Re: eq vs ==

[moritz]

I think the difference that confuses you is that some numbers can be represented by floating points without any error, while others can't. For example 0.1 is an infinite fraction in the binary system.

So while you can safely compare 0.5 * 2.0 == 1.0, you can't safely compare 0.1 * 2.0 == 0.2 (the former is true, the latter false).

The correct way to compare floating point numbers is

if (abs($x-$y) < $epsilon) {...}

Where $epsilon is a small number.

[LanX]

The correct way to compare floating point numbers is ...

Moritz, in general that's problematic.

The calculation error doubles with every calculation step, no matter how big epsilon is, you can construct a counterexample, where your rule breaks.

Consequently you have to limit the numbers of calculations before you can tell which epsilon is save!

IMHO that's a ridiculous big effort compared to the normal possibility to stay integer right away by multiplicating the fractions away.

532.2 - 23.2 
 
=>
 
5232 - 232 = 5000 
 
=> 500.0

[moritz]

The calculation error doubles with every calculation step, no matter how big epsilon is, you can construct a counterexample, where your rule breaks.

The error only doubles with every step if your algorithm is numerically badly conditioned.

For usual non-numeric calculations such errors tend to stay very small, unless you do things like substracting two numbers of nearly the same size, and dividing by the result.

If you do numerics, you should inform yourself in more detail about floating point arithmetics and error propagation (a standard subject in applied mathematics).

IMHO that's a ridiculous big effort compared to the normal possibility to stay integer right away by multiplicating the fractions away.

That might be true for literal constants, but when you read several numbers from user input, it gets very quickly very tedious to track the smallest possible multiplier, and outright stops working if you need to divide by a user-supplied number.

Another solution is to use a data type which stores numerator and denominator separately as integers, as Perl 6 does.

[LanX]

If you do numerics, you should inform yourself in more detail about floating point arithmetics and error propagation (a standard subject in applied mathematics).

Moritz it's first year computer science...

[oha]

i would say that the correct way to compare use == with floating numbers is to not use floating numbers.

Update: as moritz said, i've wrongly used "compare" instead of "use =="

[moritz]

Would you care to explain how you would do that, in the general case?

For example in one of my programs I have a few matrices in which I put parameters, solve some equation systems and in the end I calculate a trace over some of these matrices, and as a result I get another matrix. In that final matrix the sum over all rows and all columns should be equal, modulo numeric errors.

How would I compare (or even compute) these sums without using or comparing floating point numbers?

[oha]

not using float or not compare ==.

(or using abs($x-$y) < $epsilon as you already shown which is not the compare anyway)

I know my position is a bit strong, but using == on floats is going to make troubles, which depends on values, host, compiler, libc and so on. very hard to predict and replicate.

maybe a nice gift would be to have a warning?

Update: ops! i've replied to my node instead of moritz's 806454.