Solving the Primes to ONE TRILLION on the desktop! Plus PDP-11 vs Threadripper tested! 

"Much to the dismay of the 11 people on earth..." Goody, I'm one of the 11?

"Incontrovertible mathematical proof that sometimes procrastination IS the valid choice" - AMEN! Thanks for the great vid as always!

16:50 Sometimes, procrastination is the valid choice... gold lol!

I was writing a flight sim on a pdp -11/70 in the early 80’s and remember thinking if it were only 100x faster then I could be happy for the rest of my life. If you had told me I could buy a machine 2Million x faster with 1million times the memory in 40 years I would have fallen out of my chair. How lucky are we to have lived during this time in history.

"I don't think you have the monitor for it." I actually LOL'ed at that one. I had almost as much fun watching this as Dave had in making it. Thanks!

"640K should be enough for everyone" - Dave throwing shade at his former employer 😂😂

You are a son of a gun! You keep doing vids of things that I have no business needing to know, but can't help Wanting to know!! Keep 'em coming 🙂 and keep enjoying yourself. 🙂

10:36 I just want everyone to stop and take a moment to appreciate how pleasing the right-edge alignment is on the sieve program.

"And there you have it, incontrovertible mathematical proof that some times procrastination is the valid choice." For years, I have said that if one wishes to truly master procrastination one must start early. There are also many different phases of procrastination, starting with protocrastination, then eventually achieving preprocrastination, then finally taking one's crastination skills to the professional level.

You can exploit a pattern in the primes to reduce the sieve size and search space, and simultaneously decrease the runtime. Primes > 2 can be expressed in the form 2k + 1, reducing the sieve size to n/2 bytes Primes > 3 can be expressed in the form 6k + {1,5}, reducing the sieve size to n/3 bytes Primes > 5 can be expressed in the form 30k + {1,7,11,13,17,19,23,29}, reducing the sieve size to n/30 bytes Primes > 7 can be expressed in the form 210k + {one of 48 offsets}, reducing the sieve size to n/35 bytes Primes > 11 can be expressed in the form 2310k + {one of 480 offsets}, reducing the sieve size to n/38.5 bytes Primes > 13 can be expressed in the form 30030k + {one of 5760 offsets}, reducing the sieve size to n/41.7 bytes Primes > 17 can be expressed in the form 510510k + {one of 92160 offsets}, reducing the sieve size to n/44.3 bytes. In fact, for every prime, there's a corresponding expression for further reducing the memory requirement. I use the 30k rule in my own high-performance sieve, and exploit the fact that there are exactly eight offsets to check, as this (being a power of 2) makes a further optimization possible.

OMG. 32005. That number grabbed my brain. Now, an hour or so later, I figured out why! It was the designation code (I forget the actual terminology) of the ship I served on when I was in the Navy and I typed and read that code every day! Wow. Small world.

it's so nice to see all these DEC systems that I used in the past. My time at DEC was some of the best years of my career.

"A few years back".. the physically hurts me how quickly it's gone.

I just discovered your channel and I love the vintage vs. modern hardware, ASM and K&R C, and your insider's explanation of retro code. Thank you for promoting autism awareness. I hope people appreciate two examples of programming economy in the line (for j=i*i; j

My heart sank when you said we were not going to code walk the PDP11 assembly code.....

You've explained the prime algorithm 10 times better than my college programming teacher back in 2000's, and yes, we had to do it in assembly, pascal and C, as every task given.

In my college days we got a FORTRAN assignment to calculate factorials. The size of results quickly blew out the integer value limit on our DEC-10. Solving this was the true intent of the assignment. Storing one digit per integer and writing our own math routines was the order of the day. And so many people completed the 100! challenge. But this wasn't good enough for me. I wrote a nice assembly program that packed nine decimal digits per 36 bit word. 1000! was mine. But they came out and yelled at me for bogging down the entire system for those few minutes. I'd do it again.

"From Ada to Zig". I'm so happy Zig exists now. I like how it handles errors as values but for some reason this is more important.

I was hoping for the P-11 assembly code. I had a class where the teacher made us emulate a PDP-8 . We could use any language and I choose Pascal. I then made a C, C++, Java, JavaScript, C# and a few other versions.

16:28 "It would be a third done.......already" 😂 Loved the inclusion of the word "already", tongue in cheek humour......

