Does this 'for' loop stop, and why/why not? for (var i=0; 1/i > 0; i++) { }

Question

Does this for loop ever stop?

for (var i=0; 1/i > 0; i++) {
}

If so, when and why? I was told that it stops, but I was given no r

Answer 1

Answer:

The condition 1/i > 0 will always evaluate to true:

• Initially it's true because 1/0 evaluates to Infinity and Infinity > 0 is true

• It stays true since 1/i > 0 is true for all i < Infinity and i++ never reaches Infinity.

Why does i++ never reach Infinity? Due to the limited precision of the Number datatype, there is a value for which i + 1 == i:

9007199254740992 + 1 == 9007199254740992 // true

Once i reaches that value (which corresponds to Number.MAX_SAFE_INTEGER + 1), it will stay the same even after i++.

We therefore have an infinite loop.

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Appendix:

Why is 9007199254740992 + 1 == 9007199254740992?

JavaScript's Number datatype is actually an 64-bit IEEE 754 double precision float. Each Number is disassembled and stored as three parts: 1-bit sign, 11-bit exponent, and 52-bit mantissa. Its value is -1 ^sign × mantissa × 2 ^exponent.

How is 9007199254740992 represented? As 1.0 × 2 ⁵³, or in binary:

Incrementing the mantissa's least significant bit, we get the next higher number:

The value of that number is 1.00000000000000022… × 2 ⁵³ = 9007199254740994

What does that mean? Number can either be 9007199254740992 or 9007199254740994, but nothing in between.

Now, which one shall we chose to represent 9007199254740992 + 1? The IEEE 754 rounding rules give the answer: 9007199254740992.