Why is Number.MAX_SAFE_INTEGER 9,007,199,254,740,991 and not 9,007,199,254,740,992?
JavascriptEcmascript 6IntegerIeee 754Javascript Problem Overview
ECMAScript 6's Number.MAX_SAFE_INTEGER
supposedly represents the maximum numerical value JavaScript can store before issues arise with floating point precision. However it's a requirement that the number 1 added to this value must also be representable as a Number
.
> ### Number.MAX_SAFE_INTEGER
>
> NOTE The value of Number.MAX_SAFE_INTEGER
is the largest integer n
such that n
and n + 1
are both exactly representable as a Number
value.
>
> The value of Number.MAX_SAFE_INTEGER
is 9007199254740991 (2^53−1)
.
>
> – ECMAScript Language Specification
The JavaScript consoles of Chrome, Firefox, Opera and IE11 can all safely perform calculations with the number 9,007,199,254,740,992. Some tests:
// Valid
Math.pow(2, 53) // 9007199254740992
9007199254740991 + 1 // 9007199254740992
9007199254740992 - 1 // 9007199254740991
9007199254740992 / 2 // 4503599627370496
4503599627370496 * 2 // 9007199254740992
parseInt('20000000000000', 16) // 9007199254740992
parseInt('80000000000', 32) // 9007199254740992
9007199254740992 - 9007199254740992 // 0
9007199254740992 == 9007199254740991 // false
9007199254740992 == 9007199254740992 // true
// Erroneous
9007199254740992 + 1 // 9007199254740992
9007199254740993 + "" // "9007199254740992"
9007199254740992 == 9007199254740993 // true
Why is it a requirement that n + 1
must also be representable as a Number
? Why does failing this make the value unsafe?
Javascript Solutions
Solution 1 - Javascript
I would say its because while Math.pow(2, 53)
is the largest directly representable integer, its unsafe in that its also the first value who's representation is also an approximation of another value:
9007199254740992 == 9007199254740993 // true
In contrast to Math.pow(2, 53) - 1
:
9007199254740991 == 9007199254740993 // false
Solution 2 - Javascript
the only number which is in close proximity of another when compared with its next number shows true
9007199254740992 == 9007199254740993
true
9007199254740993 == 9007199254740994
false
9007199254740991 == 9007199254740992
false
9007199254740997 == 9007199254740998
false
Solution 3 - Javascript
I also have the same concern about the question. -2^53~2^53
(Including boundary values) while -2^53+1~2^53-1
.
Finally, I found the Correct interpretation in https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/isSafeInteger
It said, the "safe"means :
- can be exactly represented as an IEEE-754 double precision number, and
- whose IEEE-754 representation cannot be the result of rounding any other integer to fit the IEEE-754 representation.
So 2^53
is not a safe integer because :
it can be exactly represented in IEEE-754, but the integer 2^53 + 1
can't be directly represented in IEEE-754 but instead rounds to 2^53
under round-to-nearest and round-to-zero rounding.