# Spectral norm of the Hilbert-like matrix used by the language benchmarks game.
# A(i, j) = 1 / ((i+j)(i+j+1)/2 + i + 1). Forty applications of A twice. n = 1600.

import std.math

hot fn apply(out: exclusive lend List[f64], v: exclusive lend List[f64], n: usize):
    overflow: wrap
    for i in 0..n:
        var sum: f64 = 0.0
        var j: usize = 0
        while j < n:
            ij := i + j
            den := ij * (ij + 1) / 2 + i + 1
            sum += (1.0 / f64(den)) * trust v[j]
            j += 1
        trust out[i] = sum

fn main():
    n: usize = 1600
    var u := List[f64]()
    var v := List[f64]()
    for i in 0..n:
        u.push(1.0)
        v.push(0.0)
    for iter in 0..40:
        apply(v, u, n)
        apply(u, v, n)
    var uv: f64 = 0.0
    var vv: f64 = 0.0
    for i in 0..n:
        uv += u[i] * v[i]
        vv += v[i] * v[i]
    norm := math.sqrt(uv / vv)
    print(i64(norm * 1000000000.0))