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/**
* Warranty & Liability
* To the extent permitted by applicable law and unless explicitly
* otherwise agreed upon, XLOG Technologies AG makes no warranties
* regarding the provided information. XLOG Technologies AG assumes
* no liability that any problems might be solved with the information
* provided by XLOG Technologies AG.
*
* Rights & License
* All industrial property rights regarding the information - copyright
* and patent rights in particular - are the sole property of XLOG
* Technologies AG. If the company was not the originator of some
* excerpts, XLOG Technologies AG has at least obtained the right to
* reproduce, change and translate the information.
*
* Reproduction is restricted to the whole unaltered document. Reproduction
* of the information is only allowed for non-commercial uses. Selling,
* giving away or letting of the execution of the library is prohibited.
* The library can be distributed as part of your applications and libraries
* for execution provided this comment remains unchanged.
*
* Restrictions
* Only to be distributed with programs that add significant and primary
* functionality to the library. Not to be distributed with additional
* software intended to replace any components of the library.
*
* Trademarks
* Jekejeke is a registered trademark of XLOG Technologies AG.
*/
:- ensure_loaded(library(edge/linear)).
/**
* matexp(M, N, R):
* The predicate succeeds in R with M^N.
*/
% matexp(+Matrix, +Integer, -Matrix)
matexp(M, 1, M) :- !.
matexp(M, N, R) :- N mod 2 =:= 0, !,
I is N // 2,
matexp(M, I, H),
matmul(H, H, R).
matexp(M, N, R) :-
I is N-1,
matexp(M, I, H),
matmul(H, M, R).
/**
* fib(N, X):
* The prdicate succeds in X with fib(N).
*/
% fib(+Integer, -Integer)
fib(N, X) :-
matexp([[1,1],[1,0]], N, H),
matapply(H, [1,0], [_,X]).
% compute
compute :-
fib(1000000, X), _ is X mod 10^8.