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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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21
Task/Nth-root/Prolog/nth-root.pro Normal file
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iroot(_, 0, 0) :- !.
iroot(M, N, R) :-
M > 1,
(N > 0 ->
irootpos(M, N, R)
;
N /\ 1 =:= 1,
NegN is -N, irootpos(M, NegN, R0), R is -R0).
irootpos(N, A, R) :-
X0 is 1 << (msb(A) div N), % initial guess is 2^(log2(A) / N)
newton(N, A, X0, X1),
iroot_loop(A, X1, N, A, R).
iroot_loop(X1, X2, _, _, X1) :- X1 =< X2, !.
iroot_loop(_, X1, N, A, R) :-
newton(N, A, X1, X2),
iroot_loop(X1, X2, N, A, R).
newton(2, A, X0, X1) :- X1 is (X0 + A div X0) >> 1, !. % fast special case
newton(N, A, X0, X1) :- X1 is ((N - 1)*X0 + A div X0**(N - 1)) div N.