Exposing Floating Point – Bartosz Ciechanowski (2019) | Hacker News Reader

Exposing Floating Point – Bartosz Ciechanowski (2019)

ciechanow.ski

87 pointssubset11 comments

Meta: with regards to significant digits, it may depend on application, but this article reminded me on NASA's 'take' on π (pi):

> To start, let me answer your question directly. For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793. Let's look at this a little more closely to understand why we don't use more decimal places. […]

> 3. Let's go to the largest size there is: the known universe. The radius of the universe is about 46 billion light years. Now let me ask (and answer!) a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, the simplest atom? It turns out that 37 decimal places (38 digits, including the number 3 to the left of the decimal point) would be quite sufficient. […]

* https://www.jpl.nasa.gov/edu/news/how-many-decimals-of-pi-do...

Digital precision quickly outstrips accuracy in any number of things - eg digital calipers that read down to the ten thousands of an inch on a device that isn’t accurate to a thousandth.

Totally agree but for calculations the rules can be a bit different because error can accumulate and computers add lots of numbers really quickly.

>3.141592653589793

Use this for sin or cosine with large arguments and tell me how that goes!

For a short moment I got excited he may have started again… this post needs a [2019] :-(

Fixed

Is there a reason to believe he’s stopped? The articles are clearly very labor/time-intensive, so the current lag isn’t all that unusual.

Well, Bartosz used to publish 1–5 articles per year, but hasn't published any this or last year. I assume he's just got other things to do in his life, which is absolutely fair and I'm grateful for every one of the articles we got gifted and all—but at the very least he is taking a pause right now.

tcc also supports a binary float extension. https://github.com/TinyCC/tinycc/blob/9b8765d8baaeb2a16112d6...

long double la0 = 0B.110101100P12L;

This website needs an update for the quantization techniques in DL.

here it is - https://ngrok.com/blog/quantization

Reply on news.ycombinator.com