[civility]

> JavaScript is precise for 2^53 range

What does this mean to you? It's very easy to get horrible rounding error with real-life sized things. For instance

    document.writeln(1.0 % 0.2);

The right answer is 0.0, and the most it can be wrong is 0.2. It's nearly as wrong as possible. These are real-life sized numbers.

btw: I think IEEE-754 is really great, but it's also important to understand your tools.

[tomxor]

> document.writeln(1.0 % 0.2);

> The right answer is 0.0, and the most it can be wrong is 0.2. It's nearly as wrong as possible.

Just to clarify for others, you're implicitly contriving that to mean: you care about the error being positive. The numerical error in 0.1 % 0.2 is actually fairly ordinarily tiny (on the order of x10^-17), but using modulo may create sensitivity to these tiny errors by introducing discontinuity where it matters.

[civility]

Call it a contrivance if you want, my point was just that you can get very surprising results even for "real life" sized numbers.

Not sure why you changed it from "1.0 % 0.2" to "0.1 % 0.2". The error on the one I showed was near 0.2, not 1e-17. Did I miss your point?

[tomxor]

I mistakenly used 0.1 instead of 1.0 but the _numerical_ error is still x10-17, the modulo is further introducing a discontinuity that creates sensitivity to that tiny numerical error, whether that is a problem depends on what you are doing with the result... 0.19999999999999996 is very close to 0 as far as modulo is concerned.

I'm not arguing against you just clarifying the difference between propagation of error into significant numerical error through something like compounding; and being sensitive to very tiny errors by to depending on discontinuities such as those introduced by modulo.

[vbezhenar]

I'm talking about integer numbers. 2^53 = 9007199254740992. You can do any arithmetic operations with any integer number from -9007199254740992 to 9007199254740992 and results will be correct. E.g. 9007199254740991 + 1 = 9007199254740992. But outside of that range there will be errors, e.g. 9007199254740992 + 1 = 9007199254740992

[tomxor]

You are are describing only one of the types of numerical error that can occur, and it is not commonly a problem: this is only an edge case that occurs at the significand limit where the exponent alone must be used to approximate larger magnitudes at which point integers become non-contiguous.

The types of errors being discussed by others are all in the realm of non-integer rationals where limitations in either precision or representation introduce error and then compound in operations no matter the order of magnitude... and btw _real_ life tends to contain _real_ numbers, that commonly includes rationals in use of IEEE 754.

[civility]

I didn't see anything in your message above indicating you were restricting yourself to integers.