Code katas for ivy, with solutions

[arl]

I'd be great if we could share code katas that are fun to solve with ivy, with the solutions possibly.

I'm gonna start with the obvious:

• Russ Cox solves most of advent of code 2021 with ivy

I'll update with a list of problems I had compiled for a work meetup of apl-like languages. In the meantime, please feel free to complete.

[fzipp]

Not a kata, but a port of this Fast Fourier Transform implementation:

op fft A =
	1 > (K=(N=count A)/2): A
	0 != (2 log N) mod 1: 'Length of the input vector must be a power of 2'
	odd  = fft (N rho 1 0) sel A
	even = fft (N rho 0 1) sel A
	T = even * ** 0j-2 * pi*(-1+iota K)/N
	(odd+T),odd-T

op ifft A = (conj fft conj A)/count A

The 2D FFT implementation:

op fft2d A =
	or/ 0 != (2 log rho A) mod 1: 'Matrix dimensions must be powers of 2'
	transp mix fft@ transp mix fft@ A

op ifft2d A = (conj fft2d conj A)/count flatten A

[tcolgate]

That fft is pretty awesome!

[robpike]

On line 2 of fft, we know that N is an integer, so a faster way to test it's a power of 2 is to see if n&n-1 is zero. I believe this is easier in ivy than in APL.

op isPow2 N = 0 == N & N-1

[robpike]

Yesterday I tried fizzbuzz. Here's the best I found, but I suspect there's a nicer solution to be found.

op fizzbuzz n = ((0==n mod 3) sel "Fizz"), (0==n mod 5) sel "Buzz"