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ES6 Number Improvements in Depth

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Hey there! Glad you’re here in time for ES6 – “Back to School” – in Depth. Never heard of it? Refer to A Brief History of ES6 Tooling. Then, make your way through destructuring, template literals, arrow functions, the spread operator and rest parameters, improvements coming to object literals, the new classes sugar on top of prototypes, let, const, and the “Temporal Dead Zone”, iterators, generators, Symbols, Maps, WeakMaps, Sets, and WeakSets, proxies, proxy traps, more proxy traps, and reflection. Today we’ll learn about Number improvements.

Like I did in previous articles on the series, I would love to point out that you should probably set up Babel and follow along the examples with either a REPL or the babel-node CLI and a file. That’ll make it so much easier for you to internalize the concepts discussed in the series. If you aren’t the “install things on my computer” kind of human, you might prefer to hop on CodePen and then click on the gear icon for JavaScript – they have a Babel preprocessor which makes trying out ES6 a breeze. Another alternative that’s also quite useful is to use Babel’s online REPL – it’ll show you compiled ES5 code to the right of your ES6 code for quick comparison.

Before getting into it, let me shamelessly ask for your support if you’re enjoying my ES6 in Depth series. Your contributions will go towards helping me keep up with the schedule, server bills, keeping me fed, and maintaining Pony Foo as a veritable source of JavaScript goodies.

Thanks for reading that, and let’s go into Number improvements. These changes don’t really depend on anything we’ve covered so far – although I would strongly recommend you skim over articles in the series if you haven’t done so yet. Time to dig into Number.

Number Improvements in ES6

There’s a number of changes coming to Number in ES6 – see what I did there? First off, let’s raise the curtain with a summary of the features we’ll be talking about. We’ll go over all of the following changes to Number today.

The curtain is raising...
The curtain is raising…

Binary and Octal Literals

Before ES6, your best bet when it comes to binary representation of integers was to just pass them to parseInt with a radix of 2.

parseInt('101', 2)
// <- 5

In ES6 you could also use the 0b prefix to represent binary integer literals. You could also use 0B but I suggest you stick with the lower-case option.

console.log(0b001)
// <- 1
console.log(0b010)
// <- 2
console.log(0b011)
// <- 3
console.log(0b100)
// <- 4

Same goes for octal literals. In ES3, parseInt interpreted strings of digits starting with a 0 as an octal value. That meant things got weird quickly when you forgot to specify a radix of 10 – and that soon became a best practice.

parseInt('01')
// <- 1
parseInt('08')
// <- 0
parseInt('8')
// <- 8

When ES5 came around, it got rid of the octal interpretation in parseInt – although it’s still recommended you specify a radix for backwards compatibility purposes. If you actually wanted octal, you could get those using a radix of 8, anyways.

parseInt('100', '8')
// <- 64

When it comes to ES6, you can now use the 0o prefix for octal literals. You could also use 0O, but that’s going to look very confusing in some typefaces, so I suggest you stick with the 0o notation.

console.log(0o010)
// <- 8
console.log(0o100)
// <- 64

Keep in mind that octal literals aren’t actually going to crop up everywhere in your front-end applications anytime soon, so you shouldn’t worry too much about the seemingly odd choice (font clarity wise) of a 0o prefix. Besides, most of us use editors that have no trouble at all differentiating between 0o, 0O, 00, OO, and oo.

Those characters render just fine in Sublime Text 3
Those characters render just fine in Sublime Text 3

If you’re now perplexed and left wondering “what about hexadecimal?”, don’t you worry, those were already part of the language in ES5, and you can still use them. The prefix for literal hexadecimal notation is either 0x, or 0X.

console.log(0x0ff)
// <- 255
console.log(0xf00)
// <- 3840

Enough with number literals, let’s talk about something else. The first four additions to Number that we’ll be discussing – Number.isNaN, Number.isFinite, Number.parseInt, and Number.parseFloat – already existed in ES5, but in the global namespace. In addition, the methods in Number are slightly different in that they don’t coerce non-numeric values into numbers before producing a result.

