RE: [Algorithms] Fixed point maths.

[Tom F. <tom...@ee...>]

Most 32-bit CPUs have a 32x32->32:32 instruction. Best thing is to use that,
then shift down by 16 bits.

If you insist on C, then let's represent our 32-bit number A with
0x10000*A1+A2, i.e. top and bottom shorts:

(0x10000*A1 + A2) * (0x10000*B1 + B2)
= 0x100000000*(A1*B1) + 0x10000*(A2*B1 + A1*B2) + (A2*B2)

...and you want to shift the result down by 16 bits (coz it's fixed-point
16:16), so you want:

= 0x10000*(A1*B1) + (A2*B1 + A1*B2) + ((A2*B2)>>16)

Careful with the signs - A1 and B1 are signed, while A2 and B2 are unsigned
(for a signed mul - obviously for an unsigned one, everything is unsigned).

But as I say, much quicker to use the CPU's 32x32=32:32 instruction. It's
about two lines of assembly per platform.


TomF.

> -----Original Message-----
> From: gda...@li... 
> [mailto:gda...@li...] On 
> Behalf Of Richard E Collins
> Sent: 09 August 2004 09:01
> To: gda...@li...
> Subject: [Algorithms] Fixed point maths.
> 
> 
>     Anyone got a link to a proper implementaion of fixed 
> point maths. I'm
> intrested in the 16.16 format. I understand the basics but 
> can't decide the
> best way to do mul and div. Also need some help on the other 
> trig funcs.
> I've been wasting the last few days searching google and all 
> I come up with
> is ethier asm solutions that are no good ( I need to port to 
> a system with
> 32bit regs only) or unreadable macros that are just designed 
> to make the
> auther look cleaver. Most implementations are just hacks that 
> will not work
> on the systems that really need to used fixed point maths. 
> One method for
> the mul i've seen is to cast the two values to 64bits do the 
> divide and then
> put back to 32 bits, another converted the numbers to floats 
> did the div and
> back to ints, thats just crazzyness!
> 
>     So, in short, links to 32 fixed point maths methods that 
> only ever use
> 32 bits no floats and is written in working mans maths. ( non 
> of that j =
> p^2 - (g -1 * f) f = some fancy word for 16 and g = a big formula that
> really means shift it by your small thing. )
> 
> 
> 
> Ta from a maths notation illiterate.
> 
> Richard e Collins
> www.maddoggames.com
> 
> 
> 
> 
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