Sometimes people are surprised by the results of floating-point calculations such as julia> 5/6 0.8333333333333334 # shouldn't the last digit be 3? julia> 2.6 - 0.7 - 1.9 2.220446049250313e-16 # shouldn't the answer be 0? These are not bugs in Julia. They’re consequenc…

Nice writeup! Perhaps you could add a brief mention to prevfloat and nextfloat: it would be then less surprising for a user to see that a number x is approximated by \tilde{x} if they can see that x \in [\mathrm{prevfloat}(\tilde{x}), \mathrm{nextfloat}(\tilde{x})]. And explain that this doesn’t h…

I think though you should make it clear when decimal floating point is critically important (i.e. for example with monetary calculations - in fact, there are even laws in the EU about how currency calculations should be done).

For example, the floating-point subtraction operation \ominus : F^2 \rightarrow F approximates - : \mathbb{R}^2 \rightarrow \mathbb{R} according to x \ominus y = (x - y)(1 + \epsilon) \text{ for some } \epsilon \text{ with } |\epsilon| < \epsilon_{m} This is true, but it would perhaps be more i…

Great writeup! Extending @giordano ’s suggestion about prevfloat and nextfloat, you could also mention other functions from Base.Math, eg significand and exponent, and perhaps use them in the examples that decompose the floats.

Thanks for these suggestions. I’ll incorporate them as soon as I can, just editing the original post. It’s so easy to illustrate how floats work when you can so easily swtich and compare different floating-point types (especially BigFloat) and dive into details with all the floating-point introspec…

Somewhat naive question: There is this horrible horrible x86 extended precision. Does julia ever use this? See e.g. http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/ , http://www.exploringbinary.com/why-volatile-fixes-the-2-2250738585072011e-308-bug/ . Is there anythi…

[image] foobar_lv2: I have never seen julia emit the 80 bit stuff; I guess it is never used, but I’d be happy about reassurance. No, on x86 we only use SSE instructions (80-bit floats are only available with x87 instructions). Note there are still some ways you might get non-deterministic re…

Thanks! I feel suitably reassured now.

[image] foobar_lv2: horrible horrible x86 extended precision I wouldn’t call it horrible. The article describes a bug in PHP, not in x87. As far as I’m concerned, 80 bits was a good idea, because better to have more bits. Of course, you need the language to support them correctly. By the way…

[image] apo383: I believe they were ultimately unsuccessful. I think for Java they successfully added support for 80-bit floats?! Anyway, for Julia, I was pretty sure there was a package adding such support, but I can’t track it down. It should be the fastest option for Intel compatible, of o…

PSA: floating-point arithmetic

Offtopic

Topic		Replies	Views
Why do simple arithmetics cause weird Precision bugs General Usage	10	438	September 10, 2024
Sum of float64 vector gives slightly incorrect answer Performance question	44	5522	April 29, 2019
Why 0.2+0.09 = 0.29000000000000004? New to Julia numbers	4	942	September 6, 2021
Why does Julia say 1/26=0.038461538461538464 New to Julia question	5	784	August 20, 2023
Computation precision with Float General Usage precision	8	2176	December 3, 2022

PSA: floating-point arithmetic

Related topics