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Why does this Fibonacci number function return infinity for the 4000th value?

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攒了一身酷
攒了一身酷 2021-01-06 10:03 
function fibo() {
var first,second,add;
for(var i=0;i<4000;i++){
    if(i === 0){
        first = 1;
        second = 2;
    }
    add = first + second;
    first
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  • 天命终不由人
    2021-01-06 10:12

    fibonacci(4000) [836 digits]

    39909473435004422792081248094960912600792570982820257852628876326523051818641373433549136769424132442293969306537520118273879628025443235370362250955435654171592897966790864814458223141914272590897468472180370639695334449662650312874735560926298246249404168309064214351044459077749425236777660809226095151852052781352975449482565838369809183771787439660825140502824343131911711296392457138867486593923544177893735428602238212249156564631452507658603400012003685322984838488962351492632577755354452904049241294565662519417235020049873873878602731379207893212335423484873469083054556329894167262818692599815209582517277965059068235543139459375028276851221435815957374273143824422909416395375178739268544368126894240979135322176080374780998010657710775625856041594078495411724236560242597759185543824798332467919613598667003025993715274875

    <!doctype html>
<html lang= "en">
<head>
<meta charset= "utf-8">
<title> Javascript Big Integers</title>

<style>
body{margin: 0 1em;width: auto;font-size: 125%}
p{max-width: 800px;margin: 1ex 1em;}
div{margin: 1em;}
input, textarea, label{
    font-size: 1em;line-height: 1.2;font-family: arial, sans-serif;
    font-weight: 600;padding: 0 2px;
}
textarea{
    background-color: white;    color: black;   width: 90%; 
    border: 2px ridge silver;position: absolute;z-index: 5;overflow-y: scroll;height: 500px;
}
#fibInp{text-align: right;}
#calcfibBtn, #stopFibBtn{color:navy;cursor:pointer}
#calcfibBtn:focus, #stopFibBtn:focus, #calcfibBtn:hover, #stopFibBtn:hover{color:red}

</style>

<script>
//utilities
//ie version (if any) determines initial loop size
/*@cc_on
    @if(@_jscript_version> 5.5){
    navigator.IEmod= document.documentMode? document.documentMode: 
    window.XMLHttpRequest? 7: 6;
    }
    @end
@*/