I'd love an Assembly deep dive, please!

So now we have "Dave's Law" or otherwise know as how to justify your Procrastination to a manager or spouse. Again terrific content.

Thanks Dave! - I liked this as soon as I saw the vt220. Love the font as well

Yup one of my favorite RU-vidrs. This guy and Asianometry and Wristwatch Revival, Inheritance Maching, Sreetips...

I'm NOT procrastinating... I'm planning for the future!

Thanks, Dave, for providing so much information and putting a smile on my face for 17 minutes!

ROFL!! Love the conclusion!! OMG. Best justification ever!

At certain points I asked my self, "Why-O-why am I watching this?", but Dave came good with a verbal version of the tee-shirt I keep on meaning to create which reads "Procrastinate Now!" printed on it.

Procrastinating is definitely an option. I wrote a piece of music back in 1992that required me to process samples in order to realize the piece. Essentially working at encoding surround sound on a per sample basis. I had the venerable Mac LC 485 at the time. After processing the first sample, I went back to my prof and told him that realisation on the piece would have to wait until 2018, or until computers got faster . I finally realized the piece in 2014 with a Duo core realizing the piece in real time. 😅

I always knew procrastination was the right choice, now I have proof. Thanks!

Love these PDP11 videos, throw back to my first job selling time on a pair of PDP11s with washing machine disks running RSTS/E in the mid 80s...

Hope to see much more of the PDP-11s in future videos. Most existing YoutTube content focuses on history and not active use.

I love your final conclusions! Sometimes it's wiser to let technology catch up to match the magnitude of the problem you're trying to solve.

As someone who was unable to figure out an algorithm to multiply two numbers in assembler (I kept running out room in the stack, plus I was quite sleep deprived as that module took place during the drama club's production of Guys and Dolls for which I did props -- yeah that tanked my CompSci100 marks) and whose Fortran was definitely better, I am in awe at your mad skillz.

In the macro-11 code, why not use a SOB instruction (subtract one branch nz) for the init zero loop? You wouldn't then need to use R2, just SOB R1, INITL. If BSIZE is even, then why not CLR instead of CLRB with a loop of BSIZE / 2 iters?

I am dismayed that you did not do a detailed walk through of the assembly :) (maybe there are more than 11 of us lol ) love you content, thanks for sharing

I took a course in college called Number Theory. That class instilled in me a healthy love for Prime numbers.

I made another entry of the 1..100 sieve with a Bic pencil and a piece of paper and wound up with an impressive 3 minutes and 22 seconds. It is a valid entry : I didn't cheat with a ruler and used 0's and 1's, following the algorithm 100% and I used a 53-year old machine. So I think I should be on the ranking table.

Thank you for the pointers to the font and 'Cool Retro Terminal' app for MacOS.

Great entertainment, thanks! This reminds me of my undergraduate work, about fifty years back, with the university's DEC-10. We had just changed from cards to terminals. When I entered a huge formula into my terminal, the system crashed. Now, I wish that I had tried a second time to determine if I really was the root cause of the crash.

hi dave, i consider myself as one of the eleven people that would enjoy the assembly walkthrough video

Count me as one of the 11 people. I did a fair amount of machine language coding on z-80 machines back in the day. It was the only way to get stuff to run really fast. I would be curious as to how that experience compares to the PDP-11. Charlie in Virginia

Thanks! I enjoyed that video, interesting to see where we’ve come with processing over the years.

I'm 5 years into my software development career. Struggling to still find the magic in programming. Dude I swear your videos make me so happy. They remind me how fun and playful computer science can be. I genuinely hope to be like you after I retire

That's great! I used PDP computers in college, and at my first job we had a microvax cluster and a unix system with a couple of 68020 single board computers. It was clear even then that the 68k processors were superior, and they kept getting faster. DEC tried to sell us an upgrade to an Alpha server, but by then no one wanted a mini computer. the SBC and PC machines were cheaper and we knew they'd just keep getting faster.

