Data update

Task/Elliptic-curve-arithmetic/Pluto/elliptic-curve-arithmetic.pluto

@@ -0,0 +1,59 @@
+$define C = 7
+
+class pt
+    static function zero() return new pt(math.inf, math.inf) end
+
+    static function from_num(n) return new pt(math.cbrt(n * n - C), n) end
+
+    function __construct(public x, public y) end
+
+    function iszero() return math.abs(self.x) > 1e20 end
+
+    function double()
+        if self:iszero() then return self end
+        local l = 3 * self.x * self.x / (2 * self.y)
+        local t = l * l - 2 * self.x
+        return new pt(t, l * (self.x - t) - self.y)
+    end
+
+    function __unm() return new pt(self.x, - self.y) end
+
+    function __add(other)
+        assert(other instanceof pt, "argument must be a pt object")
+        if self.x == other.x and self.y == other.y then return self:double() end
+        if self:iszero() then return other end
+        if other:iszero() then return self end
+        local l = (other.y - self.y) / (other.x - self.x)
+        local t = l * l - self.x - other.x
+        return new pt(t, l * (self.x - t) - self.y)
+    end
+
+    function __mul(n)
+        assert(math.type(n) == "integer", "argument must be an integer")
+        local r = pt.zero()
+        local p = self
+        local i = 1
+        while i <= n do
+            if (i & n) != 0 then r += p end
+            p = p:double()
+            i <<= 1
+        end
+        return r
+    end
+
+    function __tostring()
+        return self:iszero() ? "Zero" : string.format("(%0.3f, %0.3f)", self.x, self.y)
+    end
+end
+
+local a = pt.from_num(1)
+local b = pt.from_num(2)
+local c = a + b
+local d = -c
+print($"a         = {a}")
+print($"b         = {b}")
+print($"c = a + b = {c}")
+print($"d = -c    = {d}")
+print($"c + d     = {c + d}")
+print($"a + b + d = {a + b + d}")
+print($"a * 12345 = {a * 12345}")