contrary to normal CSMP usage, several of these
FORTRAN functions use or produce integer variables.
Note also that the user may add any desired func-
tion to the S/360 CSMP library — temporarily for
his personal use , or permanently so as to be con-
veniently shared by other users at the installation.
Functions supplied by the user must be named accord-
ing to the specifications described under "Symbolic
Names"; additionally, if the output of the function is
an integer variable , the name of the function must
be placed on a FDCED translation control statement.
For operators of the same hierarchy, except expo-
nentiation, the component operations of the expres-
sion are performed from left to right. Thus, the
arithmetic expression A/B*C is evaluated as
(A/B)*C. For exponentiation, the evaluation is from
right to left. Thus, the expression A**B**C is
evaluated as A^° ).
LABELS
The first word of S/360 CSMP data and control
statements is a label that identifies to the program
the purpose of the statement. Some statements con-
tain only the label — for example, INITIAL, NOSORT,
and ENDMA C. Others contain a label and appropri-
ate data. For example, to specify the integration
PageofGH2(M)367-3,2
Added February 26, 1971
By TNL GN20-2329
interval and the "finish time" for a run, one would of COMMON and ENDJOB, the program examines
use the TIMER statement as follows: only the first four characters of a label; hence,
INITIAL and INIT, or PARAMETER and PARAM,
TIMER DELT = 0. 025, FINTIM = 450. or PROCEDURE and PROCED are equally accept-
able. Note that for all those statements in which
_, r . , u * * *. * -a -uj- additional data follows the label, the label must be
The format of each statement type is described m c~ nn * n ^A f„~™ +v,«+ ^ tn k„ „+ iL D i. „ kl ,
,,.,,. .... i It ,.,f ,, .. separated from that data by at least one blank
detail later in this manual. With the exception column
6.1
MATHEMATICAL FUNCTIONS
GENERAL FORM
FUNCTION
Y = INTGRL (IC, X)
Y (0) = IC
INTEGRATOR
Y = /qX dt + IC
EQUIVALENT LAPLACE TRANSFORM: j
Y = DERIV (IC, X)
X (t =0) = IC
DERIVATIVE
Y-4X
EQUIVALENT LAPLACE TRANSFORM: S
Y = DELAY (N, P, X)
P = DELAY TIME
N = NUMBER OF POINTS SAMPLED
IN INTERVAL P (INTEGER CONSTANT)
DEAD TIME (DELAY)
Y (t) = X (t - P) t>P
Y = t<P
EQUIVALENT LAPLACE TRANSFORM: e" PS
Y = ZHOLD (X p X 2 )
ZERO-ORDER HOLD
Y = X 2 X x >
Y = LAST OUTPUT X,<0
Y (0) = l
EQUIVALENT LAPLACE TRANSFORM:
Y = IMPL (IC, P, FOFY)
IC = FIRST GUESS
P = ERROR BOUND
FOFY = OUTPUT NAME OF LAST STATE-
MENT IN ALGEBRAIC LOOP
DEFINITION
IMPLICIT FUNCTION
Y = FUNCT (Y)
IY-FUNCT (Y)|<P|Y|
Table 1. Library of S/360 CSMP functional blocks
SYSTEM MACROS
GENERAL FORM
FUNCTION
Y=M0D1NT (IC, X r X 2 , Xj)
MODE -CONTROLLED INTEGRATOR
Y=/ t X 3 dt+ IC X^O, anyX 2
Y = IC X^ 0, X 2 >0
Y = LAST OUTPUT X^ 0, X 2 <0
Y = REALPL (IC, P, X)
Y (0) = IC
1ST ORDER LAG (REAL POLE)
PY + Y = X
EQUIVALENT LAPLACE TRANSFORM: ^^
Y = LEDLAG (P y ? r X)
LEAD -LAG
P 2 Y + Y = P 1 X + X
EQUIVALENT LAPLACE TRANSFORM:
PjS + 1
P 2 S + 1
Y =CMPXPL(IC r IC 2 , P P 2 , X)
Y (0) = \C
Y (0) = IC 2
2ND ORDER LAG (COMPLEX POLE)
Y + 2P 1 P 2 Y + P 2 Y = X
EQUIVALENT LAPLACE TRANSFORM:
1
S 2 + 2P 1 P 2 S + P 2
Table 1. (Continued)
SWITCHING FUNCTIONS
GENERAL FORM
FUNCTION
Y = FCNSW (X r X 2 , X y X 4 )
FUNCTION SWITCH
Y = X 2 Xj <
Y = X 3 X x =
Y = X 4 X l >
Y = INSW (X r X 2 , X 3 )
INPUT SWITCH (RELAY)
Y = X 2 Xj <
Y = X 3 X 1 >
Y r Y 2 = OUTSW (X r X 2 )
OUTPUT SWITCH
Y 1 = X 2 , Y 2 = X x <
Y l - 0, Y 2 - X 2 X x >
Y = COM PAR (X r X 2 )
COMPARATOR
Y = Xj<X 2
Y = 1 X X >X 2
Y = RST (X r X 2 , X 3 )
RESEHABLE FLIP-FLOP
Y =
Y-l
Y =
Y = l X^O,
Y = X 2 <0, <
Y = l
x x >o
x 2 >o, x x <o
' V^n-r 1
x 3 >o, Vl = o
V-°' Y n-r°
<
Table 1. (Continued)
FUNCTION GENERATORS
GENERAL FORM
FUNCTION
Y = AFGEN (FUNCT, X)
ARBITRARY FUNCTION GENERATOR
(LINEAR INTERPOLATION)
Y = FUNCT (X)
Y = NLFGEN (FUNCT, X)
ARBITRARY FUNCTION GENERATOR
(QUADRATIC INTERPOLATION)
Y - FUNCT (X)
V x<_x n
Y = LIMIT (P r P 2 , X)
LIMITER
Y = P 1
Y = P 2
Y - X
x<p 2
x>p 2
p 2 <x<p 2
, P 1
► Y
* A
Y - QNTZR (P, X)
QUANTIZER
Y = kP (k ■
k
■ l/2)P<X<(k + 1/2) P
■ 0, ±1, ±2, ±3...
Y'
r^.x
_j— '
' X
Y - DEADS P (P r P X)
DEAD SPACE
Y -
■ Y - X - P 2
Y ■ X - Pj
P <X<P
x>p 2
x<p x
pi
Y
p 2/ ,..
45-V
r X
Y = HSTRSS(IC, P r P 2 , X)
Y (0) - IC
HYSTERESIS LOOP
Y - X - P 2
Y-X-Pj
OTHERWISE
(X 'Vl )>0AND
Y n ,<(X - PJ
n-1 2
(X-X jfcOAND
Vi* x - p i )
Y- LAST OUTPUT
i
/
f Y
/
p 2y<45-
/ — """
Y * A
•
Table 1. (Continued)
10
SIGNAL SOURCES
GENERAL FORM
FUNCTION
Y - STEP (P)
STEP FUNCTION
Y=0
Y-l
t<P
UP
!P
Y = RAMP (P)
RAMP FUNCTION
Y=0
Y = t - P
t<P
t>P
>A*- , t
Y = IMPULS (P r P 2 )
IMPULSE GENERATOR
Y=0
Y = 1
Y=0
t<P
(t - Pj) - kP 2
(t - Pj) i« kP 2
k = 0, 1, 2, 3.
H^h
Pi
Y = PULSE (P, X) '
P = MINIMUM PULSE WIDTH
PULSE GENERATOR (WITH X>0
AS TRIGGER)
Y"l
Y=0
T k <t<(T k + P) or
X>0
OTHERWISE
i p r
■+ t
T k = TIME OF TRIGGER
Y = SINE (P 1# P 2 , P 3 )
? x = DELAY
P 2 - FREQUENCY (RADIANS PER UNIT TIME)
P 3 = PHASE SHIFT IN RADIANS
TRIGONOMETRIC SINE WAVE WITH
DELAY, FREQUENCY AND PHASE
PARAMETERS
Y=0
t<P,
Y = SIN(P 2 (t-P 1 ) + P 3 ) \>? l
P /P
3 ,r 2
■2tf/P,
Y - GAUSS (P r P 2 , P 3 )
P^ANYODD INTEGER
P 2 - MEAN
P. ■ STANDARD DEVIATION
NOISE (RANDOM NUMBER) GENERATOR
WITH NORMAL DISTRIBUTION
NORMAL DISTRIBUTION OF
VARIABLE Y
p(Y) ■ PROBABILITY DENSITY FUNCTION
Y = RNDGEN (P)
P - ANY ODD INTEGER
NOISE (RANDOM NUMBER) GENERATOR
WITH UNIFORM DISTRIBUTION
UNIFORM DISTRIBUTION OF
VARIABLE Y
p(Y) ■ PROBABILITY DENSITY FUNCTION
p(Y)
Table 1. (Continued)
11
LOGIC FUNCTIONS
GENERAL FORM
FUNCTION
Y = AND (X r X 2 )
AND
Y ■ 1 XfO, X 2 >0
Y = OTHERWISE
Y = NAND (X r X 2 )
NOT AND
Y = XjX), X 2 >0
Y « 1 OTHERWISE
Y = IOR (X r X 2 )
INCLUSIVE OR
Y = X^O, X 2 <0
Y = 1 OTHERWISE
Y = NOR (X r X 2 )
NOT OR
Y = 1 X^O, X 2 <0
Y = OTHERWISE
Y = EOR (X r X 2 )
EXCLUSIVE OR
Y - 1 X^O, X 2 >0
Y = 1 X^O, X 2 <0
Y = OTHERWISE
Y = NOT (X)
NOT
Y = 1 X<0
Y = X>0
Y = EQUIV (X r X 2 )
EQUIVALENT
Y = 1 X^O, X 2 <0
Y = 1 Xf 0, X 2 >0
Y = OTHERWISE
Table 1. (Continued)
12
GENERAL FORM
FUNCTION
Y = EXP (X)
EXPONENTIAL
Y=e X
Y = ALOG (X)
NATURAL LO GO RITHM
Y = LN (X)
Y=ALOG10(X)
COMMON LOGORITHM
Y = LOG 1Q (X)
Y = ATAN (X)
ARCTANGENT
Y =ARCTAN(X)
Y -SIN (X)
TRIGONOMETRIC SINE
Y = SIN(X)
Y = COS (X)
TRIGONOMETRIC COSINE
Y = COS (X)
Y = SQRT (X)
SQUARE ROOT
Y=x l/2
Y = TANH (X)
HYPERBOLIC TANGENT
Y = TANH (X)
Y=ABS(X)
ABSOLUTE VALUE
(REAL ARGUMENT AND
OUTPUT)
Y=|X|
Y = IABS (X)
ABSOLUTE VALUE
(INTEGER ARGUMENT
AND OUTPUT)
Y-IXl
Table 2. FORTRAN functions
13
GENERAL FORM
FUNCTION
Y = AMAXO (X r X 2 ... X n )
LARGEST VALUE
(INTEGER ARGUMENTS AND
REAL OUTPUT)
Y = MAX (X r X 2 ... X n )
Y = AMAX1 IX,, X ...X J
12 n
LARGEST VALUE
(REAL ARGUMENTS AND
OUTPUT)
Y = MAX IX, , X ...X )
l 2 n
Y = MAXO (X^ X 2 ...X )
LARGEST VALUE
(INTEGER ARGUMENTS AND
OUTPUT)
Y = MAX (X r X 2 ...X )
Y = MAX1 (X r X 2 ...X )
LARGEST VALUE
(REAL ARGUMENTS AND
INTEGER OUTPUT)
Y = MAX IX.., X ...X )
12 n
Y = AMINO IX,, X ...X )
1 2 n
SMALLEST VALUE
(INTEGER ARGUMENTS AND
REAL OUTPUT)
Y = MIN IX,, X ...X )
i i n
Y ■ AMIN1 (X r X 2 ...X )
SMALLEST VALUE
(REAL ARGUMENTS AND
OUTPUT)
Y = MIN IX,, X 9 ...X)
i L n
Y = MINO IX,, X ...X )
12 n
SMALLEST VALUE
(INTEGER ARGUMENTS
AND OUTPUT)
Y = MIN (X,, X 9 ...X)
l L n
Y = MINI IX,, X ...X )
i c n
SMALLEST VALUE
(REAL ARGUMENTS AND
INTEGER OUTPUT)
Y = MIN (X 1 , X 2 ...X n )
Table 2. (Continued)
14
STRUCTURE OF THE MODEL
The nucleus of a "continuous system simulator" is,
of course, a computer mechanism for solving the
differential equations that represent the dynamics
of the model. Usually, however, there are also
computations that must be performed before each
run, and sometimes, computations after each run.
For example, certain parameters of a model might
be considered basic; secondary parameters and
initial conditions are often expressed as functions
of these basic parameters. Evaluation of these
functions is desired just once per run. Frequently,
too, one needs to perform some terminal evaluation
of each run; in a design study, for example, one
might compute some "figure-of-merit" for each
run of a parameter search.
To satisfy these requirements, the general S/360
CSMP formulation of a model is divided into three
segments — Initial, Dynamic, and Terminal — that
describe the computations to be performed before,
during, and after each simulation run. These
represent the highest level of the structural hier-
archy. Each of the segments may comprise one
or more sections ; these, in turn, contain the struc-
ture statements that specify model dynamics and
associated computations. The sections represent
rational groupings of structure statements and may
be processed as either parallel or procedural
entities as appropriate. The overall structural
hierarchy is illustrated in Figure 6.
Statements
Statements
Statements
Statements
Statements
Statements
Statements
Statements
Statements
Segment '
INITIAL
DYNAMIC
TERMINAL
Section
Section
Section
SORT
NOSORT
Figure 6. Structural hierarchy of the System/360 CSMP language
INITIAL, DYNAMIC, AND TERMINAL SEGMENTS
The Initial segment is intended exclusively for com-
putation of initial condition values and those param-
eters that the user prefers to express in terms of
more basic parameters. Thus, if a model repeatedly
makes use of the cross-sectional area of a cylin-
drical member, the Initial segment might contain
the structure statement:
AREA = 3.1416*(R**2)
with radius R, which might be considered the more
basic parameter, specified on a data card as follows:
PARAMETER R=7. 5
Many simple simulations do not require this feature.
The Initial segment is, therefore, optional.
The Dynamic segment is normally the most ex-
tensive in the model. It includes the complete
description of the system dynamics, together with
any other computations desired during the run.
Functionally, the Dynamic segment is analogous to
the block diagram representation or to the ordinary
differential equation representation of system dy-
namics. The structure statements within this
segment are generally a mixture of S/360 CSMP
and FORTRAN statements; the following might be
considered representative:
DRAG = 0. 5*RHO*S*CD*(V**2)
VX=INTGRL(VZERO, (THRUST-DRAG)/MASS)
For most models, the Dynamic segment consists of
a single section. For more complicated systems,
however, it is often desirable, and sometimes re-
quired, that it be divided into several sections. In
modeling an industrial process, for example, it
might be desirable to separate the various unit
process models into separate sections simply be-
cause the physical units are distinct.
The Terminal segment is used for those compu-
tations desired after completion of each run. This
will often be a simple calculation based on the final
value of one or more model variables, but more
powerful use of this segment is readily possible.
For example, one might incorporate an optimization
algorithm that will modify the values of critical
system parameters. If this section includes the
statement
CALL RERUN
S/360 CSMP will automatically be recycled through
the simulation using the newly set parameters. The
section "Sample Problem" in this manual illustrates
use of this rerun feature for solution of a simple
two-point boundary value problem. Many simula-
tions require no terminal computations. The Ter-
minal segment is therefore optional; it is omitted
merely by deletion of the TERMINAL label.
Segmentation, the explicit division of the model
into computations to be performed before, during,
and after each run, is provided by the control
statements: INITIAL, DYNAMIC, TERMINAL, and
END. In the general case, as illustrated in Figure
7, INITIAL is the first statement of the specifica-
tion of model structure. (It is not normally the
first statement of the composite S/360 CSMP data
deck, since certain other translation control state-
ments and all MACRO definitions must be placed
before any structure statements. This is discussed
15
more fully under "Translation Control Statements".)
The DYNAMIC statement separates the Initial seg-
ment from the Dynamic segment. In similar man-
ner, the TERMINAL statement separates the Dy-
namic segment from the first statement of the
TerminaLsegment. The first occurrence of the
END (or CONTINUE) statement completes the spec-
ification of model structure.
INITIAL
DYNAMIC
Initial Segment
Dynamic Segment
Terminal Segment
TERMINAL ,
END
Figure 7. Structural segmentation
The Dynamic segment is required; the Initial and
Terminal segments are optional. If an Initial seg-
ment is used, it must precede the Dynamic segment.
The Terminal segment, if used, must follow the
Dynamic segment. An Initial segment should always
be preceded by an INITIAL statement; the DYNAMIC
statement must be used to separate the Initial and
Dynamic segments. The Terminal segment, when
used, must be separated from the Dynamic segment
by a TERMINAL statement. The model may con-
sist of the Dynamic segment alone, and in this case
none of these labels is required.
Most simulation studies require only a simple
superstructure such as illustrated in Figure 7,
which shows use of all three segments, but not
further divided into sections. Sectioning, the
grouping of structure statements within a segment,
is usually required only for rather sophisticated
simulations. Since the model illustrated in Figure
7 does not include SORT or NOSORT labels, the
standard options concerning parallel and procedural
structure are automatically obtained. S/360 CSMP,
in this case, assumes that the Initial and Dynamic
segments represent parallel structure while the
Terminal segment represents procedural structure.
Thus, all the structure statements within the Initial
segment will be automatically sorted by the program.
Those within the Dynamic segment will also be
sorted, but independently, of course, from those
in the Initial segment. In contrast, all structure
statements within the Terminal segment are as-
sumed to be procedural and already in the desired
computational order; the program thereby does not
rearrange the order of these statements.
These standard options may be easily overridden
by use of the labels SORT and NOSORT. For ex-
ample, one might want the entire Dynamic segment
to represent procedural structure, thus permitting
unrestricted use of FORTRAN conditional logic and
branching. This option is achieved merely by using
the label NOSORT immediately after the label
DYNAMIC. The same reasoning applies to the
Initial segment. The entire Terminal segment
could similarly be made parallel structure by
inserting the label SORT immediately after the
TERMINAL label.
SECTIONS — PARALLEL OR PROCEDURAL
A section is a group of structural statements. If a
segment contains only a single section, then sec-
tioning sometimes is not explicitly indicated. When
desired, sectioning is obtained through use of the
translation control statements SORT and NOSORT.
The former declares that the structure within the
section is to be considered parallel; that is, the
translator should arrange the statements in proper
computational sequence to achieve the same effect
as would be obtained by a parallel computer. Thus,
the user need not be concerned with the computa-
tional sequence when modeling ordinary dynamic
effects, since, in nature, most phenomena do exist
and operate "in parallel". The sections are ter-
minated by the occurrence of the next section or
segment, that is, by the next SORT or NOSORT
within the segment or by the DYNAMIC or
TERMINAL translation statement.
The NOSORT statement declares that all the
subsequent structure statements within the section
are to be considered procedural. Thus, in gener-
ating the derivative- subroutine UPDATE, the trans-
lator inserts the structure statements of a NOSORT
section without changing their sequence. Full use
of FORTRAN, including conditional branching and
input/output, is thereby permissible within a
NOSORT section. The sorting algorithm ignores
the statements in such a section and responsibility
for the computational sequence rests with the user.
It should be noted that the translator does not
change the order of the sections. For example, if
the DYNAMIC segment of a model contains three
sections ~ SORT, NOSORT, SORT, in that order
(see Figure 8) — the corresponding portion of the
derivative subroutine UPDATE will have three
sections. In the first and third, the computational
sequence will have been rearranged to satisfy the
sorting algorithm; the sequence of those statements
corresponding to the NOSORT section will be un-
changed. The rationale for sectioning a model
rests with the user. This feature of S/360 CSMP
facilitates sophisticated modeling, but the inexperi-
enced user should defer its use until needed. (See
"Modeling Techniques" for a more thorough discus-
sion of this topic. )
16
INITIAL
NOSORT
DYNAMIC
Unsorted, procedural section
inputs. The latter may be arithmetic expressions,
previously computed functional block outputs, vari-
ables, constants, or references to other functions.
Initial conditions and parameters may be variable
names or constants. Structure statements are in
FORTRAN equation form with the output variables on
the left of the equal sign and an expression on the
right. The expression may be a single constant or
variable; an output from a function or subroutine;
or a combination of constants, variables, and func-
tions connected by operators. Examples of struc-
ture statements are:
NOSORT
Sorted, parallel section
Unsorted, procedural section
SORT
Sorted, parallel section
TERMINAL
Unsorted, procedural section
END
Figure 8. Illustration of complex sectioning
STRUCTURE STATEMENTS
Structure statements define the network or model to
be simulated by describing the functional relation-
ships between the variables of the model. They also
can be viewed as connectors between the S/360 CSMP
functional blocks, which are identified by inputs, out-
puts, and function type. Various uses of the same
function are made unique by assigning different out-
put variable names for each use.
The general form of a structure statement
using a S/360 CSMP function has been shown in
Figure 1; the S/360 CSMP library of functions
has been listed in Tables 1 and 2. Specification
of a typical function involves the use of output -
variable names, initial conditions, parameters, and
Y=A*X+B
ROOT=SQRT(X**2+Y**2)
Z=PULSE(PAR, XDOT)
XDOT=INTGRL(2. 0, X**2+R/D)
In the above examples SQRT, PULSE, and INTGRL
are functional block names. The outputs are Y,
ROOT, Z, and XDOT.
Note that user-defined MACROS and
PROCEDURES also involve structure statements.
MACROs are defined before the first actual model
statements ~ that is, before the INITIAL state-
ment. The MACRO definition is not considered
part of the model but, rather, a preliminary exten-
sion of the MACRO library. A MACRO is later
used or invoked within the model by a simple
structure statement that must agree exactly with
the canonical form prescribed in its MACRO defi-
nition. A PROCEDURE is conceptually a single
functional element, but its definition usually re-
quires several structure statements. (Both of
these elements are described more fully under
"Modeling Techniques".)
