What's a Leap Year? Calculating on Commodore 64 

The Ukrainian Church only adopted the Gregorian calendar in 2023. I live in Poland, but right on the border with Ukraine (about 5km), and probably a third of our town belongs to the Ukrainian church, not to mention a lot of refugees right now. I'm rather used to them celebrating Christmas on Jan 6, so it came as a bit of shock last year to see the supermarkets, trains etc. at breaking point. The change basically doubled the demand, but the supply chain hadn't managed to keep up. Every shop was like the Toyko metro in rush hour! Hopefully this year it'll work itself out! You'd think "witnessed a change from Julian to Gregorian calendar" wouldn't be something you'd put on your CV in 2024, but there you go.

Binary division was very difficult for me to understand, but once I got it, it's beautifully simple.

Your Great Grandpa was born in 1889, Mine was 1888 and lived to 1988 Edward Dearing 12/9/1888-1/8/1988 99 Years 30 Days

Here's another fun fact: Why is February shorter than any other month? There are two reasons: 1. the month of July was named after Julius Cesar and was 31 days long. Emperor Augustus also wanted to have his own month, which is why we have the name August, but this month would only have been 30 days long, according to the 31-30 rule. Since Augustus definitely didn't want a shorter month than Caesar, this month also had to have 31 days, which is why both July and August have 31 days, even though they are back-to-back, which messes up the 31-30 rule. So much for that curiosity. But if you add a day to August, you have to take that day away from another month, and that day was taken from February, reducing it from 29 to 28 days. But wait a minute, why did February only have 29 days and why take a day out of the month when it's already the shortest? That brings us to number 2. 2. In the Roman calendar, February was the last month of the year. The new year began on March 1. This was changed by the Christians so that the new year would correspond better with the birth of Jesus, after all, this birth was chosen as the new reference date (before and after Christ, aka BC and AD). As February is the last month of the year, there were simply not enough days left to give it 30 days. If you divide the days according to the 31-30 rule, there are only 29 days left for the last month. And since it was the last month, Augustus had no problem taking another day from the end of the year to make his own month 31 days as well. Oh well... I'm afraid the next question will be: Why the 31-30 rule at all? The answer is: Originally there was no 31-30 rule. There was a 30-29 rule. The reason for this is that the calendar was not based on the sun, but on the moon, and a lunar cycle lasts about 29.5 days. Do you see the problem? So if you set the months at 29 days, you fall behind, and if you set them at 30 days, you get ahead of them, so they had to alternate between 30 and 29 to stay in sync. However, this meant that the year was far too short and the seasons shifted over time, which was pretty bad for agricultural planning. So they had to lengthen the year without introducing too many changes, thus they simply added a day to every single month and ended up with the 31-30 rule. Only now the year was too long, so they had to take away a day, and that day was taken from the last month, so that month was already shorter before Augustus stole another day from it. Naturally when they figured out, that they actually do need an extra day every 4 years, that extra day was re-added to the very last month as well, since it was the shortest, so February was alternating between 29 and 30 days prior to Augustus. In hindsight, the calendar was quite logical and well designed, it was just one Emperor who had to mess it up, followed by Christians who had to mess it up even more, yet those same Christians at least fixed it again later on, when Pope Gregory XIII realized, that years don't have 365.25 but in fact 365.2425 days. Except that this is also wrong because a year has 365.2422 days. But let's not nitpick, the error is only one day in 3,030 years, yet since the earth rotation is not constant, it fluctuates, the average error is only about one day every 7,700 years, which is pretty good, considering the Julian calendar went wrong 1 day every 128 years. The solution to the remaining inaccuracy would be to not have a leap year whenever the year is dividable by 4000. While this would fix the situation right now, the fix has never been adopted for the very simple reason that while the earth rotation around the sun is pretty constant, the earth rotation around itself is not and constantly gets slower, meaning days constantly get longer and this has to be taken into account as well. Currently every 100 years a day gets 2.3 milliseconds longer. That's not a lot but we know that a few billion years ago a day on earth was only 19 hours long. So instead of planing ahead and creating super complicated rules, the current idea is to go with the current rules and should we ever notice that we lost an entire day in the future, we just drop a leap year; the world just agrees that a year, that normally would be a leap year, is not a leap year and the problem is fixed again for another 8000 years or so.

