motivation:
if (isSafeInteger(a) && isSafeInteger(b)) {
const c = a + b;
if (isSafeInteger(b)) {
// c is actually the sum of a and b
}
}
On Sun, May 6, 2018 at 10:57 AM, Logan Smyth <[email protected]> wrote:
> To clarify, the "you can still add one to them" is probably the most
> important part in that definition, given your question.
>
> > Anyway, this definition departs from similar definitions in other
> languages and AFAICT, existing JavaScript implementations have no problems
> using 2^53 as an integer.
>
> 2^53 can be represented just fine, but `2**53 + 1 === 2**53` is `true`, so
> adding one to it does not actually increment the value, meaning it does not
> satisfy the definition of `SAFE` in this context.
>
> I think the best source of truth is likely the spec: https://www.ecma-
> international.org/ecma-262/8.0/#sec-number.max_safe_integer which states
>
> > 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.
>
>
> On Sun, May 6, 2018 at 10:47 AM, Anders Rundgren <
> [email protected]> wrote:
>
>> On 2018-05-06 18:40, Isiah Meadows wrote:
>>
>>> Technically, "safe" in this context means "can you store this number
>>> *and all numbers below it* without loss of precision", and for every single
>>> one of these numbers, you can still add one to them. When you get up to
>>> 2^53, you can no longer add just 1 - you can only add 2 or more. This is
>>> based on the number of significand bits - 2^53 - 1 has all lower 53 bits
>>> set and its exponent set to 0 (ignoring bias). You can precisely store up
>>> to this number without having to adjust the exponent, no more. This is what
>>> is meant by "safe". (The terminology of "exactly representable" is a
>>> misnomer - the highest integer you can theoretically represent without loss
>>> of precision is `(2^53-1) * (2^971)`.)
>>>
>>
>> Thanx Isiah,
>> I (sort of) understand :-)
>>
>> Anyway, this definition departs from similar definitions in other
>> languages and AFAICT, existing JavaScript implementations have no problems
>> using 2^53 as an integer.
>>
>> > var t = 9007199254740992
>> < undefined
>> > t-1
>> < 9007199254740991
>> > t
>> < 9007199254740992
>>
>> For JavaScript this may be of limited importance but for (I-)JSON
>> canonicalization [1] it is vital that all parties do the same
>> interpretation.
>> That is, for I-JSON the 2^53-1 limitation is simply put wrong.
>>
>> Anders
>>
>> 1] https://github.com/cyberphone/json-canonicalization#json-can
>> onicalization
>>
>>
>>
>>> This SO answer should help explain the situation better:
>>> https://stackoverflow.com/a/1848762
>>>
>>>
>>> -----
>>>
>>> Isiah Meadows
>>> [email protected] <mailto:[email protected]>
>>> www.isiahmeadows.com <http://www.isiahmeadows.com>
>>>
>>> On Sun, May 6, 2018 at 11:58 AM, Anders Rundgren <
>>> [email protected] <mailto:[email protected]>>
>>> wrote:
>>>
>>> If you write
>>> Number.MAX_SAFE_INTEGER
>>> into a browser console it will return
>>> 9007199254740991
>>>
>>> I believe this is wrong, 9007199254740992 the largest correct safe
>>> integer using IEEE-754 double precision.
>>>
>>> Using my own IEEE-754 debugger:
>>>
>>> Input floating point: 9007199254740991
>>> Hex value: 433fffffffffffff
>>> Binary value: 0 10000110011 111111111111111111111111111111
>>> 1111111111111111111111
>>>
>>> Input floating point: 9007199254740992
>>> Hex value: 4340000000000000
>>> Binary value: 0 10000110100 000000000000000000000000000000
>>> 0000000000000000000000
>>>
>>> Using an external IEEE-754 debugger:
>>> http://www.binaryconvert.com/result_double.html?decimal=0570
>>> 48048055049057057050053052055052048057057050 <
>>> http://www.binaryconvert.com/result_double.html?decimal=057
>>> 048048055049057057050053052055052048057057050>
>>>
>>> Anders
>>> _______________________________________________
>>> es-discuss mailing list
>>> [email protected] <mailto:[email protected]>
>>> https://mail.mozilla.org/listinfo/es-discuss <
>>> https://mail.mozilla.org/listinfo/es-discuss>
>>>
>>>
>>>
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>
>
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>
--
Cheers,
--MarkM
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