An alternative "specification" form of the
INTGRL statement is available for special applica-
tions involving arrays of integrators or integrators
within subprograms. Its use should be deferred
until one is familar with the more commonly used
features of the language. The basic form of this
usage is as follows:
Zl =r INTGRL (ZIC1, DZDT1, nn )
where nn represents a literal integer constant
corresponding to the number of elements in the
integrator array. Note that this "specification"
form requires three arguments, whereas the
normal use of the INTGRL function requires only
two. This special form does not of itself provide
integration; instead, it specifies to the S/360 CSMP
translator that the total number of integrators indi-
cated in the DYNAMIC segment of the model should
be augmented by the quantity nn. The symbols Zl,
ZIC1, and DZDT1 are usually dummies, equiva-
lenced to the first elements of corresponding vector
arrays Z, ZIC, and DZDT.
17
PageofGH20-0367-3,-2
Revised February 26, 1971
By TNL GN20-2329
Structure statements are translated and placed
into a FORTRAN subroutine called UPDATE, which
is executed at each iteration cycle. In general,
structure statements may be written in any order and
intermixed freely with data and control statements.
The system establishes the correct sequence of com-
putation, based on the inputs and outputs of each
statement. A statement is considered to be in se-
quence when all of its inputs have been processed
previously in the current iteration cycle.
Structure statements are subject to the following
general rules:
1. The operators +, -, *, /, and ** may not
appear consecutively; for example, A + -B is in
error, but A + (-B) will work correctly.
2. Function arguments in an expression must be
separated by commas and enclosed in parentheses;
for example, Z=PULSE(PAR,XDOT) should not be
written as Z=PULSE, PAR, XDOT or as
Z=PULSE (PAR) (XDOT).
3. Any expression may be enclosed in paren-
theses, and expressions may be connected by
arithmetic operators — for example,
Y=(A+B)-(C+D).
4. All variable names and constants, including
statement numbers, must be separated from each
other .by blanks, operators, or special characters,
as appropriate. For example, Y=AB is not the same
as Y=A*B, but rather AB would be a variable in
itself.
5. Expressions may be nested, that is, contained
one within another. They may also appear in combi-
nation on the same level. However, the user should
be aware that errors can often be made in the num-
ber of parentheses and commas. The only saving
with nesting is in the number of cards punched; there
is no saving in run time or storage. In brief, nesting
should generally be avoided by the beginning user.
6. If an INTGRL function is included in an ex-
pression, it must be the rightmost part of that ex-
pression; for example, Z=Y + INTGRL (IC, X) is
correct, but Z=INTGRL (IC, X) + Y is not correct.
7. The initial condition of an INTGRL function
may not be an expression. If a parameter, it should
be specified by an INCON data statement. If a vari-
able, it must be computed in the INITIAL segment
of the model.
8. The output of the INTGRL function may not be
a subscripted variable.
9. The INTGRL function may not be used directly
as the argument of any multiple-output function or
MACRO.
10. No output of a multiple-output function may be
a subscripted variable.
11. Certain names are reserved for system use
and may not be used. A list of these is given under
"Methods" in this manual.
12. With two exceptions, a statement may be con-
tinued on as many as eight cards, for a total of nine
cards. Any card concluded with three consecutive
decimal points is considered to be followed by a
continuation card. Cards should not be continued in
the middle of variable names or constants. The
first card of a MACRO definition or MACRO use may
be continued for a total of only four cards. Structure
statement cards within a MACRO definition may not
be continued.
13. An asterisk in cc 1 denotes a comments card.
Comments cards can be used to insert appropriate
reminders or explanations in the sequence of state-
ments. The card will be printed with the input and
then ignored.
14. Columns 73 - 80 are not processed by S/360
CSMP and may be used for identification.
15. Cards with a / (slash — or, properly,
virgule) in cc 1 are not processed, but the / is re-
moved and the card is transferred, as is, to the
UPDATE subroutine. A maximum of ten such cards
can be processed. This additional feature can be
used by those familiar with FORTRAN to insert
FORTRAN specification statements into the problem
definition. Continuation cards for statements with
a / in cc 1 must be in the usual FORTRAN sense
(that is, with a nonzero cc 6); these cards must also
contain a / in cc 1. All / cards appear at the be-
ginning of the UPDATE subroutine. Note that two
S/360 CSMP variables cannot be EQUIVALENCEd.
16. Blank cards can be used freely to space the
input listing.
18
DATA STATEMENTS
Data statements are used to assign numeric values
to the parameters, constants, initial conditions, and
table entries associated with the model. They can be
used to assign numeric values to those variables
that are to be fixed during a given run. The advan-
tage of assigning variable names and using data
statements to specify numeric values is that the
latter can be changed, automatically, between
successive runs of the same model structure. An
example of a data statement is:
PARAMETER PAR1=2. 97, RATE=550.
where PARAMETER is the label identifying the card
as a parameter card, PARI and RATE are the var-
iables to be assigned values, and 2. 97 and 550.0
are, respectively, the values assigned. The format
for each assignment is variable name, equal sign,
value to be assigned, and a comma if additional
assignments follow. At least one blank must follow
any card label — in this case, PARAMETER. Each
different type of data statement is identified by a
different card label punched into the card. Data
statements may appear in any order and may be
intermixed with structure statements.
Examples of each type of data statement are
shown in Table 3. They are used in the following
ways:
1. PARAMETER, INCON, and CONSTANT
PARAMETER, INCON, and CONSTANT
cards are used to assign values to variable names
used as parameters, initial conditions, and/or
constants. The three types may be used inter-
changeably. The value of the specified variable is
set to the corresponding real or integer constant.
Any number of variables may appear on a card or
on continuationcards. In data statements, the
variable name must be on the left of the equal sign.
The name must conform to the specifications for
variable names, and the numeric value must con-
form to those for constants. Blanks are not con-
sidered. A comma following a numeric value
permits another assignment. A sequence of simu-
lation runs may be designated by enclosing several
values of the variable inside parentheses. For
example, withX=(5.0, 5.5, 6.0, 6.5), four simu-
lation runs will be made. X will be 5. in the first
run, 5. 5 in the second, 6. in the third, and 6. 5
in the fourth. If increments of the variable are of
equal size as in the example, the specification
could be X = (5.0, 3*0.5). Only one multiple value
parameter may be used for each sequence of runs;
the sequence should be terminated by means of an
END card. A sequence of simulation runs may also
be specified by designating both individual parameter
values and increments. For example, if X = (4.9,
5.0, 3*0.5, 7.2, 8.0, 4*0.2), the multiple value
parameter, X, will sequence through eleven simula-
tion runs. The maximum number of runs in any
sequence is fifty.
PARAMETER
CONSTANT
INCON
FUNCTION
OVERLAY
TABLE
PARI = 4.98, X=(5.0, 5.5, 3*2.0)
CON7 = 17.95, VEL = 8.7E5
IC = 9.92, AA = -1.2, AB = 1.79E -3
FIOFX = (45., 898.0), (48.7, 917.3), ..
F20FX = 17.3, 0.3, 17.9, 0.4, ...
PRM(3) = 3.91, PARI (1-7) = 4.98,6*5.9
Table 3. Data statements
2. FUNCTION
This statement is used for specification of
pairs of x, y coordinates for use by the function
generator elements, AFGEN and NLFGEN. AFGEN
(arbitrary function generator) and NLFGEN (non-
linear function generator) are used for simulating
those portions of a model wherein some character-
istic, Y = f(X), is available in tabular or graphic
form versus the argument X. The values are con-
verted and reserved in a table to be referenced by
use of the name given it. The first value, and
alternating values thereafter, are those of the in-
dependent variable and must be presented in order
of algebraically increasing values. Increments
may be of unequal size. Each of these must be
followed by its corresponding coordinate value. The
x,y pairs may, if desired, be enclosed within paren-
theses. A comma is required between each value
but the parentheses are optional. This list of values
may extend to continuation cards. There is no
specific restriction on the number of function gen-
erators in a simulation or the number of points per
function, since they are placed in simulator data
storage (see "Program Restrictions").
3. OVERLAY
This statement permits modification of a
previously specified table of x, y coordinates used
with either an AFGEN or NLFGEN function gen-
erator element. The particular table is identified
by using the same function name as first used with
the FUNCTION statement. This feature can be
used only if the overlaying table does not contain
more x, y pairs than did the original specification.
4. TABLE
This feature allows blocks of data to be han-
dled and transmitted more conveniently. Table values
are converted and substituted for the current values
of the corresponding dimensioned variables accord-
ing to the specified index or consecutive indices.
The form K*n causes K consecutive entries of the
value n. A symbolic name for the table must ap-
pear on a STORAGE translation control statement.
A complete description of the use of this feature is
given under "Tabular Data" in this manual.
19
Data statements must be prepared in the follow-
ing format:
1. Each data type must be identified by its spe-
cific label, such as PARAMETER, INCON, or
FUNCTION. Labels do not have to start in cc 1,
but must be followed by at least one blank.
2. Any card concluded with three consecutive
decimal points is considered to be followed by a
continuation card. A data statement may be con-
tinued on as many cards as necessary. Cards may
not be continued in the middle of variable names or
constants.
3. Alphabetic and numeric data may appear any-
where on the data card (or on a continuation card)
following the label that specified the type of data;
that is, data statements are free form, like the
structure statements.
4. Columns 73-80 are not processed by S/360
CSMP and may be used for sequencing or identifi-
cation.
5. The required format for PARAMETER,
INCON, and CONSTANT cards is a variable name,
followed by an equal sign, followed by a numeric.
The numeric will be converted to a real or integer
constant and treated as the current value of the
preceding variable. Numerics may be integers or
real numbers; the latter are identified by a decimal
point and follow the rules for real constants. A
minus sign must precede a negative number.
20
CONTROL STATEMENTS
These statements are used to specify certain opera-
tions associated with the translation, execution, and
output segments of the program. Examples are to
specify a certain variable as an integer instead of a
real (floating-point) number, to specify the finish
time for the run, or to specify the names of the
variables to be printed. The control statements may
be changed as readily as the data statements. Most
of the control statements may appear in any order
and may be intermixed with structure and data state-
ments.
Control statements are, in general, "free form"
and follow the same format rules as data statements.
The only exceptions are COMMON, COMMON MEM,
ENDDATA, END JOB, and ENDJOB STACK; these
must begin in cc 1.
TRANSLATION CONTROL STATEMENTS
Translation control statements specify how the
structure and data statements are to be translated.
Each of the different types of translation control
statements is identified by a "different label. Ex-
amples of each type are shown in Table 4. Recom-
mended practice is to order the statements such
that RENAME, FIXED, MEMORY, HISTORY, and
STORAGE occur, when appropriate, before MACRO
definitions. MACRO definitions must be entered
before any structure statements.
The various statements are used as follows:
1. RENAME
By means of this card, certain reserved names can
be altered if they do not adequately describe the
variables for a specific problem. The substitute
names appear on all output and should be used in the
user's structure statements. The six reserved
names that may be changed are TIME, DELT,
DELMIN, FINTIM, PRDEL, and OUTDEL. Suc-
cessive renamings on the same card must be sep-
arated by a comma. At least one blank must follow
the card label, RENAME. No continuation cards
(...) may be used with the RENAME card; however,
multiple RENAME cards may be used if needed. If
there is more than one substitute name for a re-
served name, the last substitute name given the
reserved name will govern. RENAME cards must
appear before the TIMER card.
2. FIXED
This allows the user to declare the listed variables
as being fixed-point numbers (integers), instead of
real (floating-point) numbers, within the translated
program. The variables can then, and only then, be
used as integers in S/360 CSMP structure and/or
FORTRAN statements. FORTRAN rules for fixed-
point operations apply to computations using these
variables. In addition, names of integer FORTRAN
TIME = DISP, DELT = DELTX
K, COUNT, NUMBER
RHO(9), PH 1(3), GADGET
PAR1(4), PAR7(13)
IC(6) , PARAMS(30)
XI , X2 = FCN(IN1 , IN2, IN3)
X,Y = FUNCT(A, B, X)
RENAME
FIXED
MEMORY
HISTORY
STORAGE
DECK
MACRO
ENDMAC
INITIAL
DYNAMIC
TERMINAL
END
CONTINUE
SORT
NOSORT
PROCEDURE"
ENDPRO
STOP
ENDJOB
ENDJOB STACK
COMMON
COMMON MEM
DATA
ENDDATA
Table 4. Translation control statements
functions, beginning with I, J, K, L, M, and N,
used in structure statements must appear on a
FIXED translation control card.
3. MEMORY
This card is required when the user defines his own
MEMORY functions. It must be used to notify the
translator that the user-defined functional blocks
named on the card are memory functions and, there-
fore, require special handling. A memory function
is one in which the output depends only on past values
of the input and output. The number within the paren-
theses specifies the number of storage locations needed
to save the total number of past inputs and outputs
that influence the current output. This number of
locations is required each time the function is used
in a simulation. The sorting algorithm also re-
quires the identity of all memory functions. Since
the output of a memory functional block at any time
is independent of the input variable at that instant,
such functions can initiate a computational sequence.
A MEMORY translation control card must appear
before the first reference to the function.
21
A memory element is sometimes implemented by
a PROCEDURE which itself may be within a MACRO
definition. For proper sorting the translator must
be informed that it is a memory element, but the
PROCEDURE does not require assignment of addi-
tional storage. For such cases, the name of the
PROCEDURE must be entered on a MEMORY
statement without the set of parentheses.
4. HISTORY
This card is required when the user defines his own
HISTORY functions. It must be used to notify the
translator that the user-defined functional blocks
named on the card are history functions and, there-
fore, require special handling. A history function
is one in which the output depends on both past values
of the input and output and the present value of the
input. As in the MEMORY functions, the number
within the parentheses specifies the number of stor-
age locations required by the function each time it
is used within the structure statements. A HISTORY
translation control card must appear before the first
reference to the function.
5. STORAGE
This feature allows the user to specify that certain
variable names, which appear on the card, are sub-
scripted. The number within parentheses must be
the maximum number of storage locations necessary
to contain data for the corresponding variable. Data
is entered into these areas by use of the TABLE
data statement.
6. DECK
This option permits the user to request that a
translated deck be punched for the simulation run;
included are the UPDATE and user-supplied sub-
programs, literals of the symbol table used in the
execution phase, and all data, execution, and output
control statements. The translated deck can be
compiled and executed using a FORTRAN compile-
load-and-go procedure, bypassing the translation
phase of S/36Q CSMP for subsequent runs. The
expert user-may even wish to introduce minor
modifications directly in the translated deck.
The cards containing the literals of the symbol
table and the various data and control statements
must be prepared as a separate data set to be read
at execution time. An object deck can be obtained
by compiling the translated deck, and can be used
with the aforementioned data set. An illustration
of the use of this object deck is given in the System
Manual (Y20-0111).
If a model is known to be in final form, so that no
changes will be made in the translated FORTRAN
program, an even more efficient method is available.
If the label DECK SYMBOLS is used, and the OS/360
control cards are modified as described in the Oper-
ator's Manual (H20-0368-2), the execution phase
load module as well as the corresponding symbol
table for the model will be stored under unique data
set names. Subsequent simulation runs may
thereby be executed without again performing trans-
lation, compilation or link editing.
7. MACRO
ENDMAC
These labels are used to identify a group of state-
ments that define a MACRO. This feature allows
the user to build larger functional blocks from the
basic S/360 CSMP and FORTRAN functions. Once
defined, a MACRO can be used any number of times
in the model, just like any other function. A full
discussion of this feature is given under "Modeling
Techniques". MACRO block definitions must be
placed in the deck before any structure statements,
including any in an initialization section.
8. INITIAL
This label identifies the beginning of the INITIAL
segment of the model; the segment is terminated
by the DYNAMIC statement. The structure state-
ments within the INITIAL segment are executed
only at TIME equals zero. This option provides
a convenient means for an initializing computation
of those initial conditions and parameters which are
themselves functions of other, perhaps more basic,
parameters of the model. If sectioning of the seg-
ment is not explicitly indicated, it is assumed that
the segment comprises a single sorted section.
Note that MACRO definitions must precede the
INITIAL statement.
9. DYNAMIC
This label identifies the beginning of the DYNAMIC
segment of the model; the segment is terminated
by the TERMINAL statement, or, if there is no
TERMINAL segment, by the first END or
CONTINUE statement. The structure statements
within the DYNAMIC segment describe the dynam-
ics of the model, and the corresponding computa-
tions are performed repeatedly, under control of
the selected integration routine, during each run.
If sectioning of the segment is not explicitly indi-
cated, it is assumed that the segment comprises
a single sorted section.'
10. TERMINAL
This label identifies the beginning of the TERMINAL
segment of the model; the segment is terminated by
the first END or CONTINUE statement. The struc-
ture statements within the TERMINAL segment
prescribe the computations to be performed upon
completion of each run. The segment is automa-
tically entered when the TIME equals FINTIM or
when any FINISH condition is satisfied. Unless
sectioning is explicitly indicated, all structure
22
statements within the segment are assumed to com-
prise a single unsorted section.
11. END
The first occurrence of this statement defines the
completion of the structural description of the
model, as well as the data and control specifica-
tions for the first run. Subsequent uses of this
statement terminate the specifications for successive
runs. As explained later under "Run Control",
an END card permits the simulation to accept new
data and control statements for another run which
is automatically initiated at the conclusion of the
preceding run. The END card resets the inde-
pendent variable (TIME) to zero and resets initial
conditions. The last use of the END statement must
be followed by STOP.
12. CONTINUE
If the run is to continue from the point at which
the previous run ended, the CONTINUE card is
used in place of the END card. When restarted
after data or control statement input, the program
does not reset initial conditions or the independent
variable (TIME), but continues from the point at
which the previous run ended. The major advan-
tage of the CONTINUE feature is that it allows a
control statement to be changed during a simula-
tion. Run control by means of either a multiple-
valued parameter on a PARAMETER, INCON, or
CONSTANT card, or a TERMINAL section, should
not be used in conjunction with the CONTINUE card.
If CONTINUE follows a FINISH condition, PRDEL
and OUTDEL will be incremented from the TIME
at which the FINISH condition was encountered,
even if this TIME was not a multiple of PRDEL
and OUTDEL as originally specified.
Note also that the FORTRAN statement
CONTINUE, which is valid within procedural
portions of S/360 CSMP, must be used with a
statement number to avoid confusion with this label.
13. SORT
The SORT statement defines the beginning of a
section and declares that all structural statements
within the section are to be considered parallel.
Thus, the structure statements within a SORT
section are sorted by the translator in accordance
with the sorting algorithm. This requires that
current values for all variables appearing on the
right-hand side of a structure statement must be
available before the statement can be processed.
The section is terminated by definition of the next
section (indicated by SORT or NOSORT) or by the
next segment (indicated by DYNAMIC or TERMINAL).
14. NOSORT
The NOSORT statement defines the beginning of a
section and declares that all structure statements
within the section are to be considered procedural.
Thus, the structure statements within a NOSORT
section are not sorted but, instead, are kept in
their logical order as supplied. Full use of
FORTRAN conditional branching is permissible
within such a NOSORT section. The section is
terminated by definition of the next section (indi-
cated by SORT or NOSORT) or by the next segment
(indicated by DYNAMIC or TERMINAL).
15. PROCEDURE
ENDPRO
These labels provide a convenient means for using
the logic capabilities of FORTRAN in defining new
functions. Statements included between the cards
labeled PROCEDURE and ENDPRO are not sorted in-
ternally but are treated as a single functional entity
by the sorting algorithm. A full discussion of the
use of this feature is contained under "Modeling
Techniques".
16. STOP
This card must follow the last END card in a se-
quence of simulation runs of the same model.
17. ENDJOB
This card must be used to signify the end of a job.
If there are user-supplied FORTRAN subroutines,
this card must follow them; if not, it must follow
the STOP card. The label ENDJOB must be in
cc 1-6.
18. ENDJOB STACK
This card can be used instead of the ENDJOB card
when another S/360 CSMP job follows. For a series
of short jobs, its use will increase efficiency and
throughput. A blank card must follow this card. The
label ENDJOB must be in cc 1-6 and STACK in
cc 9-13. Note that this feature may be used only
if the operating system uses the card reader for
SYSIN. An alternate method for stacking simula-
tion jobs is described in the Operator's Manual
(H20-0368) for any other configurations.
19. COMMON
This feature allows user-supplied routines access to
data in the previously established S/360 CSMP
COMMON. The label is placed at the beginning of
the user's routine, to indicate to the translator that
access to the COMMON used for UPDATE is neces-
sary. The translator will replace this card with the
COMMON statements needed. Cards entered into
UPDATE by the / option are not included. COMMON
must appear in cc 1-6.
23
20. COMMON MEM
This label makes that portion of COMMON used for
history, memory, and implicit functional blocks
available to user-defined programs of those types.
The translator will replace this card with the neces-
sary statements. COMMON must appear in cc 1-6
and MEM in cc 9-11.
21. DATA
ENDDATA
These labels identify a set of cards as input data
that will be entered by means of a FORTRAN state-
ment READ(5,xxx). The labels advise the S/360
CSMP translator to skip over these cards without
checking their syntax, since they are not S/360
CSMP statements. The READ statement is usually
placed within a NOSORT section of the INITIAL
segment. The user is responsible to check that the
number of such data cards and their format is con-
sistent with the READ and FORMAT statements.
Note especially that the label ENDDATA must be
in cc 1-7. The label DATA should immediately
follow the END statement for the particular run.
EXECUTION CONTROL STATEMENTS
Execution control statements are used to specify
certain items relating to the actual simulation run
— for example, run time, integration interval, and
relative error. An example of an execution control
statement is:
TIMER FINTIM=8.0,DELT=,02
where TIMER is the label identifying the card as a
timer card, FINTIM and DELT (integration interval)
are the system variables to be assigned values and
8.0 and .02 are the values assigned. Successive
assignments on the same card must be separated by
a comma. At least one blank must follow the card
label. Each of the different types of execution con-
trol statements is identified by a different card
label. Examples of each type are shown in Table 5.