This is why If I get a time machine I want to go to February 30th 1712 in Sweeden February 30 was a day that happened in Sweden, 1712.[4] This occurred because, instead of changing from the Julian calendar to the Gregorian calendar by omitting a block of consecutive days, as had been done in other countries, the Swedish Empire planned to change gradually by omitting all leap days from 1700 to 1740, inclusive. Although the leap day was omitted in February 1700, the Great Northern War began later that year, diverting the attention of the Swedes from their calendar so that they did not omit leap days on the next two occasions; 1704 and 1708 remained leap years.[5]

Another way of checking if a year is divisible by 4 evenly, is to do ...IF (Y AND 3)=0 THEN PRINT Y, ...... I found this little trick a few years ago when learning assembly. You can use the AND trick instead of Modulus if you are dividing by numbers that are powers of 2. 2 4 8 16 32 64 and so on. If you were doing MOD(Y,16)=0, and since 16 is a power of 2, you can do (Y AND 15)=0. The 15 comes from subtracting 1 from 16. Thank you for your videos. I always learn something new.

How to learn WAY MORE than "what is a leap year?" in 30 minutes. Thanks so much! Too bad I didn't check your channel in 1984 when I was playing with 6502 assembly language

When coding a leap year function in BASIC, I like to take advantage of the fact that function parameters are dynamically scoped: 10 DEF FNLY(Y)=(FNYM(4)=0) AND ((FNYM(400)=0) OR FNYM(100)) 20 DEF FNYM(N)=Y-N*INT(Y/N) Inside the YM ("Y mod") function, the value of Y is inherited from the calling scope. When the caller is the LY ("leap year?") function, Y is whatever was passed in.

I feel like SO many machine language / assembly programs overlook that very important option to be able to STOP ml program execution at 14:56 -glad to see you implementing that. And I know I've seen you do it other times, too, but it seems to be so rare.

Gregorian leap year logic led to one of the few deliberate bugs in modern software. Lotus 1-2-3, the most popular spreadsheet software in the 1980s used simplified logic and added a leap day to 1900. The developers of Microsoft Excel recognized this was incorrect but chose backwards compatibility over correctness and added a leap day to 1900 also. It is worth mentioning that the earth's rotation speed is slowing so the leap year logic may need to be readjusted in the future. Leap seconds are added occasionally which always create havoc on computer systems.

I'm glad you shared that site detailing how to convert 32-bit hexadecimal to decimal values. I can't remember the title but I lost that book ages ago, it had a lot of really amazing 6502 algorithms and it gave pointers on how to use these routines on Apple II, C64, and Atari 800.

The divisible by 100 rule might seem esoteric to us but on the other hand we're privileged to have lived to experience the 400 rule applying, which is far more unique :v

Apart from enjoying the programming masterclass this video touched me in a couple of unexpected ways. Firstly, I had overlooked the "missing days" in 1582, and as someone born on October 9th (the same birthday as John Lennon, ya know!) I think I may have dodged a bullet there, somehow! The other thing was your mention of your great grandfather. My maternal Grandad (a feisty Welshman who spent some time in Alberta around the time of the Depression) was born in 1899 so missed a leap day early in his life in the Gregorian way. Not long before he passed away in 1977 he was gracious enough to seem to take an interest in my early electronics projects. I remember him sitting in his "special chair" examining my newly built two transistor signal injector/tracer and inquiring what it did!

Great stuff! I love the reference to the read and write of the cursor position. I did some math on finding PI on 3/14, but didn't take on ML. What a great program there. Lots of things to know

The 4-100-400 rule means 250 minus 10 plus 2 or 3, which is 242 or 243 leap years, depending on the millennia. The difference between the orbit and the year (0.2422) is within one day every thousand years. 7:10 - Not according to microshaft's excel.

