WEBVTT

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Welcome, my talk will be about a very old computer that was designed and operated in

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Belgium, so prepared to forget a lot of things you know about CPUs and the way you

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could, and actually well, maybe a word about where I'm from, so I'm from the

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IP computer museum, small museum located the transfer for Brussels, so you still have time

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of some more days in Brussels, on the next time you come, don't hesitate to come in

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digitized, and of course we have a lot of usual mission as a museum, like preserving

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artifact exhibition, and we sure so we, for this talk, where we devoted so I thought to study

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this machine, the machine that does not exist anymore, so we had to look back into existing

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documents, and we tried to understand how it worked really, what were the dynamics of the programs.

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So as I said, we will go back in time, so we are now in 2025, being the fifth generation

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of computing, I don't know, but we have for food generation, so first, first thing, forget about

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the microprocessor, back to the third generation, also forget about the integrated circuit,

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back to the second generation, forget about the transistor, we are back to vacuum tubes,

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magnetic drums, delay lines and tip and punch cards.

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Okay, well, a previous talk, there was some joke about the definition of a computer,

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I can go further in that, well, in the 50s, what were computers? Well, if you did not specify,

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it was device could be a human, a human computing, taburs, computing, trajectory for rockets, for

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examples, you can see a few there from the Nakya, which was before the NASA, you see by the way

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that those human computers were a bit different than us, yeah, just a joke because I look at the

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audience and the women and still not very well represented, so maybe to add to the curve for

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presenters, I hope next year there will be a woman also presenting it at my place and that we are trying

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to make more balancing in gender also here in computing, but it's the case for the human here,

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the top and are so far you see the operator also, so it's not really the operator, there were also

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the guards were also programmers for the in-ac, okay, so I close this, so yeah, so beside the

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human yourself, the electronic mechanical calculators and computers and also are really computers,

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wired or stored programs, that in fact the real, when the definition of computer

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and that will form the first generation of computer, the first one really was the attack with

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a stock computer, the enac here, actually, was at two, two payout, the first one was really wired and then

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the new man came and proposed the architecture and it was he designed and the second version was really

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also a sort of computer, while the arvart market, you see the arvart architecture to be used

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a little in my talk, it's another way to organize the computation, so my talk is about a mathematical

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machine, so what do I mean by that is just about the purpose of the computing, so the purpose

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of the machine is just to perform scientific and technical computation rather than business

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processing, what does it mean, it means that you have, you must be able to solve an

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numerical problems efficiently and in fact, it means that you need some kind of high precision arithmetic,

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could be fixed or floating point, we'll see in our case for the Belgian mathematical machine,

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it will be floating point, for other machines, there was also a fixed point, also you will

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have to be able to compute a specific function, like trigonometric function, exponential,

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the garym-6 like that, we'll see how we will do that and of course, as usual, you need control

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flow to control the flow of instruction, a bit of the context, so twice we are post-war

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two and in that job of course, we are interested in developing expertise in

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electronic computing to avoid depending on the device, like no further AI, and so we want to

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to apply that for mathematics physics and other engineering domains, and the approach they can

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was to thank people in the US, so they looked at the machine that were being built, they were also

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involved in building some machines, especially the Mark III, and of course, the Mark was designed

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by Orte Eiken, and also made connection with that guy, and you can see there the

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result, of course, to convince or funding authority that it's a good idea to invest in that,

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and of course, it was also consultant after to helping in the building, it's called ICCFNRS

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ICCFNRS, the funding organization budget that gave them money, okay, so when shortly we had

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for, for period, for about the ID and putting the project in, in production, and then

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really from 52 to 55 designing the machine for the first version, then it was inaugurated,

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there was the king and some fact that, and they decided to be for to put it in production

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to in ICCFNRS, so for two years, in 1955, there was an extension to build the capacity of the

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machine, and then from, he lived from a 57 to 62 for those five years, twice, okay, rate it.

