remove vestigial prolog/ directory (#444)

src/lib/arithmetic.pl

@@ -0,0 +1,123 @@
+:- module(arithmetic, [expmod/4, lsb/2, msb/2, number_to_rational/2,
+                       number_to_rational/3,
+                       rational_numerator_denominator/3]).
+
+:- use_module(library(charsio), [write_term_to_chars/3]).
+:- use_module(library(error)).
+:- use_module(library(lists), [append/3, member/2]).
+
+expmod(Base, Expo, Mod, R) :-
+    (   member(N, [Base, Expo, Mod]), var(N) -> instantiation_error(expmod/4)
+    ;   member(N, [Base, Expo, Mod]), \+ integer(N) ->
+        type_error(integer, N, expmod/4)
+    ;   Expo < 0 -> domain_error(not_less_than_zero, Expo, expmod/4)
+    ;   expmod_(Base, Expo, Mod, 1, R)
+    ).
+
+expmod_(_, _, 1, _, 0) :- !.
+expmod_(_, 0, _, R, R) :- !.
+expmod_(Base0, Expo0, Mod, C0, R) :-
+    Expo0 /\ 1 =:= 1,
+    C is (C0 * Base0) mod Mod,
+    !,
+    Expo is Expo0 >> 1,
+    Base is (Base0 * Base0) mod Mod,
+    expmod_(Base, Expo, Mod, C, R).
+expmod_(Base0, Expo0, Mod, C, R) :-
+    Expo is Expo0 >> 1,
+    Base is (Base0 * Base0) mod Mod,
+    expmod_(Base, Expo, Mod, C, R).
+
+lsb(X, N) :-
+    builtins:must_be_number(X, lsb/2),
+    (   \+ integer(X) -> type_error(integer, X, lsb/2)
+    ;   X < 1 -> domain_error(not_less_than_one, X, lsb/2)
+    ;   builtins:can_be_number(N, lsb/2),
+        X1 is X /\ (-X),
+        msb_(X1, -1, N)
+    ).
+
+msb(X, N) :-
+    builtins:must_be_number(X, msb/2),
+    (   \+ integer(X) -> type_error(integer, X, msb/2)
+    ;   X < 1 -> domain_error(not_less_than_one, X, msb/2)
+    ;   builtins:can_be_number(N, msb/2),
+        X1 is X >> 1,
+        msb_(X1, 0, N)
+    ).
+
+msb_(0, N, N) :- !.
+msb_(X, M, N) :-
+    X1 is X >> 1,
+    M1 is M + 1,
+    msb_(X1, M1, N).
+
+number_to_rational(Real, Fraction) :-
+    (   var(Real) -> instantiation_error(number_to_rational/2)
+    ;   integer(Real) -> Fraction is Real rdiv 1
+    ;   (rational(Real) ; float(Real)) ->
+            number_to_rational(1.0e-6, Real, Fraction)
+    ;   type_error(number, Real, number_to_rational/2)
+    ).
+
+% If 0 <= Eps0 <= 1e-16 then the search is for "infinite" precision.
+number_to_rational(Eps0, Real0, Fraction) :-
+    (   var(Eps0) -> instantiation_error(number_to_rational/3)
+    ;   \+ number(Eps0) -> type_error(number, Eps0, number_to_rational/3)
+    ;   Eps0 < 0 -> domain_error(not_less_than_zero, Eps0, number_to_rational/3)
+    ;   Eps_ is Eps0 rdiv 1,
+        rational_numerator_denominator(Eps_, EpsN, EpsD),
+        Eps = EpsN/EpsD
+    ),
+    (   var(Real0) -> instantiation_error(number_to_rational/3)
+    ;   \+ number(Real0) -> type_error(number, Eps0, number_to_rational/3)
+    ;   Real_ is Real0 rdiv 1,
+        rational_numerator_denominator(Real_, RealN, RealD),
+        Real = RealN/RealD
+    ),
+    E0/E1 = Eps,
+    P0/Q0 = Real,
+    (   P0 < 0 -> I1 is -1 + P0 // Q0
+    ;   I1 is P0 // Q0
+    ),
+    P1 is P0 mod Q0,
+    Q1 = Q0,
+    (   P1 =:= 0 -> Fraction is I1 + 0 rdiv 1
+    ;   Qn1n is max(P1 * E1 - Q1 * E0, 0),
+        Qn1d is Q1 * E1,
+        Qn1 = Qn1n/Qn1d,
+        Qp1n is P1 * E1 + Q1 * E0,
+        Qp1d = Qn1d,
+        Qp1 = Qp1n/Qp1d,
+        stern_brocot_(Qn1, Qp1, 0/1, 1/0, P2/Q2),
+        Fraction is I1 + P2 rdiv Q2
+    ),
+    !.
+
+number(X) :-
+    (   integer(X)
+    ;   float(X)
+    ;   rational(X)
+    ).
+
+stern_brocot_(Qnn/Qnd, Qpn/Qpd, A/B, C/D, Fraction) :-
+    Fn1 is A + C,
+    Fd1 is B + D,
+    simplify_fraction(Fn1/Fd1, Fn/Fd),
+    S1 is sign(Fn * Qnd - Fd * Qnn),
+    S2 is sign(Fn * Qpd - Fd * Qpn),
+    (   S1 < 0 -> stern_brocot_(Qnn/Qnd, Qpn/Qpd, Fn/Fd, C/D, Fraction)
+    ;   S2 > 0 -> stern_brocot_(Qnn/Qnd, Qpn/Qpd, A/B, Fn/Fd, Fraction)
+    ;   Fraction = Fn/Fd
+    ).
+
+simplify_fraction(A0/B0, A/B) :-
+    G is gcd(A0, B0),
+    A is A0 // G,
+    B is B0 // G.
+
+rational_numerator_denominator(R, N, D) :-
+    write_term_to_chars(R, [], Cs),
+    append(Ns, [' ', r, d, i, v, ' '|Ds], Cs),
+    number_chars(N, Ns),
+    number_chars(D, Ds).