tasks a-s

Task/Quaternion-type/OCaml/quaternion-type-1.ocaml

@@ -0,0 +1,49 @@
+type quaternion = float * float * float * float
+
+let q a b c d = (a, b, c, d)
+
+let to_real (r, _, _, _) = r
+let imag (_, i, j, k) = (i, j, k)
+
+let quaternion_of_scalar s = (s, 0.0, 0.0, 0.0)
+
+let to_list (a, b, c, d) = [a; b; c; d]
+let of_list = function [a; b; c; d] -> (a, b, c, d)
+  | _ -> invalid_arg "of_list"
+
+let ( + ) = ( +. )
+let ( - ) = ( -. )
+let ( * ) = ( *. )
+let ( / ) = ( /. )
+
+let addr (a, b, c, d) r = (a+r, b, c, d)
+let mulr (a, b, c, d) r = (a*r, b*r, c*r, d*r)
+
+let add (a, b, c, d) (p, q, r, s) = (a+p, b+q, c+r, d+s)
+
+let sub (a, b, c, d) (p, q, r, s) = (a-p, b-q, c-r, d-s)
+
+let mul (a, b, c, d) (p, q, r, s) =
+  ( a*p - b*q - c*r - d*s,
+    a*q + b*p + c*s - d*r,
+    a*r - b*s + c*p + d*q,
+    a*s + b*r - c*q + d*p )
+
+let norm2 (a, b, c, d) =
+  ( a * a +
+    b * b +
+    c * c +
+    d * d )
+
+let norm q = sqrt(norm2 q)
+
+let conj (a, b, c, d) = (a, -. b, -. c, -. d)
+let neg (a, b, c, d) = (-. a, -. b, -. c, -. d)
+
+let unit ((a, b, c, d) as q) =
+  let n = norm q in
+  (a/n, b/n, c/n, d/n)
+
+let reciprocal ((a, b, c, d) as q) =
+  let n2 = norm2 q in
+  (a/n2, b/n2, c/n2, d/n2)

Task/Quaternion-type/OCaml/quaternion-type-2.ocaml

@@ -0,0 +1,18 @@
+type quaternion = float * float * float * float
+
+val q : float -> float -> float -> float ->  quaternion
+val to_real : quaternion -> float
+val imag : quaternion -> float * float * float
+val quaternion_of_scalar : float -> quaternion
+val to_list : quaternion -> float list
+val of_list : float list -> quaternion
+val addr : quaternion -> float -> quaternion
+val mulr : quaternion -> float -> quaternion
+val add : quaternion -> quaternion -> quaternion
+val sub : quaternion -> quaternion -> quaternion
+val mul : quaternion -> quaternion -> quaternion
+val norm : quaternion -> float
+val conj : quaternion -> quaternion
+val neg : quaternion -> quaternion
+val unit : quaternion -> quaternion
+val reciprocal : quaternion -> quaternion