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.  An object type can be defined more than once as long
    as the number of elements and their names are the same.

    When an object is created, the elements are all defined with zero
    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 objfunctions' 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
	    xx_neg      1	negative
	    xx_mul      2
	    xx_div      2	non-integral division
	    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,nonequal => 0,1),
	    			   default tests elements
	    xx_rel      2	relative order, positive for >, etc.
	    xx_quo      3	integer quotient
	    xx_mod      3	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    3	round to given number of decimal places
	    xx_bround   3	round to given number of binary places
	    xx_root     3	root of value within given error
	    xx_sqrt     3	square root within given error
	    xx_or       2	bitwise or
	    xx_and      2	bitwise and
	    xx_not      1	logical not
	    xx_fact     1	factorial or postfix !
	    xx_min      1	value for min(...)
	    xx_max      1	value for max(...)
	    xx_sum      1	value for sum(...)
	    xx_assign   2	assign, defaults to a = b
	    xx_xor      2	value for binary ~
	    xx_comp     1	value for unary ~
	    xx_content  1	unary hash op
	    xx_hashop   2	binary hash op
	    xx_backslash 1	unary backslash op
	    xx_setminus 2	binary backslash op
	    xx_plus     1	unary + op

    Also see the standard resource files:

	    deg.cal
	    dms.cal
	    ellip.cal
	    hms.cal
	    mod.cal
	    natnumset.cal
	    poly.cal
	    quat.cal
	    regress.cal
	    set8700.cal
	    surd.cal
	    test2300.cal
	    test3100.cal

## Copyright (C) 1999,2010  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:	1991/07/21 04:37:22
## File existed as early as:	1991
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
