4.4BSD/usr/src/contrib/calc-1.26.4/help/obj.file
Using objects
Objects are user-defined types which are associated with user-
defined functions to manipulate them. Object types are defined
similarly to structures in C, and consist of one or more elements.
The advantage of an object is that the user-defined routines are
automatically called by the calculator for various operations,
such as addition, multiplication, and printing. Thus they can be
manipulated by the user as if they were just another kind of number.
An example object type is "surd", which represents numbers of the form
a + b*sqrt(D),
where D is a fixed integer, and 'a' and 'b' are arbitrary rational
numbers. Addition, subtraction, multiplication, and division can be
performed on such numbers, and the result can be put unambiguously
into the same form. (Complex numbers are an example of surds, where
D is -1.)
The "obj" statement defines either an object type or an actual
variable of that type. When defining the object type, the names of
its elements are specified inside of a pair of braces. To define
the surd object type, the following could be used:
obj surd {a, b};
Here a and b are the element names for the two components of the
surd object.
When an object is created, the elements are all defined with null
values. A user-defined routine should be provided which will place
useful values in the elements. For example, for an object of type
'surd', a function called 'surd' can be defined to set the two
components as follows:
define surd(a, b)
{
local x;
obj surd x;
x.a = a;
x.b = b;
return x;
}
When an operation is attempted for an object, user functions with
particular names are automatically called to perform the operation.
These names are created by concatenating the object type name and
the operation name together with an underscore. For example, when
multiplying two objects of type surd, the function "surd_mul" is
called.
The user function is called with the necessary arguments for that
operation. For example, for "surd_mul", there are two arguments,
which are the two numbers. The order of the arguments is always
the order of the binary operands. If only one of the operands to
a binary operator is an object, then the user function for that
object type is still called. If the two operands are of different
object types, then the user function that is called is the one for
the first operand.
The above rules mean that for full generality, user functions
should detect that one of their arguments is not of its own object
type by using the 'istype' function, and then handle these cases
specially. In this way, users can mix normal numbers with object
types. (Functions which only have one operand don't have to worry
about this.) The following example of "surd_mul" demonstrates how
to handle regular numbers when used together with surds:
define surd_mul(a, b)
{
local x;
obj surd x;
if (!istype(a, x)) {
/* a not of type surd */
x.a = b.a * a;
x.b = b.b * a;
} else if (!istype(b, x)) {
/* b not of type surd */
x.a = a.a * b;
x.b = a.b * b;
} else {
/* both are surds */
x.a = a.a * b.a + D * a.b * b.b;
x.b = a.a * b.b + a.b * b.a;
}
if (x.b == 0)
return x.a; /* normal number */
return x; /* return surd */
}
In order to print the value of an object nicely, a user defined
routine can be provided. For small amounts of output, the print
routine should not print a newline. Also, it is most convenient
if the printed object looks like the call to the creation routine.
For output to be correctly collected within nested output calls,
output should only go to stdout. This means use the 'print'
statement, the 'printf' function, or the 'fprintf' function with
'files(1)' as the output file. For example, for the "surd" object:
define surd_print(a)
{
print "surd(" : a.a : "," : a.b : ")" : ;
}
It is not necessary to provide routines for all possible operations
for an object, if those operations can be defaulted or do not make
sense for the object. The calculator will attempt meaningful
defaults for many operations if they are not defined. For example,
if 'surd_square' is not defined to square a number, then 'surd_mul'
will be called to perform the squaring. When a default is not
possible, then an error will be generated.
Please note: Arguments to object functions are always passed by
reference (as if an '&' was specified for each variable in the call).
Therefore, the function should not modify the parameters, but should
copy them into local variables before modifying them. This is done
in order to make object calls quicker in general.
The double-bracket operator can be used to reference the elements
of any object in a generic manner. When this is done, index 0
corresponds to the first element name, index 1 to the second name,
and so on. The 'size' function will return the number of elements
in an object.
The following is a list of the operations possible for objects.
The 'xx' in each function name is replaced with the actual object
type name. This table is displayed by the 'show objfuncs' command.
Name Args Comments
xx_print 1 print value, default prints elements
xx_one 1 multiplicative identity, default is 1
xx_test 1 logical test (false,true => 0,1),
default tests elements
xx_add 2
xx_sub 2 subtraction, default adds negative
xx_neg 1 negative
xx_mul 2
xx_div 2 non-integral division, default multiplies
by inverse
xx_inv 1 multiplicative inverse
xx_abs 2 absolute value within given error
xx_norm 1 square of absolute value
xx_conj 1 conjugate
xx_pow 2 integer power, default does multiply,
square, inverse
xx_sgn 1 sign of value (-1, 0, 1)
xx_cmp 2 equality (equal,non-equal => 0,1),
default tests elements
xx_rel 2 inequality (less,equal,greater => -1,0,1)
xx_quo 2 integer quotient
xx_mod 2 remainder of division
xx_int 1 integer part
xx_frac 1 fractional part
xx_inc 1 increment, default adds 1
xx_dec 1 decrement, default subtracts 1
xx_square 1 default multiplies by itself
xx_scale 2 multiply by power of 2
xx_shift 2 shift left by n bits (right if negative)
xx_round 2 round to given number of decimal places
xx_bround 2 round to given number of binary places
xx_root 3 root of value within given error
xx_sqrt 2 square root within given error
Also see the library files:
dms.cal
mod.cal
poly.cal
quat.cal
surd.cal