calculette_aoo: now evaluate the exact frequency, some corrections

4 files changed, 106 insertions, 39 deletions

diff --git a/calculette_aoo/lib/build.ml b/calculette_aoo/lib/build.ml
index ddefe67..5c2ac0b 100644
--- a/calculette_aoo/lib/build.ml
+++ b/calculette_aoo/lib/build.ml
@@ -9,54 +9,41 @@ type build = {
 type env = {
     cout_sort : int
   ; degat_sort : int
-  ; max_tours : float
+  ; max_tours : int
   ; fm_oponent : int
   ; cost_max : int
   ; frequencies : (int * float) list
 }
 
-let roll_and_accumulate dices =
-  Seq.repeat () |> Seq.take dices
-  |> Seq.fold_left (fun res _ -> res + (1 + Random.int 3)) 0
-
-let delta_carac level thresold =
-  Seq.repeat () |> Seq.take 10000
-  |> Seq.fold_left
-       (fun acc _ ->
-         if roll_and_accumulate thresold > roll_and_accumulate level then acc
-         else acc + 1)
-       0
-
 let get_chance : env -> int -> float =
  fun env delta ->
   match List.assoc_opt delta env.frequencies with
-  | None -> 1.0
+  | None -> 1.
   | Some v -> v
 
 (** Build a list with the differents percentages to hit *)
 let buil_freq_table from thresold =
-  let () = Random.self_init () in
-  List.init 6 (fun i ->
-      (from - thresold + i, float (delta_carac (from + i) thresold) /. 10000.))
+  List.init 10 (fun i ->
+      (from + i, Roll.compare (from + i) thresold |> Q.to_float))
 
-let eval : build -> env -> float * float =
+let eval : build -> env -> float * int =
  fun { a; m; rm; pm; fm } env ->
-  let cout_tour = (Carac.value a * env.cout_sort) - Carac.value rm in
-  let nb_tour =
-    if cout_tour > 0 then
-      float (Carac.value pm) /. float cout_tour |> Float.min env.max_tours
-    else env.max_tours
+  let mp_available = Carac.value pm + ((env.max_tours - 1) * Carac.value rm) in
+
+  (* How many attacks can be done using this cost ? (rounded down) *)
+  let nb_attacks =
+    min (env.max_tours * Carac.value a) (mp_available / env.cout_sort)
   in
 
   let degats =
-    float (Carac.value a * (env.degat_sort + Carac.value m - 5))
-    *. get_chance env (Carac.value fm - env.fm_oponent)
+    float (nb_attacks * (env.degat_sort + Carac.value m - 5))
+    *. get_chance env (Carac.value fm)
   in
-  (degats, nb_tour)
+  (degats, nb_attacks)
 
 let repr_degats : env -> Format.formatter -> build -> unit =
  fun env out build ->
-  let delta = get_chance env (Carac.value build.fm - env.fm_oponent) in
+  let delta = get_chance env (Carac.value build.fm) in
   Format.fprintf out "%d A × (%d du sorts + %d M - %d M) × %.2f %%"
     (Carac.value build.a) env.degat_sort (Carac.value build.m) 5 (delta *. 100.);
   let sum = env.degat_sort + Carac.value build.m - 5 in
@@ -71,7 +58,7 @@ let cost : build -> int =
 
 let repr : env -> Format.formatter -> build -> unit =
  fun env formatter build ->
-  let degats, nb_tour = eval build env in
+  let degats, nb_attacks = eval build env in
 
   Format.fprintf formatter
     {|Caractéristiques retenues :
@@ -84,18 +71,17 @@ let repr : env -> Format.formatter -> build -> unit =
     Carac.repr build.a Carac.repr build.m Carac.repr build.fm Carac.repr
     build.rm Carac.repr build.pm;
   Format.fprintf formatter
-    "@[Le magicien fera %.2f degats par tour pour un total de %d sur %.2f \
-     tours@;\
+    "@[Le magicien fera %.2f degats par attaque pour un total de %.2f (via %d \
+     attaques)@;\
      (@[<v 2>%a@])@;"
-    degats
-    (int_of_float (nb_tour *. degats))
-    nb_tour (repr_degats env) build;
+    (degats /. float_of_int nb_attacks)
+    degats nb_attacks (repr_degats env) build;
   Format.fprintf formatter "Le cout de ce build est de %d@]@." (cost build)
 
 let score : env -> build -> float =
  fun env build ->
   let d, v = eval build env in
-  d *. v
+  d
 