Number.isNaN

This method is almost identical to ES5 global isNaN method. Number.isNaN returns whether the provided value equals NaN. This is a very different question from “is this not a number?”.

The snippet shown below quickly shows that anything that’s not NaN when passed to Number.isNaN will return false, while passing NaN into it will yield true.

Number.isNaN(123)
// <- false, integers are not NaN
Number.isNaN(Infinity)
// <- false, Infinity is not NaN
Number.isNaN('ponyfoo')
// <- false, 'ponyfoo' is not NaN
Number.isNaN(NaN)
// <- true, NaN is NaN
Number.isNaN('pony'/'foo')
// <- true, 'pony'/'foo' is NaN, NaN is NaN

The ES5 global.isNaN method, in contrast, casts non-numeric values passed to it before evaluating them against NaN. That produces significantly different results. The example below produces incosistent results because, unlike Number.isNaN, isNaN casts the value passed to it through Number first.

isNaN('ponyfoo')
// <- true, because Number('ponyfoo') is NaN
isNaN(new Date())
// <- true

While Number.isNaN is more precise than its global isNaN counterpart because it doesn’t incur in casting, it’s still going to confuse people because reasons.

  1. global.isNaN casts input through Number(value) before comparison
  2. Number.isNaN doesn’t
  3. Neither Number.isNaN nor global.isNaN answer the “is this not a number?” question
  4. They answer whether value – or Number(value) is NaN

In most cases, what you actually want is to know whether a value identifies as a number typeof NaN === 'number' and is a number. The method below does just that. Note that it’d work with both global.isNaN and Number.isNaN due to type checking. Everything that reports a typeof value of 'number' is a number, except NaN, so we weed those out to avoid false positives!

function isNumber (value) {
  return typeof value === 'number' && !Number.isNaN(value)
}

You can use that method to figure out whether anything is an actual number or not. Here’s some examples of what constitutes actual JavaScript numbers or not.

isNumber(1)
// <- true
isNumber(Infinity)
// <- true
isNumber(NaN)
// <- false
isNumber('ponyfoo')
// <- false
isNumber(new Date())
// <- false

Speaking of isNumber, isn’t there something like that in the language already? Sort of.

Number.isFinite

The rarely-advertised isFinite method has been available since ES3 and it returns whether the provided value matches none of: Infinity, -Infinity, and NaN.

Want to take a guess about the difference between global.isFinite and Number.isFinite?

Correct! the global.isFinite method coerces values through Number(value), while Number.isFinite doesn’t. Here are a few examples using global.isFinite. This means that values that can be coerced into non-NaN numbers will be considered finite numbers by global.isNumber – even though they’re aren’t actually numbers!

In most cases isFinite will be good enough, just like isNaN, but when it comes to non-numeric values it’ll start acting up and producing unexpected results due to its value coercion into numbers.

isFinite(NaN)
// <- false
isFinite(Infinity)
// <- false
isFinite(-Infinity)
// <- false
isFinite(null)
// <- true, because Number(null) is 0
isFinite('10')
// <- true, because Number('10') is 10

Using Number.isFinite is just an all-around safer bet as it doesn’t incur in unwanted casting. You could always do Number.isFinite(Number(value)) if you did want the value to be casted into its numeric representation.

Number.isFinite(NaN)
// <- false
Number.isFinite(Infinity)
// <- false
Number.isFinite(-Infinity)
// <- false
Number.isFinite(null)
// <- false
Number.isFinite(0)
// <- true

Once again, the discrepancy doesn’t do any good to the language, but Number.isFinite is consistently more useful than isFinite. Creating a polyfill for the Number.isFinite version is mostly a matter of type-checking.

