Peterbe.com

For some reason, I always forget how to do this. Tired of that. Let's blog about it so it sticks.

To format a number with thousand-commas you do:

>>> n = 1234567
>>> f"{n:,}"
'1,234,567'

To add whitespace to a string you do:

>>> name="peter"
>>> f"{name:<20}"
'peter               '

How to combine these in one expression, you do:

>>> n = 1234567
>>> f"{n:<15,}"
'1,234,567      '

Officially, I'm one day behind, but here's how you can calculate the value of π using the Leibniz formula.

Python

import math

sum = 0
estimate = 0
i = 0
epsilon = 0.0001
while abs(estimate - math.pi) > epsilon:
    sum += (-1) ** i / (2 * i + 1)
    estimate = sum * 4
    i += 1
print(
    f"After {i} iterations, the estimate is {estimate} and the real pi is {math.pi} "
    f"(difference of {abs(estimate - math.pi)})"
)

Outputs:

After 10000 iterations, the estimate is 3.1414926535900345 and the real pi is 3.141592653589793 (difference of 9.99999997586265e-05)

JavaScript

let sum = 0;
let estimate = 0;
let i = 0;
const epsilon = 0.0001;

while (Math.abs(estimate - Math.PI) > epsilon) {
  sum += (-1) ** i / (2 * i + 1);
  estimate = sum * 4;
  i += 1;
}
console.log(
  `After ${i} iterations, the estimate is ${estimate} and the real pi is ${Math.PI} ` +
    `(difference of ${Math.abs(estimate - Math.PI)})`
);

Outputs

After 10000 iterations, the estimate is 3.1414926535900345 and the real pi is 3.141592653589793 (difference of 0.0000999999997586265)

Ruby

sum = 0
estimate = 0
i = 0
epsilon = 0.0001
while (estimate - Math::PI).abs > epsilon
    sum += ((-1) ** i / (2.0 * i + 1))
    estimate = sum * 4
    i += 1
end
print(
    "After #{i} iterations, the estimate is #{estimate} and the real pi is #{Math::PI} "+
    "(difference of #{(estimate - Math::PI).abs})"
)

Outputs

After 10000 iterations, the estimate is 3.1414926535900345 and the real pi is 3.141592653589793 (difference of 9.99999997586265e-05)

Backwards

Technically, these little snippets are checking that it works since each language already has access to a value of π as a standard library constant.

If you don't have that, you can decide on a number of iterations, for example 1,000, and use that.

Python

sum = 0
for i in range(1000):
    sum += (-1) ** i / (2 * i + 1)
print(sum * 4)

JavaScript

let sum = 0;
for (const i of [...Array(10000).keys()]) {
  sum += (-1) ** i / (2 * i + 1);
}
console.log(sum * 4);

Ruby

sum = 0
for i in 0..10000
    sum += ((-1) ** i / (2.0 * i + 1))
end
puts sum * 4

Performance test

Perhaps a bit silly but also a fun thing to play with. Pull out hyperfine and compare Python 3.12, Node 20.11, Ruby 3.2, and Bun 1.0.30:

❯ hyperfine --warmup 10 "python3.12 ~/pi.py" "node ~/pi.js" "ruby ~/pi.rb" "bun run ~/pi.js"
Benchmark 1: python3.12 ~/pi.py
  Time (mean ± σ):      53.4 ms ±   7.5 ms    [User: 31.9 ms, System: 12.3 ms]
  Range (min … max):    41.5 ms …  64.8 ms    44 runs

Benchmark 2: node ~/pi.js
  Time (mean ± σ):      57.5 ms ±  10.6 ms    [User: 43.3 ms, System: 11.0 ms]
  Range (min … max):    46.2 ms …  82.6 ms    35 runs

Benchmark 3: ruby ~/pi.rb
  Time (mean ± σ):     242.1 ms ±  11.6 ms    [User: 68.4 ms, System: 37.2 ms]
  Range (min … max):   227.3 ms … 265.3 ms    11 runs

Benchmark 4: bun run ~/pi.js
  Time (mean ± σ):      32.9 ms ±   6.3 ms    [User: 14.1 ms, System: 10.0 ms]
  Range (min … max):    17.1 ms …  41.9 ms    60 runs

Summary
  bun run ~/pi.js ran
    1.62 ± 0.39 times faster than python3.12 ~/pi.py
    1.75 ± 0.46 times faster than node ~/pi.js
    7.35 ± 1.45 times faster than ruby ~/pi.rb

Comparing Pythons

Just because I have a couple of these installed:

❯ hyperfine --warmup 10 "python3.8 ~/pi.py" "python3.9 ~/pi.py" "python3.10 ~/pi.py" "python3.11 ~/pi.py" "python3.12 ~/pi.py"
Benchmark 1: python3.8 ~/pi.py
  Time (mean ± σ):      54.6 ms ±   8.1 ms    [User: 33.0 ms, System: 11.4 ms]
  Range (min … max):    40.0 ms …  69.7 ms    56 runs

Benchmark 2: python3.9 ~/pi.py
  Time (mean ± σ):      54.9 ms ±   8.0 ms    [User: 32.2 ms, System: 12.3 ms]
  Range (min … max):    42.3 ms …  70.1 ms    38 runs

