Unroll map, mapi, and map2, and init (#27)

* Unroll `map`, `mapi`, and `map2`, and `init`

Close #22.

* Save a subtraction each iteration

* Update src/BwdNoLabels.ml

Co-authored-by: favonia <[email protected]>

* ocp-indent

---------

Co-authored-by: favonia <[email protected]>

src/BwdNoLabels.ml

@@ -57,13 +57,15 @@ let nth_opt xs i =
 let init len f =
   if len < 0 then invalid_arg "Bwd.init"
   else
-    let[@tail_mod_cons] rec go i =
-      if i >= len then Emp
+    let[@tail_mod_cons] rec go i last =
+      if i > last then Emp
+      else if i = last then Snoc (Emp, f i)
       else
-        let v = f i in
-        Snoc ((go[@tailcall]) (i+1), v)
+        let v1 = f i in
+        let v2 = f (i + 1) in
+        Snoc (Snoc ((go[@tailcall]) (i + 2) last, v2), v1)
     in
-    go 0
+    go 0 (len - 1)
 
 let append xs ys =
   let rec go =
@@ -121,14 +123,22 @@ let map f =
   let[@tail_mod_cons] rec go =
     function
     | Emp -> Emp
-    | Snoc (xs, x) -> let y = f x in Snoc ((go[@tailcall]) xs, y)
+    | Snoc (Emp, x) -> let y = f x in Snoc (Emp, y)
+    | Snoc (Snoc (xs , x2), x1) ->
+      let y1 = f x1 in
+      let y2 = f x2 in
+      Snoc (Snoc ((go[@tailcall]) xs, y2), y1)
   in go
 
 let mapi f =
   let[@tail_mod_cons] rec go i =
     function
     | Emp -> Emp
-    | Snoc (xs, x) -> let y = f i x in Snoc ((go[@tailcall]) (i + 1) xs, y)
+    | Snoc (Emp, x) -> let y = f i x in Snoc (Emp, y)
+    | Snoc (Snoc (xs, x2), x1) ->
+      let y1 = f i x1 in
+      let y2 = f (i + 1) x2 in
+      Snoc (Snoc ((go[@tailcall]) (i + 2) xs, y2), y1)
   in
   go 0
 
@@ -180,8 +190,11 @@ let map2 f xs ys =
   let[@tail_mod_cons] rec go =
     function
     | Emp, Emp -> Emp
-    | Snoc (xs, x), Snoc (ys, y) ->
-      let z = f x y in Snoc ((go[@tailcall]) (xs, ys), z)
+    | Snoc (Emp, x) , Snoc (Emp, y) -> let z = f x y in Snoc (Emp, z)
+    | Snoc (Snoc (xs , x2), x1), Snoc (Snoc (ys , y2), y1) ->
+      let z1 = f x1 y1 in
+      let z2 = f x2 y2 in
+      Snoc (Snoc ((go[@tailcall]) (xs, ys), z2) , z1)
     | _ -> invalid_arg "Bwd.map2"
   in go (xs, ys)