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

-export([pow/2, factorial/1, abs/1, sqrt/1, pow2/1, pow10/1, cbrt/1]).
-export_type([math_error/0]).

-type math_error() :: division_by_zero |
    value_out_of_range |
    unsupported_operation.

-spec pow_iter(float(), float(), float()) -> float().
pow_iter(Base, Power, Accumulator) ->
    case Power of
        +0.0 ->
            Accumulator;

        _ ->
            pow_iter(Base, Power - 1.0, Base * Accumulator)
    end.

-spec pow(float(), float()) -> float().
pow(Base, Power) ->
    pow_iter(Base, Power, 1.0).

-spec factorial_iter(float(), float()) -> float().
factorial_iter(N, Accumulator) ->
    case N of
        +0.0 ->
            Accumulator;

        _ ->
            factorial_iter(N - 1.0, N * Accumulator)
    end.

-spec factorial(float()) -> {ok, float()} | {error, math_error()}.
factorial(N) ->
    case N < +0.0 of
        true ->
            {error, unsupported_operation};

        false ->
            {ok, factorial_iter(N, 1.0)}
    end.

-spec abs(float()) -> float().
abs(N) ->
    case N < +0.0 of
        true ->
            +0.0 - N;

        false ->
            N
    end.

-spec sqrt_iter(float(), float(), float()) -> float().
sqrt_iter(X0, X1, N) ->
    case abs(X1 - X0) < 0.0001 of
        true ->
            X1;

        false ->
            X0@1 = X1,
            X1@1 = (X0@1 + (case X0@1 of
                +0.0 -> +0.0;
                -0.0 -> -0.0;
                Gleam@denominator -> N / Gleam@denominator
            end)) / 2.0,
            sqrt_iter(X0@1, X1@1, N)
    end.

-spec sqrt(float()) -> {ok, float()} | {error, math_error()}.
sqrt(N) ->
    case N < +0.0 of
        true ->
            {error, value_out_of_range};

        false ->
            {ok, sqrt_iter(+0.0, 1.0, N)}
    end.

-spec pow2_iter(float(), float()) -> float().
pow2_iter(N, Accumulator) ->
    case N of
        +0.0 ->
            Accumulator;

        _ ->
            pow2_iter(N - 1.0, 2.0 * Accumulator)
    end.

-spec pow2(float()) -> {ok, float()} | {error, math_error()}.
pow2(N) ->
    case N < +0.0 of
        true ->
            {error, value_out_of_range};

        false ->
            {ok, pow2_iter(N, 1.0)}
    end.

-spec pow10_iter(float(), float()) -> float().
pow10_iter(N, Accumulator) ->
    case N of
        +0.0 ->
            Accumulator;

        _ ->
            pow10_iter(N - 1.0, 10.0 * Accumulator)
    end.

-spec pow10(float()) -> {ok, float()} | {error, math_error()}.
pow10(N) ->
    case N < +0.0 of
        true ->
            {error, value_out_of_range};

        false ->
            {ok, pow10_iter(N, 1.0)}
    end.

-spec cbrt_iter(float(), float(), float()) -> float().
cbrt_iter(X0, X1, N) ->
    case abs(X1 - X0) < 0.0001 of
        true ->
            X1;

        false ->
            X0@1 = X1,
            X1@1 = (X0@1 + (case (X0@1 * X0@1) of
                +0.0 -> +0.0;
                -0.0 -> -0.0;
                Gleam@denominator -> N / Gleam@denominator
            end)) / 2.0,
            cbrt_iter(X0@1, X1@1, N)
    end.

-spec cbrt(float()) -> {ok, float()} | {error, math_error()}.
cbrt(N) ->
    case N < +0.0 of
        true ->
            {error, value_out_of_range};

        false ->
            {ok, cbrt_iter(+0.0, 1.0, N)}
    end.