This question already has answers here:
javascript large integer round because precision? (why?)
(2 answers)
Closed 8 years ago.
I've just run into a peculiar issue with Javascript.
An API call returns some JSON as it normally does. One of the ids returned is the long number "10151920335784069".
However, in Javascript world that becomes "10151920335784068" (one subtracted).
A quick test in the (Chrome) console demonstrates it:
x = 10151920335784069;
console.log(x);
10151920335784068
x==10151920335784069;
true
Further more:
x==10151920335784067;
true
x==10151920335784066;
false
What is going on here?
JavaScript (ECMA 262 5th Edition) uses double-precision 64bit numbers in IEEE 754 format. That representation cannot store your value in question exactly so it must round it to the nearest value per the IEEE 754 specification.
Authors and users of APIs that use JSON data should keep this limitation in mind. Many runtime environments (such as JavaScript) have potentially unexpected behavior regarding such numerical values even though the JSON format doesn't impose any such limitations.
All numerical variables in Javascript are stored as 64-bit floating point integers, so at high levels of precision, with numbers above 32 bits, it will round and give you slightly inaccurate numbers
If you want to check if two numbers are roughly even, you can use this
if(Math.abs(num-check)/check<1e-8)){
alert("For most practical intents and purposes, they are equal!");
}
Related
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 2 years ago.
I'm new with JS, and i'm learning by video lectures.
In one of the video, it was said that: "
numbers are always stored in a binary format"
and this is the reason that is very hard to represent some fraction that are very easy to represent in base 10 system we are used to..
I know some development languages (c,java,etc), Is there a difference between the way that numbers are stored in JS to the way it stored in java for example?
The way numbers are stored in JS is not different to other programming languages. The fact that all numbers are stored in base 2 (aka binary) is the reason why certain fractions are hard to store in JS (and other languages). For example, the base 10 number 0.1 is 0.000110011... in binary where 0011 is recurring indefinitely. Since your computer only has a finite number if bits, you can't store 0.1 exactly, you can only approximate it, hence the unprecision.
If you need precision for numbers, most programming languages have data types to store numbers accurately. In javascript you can use the BigInteger type to store numbers more accurately. The default number type used in JS, float, however lacks the precision and runs into the issues described above.
This question already has an answer here:
What is the standard solution in JavaScript for handling big numbers (BigNum)?
(1 answer)
Closed 7 years ago.
I have looked around at questions asking about the maximum and/or minimum limit to numbers in JavaScript. They all say things about how the limits are -2^53 to 2^53 inclusive, but none of them say if there is any way to deal with numbers outside of that range if you need to, except one answer that said you can change it into a string but it wasn't very specific and I didn't understand it.
If anyone can either expound on the idea of changing it into a string of offer a new one, that would be very helpful.
Also, as a side note that it probably much simpler. How do you make sure that numbers are not displayed in scientific notation and only in standard form?
Javascript numbers are represented internally as IEEE 754 double-precision floating point numbers.
On an absolute scale, they can represent numbers from -21023 to 21023. For small numbers like 1, they have a very high precision, down to steps of 2-52. However, as the magnitude of a number increases, the precision of the representation decreases. The ±253 range you've read about is the maximum range of integer representations — once a number exceeds 253, the minimum "step" increases from 1 to 2.
If you need to exactly represent integers greater than 253, you will need to use a Javascript bignum library. However, if you just need to represent floating-point values, you're OK; the default number type will do just fine.
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 8 years ago.
I understand that with the IEEE representation (or any binary representation) for double one can't represent 0.1 with a finite amount of bits.
I have two questions with this in mind:
When C++ also uses the same standard for double why doesn't it mess up 0.1 + 0.2 like JavaScript does?
Why does JavaScript print console.log(0.1) correctly when it can't accurately hold it in memory?
There are at least three reasonable choices for conversion of floating point numbers to strings:
Print the exact value. This seems like an obvious choice, but has downsides. The exact decimal value of a finite floating point number always exists, but may have hundreds of significant digits, most of which are of no practical use. java.util.BigDecimal's toString does this.
Print just enough digits to uniquely identify the floating point number. This is the choice made, for example, in Java for default conversion of double or float.
Print few enough digits to ensure that most output digits will be unaffected by rounding error on most simple calculations. That was the choice made in C.
Each of these has advantages and disadvantages. A choice 3 conversion will get "0.3", the "right" answer, for the result of adding 0.1 and 0.2. On the other hand, reading in a value printed this way cannot be depended on to recover the original float, because multiple floating point values map to the same string.
I don't think any of these options is "right" or "wrong". Languages typically have ways of forcing one of the non-default options, and that should be done if the default is not the best choice for a particular output.
Because it prints x to n decimal places. That happens to be correct
I read this on W3Schools:
All numbers in JavaScript are stored as 64-bit (8-bytes) base 10,
floating point numbers.
This sounds quite strange. Now, it's either wrong or there should be a good reason not to use base 2 like the IEEE standard.
I tried to find a real JavaScript definition, but I couldn't find any. Either on the V8 or WebKit documentation, the two JavaScript implementation I could find on Wikipedia that sounded the most familiar to me, I could find how they stored the JavaScript Number type.
So, does JavaScript use base 10? If so, why? The only reason I could come up with was that maybe using base 10 has an advantage when you want to be able to accurately store integers as well as floating point numbers, but I don't know how using base 10 would have an advantage for that myself.
That's not the World Wide Web Consortium (W3C), that's w3schools, a website that isn't any authority for any web standards.
Numbers in Javascript are double precision floating point numbers, following the IEEE standards.
The site got the part about every number is a 64-bit floating point number right. The base 10 has nothing with the numerical representation to do, that probably comes from the fact that floating point numbers are always parsed and formatted using base 10.
Numbers in JavaScript are, according to the ECMA-262 Standard (ECMAScript 5.1) section 4.3.19:
Primitive values corresponding to a double-precision 64-bit binary format IEEE 754 value.
Thus, any implementation using base 10 floating point numbers is not ECMA-262 conformant.
JavaScript uses, like most modern languages, IEEE754. Which isn't at all stored in base 10.
The specificity of JavaScript is that there is only one number type, which is the double precision float. Which has the side effect that you're somewhat limited contrary to other languages if you want to deal with integers : you can't store any double precision integer, only the ones fitting in the size of the fraction (52 bits).
This question already has answers here:
Understanding floating point problems
(4 answers)
Closed 11 months ago.
This page has a simple alert:
alert(185.3 + 12.37);
To me, that should equal 197.67
However, in the browsers I've tested (Chrome/Safari on OSX, FF on Win7) the answer is:
197.67000000000002
Why is that? Is this just a known bug or is there more to JavaScript addition than I realize?
javascript uses the double datatype, which can't, due to restricted binary places, express all decimal numbers accurately (not all numbers can be expressed with finite binary places). You can read more at wikipedia.
You should read this:
http://download.oracle.com/docs/cd/E19957-01/806-3568/ncg_goldberg.html
It's not a bug; it's just a well-known fact of floating point numbers for every language.
In binary, this is the infinitely repeating binary fraction 11000101.10(10101110000101000111) - which cannot be represented in a finite number of bits, so it is rounded to an approximation.