They are used as follows:
1. TIMER
This feature allows the user to specify the values of
system variables. The current value of the speci-
fied system variable is replaced by the correspond-
ing integer or real number. If there is more than
one value for a TIMER reserved word for a Simula- .
tion run, the last value given will be used. User
specifications are automatically adjusted by the
program, as necessary, to ensure a consistent re-
lationship between integration interval, run time,
and output intervals. The system variables that
may be set are:
Name Description
PRDEL Print increment for output printing. If
both PRDEL and OUTDEL are required,
the smaller is adjusted, as necessary,
to be a submultiple of the larger. If a
PRDEL is required but has not been
specified, it is set equal either to
OUTDEL if OUTDEL is required and
has been specified, or to FINTIM/100.
OUTDEL Print increment for the print-plot
output, and preparation of a data tape
for user-prepared plotting programs.
If both OUTDEL and PRDEL are
required, the smaller is adjusted, as
necessary, to be a submultiple of the
larger. If an OUTDEL is required but
has not been specified, it is set equal
either to PRDEL if PRDEL is
required and has been specified, or
to FINTIM/100.
FINTIM Maximum simulation value for the
independent variable. This must be
specified for each simulation.
FINTIM is adjusted, as necessary, to
be the highest multiple of the most
frequent output that would occur with-
in the originally specified FINTIM.
DELT Integration interval or step size for
the independent variable. If DELT is
specified, the program adjusts it, as
necessary, to be a submultiple of
PRDEL or OUTDEL, whichever is
smaller. If neither a PRDEL nor
OUTDEL has been specified, DELT is
adjusted, as necessary, to be a sub-
multiple of FINTIM/100. If DELT is
not specified, the program first at-
tempts to assign it a value equal to 1/16
of PRDEL or OUTDEL, whichever is
smaller.
DELMIN Minimum allowable integration interval
or step size for variable-step inte-
gration methods. It is taken as
FINTIM x 10-7 if unspecified.
TIMER DELT=.02,FINTIM=10.0
FINISH ALT=0.0,X=5000.0,X=Y
RELERR XDOT=5.0E-5,X=1.5E-U
ABSERR X2D0T=i+.0E-3
METHOD MILNE
Table 5. Execution control statements
24
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By TNL GN20-2329
2. FINISH
This label allows the user to specify terminating
conditions in addition to FINTIM. A run can be
ended when any dependent variable reaches or first
crosses some specific bound. In the example in
Table 5, the problem terminates if ALT reaches 0.
or X reaches 5000. , before specified FINTIM has
elapsed. X=Y can also be specified on a FINISH
card, so that the run will terminate when X is equal
to Y or the difference between X and Y changes
sign, where both X and Y are variable names. Up
to ten equivalences can be placed on the FINISH
card(s). Each use of the FINISH label overrides
any previous FINISH specifications. A RESET card
must be used to nullify FINISH specifications be-
tween successive runs. FINISH conditions are
checked at each integration interval. It is, there-
fore, possible that the run will terminate at a time
which is not a multiple of PRDEL or OUTDEL. In
this case, printing will occur at the FINISH time.
3. RELERR
This feature allows the user to specify a relative
error for each integrator output. It is used only
for the RKS and MILNE integration routines, which
are allowed to vary the integration interval to
satisfy error bounds. If relative error is specified
for any integrator, the last error specified before
an END or CONTINUE card is applied to all integra-
tors that are unspecified. If none is specified, the
error is set at 0.0001. RELERR specifications are
additive; that is, use of the RELERR label does not
override all previous RELERR specifications. A
change in the relative error for a particular
integrator can be made by specifying the desired
error and integrator output name on a new RELERR
card. The RESET feature can be used to nullify all
previous RELERR specifications. For further
information see "Modeling Techniques" and
"Integration Techniques".
4. ABSERR
This is similar to RELERR but is used to control
absolute error in the RKS method only. If none is
specified, the error is set at 0.001. As shown
under "Integration Techniques", the maximum
permissible error for each integrator is the sum
of the permissible absolute and relative errors.
Thus as the integrator output approaches zero, the
permissible absolute error dominates. As the inte-
grator output grows in magnitude, the permissible
relative error dominates.
5. METHOD
This label specifies the particular centralized in-
tegration routine to be used for the simulation. If
none is specified, the RKS method is used. Names
must be exactly as shown below:
Name Method
ADAMS Second-order Adams integration with
fixed interval
CENTRL A dummy routine that may be replaced
by a user-supplied centralized inte-
gration subroutine, if desired
MILNE Variable-step, fifth-order, pre-
dictor-corrector Milne integration
method
RECT Rectangular integration
RKS Fourth -order Runge-Kutta with
variable integration interval;
Simpson's Rule used for error esti-
mation
RKSFX Fourth-order Runge-Kutta with fixed
interval
SIMP Simpson's Rule integration with fixed
integration interval
TRAPZ Trapezoidal integration
OUTPUT CONTROL STATEMENTS
Output control statements are used to specify such
items as the variables to be printed and/or print-
plotted. An example of an output control statement
is:
PRINT X,XDOT,VELOC
where PRINT is the label identifying the card as a
print card, and X, XDOT and VELOC are the vari-
ables to be printed. A comma must be inserted
before each successive variable name. A card
without continuation marks signals the end of the
list. Each of the different types of output control
statements is identified by a different label. Il-
lustrations of the output capabilities are given
later under "Data Output". Table 6 shows each
type of output control statement:
1. PRINT
The PRINT card is used to specify variables whose
values will be printed at each PRDEL interval
during the simulation. If any variables are speci-
fied, printout of the independent variable (TIME) is
forced. Variable names are printed in printout
headings. The PRINT control card is intended for
use with real variables. If output of integer vari-
ables is desired, they should first be equated to
25
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ByTNLGN20-2329
real variables; printing of the real variable should
then be requested. For example, if printing of the
fixed variable I is desired, the user must provide
the following statement:
X=I
PRINT X
The label PRINT should appear only on the first
PRINT card if more than one card is needed to
specify all the outputs. As in other cards, three
periods (...) identify continuations. If more than
one card or group of cards is identified by the label
PRINT, the last in sequence will be used. Up to 49
variables may be specified for one simulation run.
PRINT specifications can be nullified by use of the
RESET.
PRINT X, XDOT, ALT
TITLE PROBLEM DESCRIPTION
PREPARE DIST, VELOC
PRTPLOT X(Y1, Y2), 2(3.0, 4.0, Y3), W
LABEL PRINT PLOT PAGE HEADING
RANGE ALT, DIST
RESET PRINT. PRTPLOT, FINISH
Table 6. Output control statements
2. TITLE
The TITLE statement allows the user to specify
a heading that appears at the top of each page of
printed output. The heading consists of those sym-
bols between the label TITLE and cc 72 of that
statement. The first noriblank character following
the label TITLE must be either alphabetic or numeric;
special characters may, however, be used within the
remainder of the heading.
The S/360 CSMP continuation device (...) is not
permitted with TITLE statements. However, a max-
imum of five TITLE statements may be used per run.
Multiple statements result in successive headings on
each page; thus, several lines of heading are easily
obtained.
TITLE specifications cannot be nullified by
RESET. However, all previous TITLE specifica-
tions are nullified by the first use of the TITLE
label after an END or CONTINUE card. Subse-
quent TITLE cards within this same run are then
additive.
3. PREPARE
The PREPARE card allows the user to specify vari-
ables to be written on OS/360 I/O device 15 at the
specified OUTDEL interval, during the simulation
run, for possible later plotting. If any variables
are specified, output of the independent variable
(TIME) is forced. The label PREPARE should ap-
pear only on the first PREPARE card if more than
one is required. Continuation cards are allowed.
If the label PREPARE identifies more than one card
or set of cards, the last in sequence will be used.
Information specified on TITLE cards will also be
written on the PREPARE data set. PREPARE speci-
fications can be nullified by use of RESET. Up to
49 variables may be specified.
4. PRTPLOT
The PRTPLOT card(s) allows the user to specify
which variables are to be print-plotted. Up to ten
PRTPLOT cards can be used for each simulation
run, but continuation cards are not allowed. A
number of options are available within the frame-
work of this feature, as illustrated in Table 6.
Variables not enclosed within parentheses will be
print -plotted as well as printed, and each such
variable will cause a separate print plot. Variables
inside the parentheses (up to a maximum of three)
will be printed adjacent to the corresponding print
plot. Print plotting of integer variables requires
the same procedure described for the PRINT con-
trol card. Constants inside the parentheses specify
lower and upper bounds for the corresponding print
plot. If only a lower or an upper bound is desired,
commas must be used to indicate which. For
example, Z(3. 0, , Y3) indicates only a lower bound
of 3, and Z(, 4. 0, Y3) indicates only an upper bound
of 4. The example in Table 6 shows both lower and
upper bounds. Note that commas are not needed if
neither bound is specified. Successive print-plot
designations are separated by commas. PRTPLOT
cards are additive, up to the maximum of ten; a
RESET card must, therefore, be used to nullify
previous specifications. All print plots requested
on the same card will use the same LABEL card,
as explained below.
5. LABEL
The LABEL statement allows the user to specify
a heading for each page of print-plot output. The
first noriblank character following the label LABEL
must be either alphabetic ot numeric; special char-
acters may, however, be used within the remainder
of the heading.
The S/360 CSMP continuation device (...) is not
permitted with LABEL statements. However, a
maximum of ten LABEL statements may be used per
run. The first LABEL statement is associated with
all print-plots requested by the first PRTPLOT
statement; the second with the second, and so on.
If PRTPLOT statements outnumber LABEL state-
ments, the excess print-plots will not have labels.
LABEL statements are additive, as are PRTPLOT
statements, and so must be RESET to nullify
previous designations. The name of the prints-
plot variable will also appear automatically in the
print-plot page heading. A parameter name and
its value will be printed if the multiple- value
parameter feature is used.
26
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By TNL GN20-2329
6. RANGE
The RANGE card allows a user to obtain the mini-
mum and maximum values reached, during the
simulation, for specified variables. Ranges are
automatically taken for all PREPARE and PRTPLOT
variables. The total number of different variables
that may appear on RANGE, PREPARE, and
PRTPLOT cards is 100. The names of the specified
variables, their minimum and maximum values,
and the time of occurrence of each are printed at
the integration interval. Only the first RANGE
card in a sequence should be so labeled. Continua-
tions are allowed. If there is more than one card
or set of cards labeled RANGE, the last in sequence
will be used. RANGE specifications can be nulli-
fied by use of RESET. The values provided in the
case of a multiple parameter or TERMINAL-
controlled sequence of runs are those for the entire
sequence. If a CONTINUE card is used, the values
provided are those obtained in the time period prior
to termination by the FINISH or FINTIM condition.
7. RESET
A RESET card allows the user to conveniently nul-
lify specifications previously given on certain con-
trol statement cards and used in a previous run of
a sequence of runs. It can be used with PRINT,
PREPARE, RANGE, LABEL, PRTPLOT, RELERR,
ABSERR, and FINISH. Its use with RELERR,
ABSERR, and FINISH has already been explained
under these respective headings in the section
entitled "Execution Control Statements". RESET
PRTPLOT or RESET PREPARE nullifies all previous
PRTPLOT, PREPARE, and LABEL specifications.
RESET LABEL nullifies only previous LABEL
specifications. A RESET card with only RESET on
it is interpreted as nullifying all previous PRINT,
PREPARE, PRTPLOT, RANGE, and LABEL state-
ments. Note again that TITLE cannot be RESET.
To ensure proper RESETing, the RESET card
should be placed immediately after the END or
CONTINUE card.
27
USER-DEFINED FUNCTIONS
In some simulation problems , the mix of functional
blocks available from the S/3S0 CSMP library may
not be sufficient to describe the problem adequately.
The user , therefore , has been provided with the
facility for building his own special purpose func-
tional blocks. These functions may range from a
few nonlinear statements to an extremely complex
model of a complete plant in a process control prob-
lem. To define special purpose functions, either
S/360 CSMP functional block statements or
FORTRAN, or a combination of both, may be used.
Three different types of functions may be prepared
by the user: MACROS, PROCEDURES, and subpro-
grams. They differ somewhat in their use and the way
in which they are handled in the S/360 CSMP program.
These several methods for building special func-
tions give the user a high degree of flexibility for
different problem areas . For example, by properly
preparing a set of special functions and adding them
either to the S/360 CSMP library or to the data deck
at run time, the user is able to restructure S/360
CSMP into a problem-oriented language geared to
any special purpose field in continuous system sim-
ulation.
MACRO FUNCTIONS
The MACRO type of function-defining capability in
S/360 CSMP is a particularly powerful feature of
the language. It allows the user to build larger
functional blocks from the basic functions available
in S/360 CSMP, and, thereby, to identify, as a par-
allel functional entity, a subsection of a simulation
block diagram or the corresponding subset of struc-
ture statements. Once defined, a MACRO function
may be used any number of times within the simula-
tion structure statements.
As an illustration of this feature, consider a control
system simulation study that involves several transfer
functions (s is the Laplace operator) with differing
parameter values, but all having the general form:
2
Z(s) _ s + as + b
X(s) 2 _, .
v ' s + cs + d
A simple technique for modeling such transfer
functions is to define a new variable Y such that
Y(s) =
+ cs +d
where the numerator is unity but the same denomi-
nator is used. Then, solving for the highest-order
derivative of Y, one obtains
s 2 Y = X-csY-dY
Note that this is equivalent to the time domain
statement
Y(t) = X(t) - c Y(t) - d Y(t)
which is readily modeled by the S/360 CSMP statement
S2Y = X-C*SY-D*Y
Then by two successive integrations we obtain Y(t).
Since
Z(s) = s 2 Y + asY+bY
we finally obtain Z(t) by combining terms with the
following S/360 CSMP statement
Z = S2Y + A*SY + B*Y
The user may define a MACRO to represent this
general functional relationship, assigning it some
unique name—for example, FILTER. The S/360
CSMP statements to define this new MACRO might
be as follows:
MACRO Z = FILTER( A, B, C, D, X )
S2Y = X - C*SY - D*Y
SY = INTGRL( 0.0, S2Y )
Y = INTGRL( 0.0, SY )
Z = S2Y + A*SY + B*Y
ENDMAC
Such MACRO definition cards must be placed at the
beginning of the S/360 CSMP deck before any struc-
ture statements in the initialization or dynamic seg-
ments . Several rules must be observed in defining
MACRO functions:
1 . The first card of a MACRO definition is the
translation control card containing the word MACRO
and the canonical form that the user assigns for the
new function. The names used to represent vari-
ables in the definition statements are merely
"dummy" variables; they are automatically replaced
by the corresponding variable names assigned when
the MACRO is used. The required format is as
follows :
a. If the MACRO function has a single output
variable, a dummy name for this variable
is placed to the left of the equal sign. If
the MACRO function has several output
variables, these must all appear to the
left of the equal sign, separated by
commas .
b. The unique name assigned by the user to
the function must appear to the right of
the equal sign. This is the name by which
the function will subsequently be used in
structure statements.
c. Dummy names to represent initial condi-
tions , parameters , and input variables
for the MACRO must appear within a pair
of parentheses following the function
name. Commas must be used to separate
names within the parentheses.
2 . The last card of a MACRO definition contains
merely the word ENDMAC .
28
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ByTNLGN20-2329
3. The statements between the MACRO and
ENDMAC translation control cards specify structure.
Thus, S/360 CSMP data or control statements may
not appear. Any S/360 CSMP or FORTRAN structural
statement may be used except as follows:
a. A structure" statement must be completed
on a single punched card; the S/360 CSMP
continuation device (...) is not applicable
within MACRO definitions.
b. FORTRAN control and input/output state-
ments may not be used unless embedded
within a PROCEDURE function. An input/
output statement may reference a FORMAT
statement, but the FORMAT statement
itself must not appear within the MACRO.
Good practice is to place all FORMAT
statements in a TERMINAL statement.
In general, the statements within a MACRO
definition may appear in any order, since the pro-
gram assumes that they represent parallel structure
and will automatically sort them to determine the
computational sequence. However, a MACRO may
be used within a PROCEDURE function or within a
NOSORT section. In both of these cases, the sorting
algorithm would not be applied to the MACRO. For
such use, therefore, the MACRO must be defined in
appropriate procedural order and cannot invoke a
MACRO function.
Each use of a MACRO requires a structure
statement that has exactly the same format as the
canonical statement in the MACRO definition. Thus,
the number and order of the inputs, outputs, and
parameters must exactly agree with the definition.
A MACRO function cannot be used as part of an
expression in a structure statement. This restriction
pertains not only to user-defined MACROS but also
to the system MACROs: REALPL, CMPXPL,
MO DINT, and LEDLAG. As example, the canonical
form for REALPL as illustrated in Table 1 is as
follows :
XI = REALPK IC, P, X )
It would therefore be invalid to attempt its use in the
following ways :
XI = GAIN * REALPU 0.0, 5.0, Z )
or
X2 = REALPL(X20,.TC, IN) + INTGRL (IC2,YIN)
in each of these examples an expression involving
REALPL is used rather than the primitive canonical
form.
As an example of the proper use of a MACRO,
consider the following structure statement, which
uses the FILTER function defined previously:
SIGOUT= FILTER( 0.1, PAR23, N2, 34.6, SIGIN )
This statement declares that the input to the function
is the variable SIGIN, that its output is named
SIGOUT, that two of its parameters are literals, and
that two are named parameters. The translator
portion of S/360 CSMP would automatically expand
this structure statement, in accordance with the
MACRO definition, as follows:
ZZ0027 = SIGIN - N2*ZZ0028 - 34.6*ZZ0029
ZZ0028 = INTGRL( 0.0, ZZ0027 )
ZZ0029 = INTGRL( 0.0, ZZ0028 )
SIGOUT= ZZ0027 + 0.1*ZZ0028 + PAR23*ZZ0029
Note that the dummy variables of the definition have
been replaced by the corresponding literals and
named variables of the structure statement. The
translator has assigned unique names ZZ0027,
ZZ0028, and ZZ0029 to the intermediate variables
S2Y, SY, and Y of the definition; the next time the
program is required to generate a unique name for
a variable, it will use ZZ0030. As noted in the sec-
tion entitled "Reserved Words", the names ZZ0000—
ZZ9999 are reserved to the program and may not be
assigned by the user.
Significant economies of effort as well as con-
ceptual advantages can sometimes be realized by
invoking MACROs within the definitions of other
MACROs, first defining "primitive" MACROs for
the most basic phenomena, then combining these in
MACRO definitions for progressively more complex
portions of model structure. For example, a
physiologist concerned with the distribution, binding,
and metabolism of hormones in blood plasma might
first develop the following MACRO to represent a
simple reversible reaction:
MACRO COUT, RATE = COMP( I C, KA, KR, CIN )
RATE = KA * CIN - KR * COUT
COUT = I NTGRL( I C, RATE )
ENDMAC
The outputs of this MACRO represent the con-
centration and time derivative of the reaction product.
To represent a bi-molecular reaction, the MACRO
may be invoked using as the fourth argument the
product of concentrations of the two reactants. He
might then develop the following MACRO definition,
invoking "COMP" twice since the particular hormone
is bound in reversible reactions with two different
proteins, and including terms to represent distribu-
tion and metabolism:
MACRO CCP, CAP, CTP, CCAP, CCTP, TOTCCP 7 DBM( QCORT, INFUS )
MASSFL- = QCORT + INFUS - DIFFUS - 0.63 • CCP
CCP = INTGRL( 1.77, MASSFL/VI -RATECA -RATECT )
CAP.= LIMIT( 0.0, A, A - CCAP )
CCAP, RATECA = COMP( 2.83 , KAA, KAR/CCP * CAP )
CTP = LIMIT( 0.0, T, T - CCTP*)
CCTP, RATECT = COMP( 9.27 , KTA, KTR, CCP * CTP )
DIFFUS = K12 * CCP - K21 • CC2
CC2 = INTGRL< 1.77, DIFFUS / V2 )
TOTCCP- = CCP + CCAP + CCTP
ENDMAC
29
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By TNL GN20-2329
PROCEDURE FUNCTIONS
The PROCEDURE type of user-defined function is
used for procedural coding and allows simple applica-
tion of the capabilities of FORTRAN. Any S/360
CSMP structure statement or executable FORTRAN
statement except another PROCEDURE may be used
in a PROCEDURE. Considerable power can be real-
ized fairly readily through the use of FORTRAN'S
logical, branching, and subscripted variable features.
An example of a PROCEDURE function is:
PROCEDURE VALUE = BLOCKA( PARI, PAR2, TRIG, IN
IF( TRIG ) 1,1,2
1 VALUE = LIMIT( PARI, PAR2, IN )
GO TO 3
2 VALUE = IN
3 CONTINUE
ENDPRO
This example defines a new functional element,
BLOCKA. This particular function has only a single
output, here named VALUE; PROCEDURES are
permitted to have multiple outputs (see example
INVERT below). The inputs and parameters that
make up the arguments of function BLOCKA are
listed within parentheses on the right side of the
first card; this permits the sorting algorithm to
properly process the new function.
The input variables TRIG and IN are listed as
function arguments within parentheses on the right
side of the first card of the PROCEDURE. While not
required, it is good practice to also include as
arguments all parameters used within the PROCEDURE.
Thus PARI and PAR2, which are parameters of the
LIMIT function, are included as arguments of
function BLOCKA. Unless this is done, the trans-
lator cannot check on whether internal parameters
have been properly defined by data statements and
is thereby unable either to initialize such unspecified
parameters to zero value or to generate a diagnostic
message regarding their unavailability.
The set of statements making up a PROCEDURE
function may be written anywhere in the sequence of
S/360 CSMP statements. Several rules must be
observed in preparing PROCEDURE functions:
1. The first card of the PROCEDURE is the
translation control card containing the word
PROCEDURE and the names of the function, input
variables, output variables, and parameters. The
output names must be placed to the left of the equal
sign and be separated by commas. The function name,
which is a "dummy" name, must appear to the right
of the equal sign. Names of the input variables must
appear within a pair of parentheses following the
function name. Commas must be used to separate
names within the parentheses.
2. The last card of the PROCEDURE function
contains merely the word ENDPRO.
