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. […]
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.
ua709 16 hours ago [-]
Totally agree but for calculations the rules can be a bit different because error can accumulate and computers add lots of numbers really quickly.
adampunk 22 hours ago [-]
>3.141592653589793
Use this for sin or cosine with large arguments and tell me how that goes!
ronin_niron 21 hours ago [-]
[dead]
9dev 1 days ago [-]
For a short moment I got excited he may have started again… this post needs a [2019] :-(
macintux 22 hours ago [-]
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.
9dev 21 hours ago [-]
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.
> 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...
Use this for sin or cosine with large arguments and tell me how that goes!
long double la0 = 0B.110101100P12L;