function mr(hoo){
    if(hoo){
        if(typeof hoo== 'string') return document.getElementById(hoo);
        if(hoo.nodeType=== 1) return hoo;
    }
    return null;
}
if(!Array.prototype.map){
    Array.prototype.map= function(fun, scope){
        var L= this.length, A= Array(this.length), i= 0, val;
        if(typeof fun== 'function'){
            while(i< L){
                if(i in this){
                    A[i]= fun.call(scope, this[i], i, this);
                }
                ++i;
            }
            return A;
        }
    }
}
//Big Integer Object
function BigInt(n, sign){
    if(this.constructor!= BigInt){
        if(n.constructor== BigInt) return n;
        n= n.toString();
        if(/^\d+$/.test(n)){
            var digits= n.split('').map(Number);
            return new BigInt(digits.reverse(), sign);
        }
        else{
            throw Error('base 10 integer input only');
        }
    }
    while(n.length && !n[n.length - 1]){
        --n.length;
    }
    this.digits= n;
    this.length= n.length;
    if(sign== -1) this.sign= sign;
}
BigInt.prototype.toString= function(){
    var s= this.digits.slice().reverse().join('');
    if(this.sign== -1) s= '-'+s;
    return s;
}
BigInt.prototype.plus= function(n){
    n= BigInt(n);
    var n1= this.digits, n2= n.digits,
    len1= n1.length, len2= n2.length,
    hoo= Array(Math.max(len1, len2)+ 1),
    size= Math.min(len1, len2), temp= 0, dig;
    for(var i= 0; i < size; i++){
        dig= n1[i]+ n2[i]+ temp;
        hoo[i]= dig%10;
        temp= (dig/10)|0;
    }
    if(len2> len1){
        n1= n2;
        len1= len2;
    }
    for(var i= size; temp && i < len1; i++){
        dig= n1[i]+ temp;
        hoo[i]= dig%10;
        temp= (dig/10)|0;
    }
    if(temp) hoo[i]= temp;
    while(i < len1){
        hoo[i]= n1[i];
        ++i;
    }
    return new BigInt(hoo);
}
// Math.fibonacci methods
Math.fibonacci= function(n){
    var n1= 0, n2= 1, t= 1, fib= [], i= 0;
    var limit= 9007199254740992;
    while(n1< limit){
        fib[i++]= n1;
        if(i== n) return fib;
        n2= t;
        t= n1+n2;
        n1= n2;
    }
    if(n){
        t= fib.pop(), n1= fib.pop(), i= fib.length;
        while(i<n){
            fib[i++]= n1;
            n2= BigInt(t);
            t= n2.plus(n1);
            n1= n2.toString();
        }
    }
    return fib;
}
Math.nthFibonacci= function(n, ret){
    var fibs= [0, 1], i= 78;
    while(n && --i){
        fibs[2]= fibs[0]+ fibs[1];
        fibs.shift();
        n--;
    }
    if(n){
        fibs= [BigInt(fibs[0]), BigInt(fibs[1])];
        while(n--){
            fibs[2]= fibs[0].plus(fibs[1]);
            fibs.shift();
        }
    }
    return ret? fibs: fibs[0];
}
// demonstration code
Fib={
    clear: function(){
        mr('yw_fib_tex').value= '';
        Fib.wait= false;
        mr('fibInp').value= '';
    },
    counter: 1,
    demo: function(){
        mr('calcfibBtn').onclick= Fib.getFib;
        mr('stopFibBtn').onclick= Fib.quitFib;
        mr('fibInp').onkeypress= Fib.keycheck;
        mr('fibInp').focus();
    },
    discomma: !!window.opera,
    getFib: function(){
        mr('yw_fib_tex').value= '';
        var d, c, n= mr('fibInp').value;
        n= parseInt(mr('fibInp').value);
        if(!n || n<2){
            mr('fibInp').value= '';
            mr('fibInp').focus();
            return true;
        }
        if(n<= 1100){
            d= Math.nthFibonacci(n).toString();
            var fibs= ['', n, d.length, d];
            Fib.report(fibs);
            return true;
        }
        if(n> 10000){
            d= Fib;
            c= d.counter;
            if(c> 2000){
                Fib.reach(d.low, d.high, n, c, Fib.report);
                return true;
            }
        }
        d= Math.nthFibonacci(1000, 1);
        Fib.reach(d[0], d[1], n, 1000, Fib.report);
        return true;
    },
    high: 1,
    keycheck: function(e){
        e= e || window.event;
        var k= e.charCode || e.keyCode;
        if(k== 13) Fib.getFib();
        return true;
    },
    low: 0,
    quitFib: function(){
        Fib.wait= true;
        mr('yw_fib_tex').focus();
    },
    reach: function(n1, n2, n, i, cb){
        var d, q, who, mf= Fib, F= Fib.reach;
        if(F.time=== undefined){
            F.top= n;
            F.count= i+1;
            F.time= new Date().getTime();
            F.cb= cb;
            F.tik= false;
        }
        q= n2.toString().length;
        who= mr('yw_fib_tex');
        if(who){
            if(q<2100) who.value= n2;
            else who.value= q+ ' digits...thinking...';
        }
        if(q> 20000) q= q> 100000? 10: 20;
        else if(q> 5000) q= q> 10000? 50: 100;
        else q= q> 1000? 200: 1000;
        if(navigator.IEmod) q/= 4;
        q= Math.min(q, F.top-F.count);
        while(q> 0){
            d= BigInt(n1).plus(n2);
            F.count++;
            n1= n2;
            n2= d;
            --q;
        }
        if(F.count>= F.top || Fib.wait){
            var t= (new Date()-F.time)/1000;
            d= d.toString();
            var fibs= [t, F.count, d.length, d, n1];
            F.time= undefined;
            if(typeof F.cb== 'function') return F.cb(fibs);
        }
        else{
            setTimeout(function(){
                F(n1, d)
            },
            0);
        }
    },
    report: function(fb){
        var mf= Fib, s, fibz, f1= fb[1], t= fb[0] || '', fN= fb[3];
        if(t){
            t+= mf.time;
            if(mf.wait) Fib.time+= t;
            else Fib.time= 0;
            t= t.toFixed(3)+' seconds to calculate ';
        }
        fibz= t+'fibonacci('+f1+') ['+fb[2]+' digits]';
        if(fb[4] && fN> mf.counter){
            mf.counter= f1;
            mf.low= fb[4];
            mf.high= fN;
        }
        fN= fN.toString();
        if(window.opera){
            fN= fN.replace(/(\d{10})/g, '$1 ');
        }
        fibz= fibz+'\n\n'+fN;
        mr('yw_fib_tex').value= fibz;
        Fib.wait= false;
        mr('yw_fib_tex').focus();
        return true;
    },
    time: 0,
    wait: false
}
window.onload= function(){
    Fib.demo();
}
</script>
</head>

