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Admin
Most of the articles you'll find by googling '0x5f3759df ' are garbage: the authors miss that the code isn't casting the float to an integer, but taking the pointer to the float, casting that to an int pointer, and dereferencing it. By doing this it creates an int with the same bitfield the float had, instead of an int with the same value the float had.
Treating a float as an int in this way would normally just give you garbage, but the code then goes on and does some real magic: IEEE floating-point numbers are stored as a sign bit, a mantissa and an exponent - (+-)a*2^b , packed into a single bitfield. If you right-shift this bitfield, you'll divide both the mantissa (a), and the exponent(b) by two.
It's this division of the exponent that's interesting: remember that a^n*a^m=a^(n+m), so if you half the exponent, you square-root the number. The subtraction then cleans up the last bit of exponent that might have leaked into the mantissa (the exponent is stored on MSB-end, so if its LSB is one, that would end up as the MSB of the mantissa), sorts out that IEEE floating-point is biased rather than two's complement by subtracting half the bias, negates the exponent so as to give the inverse square root instead of the square root, and does some wizardry on the mantissa as well.
It then uses the same cast trick to get the bitfield back into a float again, and needs to run only a single round of Newton-Raphson iteration to bring the guess close enough to the true value.
The best explanation I've found for what this actually does is http://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/ , all the others don't even understand what's really going on, let alone why it works.
Admin
That's amazing! it even does negatives!
"The Square Root of 5 is something like -2.2360679774997"
Why didn't they teach us this in school?
Admin
Math is beautiful. Math is gorgeous. Math is what makes us human.
You are not human, you are a well trained monkey, who has learned not to fling poo too often and to push buttons as taught.
;oP
Seriously, though -- if you don't understand the math, you can't understand why things DON'T work, or where the edges of the mathematics break down (and there are always such). This can often be a guideline towards when calculations are wrong.
I've never been one to go for mindless tedium -- that's not math, it's arithmetic. By programming it, though, you're making it clear you understand the process, which is what really matters, there, not the tedium. The tedium is just an uninventive way to show you aren't just plugging numbers into the calculator like... well, a monkey. So programming it does what the instructor (should) want of you (buying it from you does not, so that might be a legitimate "cheating" offense at most universities).
.
Admin
As opposed to, say, multiplying the number by itself ?-)
Admin
gimme teh beamz :)
Admin
Nancy?!?!
Admin
I would think they didn't write the script because it would actually be MORE WORK than maintaining the existing program and wouldn't work any better. (In fact, since it would be a wrapper for a 3rd-party app, it would probably work LESS well, since they don't actually know of the code is garbage or not, and have no way to validate it either way, and the vendor might change the interface in a revision.)
If you look at the recent information release about the code base for a brethaliser commonly used in the US for roadside checks (I hope it made the site) then you see what sort of crap makes it into commercial products all the time, so you have to wonder...