Benchmark 3: python3.10 ~/pi.py
  Time (mean ± σ):      54.7 ms ±   7.5 ms    [User: 33.0 ms, System: 11.8 ms]
  Range (min … max):    42.3 ms …  78.1 ms    44 runs

Benchmark 4: python3.11 ~/pi.py
  Time (mean ± σ):      53.8 ms ±   6.0 ms    [User: 32.7 ms, System: 13.0 ms]
  Range (min … max):    44.8 ms …  70.3 ms    42 runs

Benchmark 5: python3.12 ~/pi.py
  Time (mean ± σ):      53.0 ms ±   6.4 ms    [User: 31.8 ms, System: 12.3 ms]
  Range (min … max):    43.8 ms …  63.5 ms    42 runs

Summary
  python3.12 ~/pi.py ran
    1.02 ± 0.17 times faster than python3.11 ~/pi.py
    1.03 ± 0.20 times faster than python3.8 ~/pi.py
    1.03 ± 0.19 times faster than python3.10 ~/pi.py
    1.04 ± 0.20 times faster than python3.9 ~/pi.py

Unfortunately, the app I ported from using the Pages Router to using App Router, is in a private repo. It's a Next.js static site SPA (Single Page App).

It's built with npm run build and then exported so that the out/ directory is the only thing I need to ship to the CDN and it just works. There's a home page and a few dynamic routes whose slugs depend on an SQL query. So the SQL (PostgreSQL) connection, using knex, has to be present when running npm run build.

In no particular order, let's look at some differences

Build times

With caching

After running next build a bunch of times, the rough averages are:

• Pages Router: 20.5 seconds
• App Router: 19.5 seconds

Without caching

After running rm -fr .next && next build a bunch of times, the rough averages are:

• Pages Router: 28.5 seconds
• App Router: 31 seconds

Note

I have another SPA app that is built with vite and wouter and uses the heavy mantine for the UI library. That SPA app does a LOT more in terms of components and pages etc. That one takes 9 seconds on average.

Static output

If you compare the generated out/_next/static/chunks there's a strange difference.

Pages Router

360.0 KiB [##########################] /pages
268.0 KiB [###################       ]  726-4194baf1eea221e4.js
160.0 KiB [###########               ]  ee8b1517-76391449d3636b6f.js
140.0 KiB [##########                ]  framework-5429a50ba5373c56.js
112.0 KiB [########                  ]  cdfd8999-a1782664caeaab31.js
108.0 KiB [########                  ]  main-930135e47dff83e9.js
 92.0 KiB [######                    ]  polyfills-c67a75d1b6f99dc8.js
 16.0 KiB [#                         ]  502-394e1f5415200700.js
  8.0 KiB [                          ]  0e226fb0-147f1e5268512885.js
  4.0 KiB [                          ]  webpack-1b159842bd89504c.js

In total 1.2 MiB across 15 files.

App Router

428.0 KiB [##########################]  142-94b03af3aa9e6d6b.js
196.0 KiB [############              ]  975-62bfdeceb3fe8dd8.js
184.0 KiB [###########               ]  25-aa44907f6a6c25aa.js
172.0 KiB [##########                ]  fd9d1056-e15083df91b81b75.js
164.0 KiB [##########                ]  ca377847-82e8fe2d92176afa.js
140.0 KiB [########                  ]  framework-aec844d2ccbe7592.js
116.0 KiB [#######                   ]  a6eb9415-a86923c16860379a.js
112.0 KiB [#######                   ]  69-f28d58313be296c0.js
108.0 KiB [######                    ]  main-67e49f9e34a5900f.js
 92.0 KiB [#####                     ]  polyfills-c67a75d1b6f99dc8.js
 44.0 KiB [##                        ] /app
 24.0 KiB [#                         ]  1cc5f7f4-2f067a078d041167.js
 24.0 KiB [#                         ]  250-47a2e67f72854c46.js
  8.0 KiB [                          ] /pages
  4.0 KiB [                          ]  webpack-baa830a732d3dbbf.js
  4.0 KiB [                          ]  main-app-f6b391c808310b44.js

In total 1.7 MiB across 27 files.

Notes

What makes the JS bundle large is most certainly due to using @primer/react, @fullcalendar, and react-chartjs-2.
But why is the difference so large?

Dev start time

The way Next.js works, with npm run dev, is that it starts a server at localhost:3000 and only when you request a URL does it compile something. It's essentially lazy and that's a good thing because in a bigger app, you might have too many different entries so it'd be silly to wait for all of them to compile if you might not use them all.

Pages Router

❯ npm run dev

...

 ✓ Ready in 1125ms
 ○ Compiling / ...
 ✓ Compiled / in 2.9s (495 modules)

App Router

❯ npm run dev

...

 ✓ Ready in 1201ms
 ○ Compiling / ...
 ✓ Compiled / in 3.7s (1023 modules)

Mind you, it almost always says "Ready in 1201ms" or but the other number, like "3.7s" in this example, that seems to fluctuate quite wildly. I don't know why.