@10:10 All your Kung Fu Flash usage encouraged me to recently pick one up at VCF SoCal. @19:03 That divide-by-100 assembly routine is indeed beautiful! Thanks for highlighting that. @25:38 Yup, dyslexic programmers can get totally tripped up here. Cartesian-wise, X axis is left/right, which specifies a column (which runs up/down). Likewise, Y axis is up/down, which specifies a row (which runs left/right). However, with the routine at $FFF0, X specifies the up/down, and Y specifies the left/right, the opposite of what I'd expect (e.g., the starting cursor position at bootup would be returned as X=6, Y=0). Worse, p215 of COMPUTE!'s "Mapping the Commodore 64" gets it backwards, stating "the .Y and .X registers are loaded with the desired row and column positions respectively". (Then again, I'm dyslexic, so I may have flipped something here...)

I love how methodical you are in your explanations. Thanks for another interesting video!

I never had a c64 but I always enjoy your videos and I watch them all ;)

That was a fun exercise. Thanks, Robin! I was able to shave a couple Jiffies off execution time by utilizing the division algorithm code from 6502 org - it shifts eight bits in its mathematical loop, which saves a lot of cycles during execution.

And I thought everyone had leap day on the 24th, like we do here in Denmark. This is because Caesar's solution to the leap years was not to add the 29th, but to extend the 24th to 48 hours - ie. there were two days with the date 24th of February in leap years...

Great Video . I love seeing the C64 font - so many many fond memories

That is an excellent assembly routine for division! I am using it on an ATMEGA328P to make a new control panel for my 30 year old treadmill. There were a couple of things that tripped me up though. Firstly, the bpl operation means that the loop actually runs 17 times for a 16 bit division. I originally assumed that it was 16, and this gave me some very strange results. Secondly, the carry flag on an ATMEGA after a subtraction is set opposite from the 6502 family. I believe this is due to it using 2's complement vs. 1's complement on the 6502. I may be kinda weird, but I thoroughly enjoy programming in assembly. 😁

I already knew this, but commenting for the algorithm's benefit.

Very timely post. I shared your CBM Basic program with my 8Bit afterschool club today. Thank you.

Yet another great video. Thanks for sharing

If a number in base N ends with 00, then it's divisible by N². All you need now is to also represent the year in base 20 and you're set!

7:05 Ha, that's a cute and amusing comment. 10:00 Yep, we definitely want more Simon's (or even Simons') Basic.

Lovely video as always. Also, it's always cool to see how much faster Assembly is than anything else and that people managed to write whole games with it back in the day

Thanks for the full implementation of leap years. Most people generally understand that it is every four years, never knowing there are exceptions as explained in this video. When the video started I was wondering if leap year was going to be simplified to every four years and ignoring the full math required for a correct calculation.

My cousin has a daughter who is turing 4 this year or if you count actual birthdays she's had then she's turning 1 as she was born on the leap day. It's really cool.

Absolutely some of your best work here bro! For me, it's when the conspectus is focused on the obscure that produce some of your greatest videos. Going all the way back to the beginning with the 'Spaces' video and also notable the WandaVision episode. I especially enjoyed this episodes subject matter, because, (I'll raise my hand) I never really cared to look into the reason behind Leap Years, it was something I was just content in not caring about. Until I watched this video, LoL. I was grateful for the informative background, the subtle detail to the little BASIC routines you whipped together, (even mentioning the purpose of the comma, lol) and of course, busting out some SIMON'S BASIC of all things and all that a preface to an in depth delve into an ML version! Kudos brother!! Fantastic video! If I may, On behalf of myself and your 54+ THOUSAND other subs, "Thank you for all your efforts!"

Of course, if your loop counter incremented in steps of 4 instead of 1 (whether in assembly or BASIC), you'd speed things up a lot by having fewer loop iterations and fewer calculations per iteration. The only small caveat is that you'd need a bit more code to find the first leap year in the year range before you start looping.

