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.T CALC USER'S GUIDE
.RM 80
.NHY
.AP
.J
.F
.B 10
CALC is a calculator designed to evaluate arithmetic expressions. In
its basic form, expression evaluation is similar to that used by ANSI
FORTRAN with calculations performed on INTEGER*4 and REAL*8 constants.
Variables may also be invoked but are limited to single alphabetic
characters. It is assumed that the reader is familiar with FORTRAN data
types, constants, expression syntax, operator precedence, and the syntax
for assigning values to variables. Additional features include octal,
hexadecimal, and multiple precision arithmetic capabilities. Commonly used
commands and expressions can be placed in a file and executed when convenient.
.PG
.C 80;-GETTING STARTED-
.B 4
To run CALC on your system, you must initiate the commands appropriate
for your particular operating system. Contact your system manager for specific
details.
Once running, CALC prompts for input with
.NF
CALC>
Try typing
123+456
followed by a carriage return. CALC will evaluate the expression and
output the answer
579
It then prompts for further input. Try other expressions such as
12.0 - 99. (answer=-87.00000000000000)
-(-32767+(6-2)**8-(512/(409-401))) (answer=-32705)
3*5/7 (answer=2)
3*(5/7) (answer=0)
Mixed mode is legal, for example
1977/50. is evaluated as 39.54000000000000
Reals may be expressed using D or E format. For example
1.2E10*2.D0**3-1.D-8 is evaluated as
0.95999999999999992D+11
.J
.F
Variables may also be used to retain values for later use. CALC allows
variables consisting of a single alphabetic character. As in FORTRAN,
variable A through H and O thru Z default to type real, I thru N to type
integer. To set I to a value use the usual FORTRAN syntax, for example:
I=2**10-1
Try typing the single character 'I'. CALC will respond with its value. We
can now use I in various expressions such as
.NF
J=I-I/3*3
% is a special variable that retains the value of the last expression
evaluated. For example, to successively add up the numbers 1, 2, 3, 4, 5,
and 6 we could enter
1
%+2
%+3
%+4
%+5
%+6
Note that you can examine the value of the variables by typing the appropriate
single character followed by a carriage return. Such an examination does not
change the value of %.
To exit from CALC, type
*E (or *EXIT)
or *S (or *STOP)
.pg
.C 80;-SPECIAL FUNCTIONS-
CALC recognizes a variety of special functions. For example, to calculate
the square root of 2, we can type
SQRT(2.)
CALC responds with the value 1.41421356237310
Each function may have an expression for its argument. For example,
A=2.0*SQRT(ALOG(9.)+3.)
sets A to 3.152717335752129.
The following special functions are available:
FUNCTION NAME ARGUMENT TYPE FUNCTION VALUE DESCRIPTION
--------------------------------------------------------------------------
ABS REAL REAL absolute value
DABS REAL REAL absolute value
IABS INTEGER INTEGER absolute value
IFIX REAL INTEGER REAL to INTEGER conversion
AINT REAL REAL REAL truncation
INT REAL INTEGER REAL to INTEGER conversion
IDINT REAL INTEGER REAL to INTEGER conversion
EXP REAL REAL e**X
DEXP REAL REAL e**X
ALOG REAL REAL natural logarithm
DLOG REAL REAL natural logarithm
ALOG10 REAL REAL logarithm base 10
DLOG10 REAL REAL logarithm base 10
SQRT REAL REAL square root
DSQRT REAL REAL square root
SIN REAL REAL trigonometric sine
DSIN REAL REAL trigonometric sine
COS REAL REAL trigonometric cosine
DCOS REAL REAL trigonometric cosine
TANH REAL REAL hyperbolic tangent
DTANH REAL REAL hyperbolic tangent
ATAN REAL REAL arc tangent
DATAN REAL REAL arc tangent
.PG
.C 80;-WORKING IN OCTAL AND HEXADECIMAL-
You may change the base used to specify constants by using the
*B command. Legal forms are
command action
------- ------
*B displays current default base
*B 8 changes default base to octal
*B 10 changes default base to 10
*B 16 changes default base to 16
Suppose we have changed the default base to octal. Then adding
7 + 1
we obtain the result
00000000010 (BASE 8)
If the default base is hexadecimal, we can enter
9 + 1
which is evaluated as
0000000A (BASE 16)
Suppose we have assigned
A=1
then
1+A
gives
2.000000000000000
even when the default base is 16. If we wish to add the hexadecimal digit
'A' to 1, enter
1+0A
We now obtain the desired
0000000B (BASE 16)
This leading 0 is only necessary when the first hexadecimal digit is
greater than 9.
