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)`.)
This SO answer should help explain the situation better: https://stackoverflow.com/a/1848762 ----- Isiah Meadows m...@isiahmeadows.com www.isiahmeadows.com On Sun, May 6, 2018 at 11:58 AM, Anders Rundgren < anders.rundgren....@gmail.com> 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 > > Anders > _______________________________________________ > es-discuss mailing list > es-discuss@mozilla.org > https://mail.mozilla.org/listinfo/es-discuss >
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