Відео

we are informed viewers - götten and maloğlumalyusuf

I am in awe looking at the utter genius behind this function, and I only understood half of it

I still doesn't make sense where (1+M/2^23)*2^(E-127) comes from

Him: You might already see where this is going Me:

The fastest square root algorithm is Newton's method. We want to find the square root of X. Make a first estimate 'a' (more on that later). Divide X/a == 'b'. Take the average of a and b and you are a lot closer. This algorithm converges very very rapidly. In the IEEE implementation of floating point numbers on an Intel PC, finding the first estimate is easy. Shift both the mantissa and the exponent right one position (so divide each one by 2). That gives you a very good start. Worked example. Square root of 2. First estimate == 1. Divide 2/1 = 2. Average of 2 and 1 == 1.5 Second estimate now == 1.5 . Divide 2/1.5 == 1.333333333. Average of 1.5 and 1.3333333333 == 1.41666666 Third estimate = 1.4166666666. Divide 2/1.41666666666 = 1.4117645. Average of those == 1.4142147 In two iterations you've got slightly better than 3 significant decimal figures; in fact close to 4. In three iterations you've got 6-7 significant figures. Actually coding this in intel x86 assembler (the code is too short to make it worth compiling to assembler) is not particularly difficult and is left as an exercise for the reader LOL.

I'm curious why the exponent of floats wasn't formatted such that the first bit of the exponent describes the sign, and the remaining 7 the exponent, similar to how ints are defined, or the float itself, as a whole.

This is not an inverse square root. An inverse square root is just squaring. This is a reciprocal square root. That is why it’s named q_rsqrt. This is short for quick reciprocal square root. Otherwise great video. Very clever.

Bro create a video on rings also

There's no algorithm speedup section, just useless clickbait.

I damn love CS. Glad to study in this field.

Aren’t rationals not a group because of the neutral axioms?

5:40 it's a small thing, but I don't like the phrase "people much smarter than us". I think that most of the people interested enough to watch a video like this, are probably also smart enough to become an knowledgeable in computer science.

There has to be an easier explanation of this. I couldnt follow all the way through.

Wait a minute, how does this speed up algorithms?)

For that “what the fuck” line in the fast inverse square root code, 0x5f3759df is equal to (-0.233108f >> 1). I’m not sure what -0.233108 is though

Will you participate to the unofficial #SoMEpi?

Very clear and amazing representation of quick inverse square root algorithm, but I do believe that your demo code would be better if you give an alias to 0x5f3759df 😂

This is knot theory

When you unknowingly hire an alien in your developer team

Ok so let me get it straight: The reason why we apply the log to a number is to get a more or less accurate bit representation of it?

I hope you're doing well

Still waiting for part 2 so I can use it to solve Rubik's cube I'm gonna cry if his example is Rubik's cube.

👍👍👍

Made it to 7 minutes. Goodbye.

Thank you.

This was fantastic! It also shows why C is still around, and will continue for a long time. You can do things with C that aren't easily possible with any other language.

i dont know what else to say C just works that way..... it pretty much sums it up

I might have defined a union to overlay the long and float in memory

wow

i love your videos dude

best explanation I have seen on IEEE-754 , I understood more in those 5 min than my prof's 1hr lecture

I started my freshman year in an 8 week course for Intermediate Algebra and got to have fun talking with the tutors in the library over the more nerdy high-concept math bits I wanted to eventually try studying for my game. This was brought up as a discussion and I still don't quite get it. On top of this though, computers are way better than they were back then so we typically don't focus on micro-optimizing like this anymore, but it's still good to be conscious of as opposed to the current generation that is cosying into the idea that machines just do everything for you with one push of a button and that being slow is just something we either deal with or splurge to upgrade our rig.

Bro, your videos are incredible!!! Can’t wait for the next ones

The Fast Inverse Square Root algorithm used in Quake III is a method to approximate the inverse square root of a number without using division or square roots. It involves a bit manipulation technique that reinterprets the bits of the floating-point input as an integer. This algorithm was significant in the 90s for its efficiency in computing the reciprocal of a floating-point number, especially for vector normalization and other mathematical operations in 3D graphics rendering.

What is the name of the professor you mentioned in beginning of video? Can you give link to his video?

I’m learning C programming in an engineering course, and I showed this video to the professor. He said these clever tricks are written by people with deep insights and too much time on their hands. He also warned me against using those forbidden techniques …

You didn’t take variations due to handedness into account.

This is a good primer, but fails to explain critical things.

Great example to show older kids why they need maths

well you gotta show up and do the graph isomorphism using groups now

i took a bit operation course in first year of computer science and understood it but was always wondering why would we need it in true applications. NOW IT MAKES SENSE!

This mf-er, I just wanted to hear damned algorithm😂😂

Yo, bro naturally dropped the group theory intro. I am comp.sci and math student, was so interested in algorithm, but damn, over 20 minutes of math.. I wasn't ready for that:) Ps. That all is just the first half of the first course, further is much darker... But I am happy that some people have such a great vid to have a great start. Keep it up!

amazing stuff than you!

This is why I think I'm bad at programming.

Inverse sq is log

Bro why define threehalfs and then not define mu

I wonder why they chose u = 0.043 exactly. I have calculated the area under f(x) = log2(x+1) - (x+u) in the [0,1] interval and equaled it to 0. I came up with u = 0.057304959111 for the minimum area. Also I coded up a quick c program to check the average gap between log2(x+1) and (x+u) without any fancy math, just iteration between 0 and 1 with 100,000 points. for u = 0 the average gap was 0.057305, for u = 0.043 the average gap was 0.0262259 for u = 0.057304959111 the average gap was 0.022115 clearly u = 0.0573 is better on average, so I wonder why they opted for 0.043. Anyone knows?

I had some trouble understanding the difference between elements and operations at 13:40. It seemed you had said before that "flipped 300", "flipped 0", etc were their own elements, but when verifying they were a group under "chaining", it seemed you showed "flip" as its own element (the double arrow, given as its own inverse in the last line). Or, when you use "flip" (the double arrow) in the last line, does it carry an implied "neutral", so it's "flip neutral" (double arrow gold)? You then demonstrated that to flip and then rotate is not the same as to rotate and then flip, again treating "flip" as an element. Here I have the same question again, is "flip" shorthand for the "flip neutral" element? (Or is there a typo, or is there something I'm misunderstanding about flips/rotations as operations vs as elements)

out of this world