Data commit

Task/Elliptic-curve-arithmetic/C/elliptic-curve-arithmetic.c

@@ -0,0 +1,74 @@
+#include <stdio.h>
+#include <math.h>
+
+#define C 7
+typedef struct { double x, y; } pt;
+
+pt zero(void) { return (pt){ INFINITY, INFINITY }; }
+
+// should be INFINITY, but numeric precision is very much in the way
+int is_zero(pt p) { return p.x > 1e20 || p.x < -1e20; }
+
+pt neg(pt p) { return (pt){ p.x, -p.y }; }
+
+pt dbl(pt p) {
+	if (is_zero(p)) return p;
+
+	pt r;
+	double L = (3 * p.x * p.x) / (2 * p.y);
+	r.x = L * L - 2 * p.x;
+	r.y = L * (p.x - r.x) - p.y;
+	return r;
+}
+
+pt add(pt p, pt q) {
+	if (p.x == q.x && p.y == q.y) return dbl(p);
+	if (is_zero(p)) return q;
+	if (is_zero(q)) return p;
+
+	pt r;
+	double L = (q.y - p.y) / (q.x - p.x);
+	r.x = L * L - p.x - q.x;
+	r.y = L * (p.x - r.x) - p.y;
+	return r;
+}
+
+pt mul(pt p, int n) {
+	int i;
+	pt r = zero();
+
+	for (i = 1; i <= n; i <<= 1) {
+		if (i & n) r = add(r, p);
+		p = dbl(p);
+	}
+	return r;
+}
+
+void show(const char *s, pt p) {
+	printf("%s", s);
+	printf(is_zero(p) ? "Zero\n" : "(%.3f, %.3f)\n", p.x, p.y);
+}
+
+pt from_y(double y) {
+	pt r;
+	r.x = pow(y * y - C, 1.0/3);
+	r.y = y;
+	return r;
+}
+
+int main(void) {
+	pt a, b, c, d;
+
+	a = from_y(1);
+	b = from_y(2);
+
+	show("a = ", a);
+	show("b = ", b);
+	show("c = a + b = ", c = add(a, b));
+	show("d = -c = ", d = neg(c));
+	show("c + d = ", add(c, d));
+	show("a + b + d = ", add(a, add(b, d)));
+	show("a * 12345 = ", mul(a, 12345));
+
+	return 0;
+}