3'. The statements describing the PROCEDURE
are placed between the PROCEDURE and ENDPRO
translation control cards.
4. Variables defined within a PROCEDURE
function are not available for data output by means
[ of the PRINT, PRTPLT, RANGE, or PREPARE
option unless they appear as output names on the
PROCEDURE card.
The PROCEDURE is conceptually a single functional
element, even though its definition requires a number
of statements. During sorting, the statements that
describe a PROCEDURE are treated as a group and
the entire set is moved around as an entity in order
to satisfy the input/output sequencing requirements
of the sorting algorithm. There is no internal sort-
ing of statements within a PROCEDURE. If the
operation performed by the PROCEDURE is required
only once, the PROCEDURE is defined where needed
within the appropriate section of the INITIAL or
DYNAMIC segment. Note that the PROCEDURE is
specifically designed for use in parallel, sorted
sections of the INITIAL or DYNAMIC segments.
Use of a PROCEDURE within a NOSORT section is in-
consistent modeling and will result in an abnormal
exit. Since the TERMINAL segment is normally
procedural, there is seldom need for a PROCEDURE
within that segment.
Although FORTRAN logical, branching, and
input/output statements cannot generally be used
within a MACRO since parallel structure is the '
basic premise of the MACRO, it is permissible to
use PROCEDURES within MACROs. This feature
of S/360 CSMP permits the modeler to define
MACROs involving both parallel and procedure
structure and invoke the MACRO as often as required.
A MACRO definition may include multiple PROCE-
DURES as well as multiple invocations of other
MACROs (which latter may include additional PROCE-
DURES or MACROs). The restriction is that a
PROCEDURE within a MACRO definition may not
itself invoke another MACRO. Repeated invocation of
a MACRO will cause the translator to generate the
complete set of statements according to the pattern
given in the MACRO definition. The sorting algo-
rithm will ensure that an appropriate statement
sequence is obtained; those sets of statements that
were specified as PROCEDURES will, however, be
treated as separate entities by the sorting algorithm.
Any output name or statement number used within a
PROCEDURE will be given a unique name or number,
just like any other name or statement within a
MACRO.
Often one wishes to define a MACRO that is en-
tirely procedural, and for this case a simplified form
may be used. It is only necessary that the first
statement within the MACRO definition contain the
label "PROCEDURAL"; the statement ENDPRO must
not be used with this form. For example, one might
need a delay function with nonzero initial conditions.
Note that such an element is a memory element and
its name should appear on a MEMORY statement.
The following statements illustrate the simplified
form for such an element:
30
PageofGH20-0367-3,-2
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By TNL GN20-2329
MEMORY
DLAY
MACRO OUT = DLAY( IC, N, PAR, IN )
PROCEDURAL
IF( TIME . EQ. 0.0 ) OUT = IC
X = DELAY( N, PAR, IN )
IF( TIME . GT. PAR ) OUT = X
ENDMAC
More commonly, one needs a MACRO in which
only a portion must be procedural. For example,
a circuit designer might develop a MACRO to repre-
sent an electrical transformer. The state variables
II and 12 represent the currents flowing in the two
windings of the transformer. Their derivatives are
functions of the applied voltages El and E2 and the
inductance parameters LI, L2, and M. Computation
of the derivatives requires inversion of a two-by-
two matrix consisting of the parameter values; since
these are normally constants, it is efficient to invert
the matrix only once, when TIME is zero. One way
to model the transformer is illustrated by the
following:
MACRO
II , 12 = TRANS( LI, L2, M, El , E2 )
PROCEDURE I1DOT, l2DOT= INVERT( E
IF( TIME ) 1,1,2
1, E2 )
D = LI * L2
Bl 1 = L2 / D
B12 = -M/ D
B21 = B12
B22 = LI / D
I1DOT = Bl 1 * El
I2DOT = B21 * El
M * M
+ B.12 * E2
+ B22 * E2
ENDPRO
11 = INTGRL( 0.0, II DOT )
12 = INTGRL( 0.0, I2DOT )
ENDMAC
SUBPROGRAMS
This approach actually adds little to the algebraic
and logical modeling capabilities available through
use of the procedural MACRO, and is more difficult
to program. It does, however, permit the new
functional block to be permanently added to the
system library, thereby conveniently available to
all users at a particular installation. Since the
statements within the subprogram need not be
processed by the S/360 CSMP translator, it is also
sometimes possible to develop larger models than
would otherwise be permissible. As a general rule,
it is best to carefully test the performance of any
new subprogram independently of the complete
model for which it is being designed.
There are two forms of subprograms: the
FORTRAN function and the FORTRAN subroutine.
The function form is used in developing new func-
tional blocks whenever the output of the block is to
be a single variable. If the block is to generate
multiple outputs, the subroutine form must be used.
In developing a new subprogram, the user has
available the features of FORTRAN and, in addition,
may use many of the standard S/360 CSMP functional
elements. This combination gives the user a very
versatile modeling capability. Specifically excluded
from use within any subprograms are: INTGRL,
IMPL, DELAY, DERTV, HSTRSS, RST, IMPULS,
PULSE, ZHOLD, MODINT, REALPL, CMPXPL,
LEDLAG, and any user-defined MACRO'S.
To use a function, once defined, it is necessary
merely to conform to the ordinary S/360 CSMP
structure statement format in calling it. The argu-
ments used must, however, agree in number, order,
type, and length with the dummy arguments used in
the subprogram definition. Note that literal constants
are not permitted to be used directly as subprogram
arguments in S/360 CSMP models.
At run time, all user-defined subprograms not
cataloged in the S/360 CSMP library must be in
FORTRAN and be placed directly behind the STOP
card. They must be terminated by an ENDJOB card.
Subprograms may be cataloged or added to the S/360
CSMP library by loading them with the FORTRAN
library by means of an Operating System/360
procedure.
As an example of a simple FORTRAN subprogram,
consider a function used to model a valve that
permits only one-directional flow and includes some
internal resistance. The complete FORTRAN func-
tion definition might be as follows:
FUNCTION VALVE ( RESfS, PRES1, PRES2 )
IF ( PRES1 - PRES2 ) 1, 1, 2
1 VALVE = ( PRES1 - PRES2 ) / RESIS
GO TO 3
2 VALVE = 0.0
3 RETURN
END
An S/360 CSMP structure statement to call this
subprogram might be:
OUT = VALVE ( K, PR 1 , PR2 )
where the symbolic names PR1 and PR2 represent
pressures across some specific valve of a large
simulation model, K represents its internal resist-
ance, and OUT represents the resultant flow. Note
that the element VALUE might be used many times
withinrsuch a model, each instance representing a
distinct physical unit. Since this functional block
involves only a few statements and very simple logic,
the subprogram approach offers little advantage over
use of a procedural MACRO. This example is
therefore only illustrative; the subprogram approach
is generally reserved for much more complex
elements.
31
PigeofGH2(M)367-3 > 2
Added February 26, 1971
ByTNLGN20-2329
As noted, if a functional block generates multiple
outputs, the FORTRAN subroutine form of sub-
program must be used rather than the FORTRAN
function form. To properly design such an element,
the user must understand how the S/360 CSMP
translator processes structural statements with
multiple outputs. For example, suppose the user
wishes to define a functional block FLIP with two
outputs, a single trigger input, and an associated gain
parameter. Ultimately he will use this block within
the dynamic segment of a model with a structural
statement such as:
Yl, Y2 = FLIP ( GAIN, TRIG )
where the symbolic variables are appropriate to the
specific model. In generating the derivative routine
UPDATE, the S/360 CSMP translator will replace
the user's structural statement with the following:
CALL FLIP ( GAIN, TRIG, Yl, Y2 )
Note that the output variables of the original struc-
tural statement are placed by the translator on the
right-hand side of the subroutine argument string
without rearrangement of their order. In program-
ming the subroutine, the arguments must be
arranged in corresponding order. Thus, the initial
FORTRAN statement for the subroutine might be:
SUBROUTINE FLIP ( PARAM, XINPUT, OUT1, OUT2 )
31.1
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Revised February 26, 1971
By TNL GN20-2329
where the symbolic names PARAM, XINPUT, OUT1,
and OUT2 are used merely for definition of the sub-
routine and have no external meaning.
The S/360 CSMP function generators AFGEN and
NLFGEN may be used within a subprogram if the
names of all functions upon which they are to
operate are used as arguments of the subprogram.
As example, consider the design of a functional
block VALUE, which includes a requirement for
both linear and quadratic interpolation of asso-
ciated data arrays defining two curves. With a
specific model, one might then use the structural
statement:
OUT = VALUE ( FUNCTl, FUNCT2, INPUT )
and the associated data statements:
FUNCTION
FUNCTl = ( 0.0
( 3.5
FUNCTION FUNCT2 - (-234.0
( 437.4
10.5 )
34.6 )
5.34E-4)
34.578)
Note that the names of the two curves, as specified
on the FUNCTION statements, are used as argu-
ments of the structural statement. The subprogram
developed for the block VALUE must be prepared to
use these arguments; as example, the following
FORTRAN function definition might follow the STOP
statement of the model:
STOP
FUNCTION VALUE ( X, Y, SIGIN )
REAL NLFGEN
VALUE = 0.6 * AFGEN(X, SIGIN)
$ + 0.4* NLFGEN(Y, SIGIN)
RETURN
END
ENDJOB
Note that when used within a subprogram, NLFGEN
must be identified as real; otherwise, FORTRAN
would assume it to be an integer- valued function.
The user is reminded that within subprogram
definitions all the normal rules of FORTRAN are
applicable and all variable names beginning with the
letters I, J, K, L, M, N, are assumed to be
integer-valued.
If the new function involves past input or output
values and thus needs unique storage locations for
each use, the S/360 CSMP data deck must include
a MEMORY or HISTORY translator control card, as
appropriate. These cards tell the translator how
many storage locations are required for each use,
and must appear before the first reference to the
function. The translator assigns unique storage in
the COMMON area and inserts the index of the
assigned location as the first argument of the sub-
program.
The handling of a function that involves both the
present and past values of the input is illustrated by
another example. Consider a function MAGCOR,
which involves one present input, one past input, and
one past output value for each use. The S/360 CSMP
translation control and structure statements re-
quired to use this function are:
HISTORY MAGCOR(2)
Y=MAGCOR(Y0 , PI , XIN)
where Y0 is an initial condition, PI is a parameter,
and XIN is the input.
The HISTORY card tells the S/360 CSMP transla-
tor how many history storage locations are required
for each use of the specified function. The transla-
tor assigns the next available locations in COMMON,
and inserts the index of the assigned location as the
first argument of the calling statement for the sub-
program. For example, if the next available stor-
age were the twenty-fifth location in the particular
COMMON area, the translator would generate the
following statement to link to the subprogram:
Y=MAGCOR(25,YO,P1,XIN)
The translator index that records the location of the
next available storage would then be increased to 27,
since two locations are required for this single use
of the new element.
In developing the FORTRAN subprogram, the
user must recognize that the translator will insert
this storage location index as the first argument of
the calling statement for memory and history blocks
regardless of whether the FORTRAN function form
or the subroutine form is used. The subprogram
must be properly programmed to use this assigned
storage. As an example, the FORTRAN definition
of MAGCOR might be as follows:
32
FUNCTION MAGCOR(K, YIC, PARAM, X)
COMMON MEM
EQUIVALENCE(C(1), TIME)
I=K+KPT1-1
IF(TIME)4, 4, 5
4 SYMB(I+1)=YIC
GO TO 6
5 SYMB(I+1)=FUNCT(X, SYMB(I), SYMB(I+1), PARAM, TIME)
6 SYMB(I)=X
MAGCOR=SYMB(I+l)
RETURN
END
In these statements, KPT1 is the system name for
the first available COMMON storage location in the
execution phase, SYMB is the system name for the
storage area that includes HISTORY and MEMORY
functions, FUNCT is the name of the user-defined
FORTRAN function that operates on the indicated
variables. Note that an EQUIVALENCE card with
the name TIME equivalenced to COMMON location
C(l) is necessary if reference is made to the inde-
pendent variable, by the name TIME, in the pro-
gram.
The KPT1, C, and SYMB variable names are
automatically placed in COMMON by the system
when the COMMON MEM card is used. The cards
supplied by the system to replace COMMON MEM
are:
COMMON DDUM1(64), C(8000), NALARM, DDUM2(12)
COMMON KPT1, DDUM3(405), KEEP, DDUM4(1316), SYMB(l)
Note that in programming a history or memory
function, the user must explicitly provide for input
of initial conditions — for example, the variable YIC
in the problem above .
While not permissible to use the INTGRL state-
ment itself within the definition of a subprogram, it
is possible to achieve the same effect. This is
done by means of the special "specification" form
of the INTGRL statement, which advises the S/360
CSMP translator to assign some desired number of
integrators for each use of the subprogram within
the model. The translator assigns contiguous
locations for the group of integrator outputs and also
for the group of integrator inputs; thus operations
using subscripted variables are readily performed
within the subprogram.
As an illustration of this feature, consider a
function subprogram to provide the same perform-
ance as the MACRO function named FILTER
described earlier in this section. This second-
order transfer function requires two integrators.
The core location of the first of these can be
passed to the subprogram by using the "specifica-
tion" form of INTGRL as one of the arguments of
the subprogram. The total number of integrators
used for a particular model is available within
COMMON as the variable named NOINTG. The
core location of the input to the first of the two
integrators is thereby offset from the location of
the integrator by NOINTG locations.
A FORTRAN function subprogram to represent
the second-order filter might be programmed as
follows:
FUNCTION FILTER( A, B, C, D, X, YARRAY )
COMMON DUMMY(9798), NOINTG
DIMENSION YARRAY(I )
C NOINTG IS THE TOTAL NUMBER OF INTEGRATORS IN THE MODEL
C INPUT TO ANY INTEGRATOR IS LOCATED NOINTG WORDS FROM ITS OUTPUT
C IN S 360 CSMP COMMON
C YARRAY(1&2) CONTAIN THE TWO INTEGRATOR OUTPUTS
C YARRAY(l) REPRESENTS THE INTEGRAL OF THE HIGHEST ORDER DERIVATIVE
C YARRAY(NOIN TG * 1) CONTAINS THE CORRESPONDING INTEGRATOR INPUT
YARRAY (NOINTG- 1 ) = X -C*YARRAY(I) -D*YARRAY(2)
YARRAY(NOIN TG>2) ' YARRAY(I)
FILTER - YARR AY(NOINTG' I) ♦ A* Y ARR AY ( 1 ) -B"YARRAY(2)
RETURN
END
Note the correspondence of the executable state-
ments within this program to those used during the
discussion of the MACRO function. The subprogram
must compute the inputs to the two integrators and
store these values in the appropriate core locations,
YARRAY (NOINTG+1) and YARRAY (NOINTG + 2).
The integration mechanism of S/360 CSMP com-
putes the values of the integrals and stores these
in YARRAY (1) and YARRAY (2). The subprogram
must compute the result as a weighted sum of the
integrator outputs in correspondence with the terms
of the numerator of the transfer function.
To use the new functional block within an S/360
CSMP model, a structure statement such as the
following might be used:
SIGOUT = FILTER( 0. I, PAR23, N2, 34.6, SIGIN, INTGRL(,,2))
Note, in particular, the use of the "specification"
form of INTGRL as the final argument. This
advises the S/360 CSMP translator to assign two
integrators for this use of the FILTER block. If
this were used several times within a simulation,
additional integrations would be assigned for each
instance. The location of the first integrator is
thereby passed to the subprogram, which then
knows the location of YARRAY (1) and, by using
NOINTG, can obtain the corresponding integrator
input location.
Note also that, for this application, the first
two arguments of INTGRL were left blank.
Names for the initial condition variables were not
required; leaving the first variable blank is
equivalent to assigning a literal constant of zero.
Names for the integrator inputs were not required,
since these are used only internal to the sub-
program and do not communicate with the rest of
the model. Used in this way, the INTGRL block
creates zero initial conditions for all integrators in
the array and assumes that all derivates are
computed within the subprogram.
32.1
MODELING TECHNIQUES
Simulation is an approximation technique. The user
should be as aware as possible of the approximations
made in a particular simulation model. It is best to
carefully record any conscious approximations to
ensure that their effects will be considered during
subsequent evaluation and interpretation of the simu-
lation results.
The simulation model is developed by appro-
priately preparing S/360 CSMP structure, data, and
control statements so as to correspond with the user's
visualization of the phenomenon. Preparation of a
block diagram or differential equation representa-
tion is a critical first step in successful use of the
technique. Preparation of the S/360 CSMP state-
ments does require modest amounts of time and
attention, but the mechanics of this task should not
be of primary concern. Rather, the user should
continually ask himself whether the basic equations
and/or diagrams truly represent his visualization
of the phenomenon.
Included in this section are some comments on
modeling techniques and pertinent features of S/360
CSMP.
SORTING
S/360 CSMP was designed with a nonprocedural in-
put language to free the user from the task of cor-
rectly sequencing structure statements. The pro-
gram will automatically sort user-supplied struc-
ture statements to establish a correct execution
sequence — that is, to yield a properly organized
FORTRAN subprogram. If the user does not want
automatic sorting, he can use the NOSORT option,
PROCEDURE functional blocks, or his own sub-
routines. All of these features are explained later
in this section of the manual.
A correct sequence ensures that each statement's
output for time t is computed on the basis of
statement input values for time t. An incorrect
sequence would update a statement's output for time
t with input values for time t -At. This incorrect
sequence would introduce a phase lag that could
seriously affect stability and accuracy of the solu-
tion. A correct sequence, therefore, is one in
which the output of each statement in the sorted
sequence can be computed using values either pro-
vided as initial input or previously computed in the
current iteration cycle.
Since integration is performed between iterations,
the outputs of all integrals are known values at the
start of an iteration. The outputs of MEMORY
functional blocks are also known values. Together
with initial conditions, these provide a starting
point for the sequence of computations.
Within each sorted section of the S/360 CSMP
structure statements, the sorting algorithm operates
upon the integrator elements in the order in which
they occur in the input deck. That is, the algorithm
first determines an appropriate computational se-
quence for all those functional elements that contrib-
ute to the input of the first integrator. Next, it
^
k
c
ml ml
M
I'nur.v,
J
determines the sequence for all additional computa-
tions necessary to obtain the input to the second in-
tegrator. This procedure is repeated until all the
integrators in the particular sorted section have been
considered. Finally, any elements within the section
that have not already been added to the computational
sequence are sorted and placed in sequence.
Statement sequencing can be illustrated by a simple
feedback control system consisting of a forward con-
trol block that manipulates a process control plant.
The block diagram for such a system is shown in
Figure 9.
Input -
Figure 9. Feedback control system
Suppose that the plant's operation was represented as
a single integration and the controller provided a
signal equal to the sum of a constant times the error
and the integral of the error (proportional plus reset
type control). A set of structure statements defining
the system could be:
MANIP=G*ERROR + INTGRL (IC2, ERROR)
ERROR=INPUT-OUTPUT
OUTPUT=INTGRL (IC1, MANIP)
These statements, however, are not in a proper
sequence, because the computation of MANIP re-
quires a knowledge of ERROR. Computation based
on this sequence would introduce a phase delay. The
correct sequence that would be produced by the auto-
matic sorting algorithm is:
ERROR =INPUT-OUTPUT
MANIP=G*ERROR+INTGRL(IC2, ERROR)
OUTPUT=INTGRL(ICl, MANIP)
NOSORT OPTION
As noted previously, in some simulations it may be
desirable not to sort certain sections of the problem
configuration. S/360 CSMP provides a NOSORT op-
tion that bypasses the sorting phase for sections of
S/360 CSMP coding identified by a NOSORT label.
Thus, the user may include any type of procedural
statement capability, such as branching on conditions
and logical tests, within a sequence of either S/360
CSMP or FORTRAN statements.
Note at this point that either the PROCEDURE
capability or the NOSORT option may be used to enter
procedural coding. The two differ, however, in that
the PROCEDURE function is handled by the system as a
complete group of coding and is moved around and
sorted within the S/360 CSMP structure statements
as an entity. The NOSORT option, however, is used
to identify a section of coding that divides the other
32.2
structure statements into groups, each of which is
separately sorted.
A NOSORT section may be used to test the run
response for the purpose of switching portions of
the configuration into or out of the simulation in
order to decrease run time or alter the information
flow. Problem structure variations that can be antic-
ipated can thereby be included in a single run.
Figure 10 shows a center section of S/360 CSMP
configuration coding identified with a NOSORT label.
The purpose is to switch a portion of the flight sim-
ulation equations, the booster phase, out of the
computation sequence after TIME has reached 50.
The NOSORT block at the bottom of the statements
is to keep the CONTINUE statement at the end.
Statements for Trajectory Phase
NOSORT
IF(TIME-50.)1,1,2
1 CONTINUE
SORT
Statements for Booster Phase
NOSORT
2
CONTINUE
Figure 10. Illustration of NOSORT option
If no NOSORT card is present at the beginning of
the structure statements, a SORT card is assumed;
that is, sorting is automatic.
INITIALIZATION
Frequently a simulation involves initial conditions
or parameters that are themselves functions of
other variables or parameters. For example, the
equations describing a chemical process might re-
quire the volume of a particular reaction vessel.
To obtain maximum flexibility, the user might pre-
fer to specify the dimensions of the vessel as pa-
rameters, rather than specify the volume. How-
ever, for efficiency in the use of the computer, he
would prefer that the computation of volume be per-
formed only once, before the simulation run, rather
than repeatedly during the run.
The INITIAL and DYNAMIC translator control
cards provide this capability. These cards are used
to bound a block of nonprocedural statements that
are to be performed only at the beginning of the run.
The DYNAMIC card signifies that the portions of the
problem statement that follow it represent the
dynamic portion of the simulation rather than the
initialization. If the INITIAL translator control card
is not used, the program assumes that all statements
describe the dynamics of the simulation; hence, the
DYNAMIC card is not required in the absence of the
INITIAL card.
Use of this feature is illustrated under "sample
problem" both in this manual and in System/360
Continuous System Modeling Program : Application
Description (H20-0240).