Number.isFinite = function (value) {
  return typeof value === 'number' && isFinite(value)
}

Number.parseInt

This method works the same as parseInt. In fact, it is the same.

console.log(Number.parseInt === parseInt)
// <- true

The parseInt method keeps producing inconsistencies, though – even if it didn’t even change, that’s the problem. Before ES6, parseInt had support for hexadecimal literal notation in strings. Specifying the radix is not even necessary, parseInt infers that based on the 0x prefix.

parseInt('0xf00')
// <- 3840
parseInt('0xf00', 16)
// <- 3840

If you hardcoded another radix, – and this is yet another reason for doing so – parseInt would bail after the first non-digit character.

parseInt('0xf00', 10)
// <- 0
parseInt('5xf00', 10)
// <- 5, illustrating there's no special treatment here

So far, it’s all good. Why wouldn’t I want parseInt to drop 0x from hexadecimal strings? It sounds good, although you may argue that that’s doing too much, and you’d be probably right.

The aggravating issue, however, is that parseInt hasn’t changed at all. Therefore, binary and octal literal notation in strings won’t work.

parseInt('0b011')
// <- 0
parseInt('0b011', 2)
// <- 0
parseInt('0o800')
// <- 0
parseInt('0o800', 8)
// <- 0

It’ll be up to you to get rid of the prefix before parseInt. Remember to hard-code the radix, though!

parseInt('0b011'.slice(2), 2)
// <- 3
parseInt('0o110'.slice(2), 8)
// <- 72

What’s even weirder is that the Number method is perfectly able to cast these strings into the correct numbers.

Number('0b011')
// <- 3
Number('0o110')
// <- 72

I’m not sure what drove them to keep Number.parseInt identical to parseInt. If it were up to me, I would’ve made it different so that it worked just like Number – which is able to coerce octal and binary number literal strings into the appropriate base ten numbers.

It might be that this was a more involved “fork” of parseInt than just “not coercing input into a numeric representation” as we observed in Number.isNaN and Number.isFinite, but I’m just guessing here.

Number.parseFloat

Just like parseInt, parseFloat was just added to Number without any modifications whatsoever.

Number.parseFloat === parseFloat
// <- true

In this case, however, parseFloat already didn’t have any special behavior with regard to hexadecimal literal strings, meaning that this is in fact the only method that won’t introduce any confusion, other than it being ported over to Number for completeness’ sake.

Number.isInteger

This is a new method coming in ES6. It returns true if the provided value is a finite number that doesn’t have a decimal part.

console.log(Number.isInteger(Infinity))
// <- false
console.log(Number.isInteger(-Infinity))
// <- false
console.log(Number.isInteger(NaN))
// <- false
console.log(Number.isInteger(null))
// <- false
console.log(Number.isInteger(0))
// <- true
console.log(Number.isInteger(-10))
// <- true
console.log(Number.isInteger(10.3))
// <- false

If you want to look at a a polyfill for isInteger, you might want to consider the following code snippet. The modulus operator returns the remainder of dividing the same operands – effectively: the decimal part. If that’s 0, that means the number is an integer.

Number.isInteger = function (value) {
  return Number.isFinite(value) && value % 1 === 0
}

Floating point arithmetic is well-documented as being kind of ridiculous. What is this Number.EPSILON thing?

Number.EPSILON

Let me answer that question with a piece of code.

Number.EPSILON
// <- 2.220446049250313e-16, wait what?
Number.EPSILON.toFixed(20)
// <- '0.00000000000000022204', got it

Ok, so Number.EPSILON is a terribly small number. What good is it for? Remember that thing about how floating point sum makes no sense? Here’s the canonical example, I’m sure you remember it – Yeah, I know.

0.1 + 0.2
// <- 0.30000000000000004
0.1 + 0.2 === 0.3
// <- false

Let’s try that one more time.

0.1 + 0.2 - 0.3
// <- 5.551115123125783e-17, what the hell?
5.551115123125783e-17.toFixed(20)
// <- '0.00000000000000005551', got it

So what? You can use Number.EPSILON to figure out whether the difference is small enough to fall under the “floating point arithmetic is ridiculous and the difference is negligible” category.

5.551115123125783e-17 < Number.EPSILON
// <- true

Can we trust that? Well, 0.00000000000000005551 is indeed smaller than 0.00000000000000022204. What do you mean you don’t trust me? Here they are side by side.

0.00000000000000005551
0.00000000000000022204

See? Number.EPSILON is larger than the difference. We can use Number.EPSILON as an acceptable margin of error due to floating point arithmetic rounding operations.

