When I run the following:
parseInt('96589218797811259658921879781126'.slice(0, 16), 10);
the output is
9658921879781124
whereas the expected is, as you can see:
9658921879781125
What is the cause? I understand vaguely in googling around that there are issues with large numbers in JS and that this indeed appears to be above that threshold, but I don't know what to do about it, or what is happening in this specific case. Thank you.
Edit: Thanks for the answers, I see that depending on an integer this size is bad news. The reason for using an integer is because I need to increment by one, then compare to the rest of the string. In this case, the first half of the string should equal the second half after incrementing the first half by one. What is an alternative approach?
It is not a JavaScript issue.
JavaScript uses the double-precision 64-bit floating point format (IEEE 754) to store both integer and rational numbers.
This format allows the exact representation of integer numbers between -253 and 253 (-9007199254740992 to 9007199254740992). Outside this interval, some integer values cannot be represented by this format; they are rounded to the nearest integer value that can be represented. For example, from 253 to 254, everything is multiplied by 2, so the representable numbers are the even ones.
The JavaScript global object Number provides the constant Number.MAX_SAFE_INTEGER that represents the maximum integer value that can be stored by the IEEE 574 format (253-1).
It also provides the method Number.isSafeInteger() you can use to find out if an integer number can be safely stored by the Number JavaScript type.
The number you use (9658921879781124) is too large to be stored correctly in JavaScript or any other language that uses the double-precision floating point format to store the numbers.
Related
Assume integer below is produced by a true random number generator, and the number changes randomly between 0 and 255.
let integer = 241 // true random number
For the application I'm working on, I need to convert that number into a floating decimal between 0 and 1 to look more like the result from Math.random().
So,
let float = integer/((2**8)-1)
If integer changes to a new random integer between 0 and 255, will this provide other "quality" floating point numbers? For instance, would requesting Uint16 for numbers between 0–65535 then let float = integer/((2**16)-1) be a better approach just for the greater variety?
Note, my purposes for this is not for security, encryption, or cryptography. I just need the added decimal places similar to Math.random(). I am using these numbers to plug into a normalization transform using Box Müller to create a simulated random walk.
In JavaScript, a Number is implemented as a binary floating-point number format with 53 significant bits of precision (more specifically, the binary64 format of IEEE 754).
However, generating a "uniform" floating-point number by multiplying or dividing an integer with a constant (as is commonly the case) will generally leave some floating-point numbers with no chance of occurring, even though they lie in the correct range and even though they can be represented in the floating-point format in question. For more information, see F. Goualard, "Generating Random Floating-Point Numbers by Dividing Integers: a Case Study".
Instead, a more complicated procedure can be done to give each floating-point number the expected probability of occurring (within the limits of the floating-point format), as I have done, for example. Note how non-trivial this procedure is. See also my answer to the question: Random floating point double in Inclusive Range
look at this picture.(The underLine is input.)
why the end of JavaScript Number with trailing zeros or a not predictable number？
I checked the document with https://www.ecma-international.org/ecma-262/5.1/#sec-9.7
But I can't find anything useful for this problem.
Numbers in Javascript use Double-precision floating-point format which can represent numbers from -(2^53 - 1) and (2^53 - 1). This limits the maximum safe number (Number.MAX_SAFE_INTEGER) to 9007199254740991.
Hence any number above that will be not be represented accurately.
so the thing is there is maximum integer which can be safely manipulated in javascript after that you are supposed to get some unexpected results based on implementation
read about that max safe integer https://www.ecma-international.org/ecma-262/6.0/#sec-number.max_safe_integer
BTW there is a new bigint type which can handle large numbers https://developers.google.com/web/updates/2018/05/bigint
bigint however is not a standard yet i think
I am facing weird issued.
parseFloat(11111111111111111) converts it to 11111111111111112.
I noticed that it works fine till length is 16 but rounds off higher when input length is > 16.
I want to retain the original value passed in parseFloat after it is executed.
Any help?
Integers (numbers without a period or exponent notation) are considered accurate up to 15 digits.
More information here
Numbers in javascript are represented using 64 bit floating point values (so called doubles in other languages).
doubles can hold at most 15/16 significant digits (depends on number magnitute). Since range of double is 1.7E+/-308 some numbers can only be aproximated by double, in your case 11111111111111111 cannot be represented exactly but is aproximated by 11111111111111112 value. If this sounds strange then remember that 0.3 cannot be represented exactly as double too.
double can hold exact integers values in range +/-2^53, when you are operating in this range - you may expect exact values.
Javascript has a constant, Number.MAX_SAFE_INTEGER which is the highest integer that can be exactly represented.
