JavaScript toString limits

Question

So my problem is this, I'm writing a program that checks if number is even or odd without division. So I decided to take the number, turn it into a String with the

number.toString()

method. The problem I'm having is that if you put a number that is about 17 or more digits long the string is correct for about the first 17 digits then it's just 0's and sometimes 2's. For example,

function toStr (number) 
{
    return number.toString(10);
}

console.log(toStr(123456789123456789));

prints,

123456789123456780

any ideas?

Answer 1

The problem has nothing to do with strings or your function at all. Try going to your console and just entering the expression 123456789123456789 and pressing return.

You will likewise obtain 123456789123456780 .

Why?

The expression 123456789123456789 within the JavaScript language is interpreted as a JavaScript number type, which can only be represented exactly to a certain number of base two significant figures. The input number happens to have more significant digits when expressed in base two than the number of base two significant figures available in JavaScript's representation of a number, and so the value is automatically rounded in base two as follows:

123456789123456789 =
  110110110100110110100101110101100110100000101111100010101 (base two)
123456789123456780 =
  110110110100110110100101110101100110100000101111100001100 (base two)

Note that you CAN accurately represent some numbers larger than a certain size in JavaScript, but only those numbers with no more significant figures in base two than JavaScript has room for. For instance, 2 times a very large power of 10, which would have only one significant figure in base two.

If you are designing this program to accept user input from a form or dialog box, then you will receive the input as a string. You only need to check the last digit in order to determine if the input number is odd or even (assuming it is indeed an integer to begin with). The other answer has suggested the standard way to obtain the last character of a string as well as the standard way to test if a string value is odd or even.

Answer 2

If you go beyond Javascript's max integer size (9007199254740992) you are asking for trouble: http://ecma262-5.com/ELS5_HTML.htm .

So to solve this problem, you must treat it as a string only. Then extract the last digit in the string and use it to determine whether the number is even or odd.

if(parseInt(("123456789123456789").slice(-1)) % 2) 
 //odd
else
 //even

Answer 3

It's a 64-bit floating point number, using the IEEE 754 specification. A feature of this spec is that starting at 2^53 the smallest distance between two numbers is 2.

var x = Math.pow(2, 53);
console.log( x == x + 1 );

This difference is the value of the unit in the last place , or ULP.

This is similar in principle to trying to store fractional values in integral types in other languages; values like .5 can't be represented, so they are discarded. With integers, the ULP value is always 1 ; with floating point, the ULP value depends on how big or small the number you're trying to represent.