If constants are entered with digits that are not legal for the base
being used, the entire number is converted using a more appropriate base.
For example, if we have set the default base to octal and type
1+9
the 9 is not an octal number so it is converted to base 10. If a base 16
number is involved, the result will be in base 16.
You may temporarily change the base for a single integer constant by
preceeding it with
_^8 for octal
_^10 for base 10
_^16 for base 16
For example, if the default base is 10,
100+_^840
gives
132
a base 10 integer.
I=100+_^1610
gives
116
also a base 10 integer.
Note that the '_^' can only be used to specify the base of constants and
that expressions such as _^16I are illegal.
To declare variables to be integers of a specific base, we can use the
commands
*INTEGER (base 10)
*OCTAL (base 8)
*HEX (base 16)
for example,
*INTEGER A declares variable A to be a base 10 integer.
*HEX B,Z,F declares variables B, Z, and F to be base 16 integers.
*DECIMAL lists all the variables that have been declared to be
of type DECIMAL.
To summarize, there are three distinct ways of making base declarations
when using CALC. The first is to use the *B command to designate the base
default value. This is used to determine the base for constants when they
occur in expressions. It does not in any way influence the type of any
variables found in an expression. The only way to change the type of a variable
is with a specific CALC command such as
*INTEGER A,B
Suppose for example that the default base is 10 and we enter
*OCTAL A
A=100
then CALC responds with
00000000144 (BASE 8)
Finally, the last way to change a base is to use the explicit base
specifiers for a constant, for example
_^10 123
_^8 777
_^16 AB
.PG
.C 80;-MULTIPLE PRECISION-
.F
.J
Normally integer arithmetic (base 8, 10, and 16) is done internally with
INTEGER*4 variables. To allow for larger numbers, CALC has multiple
precision capabilities that allow numbers up to 99 digits to be manipulated.
Constants are converted to a multiple precision data type when the number
of digits specified exceeds a certain value. This value depends upon the
specified base. Leading zeroes are included in this count and can be used
to force constants to be of type multiple precision.
.NF
base maximum number of digits before conversion
---- ------------------------------------------
8 10
10 9
16 7
Suppose we type (with the default base of 10) the number
1234567890
then CALC echoes with
1,234,567,890
(BASE 10)
The commas indicate that % now has type multiple precision base 10.
Similarly, typing
1234ABCD
results in
1234,ABCD
(BASE 16)
.F
.J
Notice that base 16 multiple precision numbers are separated by commas
every 4 digits, octal and base 10 numbers every 3 digits.
You may perform the usual operations of addition, subtraction, multiplication,
division, and exponentiation. As of version 1.0, exponentiation
of a multiple precision number may only be
to a non-negative integral power.
To declare variables of type multiple precision, use
.NF
*M8 (multiple precision base 8)
*M10 (multiple precision base 10)
*M16 (multiple precision base 16)
for example,
*M8 A,B declares A and B to be multiple precision
octal variables.
Then typing
A=32768
results in CALC responding with
100,000
(BASE 8)
.PG
.C 80;-ADDITIONAL COMMANDS-
.F
.J
All commands to CALC (as distinguished from expressions to be evaluated)
begin with an asterisk. To obtain a list of all possible commands, type
a question mark followed by a carriage return. Most of the commands have
already been described. The following section gives an explanation of the
remaining commands.
.NF
COMMAND DESCRIPTION
------- -----------
*@filename Where filename is the name of a file of CALC commands.
