This question already has answers here:
What is JavaScript's highest integer value that a number can go to without losing precision?
(21 answers)
Closed 7 years ago.
I open terminal browser (Chrome for example).
I write this:
var y = "11000011010101011";
"11000011010101011"
parseInt(y)
11000011010101012
I expected 11000011010101011 but it returns me 11000011010101012.
Does anybody know why?
Every number in Javascript is represented as a double precision floating point. JavaScript can accurately represent integers only up to 9007199254740991 (2^53 - 1). Once you get over that limit, you will loose precision.
According to this page.
All number in Javascript are 64-bit floating point number, and integers are represented by the 53-bit mantisa.
Because of that, you can't store a integer larger than 2^53 -1 and smaller than -2^53 +1 without losing precission (Javascript rounds your number in order to be able to store it).
Your number is larger than 2^53 -1. Even though a String can store it, in order to store it in a "Number" variable, it has to be rounded, losing the precision and returning you a slightly different number.
Only 9007199254740991 is the safe integer in javascript.
This is case something like
9007199254740992 + 1 // 9007199254740992
9007199254740993 + 1 // 9007199254740992
9007199254740994 + 1 //9007199254740996
Please see the links for more details
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number
http://www.2ality.com/2012/04/number-encoding.html
Also see this one
how addition of Number works on max limit numbers?
This is the dublicate questions see its original
Related
This question already has answers here:
What is JavaScript's highest integer value that a number can go to without losing precision?
(21 answers)
Closed 4 months ago.
How to increase this number(you can try it on the browser console):
36893488147419103000 + 1
The result of this is:
36893488147419103000
The number stays the same no changes to it why is that? and how can I increase it by 1?
For big integers you should use the BigInt (Big Integer) type.
Note 1: you almost always cannot mix BigInt numbers with Numbers (eg for math operations) without first performing an explicit conversion.
Note 2: JSON does not currently natively support BigInt values. As a workaround you can use strings (eg. '1n' for the values and then use a reviver function when calling JSON.parse.
JavaScript currently only has two numeric types: double-precision IEEE 754 floating point Numbers, and Big Integers which can be used to represent arbitrarily large integers. You can declare a BigInt number literal using the suffix n, eg. 1n.
IEEE 754 Numbers can "only" accurately represent integers up to and including Number.MAX_SAFE_INTEGER, which has a value of 2^53 - 1 or 9,007,199,254,740,991 or ~9 quadrillion.
From MDN:
Double precision floating point format only has 52 bits to represent the mantissa, so it can only safely represent integers between -(253 – 1) and 253 – 1. "Safe" in this context refers to the ability to represent integers exactly and to compare them correctly. For example, Number.MAX_SAFE_INTEGER + 1 === Number.MAX_SAFE_INTEGER + 2 will evaluate to true, which is mathematically incorrect. See Number.isSafeInteger() for more information.
A "Decimal" number type, that will be able to represent arbitrarily precise decimal numbers, is under development.
Obviously the number is internally represented as a floating point number.When the value you want do add to this number is less then the value of the least significant bit, it will not change the the value.
The only way would be to use floating point numbers with a higher resolution i.e. with a higher number of significant bits.
Double precision floating point format only has 52 bits to represent the mantissa, so it can only safely represent integers between -(253 – 1) and 253 – 1. See Number.MAX_SAFE_INTEGER. Larger numbers may not be able to be represented exactly.
This question already has answers here:
What is JavaScript's highest integer value that a number can go to without losing precision?
(21 answers)
Closed 8 years ago.
Type this in the console of your browser:
9999999999999999==10000000000000000
It says they are equal, why?
JavaScript only supports 53 bit integers
All numbers in JavaScript are floating point which means that integers are always represented as
sign × mantissa × 2exponent
The mantissa has 53 bits. You can use the exponent to get higher integers, but then they won’t be contiguous, any more. For example, you generally need to multiply the mantissa by two (exponent 1) in order to reach the 54th bit. However, if you multiply by two, you will only be able to represent every second integer:
This question already has answers here:
What is JavaScript's highest integer value that a number can go to without losing precision?
