Maximus - 7 months ago 13

Javascript Question

Does the following for loop 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 reason for that.

Answer

gotnull's and le_m's answers are both correct and useful, but in both cases I feel the the explanations cover the parts of what's happening without really laying them out clearly in order. This is a Community Wiki post doing that.

The loop won't stop in a correctly-implemented JavaScript engine. *(The engine's host environment might eventually terminate it because it's endless, but that's another thing.)*

Here's why:

Initially, when

`i`

is`0`

, the condition`1/i > 0`

is true because in JavaScript,`1/0`

is`Infinity`

, and`Infinity > 0`

is true.After that,

`i`

will be incremented and continue to grow as a positive integer value for a long time (a further 9,007,199,254,740,990 iterations). In all of those cases,`1/i`

will remain`> 0`

(although the values for`1/i`

get**really**small toward the end!) and so the loop continues up to and including the loop where`i`

reaches the value`Number.MAX_SAFE_INTEGER`

.`Number.MAX_SAFE_INTEGER`

(9,007,199,254,740,991) is the highest positive integer value that an IEEE-754 double-precision binary number (the kind JavaScript uses) can**accurately**represent. Once we go past this point, we start losing precision even at the whole number (integer) scale.After the loop where

`i`

is`Number.MAX_SAFE_INTEGER`

,`i++`

takes us to an*inaccurate*number. If you printed out the value of`i`

at that point, it would say 9,007,199,254,740,992, but it**isn't**quite 9,007,199,254,740,992. Double precision numbers famously can't represent all numbers (`0.1 + 0.2 == 0.3`

is false, for instance), but we're used to thinking (erroneously) that it only affects the fractional part. It doesn't, and this is the point at which it starts affecting the whole-number part.`1/i`

is still`> 0`

so the loop continues.From that point forward,

`i++`

doesn't change the value of`i`

anymore; adding 1 to it doesn't change the bit pattern held for the number at all. Adding a*higher*number like 10 to it would, but adding 1 to it doesn't. So we've reached steady-state:`i`

never changes, and the loop never terminates.

Here are the various relevant calculations:

```
if (!Number.MAX_SAFE_INTEGER) {
// Browser doesn't have the Number.MAX_SAFE_INTEGER
// property; shim it. Should use Object.defineProperty
// but hey, maybe it's so old it doesn't have that either
Number.MAX_SAFE_INTEGER = 9007199254740991;
}
var i = 0;
console.log(i, 1/i, 1/i > 0); // 0, Infinity, true
i++;
console.log(i, 1/i, 1/i > 0); // 1, 1, true
// ...eventually i is incremented all the way to Number.MAX_SAFE_INTEGER
i = Number.MAX_SAFE_INTEGER;
console.log(i, 1/i, 1/i > 0); // 9007199254740991 1.1102230246251568e-16, true
i++;
console.log(i, 1/i, 1/i > 0); // 9007199254740992 1.1102230246251565e-16, true
i++;
console.log(i, 1/i, 1/i > 0); // 9007199254740992 1.1102230246251565e-16, true (no change)
console.log(i == i + 1); // true
```