libtorsion VS CPython

Most of the crypto is from my more general crypto library libtorsion: https://github.com/bcoin-org/libtorsion

I originally wanted to vendor my libtorsion code and link to it, but it felt clunky since libtorsion pulls in a ton of crypto that bitcoin doesn't need. Also, since I was focusing on just a few algorithms, it gave me the opportunity to optimize a lot of them (in particular, the ECC backend was optimized for secp256k1 whereas in libtorsion it supports all kinds of curves).

Because of all of this, there's probably some leftover comments. That comment isn't true anymore. rand.c is definitely used internally for libmako, just not libtorsion.

edit: fixed link.

The 2-by-1 and 3-by-2 division functions described in the paper result in a very measurable speedup in my code. I think you're confusing those with the reciprocal calculation itself (which can be computed with a lookup table). I agree that part doesn't really lend itself to any significant performance benefit and is probably better calculated with a single hardware division instead.

I feel it necessary to point out that the 3-by-2 division actually has multiple benefits which are easy to miss:

1. The quotient loop can be skipped as I mentioned.

2. The "Add back" step is less likely to be triggered.

3. Since a 2-word remainder is computed with the division, you can skip 2 iterations on the multiply+subtract step.

My reimplementation of GMP documents both the 2-by-1 and 3-by-2 divisions pretty thoroughly[1][2].

[1] https://github.com/bcoin-org/libtorsion/blob/master/src/mpi....

[2] https://github.com/bcoin-org/libtorsion/blob/master/src/mpi....

Thankfully, Python, the go-to coding language for loads of developers, is here to save the day. It's got some awesome features for diving into text sentiment analysis. With cool libraries like Tweepy, we can sift through X(Twitter) data and snag those interesting tweets about Bitcoin. And then there's TextBlob, a clever tool for understanding the sentiment in text. When it's time to clean up and organize all that data, libraries like pandas and numpy are there to help out. And let's not forget about matplotlib, the master of visualisations that can help us see the trends in sentiment crystal clear. Armed with these tools, developers can really dig deep into social media data and figure out what the general public thinks about Bitcoin.

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> It provides a meaningful performance improvement for at least one popular platform (realistically, on the order of 5%).

At first it will not provide a large boost, but it will set the foundations for larger gains in subsequent releases. They link a list of some proposed improvements already underway, with improvement estimates, at https://github.com/python/cpython/issues/115802

After that, with the basics of software engineering understood, I would move on to a wider use language, with a bigger ecosystem to employ, most likely Python. This would expose me to large system design / distributed systems and architectural challenges...

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