gcdLehmer

    fn gcdLehmer(result: *Mutable, xa: Const, ya: Const, limbs_buffer: *std.array_list.Managed(Limb)) !void {
        var x = try xa.toManaged(limbs_buffer.allocator);
        defer x.deinit();
        x.abs();

        var y = try ya.toManaged(limbs_buffer.allocator);
        defer y.deinit();
        y.abs();

        if (x.toConst().order(y.toConst()) == .lt) {
            x.swap(&y);
        }

        var t_big = try Managed.init(limbs_buffer.allocator);
        defer t_big.deinit();

        var r = try Managed.init(limbs_buffer.allocator);
        defer r.deinit();

        var tmp_x = try Managed.init(limbs_buffer.allocator);
        defer tmp_x.deinit();

        while (y.len() > 1 and !y.eqlZero()) {
            assert(x.isPositive() and y.isPositive());
            assert(x.len() >= y.len());

            var xh: SignedDoubleLimb = x.limbs[x.len() - 1];
            var yh: SignedDoubleLimb = if (x.len() > y.len()) 0 else y.limbs[x.len() - 1];

            var A: SignedDoubleLimb = 1;
            var B: SignedDoubleLimb = 0;
            var C: SignedDoubleLimb = 0;
            var D: SignedDoubleLimb = 1;

            while (yh + C != 0 and yh + D != 0) {
                const q = @divFloor(xh + A, yh + C);
                const qp = @divFloor(xh + B, yh + D);
                if (q != qp) {
                    break;
                }

                var t = A - q * C;
                A = C;
                C = t;
                t = B - q * D;
                B = D;
                D = t;

                t = xh - q * yh;
                xh = yh;
                yh = t;
            }

            if (B == 0) {
                // t_big = x % y, r is unused
                try r.divTrunc(&t_big, &x, &y);
                assert(t_big.isPositive());

                x.swap(&y);
                y.swap(&t_big);
            } else {
                var storage: [8]Limb = undefined;
                const Ap = fixedIntFromSignedDoubleLimb(A, storage[0..2]).toManaged(limbs_buffer.allocator);
                const Bp = fixedIntFromSignedDoubleLimb(B, storage[2..4]).toManaged(limbs_buffer.allocator);
                const Cp = fixedIntFromSignedDoubleLimb(C, storage[4..6]).toManaged(limbs_buffer.allocator);
                const Dp = fixedIntFromSignedDoubleLimb(D, storage[6..8]).toManaged(limbs_buffer.allocator);

                // t_big = Ax + By
                try r.mul(&x, &Ap);
                try t_big.mul(&y, &Bp);
                try t_big.add(&r, &t_big);

                // u = Cx + Dy, r as u
                try tmp_x.copy(x.toConst());
                try x.mul(&tmp_x, &Cp);
                try r.mul(&y, &Dp);
                try r.add(&x, &r);

                x.swap(&t_big);
                y.swap(&r);
            }
        }

        // euclidean algorithm
        assert(x.toConst().order(y.toConst()) != .lt);

        while (!y.toConst().eqlZero()) {
            try t_big.divTrunc(&r, &x, &y);
            x.swap(&y);
            y.swap(&r);
        }

        result.copy(x.toConst());
    }