TERMINATION
It is often desirable to perform a set of computations
only at the completion of a simulation run. For
example, the user may wish to totalize the results
or to process them in accord with his own print or
$lot routine. Also, in many problems, it is desir-
able to use the results obtained in a run to control
subsequent runs, possibly to decide whether or not
these runs should be made. Examples are param-
eter optimization and two-point boundary value
problems that require modification of parameters,
between iterative simulations, based on the results
obtained in prior runs. A criterion is required in
these cases for terminating this iterative sequence
when a "sufficiently accurate" solution has been
obtained .
The TERMINAL control card allows the user to
efficiently and conveniently perform this type of
computation or achieve this type of program control.
All of the structure statements that follow a
TERMINAL card will be performed only at the comple-
tion of the run — that is, only when a FINISH condition
or FINTIM has been reached. Note that TERMINAL
allows both decisions and prescribed parameter modi-
fications to be made after a run, whereas the END
control card can be used only for modifications pre-
scribed before the run. Care should be exercised
when the TERMINAL feature is used in combination
33
with run or initialization options to ensure that
modifications are actually made in the order desired.
It must be recognized that until the conditions im-
posed in the TERMINAL section are satisfied, the
program will return from TERMINAL to the
structure statements in the initialization section, if
one is included. In any case, the specified TERMI-
NAL operations will always be completed before the
implementation of run options given by multiple
PARAMETER, CONTINUE, or END cards. Compu-
tations performed in the TERMINAL section over-
ride any specifications on data statements anywhere
in the run, but do not override structure statements.
An illustration of the use of TERMINAL is given
by the following example:
* INITIAL CONDITIONS
PARAMETER TTOP=2.0,X0=20.0,WTFCT=100.0
PARAMETER TEMP= 1000.0
* PROBLEM EQUATIONS
TZRO=
TGPR=
* THESE STATEMENTS FORM THE CONVERGENCE CRITERION
TERMINAL
ERROR=T ZRO-TGPR
IF(ABS(ERROR)- 0.5) 50,50,40
40 TTOP=X0+(TTOP-X0)*WTFCT/(WTFCT -ERROR)
CALL RERUN
GO TO 60
50 H=TZRO**2*TEMP**4
WRITE(6,51)H,TZRO
51 FORMAT(10X, F8. 2, 10X, F8. 2)
60 CONTINUE
END
In this example, the objective is to converge on an
optimum value of the parameter TTOP , starting
with an initial guess of 2. 0. After convergence,
the program is to calculate an output variable H
based on the optimum TTOP, and to output results
in accordance with the user's own format and
routine .
The statements following the identifying TERMINAL
control card form the convergence criterion, which
is a comparison between the absolute value of the
variable ERROR and 0.5. As long as ABS (ERROR)
is greater than 0.5, the iteration continues with a
new estimate of TTOP computed as indicated in
statement 40. Note that the user must indicate his
desire to rerun the simulation with the new value of
TTOP, by explicitly using the statement CALL
RERUN. This is a specific S/360 CSMP statement
that should be used only in connection with
TERMINAL.
The GO TO and CONTINUE cards are a convenient
method for bypassing the intervening computations.
The CONTINUE card may be considered to establish
a collection point for the preceding FORTRAN
logical statements.
When ABS(ERROR) is either equal to or less than
0.5, iteration is terminated. The program then
computes H and prints out H and TZRO in the format
specified in statement 51. The user should, of
course, always provide an optional termination pro-
cedure that can be automatically invoked if his cri-
terion fails to provide convergence after some
specified number of iterations .
The control card END signals the completion of
this particular sequence of parameter optimization
runs. Additional statements could be entered fol-
lowing this card with new parameters — for example,
a different value of TEMP to initiate another optimi-
zation sequence.
Another illustration of the use of TERMINAL
is found later under "Sample Problem".
INTEGRATION
Selection of an integration method and integration
interval for a particular simulation study should not
be made casually, but only after considering a num-
ber of interrelated factors. The objective is to
choose the combination of routine and interval that
will provide the fastest execution, while maintaining
enough accuracy for the purposes of the simulation
study and obtaining enough output data for easy in-
terpretation of results .
In general , as the complexity of the integration
method increases, the computer time required for
a single step also increases. On the other hand,
stability in numeric method may also increase, per-
mitting larger time steps. Thus, a number of
tradeoffs between accuracy and running time are
possible.
Basically two types of integration method are
available in S/360 CSMP: variable-step and fixed-
step. The mathematical formulas for these tech-
niques are given later under "Methods". The former
provide automatic adjustment of integration interval
consistent with the user's specifications on the
ABSERR or RELERR execution control cards. An
estimate of error is made in these methods by com-
puting Y(t+At) by two different formulas having
complementary error terms , and applying the
results in an estimation equation. The advantage of
these methods is that they achieve the specified
accuracy with the maximum possible step size.
Two variable-step routines are provided: MILNE
and Runge-Kutta (RKS). Both are sophisticated
methods involving somewhat lengthy computation.
They have the advantage of virtually ensuring a
satisfactory solution — but possibly at the cost of
excessive running time, if the error criterion has
been set too stringently. Note that the error cri-
teria can be set independently for each integrator in
the simulation, thereby allowing the severe con-
straints to be set only as necessary.
34
Within the set of fixed-step routines, these op-
tions, in order of decreasing complexity, are
Runge-Kutta (RKSFX), Simpson's (SIMP), trape-
zoidal (TRAPZ), ADAMS, and rectangular (RECT).
For a given step size, speed of solution would be
rated in the reverse order. Generally, however,
for reasons of stability, the less sophisticated
methods require shorter integration intervals to
achieve comparable accuracy.
Selection from among these several options is
simplified by first considering what output is re-
quired from the runs. Are both tabular and plotted
output required? At what time interval is tabular
output required? What should be the overall dura-
tion of a simulation run? Clearly, one should, in
any case, first specify FINTIM, PRDEL, and
OUTDEL. Note that the program is so designed
that the larger of OUTDEL and PRDEL will be
satisfied exactly. The lesser will be automatically
adjusted by the program to be a commensurable
submultiple ; FINTIM will likewise be automatically
adjusted to be a multiple of the lesser output inter-
val after adjustment.
Note too that the smaller output interval is auto-
matically treated as the maximum possible integra-
tion interval in a variable-step method. According-
ly, if either tabular or plotted output requires an
interval very small compared with FINTIM, it is
possible that no significant advantage will be real-
ized by selection of an integration method using
variable step-size adjustment. If the maximum
step size is constrained by the relatively small out-
put interval, use of the variable-step integration
methods may increase solution time without signif-
icantly improving accuracy. In such a case, the
less sophisticated integration methods should be
considered.
If no integration method is specified, the pro-
gram automatically utilizes the RKS method.
This method is generally a good choice for the
initial runs of a simulation study, if the user is un-
sure of the dynamic response of the simulated phe-
nomenon. It is advisable to make the initial choice
of DELT sufficiently small to ensure accurate,
stable solution even at the expense of a longer-than-
necessary initial computer run. After obtaining
greater familiarity with a particular problem, the
user may choose a more optimal combination of
timing specifications and integration method.
Some additional considerations apply to simula-
tions involving discontinuous functions , such as
MODINT, STEP, RAMP, and ZHOLD, or ele-
ments involving critical time relationships, such as
PULSE and IMPULS. In such problems, the sim-
pler integration methods using short integration
steps may give better results. For example, to
accurately represent the pulse train generated by
the IMPULS element, a fixed-step method should be
used with an integration step that is a submultiple
of the desired pulse interval.
Above all, the user should be prepared to do
some experimentation to achieve an optimal solution
in terms of running time and accuracy.
ARBITRARY FUNCTIONS
For handling functions of one variable, S/360 ,
CSMP provides two functional blocks: AFGEN
(arbitrary function generator) and NLFGEN (non-
linear function generator) .
A particular function is defined and used by
means of corresponding data and structure state-
ments. The x, y coordinates of the function points
are entered sequentially in a data statement, follow-
ing the function label and the symbolic name of the
function. For example:
FUNCTION CURVE1=-10. 2, 2. 3, -5. 6, 6.4, 1. 0, 5. 9, etc.
defines a function called CURVE 1, where the data
points on the curve are given in pairs, x and y. The
first point is (-10.2, 2 . 3) ; the second , (-5.6, 6.4);
the third, (1.0, 5.9); and so on. The correspond-
ing S/360 CSMP structure statement would be:
Y3=AFGEN(CURVE 1 , XIN)
Although the total number of data storage locations
is necessarily fixed by machine size, there is no
specific restriction on the number of points one may
use to define any particular function. The only re-
quirement is that the x coordinates in the sequence
x l' yi' x 2> v 2 • • • k e monotonically increasing.
Any number of arbitrary functions may be defined,
identified only by the symbolic names assigned by
the user.
AFGEN provides linear interpolation between
consecutive points, while NLFGEN uses a Lagrange
quadratic interpolation. Caution should be exer-
cised in the use of the NLFGEN functional element.
In particular , if the desired function contains an
abrupt discontinuity, it must be recognized that a
quadratic interpolation formula cannot represent
such a discontinuity without distortion. For such
situations it may be preferable to use the AFGEN
element, even though it might, at first glance,
appear to offer the less precise representation of
nonlinear functions in general.
IMPLICIT FUNCTIONS
The library includes an implicit function for the
solution of algebraic loops defined by algebraic
equations containing no memory function. This fea-
ture, in effect, directs the system to perform a
subiteration within the implicit loop, at each instant
of time, until the algebraic relationship has been
satisfied. A standard convergence formula is pro-
vided for which the user can specify the error cri-
terion. However, should this formula not prove
satisfactory for a particular problem, the user can
program his own convergence routine. A descrip-
tion of how this is done is given in the System
Manual. In the standard function, if there is no
convergence after 100 iterations, the run termi-
nates and a diagnostic message is provided.
An important point to note in connection with the
implicit function is the difference between memory
35
PageofGH20-0367-3,-2
Revised February 26, 1971
By TNL GN20-2329
and history functions. A memory function is one in
which the output depends only on past values of the
input and output. A history function is one in which
the output depends on the present value of the input,
as well as past input and output values. According-
ly, the output of a memory function can be obtained
without knowing the current input; the output of a
history function cannot. A memory function, there-
fore, breaks a loop in which it is contained, but a
history function does not. It follows that a closed
loop containing a history element, but no memory
element, is an implicit relationship — and requires
an IMPL functional block to break the loop. The
standard functions of S/360 CSMP should be treated
as follows:
Memory Functions
>
INTGRL
DELAY
History Functions
DERIV
RST
HSTRSS
IMPULS
ZHOLD
PULSE
Should the user not recognize that the problem in-
volves an algebraic loop, a diagnostic message will
be provided which indicates failure of the sorting al-
gorithm and lists the variables in the loop. To use
the implicit function, the user starts by writing the
following type of S/360 CSMP structure statement:
Y=IMPL(IC,P,FOFY)
where Y is the variable whose convergence is being
tested, IMPL is the name of the implicit functional
block, IC is the initial guess of the variable Y pro-
vided by the user, P is the error criterion that is to
be met, and FOFY is the output name of the last
statement in the definition of the algebraic loop.
This statement must be followed immediately by
a logical set of S/360 CSMP and/or FORTRAN
statements evaluating FOFY. S/360 CSMP sets up
the necessary iterative loop, which includes the
proper sequencing for information flow.
This procedure is illustrated for the implicit
equation:
Z=f(Z)=Ae _t +B sin(Z)
where A and B are given parameters. Since the
first term does not include Z, it need not be included
within the iterative loop.
The S/360 CSMP statements might be as follows:
CI = A * EXP( -TIME )
Z = IMPL( ZO, ERROR, FOFZ )
C2 = B * SIN( Z )
FOFZ = CI + C2
Note that the statements defining a function f(Z)
must meet the following requirements.
1 . As many statements as necessary may be
used to define f(Z), but the output name in the last
statement of the definition must be identical to the
third argument of the IMPL statement. There is
one restriction: this output name cannot be the out-
put of a MACRO or PROCEDURE function.
2. . The implicit variable (in this example Z) must
appear on the right side of an equal sign at least
once in the definition statements.
3. An implicit loop can be defined within a
MACRO or PROCEDURE, provided that the entire
set of required statements is contained within the
MACRO or PROCEDURE.
4. An implicit loop cannot be defined within
another implicit loop.
For the example above, the S/360 CSMP transla-
tor automatically generates the following statements :
30001 Z=IMPL(Z0, ERROR, FOFZ)
IF (NALARM) 30003, 30003, 30002
30002 CONTINUE
C2=B*SIN(Z)
F0FZ=C1+C2
GO TO 30001
30003 CONTINUE
Only four statements are added to those written by
the user. The statement numbers are assigned by
the program.
The first time the IMPL routine is entered ,
NALARM is set to one, and Z is given the user's
initial guess Z0. After each calculation of f(Z), the
program flow returns to the IMPL subroutine where
the convergence criterion is tested. If the criterion
is satisfied, NALARM is set equal to zero and Z
assumes the most recently calculated value of FOFZ.
If the convergence criterion is not satisfied, the
iteration continues. If convergence fails after 100
iterations, NALARM is set negative and the simula-
tion run is terminated with an appropriate comment.
Convergence is indicated if:
n+1 n
J n+1
Z ^-Z
n+1 n
< ERROR,
< ERROR,
n+1
n+1
> 1
< 1
The implicit function feature of S/360 CSMP is
specifically designed to solve relationships of the
form Z=f(Z). Thus, the IMPL statement, together
with the entire set of statements required to define
f(Z), may be viewed as a single "functional block"
with variable Z as its output. To avoid possible
erroneous results, special precautions must be ob-
served when the feature is used in any other manner.
36
PageofGH20-0367-3,-2
Revised February 26, 1971
By TNL GN20-2329
One such instance would be the use, in some other
portion of the model, of an intermediate variable
computed within an implicit loop. For the example
above, suppose that the quantity B sin(Z) were of
use outside the implicit loop — in addition to Z , the
nominal output of the implicit relationship. Program
errors may result if the user should attempt to use
the variable C2 in portions of the model outside the
loop. If a term computed within a loop is required
elsewhere, it is simplest to recompute the term
where needed. Alternatively, for some models it
may be possible to place the entire implicit loop
within a multiple- output PROCEDURE thus:
PROCEDURE C2, Z = LOOP ( ZO, ERROR, B, CI )
Z = IMPL( ZO, ERROR, FOFZ )
C2 = B * SIN( Z )
FOFZ = CI + C2
ENDPRO
Note that the PROCEDURE statement must have
listed as arguments of the function all variables and
parameters used within the PROCEDURE. For this
example parameters ZO, ERROR, and B and variable
CI are thereby listed as arguments of function
LOOP. Use of the implicit function within a PRO-
CEDURE does require that the user properly sequence
the statements within the loop.
TABULAR DATA
This feature of S/360 CSMP allows subscripted
variables and blocks of data to be handled conveni-
ently. For example, it permits data stored in a
one -dimensional array to be identified in structure
statements by the location of the data in that array.
Also, in the construction of a special function, the
user may have to transfer, to a subroutine, large
amounts of data such as input parameters , initial
conditions, matrix elements, or history. With this
feature the need for a lengthy subroutine argument
str ing is eliminated.
Use of the Tabular Data feature is illustrated by
the following set of statements:
STORAGE IC(5), PAR(3), MATRK(6)
TABLE IC(1)=25. 1, IC(2)=4. 0, IC(3-5)=3*41. 1, . .
PAR(l-3)=3*4. 1, MATRK(1)=2. 9E4, . . .
MATRrX(2-6)=5*31.7
Z=PAR(1)+LIMIT (IC (2) , IC (3) , XIN)
Y=FUNCT(IC, MATRK, MATRDC(3), X)
The first statement, STORAGE, instructs the pro-
gram to assign a total of 14 locations: five for the
array IC, three for PAR, and six for MATRK. The
second statement; TABLE, enters the indicated
numeric values into the specified locations . The
third statement shows an elementary use of the
ability to reference individual items in the table
within structure statements. The fourth statement
uses the stored variables in a user-defined sub-
program that references the entire IC and MATRK
arrays, as well as the individual element
MATRK(3).
An additional illustration of this feature is shown
in the following statements:
FIXED
L, IBAND
STORAGE
IBAND(J2)
TABLE
1 BAND(1 -12) - 12*0
G =
- DEVICE( PARI , XIN )
XIN -
- GAUSS( 3,0.0, 2.0 )
PROCEDURE
L --- BAND( G )
L - G - 7.0
L = MAX0( 1 , L )
L - MIN0( 12, L )
IBAND(L) IBAND(L) + 1
ENDPRO
The purpose of these statements is to prepare a
histogram showing the distribution of the variable
G within a range of -6. to +6. 0. G is obtained,
according to the problem definition, as the output of
a DEVICE with parameter PARI, and input from the
Gaussian noise generator. The STORAGE statement
sets up the necessary locations for the bands of the
histogram. The TABLE statement simply initial-
izes the contents of those locations. A PROCEDURE
function takes the generated values of G and pro-
duces the desired histogram. The results can be
displayed using FORTRAN output statements in a
TERMINAL section.
Note that the following rules must be observed
when using the Tabular Data feature:
1. STORAGE card(s) must be placed before any
reference to variable names on the card.
2. Dimensioned variables cannot appear to the
left of an equal sign, except, as illustrated above,
within a PROCEDURE or NOSORT function.
3. MACRO and PROCEDURE arguments cannot
be dimensioned.
The S/360 CSMP "TABLE" form of data entry,
used in conjunction with a STORAGE declaration
statement, is applicable only for one-dimensional
arrays. This combination permits convenient mod-
ification of tabular data from run to run. Alternate
methods using FORTRAN statements are available,
however, and must be used for multidimensional
arrays. The dimensions of a multidimensional
array can be specified using the FORTRAN
"DIMENSION' statement.
37
PageofGH20-0367-3,2
Revised February 26, 1971
By TNL GN20-2329
One means of initializing such an array is by the
FORTRAN "DATA" statement. With this method,
however, the data stored in the array cannot be
conveniently replaced by a new set of data for a
subsequent run. Thus, this method is often used
where the parameters remain unchanged for the
entire sequence of runs. For example, one might
specify an array X and initialize its elements as
follows:
/ DIMENSION X(2,5)
/ DATA X/3*0. 0,27. 4, 34. 4, 0.0, 4*5.0/
Note that whenever DIMENSION or DATA statements
are used with S/360 CSMP, it is necessary that a
virgule (/) be used in column 1.
In rare instances it may be desirable to specify
an array by means of LABELED COMMON so that
the data are available to a user-supplied subprogram.
In such cases, the data must be initialized using the
BLOCK DATA feature of FORTRAN. This method
is not recommended for the novice.
Another method of initializing an array is by
means of the FORTRAN "READ (5, xxx)" statement,
where xxx is the statement number of the corre-
sponding FORMAT statement. The data cards to be
read must be placed between the labels DATA and
ENDDATA immediately following the END statement
for the corresponding run. As example, the follow-
ing statements would be equivalent to the preceding
example:
ENDDATA,
TITLE SECOND RUN WITH NEW DATA FOR X ARRAY
END
DATA
1.0 1.0 34.4 7.0 7.8
0.105 8.37 12.06 7.8 8.0
ENDDATA
STOP
ENDJOB
Note that for the second run the second set of data
cards would be read assigning new parameter values
for the array X. Note also that the second DATA
label immediately follows the second END statement.
In this manner, a series of runs may be specified
and, if desired, new data may be read for each run.
By use of logical control statements in conjunction
with the READ statement, it is possible to read data
for selected runs only. The user must, however,
take care that the proper number of data cards are
available for each run, and that the format of the
data agrees with the FORMAT specification. AH
continuation cards for FORMAT statements must
have a $ in card column 6 and must immediately
follow the cards they continue.
/ DIMENSION X(2,5)
FIXED |,J
INITIAL
NOSORT
READ (5, 100 ) ( (X(I,J), J = 1, 5), 1
= 1,2 )
100 FORMAT ( 5F8.3)
END
DATA
0.0 0.0 34.4 5.0 5.0
0.0 27.4 0.0 5.0 5.0
38
RUN CONTROL
SEQUENTIAL RUNS
Several means are available for obtaining an auto-
matic sequence of runs of the same structure state-
ments with different data and control statements .
These permit easy variation of parameters, output
variables, and output options between runs.
Figure 11 illustrates the use of the CONTINUE and
END execution control statements for this purpose.
When a run is completed, these operate as follows:
1. A CONTINUE card permits the simulation to
accept changed data and control statements, without
resetting of TIME, and continues the run. For
example, this feature permits such items as inte-
gration method, integration interval, and data out-
put interval to be modified during the progress of a
simulation. In the illustration, the run halts at
TIME = 10. and then continues with a new printout
interval of 1.0 in place of the previous interval of
0.1. Note that the run will continue to the point at
which TIME is equal to 15.0.
2. An END card permits the simulation to accept
changed data and control statements, resets TIME,
and initiates a new run. In this illustration, the
parameter PI is equal to 5. in the first run, and
9.0 in the second run. Note that, unless additional
specifications are made, FINTIM will be 15.0 and
PRDEL will be 1.0 for the entire second run.
3 . A combination of END and STOP cards indi-
cates termination of the sequence.
PARAMETER
Pl=5.0
•
Structure, data, and control statements defining the run
TIMER
FINTlM=10. 0, PRDEL=0. 1
CONTINUE
TIMER
FINTIM=15 . 0, PRDEL=1 .
•
Data statements changing certain parameters
END
PARAMETER
Pl=9.0
.
Other data statements changing parameters
END
STOP
Figure 11. Illustration of sequential runs
As explained earlier under "Data Statements",
changes in either a parameter, initial condition, or
constant can also be performed automatically by
specifying multiple values on an appropriate data
card. For example, the statement:
PARAMETER RATE=(5.0, 5.5,6.0)
will initiate a sequence of three runs in which
RATE = 5. for the first run, RATE = 5. 5 for the
second run, and RATE =6.0 for the third run.
Only one parameter can use the multiple parameter
option at a time. The multiple value parameter
option is not intended for use with the CONTINUE
option. A multiple value parameter is limited so
that the maximum number of runs in any sequence
may not exceed fifty. See also section on data
statements for use of PARAMETER statement.
