Vicente J. Botet Escriba wrote:
Hi,
the recent discussion on the MultiplePrecission Arithmetic library has show that some people has its ow fixed point library.
Is there an interest in a Boost library having as base http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html?
I have started a prototype http://svn.boost.org/svn/boost/sandbox/fixed_point (there is no doc yet but the basic goal is quite close to the N3352 C++ proposal). This prototype should allow you to play a little bit with.
If yes, what would you like to be changed, added or improved in n3352? Next follows some design decisions that IMO need to be decided before hand.
* Should integers and reals be represented by separated classes? * Should signed and unsigned be represented by separated classes? * Should the library use a specific representation for signed numbers (separated sign, 2-complement? Let the user choose? * Should the library provide arbitrary range and resolution and allocators? * Should the library be open to overflow and rounding or just implement some of the possible policies? and in this case which ones? * Should fixed_point be convertible to/from integer/float/double? * Could the result of an arithmetic operation have more range and resolution than his arguments? * Is there a need for a specific I/O? * is there a need for radix other than 2 (binary)? * Should the library implement the basic functions, or should it imperatively implement the C++11 math functions? Could a first version just forward to the c++11 math functions? * Should the library support just one of the know ways to name a fixed-point, a U(a,b), nQm, ...? Provide some ways to move from one to another? * Could expect the same/better performances respect to hand written code? * What should be the size used by a fixed_point instance? _fast? _least? Should the user be able to decide which approach is better for his needs? * Which should be the namespace? boost? boost/fixed_point? boost/binary_fixed_point? boost/bfp? ... * others you can think of.
Please, replay if you are interested, have some experience in the domain, good ideas, ..
Best regards, Vicente
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-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 Good luck, Michael Marcin