The RAM limit is why I wanted to go with disk storage. But it would take some thought to optimize the reads and writes to reduce the overhead of using the disk. Even with today's NVME drives, there would still be some overhead, just not as much. My first prime sieves were run on an original Atari 400. I had a Tandy PC-1 pocket computer, but with about 1200 bytes of RAM usable, I didn't see the point in even attempting a sieve on it. A point on the 386SX, that's only got a 16 bit path to the RAM, so a 386DX at the same speed should be almost twice as fast. With today's processors, you could pass off to extra threads, and really accelerate the process. Processors have come a long way in the last 45 years, from a few hundred kilohertz to several gigahertz. I remember being amazed by the results of freezing an 8088 and clocking it up over 20MHz.

For primes up to 120, you don’t need to remove multiples of 11. For primes up to n, you only need to test primes strictly less than sqrt(n+1) or alternatively

Now imagine hitting all 96 cores simultaneously on the Threadripper. The performance upliftment obviously wound't scale 1:1 but it's still crazy to think about that the real difference in performance improvement over PDP-11 and 386SX can be another order of magnitude greater.

If you are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} any of these years old we would say you're in the prime of your life.

I am one of the 11, and i could understand just about all the terminology you used. I could program in 6502, 8086 and DEC10 assembly, but migrated onto C and then IBM AS400 and Oracle and unix etc....

Beautiful log scale in that last graph!

Thanks Dave, I would have never dreamed the Thread Ripper was going to be that much faster then the PDP-11/34.

50 years of tech evolution

Thanks for putting together this informative video, Dave! 🌟

Looked at the Primes Project. As a dane, i',m happy to see, that the good old danish Comal80 is represented, invented by Børge Christensen a teacher of high school. Not many today knows about this old programming language. My first teaching of programming, was in this language, on a likewise danish computer named Piccoline, made by danish Regne Centralen (RC), a computer system build around the Intel 80186 CPU. I very like, when you Dave, puzzle with old hardware. I like to see (and learn) what was before, what we have today. Keep up the good work.

Thanks Dave.

I want a detailed run through of the MACRO-11 ASM code! Maybe as a supplemental video?

Twelve. I was liaison to a company that we bought automated warehouses, including automated material handling carts which followed segmented wires embedded in floor. All of it was controlled by a PDP-11/44 running inventory control and master dispatching (actually two, backup system kept in sync, with God's own A/B switch to manually switch primary (active) system. PDP-11/23 was used for control of carts, using wiring as radio antenna. All code was developed in MACRO-11. Yep, inventory database manager was in MACRO-11, cart and automated crane dispatching in MACRO-11, reporting in MACRO-11, operator display (VT-100s) handling in MACRO-11. It was gloriously fun!

It's so funny to see that KR C used to specify types separately in functions 😅

Hmmm, I wonder why it said "Prime validator :FAIL" at 10:59...

Your VT220 term is missing the curved glare of the glass screen AND the screen burn-in from the electrons hitting the phosphor coating! Oh, and love the conclusion! Procrastination. I think I'll just wait.

Brilliant - Uncle Dave can write Assembly easier than C for older machines 👏

cool episode man. thanks!

I would try to go non-variadic though... probably... I dunno. Love the video and You, Dave! thx so much for uploading all this cool stuff.

I love it. I have tried the two assembly examples with my PiDP11 and would love to see a walkthrough of that code as I had a couple of hiccups.

Dave, man, I love hearing a true programmer who still understands the value of a C bitmask. I deal with developers who barely comprehend the word. As a K&R C guy from college and someobe who grew up on UNIX, MS-DOS, and even QuickC, I think I'd have loved working with you and your teams had I that chance back in the day. Love your channel and this video in particular.

Great video Dave! Always fun to see how these older machines used to work! Perhaps I need look for an emulator for the PDP11

entertaining as always. Procrastination finally proven to be the best approach.

The Fortran programs I worked on for a PDP 11 in 1983 communicated over serial ports. The serial port code was written in assembler.

When Dave explains anything it is like listening to poetry.

The Mach 10! You’re the only other person I’m aware of who has one. 😂 love this episode

Nice programming Dave. More than your programming skill, I love how readable and literate your code is. It may seem pedantic, but I have worked with many brilliant programmers whose code is garbage due to being completely unmaintainable.

The next logical test would be to run the sieve against GPUs and NPUs, since they focus floating point and integer based calculations in parallel.