<body>
<h2 id= "yw_fib_head"> Fibonacci numbers in javascript</h2>
<p>
This is a demonstration of Big Integer Math in Javascript, handling numbers of arbitrary precision.
The time it takes to calculate a large Fibonacci number depends on your computer and browser.</p>
<div>
<label> fibonacci#<input size= "5" id= "fibInp" type= "text" value= "1000"> </label>
<input type= "button" id= "calcfibBtn" value= "Calculate">
<input type= "button" id= "stopFibBtn" value= "Stop">
<br>
<textarea readonly= "readonly" id= "yw_fib_tex">
</textarea>
</div>
</body>
</html>
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  • 无人共我
    2021-01-06 10:18

    Ok, this is extremely late to the party, but just for the sake of completeness, here is a pure javascript solution. It uses a couple of libraries.

    You will need biginteger (http://silentmatt.com/biginteger/) and sloth (https://github.com/rfw/sloth.js). The solution also requires Javascript 1.7 Generators (see https://developer.mozilla.org/en-US/docs/JavaScript/Guide/Iterators_and_Generators).

    var window = {};
load('biginteger.js');
load('sloth.js');
var sloth = window.sloth;


function fibonacci(){
  var fn1 = new BigInteger(1);
  var fn2 = new BigInteger(1);

  while (1){
    var current = fn2;
    fn2 = fn1;
    fn1 = fn1.add(current);
    yield current;
  }
}

var iter = sloth.iter(fibonacci());
var some = sloth.ify(iter).take(4000).force();
print(some[299]); 
print(some[3999]);

    The code is a little eccentric (the use of load() and window) because I wanted to test it in rhino, without adding npm support. If that confuses you, just pretend you're seeing a require() call :)

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  • 花落未央
    2021-01-06 10:19

    You can use WebWorkers and BigInt to calculate huge values of the fibonacci sequence: 

    var input = document.querySelector('input');
var output = document.querySelector('#output');
var fulloutput = document.querySelector('#fulloutput');
var time = document.querySelector('#time');
var start, end;
var worker;

var createWorker = function () {
  if (worker) worker.terminate();
  var workerContent = "self.onmessage = " + workerFunction.toString();
  var blob = new Blob([workerContent], {type: 'application/javascript'}); 
  worker = new Worker(URL.createObjectURL(blob));
  worker.onmessage = receive;
};

var workerFunction = function(event) {
  var total = BigInt(event.data);
  var fib = function(index) {
    var temp;
    var last = BigInt(0);
    var sum = BigInt(1);
    for (; index >= BigInt(2); index--) {
      if (index % BigInt(1000) === BigInt(0)) 
        self.postMessage({
          total: total,
          calculating: index
        });
      temp = last;
      last = sum;
      sum += temp;
    }
    return sum;
  };
  if (total > BigInt(0)) self.postMessage({done: fib(total)});
  else self.postMessage({error: 'Input error'});
};

