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POI need a fast 96-bit on 64-bit specific division algorithm for a fixed-point math library
 

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  1. POI need a fast 96-bit on 64-bit specific division algorithm for a fixed-point math library
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    <p>I am currently writing a fast 32.32 fixed-point math library. I succeeded at making adding, subtraction and multiplication work correctly, but I am quite stuck at division.</p> <p>A little reminder for those who can't remember: a 32.32 fixed-point number is a number having 32 bits of integer part and 32 bits of fractional part.</p> <p>The best algorithm I came up with needs 96-bit integer division, which is something compilers usually don't have built-ins for.</p> <p>Anyway, here it goes:</p> <pre><code>G = 2^32 notation: x is the 64-bit fixed-point number, x1 is its low nibble and x2 is its high G*(a/b) = ((a1 + a2*G) / (b1 + b2*G))*G // Decompose this G*(a/b) = (a1*G) / (b1*G + b2) + (a2*G*G) / (b1*G + b2) </code></pre> <p>As you can see, the <code>(a2*G*G)</code> is guaranteed to be larger than the regular 64-bit integer. If uint128_t's were actually supported by my compiler, I would simply do the following:</p> <pre><code>((uint128_t)x &lt;&lt; 32) / y) </code></pre> <p>Well they aren't and I need a solution. Thank you for your help.</p>
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    1. CO"typedef struct {unsigned long u[4];} __attribute((aligned(16))) __uint128_t;" Stolen from GCC, and probably won't work elsewhere (and probably isn't necessary with GCC. Yeah, I doubt this helps at all.
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