On Sep 18, 2008, at 1:06 AM, Mark S. Miller wrote: > "apart from somthing like significance" is a huge new set of > exceptions. A large enough set that we can no longer understand === > as approximating operational equivalence. If instead we understand > === to be asking whether two operands are cohorts, and we define > cohorts to be those numeric values that exactly represent a given > real number, then > 1) -0 vs 0 is no longer irregular
0 and -0 are in different cohorts, thanks to MFC for making this clear (it seemed implied by past discussion of 1.5m, 1.50m, 1.500m, etc. all being in the same cohort -- no sign difference --but it's good to have clarity). > 2) We can explain why 1.5 === 1.5m === 1.5000m That's explained by cohorts in 754r. > 3) We can explain why 1.1 !== 1.1m. The alternative to real number projection is conversion with rounding, which is what people will actually run into when mixing modes. (I smell lots of bugs there, btw, but that's a separate topic.) The point here is that, for all practical meanings of "operational" that I can think of, and excluding the -0 vs. 0 issue (or non-issue -- it's been that way since ES1 and numerical analysts prefer it for subtle reasons), defining decimal and binary floating point equivalence based on projection idealizes away from the concrete operational semantics, as Maciej pointed out with 1.5m/10 vs. 1.5/10. Real numbers are wonderful (I mean this sincerely, in a Mathematical sense), but they're neither well-supported in ES or most languages and all hardware, nor well-understood by most programmers (IMHO). If we did make typeof 1.1m == "number" then I suspect we would break some current code that "knows" about IEEE-754 double (precision limits, e.g.). The safest course still seems to me to be typeof 1.1m == "decimal". /be _______________________________________________ Es-discuss mailing list Es-discuss@mozilla.org https://mail.mozilla.org/listinfo/es-discuss
