/sci/ - Science & Math » Thread #11099584

277KiB, 658x1050, 2019-10-28 19.51.23.png

View Same Google iqdb SauceNAO

Anonymous Mon 28 Oct 19:01:45 2019 No.11099584 View Reply Original Report

Quoted By: >>11099629 >>11099633 >>11101665

Let's say someone hands you this sheet of paper and a pen and asks you to find $\sin 9.6$ (that's 9.6 radians), can you do it easily?

I made this table and I'm wondering if it makes sense to anyone else as I'm preparing a video about using polynomial lookup tables.

Anonymous

Anonymous Mon 28 Oct 2019 19:04:09 No.11099587 Report

Quoted By:

>can you do it easily
Yes. Pull out my phone, open the calculator and calculate it.

Anonymous

Anonymous Mon 28 Oct 2019 19:04:31 No.11099591 Report

Quoted By: >>11099595

Why not just use a calculator?

Anonymous

Anonymous Mon 28 Oct 2019 19:06:04 No.11099595 Report

Quoted By: >>11099635

>>11099591
I want to explain how to use polynomial lookup tables for high speed number crunching on a computer, but I thought that it would be more interesting and understandable to explain how people can use that approach manually with a one page table.

Anonymous

Anonymous Mon 28 Oct 2019 19:23:21 No.11099629 Report

Quoted By: >>11099651

>>11099584
no. does that mean i'm retarded?
please enlighten

Anonymous

Anonymous Mon 28 Oct 2019 19:25:50 No.11099633 Report

Quoted By: >>11099651 >>11099666

>>11099584
Divide by 2pi to get
1.52788745368 revolutions
same as
0.52788745368 revolutions

sin(0.52788745368 revolutions) = cos (0.25 - 0.52788745368 revolutions) = cos(-0.27788745368 revolutions) = cos(0.27788745368 revolutions)

Look up the coefficients in your table for 0.28

4.30562x^2 -8.585313x + 1.878947

-0.17431760541550934

Alternative solution:
subtract 3pi (remember to negate answer later since odd) to get 0.1752220392306203
Compute -(a - a*a*a / 6)
-0.17432540577253602

Anonymous

Anonymous Mon 28 Oct 2019 19:26:20 No.11099635 Report

Quoted By: >>11099651

>>11099595
>lookup tables
why not just make a sin table?

Anonymous

Anonymous Mon 28 Oct 2019 19:33:18 No.11099651 Report

Quoted By: >>11099665

>>11099629
well, if you start with radius you could multiply by 0.159154943 to convert to turns. If it's sin you want instead of cos then you need to add 0.75 turns. Then discard the integer part of the number, this makes $x$ and find the line in the table that starts with the two first digits, and do the quadratic polynomial.

>>11099633
based, but wait, what is that alternative solution?

>>11099635
With cos instead of sin I can discard the sign of $x$ from the start and not have to remember what it originally was at the end. The table covers all 4 quadrants so this keeps it rather simple and fast. And since all it takes is +0.75 to use sin it's fine this way.

Anonymous

Anonymous Mon 28 Oct 2019 19:39:36 No.11099665 Report

Quoted By: >>11099670 >>11099691

>>11099651
That's taylor expansion of order 3 around 0

Anonymous

Anonymous Mon 28 Oct 2019 19:39:44 No.11099666 Report

Quoted By:

>>11099633
wait actually there's a slight mistake, but that's because I didn't explain it. The range that each polynomial covers is from the indicated number until the next. so if $x$ is 0.27788.. you'd look at the coefficients at .27. If you pick those at .28 it works too but is a bit less precise.

Anonymous

Anonymous Mon 28 Oct 2019 19:40:59 No.11099670 Report

Quoted By:

>>11099665
It's not, it's a quadratic fit for each range of 0.01 units

Anonymous

Anonymous Mon 28 Oct 2019 19:48:39 No.11099691 Report

Quoted By:

>>11099665
Ah I see, thanks. I guess it's not super precise though (my quadratic table is all within about 1.5e-6, you should see my quintic table).

Anonymous

Anonymous Tue 29 Oct 2019 07:22:32 No.11101665 Report

Quoted By: >>11101694

>>11099584
Not at all. I don't have pi memorized to any significant degree nor do I feel comfortable squaring 6 decimal places in my head. Literally not a good analogy for speedy computation.

Anonymous

Anonymous Tue 29 Oct 2019 07:47:18 No.11101694 Report

Quoted By:

>>11101665
>squaring
you don't need squaring, you do (c2*x + c1)*x + c0, and it's more precise than doing it the naive way, besides squaring is just a multiplication so I don't see the problem. The whole thing is literally two multiplications and two additions, plus another multiplication for converting to from radians/degrees to turns and a small addition for sin to cos.

>not a good analogy for speedy computation.
That's not even an analogy, that's exactly how my actual computer algorithms do it except more suited for base 2 than base 10. Try to find a faster/simpler algorithm for computing sin or cos with that degree of accuracy (about 1.5e-6), protip, you can't.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches