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Did you read the entire article? The author says that floating point math is both 1) fine 2) not the cause of the issue under discussion. Floating point is a tiny digression in a much larger piece.

> Floating point arithmetic might be weird, but it’s very consistent and well-specified: the IEEE 754 specification is rigorously implemented. So it’s not arithmetic...

actually I did get bored about half way through . .

Your edit is basically what the article talks about, not what you ragged on it for.

I'm ragging on it for its banality.

"ragging". My favorite 80's term.

It's not floating point's fault exactly. Seems to me it's that these implementations are less accurate than the number of digits they're returning. You could get a similar thing with fixed point arithmetic.

> We've been computing these functions for over 60 years electronically (and longer analog), and I guarantee there is an implementation that fits your constraints.

TLDR; Math keeps changing because Javascript's spec is weak. Users almost always want the most accurate, most stable and most reliable answer by default. It's the principle of least surprise.

While I mostly agree with your comment (and upvoted you), I think the main problem the author runs into is that Javascript's Math library is underspecified in a bad way. The trig functions have precision that is really only held up by Web Reality, meaning the least precision that the bulk of websites can function under before something breaks and someone starts complaining.

I saw this firsthand. I worked on V8 during the time a number of precision-altering changes were made to its implementation of Math.*. Some had to be reverted because websites did indeed misbehave. I could claim it "wasn't our fault" because we were legally allowed to do so according to the spec....but not sure I want to own that ;-)

Compare this to e.g. Java, which specifies that all math functions in its standard library are accurate to 1up. They absolutely should give you bit-accurate results on every implementation.

So how would you calculate the sine function? Exactly how?

> Exactly how?

Are you being sarcastic?

EDIT: Assuming you aren't being sarcastic, you clearly aren't thinking like an engineer. As the OP points out, there are many ways to compute sine. And they all have tradeoffs. So you need to decide what tradeoffs describe your constraints. Otherwise you can simply use an infinite series. See, you didn't define what you meant by "exactly". Exactly to infinite precision? Or exactly in 100 clock cycles?

The point of the article is that the fine details of the calculation of transcendetal functions often change between javascript versions. The standards committee -- possibly deliberately -- didn't pin them down tightly.

I'll repeat once again: do your engineering homework and decide if you can live with a spec that changes the Nth digit of precision, or if you need more precision roll your own. If you're just making an SVG rotate, then why are you arguing?

The Nth digit in this case is digit 0, as the article points out. You're interpreting it as the usual "floating point is inaccurate" article/conversation instead of what it actually is - a surprising detail in the ECMAScript standard.

It absolutely is filed under "FP is inaccurate".

If you need increased precision beyond a few digits, you must approach the problem armed with numerical computation knowledge and not rely on libraries or generic implementations: even between versions.

It's not a surprise, its why the Numerical Recipes books are so famous. (Heck it's even discussed in Abrash's Graphics Programming Book!)

I guess this article is more valuable that I expected: it is exposing some really glaring flaws in what people expect from their underlying language. Kinda scary, but I guess it is better late then never to learn the basics.

How is it filed under "FP is inaccurate" if it can be fixed by choice of algorithm and is about algorithms changing? Would be true of fixed point as well.

Also it's generally considered poor form to continually talk about people needing to learn the basics/go to school/think like an engineer on HN - generally the focus here is on the content not on how you view the author/readers.

Is it surprising? What languages specify the exact result of mathematical functions?

E.g. java.lang.Math spends a lot of time defining the required accuracy of functions https://docs.oracle.com/javase/7/docs/api/java/lang/Math.htm...

Using a Taylor series, usually.