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Implemented predicate mediants/2 with Stern-Brocot tree

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notoria
2020-04-29 02:44:13 +02:00
parent a3bb288f01
commit 1d339f74d1
1 changed files with 26 additions and 1 deletions
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27
src/prolog/lib/arithmetic.pl
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@@ -1,4 +1,4 @@
:- module(arithmetic, [msb/2, lsb/2]). :- module(arithmetic, [lsb/2, msb/2, mediants/2]).
:- use_module(library(error)). :- use_module(library(error)).
@@ -25,3 +25,28 @@ msb_(X, M, N) :-
X1 is X >> 1, X1 is X >> 1,
M1 is M + 1, M1 is M + 1,
msb_(X1, M1, N). msb_(X1, M1, N).
mediants_precision(1.0e-15).
mediants(Real, Fraction) :-
builtins:must_be_number(Real, mediants),
Fraction = P/Q,
mediants_precision(Eps),
R is abs(Real),
stern_brocot(Eps, R, P1/Q),
P is sign(Real) * P1.
% If 0 <= Eps <= 1e-16 then the search is for "infinite" precision.
stern_brocot(Eps, Real, Fraction) :-
Rn is Real - Eps,
Rp is Real + Eps,
stern_brocot_(Rn, Rp, 0/1, 1/0, Fraction).
stern_brocot_(Rn, Rp, A/B, C/D, Fraction) :-
M0 is A + C,
M1 is B + D,
M is M0 / M1,
( M < Rn -> stern_brocot_(Rn, Rp, M0/M1, C/D, Fraction)
; M > Rp -> stern_brocot_(Rn, Rp, A/B, M0/M1, Fraction)
; Fraction = M0/M1
).