Thus, the following piece of code figures out whether the result of a floating point operation is within the expected margin of error. We use Math.abs because that way the order of left and right won’t matter. In other words, withinErrorMargin(left, right) will produce the same result as withinErrorMargin(right, left).

function withinErrorMargin (left, right) {
  return Math.abs(left - right) < Number.EPSILON
}
withinErrorMargin(0.1 + 0.2, 0.3)
// <- true
withinErrorMargin(0.2 + 0.2, 0.3)
// <- false

While, yes, you could do this, it’s probably unnecessarily complicated unless you have to deal with very low-level mathematics. You’ll be better of pulling a library like mathjs into your project.

Last but not least, there’s the other weird aspect of number representation in JavaScript. Not every integer can be represented precisely, either.

Number.MAX_SAFE_INTEGER

This is the largest integer that can be safely and precisely represented in JavaScript, or any language that represents integers using floating point as specified by IEEE-754 for that matter. The code below show just how large that number is. If we need to be able to deal with numbers larger than that, then I would once again point you to mathjs, or maybe try another language for your computationally intensive services.

Number.MAX_SAFE_INTEGER === Math.pow(2, 53) - 1
// <- true
Number.MAX_SAFE_INTEGER === 9007199254740991
// <- true

And you know what they say – If there’s a maximum…

Number.MIN_SAFE_INTEGER

Right, nobody says that. However, there’s a Number.MIN_SAFE_INTEGER regardless, and it’s the negative value of Number.MAX_SAFE_INTEGER.

Number.MIN_SAFE_INTEGER === -Number.MAX_SAFE_INTEGER
// <- true
Number.MIN_SAFE_INTEGER === -9007199254740991
// <- true

How exactly can you leverage these two constants, I hear you say? In the case of the overflow problem, you don’t have to implement your own withinErrorMargin method like you had to do for floating point precision. Instead, a Number.isSafeInteger is provided to you.

Number.isSafeInteger

This method returns true for any integer in the [MIN_SAFE_INTEGER, MAX_SAFE_INTEGER] range. There’s no type coercion here either. The input must be numeric, an integer, and within the aforementioned bounds in order for the method to return true. Here’s a quite comprehensive set of examples for you to stare at.

Number.isSafeInteger('a')
// <- false
Number.isSafeInteger(null)
// <- false
Number.isSafeInteger(NaN)
// <- false
Number.isSafeInteger(Infinity)
// <- false
Number.isSafeInteger(-Infinity)
// <- false
Number.isSafeInteger(Number.MIN_SAFE_INTEGER - 1)
// <- false
Number.isSafeInteger(Number.MIN_SAFE_INTEGER)
// <- true
Number.isSafeInteger(1)
// <- true
Number.isSafeInteger(1.2)
// <- false
Number.isSafeInteger(Number.MAX_SAFE_INTEGER)
// <- true
Number.isSafeInteger(Number.MAX_SAFE_INTEGER + 1)
// <- false

As Dr. Axel Rauschmayer points out in his article about ES6 numbers, when we want to verify if the result of an operation is within bounds, we must verify not only the result but also both operands. The reason for that is one (or both) of the operands may be out of bounds, while the result is “safe” (but incorrect). Similarly, the result may be out of bounds itself, so checking all of left, right, and the result of left op right is necessary to verify that we can indeed trust the result.

In all of the examples below, the result is incorrect. Here’s the first example, where both operands are safe even though the result is not.

Number.isSafeInteger(9007199254740000)
// <- true
Number.isSafeInteger(993)
// <- true
Number.isSafeInteger(9007199254740000 + 993)
// <- false
9007199254740000 + 993
// <- 9007199254740992, should be 9007199254740993

In this example one of the operands wasn’t within range, so we can’t trust the result to be accurate.

Number.isSafeInteger(9007199254740993)
// <- false
Number.isSafeInteger(990)
// <- true
Number.isSafeInteger(9007199254740993 + 990)
// <- false
9007199254740993 + 990
// <-  9007199254741982, should be 9007199254741983

Note that in the example above, a subtraction would produce a result within bounds, and that result would also be inaccurate.

