Data update

Task/Pells-equation/Langur/pells-equation.langur

@@ -1,5 +1,3 @@
-val fun = fn a, b, c: [b, b * c + a]
-
 val solvePell = fn(n) {
     val x = trunc(n ^/ 2)
     var y, z, r = x, 1, x * 2
@@ -20,9 +18,9 @@ val C = fn(x) {
     # format number string with commas
     var neg, s = "", x -> string
     if s[1] == '-' {
-        neg, s = "-", s -> rest
+        neg, s = "-", less(s, of=1)
     }
-    neg ~ join(",", split(-3, s))
+    neg ~ join(split(s, by=-3), by=",")
 }
 
 for n in [61, 109, 181, 277, 8941] {

Task/Pells-equation/Zig/pells-equation-1.zig

@@ -0,0 +1 @@
+@subWithOverflow()

Task/Pells-equation/Zig/pells-equation-2.zig

@@ -0,0 +1 @@
+u256

Task/Pells-equation/Zig/pells-equation-3.zig

@@ -0,0 +1,60 @@
+const std = @import("std");
+
+pub fn main() !void {
+    const writer = std.io.getStdOut().writer();
+
+    try printSolvedPell(61, writer);
+    try printSolvedPell(109, writer);
+    try printSolvedPell(181, writer);
+    try printSolvedPell(277, writer);
+}
+
+const Pair = struct {
+    v1: u256,
+    v2: u256,
+
+    fn init(a: u256, b: u256) Pair {
+        return Pair{
+            .v1 = a,
+            .v2 = b,
+        };
+    }
+};
+
+fn solvePell(n: u256) Pair {
+    const x: u256 = std.math.sqrt(n);
+
+    // n is a perfect square - no solution other than 1,0
+    if (x * x == n)
+        return Pair.init(1, 0);
+
+    // there are non-trivial solutions
+    var y = x;
+    var z: u256 = 1;
+    var r = 2 * x;
+    var e = Pair.init(1, 0);
+    var f = Pair.init(0, 1);
+    var a: u256 = 0;
+    var b: u256 = 0;
+
+    while (true) {
+        y = r * z - y;
+        z = (n - y * y) / z;
+        r = (x + y) / z;
+        e = Pair.init(e.v2, r * e.v2 + e.v1);
+        f = Pair.init(f.v2, r * f.v2 + f.v1);
+        a = e.v2 + x * f.v2;
+        b = f.v2;
+        const ov = @subWithOverflow(a * a, n * b * b);
+        if (ov[1] != 0)
+            continue;
+        if (ov[0] == 1) // a * a, n * b * b == 1
+            break;
+    }
+    return Pair.init(a, b);
+}
+
+fn printSolvedPell(n: u256, writer: anytype) !void {
+    const r = solvePell(n);
+    try writer.print("x^2 - {d:3} * y^2 = 1 for x = {d:21} and y = {d:19}\n", .{ n, r.v1, r.v2 });
+}