Const As Double INF  = 1e30

Type Punto
    As Double x, y
    Declare Constructor (x As Double = INF, y As Double = INF)
    Declare Function copy() As Punto
    Declare Function isZero() As Integer
    Declare Function neg() As Punto
    Declare Function dbl() As Punto
    Declare Function sum(q As Punto) As Punto
    Declare Function mul(n As Integer) As Punto
    Declare Function ToString() As String
End Type

Dim Shared As Integer bCoeff = 7  ' Coeficiente de la curva elíptica

Constructor Punto(x As Double, y As Double)
    This.x = Iif(Abs(x) > 1e20, INF, x)
    This.y = Iif(Abs(y) > 1e20, INF, y)
End Constructor

Function Punto.copy() As Punto
    Return Type(This.x, This.y)
End Function

Function Punto.isZero() As Integer
    Return This.x >= 1e20 Or This.x <= -1e20 Or This.x = INF
End Function

Function Punto.neg() As Punto
    Return Type(This.x, -This.y)
End Function

Function Punto.dbl() As Punto
    If This.isZero() Then Return This.copy()

    If Abs(This.y) < 1e-15 Then Return Punto()

    Dim As Double L = (3 * This.x * This.x) / (2 * This.y)
    Dim As Double x3 = L * L - 2 * This.x
    Return Type(x3, L * (This.x - x3) - This.y)
End Function

Function Punto.sum(q As Punto) As Punto
    If This.x = q.x And This.y = q.y Then Return This.dbl()
    If This.isZero() Then Return q.copy()
    If q.isZero() Then Return This.copy()

    If Abs(q.x - This.x) < 1e-15 Then Return Punto()

    Dim As Double L = (q.y - This.y) / (q.x - This.x)
    Dim As Double x3 = L * L - This.x - q.x
    Return Type(x3, L * (This.x - x3) - This.y)
End Function

Function Punto.mul(n As Integer) As Punto
    Dim As Punto r = Punto(), p = This.copy()

    While n > 0
        If (n And 1) Then r = r.sum(p)
        p = p.dbl()
        n = n Shr 1
    Wend
    Return r
End Function

Function Punto.ToString() As String
    If This.isZero() Then Return "Zero"
    Return "(" & Str(Int(This.x * 1000) / 1000) & ", " & Str(Int(This.y * 1000) / 1000) & ")"
End Function

Sub show(s As String, p As Punto)
    Print s & " " & p.ToString()
End Sub

Function from_y(y As Double) As Punto
    Dim As Double n = y * y - bCoeff
    Dim As Double x = Sgn(n) * Abs(n)^(1.0/3.0)
    Return Type(x, y)
End Function

' Demonstrate
Dim As Punto a = from_y(1)
Dim As Punto b = from_y(2)
show("a =", a)
show("b =", b)

Dim As Punto c = a.sum(b)
show("c = a + b =", c)

Dim As Punto d = c.neg()
show("d = -c =", d)

show("c + d =", c.sum(d))
show("a + b + d =", a.sum(b.sum(d)))
show("a * 12345 =", a.mul(12345))

Sleep