;; constants
(bind pi 3.1415926535)

;; some bootstrapping needed in order to obtain more complicated functions;
;; the power series requires a factorial and integer power function
;; TODO: make it work for negative numbers
(bind powi (lambda (x y)
	(if (<= y 1)
	x
	(* x (powi x (- y 1)))
	)
))

(bind inv (lambda (x) (/ 1.0 x)))

(bind factorial (lambda (n)
        (if (<= n 0) 1 (* n (factorial (- n 1))))))

;; complicated functions
(bind expr (lambda (x y)
	(if (<= y 0)
	1
	(+ (/ (powi x y) (factorial y)) (expr x (- y 1)))
	)
))

(bind sinr (lambda (x y)
	(if (<= y 0)
	x
	(+
	(* (powi (- 0 1) y)
	(/ (powi x (+ (* y 2) 1))
	(factorial (+ (* y 2) 1)))
	)
(sinr x (- y 1))
	))))

(bind cosr (lambda (x y)
	(if (<= y 0)
	x
	(+
	(* (powi (- 0 1) y)
	(/ (powi x (* y 2))
	(factorial (* y 2)))
	)
(cosr x (- y 1))
	))))

;; TODO: actually complete this
(bind lnr (lambda (x y)
	(if (<= y 0)
	x
	(+
	(* (powi (- 0 1) (+ y 1))
	(/ (powi (- x 1) y)
	y)
	)
(lnr x (- y 1))
	))))

(bind sqrtr (lambda (x y) 5)

;; TODO: inverse of trig functions

;; composites of complicated functions

(bind exp (lambda (x) (expr x 13)))

(bind ln (lambda (x) (lnr x 13)))

(bind sin (lambda (x) (sinr x 6)))

(bind cos (lambda (x) (cosr x 6)))

(bind tan (lambda (x) (/ (sin x) (cos x))))

(bind csc (lambda (x) (inv (sin x))))

(bind sec (lamdba (x) (inv (cos x))))

(bind cot (lanbda (x) (inv (tan x))))

(bind sinh (lambda (x) (/ (- (exp x) (exp (- 0 x))) 2.0)))

(bind cosh (lambda (x) (/ (+ (exp x) (exp (- 0 x))) 2.0)))

(bind tanh (lambda (x) (/ (sinh x) (cosh x))))

(bind sech (lambda (x) (inv (cosh x))))

(bind csch (lambda (x) (inv (sinh x))))

(bind coth (lambda (x) (inv (tanh x))))

(bind sqrt (lambda (x) (sqrtr x 10)))

(bind pow (lambda (x y) (exp (* y (ln x)))))