If the structural statements are to be changed,
multiple jobs must be submitted. Each must be
provided either with an ENDJOB STACK card fol-
lowed by a blank card, as the last cards in the set,
or its own OS/360 control cards. This is explained
in the Operator's Manual.
38.1
Note that if one job in a stack is terminated by
the Operating System, the remaining S/360 CSMP
jobs in the stack will be bypassed until the next set
of OS/360 control cards is read. If a job is ter-
minated by S/360 CSMP, the other jobs will be
processed.
MAIN PROGRAM CONTROL
The entire S/360 CSMP simulation can be put under
control of a conventional FORTRAN program. This
can be done by changing a small program called
MAIN, which controls the execution phase of
S/360 CSMP. MAIN consists of a series of calls
that initialize, scan the input data, and perform the
simulation. At the completion of a simulation run,
control is returned to the MAIN program and a test
. is made to see whether there are any more data
cards describing parameter changes for another run.
Virtually all of the capabilities available by using
MAIN are more readily available by using the
TERMINAL segment discussed previously. However,
MAIN does permit flexible use of the S/360 CSMP
system modules, including substitution of user-
supplied modules, which TERMINAL does not. Appli-
cation of this feature, however, requires familiarity
with the details of FORTRAN, since the MAIN pro-
gram is a FORTRAN routine.
The procedure for changing the MAIN program
is quite involved; an explanation of it is therefore
deferred to the System Manual.
38.2
DATA OUTPUT
The output options available are the printing of
variables, print-plotting of variables, output of
minimum and maximum values of specified vari-
ables, and preparation of a data set for user-
prepared plotting programs. A title can be speci-
fied as a page heading to printed output and a
label can be put on the print plots. In addition to
these standard options, FORTRAN output capa-
bilities are available to the user through use of a
NOSORT section, PROCEDURE function, or
TERMINAL segment.
There are two print formats: one in column form
with the variable names at the top of the columns ,
and one in equation form. The column form is used
if eight or fewer dependent variable names are re-
quested; the equation form is used if from 9 to 49
dependent variable names are requested. A maxi-
mum of 49 dependent variables can be printed per
simulation run. The independent variable (TIME) is
automatically printed. Up to five lines in a TITLE
will be printed at the top of each page of printed out-
put. In addition, the integration method and the spe-
cific value of the parameter (if there is a sequence
of multiple parameter runs) will be shown on the
first line of the title. Printout occurs at the speci-
fied or adjusted PRDEL interval, as explained ear-
lier under "Output Control Statements". As also ex-
plained in that section, the PRINT statement and all
other data output statements can be used only with
real variables. Figure 12 illustrates the column
format; Figure 13 illustrates the equation format.
CABLE REEL CUNTROL UfcSIGN
SECT
INTEGRATION
gain = l.oor^p on
TIME
0.0
5.0000E-01
1.0000E 00
I.SOOOE 00
2.0000E 00
2.50C0E 00
3.0000E 00
3.5000E 00
4.0000b 00
4.5000E 00
5.000Gb 00
5.500UE 00
6.0000b 00
6. 5000b 00
7.0000E 00
7.5000E 00
a.ooooE oo
8.5000E 00
9.0000E 00
9.5000b 00
1.0000E 01
1.0500E 01
1.1000E 01
1.1500b 01
1.2000E 01
1.2500E 01
1.300UE 01
1.3500b 01
1.4000E 01
1.450QE 01
1.5000b 01
1.5500E 01
l.bOOOb 01
1.6500E 01
1.7000b 01
1.7500E 01
1.8000E 01
1.6500E 01
1.9000E 01
1.9500E 01
2.0000E 01
VACT
0.0
2.1856E 00
7.8819E 00
1.5435E 01
2.3635E 01
3.1606E 01
3.8755E 01
4.4733b 01
4.9385E 01
5.2709E 01
5.4812E 01
5.5871t 01
5.6097E 01
5.5711b 01
5.4921C 01
5.3309E 01
5.2826b Ul
5.1785E 01
5.0864E 01
5.0108E 01
4.9535E 01
4.9144E 01
4.8917E 01
4.8828E 01
4.U845E 01
4.8937E 01
4.9075E 01
4.9233E 01
4.9392E 01
4.9537E 01
4.9659E 01
4.9753b 01
4.9819b 01
4.9859E 01
4.9875b 01
4.9875E 01
4.98&IE 01
4.9839b 01
4.9814E 01
4.97b9fc 01
4.9765E 01
VM
0.0
5.1229E-01
3.4462E 00
8.9041E 00
1.6009E 01
2.3787E 01
3.1430E 01
3.8357E 01
4.4207E 01
4.8810E 01
S.2146E 01
5.4304E 01
5.5443b 01
5.5702E 01
5.5470E 01
5.4767E 01
.5.3831E 01
5.2809E 01
5.1813E 01
5.0921E 01
5.0181E 01
4.9614E 01
4.9221E 01
4.8985E 01
4.8884b 01
4.8888E 01
4.8966E 01
4.9092E 01
4.9240E 01
4.9390E 01
4.9530E 01
4.9648b 01
4.9741E 01
4.9807E 01
4.9847E 01
4.9866E 01
4.9867E 01
4.9856E 01
4.9836E 01
4.9813E 01
4.9789E 01
ERROR
5.0000E 01
4.9488E 01
4.6554E 01
4.1096E 01
3.3991b 01
2.6213E 01
1.8570E 01
1.1643E 01
5.7933E 00
1.1903E 00
-2.1458E 00
-4.3037E 00
-5.4433E 00
-5.7624E 00
-5.4703E00
-4.7673E 00
-3.8313E 00
-2.8089E 00
-1.8127E 00
-9.2104E-01
-1.8129E-01
3.8560E-01
7.7939E-01
1.0148E 00
1.1161E 00
1.U25E 00
1.0338E 00
9.0831E-01
7.6045E-01
6.0970E-01
4.7041E-01
3.5193E-01
2.5908E-01
1.9312E-01
1.5251E-01
1.3382E-01
1.32fa3E-0l
1.4413E-01
1.6368E-01
1.8719E-01
2.U26E-01
C0NTL
5.0000E 01
4.9488E 01
4.6554E 01
4.1096E 01
3.3991 E 01
2.6213E 01
1.8570E 01
1.1643E 01
5.7933E 00
1.1903E 00
-2.1458E 00
-4.3037E 00
-5.4433E 00
-5.762-VE 00
-5.4703E 00
-4.7673E 00
-3.8313E 00
-2.8089E 00
-1.8127E 00
-9.2104E-01
-1.8129E-01
3.8560E-01
7.7939E-01
1.0148E 00
1.1161E 00
1.1125E 00
1.0338E 00
9.0831E-01
7.6045E-01
6.0970E-01
4.7041E-01
3.5193E-01
2.5908E-01
1.9312 E-01
1.5251E-01
1.3382E-01
1.3263E-01
1.4413E-01
1.6368E-01
1.8719E-01
2.1126E-01
TORQUE
0.0
1.0009E 04
1.5679E 04
1.8225E 04
1.8475E 04
1.7117E 04
1.4745E 04
1.1854E 04
8.8357E 03
5.9764E 03
3.4668E 03
1.4134E 03
-1.4530E 02
-1.2227E 03
-1.8679E 03
-2.1518E 03
-2.1550E 03
-1.9584E 03
-1.6365E 03
-1.2532E 03
-8.5928E 02
-4.9190E 02
-1.-7543E 02
7.7063E 01
2.6177E 02
3.8182E 02
4.4505E 02
4.6206E 02
4.4448E 02
4.0372E 02
3.5001E 02
2.9184E 02
2.3572E 02
1.8615E 02
1.4579E 02
1.1571E
9.5755E
8.V903E 01
8.1583E 01
8.3973E 01
02
01
4.0000E 00
3.9999E 00
3.9995F 00
3.9984F Q0
3.9965E 00
3.9937b 00
3.9902E
3.9861b
00
00
3.9814E 00
3.9763L 00
3.9709E 00
3.9654E 00
3.9597b 00
3.9541F 00
3.9485E 00
3.9430E 00
3.9376E 00
3.9323E 00
3.9271E 00
3.9220E 00
3.9169E
3.9119E
3.9069E
00
00
00
3.9019E 00
3.8969E
3.8920E
3.8869E
3.8819E 00
3.8 768E 00
3.8718E 00
3.8666E 00
3.8615E 00
3.8564E 00
3.8512E 00
3.8461E 00
3.8409E 00
3.8357E 00
3.8306E 00
3.8254E 00
3.8202E 00
I
4.5150E 03
4.5147E 03
4.512 5E 03
4.5072E 03
4.4982E 03
4.4854E 03
4.4690F 03
4.4495E 03
4.4276E 03
4.403HF 03
4.3788E 03
4.353 IF 13
4.3271F 03
4.3013E 03
4. 275TE 03
4.2509E 03
'•.22 6'.F 03
4.2025E 03
4.1792E
4.1562E
4.133 7E
4.U14F 03
4.0893F 03
4.0674F 03
4.04t>5E 03
4.0236F 03
4.')018E 03
3.9800F 03
3.9581E 03
3.9362E
3.914 3F
3.R925E
3.8706b 03
3.848 8E 03
3.827 1b 3
3.3053E 03
3.7837E 03
3.7621F 03
3.7406F 03
3.7191E 03
03
03
03
03
03
03
9.0224E 01 3.8150E 00 3.6978E 03
Figure 12. Illustration of column format
39
S/3cO
continuous
SYSTEM .<1UUtLlNu PKGu^AM
-- OUTPJT
MILNE INTFliRATUN
TIMfc =
UVCAr 1 =
K =
f- LUWAV= '
b.2000E-01
1.1000E-J1
0.0
02TIS =
FLOW =
P(J2TAV =
2.1000E 00
b.2 707F-08
0.0
P04
02CCAM=
"i.fcOOOE-'H
1.3000E 0'
LAP
Pi)2CAP =
1 . '?")1?F
•*. -J960 1 -
IIMt =
2
SOOOE-
-01
U2CAP =
K =
FLIJWAV =
5.tf335fc-01
*.6b2 0E 00
I.d408t-J2
02ns =
FLOW =
PU2TAV=
2. 391 IE 00
1.7006E-01
8.3480E 00
Pt.'4 =
D2CCAP=
-7.9163t-0c>
I .A534F. 02
CAP
PM2CAP*
1 . r> o ? ? f
4. 1079T
TO
01
IIMt =
b
.OOOUt-
-01
U2oAP =
FLUwAV=
6.1200t-'Jl
4.6618E-01
4.b9 70E-02
02TIS =
FLOW =
PU2TAV =
2.6458E OJ
l : . 7003E-C5
1.9618E CI
PIS 4
02CCAP=
3.9844E-14
1.6300E 02
cap =
PC2CA0-
1 . nn^op
4.424T :
in
11
TIMt =
7
sooot-
-01
U2CAP =
K =
rLCJWAV-
o.20b7E-0l
4.0916E-01
b.920SL-02
U2TIS =
FLJW =
P02TAV=
2.72446 00
1.0089E-05
3.0883E 01
PU4
02CCAP=
4.7665F-04
1.5514E 02
CAP =
P02CAP=
1 . ")0" ne
(t . S 5 S 4 F
01
IIMt =
1
OuOOE
00
D2'CAP =
K =
FLiJwAV=
6.2887E-01
9.64476-01
9.2<t77E-0?
U2TIS =
FLOW =
P02TAV=
2.6040E 00
3.1150E-04
4.2119E 01
P04
02CCAP=
4.40646-04
1.5722E 02
CAP
Pfl2C«P =
1.0T>OF
4.6H67F
0"
01
TIME =
1
250OE
OJ
U2LAP =
t-LOr, AV =
6.-3644E-01
3.9941E 00
1.1409fc-01
CJ2T I i» =
FLOW =
P02TAV=
2.8484E 00
9.16136-02
i.3313E 01
P04 =
02CCAP=
2.7735E-04
1.591 IE 02
CAP
P02CAP=
1.0000F
4.8104E
00
01
TIrtb ^
1
SJOOt
u2i-AP =
K
t-LUwAV=
&.360BE-01
<*.<tl42E 00
1.3497E-01
02T1S =
FLUW =
P02TAV=
2. 8 32 IE 00
1.3669E-01
6.4513E 01
PU4
02CCAP=
1. 1216F-04
l.b902E 02
CAP
P02CAP=
l.lOOOr
4.8045E
01
IIMt ^
1
7t>UUL
00
U2CAP =
r-LJwAV =
6. J063E-01
4.6b08E 00
1 .531346-01
U2TIS =
FLOW =
P02TAV=
2.7694E 00
1.68426-01
7.5725E 01
P04 =
02CCAP=
8.3399F-06
1.6766E 02
CAP =
Pf!2CAP =
l.OOOOF
4.7152E
no
01
TME -
2
OOOOE
00
J2CAr> =
FLUWAV=
6.2324E-01
4.6620E 00
1.72S3E-01
(J2TIS =
FLOW =
P02TAV=
2.6949E 00
1.7006E-01
8.6972E 01
P04
02CCAP=
-9.84896-06
1.5531E 02
CAP =
P02CAP=
l.OOonE
4.5972E
03
01
TIME =
2
.2S00E
00
U2CAP =
K =
FLUkvAV =
6.13H1E-01
4.6620E 00
1.9102E-01
02TIS =
FLOW =
P02TAV=
2.6046E 00
1.7006E-01
9.8256E 01
P04 =
02CCAP=
-5.11&9E-36
1.5345E 02
CAP
P02CAP=
l.OOOOE
4.4520E
00
01
IIMt =
2
.'jJOOE
00
U2LAP =
r( =
FLiJWA\/ =
6.0328E-.01
4.5o8dE 00
2.3985E-01
02TIS =
FLOW =
P02TAV=
2.51516* 00
1.5685E-01
1.0962E 02
P04
02CCAP=
-3.9837E-06
1.5082E 02
C4P =
Pl)2CAP =
l.OOOOF.
4.2968F
00
01
TIMt =
2
7b00t
00
J2CAP =
FLUwAV=
6.Jl42t-01
1.J905E 00
2.3L92E-01
02TIS =
FLOW =
P02TAV-
2.5534E 00
5.0905E-04
1.2096E 02
P04
02CCAP=
1.3468E-04
1.5035E 02
CAP
P02CAP=
l.OOOOE
4.2701F
00
01
TIME =
3
.UOOOE
00
U2CAP =
K =
FLJwAV=
6.1016E-01
b.0034fc-01
2.5520E-01
Q2TIS .=
FLOW =
P02TAV=
2.6297E 00
2.2S61E-05
1.3232E 02
P04 =
02CCAP*
3.6808E-04
1.5254E 02
CAP
P02CAP=
l.OOOOE
4.3974E
on
01
TIME =
3
,2!>00E
00
J2CAP =
K =
FLl)WAV=
6.1890E-01
4.0914E-01
2.7843£-01
02TIS =
FLOW =
P(J2TAV =
2.7150E 00
1.0088E-0S
1.4350E 02
P04 =
02CCAP=
4.7169E-04
1.5472E 02
CAP =
P02CAP=
l.OOOOE
4.5296E
30
01
Figure 13. Illustration of equation format
For the print-plot output, the dependent variable
is print-plotted across the page and the independent
variable (TIME) down the page. In addition, the
values of time and the plotted variable are printed to
the left side of the print plot. The minimum and
maximum values of the dependent variable are listed
at the top of the page along with a supplementary
title of the form "Name of Variable Plotted" versus
"Independent Variable". In addition, the specific
value of the parameter, in a sequence of multiple
parameter runs, is shown. Up to three other vari-
ables can be printed to the right side of the plot.
One-line labels can be printed on each print plot.
PRTPLT occurs at the specified or adjusted
OUTDEL, as explained under "Output Control State-
ments". Figure 14 illustrates this type of output.
Minimum and maximum values of variables
can be obtained by use of the RANGE control
card, and are also automatically provided if the
variable is specified for the PRTPLT or PREPAR
output options. Output from use of the RANGE
card is in five columns. The first column gives
the variable name; the second gives its minimum
value; the third indicates the time when the
minimum value was reached; the fourth gives the
variable's maximum value; and the fifth gives the
time when the maximum value was reached.
The TIME interval over which the RANGE values
were obtained is shown at the top of the RANGE
listing. Figure. 15 illustrates this output option.
40
CABLE KdtfL OGNTKUL JcSIGN
TEST UP SYSThM STABILITY
PAGE
TIME
0.0
5.00GUE-01
l.OOOOE 00
1.5000b 00
2.0000b 00
2.5000E 00
3.0000E 00
3.5uu0b 00
4.0GOUE 00
4.5000E 00
ti.OoOOE 00
5.5000b 00
6.0C00E 00
6.5000b 00
7.0000E OC
/.50u0b 00
8.0000E 00
8.5000b 00
9.0000E 00
9.5JG0E 00
l.OOOOE 01
l.OaOOt 01
1.1000E 01
1. lbOOE 01
1.2000b 01
1.25O0E 01
1.3CG0E 01
1.3500b 01
1.4000b 01
1.4500b 01
1.5000b 01
1.550GE 01
l.oOOOE 01
1.6500b 01
1.7000b 01
1.7500b 01
l.hOOJE 01
i. 8500b 01
1.9000b 01
1.9500E 01
2.0000E 01
MINIMUM
0.0
I
VACT
GAIN
VERSUS TIME
= l.OOOOE 00
VALT
0.0 +
2.1856b 00 -+
7.0819b 00 *■
1. 5435b 01 +
2.3635b 01 +
3.1606b 01 ♦
3.8 755L 01 " +
4.4733b 01 ♦
4.9385b 01 ♦
5.2709b 01 ■ ^
5.4812b Jl
5.5871b 01
5.6097b 01
5.5711b 01
5.4921b 01 ■
5.39C9E 01
5.2826E. 01' *
5.1785b 01 — : ♦
5.0108b 01 ♦
4.S535b 01 '■ ♦
4.9144E 01 +
4.8917b 01 +
4.8828b 01 ♦
4.8845E 01 +
4.8937E 01 +
4.9075b 01 ♦
4.9233b 01 • +
4.9392E 01 +
4.9337b 01 -+
4.96 59E 01 — — ♦
4.9753b 01 ' +
4.9819b 01 : ♦
4.9859E 01 ♦
4.9875b 01 +
4.9875b 01 ♦
4.9861b 01 ♦
4.9839b 01 +
4.9814E 01 *■
4.9789E 01 «■
4.9765c 01 ♦
MAXIMUM
3492E 01
I
VM
ERkOK
'■<
0.0
5.0000F
01
4.T010F
0?
5. 1229F-
01
4.9488F.
01
3.9999E
00
3.4462F
00
4.6554F
01
3.9995E
00.
3.9041 E
00
4. 1096b
01
3.9984F
00
1.6009F
01
3. 399 If
01
3.9965E
00
2.3797E
01
2.6213b
01
3.9937E
00
3.1430E
01
1.8570F
01
3.9902E
00
3.8357b
01
1.1643E
01
3.9861F
00
4.4207F
01
5.7933E
00
3.9814F
00
4.8810E
01
1. 1903E
00
3.9763E
00
5.2146E
01
-2.1458E
00
3.9709E
00
5.43040
01
-4. 30 37 E
00
3.9654F
00
5.5443E
01
-5.4433E
00
3.9597F
00
5.5762E
01
-5.7624E
00
3.9541E
00
5.5470E
01
-5.4703E
00
3.9485E
on
5.4767E
01
-4.7673E
00
3.9430E
00
5.3831E
01
-3.8313E
00
3.9376E
00
5.2809E
01
-2.8089E
00
3.9323E
00
5.1813E
01
-1.8127E
00
3.9271E
00
5.0921E
01
-9.2104E-
■01
3.9220F
00
5.0181E
01
-1.8129E-
-01
3.9169E
00
4.9614E
01
3.8560E-
-01
3.9119E
00
4.9221E
01
7.7939E-
-01
3.9069E
00
4.8985E
01
1.0148E
00
3.9019E
00
4.8884E
01
1.1161E
00
3.8969E
00
4.8888E
01
1.1125E
00
3.8920E
00
4.3966E
01
1.0338E
00
3.8869E
00
4.9092E
31
9.0831E-
-01
3.8819E
00
4.9240E
01
7.6045E-
-01
3.8768E
00
4.9390E
01
6.0970E-
-01
3.8718E
00
4.9530E
01
4.7041E-
-01
3.8666E
00
4.9648E
01
3.5193E-
-01
3.8615E
00
4.9741E
01
2.5908E-
-01
3.8564E
00
4.9807E
01
1.9312E-
-01
3.8512E
00
4.9847E
01
1.5251E-
-01
3.8461E
00
4.9866E
01
1.3382E-
-01
3.8409E
00
4.9867E
01
1.3263E-
-01
3.8357E
00
4.9856E
01
1.4413E-
-01
3. 8306E
00
4.9836E
01
1.6368E-
-01
3.8254E
00
4.9813E
01
1.8719E-
-01
3.8202E
00
4.9789E
01
2.H26E-
-01
3.8150E
00
Figure 14. Illustration of print plot
PKUtJLEM UURATIUN 0.0
ro 3. SOOSfc
00
VJRIAdLE
MINIMUM
TlMt
MAXIMUM
TIME
C2CAP
4.3l9i)E-01
1.3-«77L-
Jl
6.3739E-01
3
.1796E
00
G2TIS
1.7541E 00
1.4062E-
01
2.dS20fc 00
1
,52b3k
FC4
-l.t>799t-0b
l.J37bt
JO
5.O000L-03
.0
LAP
l.OOOOE 00
J.J
l.OOOOt 00
R
1.0309E-01
J. 9d<«tE-
02
4.6622E 00
2
.1484E
-0 1
FLUh
4.0ob3t-0a
3.yd44L-
02
1.700BE-01
2
1484E
-01
G2CLAF
1.0799L 02
i.it/rt-
01
l.b935L 02
3
1 7961-
00
PU2CAP
2.959it 01
1. 3-.77E-
01
4.H263E Jl
}
1 796E
00
FLUhAV
0.0
O.J
3.0166E-01
3
■J009E
00
P02TAV
0.0
J.J
1.3476E 02
3
5009E
00
Figure 15. Illustration of RANGE output
For installations with plotting devices , a tape or
disk may be prepared with the values of up to 49
variables in addition to TIME. Detailed information
on the use of the PREPAR data set is given in the
System Manual.