(21 answers)
Closed 8 years ago.
Can anybody solve the following problem with javascript
var i = 10152233307863175;
alert(i.toString());
alert shows value 10152233307863176. Any solution. Problem is when I get json object on client and when string is converted to json it contains wrong values.
This is a limitation in the precision of the numeric data format that javascript uses (double precision floating point).
The best way of storing that value, assuming you don't need to do any mathematical operations, is storing it as a string in the first place.
MDN has this to say about numbers in JavaScript.
Numbers in JavaScript are "double-precision 64-bit format IEEE 754 values", according to the spec.
There is no real integers in JavaScript. According to this source:
ECMAScript numbers are represented in binary as IEEE-754 (IEC 559) Doubles, with a resolution of 53 bits, giving an accuracy of 15-16 decimal digits; integers up to just over 9e15 are precise, ...
Your number 10152233307863175 contains 17 digits. Since the number is represented as a floating point number, JavaScript tries to do it's best and set bits in a way that the resulting number is closest to the supplied number.
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 9 years ago.
'-15.48' - '43'
Just wrote this in console and result is the following:
-58.480000000000004
Why Is it so? And what to do to get correct result?
Because all floating point math is like this and is based on the IEEE 754 standard. JavaScript uses 64-bit floating point representation, which is the same as Java's double.
to fix it you may try:
(-15.48 - 43).toFixed(2);
Fiddle demo
use: toFixed()
var num = 5.56789;
var n=num.toFixed(2);
result:5.57
http://en.wikipedia.org/wiki/Machine_epsilon
Humans count in decimal numbers, machines mostly use binary. 10 == 2x5; 2 and 5 are mutually prime numbers. That trivial fact has an unpleasant consequence though.
In most calculations (except lucky degenerate cases) with "simple" decimal numbers, that include division, the result would be an indefinite repeating binary number.
In most calculations (except lucky degenerate cases) with "simple" binary numbers, that include division, the result would be an indefinite repeating decimal number.
One can check this using pen and pencil as described http://en.wikipedia.org/wiki/Repeating_decimal#Every_rational_number_is_either_a_terminating_or_repeating_decimal
That means that almost every time you see the the result of floating point calculations on your screen - as a finite number - the computer somewhat cheats at you and shows you some approximation instead of the real result.
That means that almost every time you store the results of the calculation in the variable - which has a finite size, not any larger than the computer's available memory - the computer somewhat cheats at you and retains some approximation instead of the real result.
The typical gotchas then may include.
Program is accounting for the sum of some looong sequence, an infinite loop of x AVG := AVG + X[i]; kind where 0 < X[i] < const. If the loop would run long enough, you would see that at some point AVG no more changes the value, all the elements fro mthatpoint further on are just discarded.
Program calculates some value twice using different formulas and then makes a safety check like Value_1 == Value_2. For theoretical mathematics the values are equal, for the real computers they are not.
This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
Large numbers erroneously rounded in Javascript
I am experiencing some strange behavior when working with numbers in javascript. When I use the following code:
CLICK HERE
I get the number 9200000000032336 in my console. I think it most be something with rounding or max values for numbers, but I don't understand it completely. Anyone?
I'm not a Javascript expert, but it sounds like your number is being stored as an IEEE-754 64-bit floating point number. Certainly that's what I get from C# code which will display the exact value of a double:
double d = 9200000000032337;
Console.WriteLine(DoubleConverter.ToExactString(d));
(Using my own DoubleConverter class.) My output is the same as yours: 9200000000032336
Floating point values only ever hold a certain number of significant digits accurately - and when the numbers get high enough, even integers can't be stored exactly.
ECMA-262 seems to confirm this:
4.3.19
Number value
primitive value corresponding to a double-precision 64-bit binary format IEEE 754 value
and from section 7.8.3 (numeric literals):
A numeric literal stands for a value of the Number type. This value is determined in two steps: first, a
mathematical value (MV) is derived from the literal; second, this mathematical value is rounded as described
below.
Section 8.5 contains more details.