Re: [boost] GSOC 2013

Subject: Re: [boost] GSOC 2013
From: Michael Marcin (mike.marcin_at_[hidden])
Date: 2013-04-23 19:05:11

On 4/23/13 5:24 PM, Vicente J. Botet Escriba wrote:
> Michael, I was not aware that you have already a fixed-point library in
> http://code.google.com/p/libfixmath/.
>
> Could you give us pointer where this file cross/math/fixed/fixed.hpp is
> located?
>

Sure I had necro'd a thread a while back but it probably got missed. 
Reposting:

On 2/1/13 11:09 PM, Michael Marcin wrote:>
 > Missed this thread, only just came across it while catching up on things.
 >
 > I think fixed-point is a very worthwhile thing although in past
 > discussions it seems like the functionality that everyone agrees upon is
 > a very small subset of what people need in their fixed point types.
 >
 > I worked with fixed-point numbers for embedded systems without FPUs for
 > a few years. Mostly doing real time 3d software rendering with fixed
 > point numbers.
 >
 > I always imagined a boost fixed point library would use some expression
 > template patterns probably built on boost proto and be a drop in
 > replacement for float with no abstraction penalty. That way you could
 > preserve full precision until the end of the full expression.
 > Unfortunately I had neither the time or the TMP expertise to pull it
 > off. Trig functions should be implemented with CORDIC-based algorithms.
 >
 > Here's the fixed point abstraction I used for reference.
 >
 > http://www.mikemarcin.com/media/programming/fixed.7z
 >
 > The main class acts as a drop in replacement for float.
 >
 > template< std::size_t MagnitudeBits, std::size_t FractionalBits >
 > class fixed;
 >
 > The fixed class includes:
 >   - various converting constructors from integers, floating point, and
 > different precision fixed-point types
 >   - comparison operators
 >   - arithmetic operators
 >   - some mixed type arithmetic operators (like fixed * int)
 >   - some really simple expression templates for multiplication
 >
 > as_fixed() function which takes an integral type and returns a type
 > convertible to a fixed-point type
 > i.e.
 > fixed<16,16> a = as_fixed( 1<<16 );
 > assert( a == fixed<16,16>(1) );
 >
 > numeric_limits is specialized for fixed types
 >
 > some math functions:
 >   - abs
 >   - fmod
 >   - floor
 >   - ceil
 >   - ceil_int
 >   - sqrt
 >   - sign_equal
 >   - sign_not_equal
 >   - *missing* true fixed-point trig functions
 >
 > conversion functions:
 >   - to_integer
 >   - to_float
 >   - to_double
 >
 > lame stream operators (convert to/from float):
 >   - std::istream& operator>>(std::istream& stream, fixed<M,F>& x)
 >   - std::ostream& operator<<(std::ostream& stream, const fixed<M,F>& x)
 >
 >
 > Here's some interesting fixed-point resources
 >
 > Anthony Williams wrote an interesting article on fixed-point math.
 > 
http://www.justsoftwaresolutions.co.uk/news/optimizing-applications-with-fixed-point-arithmetic.html 

 >
 >
 > Nils Pipenbrinck wrote an interesting article of fixed-point math which
 > all but disappeared unfortunately.
 > 
http://web.archive.org/web/20080704062813/http://www.devmaster.net/articles/fixed-point-optimizations 

 >
 > Discussion:
 > 
http://web.archive.org/web/20071220190103/http://www.devmaster.net/forums/showthread.php?t=9531 

 >
 >
 > Ken Turkowski's fixed-point square root algorithm
 > http://www.realitypixels.com/turk/computergraphics/FixedSqrt.pdf
 >
 > ARM code inverse square root routines
 > http://www.finesse.demon.co.uk/steven/invsqrt.html
 >