Conclusion

Was it worth it? Yes and no.

I've never liked next/router. With App Router you instead use next/navigation which feels much more refined and simple. The old next/router is still there which exposes a useRouter hook which is still used for doing push and replace.

The getStaticPaths and the getStaticProps were not really that terrible in Pages Router.

I think the whole point of App Router is that you can get external data not only in getStaticProps (or getServerSideProps) but you can more freely go and get external data in places like layout.tsx, which means less prop-drilling.

There are some nicer APIs with App Router. And it's the future of Next.js and how Vercel is pushing it forward.

Suppose you have a complex Django QuerySet query that is somewhat costly (in other words slow). And suppose you want to return:

1. The first N results
2. A count of the total possible results

So your implementation might be something like this:

def get_results(queryset, fields, size):
    count = queryset.count()
    results = []
    for record in queryset.values(*fields)[:size]
        results.append(record)
    return {"count": count, "results": results}

That'll work. If there are 1,234 rows in your database table that match those specific filters, what you might get back from this is:

>>> results = get_results(my_queryset, ("name", "age"), 5)
>>> results["count"]
1234
>>> len(results["results"])
5

Or, if the filters would only match 3 rows in your database table:

>>> results = get_results(my_queryset, ("name", "age"), 5)
>>> results["count"]
3
>>> len(results["results"])
3

Between your Python application and your database you'll see:

query 1: SELECT COUNT(*) FROM my_database WHERE ...
query 2: SELECT name, age FROM my_database WHERE ... LIMIT 5

The problem with this is that, in the latter case, you had to send two database queries when all you needed was one.
If you knew it would only match a tiny amount of records, you could do this:

def get_results(queryset, fields, size):
-   count = queryset.count()
    results = []
    for record in queryset.values(*fields)[:size]:
        results.append(record)
+   count = len(results)
    return {"count": count, "results": results}

But that is wrong. The count would max out at whatever the size is.

The solution is to try to avoid the potentially unnecessary .count() query.

def get_results(queryset, fields, size):
    count = 0
    results = []
    for i, record in enumerate(queryset.values(*fields)[: size + 1]):
        if i == size:
            # Alas, there are more records than the pagination
            count = queryset.count()
            break
        count = i + 1
        results.append(record)
    return {"count": count, "results": results}

This way, you only incur one database query when there wasn't that much to find, but if there was more than what the pagination called for, you have to incur that extra database query.

When you, in a Node program, use sharp to convert an image buffer to a WebP buffer, you have an option of effort. The higher the number the longer it takes but the image it produces is smaller on disk.

I wanted to put some realistic numbers for this, so I wrote a benchmark, run on my Intel MacbookPro.

The benchmark

It looks like this:

async function e6() {
  return await f("screenshot-1000.png", 6);
}
async function e5() {
  return await f("screenshot-1000.png", 5);
}
async function e4() {
  return await f("screenshot-1000.png", 4);
}
async function e3() {
  return await f("screenshot-1000.png", 3);
}
async function e2() {
  return await f("screenshot-1000.png", 2);
}
async function e1() {
  return await f("screenshot-1000.png", 1);
}
async function e0() {
  return await f("screenshot-1000.png", 0);
}

async function f(fp, effort) {
  const originalBuffer = await fs.readFile(fp);
  const image = sharp(originalBuffer);
  const { width } = await image.metadata();
  const buffer = await image.webp({ effort }).toBuffer();
  return [buffer.length, width, { effort }];
}

Then, I ran each function in serial and measured how long it took. Then, do that whole thing 15 times. So, in total, each function is executed 15 times. The numbers are collected and the median (P50) is reported.

A 2000x2000 pixel PNG image

1. e0: 191ms                   235KB
2. e1: 340.5ms                 208KB
3. e2: 369ms                   198KB
4. e3: 485.5ms                 193KB
5. e4: 587ms                   177KB
6. e5: 695.5ms                 177KB
7. e6: 4811.5ms                142KB

What it means is that if you use {effort: 6} the conversion of a 2000x2000 PNG took 4.8 seconds but the resulting WebP buffer became 142KB instead of the least effort which made it 235 KB.

This graph demonstrates how the (blue) time goes up the more effort you put in. And how the final size (red) goes down the more effort you put in.

A 1000x1000 pixel PNG image

1. e0: 54ms                    70KB
2. e1: 60ms                    66KB
3. e2: 65ms                    61KB
4. e3: 96ms                    59KB
5. e4: 169ms                   53KB
6. e5: 193ms                   53KB
7. e6: 1466ms                  51KB

A 500x500 pixel PNG image

1. e0: 24ms                    23KB
2. e1: 26ms                    21KB
3. e2: 28ms                    20KB
4. e3: 37ms                    19KB
5. e4: 57ms                    18KB
6. e5: 66ms                    18KB
7. e6: 556ms                   18KB

Conclusion

Up to you but clearly, {effort: 6} is to be avoided if you're worried about it taking a huge amount of time to make the conversion.

Perhaps the takeaway is; that if you run these operations in the build step such that you don't have to ever do it again, it's worth the maximum effort. Beyond that, find a sweet spot for your particular environment and challenge.