/* basic arithmetic for objects
 */
Arithmetic = class {
	/* add a and b
	 */
	Add a b = map_binary add a b;

	/* subtract b from a 
	 */
	Subtract a b = map_binary subtract a b;

	/* multiply a by b
	 */
	Multiply a b = map_binary multiply a b;

	/* divide a by b
	 */
	Divide a b = map_binary divide a b;

	/* remainder after dividing a by b
	 */
	Remainder a b = map_binary remainder a b;

	sep1 = Separator;

	/* absolute value of x
	 */
	Absolute_value x = map_unary abs x;

	/* like Absolute_value, but treat pixels as vectors
	 */
	Absolute_value_vector x = map_unary abs_vec x;

	/* calculate unit vector for band elements
	 */
	Sign x = map_unary sign x;

	/* multiply by -1
	 */
	Negate x = map_unary unary_minus x;
}

/* trigonometry operations (all in degrees)
 */
Trig = class {
	/* calculate sine x
	 */
	Sin x = map_unary sin x;

	/* calculate cosine x
	 */
	Cos x = map_unary cos x;

	/* calculate tangent x
	 */
	Tan x = map_unary tan x;

	sep1 = Separator;

	/* calculate arc sine x
	 */
	Asin x = map_unary asin x;

	/* calculate arc cosine x
	 */
	Acos x = map_unary acos x;

	/* calculate arc tangent x
	 */
	Atan x = map_unary atan x;

	sep2 = Separator;

	/* convert degrees to radians
	 */
	Rad x = map_unary rad x;

	/* convert radians to degrees
	 */
	Deg x = map_unary deg x;

	sep3 = Separator;

	/* is angle within t degrees of r, mod 360
	 */
	Angle_range t r angle
	      =	clock (max - angle) < 2*r
	{
		max = clock (t + r);

		clock a 
		      =	a + 360, a < 0;
		      =	a - 360, a >= 360;
		      = a;
	}
}

/* logarithms and anti-logs
 */
Log = class {
	/* calculate e ** x
	 */
	Exponential x = map_unary (power e) x;

	/* log base e of x
	 */
	Log_natural x = map_unary log x;

	sep1 = Separator;

	/* log base 10 of x
	 */
	Log10 x = map_unary log10 x;

	/* calculate 10 ** x
	 */
	Exponential10 x = map_unary (power 10) x;

	sep2 = Separator;

	/* calculate x ** y
	 */
	Raise_to_power x y = map_binary power x y;
}

/* operations on complex numbers and images
 */
Complex = class {
	/* extract fields from complex
	 */
	Complex_extract = class {
		/* extract real part of complex
		 */
		Real in = map_unary re in;

		/* extract imaginary part of complex
		 */
		Imaginary in = map_unary im in;
	}

	/* join a and b to make a complex 
	 */
	Complex_build a b = map_binary comma a b;

	sep1 = Separator;

	/* convert real and imag to amplitude and phase
	 */
	Polar a = map_unary polar a;

	/* convert (amplitude, phase) image to rectangular coordinates
	 */
	Rectangular x = map_unary rectangular x;

	sep2 = Separator;

	/* invert imaginary part
	 */
	Conjugate x = map_unary conj x;
}

/* bitwise boolean operations for integer objects
 */
Boolean = class {
	/* bitwise and of a and b
	 */
	And a b = map_binary bitwise_and a b;

	/* bitwise or of a and b
	 */
	Or a b = map_binary bitwise_or a b;

	/* bitwise exclusive or of a and b
	 */
	Eor a b = map_binary eor a b;

	/* invert a
	 */
	Not a = map_unary not a;

	sep1 = Separator;

	/* shift a right by b bits
	 */
	Right_shift a b = map_binary right_shift a b;

	/* shift a left by b bits
	 */
	Left_shift a b = map_binary left_shift a b;

	sep2 = Separator;

	/* b where a is non-zero, c elsewhere
	 */
	If_then_else a b c = map_trinary if_then_else a b c;

	/* or the bands of an image together
	 */
	Band_or im = foldr1 bitwise_or (bandsplit im);

	/* and the bands of an image together
	 */
	Band_and im = foldr1 bitwise_and (bandsplit im);
}

/* all comparison operations
 */
Relational = class {
	/* find points at which a is equal to b
	 */
	Equal a b = map_binary equal a b;

	/* find points at which a is not equal to b
	 */
	Not_equal a b = map_binary not_equal a b;

	/* find points at which a is greater than b
	 */
	More a b = map_binary more a b;

	/* find points at which a is less than b
	 */
	Less a b = map_binary less a b;

	/* find points at which a is greater than or equal to b
	 */
	More_equal a b = map_binary more_equal a b;

	/* find points at which a is less than or equal to b
	 */
	Less_equal a b = map_binary less_equal a b;
}

/* operations on lists
 */
List = class {
	/* take first element of list
	 */
	Head x = hd x;

	/* drop the first element of list 
	 */
	Tail x = tl x;

	/* drop the last element of list
	 */
	Init x = init x;

	/* take the last element of list
	 */
	Last x = last x;

	sep1 = Separator;

	/* reverse order of elements in list 
	 */
	Reverse x = reverse x;

	/* sort elements of list into ascending order
	 */
	Sort x = sort x;

	/* remove duplicates from list
	 */
	Make_set x = mkset equal x;

	/* exchange rows and columns in a list of lists
	 */
	Transpose_list x = transpose x;

	/* flatten a list of lists into a single list
	 */
	Concat l = concat l;

	sep2 = Separator;

	/* find the length of list 
	 */
	Length x = len x;

	/* return element n from list (index from zero)
	 */
	Subscript n x = n ? x;

	/* take the first n elements of list x
	 */
	Take n x = take n x;

	/* drop the first n elements of list x
	 */
	Drop n x = drop n x;

	sep3 = Separator;

	/* join two lists end to end
	 */
	Join a b = a ++ b;

	/* put element a on the front of list x
	 */
	Cons a x = a : x;

	/* join two lists, pairwise
	 */
	Zip a b = zip2 a b;
}

/* various rounding operations
 */
Round = class {
	/* smallest integral value not less than x 
	 */
	Ceil x = map_unary ceil x;

	/* largest integral value not greater than x 
	 */
	Floor x = map_unary floor x;

	/* round to nearest integer
	 */
	Rint x = map_unary rint x;
}

/* forward and reverse fourier transforms
 */
Fourier = class {
	/* find fourier transform of image
	 */
	Forward a = map_unary (rotquad @ fwfft) a;

	/* find inverse fourier transform of image
	 */
	Reverse a = map_unary (invfft @ rotquad) a;

	/* rotate quadrants 
	 */
	Rotate_quadrants a = map_unary rotquad a;
}