-module(rational).
-compile([no_auto_import, nowarn_unused_vars]).

-export([new/2, new_improper/3, from_float/2, from_int/1, to_float/1, truncate/1, to_mixed_fraction/1, add/2, subtract/2, multiply/2, divide/2, reciprocal/1, pow/2, absolute_value/1, compare/2]).
-export_type([rational/0]).

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

-spec gcd(integer(), integer()) -> integer().
gcd(X, Y) ->
    case {X, Y} of
        {0, _} ->
            Y;

        {_, 0} ->
            X;

        {_, _} ->
            _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 => <<"Assertion pattern match failed"/utf8>>,
                                value => _assert_fail,
                                module => <<"rational"/utf8>>,
                                function => <<"gcd"/utf8>>,
                                line => 15})
            end,
            gcd(Z, X)
    end.

-spec reduce(integer(), integer()) -> rational().
reduce(Num, Den) ->
    G = gcd(gleam@int:absolute_value(Num), gleam@int:absolute_value(Den)),
    case Den < 0 of
        true ->
            {rational, case G of
                    0 -> 0;
                    Gleam@denominator -> - Num div Gleam@denominator
                end, case G of
                    0 -> 0;
                    Gleam@denominator@1 -> Den div Gleam@denominator@1
                end};

        false ->
            {rational, case G of
                    0 -> 0;
                    Gleam@denominator@2 -> Num div Gleam@denominator@2
                end, case G of
                    0 -> 0;
                    Gleam@denominator@3 -> Den div Gleam@denominator@3
                end}
    end.

-spec do_pow(integer(), integer()) -> integer().
do_pow(X, N) ->
    case N of
        0 ->
            1;

        1 ->
            X;

        2 ->
            X * X;

        N@1 ->
            case N@1 rem 2 of
                0 ->
                    do_pow(X * X, N@1 div 2);

                1 ->
                    X * do_pow(X, N@1 - 1)
            end
    end.

-spec new(integer(), integer()) -> {ok, rational()} | {error, nil}.
new(Num, Den) ->
    case Den of
        0 ->
            {error, nil};

        _ ->
            {ok, reduce(Num, Den)}
    end.

-spec new_improper(integer(), integer(), integer()) -> {ok, rational()} |
    {error, nil}.
new_improper(Whole, Num, Den) ->
    new(Num + (Whole * Den), Den).

-spec from_float(float(), rational()) -> rational().
from_float(F, Inc) ->
    reduce(gleam@float:round(case gleam@int:to_float(erlang:element(2, Inc)) of
                0.0 -> 0.0;
                Gleam@denominator -> (F * gleam@int:to_float(
                    erlang:element(3, Inc)
                ))
                / Gleam@denominator
            end), erlang:element(3, Inc)).

-spec from_int(integer()) -> rational().
from_int(From) ->
    _assert_subject = new(From, 1),
    {ok, R} = case _assert_subject of
        {ok, _} -> _assert_subject;
        _assert_fail ->
            erlang:error(#{gleam_error => let_assert,
                        message => <<"Assertion pattern match failed"/utf8>>,
                        value => _assert_fail,
                        module => <<"rational"/utf8>>,
                        function => <<"from_int"/utf8>>,
                        line => 72})
    end,
    R.

-spec to_float(rational()) -> float().
to_float(R) ->
    case gleam@int:to_float(erlang:element(3, R)) of
        0.0 -> 0.0;
        Gleam@denominator -> gleam@int:to_float(erlang:element(2, R)) / Gleam@denominator
    end.

-spec truncate(rational()) -> integer().
truncate(R) ->
    case erlang:element(3, R) of
        0 -> 0;
        Gleam@denominator -> erlang:element(2, R) div Gleam@denominator
    end.

-spec to_mixed_fraction(rational()) -> {integer(), rational()}.
to_mixed_fraction(R) ->
    {case erlang:element(3, R) of
            0 -> 0;
            Gleam@denominator -> erlang:element(2, R) div Gleam@denominator
        end, reduce(case erlang:element(3, R) of
                0 -> 0;
                Gleam@denominator@1 -> erlang:element(2, R) rem Gleam@denominator@1
            end, erlang:element(3, R))}.

-spec add(rational(), rational()) -> rational().
add(A, B) ->
    reduce(
        (erlang:element(2, A) * erlang:element(3, B)) + (erlang:element(2, B) * erlang:element(
            3,
            A
        )),
        erlang:element(3, A) * erlang:element(3, B)
    ).

-spec subtract(rational(), rational()) -> rational().
subtract(A, B) ->
    reduce(
        (erlang:element(2, A) * erlang:element(3, B)) - (erlang:element(2, B) * erlang:element(
            3,
            A
        )),
        erlang:element(3, A) * erlang:element(3, B)
    ).

-spec multiply(rational(), rational()) -> rational().
multiply(A, B) ->
    reduce(
        erlang:element(2, A) * erlang:element(2, B),
        erlang:element(3, A) * erlang:element(3, B)
    ).

-spec divide(rational(), rational()) -> {ok, rational()} | {error, nil}.
divide(A, B) ->
    case erlang:element(2, B) of
        0 ->
            {error, nil};

        _ ->
            {ok,
                reduce(
                    erlang:element(2, A) * erlang:element(3, B),
                    erlang:element(3, A) * erlang:element(2, B)
                )}
    end.

-spec reciprocal(rational()) -> rational().
reciprocal(A) ->
    reduce(erlang:element(3, A), erlang:element(2, A)).

-spec pow(rational(), integer()) -> rational().
pow(A, N) ->
    case gleam@int:compare(N, 0) of
        gt ->
            reduce(
                do_pow(erlang:element(2, A), N),
                do_pow(erlang:element(3, A), N)
            );

        eq ->
            from_int(1);

        lt ->
            reduce(
                do_pow(erlang:element(3, A), - N),
                do_pow(erlang:element(2, A), - N)
            )
    end.

-spec absolute_value(rational()) -> rational().
absolute_value(A) ->
    reduce(gleam@int:absolute_value(erlang:element(2, A)), erlang:element(3, A)).

-spec compare(rational(), rational()) -> gleam@order:order().
compare(A, B) ->
    gleam@int:compare(
        erlang:element(2, A) * erlang:element(3, B),
        erlang:element(2, B) * erlang:element(3, A)
    ).