Add rational_numerator_denominator/3, number_to_rational/2 and renamed stern_brocot/3 to number_to_rational/3
This commit is contained in:
notoria
@@ -1,6 +1,10 @@
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:- module(arithmetic, [lsb/2, msb/2, stern_brocot/3]).
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:- 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(error)).
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:- use_module(library(lists), [append/3, member/2]).
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lsb(X, N) :-
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lsb(X, N) :-
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builtins:must_be_number(X, lsb/2),
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builtins:must_be_number(X, lsb/2),
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@@ -26,76 +30,79 @@ msb_(X, M, N) :-
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M1 is M + 1,
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M1 is M + 1,
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msb_(X1, M1, N).
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msb_(X1, M1, N).
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stern_brocot(E0/E1, Fraction0, Fraction) :-
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number_to_rational(Real0, Fraction) :-
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P1/Q1 = Fraction0,
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( var(Real) -> instantiation_error(number_to_rational/2)
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!,
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; Real0 = R1/R2 ->
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( \+ integer(E0) -> type_error(integer, E0, stern_brocot/3)
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( member(R, [R1, R2]), \+ number(R) ->
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; \+ integer(E1) -> type_error(integer, E1, stern_brocot/3)
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type_error(number, R, number_to_rational/2)
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; \+ integer(P1) -> type_error(integer, P1, stern_brocot/3)
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; Real = R1/R2
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; \+ integer(Q1) -> type_error(integer, Q1, stern_brocot/3)
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)
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; S is sign(E0) * sign(E1), S < 0 ->
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; number(Real0),
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domain_error(not_less_than_zero, E0/E1, stern_brocot/3)
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Real = Real0/1
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; P2 is abs(P1),
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),
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Q2 is abs(Q1),
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number_to_rational(1.0e-6/1, Real, Fraction).
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Qn1n is P2 * E1 - Q2 * E0,
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Qn1d is Q2 * E1,
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simplify_fraction(Qn1n/Qn1d, Qn1),
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Qp1n is P2 * E1 + Q2 * E0,
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Qp1d = Qn1d,
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simplify_fraction(Qp1n/Qp1d, Qp1),
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fraction_stern_brocot_(Qn1, Qp1, 0/1, 1/0, P3/Q3),
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P4 is sign(P1) * sign(Q1) * P3,
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Fraction = P4/Q3
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).
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% If 0 <= Eps0 <= 1e-16 then the search is for "infinite" precision.
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% If 0 <= Eps0 <= 1e-16 then the search is for "infinite" precision.
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stern_brocot(Eps0, Real0, Fraction) :-
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number_to_rational(Eps0, Real0, Fraction) :-
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( Real0 = R1/R2 ->
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( var(Eps0) -> instantiation_error(number_to_rational/3)
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builtins:must_be_number(R1, stern_brocot/3),
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; Eps0 = E0/E1 ->
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builtins:must_be_number(R2, stern_brocot/3),
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( member(E, [E0, E1]), \+ number(E) ->
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Real is R1/R2
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type_error(number, E, number_to_rational/3)
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; builtins:must_be_number(Real0, stern_brocot/3),
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; Eps = E0/E1
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Real = Real0
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)
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; number(Eps0),
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Eps = Eps0/1
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),
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),
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( Eps0 = E0/E1 ->
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( var(Real0) -> instantiation_error(number_to_rational/3)
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builtins:must_be_number(E0, stern_brocot/3),
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; Real0 = R1/R2 ->
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builtins:must_be_number(E1, stern_brocot/3),
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( member(R, [R1, R2]), \+ number(R) ->
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% Eps is Eps0 % doesn't work
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type_error(number, R, number_to_rational/3)
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Eps is E0/E1
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; Real = R1/R2
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; Eps = Eps0
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)
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; number(Real0),
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Real = Real0/1
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),
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),
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S is sign(Eps),
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E0/E1 = Eps,
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( S < 0 -> domain_error(not_less_than_zero, Eps0, stern_brocot/3)
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P0/Q0 = Real,
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; Rn is abs(Real) - Eps,
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S is sign(E0) * sign(E1),
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Rp is abs(Real) + Eps,
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( S < 0 -> domain_error(not_less_than_zero, Eps0, number_to_rational/3)
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stern_brocot_(Rn, Rp, 0/1, 1/0, P1/Q),
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; P1 is abs(P0),
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P is sign(Real) * P1,
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Q1 is abs(Q0),
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Fraction = P/Q
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Qn1n is P1 * E1 - Q1 * E0,
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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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P3 is sign(P0) * sign(Q0) * P2,
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Fraction is P3 rdiv Q2
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).
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).
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fraction_stern_brocot_(Qnn/Qnd, Qpn/Qpd, A/B, C/D, Fraction) :-
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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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Fn1 is A + C,
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Fd1 is B + D,
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Fd1 is B + D,
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simplify_fraction(Fn1/Fd1, Fn/Fd),
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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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S1 is sign(Fn * Qnd - Fd * Qnn),
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S2 is sign(Fn * Qpd - Fd * Qpn),
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S2 is sign(Fn * Qpd - Fd * Qpn),
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( S1 < 0 ->
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( S1 < 0 -> stern_brocot_(Qnn/Qnd, Qpn/Qpd, Fn/Fd, C/D, Fraction)
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fraction_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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; S2 > 0 ->
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fraction_stern_brocot_(Qnn/Qnd, Qpn/Qpd, A/B, Fn/Fd, Fraction)
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; Fraction = Fn/Fd
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; Fraction = Fn/Fd
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).
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).
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stern_brocot_(Rn, Rp, A/B, C/D, Fraction) :-
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M0 is A + C,
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M1 is B + D,
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M is M0 / M1,
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( M < Rn -> stern_brocot_(Rn, Rp, M0/M1, C/D, Fraction)
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; M > Rp -> stern_brocot_(Rn, Rp, A/B, M0/M1, Fraction)
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; Fraction = M0/M1
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).
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simplify_fraction(A0/B0, A/B) :-
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simplify_fraction(A0/B0, A/B) :-
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G is gcd(A0, B0),
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G is gcd(A0, B0),
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A is A0 div G,
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A is A0 div G,
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B is B0 div G.
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B is B0 div 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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