Of course knowing that it would take decades, the program could be structured to write the current state of the sieve to disk when prompted so it can be transfered to new hardware every few years as upgrades become availible. (Assuming the algorithm output is desired for somthing other than a benchmark, and if the algorithm is the most efficient known for the task. I know there are faster algorithms than the sieve if primes were the only purpose.)

Some of your best ever one-liners Dave 😂

Infinity procrastination achieved, best not to start at all and go fishing instead.

The visual here is really helpful. Cool. I see you algorithm without reading it.

Very cool and fun!! Question: Why in some cases does Prime Validator say PASS and others times it says FAIL?? Thanks for sharing

Happy (prime?) birthday and thanks you for the content,

Finally... an empirical evidence that procrastination is the right choice! Thank you Dave!! :)

This was funny.. I need to write the part about procrastination!

🤣 "procrastination is the best choice" you killing me 🤣.. Mythical Man Month stuff here... you the best

brilliant

I used to cross assemble around 8k of microprocessor code on a pdp11/34 under rsx-11m. I was allowed ONE assemble per DAY. Each assembler run took AGES. You soon made sure that any code you submitted had a 99% chance of working!

It’s always fun to see the ping-ponging of projects between developers isn’t anything new

“So the code will look a little retro”. Just like me. 😂 (And some of my code. I still have my copy of K&R somewhere…)

The naive implementation of the sieve algorithm is inefficient in modern hardware. That's because since it's going linearly through the entire enormous bit array again and again, it's constantly causing cache misses. The worst case is when the bit array is larger than even the outermost L3 cache, in which case each pass will cause one or more worst-case-scenario cache misses. The exact same algorithm can be implemented in a more cache-friendly manner: Rather than going through the entire bit array, marking multiples of the current prime, instead you do it in segments: Select a segment size that's slightly smaller than the size of L1 cache, and mark each segment fully before going to the next segment. This maximizes the work done on the L1 cache and, thus, minimizes the number of cache misses. The speed difference is not inconsequential. You can easily double, triple, even quadruple the speed of the entire thing in this manner (depending on the particular hardware you are using). Those cache misses are extraordinarily expensive. There's also another advantage of doing it like that: As you might have surmised, the calculations done on each segment are completely independent on each other, and can be done independently. Things done in one segment do not depend in any way on things done in other segments. So you might guess where this is going: Indeed, this segmented version of the algorithm is very easy to parallelize to multiple cores, and the increase in speed is almost linear to the number of cores. Have 16 cores? The entire thing will be done almost 16 times faster compared to doing it with one single core. What's better, if you select a segment size that's a multiple of the cache stride, you don't even need any mutual exclusion, no locking, nothing. You can bypass all that and thus get maximum multithreaded speed. Because each thread will operate on its own independent segment, separate from the rest, they don't interfere with each other.

A friend and I used to race programmable calculators and early microcomputers to see who could get a prime number above 10,000 first. Later, as I learned about the Sieve of Eratosthenes I realized we were doing it all wrong. But we usually didn't have the memory to do it right. Then I got access to a LSI 11/23. And it was a huge step forward. But by then we had actual work to do, so my interest stopped there. Nevertheless, your presentation brought back many memories. And by the way, Macro-11 was one of my favorite programming languages. I liked writing libraries of macros so that it practically looked like a different language. And I know I'm likely to start a flame war, but I kinda liked using TECO with a series of TECO macros and a WYGIWYAF display screen.

That is one of the nerdiest things I've ever seen and it made me smile... Awesome content ...

Love it Dave!

Good video. I love your videos, sir. you have a subscriber for life!

11 people on earth for MACRO-11. Count me in. Make it 12!

11:01 "Count of primes found: 41538 ; Prime validator: FAIL". 11:48 "Count of primes found: 41538 ; Prime Validator: PASS". I suspect a source change without a version change from "v2.02".

I'm hoping that just one day I might understand something you are talking about, I just hope it does'nt spoil the enjoyment if it happens.😂😂 Thanks Dave.

thank you for validating my procrastination method of doing things....... :-)

Reminds me of "Deep Thought" that got the answer of 42 but couldn't remember the original question because it took so long to compute the answer

Keep up the good work!

the level of geekdom is legendary and I love it ha

When I got it, may 386DX at 25MHz was "spooky fast". On many things the "I'm done" would seem to come up as soon as I hit return.

informative AND entertaining!