ratioed

-module(ratioed).
-compile([no_auto_import, nowarn_unused_vars, nowarn_unused_function, nowarn_nomatch]).

-export([from_i/1, to_i/1, to_f/1, to_string/1, compare/2, from_i2/2, add/2, sub/2, mul/2, 'div'/2, from_f_epsilon/2, from_f/1]).
-export_type([ratio/0]).

-opaque ratio() :: {ratio, integer(), integer()}.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 14).
-spec from_i(integer()) -> ratio().
from_i(N) ->
    {ratio, N, 1}.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 38).
-spec to_i(ratio()) -> integer().
to_i(A) ->
    case erlang:element(3, A) of
        0 -> 0;
        Gleam@denominator -> erlang:element(2, A) div Gleam@denominator
    end.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 43).
-spec to_f(ratio()) -> float().
to_f(Ratio) ->
    case gleam@int:to_float(erlang:element(3, Ratio)) of
        +0.0 -> +0.0;
        -0.0 -> -0.0;
        Gleam@denominator -> gleam@int:to_float(erlang:element(2, Ratio)) / Gleam@denominator
    end.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 48).
-spec to_string(ratio()) -> binary().
to_string(Ratio) ->
    <<<<(gleam@int:to_string(erlang:element(2, Ratio)))/binary, "/"/utf8>>/binary,
        (gleam@int:to_string(erlang:element(3, Ratio)))/binary>>.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 53).
-spec compare(ratio(), ratio()) -> gleam@order:order().
compare(A, B) ->
    gleam@int:compare(
        erlang:element(2, A) * erlang:element(3, B),
        erlang:element(3, A) * erlang:element(2, B)
    ).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 82).
-spec abs(integer()) -> integer().
abs(X) ->
    case X < 0 of
        true ->
            - X;

        false ->
            X
    end.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 93).
-spec do_gcd(integer(), integer()) -> integer().
do_gcd(X, Y) ->
    case X =:= 0 of
        true ->
            Y;

        false ->
            _assert_subject = gleam@int:modulo(Y, X),
            {ok, Z} = case _assert_subject of
                {ok, _} -> _assert_subject;
                _assert_fail ->
                    erlang:error(#{gleam_error => let_assert,
                                message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
                                value => _assert_fail,
                                module => <<"ratioed"/utf8>>,
                                function => <<"do_gcd"/utf8>>,
                                line => 97})
            end,
            do_gcd(Z, X)
    end.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 89).
-spec gcd(integer(), integer()) -> integer().
gcd(X, Y) ->
    do_gcd(abs(X), abs(Y)).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 77).
-spec simplify(integer(), integer()) -> ratio().
simplify(N, D) ->
    Gcd = gcd(N, D),
    {ratio, case Gcd of
            0 -> 0;
            Gleam@denominator -> N div Gleam@denominator
        end, case Gcd of
            0 -> 0;
            Gleam@denominator@1 -> D div Gleam@denominator@1
        end}.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 19).
-spec from_i2(integer(), integer()) -> ratio().
from_i2(N, D) ->
    case {N, D} of
        {_, 0} ->
            {ratio, 0, 1};

        {0, _} ->
            {ratio, 0, 1};

        {_, _} when D < 0 ->
            simplify(- N, - D);

        {_, _} ->
            simplify(N, D)
    end.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 58).
-spec add(ratio(), ratio()) -> ratio().
add(A, B) ->
    from_i2(
        (erlang:element(2, A) * erlang:element(3, B)) + (erlang:element(3, A) * erlang:element(
            2,
            B
        )),
        erlang:element(3, A) * erlang:element(3, B)
    ).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 63).
-spec sub(ratio(), ratio()) -> ratio().
sub(A, B) ->
    from_i2(
        (erlang:element(2, A) * erlang:element(3, B)) - (erlang:element(3, A) * erlang:element(
            2,
            B
        )),
        erlang:element(3, A) * erlang:element(3, B)
    ).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 68).
-spec mul(ratio(), ratio()) -> ratio().
mul(A, B) ->
    from_i2(
        erlang:element(2, A) * erlang:element(2, B),
        erlang:element(3, A) * erlang:element(3, B)
    ).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 73).
-spec 'div'(ratio(), ratio()) -> ratio().
'div'(A, B) ->
    from_i2(
        erlang:element(2, A) * erlang:element(3, B),
        erlang:element(3, A) * erlang:element(2, B)
    ).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 109).
-spec continued_fraction(
    any(),
    integer(),
    integer(),
    integer(),
    integer(),
    float(),
    float(),
    float(),
    float(),
    float(),
    float(),
    float()
) -> ratio().
continued_fraction(Tol, P, Q, Pp, Qq, X, Y, R, A, Nt, T, Tt) ->
    case R > Nt of
        true ->
            Np = (gleam@float:truncate(A) * P) + Pp,
            Nq = (gleam@float:truncate(A) * Q) + Qq,
            Pp@1 = P,
            P@1 = Np,
            Qq@1 = Q,
            Q@1 = Nq,
            X@1 = Y,
            Y@1 = R,
            R@1 = math:fmod(X@1, Y@1),
            A@1 = gleam@float:floor(case Y@1 of
                    +0.0 -> +0.0;
                    -0.0 -> -0.0;
                    Gleam@denominator -> X@1 / Gleam@denominator
                end),
            Tt@1 = T,
            T@1 = Nt,
            Nt@1 = (A@1 * T@1) + Tt@1,
            continued_fraction(
                Tol,
                P@1,
                Q@1,
                Pp@1,
                Qq@1,
                X@1,
                Y@1,
                R@1,
                A@1,
                Nt@1,
                T@1,
                Tt@1
            );

        false ->
            I = gleam@float:truncate(gleam@float:ceiling(case (Y + T) of
                        +0.0 -> +0.0;
                        -0.0 -> -0.0;
                        Gleam@denominator@1 -> (X - Tt) / Gleam@denominator@1
                    end)),
            from_i2((I * P) + Pp, (I * Q) + Qq)
    end.

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 103).
-spec approx_ratio(float(), float()) -> ratio().
approx_ratio(Tol, X) ->
    A = gleam@float:floor(X),
    R = X - A,
    continued_fraction(Tol, 1, 0, 0, 1, X, 1.0, R, A, Tol, +0.0, Tol).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 33).
-spec from_f_epsilon(float(), float()) -> ratio().
from_f_epsilon(F, E) ->
    approx_ratio(E, F).

-file("/home/julian/projects/ratioed/src/ratioed.gleam", 28).
-spec from_f(float()) -> ratio().
from_f(F) ->
    approx_ratio(4.440892098500626e-16, F).