Safe in this context refers to the ability to represent integers exactly and to correctly compare them. For example, Number.MAX_SAFE_INTEGER + 1 === Number.MAX_SAFE_INTEGER + 2 will evaluate to true, which is mathematically incorrect.
The value is 9007199254740991 (2^53 - 1) which makes a maximum of 15 digits safe.
JavaScript now has BigInt
BigInt is a built-in object that provides a way to represent whole numbers larger than 253 - 1, which is the largest number JavaScript can reliably represent with the Number primitive.
BigInt can be used for arbitrarily large integers.
As you can see in the following blog post, JavaScript only supports 53 bit integers.
if you type in the console
var x = 11111111111111111
and then type
x
you'll get
11111111111111112
This has nothing to do with the parseFloat method.
There's also a related question here about working with big numbers in JavaScript.
Try using the unary + operator.
Like this + ("1111111111111111") + 1 = 1111111111111112
So my problem is this, I'm writing a program that checks if number is even or odd without division. So I decided to take the number, turn it into a String with the
number.toString()
method. The problem I'm having is that if you put a number that is about 17 or more digits long the string is correct for about the first 17 digits then it's just 0's and sometimes 2's. For example,
function toStr (number)
{
return number.toString(10);
}
console.log(toStr(123456789123456789));
prints,
123456789123456780
any ideas?
The problem has nothing to do with strings or your function at all. Try going to your console and just entering the expression 123456789123456789 and pressing return.
You will likewise obtain 123456789123456780.
Why?
The expression 123456789123456789 within the JavaScript language is interpreted as a JavaScript number type, which can only be represented exactly to a certain number of base two significant figures. The input number happens to have more significant digits when expressed in base two than the number of base two significant figures available in JavaScript's representation of a number, and so the value is automatically rounded in base two as follows:
123456789123456789 =
110110110100110110100101110101100110100000101111100010101 (base two)
123456789123456780 =
110110110100110110100101110101100110100000101111100001100 (base two)
Note that you CAN accurately represent some numbers larger than a certain size in JavaScript, but only those numbers with no more significant figures in base two than JavaScript has room for. For instance, 2 times a very large power of 10, which would have only one significant figure in base two.
If you are designing this program to accept user input from a form or dialog box, then you will receive the input as a string. You only need to check the last digit in order to determine if the input number is odd or even (assuming it is indeed an integer to begin with). The other answer has suggested the standard way to obtain the last character of a string as well as the standard way to test if a string value is odd or even.
If you go beyond Javascript's max integer size (9007199254740992) you are asking for trouble: http://ecma262-5.com/ELS5_HTML.htm.
So to solve this problem, you must treat it as a string only. Then extract the last digit in the string and use it to determine whether the number is even or odd.
if(parseInt(("123456789123456789").slice(-1)) % 2)
//odd
else
//even
It's a 64-bit floating point number, using the IEEE 754 specification. A feature of this spec is that starting at 2^53 the smallest distance between two numbers is 2.
var x = Math.pow(2, 53);
console.log( x == x + 1 );
This difference is the value of the unit in the last place, or ULP.
This is similar in principle to trying to store fractional values in integral types in other languages; values like .5 can't be represented, so they are discarded. With integers, the ULP value is always 1; with floating point, the ULP value depends on how big or small the number you're trying to represent.
Is "Number" in JavaScript entirely synonymous with "Integer"?
What piqued my curiosity:
--- PHP, Python, Java and others use the term "Integer"
--- JavaScript has the function parseInt() rather than parseNumber()
Are there any details of interest?
Is "Number" in JavaScript entirely synonymous with "Integer"?
No. All numbers in JavaScript are actually 64-bit floating point values.
parseInt() and parseFloat() both return this same data type - the only difference is whether or not any fractional part is truncated.
52 bits of the 64 are for the precision, so this gives you exact signed 53-bit integer values. Outside of this range integers are approximated.
In a bit more detail, all integers from -9007199254740992 to +9007199254740992 are represented exactly (-2^53 to +2^53). The smallest positive integer that JavaScript cannot represent exactly is 9007199254740993. Try pasting that number into a JavaScript console and it will round it down to 9007199254740992. 9007199254740994, 9007199254740996, 9007199254740998, etc. are all represented exactly but not the odd integers in between. The integers that can be represented exactly become more sparse the higher (or more negative) you go until you get to the largest value Number.MAX_VALUE == 1.7976931348623157e+308.
In JavaScript there is a single number type: an IEEE 754 double precision floating point (what is called number.)
This article by D. Crockford is interesting:
http://yuiblog.com/blog/2009/03/10/when-you-cant-count-on-your-numbers/