 (* Upgrade each caracteristic and keep only the values in range *)
 let upgrade : env -> build -> build list =
@@ -125,9 +111,7 @@ let rec traverse env (last_cost, last_score) = function
           upgrade env hd
           |> List.filter (fun build ->
                  List.for_all
-                   (fun element ->
-                     cost build > cost element
-                     || score env build > score env element)
+                   (fun element -> score env build > score env element)
                    tl)
         in
 
diff --git a/calculette_aoo/lib/build.mli b/calculette_aoo/lib/build.mli
index 3e2e690..7e39b71 100644
--- a/calculette_aoo/lib/build.mli
+++ b/calculette_aoo/lib/build.mli
@@ -9,7 +9,7 @@ type build = {
 type env = {
     cout_sort : int
   ; degat_sort : int
-  ; max_tours : float
+  ; max_tours : int
   ; fm_oponent : int
   ; cost_max : int
   ; frequencies : (int * float) list
diff --git a/calculette_aoo/lib/dune b/calculette_aoo/lib/dune
index 54b5a85..176147c 100644
--- a/calculette_aoo/lib/dune
+++ b/calculette_aoo/lib/dune
@@ -1,2 +1,4 @@
 (library
- (name aoo))
+ (name aoo)
+ (libraries zarith)
+ )
diff --git a/calculette_aoo/lib/roll.ml b/calculette_aoo/lib/roll.ml
new file mode 100644
index 0000000..00d8465
--- /dev/null
+++ b/calculette_aoo/lib/roll.ml
@@ -0,0 +1,81 @@
+open StdLabels
+
+(** Evaluate the coefficient for the product of two polynamials *)
+let mul p1 p2 =
+  let n1 = Array.length p1 and n2 = Array.length p2 in
+  let n = n1 + n2 in
+  let res = Array.make n 0 in
+  for i = 0 to n1 - 1 do
+    for j = 0 to n2 - 1 do
+      res.(i + j + 1) <- res.(i + j + 1) + (p1.(i) * p2.(j))
+    done
+  done;
+  res
+
+(** Apply a power function over a polynomial *)
+let pow p1 n =
+  let result = ref p1 in
+  for _ = 1 to n - 1 do
+    result := mul !result p1
+  done;
+  !result
+
+(** Evaluate the odd to win agains a give difficulty *)
+let against : int -> int array -> Q.t array =
+ fun n difficulties ->
+  match n with
+  | 0 -> Array.map ~f:(fun _ -> Q.zero) difficulties
+  | _ ->
+      (* Create the polynomial with the odd ratio for the given caracteristic *)
+      let arr = Array.make 3 1 in
+      let frequencies = pow arr n in
+      let ratio = Z.(of_int 3 ** n) in
+
+      let get_chances difficulty =
+        (* Evaluate the ratio to win the roll *)
+        let chances = ref Z.zero in
+        for i = difficulty - 1 to Array.length frequencies - 1 do
+          (* The index in the table is the odd to get exactly this value in the roll.
+             Here, we just add every value in the array from the index strarting from
+             the given difficulty. *)
+          chances := Z.(!chances + of_int frequencies.(i))
+        done;
+        Q.make !chances ratio
+      in
+      Array.map ~f:get_chances difficulties
+
+(** Compare two caracteristics. 
+    [compare v1 v2] will evaluate the odds to win if the player has the
+    caracteristics [v1] against the openent [v2]. 
+
+    In case of equality, the win is given to [v1] *)
+let compare : int -> int -> Q.t =
+ fun carac1 carac2 ->
+  let arr = Array.make 3 1 in
+  let z3 = Z.of_int 3 in
+
+  let ordinal1 = Z.(z3 ** carac1)
+  and ordinal2 = Z.(z3 ** carac2)
+  (*Number of possibles values for each caracteristc *)
+  and elements1 = 3 * carac1
+  and elements2 = 3 * carac2 in
+
+  (* The number of iterations to do is elements1 × elements2. For every iteration of elements2, we have ordinal1 points to get.  *)
+  let cases = Z.(ordinal1 * ordinal2) in
+
+  let frequencies_1 = pow arr carac1 |> Array.map ~f:(fun v -> Z.(of_int v))
+  and frequencies_2 = pow arr carac2 |> Array.map ~f:(fun v -> Z.(of_int v)) in
+
+  (* Now, compare for each values the probabily to win *)
+  let res = ref Z.zero in
+  let () =
+    for i = 0 to elements1 - 1 do
+      for j = 0 to elements2 - 1 do
+        if i >= j then
+          (* Number of times this combinaison is occuring *)
+          let freq = Z.(frequencies_1.(i) * frequencies_2.(j)) in
+          Z.(res := !res + freq)
+      done
+    done
+  in
+  Q.make !res cases