102 lines
3.1 KiB
Prolog
102 lines
3.1 KiB
Prolog
:- module(arithmetic, [lsb/2, msb/2, number_to_rational/2,
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number_to_rational/3,
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rational_numerator_denominator/3]).
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:- use_module(library(charsio), [write_term_to_chars/3]).
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:- use_module(library(error)).
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:- use_module(library(lists), [append/3, member/2]).
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lsb(X, N) :-
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builtins:must_be_number(X, lsb/2),
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( \+ integer(X) -> type_error(integer, X, lsb/2)
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; X < 1 -> domain_error(not_less_than_one, X, lsb/2)
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; builtins:can_be_number(N, lsb/2),
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X1 is X /\ (-X),
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msb_(X1, -1, N)
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).
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msb(X, N) :-
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builtins:must_be_number(X, msb/2),
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( \+ integer(X) -> type_error(integer, X, msb/2)
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; X < 1 -> domain_error(not_less_than_one, X, msb/2)
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; builtins:can_be_number(N, msb/2),
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X1 is X >> 1,
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msb_(X1, 0, N)
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).
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msb_(0, N, N) :- !.
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msb_(X, M, N) :-
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X1 is X >> 1,
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M1 is M + 1,
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msb_(X1, M1, N).
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number_to_rational(Real, Fraction) :-
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( var(Real) -> instantiation_error(number_to_rational/2)
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; integer(Real) -> Fraction is Real rdiv 1
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; (rational(Real) ; float(Real)) ->
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number_to_rational(1.0e-6, Real, Fraction)
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; type_error(number, Real, number_to_rational/2)
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).
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% If 0 <= Eps0 <= 1e-16 then the search is for "infinite" precision.
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number_to_rational(Eps0, Real0, Fraction) :-
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( var(Eps0) -> instantiation_error(number_to_rational/3)
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; \+ number(Eps0) -> type_error(number, Eps0, number_to_rational/3)
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; Eps0 < 0 -> domain_error(not_less_than_zero, Eps0, number_to_rational/3)
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; Eps_ is Eps0 rdiv 1,
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rational_numerator_denominator(Eps_, EpsN, EpsD),
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Eps = EpsN/EpsD
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),
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( var(Real0) -> instantiation_error(number_to_rational/3)
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; \+ number(Real0) -> type_error(number, Eps0, number_to_rational/3)
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; Real_ is Real0 rdiv 1,
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rational_numerator_denominator(Real_, RealN, RealD),
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Real = RealN/RealD
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),
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E0/E1 = Eps,
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P0/Q0 = Real,
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( P0 < 0 -> I1 is -1 + P0 // Q0
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; I1 is P0 // Q0
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),
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P1 is P0 mod Q0,
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Q1 = Q0,
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( P1 =:= 0 -> Fraction is I1 + 0 rdiv 1
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; Qn1n is max(P1 * E1 - Q1 * E0, 0),
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Qn1d is Q1 * E1,
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Qn1 = Qn1n/Qn1d,
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Qp1n is P1 * E1 + Q1 * E0,
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Qp1d = Qn1d,
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Qp1 = Qp1n/Qp1d,
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stern_brocot_(Qn1, Qp1, 0/1, 1/0, P2/Q2),
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Fraction is I1 + P2 rdiv Q2
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),
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!.
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number(X) :-
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( integer(X)
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; float(X)
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; rational(X)
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).
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stern_brocot_(Qnn/Qnd, Qpn/Qpd, A/B, C/D, Fraction) :-
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Fn1 is A + C,
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Fd1 is B + D,
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simplify_fraction(Fn1/Fd1, Fn/Fd),
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S1 is sign(Fn * Qnd - Fd * Qnn),
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S2 is sign(Fn * Qpd - Fd * Qpn),
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( S1 < 0 -> stern_brocot_(Qnn/Qnd, Qpn/Qpd, Fn/Fd, C/D, Fraction)
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; S2 > 0 -> stern_brocot_(Qnn/Qnd, Qpn/Qpd, A/B, Fn/Fd, Fraction)
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; Fraction = Fn/Fd
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).
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simplify_fraction(A0/B0, A/B) :-
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G is gcd(A0, B0),
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A is A0 // G,
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B is B0 // G.
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rational_numerator_denominator(R, N, D) :-
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write_term_to_chars(R, [], Cs),
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append(Ns, [' ', r, d, i, v, ' '|Ds], Cs),
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number_chars(N, Ns),
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number_chars(D, Ds).
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