Other pertinent information is automatically pro-
vided by S/360 CSMP in the printer record of the
problem, in the following order:
1. The S/360 CSMP input statements.
2. The output variable sequence, indicating the
order of execution of the sorted functions
3. A problem statistics summary, showing
the number of output variables, input variables,
parameters, integrators, memory blocks,
FORTRAN statements, and data and control
cards
4. A listing of the subroutine data, as described
in the System Manual
5. A listing of user-supplied subprograms
6. A listing of the subroutine Update, showing
the sorted structure statements, as described in the
System Manual
7. A listing of the data, execution control, and
output control statements for each run, followed by
the specified output for that run
41
SAMPLE PROBLEM
A simple example illustrating several S/360 CSMP
features is the design of a radiating heat fin of the
type shown in Figure 16. The fins are attached to
the coolant tube in order to increase heat dissipation
by thermal radiation. This method might, for
example, be used to control the thermal environment
of a space station power plant.
A typical design problem would be to dimension
the fins such that each dissipated a specified amount
of heat per hour, with a specified temperature along
the root end of the fin. If the metal and the surface
roughness are fixed by other considerations, the
available design parameters are fin length, L, and
fin thickness, H. Since physical constraints on fin
length make that dimension less readily manipulated ,
the engineer would generally first seek a solution
using only fin thickness as the design parameter.
Figure 16. Radiating heat fin
In most simulation studies , it is the time or
transient response that is of interest. Here, how-
ever, the engineer is concerned with the steady-
state heat flow within the fin, at thermal equilib-
rium. Assuming negligible thermal interaction
between fins, the situation is described by the fol-
lowing differential equation:
d 2 T/dX 2 = 2crE (T 4 - T 4 ) /KH
s
where:
X = distance from fin root
T = temperature in degrees R
T = temperature of surrounding space
a = Stefan-Boltzmann constant
E = thermal emissivity
K = thermal conductivity
H = fin thickness
The independent variable is X, the distance from the
fin root, rather than time.
The simplicity of this differential equation is
disarming. Although only a few S/360 CSMP struc-
ture statements are needed to represent the rela-
tionship, design requires solution of a two-point
boundary value problem. The two conditions needed
to solve a second-order differential equation are
available here as one condition at X = 0. and the
other at X = L. At the point X = 0. 0, T must equal
the specified, constant fin root temperature, T .
At the edge of the fin (X = L) , radiation must
approach zero; that is, dT/dX must equal zero.
Solution of this type of problem involves a trial
and error process. The basic procedure is to
search for a value of dT/dX at X = 0. 0, which,
together with the specified temperature condition
at X = 0.0, yields a solution that also satisfies the
other end-point condition, dT/dX = 0. at X = L.
In this case, the actual implementation involves
a search over values of the design parameter H, by
use of the relationship:
atX = 0.0, -^ =
dT
dX
-Q
KBH
where Qq is the specified heat dissipation rate and
B is the width of the fin. The fin thickness, H, is
varied until the initial condition on dT/dX yields a
value at the fin edge sufficiently close to zero to be
considered a solution. A common approach is to
make an arbitrary first guess for the design param-
eter and then, by means of some algorithm, suc-
cessively modify that value after each run until all
constraints are satisfied. This procedure may be
easily automated within S/360 CSMP.
Suppose now that a solution is to be obtained for
a specific fin for which;
T = 0°R
s
E = 0.8
K = 25 Btu/hr/ft/°R
B = 0.5 ft
L = 0.25 ft
T Q = 2000. °R
Q Q = 1000. Btu/hr
Suppose, too, that the fin thickness , H, is con-
strained to be less than 0.01 feet.
42
Figure 17 shows the complete set of S/360 CSMP
statements for one possible approach to this design
problem. A LABEL card provides a heading for the
output that will be generated at the end of the com-
putation. The RENAME feature is used so that, for
convenience, the independent variable will be repre-
sented by the symbol X, rather than by TIME.
Note that the structure statements are separated
into three segments by use of the INITIAL,
DYNAMIC and TERMINAL control statements. The
computations in the initial segment are performed
only at the beginning of each run. For the first
run, the value of H is computed using values of
HIGH and LOW as specified in a CONSTANT state-
ment. On subsequent runs during the iterative
search, HIGH and LOW will be adjusted by the
algorithm embedded in the terminal segment. Using
this value for H, the program next calculates the
variables COEF and DTDXO for use in the dynamic
segment. It should be remembered that structure
statements within the initial segment are presumed
to represent parallel structure. Accordingly, the
actual order of the statements within this segment
is of no concern. Unless the user deliberately
chooses otherwise, by use of the NOSORT option
or by placing statements within a PROCEDURE
function, the sorting algorithm of S/360 CSMP
automatically determines an appropriate compu-
tational sequence.
♦♦♦♦CONTINUOUS SYSTEM MUDELING PROGRAM****
♦ ♦♦PROBLEM INPUT STATEMENTS'^
LABEL COOLING FIN DESIGN
RENANE TIME = X
INITIAL
CONSTANT
OYNAMIC
H = 0.5^ ( HIGH + LOW )
COEF = { 2.^SIGMA^E ) / ( K*H )
DTDXO = -Q0 / ( K*B*H J
Q0 = 1000. t TO = 2000. t LOW = 0.0,
SIGMA = 0.173E-8, E = 0.8, < = 25.0,
D2TDX2 = COEF * ( TEMP**4 )
DTDX = INTGRH DTDXO, D2TDX2 )
T = INTGRLI TO, DTDX )
TEMP = LIMIT! 0.0, TO, T )
HIGH =.0L, .
B = 0.5
TERMINAL
IF
( (HIjGH - LOW) .LT. 0.00001 ) GO TO
IF
( DTDX .LT.
0.0 ) GO TO 1
HIGH =
H
GO
TO 2
1
LOW =
H
2 CALL RERUN
3 CONTINUE
TIMER
DELT =
0.0001, FINTIM = 0.25
EN0
TIMER
OUTDEL =
0.01
PRTPLT
TEMP(DTDX,D2TDX2,H)
END
STOP
Figure 17. Listing of cooling fin design input
The statements between the DYNAMIC and
TERMINAL control cards represent the dynamics
of the differential equation relationship. Note that
this is merely one possible representation of this
relationship. There is no single "best?' formulation;
many others would be equivalent and just as efficient.
Some users prefer to "nest" expressions in order
to achieve a very compact problem formulation;
others find that fewer errors occur if a single func-
tional relationship is expressed in each statement.
Note, in particular, that the integrator that develops
DTDX uses, as an initial condition, the value
DTDXO computed in the initial segment. An inter-
esting refinement of the search procedure is the use
of a limiting function, applied to T, to obtain the
variable TEMP. Clearly, in a correct solution, the
43
temperature along the fin must be less than that at
the fin root and greater than the temperature of the
surrounding space. The limiting function imposes
this restriction explicitly, as a precaution, in the
event that an estimate of H causes a "wild" solution.
A TIMER control card specifies the integration
interval and also specifies that the dynamic compu-
tation should terminate in each run when X reaches
0.25, the fin length. Since no integration method
has been specified, the program will automatically
use the variable-step RKS method.
This simple example calls for only two types of
S/360 CSMP functional elements: the integrator and
the limiter. Typical problems would generally use
many types of functional elements in addition to
algebraic statements. By definition, the structure
statements within a terminal segment represent
procedural programming. In this example, the ter-
minal segment implements a binary search algo-
rithm that adjusts the values of HIGH and LOW
according to the final value of DTDX. Consistent
with the physics of the problem, this algorithm re-
duces the estimate of H used in the next run if the
final value of DTDX is positive, and increases the
estimate if DTDX is negative. The algorithm is
designed to ensure convergence, subject to the
dimensional constraints on fin thickness imposed by
the HIGH and LOW values specified on the CONST
data card. The designer has made his own definition
of "sufficient accuracy" by his choice of the constant
term in the first IF statement. When convergence is
obtained, the program bypasses the adjustment al-
gorithm. Until convergence is obtained, the pro-
gram calls RERUN, thereby signifying that yet
another iteration is required.
Note that no output statements are used before the
first END card. This allows the entire search to
occur without either tabular or plot output until con-
vergence. When convergence occurs, the program
next encounters statements requesting a print plot
of the temperature profile. S/360 CSMP then per-
forms one additional run, using the final value of
H obtained from the iterative search, and outputs
the results of this run as requested on the TIMER
and PRTPLT control cards.
44
PageofGH20-0367-3,-2
Revised February 26, 1971
By TNL GN20-2329
PROBLEM CHECKOUT FACILITIES
The program provides an option for the printing of
the current values of variables at a specified time,
as well as diagnostic messages when the program
detects a suspected error.
The subroutine DEBUG, which is used to obtain
the values, may have considerable utility in the
problem checkout phase. The subroutine is called
as follows:
CALL DEBUG( n, r )
where n must be an integer constant and t is a real
constant. The statement can be used any number of
times in a run. The variable names and current
values are printed for each simulation variable, in-
cluding system variables and parameters. The
DEBUG output will occur a maximum of n times
during a run; the first output will occur when TIME
equals or exceeds the real constant t. Figure 18
illustrates this checkout feature. Note that output
with system variable KEEP equal to zero is a trial
evaluation; that with KEEP = 1 represents a valid
integration step.
CABLE KEEL CONTROL DESIGN
DEBUG OUTPUT
T1HE = 0.0
DEBUG OUTPUT
TIME = 0.0
KEEP=
DELT =
UUTDEL=
VM
zzooio=
ZZ0009=
PI
Kl
T0RQUE=
KfcfcP = 1
DELT =
0UTDEL=
VM
ZZ0010=
ZZ0009=
PI
Kl
TURC
5.0000E-02
5.0000E-01
0.0
0.0
0.0
3.1<»16E 00
7.9577E-04
0.0
5.0000E-02
5.0000E-01
0.0
0.0
0.0
3.1416E 00
7.9577E-04
DELMIN=
TH1D0T=
TH2D0T=
ZZ0002=
ZZ0OOO=
REMPTY=
I
VACT =
DELMIN=
TH1D0T=
TH2D0T=
ZZ0002=
ZZOOO0=
REMPTY=
I
VACT =
RECT INTEGRATION
GAIN = 1.03C0F 00
2.0000E-
-06
FINTIM=
2.0000E 01
PRDEL =
S.flOOOE-
-01
0.0
R
4.0000E 00
DUMMY =
0.0
0.0
ZZC004=
0.0
Z 7.000 7=
5.0000E
01
0.0
RFULL =
-V.0000E 00
Z 7.0006=
0."
0.0
D
1.0000E-01
W =
2.0000F
00
2.0000E
00
VDtSIR=
5.0000E 01
GAIN =
I. 000 OF
"0
4.5150E
03
ERROR =
5.0000E 01
CONTL =
5.0000E
01
0.0
Zl
0.0
2.0000E-
-06
FINTIM=
2.0000E 01
PRDEL =
5.0000F-
-01
0.0
R
A.0000E 00
DUMMY =
0.0
0.0
ZZ0004=
0.0
ZZ0007=
5.0000E
01
0.0
RFULL =
4.0000E 00
ZZ000fe=
0.0
0.0
D
1.0000E-01
W =
2.0000E
oo
2.0000E
od
VDESIR=
5.0000E 01
GAIN =
1.0000E
00
4.5150E
03
ERROR =
5.000J1E-— ~"
CQNTL =
5.0000F
01
0.0
Zl
TIME
0.0
= 0.0
Figure lb. Illustration of DEBUG output
DEBUG may be used only from a procedural section.
While permissible from such a section of the INITIAL
segment, it is ordinarily called from the DYNAMIC
segment. A restriction on use of DEBUG is that it
must be called at time zero; logical control statement
should not be used in such manner as to "branch
around" the statement at time zero. This restriction
is imposed in order that the DEBUG Counters may be
properly initialized. DEBUG may not be used from
the TERMINAL segment since this segment is not
entered at time zero. This DEBUG feature of S/360
CSMP should not be confused with the FORTRAN IV
(G) Debug Facility. The latter is not supported
within S/360 CSMP and may cause inaccurate
numerical results.
Most commonly, DEBUG is called after all other
computations concerned with model structure are
completed. The best way to accomplish this is to
define a procedural section at the end of the DYNAMIC
segment as follows:
NOSORT
CALL DEBUG( 20, 15.0 )
TERMINAL
This usage would result in a maximum of 20 DEBUG
outputs, the first occurring no earlier than 15.0 time
units. All values printed at each output would repre-
sent computations for the current call to the UPDATE
subroutine.
Sometimes it is helpful to check on the performance
of a specific statement within the model. This is
readily accomplished by grouping that statement and
a call to DEBUG as part of a PROCEDURE. Suppose,
for example, that a model includes the statement
Y = SQRT( X )
and that X, for reasons not apparent, assumes
negative values during portions of the simulation.
One might investigate this situation as follows:
PROCEDURE Y = TEST( X )
IF( (TIME .EQ. 0.0) .OR. (X .LT. 0.0) ) CALL DEBUG( 10, 0.0 )
Y = SQRT( X )
ENDPRO
For testing a user-supplied function, one might
extend this technique, calling DEBUG both immedi-
ately before and immediately after use of the suspect
function. Note also that DEBUG may be used within
a procedural MACRO or a PROCEDURE contained
within a MACRO. Finally, it should be mentioned
that if debugging requires only a few values, rather
than those on the entire model, the FORTRAN
"WRITE" statement may be used as an alternative
to DEBUG.
45
PageofGH20-0367-3,-2
Revised February 26, 1971
ByTNLGN20-2329
DIAGNOSTIC MESSAGES
Diagnostic messages may occur during both the translation and execution phases of the
program and are designed to be self-explanatory. Some of the diagnostic checks
detect illegal characters or incorrect syntax; the symbol "$" is printed below the
detected error prior to the associated diagnostic message. A "warning only"
message is printed when an error is not wholly discernible in translation or does
not destroy the "validity" of simulation. Some examples of these errors are:
Output variable name not unique
Control variable name not a systems variable
Parameter value not specified
Variable used as input to a section not available from any prior section
Some examples of errors causing a run halt at the end of translation are:
Incorrect structure or data statement format
Invalid data card type
Unspecified implicit loop
RELERR specification on other than an integrator output name
Examples of errors causing a run halt during execution are:
Failure of an integration or implicit function to meet the error criterion
A misspelled subroutine name
The following is a list of the diagnostic messages with their explanations and suggested
corrections :
"CALL RERUN" CAN ONLY BE USED IN A TERMIN SEGMENT.
PROBLEM TERMINATED.
CALL RERUN can be used only in a TERMINAL segment. If it is used elsewhere, the
run terminates.
CSMP STATEMENT INCORRECTLY WRITTEN
The translation phase has detected an error in the statement printed before this mes-
sage. The statement should be checked carefully, including parentheses and commas.
Although translation of the source statements will continue, the run will be termi-
nated before the execution phase.
CSMP STATEMENT OUT OF SEQUENCE
The sequence of input statements cannot be processed and the run will be terminated
before the execution phase. The statement should be checked for sequence in the input
deck to see if it has been misplaced. MACRO definitions must precede all structure
statements. An INITIAL segment, when used, must precede the DYNAMIC segment.
If used, the TERMINAL segment must follow the DYNAMIC segment.
DATA HAS NOT BEEN SPECIFIED FOR AN AFGEN FUNCTION
DATA HAS NOT BEEN SPECIFIED FOR AN NLFGEN FUNCTION
An AFGEN (or NLFGEN) function generator has been used in a structure state-
ment but the corresponding data has not been specified using the FUNCTION
statement. The run will be terminated.
46
DYNAMIC STORAGE EXCEEDED. THIS CASE CANNOT BE RUN.
The 8000-word limitation on simulator data storage has been exceeded. The storage
in this array includes the current values of model variables, function and error tables,
central integration history, and subscripted variable values. The problem should be
analyzed to determine where equations can be combined to reduce the number of
required entries in the array.
ERROR - CENTRAL INTEGRATION ROUTINE NOT SUPPLIED
The user has used the word CENTRL for his integration method on the METHOD
execution control card; however, he has not supplied the integration deck to the pro-
gram. The run will be terminated.
ERROR IN COORDINATE ENTRffiS
An error has been detected in the previously printed FUNCTION data statement .
There is either an odd number of entries in the data table or an improper sequence
of X-coordinate values. The run will be terminated.
ERROR IN TABLE ENTRY
In the previously printed TABLE data statement, an error has been detected. Although
reading of the data statements will continue, the run will be terminated before execution.
ERROR IN PRINT-PLOT STATEMENT
An error has been detected in the PRTPLOT output control statement. The statement
should be checked for a correct number of parentheses and commas for specifying
lower and upper limits, particularly if one or the other is missing, and commas are
used to indicate this. Although the run continues, everything on the card after the
error is disregarded.
EXCEEDED MAXIMUM ITERATIONS ON IMPLICIT LOOP
One hundred iterations of the implicit loop have been run and convergence has not yet
occurred. The run has been terminated. One possibility is to change the error con-
dition, so that the convergence criteria can be met.
FINTIM IS ZERO. THIS CASE CANNOT BE EXECUTED.
FINTIM either has not been specified or has been specified as being equal to zero.
GENERATED STATEMENT No. xx
The translator has detected an error during generation of statement xx of an in-
voked MACRO in the structure of the model. Carefully check the corresponding
statement of the MACRO definition for proper spelling and punctuation.
47
ILLEGAL CHARACTER OR DOUBLE OPERATOR
In the previously printed statement, an illegal character or double operator has been
detected. Although translation of the source statements will continue, the run will
be terminated before the execution phase.
INCORRECT IMPLICIT STATEMENT
The translation phase has detected an error in the IMPL structure statement printed
before this message. The statement should be checked to see that the third argument
is the output name of the last statement in the definition and that the block output
appears at least once to the right of an equal sign. Although translation of the source
statements will continue, the run will be terminated before the execution phase.
INCORRECT MACRO STATEMENT
The translation phase has detected an error in the MACRO use statement printed
before this message. The statement should be checked to ensure that the number of
arguments and outputs is correct and that argument list ends with a parenthesis .
Although translation of the source statements will continue, the run will be termi-
nated before the execution phase.
INCORRECT TIMER VAR. NAME**WARNING ONLY
One of the system variable names (FINTIM, DELT, PRDEL, OUTDEL, or
DELMIN) has been misspelled on the TIMER execution control card. The user should
also check the possibility that the system variable has been renamed. Although the
run will continue, the system variable misspelled will be unchanged.
INPUT NAME SAME AS OUTPUT NAME
The output variable name to the left of the equal sign has also been used as an input
name on the right side of the equal sign. Except as output of a memory type functional
element, such usage is not permissible in a parallel, sorted section. The run will
be terminated.
INPUT TO FUNCTION GENERATOR nnnnnn BELOW SPECIFIED RANGE
INPUT =xxxx.xxxx
The input (xxxx.xxxx) to the function generator named nnnnnn is below the minimum
specified range. The program will take the value for the minimum specified and con-
tinue. This message will be printed only once, even though the condition is reached
several times.
INPUT TO FUNCTION GENERATOR nnnnnn ABOVE SPECIFIED RANGE
INPUT = xxxx.xxxx
The input (xxxx.xxxx) to the function generator named nnnnnn is above the maximum
specified range. The program will take the value for the maximum specified and
continue . This message will be printed only once , even though the condition is
reached several times.
48
LABEL INCORRECTLY WRITTEN
The label used in the preceding statement cannot be recognized by the program. Check
for proper spelling. The statement will be disregarded; the run will continue.
MACRO xxxxxx WITHIN MACRO yyyyyy USED IN A PROCEDURAL SECTION
MACROs, separately defined, may be invoked within the definition of other MACROs
if overall parallel structure is implied. Invocation of a MACRO within a PROCEDURE
within a MACRO definition is therefore not permissible. Similarly, a MACRO containing
other MACROs in its definition may not be invoked from a PROCEDURE or from a
procedural section.
MORE THAN 10 PRTPLOT STATEMENTS
More than ten PRTPLOT output control statements have been specified. Only the first
ten will be used.
NUMBER EXCEEDS 12 CHARACTERS
In the previously printed statement, a number exceeding twelve characters in a
MACRO argument or integrator block initial condition has been detected. Although
translation of the source statements will continue, the run will be terminated before
the execution phase.
NUMBER INCORRECTLY WRITTEN
In the previously printed statement, a number written incorrectly has been
detected. If detected during the translation phase, translation of the source
statements will continue; however, the run will be terminated before the execution
phase.
ONLY FIRST 10 CONDITIONS FOR JOB END WILL BE TESTED
More than ten specifications have been given with the FINISH execution control state-
ment. Although the run will continue, only the first ten specifications will be used.
ONLY FIRST 50 VALUES WILL BE USED
The multiple value form of the PARAMETER data statement has been used with
more than 50 values for the parameter. A sequence of runs will be performed,
but using only the first 50 values for the parametric study.
ONLY FIRST 50 VARIABLES WILL BE PREPARED
More than 50 variables (including TIME) have been specified with PREPARE or
PRTPLOT output control statements. Although the run will continue, only the
first 50 variables will be used.
ONLY FIRST 50 VARIABLES WILL BE PRINTED
More than 50 variables (including TIME) have been requested with PRINT execution
control statements. Only the first 50 will be printed; others will be ignored.
49
ONLY FIRST 100 VARIABLES WILL BE RANGED
More than 100 variables (including TIME) have been specified with the RANGE
output control statement. Although the run will continue, only the first 100
variables will be used.
ONLY LAST VALUE OF FAMILY USED FOR CONTIN RUN
A multiple-value parameter has been used with a CONTINUE card. THE CONTINUE
control feature will be implemented only with the last value of the parameter. This
is a warning message; the run will continue.
