Data commit

Task/Elliptic-curve-arithmetic/11l/elliptic-curve-arithmetic.11l

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+T Point
+   :b = 7
+
+   Float x, y
+
+   F (x = Float.infinity, y = Float.infinity)
+      .x = x
+      .y = y
+
+   F.const copy()
+      R Point(.x, .y)
+
+   F.const is_zero()
+      R .x > 1e20 | .x < -1e20
+
+   F neg()
+      R Point(.x, -.y)
+
+   F dbl()
+      I .is_zero()
+         R .copy()
+      I .y == 0
+         R Point()
+      V l = (3 * .x * .x) / (2 * .y)
+      V x = l * l - 2 * .x
+      R Point(x, l * (.x - x) - .y)
+
+   F add(q)
+      I .x == q.x & .y == q.y
+         R .dbl()
+      I .is_zero()
+         R q.copy()
+      I q.is_zero()
+         R .copy()
+      I q.x - .x == 0
+         R Point()
+      V l = (q.y - .y) / (q.x - .x)
+      V x = l * l - .x - q.x
+      R Point(x, l * (.x - x) - .y)
+
+   F mul(n)
+      V p = .copy()
+      V r = Point()
+      V i = 1
+      L i <= n
+         I i [&] n
+            r = r.add(p)
+         p = p.dbl()
+         i <<= 1
+      R r
+
+   F String()
+      R ‘(#.3, #.3)’.format(.x, .y)
+
+F show(s, p)
+   print(s‘ ’(I p.is_zero() {‘Zero’} E p))
+
+F from_y(y)
+   V n = y * y - Point.:b
+   V x = I n >= 0 {n ^ (1. / 3)} E -((-n) ^ (1. / 3))
+   R Point(x, y)
+
+V a = from_y(1)
+V b = from_y(2)
+show(‘a =’, a)
+show(‘b =’, b)
+V c = a.add(b)
+show(‘c = a + b =’, c)
+V d = c.neg()
+show(‘d = -c =’, d)
+show(‘c + d =’, c.add(d))
+show(‘a + b + d =’, a.add(b.add(d)))
+show(‘a * 12345 =’, a.mul(12345))