CALC reads the file and executes the commands. Up to
5 nested calls can be made. Recursive calls are not
allowed. CALC prompts with CALC<n> before each command
line is executed, where n is the calling level.
You may optionally follow the file name with a blank
followed by a single variable name (a single alphabetic
character or %). CALC will then execute the file until
the value of that variable is zero or negative. The test
of this variable is made before the file is executed and
not during execution of commands within the file. If the
variable's value is not positive when the command is
initially encountered, the file will not be opened for
execution. See the section on command file examples for
ways to use this option.
*ASCII Declares a list of variables to be of type ASCII. Useful
when decoding ASCII characters. For example, if we set
A to be of type ASCII, then typing
A=77
results in the character 'M' being output. The inverse
operation is the single quote. It allows us to specify
a single ASCII constant. For example, if we type
'M
then the character 'M' is echoed and indicates that
% holds that character and has data type ASCII. Suppose
that the variable I has data type INTEGER. Then we can
output the base 10 code for the ASCII character 'M' by
entering
I='M
which results in 77 being output. Notice that you may
not be able to enter certain control characters that are
intercepted by your operating system. Characters whose
value is less than 32. are output by printing the
character '_^' followed by the equivalent ASCII character
of that number plus 32. For example,
A=10
results in
_^*
being output since 42 is the ASCII code for the character
'*'. See apendix A for a table of the characters output
by CALC to represent such non-printable characters.
*C COMMENT line. The characters that follow are ignored by
CALC. This is useful when documenting files containing
CALC commands.
.TP 6
*N NOVIEW. Prevents CALC from outputting the value of the
expressions evaluated. This is especially useful when
executing files containing CALC commands that initialize
variables to special values. Equivalent to *V 1
*V VIEW. Controls CALC's printing options:
command output class
------------- --------------
*V 0 error messages
*V 1 error messages
command lines read from files
*V 2 error messages
value of expressions evaluated
*V 3 error messages
command lines read from a file
value of expressions evaluated
*V same as *V 3
The default setting is *V 3. Notice that other legal
forms are *VIEW 1 and *V2
*R READ. Allows a single line to be read from the terminal.
Useful in files of CALC commands to allow additional
commands to be entered (like *S to exit from that file)
or simply as a way to halt terminal output until the
carriage return key is pressed.
*REAL declares specified variables to be REAL*8. When the value
of such variables are output, FORTRAN's D format is used.
*DECIMAL Declares specified variables to be REAL*8. When the value
of such variables are output, FORTRAN's F format is used.
Variables A-H and O-Z default to type DECIMAL.
*S STOP. Same as *E
*E EXIT. Terminates CALC session unless it is used within
a file of CALC commands. In this case, CALC closes the
file and continues with the next command.
*Z ZERO. Zeroes all variables except %. Data types are not
changed.
.PG
.C 80;-ADDITIONAL FEATURES-
.J
.F
CALC is similar to FORTRAN with respect to operator precedence. Blanks may
occur anywhere on a command line without effect except after a single quote
mark used to specify a single ASCII character constant. CALC extends the ANSI
FORTRAN syntax by allowing the following:
.NJ
.NF
1. multiple assignments on one line, for example
I=J=K=812
2. Unary + and unary - are allowed, for example
2*-3
+2+-7
-2**4
are all legal. The last expression evaluates to 16 because the
unary - has a higher precedence than exponentiation.
3. exponentiation may be indicated by using ! as well as **
.J
.F
If any of the declarations are entered (such as *INTEGER or *M8) and
no argument to this command is given, then CALC will print out the
variables that have been assigned that data type. Note that a variable can
be assigned to different data types using such commands and still not be
assigned a value. If you attempt to output the value of such a variable, an
error message will result.
.PG
.C 80;-COMMAND FILE EXAMPLES
.NF
EXAMPLE 1:
PROBLEM: be able to enter the coefficients of a second
degree polynomial and have the roots output.