Robin, you should do a video on Lemonade Stand. I remember as a kid, the way the program counted money never looked right but would get it correct at the end. A great Canadian program.

my 99% experience with assembly code, is writting emulators, so seeing someone coding it natively is always very interesting. Nice job as always !

Hey friend! Thanks for the explanation. We just got back from a birthday party for a leap year baby. He's had 60 years around the sun but just turned 15. I told him it's time he started acting his age. He's the chaplain here at the college. I hope you and the fam are keeping well.

Yay leap day! Love your vids so much.

I think that the last version of the calendar we use was perfected by a scientist Milan Milanković - and it is currently the most accurate version in current use.

Got recommended this today, 29th Feb!

On a Linux or Unix prompt enter ‘cal 1752’ and checkout month of September. Can see when it was implemented for computers.

Feel privileged to have seen this on leap day. Thanks Robin!!

SCIENCE! As a kid, it took me forever to figure out how to use "The Visible Solar System" on my C64. Just tried it now, and I still had to look at the manual ;-) 6:28 "If I could derail us further" could easily be a single sentence to describe me. I feel better that I'm not the only one. 10:05 Thumbs up for more Simon's (and Super Expander) 21:50 Great explanation of this code 27:45 Hey, that's neat!

I was going to comment that my favourite part was when the characters lined up with your illustrative calculation of month days, then you shared your wonderful family memory, and finished with my favourite BLE song. Maybe in 12000AD they'll find a C64 and use it to calculate if it's supposed to be a leap year. Only to give up on waiting for an answer from BASIC and so have to learn assembly. They finally have it ready to run... They type

Robin, the the Royal Astronomical Society of Canada publishes an annual guide and has a really detailed explanation on the leap year and leap seconds.

Came for the simple coding, stayed for the mindblowing Earth-moon animation at 0:43 :) I want to know how that's done! I mean, I've seen some spectacular things on 8-bits, starting with a first person perspective flight sim on a ZX81, (awesome achievement, terrible result thanks to 1bpp graphics, ;) but I still don't know how they're done. [EDIT: "Simple"? I forgot the 6502 has no division op. That's some interesting code.]

The current rules still let us slowly drift off from astronomical observation. I read once that we'd be much closer to true if the rule was to skip a leap year every 128 years instead of the 100/400 thing. This idea pleases me since 128 is also a power of 2.

EDUCATIONAL! THANK YOU!

I tried your code on a C16 (emulator, but was my computer in the 80's), it ran fine. Will try on Commander X16, and color Maximite 2. I have the C64 maxi so I know it will run on that.

Instead of doing a divide by four, couldn't you AND the low byte with 0x03 and check for zero instead? I know it's needed for the MOD, technically, but since you're also already doing the divide routine anyway you could divide by 400 after doing the AND check and you're doing less work overall. LDA lobyte AND #$03 BEQ divide400 JMP notleap

How about using "STEP 4" instead of checking every number for MOD 4? It would make the Programm run more than 4 times faster...

LOL "and then we'll print out why? because it's a leap year"

Fun video, Robin! Very cool way to show programming in Basic and Assembly. 👍 Also, a bit of trivia here. While the English-speaking world wasn’t as slow as Greece to adopt the Gregorian Calendar, it didn’t adopt it until 1752, which was much later than most of Western Europe. I remember reading a letter from an elderly Thomas Jefferson explaining the change to someone who was much younger

No surprises that many people don't know this. Especially since we actually have Flat Earthers walking around these days. Great video!

Wow that assembly language version was only slightly more work than the BASIC version. I wonder why it never caught on more widely? I think I finally found peace with myself as a simple C# developer.

Appears they made a mistake in Auss with the petrol pumps.

if you have the hard book called the computer tutor there is a a 6502 machine code divide routine that you might use.