OUTPUT NAME HAS ALREADY BEEN SPECIFIED
In the previously printed statement, the output variable name to the left of the equal
sign has been used before as an output variable name; that is, it has occurred to
the left of the equal sign in a preceding section. The run will be continued.
PARAMETERS NOT INPUT OR OUTPUTS NOT AVAILABLE TO
SORT SECTION***SET TO ZERO***
A list of variable names will be printed following this heading. The run is continued.
Variables that are not parameters specified on data cards are set to zero. Output
variable names that are not available to this sort section are initially set to zero, but
may change as the problem is run.
PROBLEM CANNOT BE EXECUTED
At least one diagnostic message will have been printed among the source statements
indicating the reason why the problem cannot be executed. The run will be terminated.
PROBLEM INPUT EXCEEDS TRANSLATION TABLE nn
During translation of the problem, a table has been exceeded and the run will termi-
nate. The specific table is identified by nn in the following list:
nn Translation Table
1 More than 500 statement output names
2 More than 1400 statement input names
3 More than 400 parameter names
4 More than 300 INTGRL or MEMORY outputs
5 More than 1400 input names and unique block names
6 More than 20 FKED variable names
7 More than 100 initial condition numeric values
8 More than 10 FORTRAN specification cards
9 More than 100 unique block names and symbolic names with first letter I, J,K, L,
M, or N but not appearing on FDCED statements
10 More than 25 STORAGE variable names
11 More than 15 sections (SORT or NOSORT)
50
nn Translation Table
12 More than 100 MACRO arguments, outputs, and statement numbers for one
MACRO
13 More than 50 MACRO functions
14 More than 120 MACRO definition cards
15 More than 50 HISTORY or MEMORY functions
16 More than 15 MEMORY functions
17 More than 85 variables that are neither parameters specified on data cards
nor outputs of a following SORT section
18 More than 150 duplicate names in COMMON (outputs or inputs to INTGRL
blocks)
19 More than 100 parameters in one SORT sequence
21 More than 600 structure statements in a single SORT section
PRTPLOT, PREPARE, AND RANGE VARIABLES EXCEED 100. ALL RANGE
VARIABLES STARTING WITH xxxxxx HAVE BEEN DELETED.
More than 100 variables (including TIME) have been specified with PRTPLOT,
PREPARE , and RANGE output control statements. Although the run will
continue, only the first 100 variables will be used for this run.
RERUN FROM TERMIN CANCELED FOR CONTIN RUN
The TERMINAL segment cannot be used to cause a rerun when a CONTINUE translation
control statement started the run. The TERMINAL computation statements will be
executed but any CALL RERUN will be ignored.
SIMULATION HALTED
The run was terminated because a FINISH condition was satisfied. The variable
name and its value are printed.
SIMULATION INVOLVES AN ALGEBRAIC LOOP CONTAINING THE
FOLLOWING ELEMENTS
A list of output variable names will be printed following this diagnostic. The sort
subprogram has been unable to find an integration or memory block in the loop
involving these variables. The run will be terminated before the execution phase.
SYMBOLIC NAME xxxxxx NOT DEFINED
An error has been detected on the PARAMETER, INCON, CONSTANT, or TIMER
card printed before this message. Although input to the execution phase will con-
tinue, the simulation will not be run.
51
SYMBOLIC NAME EXCEEDS 6 CHARACTERS
In the previously printed statement, a symbolic name exceeding six characters
has been detected. Although translation of the source statements will continue,
the run will be terminated before execution.
SYMBOLIC NAME INCORRECTLY WRITTEN
In the previous statement, an incorrectly written symbolic name has been
detected. The run will be terminated.
TOO MANY CONTINUATION CARDS. MAX=n
The previously printed statement has been continued on too many cards. If N = 3, a
MACRO label statement has over three continuation statements. If N = 8, a structure
statement has over eight continuation statements. The user should make multiple
statements or use more columns on individual cards . Although translation of the
source statements will continue, the run will be terminated before the execution
phase.
TOO MANY LEFT PARENTHESES
TOO MANY RIGHT PARENTHESES
Too many left (or right) parentheses have been detected in the statement printed before
this diagnostic. Although the translation of the source statements will continue, the
run will be terminated before the execution phase.
VARIABLE STEP DELT LESS THAN DELMIN. SIMULATION HALT.
The simulation will not be continued because the specified DELT is less than the
specified DELMIN.
52
METHODS
This section of the manual describes some of the
basic techniques and restrictions of the program.
The topics included are:
1. Integration techniques
2. Dynamic storage allocation
3. Program restrictions
4. Reserved words
5. Statement ordering
6. System macros
INTEGRATION TECHNIQUES
S/360 CSMP uses centralized integration. This
means that all integration statements are placed at
the end of the structure coding, so that all current
inputs to integration functional blocks are defined
before integration. A single routine is then used to
update each of the integrator output variables used
in the simulation.
Several different types of routines are available
to perform the integration operation. They include
both fixed integration step-size routines and vari-
able step-size routines. Five fixed step-size rou-
tines are available: fixed Runge-Kutta, Simpson's,
trapezoidal, rectangular, and second-order Adams.
Two variable step-size routines are available:
fifth-order Milne predictor-corrector and fourth-
order Runge-Kutta. In these latter routines, the
integration interval A t is varied, under program
control, during problem execution. Both routines
provide an estimate of the integration error, which
is compared with a user-specified error bound.
The step size is adjusted accordingly by the pro-
gram.
If none of the above methods satisfies the user's
requirement, a dummy integration routine named
CENTRL is provided to allow the user to specify his
own integration method. He enters it into S/360
CSMP by giving it the name CENTRL. The System
Manual contains a complete discussion of the steps
involved.
The mathematics of the integration methods are
as follows:
1. Milne' Fifth-Order Predictor-Corrector
Predictor:
Estimate:
+ 4
X t-2At" X t-3At)
"t+At
= . 96116- Y + a + . 03884. Y
t+At
Integration interval control is based on the
following criteria:
0.04 1 Y C - Y^l | y c| >
R-l Y C |
0.04 I Y C - Y P
R
< 1
Y C | < 1
2. Runge-Kutta (Fourth Order)
Y t + At = Y t + 6 (V 2 V 2 V K 4)
Kl =At.f(t, Y t )
K 2 =At.f(t + 4i, Y t+ 3)
K.
At.f(t + f*. vir)
K 4 -At-f (t + At, Y t + K 3 )
If variable-step integration is used, the
interval will be reduced to satisfy the follow-
ing criterion:
l Y
t+At
- Y c
Error
A +R
t+At
A + R -I Y
< 1
t+At|
r s .
where Y is Y^+ At calculated by Simpson's
Rule, and A and R are the absolute and rela-
tive errors corresponding to the particular
integrator value.
3. Adams-Second Order
Y t+At = Y t + T ( 3 • Y t " Y t- At)
4. Simpson's Rule
Predictor:
Corrector:
Y t+ At = 8 ( Y t + 7 ' Y t- At) + 192 ( 65 ' X t+M
+ 243.X t + 51.X t _ At + X t _ 2M )
t+-
At
= y +AL x
At
t+At t+.
= * P M +J f * t+ M
53
Corrector:
t+A t
5 . Trapezoidal
Predictor:
Y t"At = Y t +At - X t
Estimate:
Y t+At ~ Y t + "2~-( X t + X t+At)
NOTE: In these equations, the common terminol-
ogy is X = Y =f(t). A value X. . used in the
estimation is based on the prediction Y
H t+ At
DYNAMIC STORAGE ALLOCATION
S/360 CSMP uses dynamic storage allocation.
Storage areas are assigned, at execution time,
to tables, integration history, etc., on the basis
of the actual problem requirement. Standard
S/360 CSMP functions as well as FORTRAN
functions are loaded only if used. The alterna-
tive approach would be to assign fixed areas
to these tasks and functions . Dynamic alloca-
tion leaves more space available for the user's
program because routines and tables not required
do not take up core.
6. Rectangular
Y t + At = V At - X t
PROGRAM RESTRICTIONS
Dynamic storage allocation is not practical
during the translation phase. The size of cer-
tain tables used during that phase, therefore,
have been set at fixed values. Consequently,
for some of the components,' there are limitations
as to how many can be used in a simulation.
The following list of restrictions may be of
value when a very large problem is to be solved
with S/360 CSMP:
10.
11.
12.
13.
14.
15.
16.
Item
Output variable names, including intermediate output names generated by
S/360 CSMP for MACRO and INTGRL functions
Input variable names, including parameter names
Parameter names
Integrators plus statements with memory and history functions
User-supplied memory and history functions
User-supplied memory functions
Tables (STORAGE variables)
Structure statements, including those generated by S/360 CSMP for MACRO
and INTGRL functions in a single SORT section
Simulator data storage locations, including areas for the current values of
model variables, function and error tables, centralized integration history,
and subscripted variable values
Print output variables , including TIME
Print-plot output variables , including TIME
PREPARE output variables, including TIME
Range variables, including print-plot and PREPARE variables
FINISH specifications, not including FINTM
Statements sent directly to FORTRAN (identified by a / in cc 1)
Fixed-point variable names
Maximum
500
1400
400
300
50
15
25
600
8000
50
50
50
100
10
10
20
54
These restrictions can be modified for specific
uses of available core or to take advantage of addi-
tional core . The method is discussed in the System
Manual .
RESERVED WORDS
Because the words listed below have been reserved
by the FORTRAN compiler, they should be used in
the input program only as specified by FORTRAN.
They may not be used as variable or subprogram
names.
ABS
GO
GOTO
BACKSPACE
CALL
IABS
COMMON
HDIM
CONTINUE
IF
ifdc
DABS
INTEGER
DBLE
ISIGN
DEFINE
DIM
DIMENSION
PAUSE
DFLOAT
DO
DOUBLE
READ
DSIGN
REAL
RETURN
END
REWIND
ENDFILE
EQUIVALENCE
EXIT
SIGN
EXTERNAL
SNGL
STOP
FIND
SUBROUTINE
FLOAT
FORMAT
FUNCTION
WRITE
In addition to the words reserved by the FORTRAN
compiler, S/360 CSMP has the following restric-
tions on variable names:
1. Certain variable names are reserved for
use of the system, and cannot appear in a S/360
CSMP structure statement. These names are
NALARM, IZxxxx, and ZZxxxx, where x is any
digit.
2. KEEP is a COMMON variable, but it can be
used consistent with its intended purpose.
3. The names DELT, DELMIN, DELMAX,
FINTIM, TIME, PRDEL, and OUTDEL are system
reserved names and must appear only in their
intended context unless RENAMEd. This has been
explained under "Input Language" , in the paragraphs
on TIMER execution and RENAME translation
control statements.
4 . TIME is the name for the independent vari-
able and should be used only for that purpose.
5 . S/360 CSMP subroutines must be used
only as intended. These are MAINEX, INTRAN,
RKS, MILNE, RECT, TRAPZ, SIMP, CENTRL,
ADAMS, INITLZ, NUMER, ALPHA, DEBUG,
UPDATE, F, PLOTR, CSTORE, BUILDR,
SPLITR, UND, ZOR, COMPL, MLEFT, MRIGHT,
BOOLE, SHIFT, and the standard S/360 CSMP
functional block names.
STATEMENT ORDERING
S/360 CSMP was designed as a nonprocedural
language to free the user from the task of sequencing
his input. As has been noted, however, there are
some situations when he must observe statement
ordering rules. They are summarized here as fol-
lows:
1. PROCEDURE functional blocks are not sorted
internally.
2. NOSORT functional blocks are not sorted.
3. MACRO block definitions must be placed in
the deck before any structure statements, including
any in an initializing section. Data and control
statements cannot be embedded in MACRO defini-
tions .
4. STORAGE, HISTORY, and MEMORY trans-
lation control cards must appear before the first
reference to the related functions.
5. RENAME translation cards must appear
before the first reference to the variable being
renamed or to their new name.
6. Translation control cards and the correspond-
ing statements identifying an initializing computa-
tion must be placed in the deck before any other
structure statements.
7. To ensure proper RESETing, the RESET
card should be placed immediately after the END
or CONTINUE card.
8. Statements defining the operations in an
implicit loop must be placed immediately after the
corresponding IMPL structure statement.
9. Multiple SORT sections require the inputs to
have been computed before each section or within
the section.
10. The translation control statement END or
CONTINUE delineates the set of statements defining
a run.
11. The translation control statement STOP
must follow the last END card in order to define a
sequence of runs of the same structure statements .
12. The translation control statement ENDJOB
or ENDJOB STACK must be used to. signify the end
of a job. It must follow either the STOP card or
user -supplied subprograms, if any.
13. Continue cards (...) must immediately
follow the cards they continue.
14. FORTRAN FORMAT continuation cards
must have a $ in cc 6 and must immediately follow
the cards they continue.
55
SYSTEM MACROS statements using the INTGRL function and are not
called as subroutines, as are the other functions.
The four functional blocks REALPL, CMPXPL, (Similarly, INTGRL, cannot be called from user-
MODINT, and LEDLAG are system macros and defined subprograms, since all INTGRL state-
cannot be used in user-defined subprograms. ments are calculated at the end of each iteration.
These four functions produce inline structure
56
APPENDIX: INDEX OF S/360 CSMP FUNCTIONS AND STATEMENTS
FUNCTIONS
Name
Arbitrary Function Generator
(Linear Interpolation)
And
Comparator
Second -Order Lag (Complex
Pole)
Dead Space
Statement Form
Y=AFGEN(FUNCT,X)
Y=AND(X r X 2 )
Y=COMPAR(X r X 2 )
Y=CMPXPL(IC , IC 2 , P , P 2 , X)
Y=DEADSP(P ,P 2 ,X)
Page
10, 19, 32, 35, 46, 48
12
9
8, 31, 56
10
Dead Time (Delay)
Derivative
Exclusive Or
Equivalent
Function Switch
Noise (Random Number)
Generator (Normal
Distribution)
Hysteresis Loop
Implicit Function
Impulse Generator
Input Switch (Relay)
Integrator
Inclusive Or
Lead- Lag
Limiter
Mode-Controlled Integrator
Not And
Arbitrary Function Generator
(Quadratic Interpolation)
Not Or
Not
Output Switch
Y=DELAY(N,P,X)
Y=DERIV(IC,X)
Y=EOR(X r X 2 )
Y=EQUIV(X 1> X 2 )
Y=FCNSW(X r 'X 2 ,X 3 ,X 4 )
Y=GAUSS(P r P 2 -,P 3 )
Y=HSTRSS(IC,P r P 2 ,X)
Y=IMPL(IC,P,FOFY)
Y=IMPULS(P 1 ,P 2 )
Y=INSW(X 1 ,X 2 ,X 3 )
Y=INTGRL(IC,X)
Y=IOR(X ls X 2 )
Y=LEDLAG(P lf P 2 ,X)
Y=LIMIT(P 1 ,P 2 ,X)
Y=MODINT (IC , X x , X 2 , Xg)
Y=NAND(X 1 ,X 2 )
Y=NLFGEN(FUNCT , X)
Y=NOR(X 1 ,X 2 )
Y=NOT(X)
Y 1 ,Y 2 =OUTSW(X 1 ,X 2 )
7, 30, 31, 36
7, 31, 36
12
12
9
11, 37
10, 31, 36
7, 31, 35, 47
11, 31, 35
9
7, 17, 18, 25, 31, 32.1,
34, 36,
53,
56
12
8, 31, 56
10, 29, 43
8, 31, 35, 56
12
10, 19, 32, 35, 46, 48
12
12
9
57
Name
Pulse Generator
Quantizer
Ramp Function
First-Order Lag (Real Pole)
Noise (Random Number)
Generator (Uniform
Distribution)
Resettable Flip- Flop
Sine
Step Function
Zero-Order Hold
STATEMENTS
Statement
ABSERR
CALL DEBUG (n,t)
CALL RERUN
COMMON
COMMON MEM
CONSTANT
CONTINUE
CONTINUE
DATA
DATA
DECK
DIMENSION
DYNAMIC
END
ENDDATA
ENDJOB
ENDJOB STACK
ENDMAC
Statement Form
Y=PULSE(P,X)
Y=QNTZR(P,X)
Y=RAMP(P)
Y=REALPL(IC,P,X)
Y=RNDGEN(P)
Y=RST(X 1S X 2 ,X 3 )
Y=SINE(P r P 2 ,P 3 )
Y=STEP(P)
Y=ZHOLD(X 1 ,X 2 )
Type
Exec. Control
Structure
Structure
Trans. Control
Trans. Control
Data
Trans. Control
FORTRAN
Trans. Control
FORTRAN
Trans. Control
FORTRAN
Trans. Control
Trans. Control
Trans. Control
Trans. Control
Trans. Control
Trans. Control
Page
11, 31, 35
10
11, 35
8, 31, 56
11
9, 31
11
11, 35
7, 31, 35
Page
24, 25, 34, 53
45
15, 34, 43, 46
21, 23, 31, 32.1
21, 24, 31, 32.1
19, 43
23, 34, 38.1
23, 30
21, 24, 38
37
22
6, 37, 38
15, 22, 33
16, 23, 38, 38.1, 43
21, 24, 38
23, 31, 32, 38, 55
23, 38.1, 55
22, 28, 29, 30, 31
58
Statement
Type
Page
ENDPRO
EQUIVALENCE
FINISH
FIXED
FORMAT
FUNCTION
GO TO xxx
HISTORY
IF
INCON
INITIAL
LABEL
MACRO
MAIN
MEMORY
METHOD
NOSORT
OVERLAY
PARAMETER
PREPARE
PRINT
PRTPLOT
PROCEDURE
RANGE
RE AD (5, xxx)
RELERR
RENAME
RESET
SORT
STOP
Trans. Control
FORTRAN
Exec. Control
Trans. Control
FORTRAN
DATA
FORTRAN
Trans. Control
FORTRAN
Data
Trans. Control
Output Control
Trans. Control
Trans. Control
Trans. Control
Exec. Control
Trans. Control
Data
Data
Output Control
Output Control
Output Control
Trans. Control
Output Control
FORTRAN
Exec. Control
Trans. Control
Output Control
Trans. Control
Trans. Control
23, 30, 31
17, 18, 32.1
24, 51, 54
5, 21, 37, 38
29, 38, 55
19, 32, 35, 46, 48
30, 31, 43
22, 32, 36
30, 31, 43, 45
19
15, 22, 33, 43
26, 40, 43
22, 28
38.2
21, 32, 36
25, 34, 53
15, 23, 32.2
19
19, 38.1
26, 41, 54
25, 39, 54
26, 40, 54
23, 29, 30, 32.2, 37
26, 40
24, 38
25, 53
21, 43
25, 26, 27
15, 23, 32.2
23, 38.1, 43
59
STORAGE
SUBROUTINE
TABLE
TERMINAL
TIMER
TITLE
WRITE (6, xxx)
Trans. Control
FORTRAN
Data
Trans. Control
Exec. Control
Output Control
FORTRAN
5, 22, 37
31
5, 19, 37
15, 22, 33, 43
24, 34, 43
26, 39
29, 45
GLOSSARY
Block diagram . A diagrammatic representation of
the interconnection of functional blocks constituting
the simulation model .
Continuous system . A system that can be adequately
modeled by a set of differential equations in which
time is the independent variable.
Continuous system simulator . A simulation lan-
guage that provides the block modeling capability of
the digital analog simulators plus a powerful alge-
braic and logical modeling capability.
Digital analog simulator. A simulation language
that provides a complement of functional block ele-
ments and a block-oriented language for specifying
their interconnection.
Discrete system. A system that can be adequately
modeled by a sequence of events that occur at dis-
crete points in time.
Functional block (function) . The basic structural
unit of the simulation configuration.
History function. A function for which the output
depends on both the present value of the input, and
the past values of the input and output.
Memory function. A function for which the output
depends only on past values of the input and output.
Nonlinear element . An element in which the output
is not directly proportional to the input but is some
complex function of it — for example, square, ex-
ponential, sine.
Parameter. A value associated with a specific
block to particularize the desired functional opera-
tion. For example, the parameters associated with
a limiter define its upper and lower limits.
Procedural program . A program in which the order
of presentation of language statements determines
the order of execution of the corresponding computer
operations.
Simulation (modeling) . The act of representing
some aspects of the real world by numbers or by
symbols that may be easily manipulated to facilitate
their study.
Time-variant system . A system in which the
parameters defining the functional relationships
between variables are not constant but vary with time.
60
BIBLIOGRAPHY
1130 Continuous System Modeling Program, Application Description (H20-0209-1), IBM Corporation, Data
Processing Division, 112 East Post Road, White Plains, New York, 1966.
Brennan, R.D. , and Linebarger, R.N. , "A Survey of Digital Simulation: Digital Analog Simulator Pro-
grams", Simulation , vol. 3, no. 6, December 1964, pp. 22-36.
Clancy, J.J. , and Fineberg, M.S. , "Digital Simulation Languages: A Critique and Guide", 1965 Fall Joint
Computer Conference , vol. 27, pp. 23-26.
Syn, W.M. , and Linebarger, R.N. , "DSL/90 — A Digital Simulation Program for Continuous System
Modeling", 1966 Spring Joint Computer Conference , April 26-28, 1966.
James, M.L., Smith, G.M., andWolford, J.C., Analog and Digital Computer Methods in Engineering
Analysis, International Text Book Co. , Scranton, Pennsylvania, 1964, pp. 171-179.
61
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Technical Newsletter
Base Publ. No. GH20-0367-3, -2
This Newsletter No. GN20-2329
Date February 26, 1971
Previous Newsletter Nos. None for GH20-0367-3
GN20-1938 and GN20-2039
for GH20-0367-2.
SYSTEM/360 CONTINUOUS SYSTEM
MODELING PROGRAM
USER'S MANUAL
PROGRAM NUMBER 360A-CX-16X
© IBM Corp. 1967, 1968, 1969
This Technical Newsletter, a part of Version 1 , Modification Level 2, of System/360 Continuous
System Modeling Program, provides replacement pages for the subject manual. These replacement
pages remain in effect for subsequent versions and modifications unless specifically altered. Pages
to be inserted and/or removed are listed below.
Table of Contents
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Please file this cover letter at the back of the manual to provide a record of changes.
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