Initial data commit

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-1.pro

@@ -0,0 +1,6 @@
+fib(1, 1) :- !.
+fib(0, 0) :- !.
+fib(N, Value) :-
+  A is N - 1, fib(A, A1),
+  B is N - 2, fib(B, B1),
+  Value is A1 + B1.

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-10.pro

@@ -0,0 +1,7 @@
+% Fibonacci sequence generator
+fib(C, [P,S], C, N)  :- N is P + S.
+fib(C, [P,S], Cv, V) :- succ(C, Cn), N is P + S, !, fib(Cn, [S,N], Cv, V).
+
+fib(0, 0).
+fib(1, 1).
+fib(C, N) :- fib(2, [0,1], C, N). % Generate from 3rd sequence on

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-11.pro

@@ -0,0 +1,12 @@
+% John Devou: 26-Nov-2021
+% Efficient program to calculate n-th Fibonacci number.
+% Works fast for n ≤ 1 000 000 000.
+
+b(0,Bs,Bs).
+b(N,Bs,Res):- N > 0, B is mod(N,2), M is div(N,2), b(M,[B|Bs],Res).
+
+f([],A,_,_,A).
+f([X|Xs],A,B,C,Res):- AA is A^2, BB is B^2, A_ is 2*BB-3*AA-C, B_ is AA+BB,
+    (X =:= 1 -> T is A_+B_, f(Xs,B_,T,-2,Res); f(Xs,A_,B_,2,Res)).
+
+fib(N,F):- b(N,[],Bs), f(Bs,0,1,2,F), !.

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-2.pro

@@ -0,0 +1,19 @@
+?- time(fib(0,F)).
+% 2 inferences, 0.000 CPU in 0.000 seconds (88% CPU, 161943 Lips)
+F = 0.
+
+?- time(fib(10,F)).
+% 265 inferences, 0.000 CPU in 0.000 seconds (98% CPU, 1458135 Lips)
+F = 55.
+
+?- time(fib(20,F)).
+% 32,836 inferences, 0.016 CPU in 0.016 seconds (99% CPU, 2086352 Lips)
+F = 6765.
+
+?- time(fib(30,F)).
+% 4,038,805 inferences, 1.122 CPU in 1.139 seconds (98% CPU, 3599899 Lips)
+F = 832040.
+
+?- time(fib(40,F)).
+% 496,740,421 inferences, 138.705 CPU in 140.206 seconds (99% CPU, 3581264 Lips)
+F = 102334155.

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-3.pro

@@ -0,0 +1,9 @@
+%:- dynamic fib/2.  % This is ISO, but GNU doesn't like it.
+:- dynamic(fib/2).  % Not ISO, but works in SWI, YAP and GNU unlike the ISO declaration.
+fib(1, 1) :- !.
+fib(0, 0) :- !.
+fib(N, Value) :-
+  A is N - 1, fib(A, A1),
+  B is N - 2, fib(B, B1),
+  Value is A1 + B1,
+  asserta((fib(N, Value) :- !)).

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-4.pro

@@ -0,0 +1,19 @@
+?- time(fib(0,F)).
+% 2 inferences, 0.000 CPU in 0.000 seconds (90% CPU, 160591 Lips)
+F = 0.
+
+?- time(fib(10,F)).
+% 37 inferences, 0.000 CPU in 0.000 seconds (96% CPU, 552610 Lips)
+F = 55.
+
+?- time(fib(20,F)).
+% 41 inferences, 0.000 CPU in 0.000 seconds (96% CPU, 541233 Lips)
+F = 6765.
+
+?- time(fib(30,F)).
+% 41 inferences, 0.000 CPU in 0.000 seconds (95% CPU, 722722 Lips)
+F = 832040.
+
+?- time(fib(40,F)).
+% 41 inferences, 0.000 CPU in 0.000 seconds (96% CPU, 543572 Lips)
+F = 102334155.

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-5.pro

@@ -0,0 +1,51 @@
+?- listing(fib).
+:- dynamic fib/2.
+
+fib(40, 102334155) :- !.
+fib(39, 63245986) :- !.
+fib(38, 39088169) :- !.
+fib(37, 24157817) :- !.
+fib(36, 14930352) :- !.
+fib(35, 9227465) :- !.
+fib(34, 5702887) :- !.
+fib(33, 3524578) :- !.
+fib(32, 2178309) :- !.
+fib(31, 1346269) :- !.
+fib(30, 832040) :- !.
+fib(29, 514229) :- !.
+fib(28, 317811) :- !.
+fib(27, 196418) :- !.
+fib(26, 121393) :- !.
+fib(25, 75025) :- !.
+fib(24, 46368) :- !.
+fib(23, 28657) :- !.
+fib(22, 17711) :- !.
+fib(21, 10946) :- !.
+fib(20, 6765) :- !.
+fib(19, 4181) :- !.
+fib(18, 2584) :- !.
+fib(17, 1597) :- !.
+fib(16, 987) :- !.
+fib(15, 610) :- !.
+fib(14, 377) :- !.
+fib(13, 233) :- !.
+fib(12, 144) :- !.
+fib(11, 89) :- !.
+fib(10, 55) :- !.
+fib(9, 34) :- !.
+fib(8, 21) :- !.
+fib(7, 13) :- !.
+fib(6, 8) :- !.
+fib(5, 5) :- !.
+fib(4, 3) :- !.
+fib(3, 2) :- !.
+fib(2, 1) :- !.
+fib(1, 1) :- !.
+fib(0, 0) :- !.
+fib(A, D) :-
+	B is A+ -1,
+	fib(B, E),
+	C is A+ -2,
+	fib(C, F),
+	D is E+F,
+	asserta((fib(A, D):-!)).

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-6.pro

@@ -0,0 +1,13 @@
+:- use_module(lambda).
+fib(N, FN) :-
+	cont_fib(N, _, FN, \_^Y^_^U^(U = Y)).
+
+cont_fib(N, FN1, FN, Pred) :-
+	(   N < 2 ->
+	    call(Pred, 0, 1, FN1, FN)
+	;
+	    N1 is N - 1,
+	    P = \X^Y^Y^U^(U is X + Y),
+	    cont_fib(N1, FNA, FNB, P),
+	    call(Pred, FNA, FNB, FN1, FN)
+	).

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-7.pro

@@ -0,0 +1,4 @@
+fib([0,1|X]) :-
+    ffib(0,1,X).
+ffib(A,B,X) :-
+    freeze(X, (C is A+B, X=[C|Y], ffib(B,C,Y)) ).

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-8.pro

@@ -0,0 +1,2 @@
+?- fib(X), length(A,15), append(A,_,X), writeln(A).
+[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

Task/Fibonacci-sequence/Prolog/fibonacci-sequence-9.pro

@@ -0,0 +1,10 @@
+take( 0, Next, Z-Z, Next).
+take( N, Next, [A|B]-Z, NZ):- N>0, !, next( Next, A, Next1),
+  N1 is N-1,
+  take( N1, Next1, B-Z, NZ).
+
+next( fib(A,B), A, fib(B,C)):- C is A+B.
+
+%% usage: ?- take(15, fib(0,1), _X-[], G), writeln(_X).
+%% [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]
+%% G = fib(610, 987)