46 lines
1.6 KiB
Typst
46 lines
1.6 KiB
Typst
#import "@local/handout:0.1.0": *
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= Introduction
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In 2005, ID Software published the source code of _Quake III Arena_, a popular game released in 1999. \
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This caused quite a stir: ID Software was responsible for many games popular among old-school engineers (most notably _Doom_, which has a place in programmer humor even today).
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#v(2mm)
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Naturally, this community immediately began dissecting _Quake_'s source. \
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One particularly interesting function is reproduced below, with original comments: \
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#v(3mm)
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```c
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float Q_rsqrt( float number ) {
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long i;
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float x2, y;
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const float threehalfs = 1.5F;
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x2 = number * 0.5F;
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y = number;
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i = * ( long * ) &y; // evil floating point bit level hacking
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i = 0x5f3759df - ( i >> 1 ); // [redacted]
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y = * ( float * ) &i;
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y = y * ( threehalfs - ( x2 * y * y ) ); // 1st iteration
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// y = y * ( threehalfs - ( x2 * y * y ) ); // 2nd iteration, this can be removed
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return y;
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}
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```
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#v(3mm)
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This code defines a function `Q_sqrt`, which was used as a fast approximation of the inverse square root in graphics routines. (in other words, `Q_sqrt` efficiently approximates $1 div sqrt(x)$)
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#v(3mm)
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The key word here is "fast": _Quake_ ran on very limited hardware, and traditional approximation techniques (like Taylor series)#footnote[Taylor series aren't used today, and for the same reason. There are better ways.] were too computationally expensive to be viable.
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#v(3mm)
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Our goal today is to understand how `Q_sqrt` works. \
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To do that, we'll first need to understand how computers represent numbers. \
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We'll start with simple binary integers---turn the page.
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