Solution: create the following file and call it ROOT:
*CALCULATES THE ROOTS OF A 2ND DEGREE EQUATION
*C YOU WILL BE ASKED TO ENTER THE VALUES OF
*C A,B AND C WHERE
*C
*C 2
*C A X +B X + C = 0
*C
*C
*C ENTER THE VALUE OF A
*R
A=%
*C ENTER THE VALUE OF B
*R
B=%
*C ENTER THE VALUE OF C
*R
C=%
*C THE ROOTS ARE:
X=(-B+SQRT(B*B-4.*A*C))/2.*A
Y=(-B-SQRT(B*B-4.*A*C))/2.*A
*C
*C AS YOU CAN SEE BECAUSE
A*X*X+B*X+C
A*Y*Y+B*Y+C
Then run the procedure by entering CALC and typing
*@ROOT
.PG
EXAMPLE 2:
PROBLEM: Suppose we are working on a problem that requires
us to convert many decimal 16 bit word addresses to
octal byte address. We would like to be able to
simply enter the decimal word address and have CALC
respond with the octal byte address.
SOLUTION: Create a file of the following commands and call
it BYT:
*C
*C
*C
*C
*C ENTER DECIMAL WORDS
*R
A=%+%
Then we enter CALC and type the following:
*OCTAL A (to make A an octal variable)
1 (to set % to a non-zero number)
*@BYT % (to execute the file of conversion commands)
We will then repeatedly execute the file BYT until we
enter a zero as the number to be converted.
.PG
EXAMPLE 3:
Problem: We wish to set up a command file called SIGN that
allows us to enter a number, and then execute the
files MINUS, ZERO, and PLUS according to the value
entered.
Solution: Create the file SIGN consisting of:
*C ENTER THE NUMBER WHOSE SIGN IS TO BE DETERMINED
*R
I=J=%
I=-I
K=1
*C K STAYS AT 1 IF NUMBER IS NON-ZERO
*@MINUS I
*@PLUS J
*@ZERO K
The file MINUS:
*C THE NUMBER IS NEGATIVE
I=K=0
The file PLUS:
*C THE NUMBER IS POSITIVE
J=K=0
and the file ZERO:
*C THE NUMBER IS ZERO
K=0
Notice that K is used to control the execution of the file ZERO
by initializing it to 1 and resetting it to zero if either of the files
PLUS or MINUS are executed.
.PG
EXAMPLE 4:
PROBLEM: Enter the number N and calculate the numbers
1!, 2!, 3!, 4!, ... N!
where
N! = N*(N-1)*(N-2)*...*3*2*1
SOLUTION: Since the numbers may grow very large, we
will use a multiple precision variable. Create
the following files:
MFACT:
*C INPUT THE LIMIT OF THE FACTORIAL LIST
*V 0
*R
N=%
*M10 A
I=0
*@MF1 N
*C SET VIEW AND TYPE FOR VARIABLE A AT DEFAULT VALUES
*DECIMAL A
*V
MF1:
A=1
N=N-1
I=I+1
J=I
*@MF2 J
*V2
A
*V0
MF2:
A=A*J
J=J-1
We then enter CALC and type
*@MFACT
A typical run of this procedure would look like:
>CAL
CALC>*@MFACT
CALC<2>*C INPUT THE LIMIT OF THE FACTORIAL LIST
CALC<2>*V 0
CALC<2>4
1
(BASE 10)
2
(BASE 10)
6
(BASE 10)
24
(BASE 10)
CALC>
.PG
EXAMPLE 5:
PROBLEM: we wish to specify a default base and successively add
numbers into a sum.