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So what does it look like? You see, a very big machine, about 70,

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meternal, for the version, and 30m for the second machine, so the double the capacity,

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for the hardware, we had from 3,000, then 5,000 out of the cube cube, so it means gates,

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so the equivalent of transistors, so if you remember the intel of 4,000, 4, it's about

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2,000, 60 and rate transistors, so you have an ID, we have 3 kind of memory, very fast memory,

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so fast memory is based on delay lines, so information is kept by propagating in that kind of

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line, it is implemented using a gas tube, you can see that there, so this is as the capacity of

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18, the cement digits, so it could be called a register, but at that time, it didn't call that

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register yet, then we have the fast memory, fast memory, what is it? It's just a drum, you have

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actually two drums, fast means 7mg, so you see what, what fast is it, you could draw it on the

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on the diagram, if the more slow to see if you are in line, so two drums, one for the data,

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one for the program, so it's here that we have the other style because it's really separated,

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the data from the program, one drum at 100 tracks, 20 sector, stirring, of course,

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the same content as the register, so 18 digits, so decimal digits, we will see what is in,

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so it's about 20 kilobytes and then third, the sort of level of memory, a slow memory is just

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tapes, or tape was, it's neat tape, so it was a loop, you can see the loop here actually,

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so the tape was just going there and back and forth, so they just had to pass the end with the

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beginning, conception about 25 kilobytes, so it's about at that time the consumption of a smaller

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street in the town, so it was very odd there to install some cooling otherwise it started to

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also to have a problem with the dilatation and six-sided, okay logical architecture, so this is a

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real picture, well just translated, so it's very high level, you see well you of course,

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central control here, you have apart the drum with the program where you read the instruction

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and then based on the instruction you will go into the other drum to take the data to write back

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and forth the data and you can also use, well I call it arithmetic and logic unit but it's

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was not the name, the name was in French group, calculators, calculating group, so it was really

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the hardware that was able to perform computation and what could do, actually it could just

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do this kind of operation, A times B plus C and also with the carry, the carry, yeah,

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so you see there is something missing for arithmetic but don't we what is missing,

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now we have minus is done using nine components, it's a good point,

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divide yes, there is no divide, okay, so we will see or we do divide later,

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okay for the data instruction, so I told you 18 digits, so at the very low level there was

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still of course in kind of binary code it in decimal but it was not the user way, you can see

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the encoding there, it's called B canary encoding, so it's well because zero is zero, one is one

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but two or so two but then three becomes five four becomes eight, so it's a different encoding,

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the ID is also used for the machine hypothesis that you use less power because you use less one

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and also you don't you try to have to have a one not too close together because

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good interfere I guess, so it's really the low level encoding, so I had some friends who

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uncovered and they got that of course in my emulator but of course it does not help a lot,

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you don't have any kind of code the error detection or correction, it's just more

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playable to use that kind of coding and number representation, well for this talk I will just

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focus on the floating point, you could also encourage fixed point and double precision if you

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went but the presentation was like this you have a sign then the manufacturer is 15 number

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supposed after the decimal point so it's zero dot then the manufacturer and then the

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exponent you have a sign and you have two numbers so it means that you can go from

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minus 10 to the 99 999 but actually 12 out of a flow they limited to 49 49

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okay and the other way the other representation or also you could store a pair of

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instruction in that 18 bytes or two two block of 9 number us five for the type of the instruction

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and four for the for another right visually in that race could also represent a small number and of

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course it means that if you have two uh two instruction in one one block only uh when the

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address it will be addressable only uh well both instruction will only have one address so we can

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not jump on the second one you just have kind of a pair anignment okay a register well

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uh what's fun the documentation they use Greek letters for the for all different registers so it

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means two things first really it was mathematician that we're using that and second the the the the

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code was written on paper because you cannot type uh wheat lettering to a computer so it means

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that all the design was done on paper and then manually compiled of course in my work I wrote a

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compiler the compiler so I use other uh characters so I use uh ASCII characters like the value for

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omega i a for alpha b for beta so basically you have an accumulator not called an accumulator

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it's the ID it's called omega uh that's what's the entry and uh or two of the calculating group

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you have two internal register called E and F uh also with fast access time so it's really the

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core of the system you have also in this register that are can interfere with the addressing

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and that are useful for of course uh say bars matrix and things like that and of course in

