operator

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Operators

	The operators are similar to C, but the precedence of some of
	the operators differs.  In addition, there are several additional
	operators, and some C operators are missing.  The following list
	gives the operators arranged in order of precedence, from the
	least tightly binding to the most tightly binding:

	,	Comma operator.
		For situations in which a comma is used for another purpose
		(function arguments, array indexing, and the print statement),
		parenthesis must be used around the comma operator.

	? :	Conditional value.
		a ? b : c  returns b if a is nonzero, c otherwise.
		Thus it is equivalent to: if (a) return b; else return c;.
		All that is required of the arguments in this function
		is that the is-it-nonzero test is meaningful for a.

	=  +=  -=  *=  /=  %=  //=  &=  |=  <<=  >>=  ^=  **=
		Assignments.

	||	Logical OR.
		Unlike C, the result is the first non-zero expression or 0,
		instead of just 0 or 1.  Thus a || b is equivalent to
		a ? a : b.

	&&	Logical AND.
		Unlike C, the result is the last expression or 0,
		instead of just 0 or 1.  Thus a && b is equivalent to
		!a ? 0 : (!b ? 0 : b).

	==  !=  <=  >=  <  >
		Relations.

	+  -
		Binary plus and minus.

	*  /  //  %
		Multiply, divide. and modulo.
		Please Note: The '/' operator is a fractional divide,
		whereas the '//' is an integral divide.  Thus think of '/'
		as division of real numbers, and think of '//' as division
		of integers (e.g., 8 / 3 is 8/3 whereas 8 // 3 is 2).
		The '%' is integral or fractional modulus (e.g., 11%4 is 3,
		and 10%pi() is ~.575222).

	|	Bitwise OR.
		In a | b, both a and b are to be real integers;
		the signs of a and b are ignored, i.e.
		a | b = abs(a) | abs(b) and the result will
		be a non-negative integer.

	&	Bitwise AND.
		In a & b, both a and b are to be real integers;
		the signs of a and b are ignored as for a | b.

	^  **  <<  >>
		Powers and shifts.
		The '^' and '**' are both exponentiation, e.g. 2^3
		returns 8, 2^-3 returns .125.  In a ^ b, b has to be
		an integer and if a is zero, nonnegative.  0^0 returns
		the value 1.

		For the shift operators both arguments are to be
		integers, or if the first is complex, it is to have
		integral real and imaginary parts.  Changing the
		sign of the second argument reverses the shift, e.g.
		a >> -b = a << b.  The result has the same sign as
		the first argument except that a nonzero value is
		reduced to zero by a sufficiently long shift to the
		right.  These operators associate right to left,
		e.g.  a << b ^ c = a << (b ^ c).

	+  -  !
		Unary operators.
		The '!' is the logical NOT operator: !a returns 0 if
		a is nonzero, and 1 if a is zero, i.e. it is
		equivalent to a ? 0 : 1.  Be careful about
		using this as the first character of a top level command,
		since it is also used for executing shell commands.

	++  --
		Pre or post incrementing or decrementing.
		These are applicable only to variables.

	[ ]  [[ ]]  .  ( )
		Indexing, double-bracket indexing, element references,
		and function calls.  Indexing can only be applied to matrices,
		element references can only be applied to objects, but
		double-bracket indexing can be applied to matrices, objects,
		or lists.

	variables  constants  .  ( )
		These are variable names and constants, the special '.' symbol,
		or a parenthesized expression.  Variable names begin with a
		letter, but then can contain letters, digits, or underscores.
		Constants are numbers in various formats, or strings inside
		either single or double quote marks.


	The most significant difference from the order of precedence in
	C is that | and & have higher precedence than ==, +, -, *, / and %.
	For example, in C a == b | c * d is interpreted as:

		(a == b) | (c * d)

	and calc it is:

		a == ((b | c) * d)


	Most of the operators will accept any real or complex numbers
	as arguments.  The exceptions are:

	/  //  %
		Second argument must be nonzero.

	^
		The exponent must be an integer.  When raising zero
		to a power, the exponent must be non-negative.

	|  &
		Both both arguments must be integers.

	<<  >>
		The shift amount must be an integer.  The value being
		shifted must be an integer or a complex number with
		integral real and imaginary parts.