A Python implementation in Javascript for use by JSage
npm install @jsage/jpythonHistory: This is built from RapydScript-ng that I'm playing around withmodifying for use by the sagejs project. Seehttps://github.com/kovidgoyal/rapydscript-ng for some helpful documentation.
Some goals:
- Very lightweight: this should build from source in a few seconds, rather than a few hours like pypy. The architecture of jpython is similar to pypy on some level -- there is a JIT (coming from Javascript), and JPython is an implementation of "the Python language" in Python. I put that in quotes since we are definitely not going to implement something 100% compatible with Python.
- Math friendly: create something that feels similar to Sage with its preparser, i.e., support ^ for exponent, [a..b] for making range(a,b+1), and arbitrary precision integer and floating point numerical literals. However, instead of an adhoc preparser, we built this extra functionality into the language parser/AST/generator itself, i.e., we do it properly. Also, each sage-like piece of functionality can be enabled via an explicit import from __python__, similar to how official Python enables new functionality via imports.
- The main purpose of JPython is as an interactive REPL, Jupyter kernel (eventually), and language for writing small scripts and projects. It's probably (?) not meant to be the implementation language for _low_ _level_ parts of JSage, though maybe it will be for high level things (not sure). First and foremost, this provides a way to _use_ JSage on a random computer or in a web browser, which is much more lightweight than running Python itself via WASM. Having a language other than Javascript is necessary because Javascript is an _absolutely terrible language_ for interactive mathematics computations, e.g., it doesn't have operator overloading, and only has single inheritance. I love Javascript, but only for what Javascript is good for.
- Since JPython will be used for mathematical computations, speed is very important.
The directory bench/ has a collection of microbenchmarks which all run in Python3, pypy3, and JPython, so they are useful for comparing the performance of different Python implementations. These range from pystones to tests from mypy, computer language shootout, etc. and many others I found or made. Here's what the numbers are as of Nov 2021. Nothing is run in parallel, and in each case this is result of running [pypy3|python3|jpython] all.py in the bench directory. The timings hardly change if you rerun the benchmarks. We do not make any attempt to compensate for the JIT (e.g., by running a benchmark multiple times and taking the best result) -- we just run all the benchmarks one by one and add up the times.
pypy3: 3474 ms
jpython: 6434 ms
python3.9: 11872 ms
pypy3: 2902 ms
jpython: 2960 ms
python3.10: 6200ms
It's interesting that jpython and pypy3 are exactly the same speed on M1 overall for these benchmarks. This suggests that pypy3 is less optimized for aarch64, since pypy3 is only about twice as fast as python3.10, but is usually advertised as 4x faster. Anyway, who knows.
Please don't take the above numbers too seriously. It's trivial with any collection of benchmarks to play around with parameters in such a way to skew them to tell a certain tail, which is why some people call this "benchmarketing". That's NOT our goal here! The only point is that we can use microbenchmarks to identify areas for improvement in our implementation.
pypy3: 1659ms
jpython: 4728 ms
python3.8: 6005 ms
Notice that pypy3 is _much_ faster under Linux than MacOS on the exact same hardware. Strangely, Jpython is significantly slower under Linux than under MacOS. The node.js versions that are being used are identical, so this is kind of surprising.
Install into a temporary node.js directory:
``bash`
$ mkdir jsage # you can delete this later
$ cd jsage
$ npm init -y
$ npm install @jsage/jpython
Start up JPython and use some of the JSage functionality. Of course you could also
require any module you install from https://npmjs.com. You can also create .py files
and import them.
`python
$ npx jpython
Welcome to JPython. Using Node.js v16.9.0.
>>> s = range(10); s # this is the "Python language", not Node.js
range(0, 10)
>>> sum(s)
45
>>> list(reversed(list(s)))
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
>>> list(s)[-3:]
[7, 8, 9]
>>> d = require('@jsage/lib/modular/dims'); # WASM code written in ziglang.
>>> d.eulerPhi(100)
40
>>> %time d.dimensionCuspForms(1234567)
103699
Wall time: 2ms
>>> pari = require('@jsage/lib/pari'); # WASM pari with GMP built with 'zig cc'
>>> pari.init()
[object Promise]
>>> pari.exec('ellinit([1..5])') # returns string
[1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351, Vecsmall([1]), [Vecsmall([96, -1])], [0, 0, 0, 0, 0, 0, 0, 0]]
>>> an = eval(pari.exec("ellan(ellinit([1..5]), 50)")); an
[1, 1, 0, -1, -3, 0, -1, -3, -3, -3, -1, 0, 1, -1, 0, -1, 5, -3, 4, 3, 0, -1, -6, 0, 4, 1, 0, 1, -2, 0, 2, 5, 0, 5, 3, 3, 7, 4, 0, 9, 6, 0, 8, 1, 9, -6, 0, 0, -6, 4]
>>> an = eval(pari.exec("ellan(ellinit([1..5]), 10000)"));
>>> sum(an)/len(an)
0.152
>>> pari.exec("factor(2021)")
[43 1]
[47 1]
>>> a = pari.exec("B=10^4;an=ellan(ellinit([1..5]),B);sum(i=1,B,an[i])/B"); a
19/125
>>> eval(a)
0.152
`
Use jsage and the compiler is modified with some more
mathematics friendly syntax.
`python`
$ npx jsage
>>> 2^3
8
Right now only the notation [a..b] for ranges and caret for exponentiation (and
^^ for xor) is implemented. I might implement more, though maybe that's enough.
You can get the same effect in a .py file as follows:
`python`a.py
from __python__ import exponent
print(2^3)
`bash`
$ npx jpython a.py
8
You can also use the library functionality from node.js. However,
playing around with mathematics tends to be a lot more comfortable with the
Python _language_ than Javascript.
`js``
$ node
Welcome to Node.js v16.7.0.
Type ".help" for more information.
> d = require('@jsage/lib/modular/dims');null
null
> d.dimensionCuspForms(1234567)
103699
> pari = require('@jsage/lib/pari');pari.init(); null
null
> an = eval(pari.exec("ellan(ellinit([1..5]), 50)")); an
[
1, 1, 0, -1, -3, 0, -1, -3, -3, -3, -1,
0, 1, -1, 0, -1, 5, -3, 4, 3, 0, -1,
-6, 0, 4, 1, 0, 1, -2, 0, 2, 5, 0,
5, 3, 3, 7, 4, 0, 9, 6, 0, 8, 1,
9, -6, 0, 0, -6, 4
]
> an = eval(pari.exec("ellan(ellinit([1..5]), 10000)")); an.length
10000
> s=0;for(a of an) {s+=a}; s/an.length
0.152