JavaScript calculate the day of the year (1 - 366)

Question

Following OP's edit:

var now = new Date();
var start = new Date(now.getFullYear(), 0, 0);
var diff = now - start;
var oneDay = 1000 * 60 * 60 * 24;
var day = Math.floor(diff / oneDay);
console.log('Day of year: ' + day);

Edit: The code above will fail when now is a date in between march 26th and October 29th andnow's time is before 1AM (eg 00:59:59). This is due to the code not taking daylight savings time into account. You should compensate for this:

var now = new Date();
var start = new Date(now.getFullYear(), 0, 0);
var diff = (now - start) + ((start.getTimezoneOffset() - now.getTimezoneOffset()) * 60 * 1000);
var oneDay = 1000 * 60 * 60 * 24;
var day = Math.floor(diff / oneDay);
console.log('Day of year: ' + day);

This works across Daylight Savings Time changes in all countries (the "noon" one above doesn't work in Australia):

Date.prototype.isLeapYear = function() {
    var year = this.getFullYear();
    if((year & 3) != 0) return false;
    return ((year % 100) != 0 || (year % 400) == 0);
};

// Get Day of Year
Date.prototype.getDOY = function() {
    var dayCount = [0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334];
    var mn = this.getMonth();
    var dn = this.getDate();
    var dayOfYear = dayCount[mn] + dn;
    if(mn > 1 && this.isLeapYear()) dayOfYear++;
    return dayOfYear;
};

I find it very interesting that no one considered using UTC since it is not subject to DST. Therefore, I propose the following:

function daysIntoYear(date){
    return (Date.UTC(date.getFullYear(), date.getMonth(), date.getDate()) - Date.UTC(date.getFullYear(), 0, 0)) / 24 / 60 / 60 / 1000;
}

You can test it with the following:

[new Date(2016,0,1), new Date(2016,1,1), new Date(2016,2,1), new Date(2016,5,1), new Date(2016,11,31)]
    .forEach(d => 
        console.log(`${d.toLocaleDateString()} is ${daysIntoYear(d)} days into the year`));

Which outputs for the leap year 2016 (verified using http://www.epochconverter.com/days/2016):

1/1/2016 is 1 days into the year
2/1/2016 is 32 days into the year
3/1/2016 is 61 days into the year
6/1/2016 is 153 days into the year
12/31/2016 is 366 days into the year

Date.prototype.dayOfYear= function(){
    var j1= new Date(this);
    j1.setMonth(0, 0);
    return Math.round((this-j1)/8.64e7);
}

alert(new Date().dayOfYear())

Luckily this question doesn't specify if the number of the current day is required, leaving room for this answer.
Also some answers (also on other questions) had leap-year problems or used the Date-object. Although javascript's Date object covers approximately 285616 years (100,000,000 days) on either side of January 1 1970, I was fed up with all kinds of unexpected date inconsistencies across different browsers (most notably year 0 to 99). I was also curious how to calculate it.

So I wrote a simple and above all, small algorithm to calculate the correct (Proleptic Gregorian / Astronomical / ISO 8601:2004 (clause 4.3.2.1), so year 0 exists and is a leap year and negative years are supported) day of the year based on year, month and day.
Note that in AD/BC notation, year 0 AD/BC does not exist: instead year 1 BC is the leap-year! IF you need to account for BC notation then simply subtract one year of the (otherwise positive) year-value first!!

I modified (for javascript) the short-circuit bitmask-modulo leapYear algorithm and came up with a magic number to do a bit-wise lookup of offsets (that excludes jan and feb, thus needing 10 * 3 bits (30 bits is less than 31 bits, so we can safely save another character on the bitshift instead of >>>)).

Note that neither month or day may be 0. That means that if you need this equation just for the current day (feeding it using .getMonth()) you just need to remove the -- from --m.

Note this assumes a valid date (although error-checking is just some characters more).

function dayNo(y,m,d){
  return --m*31-(m>1?(1054267675>>m*3-6&7)-(y&3||!(y%25)&&y&15?0:1):0)+d;
}

<!-- some examples for the snippet -->
<input type=text value="(-)Y-M-D" onblur="
  var d=this.value.match(/(-?\d+)[^\d]+(\d\d?)[^\d]+(\d\d?)/)||[];
  this.nextSibling.innerHTML=' Day: ' + dayNo(+d[1], +d[2], +d[3]);
" /><span></span>

<br><hr><br>

<button onclick="
  var d=new Date();
  this.nextSibling.innerHTML=dayNo(d.getFullYear(), d.getMonth()+1, d.getDate()) + ' Day(s)';
">get current dayno:</button><span></span>

---

Here is the version with correct range-validation.

function dayNo(y,m,d){
  return --m>=0 && m<12 && d>0 && d<29+(  
           4*(y=y&3||!(y%25)&&y&15?0:1)+15662003>>m*2&3  
         ) && m*31-(m>1?(1054267675>>m*3-6&7)-y:0)+d;
}

<!-- some examples for the snippet -->
<input type=text value="(-)Y-M-D" onblur="
  var d=this.value.match(/(-?\d+)[^\d]+(\d\d?)[^\d]+(\d\d?)/)||[];
  this.nextSibling.innerHTML=' Day: ' + dayNo(+d[1], +d[2], +d[3]);
" /><span></span>

Again, one line, but I split it into 3 lines for readability (and following explanation).

The last line is identical to the function above, however the (identical) leapYear algorithm is moved to a previous short-circuit section (before the day-number calculation), because it is also needed to know how much days a month has in a given (leap) year.

The middle line calculates the correct offset number (for max number of days) for a given month in a given (leap)year using another magic number: since 31-28=3 and 3 is just 2 bits, then 12*2=24 bits, we can store all 12 months. Since addition can be faster then subtraction, we add the offset (instead of subtract it from 31). To avoid a leap-year decision-branch for February, we modify that magic lookup-number on the fly.

That leaves us with the (pretty obvious) first line: it checks that month and date are within valid bounds and ensures us with a false return value on range error (note that this function also should not be able to return 0, because 1 jan 0000 is still day 1.), providing easy error-checking: if(r=dayNo(/*y, m, d*/)){}.
If used this way (where month and day may not be 0), then one can change --m>=0 && m<12 to m>0 && --m<12 (saving another char).
The reason I typed the snippet in it's current form is that for 0-based month values, one just needs to remove the -- from --m.

Extra:
Note, don't use this day's per month algorithm if you need just max day's per month. In that case there is a more efficient algorithm (because we only need leepYear when the month is February) I posted as answer this question: What is the best way to determine the number of days in a month with javascript?.

Math.floor((Date.now() - Date.parse(new Date().getFullYear(), 0, 0)) / 86400000)

this is my solution