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-canonicalization
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 1111111111111111111111111111111111111111111111111111 Input floating point: 9007199254740992 Hex value: 4340000000000000 Binary value: 0 10000110100 0000000000000000000000000000000000000000000000000000 Using an external IEEE-754 debugger: http://www.binaryconvert.com/result_double.html?decimal=057048048055049057057050053052055052048057057050 <http://www.binaryconvert.com/result_double.html?decimal=057048048055049057057050053052055052048057057050> Anders _______________________________________________ es-discuss mailing list [email protected] <mailto:[email protected]> https://mail.mozilla.org/listinfo/es-discuss <https://mail.mozilla.org/listinfo/es-discuss>
_______________________________________________ es-discuss mailing list [email protected] https://mail.mozilla.org/listinfo/es-discuss