Watching on 29/02/2024! Love your videos Robin! (and yes, I use DD/MM/YYYY)

Great video, nice to see it also done in Assembly! From a pure performance point of view, in this instance wouldn't it be better to compare the low byte first as the stopping condition, since it will only match 1 time in every 100 years, versus the high byte which will match every year for the target century? Seems like a few wasted cpu cycles doing extra compares as we close in on the end year... why yes, now that you ask, I did grow up with 8-bit machines and spend far too much time on optimising my code :)

so if they had made the rule just "every forth year" instead of divisible by 4 you would have to implement an offset and then basically calculate the same thing?

US Navy here, we still use Julian dates (at least in the aviation community)

To test for mod 4, you could use if (y/4)int(y/4) To use normal basic to test for divisibility by hundreds, you could try: if (y/4)int(y/4) or (y/400)int(y/400) then dummy=1 else print y, The dummy=1 is because since this tests for two negatives rather than a positive, you are just going to skip over the case of 'true'. Its ugly as sin, but it gets around an even uglier mod statement, and the need for expansions.

A year is actually 365.25 days long

If our calendar had 13 months, every month would have 28 days (4 weeks). But would still be off by one day every four years.

Your loop end check is slightly flawed because it doesn’t perform carry between low and high bytes. Granted in this case I don’t think it matters because of the end value chosen, and because you’re always incrementing by one. ;) To correctly compare multibyte unsigned integers for year

I am the expert on correct apostrophe usage. You will use the apostrophe correctly if you know whats good for you.

At the end you went past 999.M41

Can the for-next loop skip odd years?

Hi Robin, many thanks for your videos - I enjoy watching you!!! I have a bread bin Commodore 64 connected via a "composite to HDMI" adapter to my Smart TV. The image is not that great due to resolution differences but I can read the characters and play games fine. However, I see the screens you show are crystal clear. How can I get such clarity in mine? Will a device such as RetroTINK-2X make my screen like yours? Can you give me some direction? I'd be interested to know what you use. Many thanks!! Leo M., Chicago

I get paid per month; I hate leap years.

Simon's/Simons' Basic is way better than the built-in C64 Basic, and definitely deserves a few videos. In fact, C64 Basic sucks big time and should never be used - but I understand you can't ditch it in this channel. Let's be honest though, real men do it in Assembly (even if execution time in Basic is not as issue). Assembly it is, not because it is always necessary (in this case it isn't) but because we can. 😆

Dunno if this would simplify your assembly code; but, you: If a number is divisible by 25, then the year is a leap year only if divisible by 16. All other numbers follow divisibility by 4. This, slightly ugly JS one-liner prints all leap years below 3000: i=0;while(i

Hey Robin, at 15:40 or so, why did you use bne instead of bcs? Isn't it a bit clearer to branch on carry to show that that's what the branch is really doing? EDIT: Also it's so cool seeing my name in the credits :D

Is it not possible to use NEXT 4 in for loop in basic to get rid of checking the modulus of divide by 4? But this is only works if the start year can be divided by4 without modulus. Maybe worth a check to use this kind of loop. Or not. :)

What if we check the number could be divided by 4 without modulus in assembly with OR%11111100. If it gives back %11111100 then this number could be divided by4 without mod, becuase the last 2 bits is zero.

Leap years are skipped every 4000 years too.

orthodox church uses Julian calendar btw

The leap years seem also to be olympic years.

Kind of irresponsible to deliberately include the Y64k bug in your code, don't you think? Sure, this might only be demo code, but how can you be sure management won't put it into a mission critical system before the year 65536?

All hail our roman rulers.

START: LDA #$00 STA QUOT STA RMNDR LDX #$08 LDA DVDHI SEC SBC DIVSR LOOP0:PHP ROL QUOT ASL DVDLO ROL A PLP BCC CONT1 SBC DIVSR JMP CONT2 CONT1:ADC DIVSR CONT2:DEX BNE LOOP0 BCS EXIT ADC DIVSR CLC EXIT: ROL QUOT STA RMNDR RTS DIVSR: DB $F9 DVDLO: DB $E8 DVDHI: DB $FD QUOT: DB $00 RMNDR:DB $00 Sorry for shouting but some machines don't have lower case.

