;;;;;
;;;;;
;;;;; Mathematical Functions
;;;;;
;;;;;

(define $exp
  (lambda [$x]
    (if (float? x)
      (b.exp x)
      (if (term? x)
        (match x term-expr
          {[,0 1]
           [,1 e]
           [<term $a <cons ,i <cons ,pi <nil>>>> (** -1 a)]
           [_ (to-math-expr <Apply exp (map from-math-expr {x})>)]})
        (to-math-expr <Apply exp (map from-math-expr {x})>)))))

(define $log
  (lambda [$x]
    (if (float? x)
      (b.log x)
      (match x math-expr
        {[,1 0]
         [,e 1]
         [_ (to-math-expr <Apply log (map from-math-expr {x})>)]}))))

(define $cos
  (lambda [$x]
    (if (float? x)
      (b.cos x)
      (match x math-expr
        {[,0 1]
         [,(* 2 pi) 1]
         [_ (to-math-expr <Apply cos (map from-math-expr {x})>)]}))))

(define $sin
  (lambda [$x]
    (if (float? x)
      (b.sin x)
      (match x math-expr
        {[,0 0]
         [_ (to-math-expr <Apply sin (map from-math-expr {x})>)]}))))

(define $tan
  (lambda [$x]
    (if (float? x)
      (b.tan x)
      (match x math-expr
        {[,0 0]
         [_ (to-math-expr <Apply tan (map from-math-expr {x})>)]}))))

(define $cosh
  (lambda [$x]
    (if (float? x)
      (b.cosh x)
      (match x math-expr
        {[,0 1]
         [_ (to-math-expr <Apply cosh (map from-math-expr {x})>)]}))))

(define $sinh
  (lambda [$x]
    (if (float? x)
      (b.sinh x)
      (match x math-expr
        {[,0 0]
         [_ (to-math-expr <Apply sinh (map from-math-expr {x})>)]}))))

(define $tanh
  (lambda [$x]
    (if (float? x)
      (b.tanh x)
      (match x math-expr
        {[,0 0]
         [_ (to-math-expr <Apply tanh (map from-math-expr {x})>)]}))))


(define $sinc
  (lambda [$x]
    (if (float? x)
      (if (eq? x 0.0)
        1.0
        (/ (b.sin x) x))
      (match x math-expr
        {[,0 1]
         [_ (/ (sin x) x)]}))))


(define $sigmoid
  (lambda [$z]
    (/ 1 (+ 1 (exp (* -1 z))))))


(define $kronecker-delta
  (cambda $js
    (if (all (eq? $ (car js)) (cdr js)) 1 0)))