Re: [boost] GSOC 2013

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& x) - std::ostream& operator<<(std::ostream& stream, const fixed& 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-fix...

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/...

Discussion:

http://web.archive.org/web/20071220190103/http://www.devmaster.net/forums/sh...

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