parseInt rounds incorrectly

Question

I stumbled upon this issue with parseInt and I'm not sure why this is happening.

console.log(parseInt("16980884512690999"));   // gives 16980884512691000
console.log(parseInt("169808845126909101"));​  // gives 169808845126909100

I clearly not hitting any number limits in JavaScript limits (Number.MAX_VALUE = 1.7976931348623157e+308)

Running Win 7 64 bit if that matters.

What am I overlooking?

Fiddle

Answer 1

Don't confuse Number.MAX_VALUE with maximum accurate value. All numbers in javascript are stored as 64 bit floating point, which means you can get high (and low) numbers, but they'll only be accurate to a certain point.

Double floating points (i.e. Javascript's) have 53 bits of significand precision, which means the highest/lowest "certainly accurate" integer in javascript is +/-9007199254740992 (2^53). Numbers above/below that may turn out to be accurate (the ones that simply add 0's on the end, because the exponent bits can be used to represent that).

Or, in the words of ECMAScript: "Note that all the positive and negative integers whose magnitude is no greater than 2^53 are representable in the Number type (indeed, the integer 0 has two representations, +0 and −0)."

Update

Just to add a bit to the existing question, the ECMAScript spec requires that if an integral Number has less than 22 digits, .toString() will output it in standard decimal notation (e.g. 169808845126909100000 as in your example). If it has 22 or more digits, it will be output in normalized scientific notation (e.g. 1698088451269091000000 - an additional 0 - is output as 1.698088451269091e+21).

Answer 2

From this answer

All numbers in Javascript are 64 bit "double" precision IEE754 floating point.

The largest positive whole number that can therefore be accurately represented is 2^53. The remaining bits are reserved for the exponent.

2^53 = 9007199254740992