calc/help/types

Builtin types

    The calculator has the following built-in types.

    null value
	    This is the undefined value type.  The function 'null'
	    returns this value.  Functions which do not explicitly
	    return a value return this type.  If a function is called
	    with fewer parameters than it is defined for, then the
	    missing parameters have the null type.  The null value is
	    false if used in an IF test.

    rational numbers
	    This is the basic data type of the calculator.
	    These are fractions whose numerators and denominators
	    can be arbitrarily large.  The fractions are always
	    in lowest terms.  Integers have a denominator of 1.
	    The numerator of the number contains the sign, so that
	    the denominator is always positive.  When a number is
	    entered in floating point or exponential notation, it is
	    immediately converted to the appropriate fractional value.
	    Printing a value as a floating point or exponential value
	    involves a conversion from the fractional representation.

	    Numbers are stored in binary format, so that in general,
	    bit tests and shifts are quicker than multiplies and divides.
	    Similarly, entering or displaying of numbers in binary,
	    octal, or hex formats is quicker than in decimal.  The
	    sign of a number does not affect the bit representation
	    of a number.

    complex numbers
	    Complex numbers are composed of real and imaginary parts,
	    which are both fractions as defined above.  An integer which
	    is followed by an 'i' character is a pure imaginary number.
	    Complex numbers such as "2+3i" when typed in, are processed
	    as the sum of a real and pure imaginary number, resulting
	    in the desired complex number.  Therefore, parenthesis are
	    sometimes necessary to avoid confusion, as in the two values:

		    1+2i ^2		(which is -3)
		    (1+2i) ^2	(which is -3+4i)

	    Similar care is required when entering fractional complex
	    numbers.  Note the differences below:

		    3/4i		(which is -(3/4)i)
		    3i/4		(which is (3/4)i)

	    The imaginary unit itself is input using "1i".

    strings
	    Strings are a sequence of zero or more characters.
	    They are input using either of the single or double
	    quote characters.  The quote mark which starts the
	    string also ends it.  Various special characters can
	    also be inserted using back-slash.  Example strings:

		    "hello\n"
		    "that's all"
		    'lots of """"'
		    'a'
		    ""

	    There is no distinction between single character and
	    multi-character strings.  The 'str' and 'ord' functions
	    will convert between a single character string and its
	    numeric value.  The 'str' and 'eval' functions will
	    convert between longer strings and the corresponding
	    numeric value (if legal).  The 'strcat', 'strlen', and
	    'substr' functions are also useful.

    matrices
	    These are one to four dimensional matrices, whose minimum
	    and maximum bounds can be specified at runtime.  Unlike C,
	    the minimum bounds of a matrix do not have to start at 0.
	    The elements of a matrix can be of any type.  There are
	    several built-in functions for matrices.  Matrices are
	    created using the 'mat' statement.

    associations
	    These are one to four dimensional matrices which can be
	    indexed by arbitrary values, instead of just integers.
	    These are also known as associative arrays.  The elements of
	    an association can be of any type.  Very few operations are
	    permitted on an association except for indexing.  Associations
	    are created using the 'assoc' function.

    lists
	    These are a sequence of values, which are linked together
	    so that elements can be easily be inserted or removed
	    anywhere in the list.  The values can be of any type.
	    Lists are created using the 'list' function.

    files
	    These are text files opened using stdio.  Files may be opened
	    for sequential reading, writing, or appending.  Opening a
	    file using the 'fopen' function returns a value which can
	    then be used to perform I/O to that file.  File values can
	    be copied by normal assignments between variables, or by
	    using the result of the 'files' function.  Such copies are
	    indistinguishable from each other.