with Ada.Numerics.Elementary_Functions;
with Ada.Text_IO;
with Ada.Float_Text_IO;
with Ada.Integer_Text_IO;

procedure Numerics is
    procedure Quadro_Equation (
        A, B, C : Float;
        R1, R2  : out Float;
        Valid   : out Boolean) with
    Pre => A /= 0.0,
    Post => A /= 0.0
    is
        EPS: constant Float := 0.01;
        package n renames Ada.Numerics.Elementary_Functions;
        Z: Float;
        d: Float;
    begin
        Z :=  B*B - 4.0 * A * C;
        if Z < 0.0 or abs(A) < EPS then
            R1 := 0.0;
            R2 := 0.0;
            Valid := False;
            return;
        end if;
        d := n.Sqrt(Z);
        R1 := (-B - d) / (2.0 * A);
        R2 := (-B + d) / (2.0 * A);
        Valid := True;
    end Quadro_Equation;

    R1, R2: Float;
    Valid : Boolean;

    function Min (
        v1, v2: Integer) return Integer is
    begin
        if v1 < v2 then
            return v1;
        else
            return v2;
        end if;
    end Min;

    function Max (A, B: Integer) return Integer is
        (if A >= B then A else B);

    function Factorial (N: Positive) return Positive is
    begin
        if N <= 1 then
            return 1;
        else
            return N * Factorial(N - 1);
        end if;
    end;

    procedure Solve (
        A, B, C : Float;
        R1, R2  : out Float;
        Valid   : out Boolean) renames Quadro_Equation;

    package to renames Ada.Text_IO;
    package fo renames Ada.Float_Text_IO;
    package io renames Ada.Integer_Text_IO;

    X: Integer;

begin
    Solve(1.0, 2.0, -1.0, R1, R2, Valid);

    if Valid then
        to.Put_Line("Valid");
    else
        to.Put_Line("Not valid");
    end if;

    to.Put_Line("Solutions:");

    to.Put("Solution 1: ");
    fo.Put(R1, EXP => 0, AFT => 2);
    to.New_Line;

    to.Put("Solution 2: ");
    fo.Put(R2, EXP => 0, AFT => 2);
    to.New_Line;

    X := Min (1,2);

    to.Put("min(1,2) is = ");
    io.Put(X, WIDTH => 0);
    to.New_Line;

    X := Max (2,3);

    to.Put("max(2,3) is = ");
    io.Put(X, WIDTH => 0);
    to.New_Line;

    X := Factorial(10);

    to.Put("10! is = ");
    io.Put(X, WIDTH => 0);
    to.New_Line;

end Numerics;