//  en(x) Esponential Notation
//  trunc(x,n)
//  sn(x) Scientifi Notatio
//  intrnd(a,b)
//  realrnd(a,b)  
//  trunc(x,n)
//
//
//
//
//
//
dot='.'

function trunc(x,n){
	eval("y=10E"+(n-1))
	return parseInt(x*y)/y
}


function round(x,n){
	eval("y=10E"+(n-1))
	return Math.round(x*y)/y
}

function en(x){ // Esponential Notation
	k=-22
	while(Math.pow(10,k+=3)<=Math.abs(x)){}
	s=" "+ trunc(x/Math.pow(10,k-2),3)+" "+dot+"10"+"<sup>"+(k-2)+"</sup>"
	return s
}

function sn(x){ // Scientific Notation
	var s=""
	k=-25
	while(Math.pow(10,k++)<=Math.abs(x)){}
	s=" "+ round(x/Math.pow(10,k-2),3)+"<sup> "+dot+"</sup>10"+"<sup>"+(k-2)+"</sup>"
	return s
}

function hide(x,n){ // construct a vector with many wrong results and the n-th result correct
	var vv=new Array(11); // each wrong result is the double of the preceding
	var y=x/Math.pow(2,n);
	for(var i=1;i<=10;i++){
		vv[i]=sn(y*Math.pow(2,i));
	}
	return vv;
}

function hide2(x,n){ // idem like hide but with alternate sign to confuse ideas
	vv=new Array(11);
	var y=x/Math.pow(2,n)*Math.pow(-1,n);
	for(var i=1;i<=10;i++){
		vv[i]=sn(y*Math.pow(2,i)*Math.pow(-1,i));
	}
	return vv;
}



function rnd(){return Math.random()} // returns a  real number between 0-1
function intrnd(a,b){x=parseInt(Math.random()*(b-a)+a); return x;}
function realrnd(a,b){ // return a real number between a and b 
	return rnd()*(b-a)+a
}
function intRnd(a,b){return intrnd(a,b)}
function realRnd(a,b){return realrnd(a,b)}
function scegli(a){return ' '+a[intero(0,a.length)]+' '}
function choise(a){return ' '+a[intero(0,a.length)]+' '}

//function E(x){	return 	' 10<sup>'+x+'</sup> '}


function mischia(v){    // scambia (lunghezza Vettore*4) volte coppie del vettore
	var l=v.length;
	for(var i=1;i<=v.length*4;i++){
		var a=parseInt(Math.random()*l);
		var b=parseInt(Math.random()*l);
		var x=v[a];var y=v[b];
		v[b]=x;v[a]=y;
	}
	return v;
}
	


function intero(a,b){x=parseInt(Math.random()*(b-a)+a); return x;}
function scegli(a){return ' '+a[intero(0,a.length)]+' '}
//function E(x){	return 	' 10<sup>'+x+'</sup> '}

function mischia(v){    // scambia (lunghezza Vettore*4) volte coppie del vettore
	l=v.length;
	for(var i=1;i<=v.length*4;i++){
		a=parseInt(Math.random()*l);
		b=parseInt(Math.random()*l);
		x=v[a];y=v[b];
		v[b]=x;v[a]=y;
	}
	return v;
}