source code
// The Computer Language Benchmarks Game
// http://benchmarksgame.alioth.debian.org/
//
// contributed by Ian Osgood
// Optimized by Roy Williams
// modified for Node.js by Isaac Gouy
function A(i,j) {
return 1/(((i+j)*(i+j+1)>>>1)+i+1);
}
function Au(u,v) {
var n = u.length;
for (var i=0; i<n; ++i) {
var t = 0;
for (var j=0; j<n; ++j)
t += A(i,j) * u[j];
v[i] = t;
}
}
function Atu(u,v) {
var n = u.length;
for (var i=0; i<n; ++i) {
var t = 0;
for (var j=0; j<n; ++j)
t += A(j,i) * u[j];
v[i] = t;
}
}
function AtAu(u,v,w) {
Au(u,w);
Atu(w,v);
}
function spectralnorm(n) {
var storage_ = new ArrayBuffer(n * 24);
var u = new Float64Array(storage_, 0, n),
v = new Float64Array(storage_, 8*n, n),
w = new Float64Array(storage_, 16*n, n);
var i, vv=0, vBv=0;
for (i=0; i<n; ++i) {
u[i] = 1; v[i] = w[i] = 0;
}
for (i=0; i<10; ++i) {
AtAu(u,v,w);
AtAu(v,u,w);
}
for (i=0; i<n; ++i) {
vBv += u[i]*v[i];
vv += v[i]*v[i];
}
return Math.sqrt(vBv/vv);
}
console.log(spectralnorm(+process.argv[2]).toFixed(9));