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other register you have the signed register for the conditional jumps and of course something that

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is looks like a program counter actually it points to the to the next infection

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then switch on actually I told you already about the tracks the sector the sector are number five by five

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so not all the address are valid so and you see the program counter to the points to the next

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address so it means that address is fine okay I will go very fast on the on the

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the infection set it's not too difficult to to understand you find your way when when you know

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some assembly uh you you have of course for the arithmetic operation you can take source

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from other register like the E and F register you can also an immediate uh value means that

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the value that is specified here so this is the type of the instruction and the value that is here

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usually is an address between that case is used really as a as a value that is of course only

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part of the of the manufacturer is the fourth the fourth first digit of the manufacturer so this could

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mean 0.9 actually if we use it as immediate value and from memory of course the most used

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way to to load the tab it because then you can of load a full floating point and about the

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operation of course you see plus minus plus minus you have another kind of multiplication

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internal you're using in internal data so and you can also have it in normalize or not normalize

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well let me that you you align the result again to avoid the zero after the digital point

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accumulator you can of course white back in in the memory so this is writing back in memory

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the two variants one will reset the accumulator and the other will keep the information that

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accumulator you have the same for the E and F so you can write in E writing F or put the information

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in the in the sign back and and the program and also all those stuff like alarms

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we'll see why why we can have alarms I saw yeah what is very interesting is that the encoding you

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have two two way to represent zero minus zero plus zero so it's used actually for for me some comparison

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if you want to have a greater or equal or greater you have to change the order so it means that

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minus a plus b is not the same as plus b minus a so yeah it's a bit of time so you have to do

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not the pattern and when you read the code also you have to recognize those pattern and there

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are some some exceptions so I leave it to you but does not work for for a lesser or equal b b if

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b is zero there are some problems okay another subtlety is that we have a specific class of

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operation that will actually alter the instruction that will come after so actually you have to read

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the two instruction together to understand what is going on and typically it's operation that will

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extract the mantis are find the sign change the exponent and things like that and it will affect

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the operation the the information that comes in the accumulator by in the next instruction

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we'll see on the example so about the way it works you say I told you well the code it on paper

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like this so they write this to the doc what this many code with with the week later here and then

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they translate it not quite totally in machine code it's almost machine code actually

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you have to address here you have some some part of the instruction here maybe if it's a common part

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and some other part there and using that you have most of the information you have only information

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actually to to compile it you could compile it with an utility or do it by hand of course I have

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done it in my my code and of course when you have that you simply meant that you don't have

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all you need to to build a real application for example to compute ballistics you need all the

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primitives like trigonometry exponentials and of course the division

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so they have a set of minimal set of instruction you have function you can see them there and based on

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that you can compute all the rest very quick look at a code so this this is part of the

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the library that is in the run so this this code is about the inversion so it's it's a

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dump of the of the memory so it's you see it's not not so not so long so if I decode it here you

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you see the the instruction that is assembled in block the first part is just about you

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information we will store the information in some some address here this address actually it's

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the number we want to to invert actually for fourth one yeah for the division we multiply by the

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inverse so the purpose is to compute the inverse and the number we want to invert we store it in

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memory because we use it at the end again we see why and then we have one big block here that

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is actually just computing a first raw estimate of the inverse and then we have iteration five

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five iteration that looked really similar just just a number that change usually if you use Newton

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the formula here that one with a equals to two and then at the end here you are guaranteed to have

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the arms that's not very reliable so it could it could be a problem so what do they do here you see

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you have air information that you have stored previously and you multiply you have the result

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here the still in the in the in memory so you have the inverse here in the accumulator you

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multiply by the number the original number so you compute x by what on x and you should be one so this

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constant is one okay so I close and if it's not one what you do what do you do when what you try

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again so you have three trials so you have the constant three here actually here and you have

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actually a big loop this is a big loop you see if there is a problem if the check does not work

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you try again three times if it does not work after three times then you have you raise an alarm

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and then the human will come and we check where there is a problem in the in the machine okay

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so sorry my time is up so this is the demo so you can see the convergence from one one one

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court you have at the end you have you have here zero dot 25 and that's it thank you

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thanks mister