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Valider b7ac4c84 rédigé par EdouardParis's avatar EdouardParis
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main.ml
+ 8
− 18
Voir le fichier @ b7ac4c84
......@@ -28,26 +28,16 @@ print_string "addition polynome:\np1 + p2 = ";
print_string (P.print(P.add p1 p2));;
print_string "\n";
print_string "naive multiplication:\np1 x p2 = ";
print_string (P.print(P.naive_mul p2 p1));;
print_string "naive multiplication:\np1 x p2 = ";;
let naive = P.naive_mul p2 p1;;
print_string (P.print(naive));;
print_string "\n";
print_string "decoupe p1 en 2 = \n";
let first (pp1, pp2) = pp1 in
print_string (P.print(first (P.cut_2 p1)));;
print_string "\n";
let second (pp1, pp2) = pp2 in
print_string (P.print(second (P.cut_2 p1)));;
print_string "\n";
print_string "decoupe p2 en 2 = \n";
let first (pp1, pp2) = pp1 in
print_string (P.print(first (P.cut_2 p2)));;
print_string "\n";
let second (pp1, pp2) = pp2 in
print_string (P.print(second (P.cut_2 p2)));;
print_string "karatsuba multiplication:\np1 x p2 = ";;
let karatsuba = (P.karatsuba_mul p1 p2);;
print_string (P.print(karatsuba));;
print_string "\n";
print_string "karatsuba multiplication:\np1 x p2 = ";
print_string (P.print(P.karatsuba_mul p1 p2));;
print_string "diff\n naive_mul - karatsuba = ";;
print_string (P.print(P.sub naive karatsuba));;
print_string "\n";
polynome.ml
+ 30
− 19
Voir le fichier @ b7ac4c84
......@@ -14,6 +14,7 @@ module type Coefficient =
val is_null: coeff -> bool
val equal: coeff -> coeff -> bool
val add: coeff -> coeff -> coeff
val sub: coeff -> coeff -> coeff
val mul: coeff -> coeff -> coeff
val minus: coeff -> coeff
val generate: int -> coeff
......@@ -25,7 +26,7 @@ module type Degree =
type degree
val print: degree -> string
val add: degree -> degree -> degree
val subtract: degree -> degree -> degree
val sub: degree -> degree -> degree
val div: degree -> int -> degree
val equal: degree -> degree -> bool
val is_bigger: degree -> degree -> bool
......@@ -42,8 +43,8 @@ module type Polynomes =
val print: polynome -> string
val equal: polynome -> polynome -> bool
val add: polynome -> polynome -> polynome
val cut_2: polynome -> polynome*polynome
val naive_mul: polynome -> polynome -> polynome
val sub: polynome -> polynome -> polynome
val generate: int -> polynome
end
;;
......@@ -83,13 +84,28 @@ module Polynome (C : Coefficient) (D : Degree) =
then NotNull (cy, dy, add x yy)
else
if D.is_bigger dx dy
then NotNull (cx, dx, add xx yy)
then NotNull (cx, dx, add xx y)
else
let m = C.add cx cy in
if C.is_null m
then add xx yy
else NotNull (m, dx, add xx yy)
let rec sub x y = match x, y with
|Null,_ -> y
|_, Null -> x
|NotNull (cx, dx, xx), NotNull (cy, dy, yy)->
if D.is_bigger dy dx
then NotNull ((C.minus cy), dy, sub x yy)
else
if D.is_bigger dx dy
then NotNull (cx, dx, sub xx y)
else
let m = C.sub cx cy in
if C.is_null m
then sub xx yy
else NotNull (m, dx, sub xx yy)
(*fonction privée pour incrémenter les degrees des monomes d'un polynome*)
let rec increment_degree d x = match x with
|Null -> Null
......@@ -109,12 +125,6 @@ module Polynome (C : Coefficient) (D : Degree) =
|NotNull (cx, dx, xx), _ ->
let xxy = naive_mul xx y in
add xxy (increment_degree dx (multiply_coeffs cx y))
(*fonction privée de soustraction de deux polynomes pour karatsuba*)
let rec subtract x y =
let rec minus p = match p with
|Null -> Null
|NotNull (cp, dp, pp) -> NotNull (C.minus cp, dp, minus pp)
in add x (minus y)
(*fonction privée pour couper un polynome selon un degree*)
(*polynome -> degree -> degree *)
......@@ -129,30 +139,28 @@ module Polynome (C : Coefficient) (D : Degree) =
|NotNull (ccp, ddp, ppp) ->
NotNull (ccp, ddp, (insert cc dd ppp))
) in
let new_acc = insert cp (D.subtract dp i) acc in
let new_acc = insert cp (D.sub dp i) acc in
acc_cut new_acc pp i
else acc, p
in acc_cut Null x n
let cut_2 x = match x with
|Null-> Null, Null
|NotNull (cx, dx, xx) -> cut x (D.div dx 2)
(*multiplication de Karatsuba offman *)
let rec karatsuba_mul x y = match x, y with
|Null,_ -> Null
|_,Null -> Null
|NotNull (cx, dx, xx), NotNull (_, dy, _) ->
if D.is_null (D.div dx 2) || D.is_null (D.div dy 2) then
if D.equal dx D.unit || D.equal dy D.unit
then
naive_mul x y
else
let degree_max = if D.is_bigger dx dy then dx else dy in
let n = D.div degree_max 2 in
let x1, x2 = cut x n in
let y1, y2 = cut y n in
let xy1 = karatsuba_mul x1 y1 in
let xy2 = karatsuba_mul x2 y2 in
let xy3 = subtract (karatsuba_mul (add x1 y1) (add x2 y2)) (add xy1 xy2) in
add (add (increment_degree (D.double n) xy1) (increment_degree n xy3)) xy2
let xy1 = naive_mul x1 y1 in
let xy2 = naive_mul x2 y2 in
let xy3 = sub (naive_mul (add x1 y1) (add x2 y2)) (add xy1 xy2) in
add xy2 (add (increment_degree (D.double n) xy1) (increment_degree n xy3))
(*generate polynome from another polynome*)
let generate n =
......@@ -160,7 +168,10 @@ module Polynome (C : Coefficient) (D : Degree) =
if count == 0 then acc else
let add_monome x c = match x with
|Null -> NotNull(C.generate c, D.unit, x)
|NotNull(_,dx,_) -> NotNull(C.generate c, D.increment dx, x) in
|NotNull(_,dx,_) ->
let cx = C.generate c in
if C.is_null cx then x
else NotNull(cx, D.increment dx, x) in
gen (add_monome acc (count - 1)) (count-1) in
gen Null n
end
......
simplepolynome.ml
+ 2
− 1
Voir le fichier @ b7ac4c84
......@@ -10,7 +10,7 @@ module SimpleDegree =
type degree = int
let print d = (string_of_int d)
let add d1 d2 = d1 + d2
let subtract d1 d2 = d1 - d2
let sub d1 d2 = d1 - d2
let div d i = d/i
let equal d1 d2 = (d1 == d2)
let is_bigger d1 d2 = (d1 > d2)
......@@ -26,6 +26,7 @@ module SimpleCoeff =
type coeff = big_int
let print c = (string_of_big_int c)
let add c1 c2 = add_big_int c1 c2
let sub c1 c2 = sub_big_int c1 c2
let equal c1 c2 = eq_big_int c1 c2
let is_null c = eq_big_int c zero_big_int
let mul c1 c2 = mult_big_int c1 c2
......
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