window.addEventListener('load', function () {
  if (!window.Worker || 
      !window.Blob   || 
      !window.URL    || 
      !window.BigInt) {
    output.textContent = 'Browser not supported'; 
  } else {
    start = performance.now();
    createWorker();
    output.textContent = 'Worker created, starting calculations';
    worker.postMessage(input.value);
    input.addEventListener('change', function () {
      createWorker();
      start = performance.now();
      output.textContent = 'Calculating';
      worker.postMessage(input.value);
    });
  }
});

var receive = function(event) {
  if (event.data.error) {
    output.textContent =  event.data.error;
  }
  if (event.data.calculating) {
    var total = BigInt(event.data.total);
    var index = BigInt(event.data.calculating);
    var progress = (BigInt(100) * (total - index) / total);
    output.textContent = 'Calculating ' + progress + '%';
  } 
  if (event.data.done) {
    var formatter = new Intl.NumberFormat('en', {
      notation: 'scientific'
    });
    output.textContent = formatter.format(event.data.done);
    fulloutput.textContent = event.data.done;
    end = performance.now();
    time.textContent = 'It took ' + ((end - start) / 1000) + ' seconds';
  }
};
    body {
  display: grid;
  place-content: center;
  min-height: 100vh;
}
p, pre  {
  text-align: center;
  width: 80vw;
  white-space:normal;
  word-wrap: break-word;
}
    <p>N: <input type="number" value="4000"></p>
<pre id="output"></pre>
<pre id="fulloutput"></pre>
<pre id="time"></pre>

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  • 时光说笑
    2021-01-06 10:23

    PubNub's Ariya Hidayat taught us this last night:

    function fibo(n) {
    return Array.apply(0, Array(n)). reduce(function(x, y, z){ return x.concat((z < 2) ? z : x[z-1] + x[z-2]); }, []);
     }
    0 讨论(0)
  • 天命终不由人
    2021-01-06 10:25

    Simple: because it's too big.

    The 300th term is 222232244629420445529739893461909967206666939096499764990979600, so you might imagine how big the 4000th is. You can't hold such value in a JavaScript variable.

    If you really want to calculate it, use an arbitrary precision library, and maybe something other than JavaScript if you want to calculate it fast.

    Check GNU Multiple Precision Arithmetic Library - GMP. Nice to use with C, and it even has special Fibonacci functions.

    Here's a little C program to do the job:

    #include <gmp.h>

int main()
{
    mpz_t num;
    mpz_init(num);

    mpz_fib_ui(num, 4000);
    gmp_printf("%Zd\n", num);

    return 0;
}

    Compile with:

    cc fib.c -lgmp

    And run :-)

    time ./a.out
39909473435004422792081248094960912600792570982820257852628876326523051818641373433549136769424132442293969306537520118273879628025443235370362250955435654171592897966790864814458223141914272590897468472180370639695334449662650312874735560926298246249404168309064214351044459077749425236777660809226095151852052781352975449482565838369809183771787439660825140502824343131911711296392457138867486593923544177893735428602238212249156564631452507658603400012003685322984838488962351492632577755354452904049241294565662519417235020049873873878602731379207893212335423484873469083054556329894167262818692599815209582517277965059068235543139459375028276851221435815957374273143824422909416395375178739268544368126894240979135322176080374780998010657710775625856041594078495411724236560242597759185543824798332467919613598667003025993715274875

real    0m0.005s
user    0m0.001s
sys     0m0.002s
    0 讨论(0)
  • 傲寒
    2021-01-06 10:27

    For better results you can use the jsperf.com: http://jsperf.com/fib-vs-fib-loga/

    Just a lite change in the function to get the max position possible to calculate by javascript.

    Yes, the result will be diferent on each browser and arch bean used.

    function fibo() {
    var first,second,add;
    for(var i=0;i<4000;i++){
        if(i === 0){
            first = 1;
            second = 2;
        }
        if(first+second > Number.MAX_VALUE){
            console.debug(i, first, second);
            return;
        }
        add = first + second;
        first = second;
        second = add;
    }
    alert(add);
}
fibo();

    The result is: 1473 8.077637632156222e+307 1.3069892237633987e+308 Where 1473 is the maximum fibonacci position possible to calculate with javascript.

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