Question about Simons' Basic cart. I have one, none of the string functions works right. INSERT, INST, PLACE, none works right. What's up with that?

They did an amazing job of calculating this back in the day but we should have re-defined the second rather than dork around with extra days and missing leap years.

From your thumbnail, I see you've got the 100- and 400-year rules in place. They'll have to add a new rule in a few thousand years, since there are 365.242189 ephemeris days in a tropical Earth-orbit year, but 365.2425 days in a Gregorian-calendar year, an error of one day too many every 3215 years. Maybe they'll add 1000- and 4000-year exceptions to leap days. BTW, what's the deal with calling them "leap days" when you're not leaping over anything; you're going *through* an extra thing. *NON*-leap years should be called "Leap Years"! (Cue "Seinfeld" music.) 3:30 You could also do «Y=INT(Y/4)*4», or «Y/4=INT(Y/4)», or, in this case, «(Y AND 3)=0». 4:12 What percentage of the people you polled had even *heard* of the "Gregorian" Calendar? 5:21 Monthly renters were annoyed about paying for 10 days that never happened! 6:20 "In our lifetimes"… I guess you're right, since the oldest person currently alive is slightly under 117. 7:44 Good call - multiple Simons are better than one! 9:00 In general, you need to be careful about the precedence of your ANDs and ORs. 16:06 I /guess/ this works. The method I've seen for 16-bit comparisons is «LDA year+0 : CMP #end : BCC loop». The first CMP acts as an SEC:SBC, so it's a 16-bit subtraction. Your method might not work if the increment is anything greater than 1 (e.g., start=0, increment=257, limit=100). 16:51 Divisibility by 4 is trivial here, too: «LDA year+0 : AND #$03 : BEQ yep». 17:12 Yeah, so they gave us Carry and non-Carry versions of the shifting operations, but not for Add and Subtract! 19:26 Huh? Dividing by 10 for binary→decimal conversion is needlessly slow. Just use the binary-shift/BCD-add method popularized by Jim Butterfield. 19:51 I take it that kids don't learn long-division anymore. The sad thing is, this is still how even the most modern CPUs implement it, since there's no general method that's faster. The trouble is that it contains conditional branching, which means you have to run it in multiple steps, which is slow. It's faster to substitute a multiplication if you can, since multiplication is unconditional, so hardware makers can take the long-multiplication from Elementary School and expand it out into a bit-shifted array of adder cells (or equivalent) and execute the multiplication in one clock cycle. Here, year / 100 = year * 0.01. For integer operations, you just take a fine enough approximation of a binary fraction of 0.01 and run it with an implied decimal (binary) point. 25:01 Instead of a tab index, you could just track the column value to use with Kernal PLOT, and set it back to 0 with a CR when you go past 30. 30:08 They'll definitely need to change the leap rules by the year 12000.

As an Irishman trying to guess your great grandfather's nationality from the accent you used, I'm going to say, Mexican?

I want SIMONS BASIC not SIMONS BASIC.

Who's watching this on Feb 29th (sorry I must do this) 👇

Calculating a leap year isn't as simple as just every fourth year you have a leap year. The calculation needs to be more complicated because even adding one day every four years still allows "slippage" so that the movement of the Earth around the Sun gets out of synch with the years. Here's how to do it, really: First, divide the year number by 4. If it does not divide evenly, it's not a leap year, otherwise it might be a leap year and you go to the next step. Second, divide the year number by 100. If it does not divide evenly then it's a leap year, otherwise it might not be a leap year and you go to the next step. Finally, you divide the year number by 400. If it does not divide evenly then it's not a leap year, otherwise it is a leap year. It's a complicated procedure but it was calculated to keep the years and the Earth's days lined up accurately for at least a few thousand more years before any great adjustment will be needed.

I'm a leap year