Number.isSafeInteger(9007199254740993)
// <- false
Number.isSafeInteger(990)
// <- true
Number.isSafeInteger(9007199254740993 - 990)
// <- true
9007199254740993 - 990
// <-  9007199254740002, should be 9007199254740003

It doesn’t take a genius to figure out the case where both operands are out of bounds but the result is deemed “safe”, even though the result is incorrect.

Number.isSafeInteger(9007199254740993)
// <- false
Number.isSafeInteger(9007199254740995)
// <- false
Number.isSafeInteger(9007199254740993 - 9007199254740995)
// <- true
9007199254740993 - 9007199254740995
// <- -4, should be -2

Thus, as you can see, we can conclude that the only safe way to assert whether an operation is correct is with a method like the one below. If we can’t ascertain that the operation and both its operands are within bounds, then the result may be inaccurate, and that’s a problem. It’s best to throw in those situations and have a way to error-correct, but that’s specific to your programs. The important part is to actually catch these kinds of difficult bugs to deal with.

function trusty (left, right, result) {
  if (
    Number.isSafeInteger(left) &&
    Number.isSafeInteger(right) &&
    Number.isSafeInteger(result)
  ) {
    return result
  }
  throw new RangeError('Operation cannot be trusted!')
}

You could then use that every step of the way to ensure all operands remain safely within bounds. I’ve highlighted the unsafe values in the examples below. Note that even though none of the operations in my examples return accurate results, certain operations and numbers may do so even when operands are out of bounds. The problem is that that can’t be guaranteed – therefore the operation can’t be trusted.

trusty(9007199254740000, 993, 9007199254740000 + 993)
// <- RangeError: Operation cannot be trusted!
trusty(9007199254740993, 990, 9007199254740993 + 990)
// <- RangeError: Operation cannot be trusted!
trusty(9007199254740993, 990, 9007199254740993 - 990)
// <- RangeError: Operation cannot be trusted!
trusty(9007199254740993, 9007199254740995, 9007199254740993 - 9007199254740995)
// <- RangeError: Operation cannot be trusted!
trusty(1, 2, 3)
// <- 3

I don’t think I want to write about floating point again for a while. Time to scrub myself up.

Conclusions

While some of the hacks to guard against rounding errors and overflow safety are nice to have, they don’t attack the heart of the problem: math with the IEEE-754 standard is hard.

These days JavaScript runs on all the things, so it’d be nice if a better standard were to be implemented alongside IEEE-754. Roughly a year ago, Douglas Crockford came up with DEC64, but opinions on its merits range from “this is genius!” to “this is the work of a madman” – I guess that’s the norm when it comes to most of the stuff Crockford publishes, though.

It’d be nice, to eventually see the day where JavaScript is able to precisely compute decimal arithmetic as well as able to represent large integers safely. That day we’ll probably have something alongside floating point.

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Comments (10)

John-David Dalton wrote

I’d say don’t get hung up on the isNumber bit as you usually want to do some other validation beyond is it a number. Most of the time you want to either coerce the value to an integer or do some range checking on it. I’m leaning more towards isSafeInteger for things like index or position values since it not only avoids Infinity and NaN but also those less useful unsafe integer values too.

Šime Vidas wrote

“If it were up to me, I would’ve made it different so that it worked just like Number

But that would defeat the purpose of having Number.parseInt to begin with, or? Are there other differences between Number and Number.parseInt besides that?

Nicolas Bevacqua wrote

Just for completeness’ sake, like with Number.parseFloat. Having three different ways of parsing ints just introduces more and more confusion – “should I use Number, Number.parseInt, parseInt?”

Nicolas Bevacqua wrote

Anyways, the Number.parseInt would also .floor positive values and .ceil negative ones.

Gaby wrote

You mention that the parseInt will not handle octal encoded strings 0o.. and that is correct. Bu the examples you give are wrong because they would fail anyway since they are not in the octal.

parseInt('0o800')
// 
Gaby wrote

The 8 is not in the octal :)