
14 Character Random Number Generator in C - orangeduck
http://theorangeduck.com/page/14-character-random-number-generator
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unwind
Cool, and even cooler that the idea is due to Knuth.

I found this typo entertaining:

 _Technically it could be replaced by any other large prime number. The most
important thing is that it must have few factors, and be large enough to
distribute information into the higher value bits when the integer overflows._

Surely any _prime_ number has "few factors", i.e. none other than itself and
1? I guess the "prime" in the first sentence is a typo, since the second
sentence reads as if the first one didn't say "prime".

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quinnftw
I noticed that too, I think he may be referring to the fact that generating
super large actual prime numbers is hard, so people use probabilistic
algorithms to generate probably almost primes

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Someone
This one isn't superlarge, by a wide shot. √2,654,435,761 = 51521.2166102, so
even an extremely naive trial division loop needs just over 50k trial
divisions.

I haven't benchmarked it, but I think that should easily run in under a second
on any phone sold in the last 10 years. If you do it a bit smarter and skip
even divisors, I think it could run in under a second on 30 year old hardware
(25k iterations, 200-ish cycles per loop (division was very expensive, back
then) takes a 5MHz CPU)

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mark-r
The problem wasn't in proving this particular number was prime, it was
_finding_ a large prime number to begin with. I don't know what the state of
the art was back in the day, but 32 bits would certainly have been too large
for the Sieve of Eratosthenes.

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Someone
No, it wasn’t. ln(2654435761) is about 22, so if you limit yourself to odd
numbers, about one in 11 attempts near that number will give you a prime.

At a generous one minute to prove primality of numbers in that range using
trial division, and assuming you forget to bail out early when you find the
first divisor, you still very likely will find a prime within an hour.

Even in the 70s, when computer time cost real money, that shouldn’t deter you.

(I just tried this on a Mac Mini, in Swift; finding 1000 primes took about a
third of a second; 3 seconds if I forget to bail out early)

Edit: as further evidence that this isn't that large a prime: we knew 2^31-1
to be prime by trial division in 1772 (Euler somehow found time to do that)

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FabHK
I'm glad that the author included a disclaimer: this is fine for generating
pleasing pictures, but should not be used for anything serious (such as
crypto, or even Monte Carlo simulations etc.)

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peff
[https://en.wikipedia.org/wiki/Linear_congruential_generator](https://en.wikipedia.org/wiki/Linear_congruential_generator)

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eutectic
A 15 character 64 to 32-bit generator I devised which passes dieharder:

    
    
        (x+=x*x+9)>>32;

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joegosse
Is dieharder considered as the industry standard tool for testing randomness?
Is it commonly used by experts?

[https://www.phy.duke.edu/~rgb/General/dieharder.php](https://www.phy.duke.edu/~rgb/General/dieharder.php)

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eutectic
Dieharder works OK, and you can easily install it on Ubuntu as a command-line
tool. PractRand and TestU01 are more stringent and give you more knobs to play
with.

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jcahill84
This is really elegant. It's always fun to find something artsy in code. We
often forget how important creativity is in software engineering.

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joegosse
Thank you for the writeup. What was the tool used to generate the .GIF of the
shell?

