;; Derived Operations
;;
;; These are built from true primitives using S-expressions.
;; Load with: (require "derived")

;; =============================================================================
;; Math Helpers (derivable from where + basic ops)
;; =============================================================================

;; Absolute value
(define (abs x) (where (< x 0) (- x) x))

;; Minimum of two values
(define (min2 a b) (where (< a b) a b))

;; Maximum of two values
(define (max2 a b) (where (> a b) a b))

;; Clamp x to range [lo, hi]
(define (clamp x lo hi) (max2 lo (min2 hi x)))

;; Square of x
(define (sq x) (* x x))

;; Linear interpolation: a*(1-t) + b*t
(define (lerp a b t) (+ (* a (- 1 t)) (* b t)))

;; Smooth interpolation between edges
(define (smoothstep edge0 edge1 x)
  (let ((t (clamp (/ (- x edge0) (- edge1 edge0)) 0 1)))
    (* t (* t (- 3 (* 2 t))))))

;; =============================================================================
;; Channel Shortcuts (derivable from channel primitive)
;; =============================================================================

;; Extract red channel as xector
(define (red frame) (channel frame 0))

;; Extract green channel as xector
(define (green frame) (channel frame 1))

;; Extract blue channel as xector
(define (blue frame) (channel frame 2))

;; Convert to grayscale xector (ITU-R BT.601)
(define (gray frame)
  (+ (* (red frame) 0.299)
     (* (green frame) 0.587)
     (* (blue frame) 0.114)))

;; Alias for gray
(define (luminance frame) (gray frame))

;; =============================================================================
;; Coordinate Generators (derivable from iota + repeat/tile)
;; =============================================================================

;; X coordinate for each pixel [0, width)
(define (x-coords frame) (tile (iota (width frame)) (height frame)))

;; Y coordinate for each pixel [0, height)
(define (y-coords frame) (repeat (iota (height frame)) (width frame)))

;; Normalized X coordinate [0, 1]
(define (x-norm frame) (/ (x-coords frame) (max2 1 (- (width frame) 1))))

;; Normalized Y coordinate [0, 1]
(define (y-norm frame) (/ (y-coords frame) (max2 1 (- (height frame) 1))))

;; Distance from frame center for each pixel
(define (dist-from-center frame)
  (let* ((cx (/ (width frame) 2))
         (cy (/ (height frame) 2))
         (dx (- (x-coords frame) cx))
         (dy (- (y-coords frame) cy)))
    (sqrt (+ (sq dx) (sq dy)))))

;; Normalized distance from center [0, ~1]
(define (dist-norm frame)
  (let ((d (dist-from-center frame)))
    (/ d (max2 1 (βmax d)))))

;; =============================================================================
;; Cell/Grid Operations (derivable from floor + basic math)
;; =============================================================================

;; Cell row index for each pixel
(define (cell-row frame cell-size) (floor (/ (y-coords frame) cell-size)))

;; Cell column index for each pixel
(define (cell-col frame cell-size) (floor (/ (x-coords frame) cell-size)))

;; Number of cell rows
(define (num-rows frame cell-size) (floor (/ (height frame) cell-size)))

;; Number of cell columns
(define (num-cols frame cell-size) (floor (/ (width frame) cell-size)))

;; Flat cell index for each pixel
(define (cell-indices frame cell-size)
  (+ (* (cell-row frame cell-size) (num-cols frame cell-size))
     (cell-col frame cell-size)))

;; Total number of cells
(define (num-cells frame cell-size)
  (* (num-rows frame cell-size) (num-cols frame cell-size)))

;; X position within cell [0, cell-size)
(define (local-x frame cell-size) (mod (x-coords frame) cell-size))

;; Y position within cell [0, cell-size)
(define (local-y frame cell-size) (mod (y-coords frame) cell-size))

;; Normalized X within cell [0, 1]
(define (local-x-norm frame cell-size)
  (/ (local-x frame cell-size) (max2 1 (- cell-size 1))))

;; Normalized Y within cell [0, 1]
(define (local-y-norm frame cell-size)
  (/ (local-y frame cell-size) (max2 1 (- cell-size 1))))

;; =============================================================================
;; Fill Operations (derivable from iota)
;; =============================================================================

;; Xector of n zeros
(define (zeros n) (* (iota n) 0))

;; Xector of n ones
(define (ones n) (+ (zeros n) 1))

;; Xector of n copies of val
(define (fill val n) (+ (zeros n) val))

;; Xector of zeros matching x's length
(define (zeros-like x) (* x 0))

;; Xector of ones matching x's length
(define (ones-like x) (+ (zeros-like x) 1))

;; =============================================================================
;; Pooling (derivable from group-reduce)
;; =============================================================================

;; Pool a channel by cell index
(define (pool-channel chan cell-idx num-cells)
  (group-reduce chan cell-idx num-cells "mean"))

;; Pool red channel to cells
(define (pool-red frame cell-size)
  (pool-channel (red frame)
                (cell-indices frame cell-size)
                (num-cells frame cell-size)))

;; Pool green channel to cells
(define (pool-green frame cell-size)
  (pool-channel (green frame)
                (cell-indices frame cell-size)
                (num-cells frame cell-size)))

;; Pool blue channel to cells
(define (pool-blue frame cell-size)
  (pool-channel (blue frame)
                (cell-indices frame cell-size)
                (num-cells frame cell-size)))

;; Pool grayscale to cells
(define (pool-gray frame cell-size)
  (pool-channel (gray frame)
                (cell-indices frame cell-size)
                (num-cells frame cell-size)))

;; =============================================================================
;; Blending (derivable from math)
;; =============================================================================

;; Additive blend
(define (blend-add a b) (clamp (+ a b) 0 255))

;; Multiply blend (normalized)
(define (blend-multiply a b) (* (/ a 255) b))

;; Screen blend
(define (blend-screen a b) (- 255 (* (/ (- 255 a) 255) (- 255 b))))

;; Overlay blend
(define (blend-overlay a b)
  (where (< a 128)
         (* 2 (/ (* a b) 255))
         (- 255 (* 2 (/ (* (- 255 a) (- 255 b)) 255)))))

;; =============================================================================
;; Simple Effects (derivable from primitives)
;; =============================================================================

;; Invert a channel (255 - c)
(define (invert-channel c) (- 255 c))

;; Binary threshold
(define (threshold-channel c thresh) (where (> c thresh) 255 0))

;; Reduce to n levels
(define (posterize-channel c levels)
  (let ((step (/ 255 (- levels 1))))
    (* (round (/ c step)) step)))