SOLUTION: create the following files of CALC commands:
ADD:
*V
*C ENTER DEFAULT BASE
*R
*C CHANGE DATA TYPE OF SUM
*C BY SPECIFYING THE DATA TYPE FOR I
*R
*C TO EXIT, TYPE 0
*V0
I=0
1
*@ADD1 %
*V
ADD1:
*V
*R
*V0
J=%
I=I+%
*V2
I
*V0
%=IABS(J)
Then we invoke the procedure by typing
*@ADD
A typical run follows:
CALC>*@ADD
CALC<2>*V
CALC<2>*C ENTER DEFAULT BASE
CALC<2>*R
CALC<2>*B 8
DEFAULT BASE IS 8
CALC<2>*C CHANGE DATA TYPE OF SUM
CALC<2>*C BY SPECIFYING THE DATA TYPE FOR I
CALC<2>*R
CALC<2>*OCTAL I
CALC<2>*C TO EXIT, TYPE 0
CALC<2>*V0
CALC<3>177
00000000177 (BASE 8)
CALC<3>1
00000000200 (BASE 8)
CALC<3>0
00000000200 (BASE 8)
CALC>
.PG
.C 80;USAGE NOTES VERSION 1.0
1. When you iterate on a file by a call such as
*@REPEAT X
then note that
A) X must have been set to a positive value when the command
is executed or else the file will not be executed.
B) If the file of commands does not change the value of the
variable X you will enter an infinite loop. You can explicitly
set X to a non-positive value, use the *Z command to zero it
(if it is not %), or include a
*R
command to give you a chance to reset the variable and get out
of the loop.
C) *E and *S will allow you to exit from the command file REPEAT
but will not of themselves prevent repetitions.
D) Entering constants echo on the terminal (assuming *V is properly
set) and can change the value and type of the variable %. This
is important to remember when using % to control the iteration
of a file.
2. When you first enter CALC, the variable % has type INTEGER and holds
the version number of the program.
3. In practice, multiple precision arithmetic may be limited to less
than 99 digits because of your terminal's inability to print that
many characters.
4. No implicit conversion is made to multiple precision when operations
with reals or integers cause an overflow. This was done in version 1.0
in case the multiple precision routines have to be removed when
creating a small task image for some operating system.
5. In FORTRAN,
-A**2 is the same as -(A**2)
with CALC,
-A**2 is the same as (-A)**2 (just like SNOBOL!)
6. If R and A are positive reals and I is a positive integer, some
compilers like RSX-11M's F4P won't allow (at run time) evaluation
of
(-I)**R
(-A)**R
7. Under RSX-11M F4P you will find
2**.5 to have value 1
while
2.**.5 has value 1.41421356237310
8. 10E10 is a hexadecimal constant (integer) while 10.E10 is a real.
.PG
.C 80;APPENDIX A
.NF
.NJ
.B2
ASCII CALC ASCII CALC ASCII CALC ASCII CALC
CODE PRINTS CODES PRINTS CODE PRINTS CODE PRINTS
---- ------ ----- ------ ---- ------ ---- ------
.B1
0 _^ 32 64 @ 96 `
1 _^! 33 ! 65 A 97 a
2 _^" 34 " 66 B 98 b
3 _^_# 35 _# 67 C 99 c
4 _^$ 36 $ 68 D 100 d
5 _^% 37 % 69 E 101 e
6 _^_& 38 _& 70 F 102 f
7 _^' 39 ' 71 G 103 g
8 _^( 40 ( 72 H 104 h
9 _^) 41 ) 73 I 105 i
10 _^* 42 * 74 J 106 j
11 _^+ 43 + 75 K 107 k
12 _^, 44 , 76 L 108 l
13 _^- 45 - 77 M 109 m
14 _^. 46 . 78 N 110 n
15 _^/ 47 / 79 O 111 o
16 _^0 48 0 80 P 112 p
17 _^1 49 1 81 Q 113 q
18 _^2 50 2 82 R 114 r
19 _^3 51 3 83 S 115 s
20 _^4 52 4 84 T 116 t
21 _^5 53 5 85 U 117 u
22 _^6 54 6 86 V 118 v
23 _^7 55 7 87 W 119 w
24 _^8 56 8 88 X 120 x
25 _^9 57 9 89 Y 121 y
26 _^: 58 : 90 Z 122 Z
27 _^; 59 ; 91 [ 123 {
28 _^< 60 < 92 _\ 124 |
29 _^= 61 = 93 ] 125 }
30 _^> 62 > 94 _^ 126 ~
31 _^? 63 ? 95 __ 127