Is the value of Number.MAX_VALUE a limitation only for numbers of data type Number?
Doesn't BigInt have the same upper bound?
And another one question... Does BigInt represent number in 64-bit format IEEE-754?
Since the BigInt format represents large numbers, can the BigInt value take up more space than 64 bits?
Doesn't BigInt have the same upper bound?
No, BigInts have no specified limit. That said, realistically, there will always be implementation-defined limits (just like for Strings, Arrays, etc.). Currently, Chrome allows a billion bits, and Firefox allows a million bits. The expectation is that most realistically-occurring BigInts won't run into this limit.
Does BigInt represent number in 64-bit format IEEE-754?
No, IEEE-754 is a floating-point format, so it's not useful for BigInts, which have integer values. Besides, they have "unlimited" precision.
can the BigInt value take up more space than 64 bits?
Yes, BigInts can consume a lot more than 64 bits. For example, a BigInt with a thousand bits (such as 2n ** 999n) will need (about) a thousand bits of memory (likely rounded up to the next multiple of 4 or 8 bytes, plus a small object header, specifics depend on the engine).
Related
JavaScript uses a fixed number of bits, 64 of them, to store a single number value. There are only so many patterns you can make with 64 bits, which means that the number of different numbers that can be represented is limited. With N decimal digits, you can represent 10^N numbers. Similarly, given 64 binary digits, you can represent 2^64 different numbers, which is about 18 quintillion (an 18 with 18 zeros after it).
Javascript traditionally stores numbers as a 64 bit floating point with a 52 bit mantissa an 11 bit exponent and the sign is 1 bit. Effectively this means that
Integers are accurate up to 15 digits.
-- w3schools.com
Now with ES6 the BigInt proposal has been finalized, so you can access a second type of number when dealing with integers that may be larger than 52 bits. There also exist some libraries for operations on large numbers provided as strings.
I'm trying to write a function that would fetch me the number of decimal places after the decimal point in a floating-point literal using the answer as a reference from here.
Although this seems to work fine when tried in the browser consoles, in the Node.js environment while running test cases, the precision is truncated only up to 14 digits.
let data = 123.834756380650877834678
console.log(data) // 123.83475638065088
And the function returns 14 as the answer.
Why is the rounding off happening at rest? Is it a default behavior?
The floating-point format used in JavaScript (and presumably Node.js) is IEEE-754 binary64. When 123.834756380650877834678 is used in source code, it is converted to the nearest representable value, which is 123.834756380650873097692965529859066009521484375.
When this is converted to a string with default formatting, JavaScript uses just enough digits to uniquely distinguish the value. For 123.834756380650873097692965529859066009521484375, this should produce “123.83475638065087”. If you are getting “123.83475638065088”, which differs in the last digit, then the software you are using does not conform to the JavaScript specification (ECMAScript).
In any case, the binary64 format does not have sufficient precision to preserve the information that the original numeral, “123.834756380650877834678”, has 21 digits after the decimal point.
The code you link to also does not and cannot compute the number of digits in an original numeral. It computes the number of digits needed to uniquely distinguish the value represented after conversion to binary64. For sufficiently short numerals without trailing zeros after the decimal point, this is the same as the number of digits after the decimal point in the original numeral. For others, it may not be.
it is default behavior of JavaScript.I think it will be same in node.js.
in JS The maximum number of decimals is 17.
for more details take a look at here
I just started reading Javascript (Professional JavaScript for Web Developers, 3rd Edition) and the text variously says that integers are:
[1] Stored as IEEE-754 format (pg. 35).
[2] Have a -0 value (pg. 36).
[3] Stored as a 32-bit two's complement number (pg. 50).
[4] Stored as a IEEE-754 64-bits number (pg. 49).
These are inconsistent definitions. What is the format of an integer in Javascipt?
thanks
Here is the specification:
http://ecma262-5.com/ELS5_HTML.htm#Section_8.5
According to the specification, javascript doesn't have integers, only floating point numbers.
IEEE-754 floats do have a -0 value, so there's no inconsistency between 1, 2 and 4. Only 3 appears to be inconsistent.
Javascript numbers are always stored as IEEE-754 64-bit floating point numbers. In some expressions (usually with bitwise operators) they may be temporarily converted to 32-bit integers and then converted back to 64-bit floats, but they're always stored as floats. I assume this conversion is what #3 is actually referring to.
A JIT compiler for Javascript may use actual integers in the compiled code as an optimization (especially if asm.js is involved), but during interpretation it's still all floats.
I'm using a server-side calculation which needs to generate (with * and + operations) and compare 40-bit integers. I'm aware that at that point the V8 engine stores the numbers as Double rather than int. Can I rely on these numbers to be generated and compared correctly?
My intuition says yes - doubles shouldn't have trouble with that - but I'm not sure how to check or where to find information on this.
Yes.
A JavaScript Number, which is a 64-bit IEEE 754 floating point value, can store integers from -253 to 253 without loss of precision, since doubles can store up to 53 bits of mantissa (52 explictly).
References:
ECMA-262: 4.3.19 Number value
Double-precision floating point numbers (Wikipedia)
This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
Is JavaScript's Math broken?
...and what can I do against that? After the calculation I want to have a String representation of the result. Because of that the zeros (plus the one) are desturburbing. "toFixed()" is not a perfect solution because I want to have all (correct) decimals of the potential result and I do not know the result (and the number of decimals) before. So the calculation shown above is only an example.
The short answer is: computers represent numbers in binary, so they can't represent all base 10 fractions perfectly as JavaScript numbers.
The (slightly) longer answer is that, because JavaScript numbers are 64-bit floating-point (equivalent to the double type in Java, C#, etc.), as Wikipedia describes here, there is a limited number of significand bits. For this reason, the precision of this base-2 number is limited.
As an analogy, consider representing the fraction 1/3 in base 10. Say that you only have so many digits to use. That means that you can never ever ever represent 1/3 exactly in base 10, because 1/3 requires an infinite number of digits to represent in base 10. Similarly, you can never represent 1/10 perfectly in a finite number of bits, because 1/10 requires an infinite number of bits to represent exactly. What you're seeing here is a fraction (58/10) that a computer can't represent exactly in a limited number of bits, so the computer is coming as close as it can.
Squeezing infinitely many real numbers into a finite number of bits requires an approximate representation. Although there are infinitely many integers, in most programs the result of integer computations can be stored in 32 bits. In contrast, given any fixed number of bits, most calculations with real numbers will produce quantities that cannot be exactly represented using that many bits. Therefore the result of a floating-point calculation must often be rounded in order to fit back into its finite representation. This rounding error is the characteristic feature of floating-point computation.
Above from http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html