Fixed Point Math library « LeafLabs Garden

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Fixed Point Math library

(57 posts) (12 voices)

Started 5 years ago by gbulmer
Latest reply from iainism

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gbulmer
Moderator

poslathian and I were exchanging posts about Fixed Point maths libaries on http://forums.leaflabs.com/topic.php?id=259&page=2, and I thought we should break FixedPoint out into a new thread.

This is my initial stab at what would be good, i.e. more than adequate:

I think one FixedPoint32 class would be fine to start with, and we can flesh it out as we go.

I am happy to start with a fixed 16.16 format, or a single common format for all instances of the Fixed32 class, to make it easy to get going.

I do think that template classes are the 'right' final solution, but we might find one on the net we can use, and hence avoid ever having to do that ourselves :-)

I would like to get to operator overloading. I did a little bit of programming on PowerPC Macs using the AltiVec function wrappers, and it was pretty ugly.

To start with, we probably only need a constructor, +, -, * and /. If we use int32, we should get ==, <, >, (etc) for free. We'll need a way to get a text string representation of the number.

I assume we are representing the number as an int32, and there are no virtual functions.

An adequate solution is to have some macros which wrap stuff up.
So, typing straight out of my head, with no real planning (no compiler), and no clue ...

Something like:

typedef int FixedPoint32;
#define DECPOS (16)
#define FRACNORM (32-DECPOS)
#define INTNORM (DECPOS)
#define INTPART (0xFFFFFFFF<<DECPOS)
#define FRACPART (0xFFFFFFFF>>FRACNORM)
#define INT(a) (((a)&INTPART)>>DECPOS)
#define FRAC(a) ((a)&FRACPART)
#define FIX(i,f) ((i)<<DECPOS) | ((f)&FRACPART)
#define add(a, b) ((a)+(b))
#define sub(a, b) ((a)-(b))
#define mul(a, b) (FIX(INT(a)*INT(b),(FRAC(a)*FRAC(b))>>FRACNORM))
etc.

This is highly likely to be utter nonsense, it's just to illustrate that it should be a relatively small amount of work to get something working.

I am more than happy if someone can point out a reasonably compact, Open Source C/C++ library that would work nicely on the STM32F.

Is this interesting as a project?
If it is, should we add a little github repo to work on it?

Posted 5 years ago #
poslathian
LeafLabs

this is exactly along the lines i was thinking: I created a personal repo for it, we had a user patch the other day to clean up how to include external libs into builds, ill see if we cant mesh with that new scheme nicely. Ill be out for the rest of the week though, so Ill catch up with this next week.

https://github.com/poslathian/MapleFixedPoint (empty repo)

Posted 5 years ago #
gbulmer
Moderator

poslathian - I'm working through the week, and going to Madlab at the weekend, so no rush.

I literally wrote that off the top of my head, so whatever you have is likely better.

(I could copy and paste it into a Maple file, and get the systax errors out of it :-)

Posted 5 years ago #
gbulmer
Moderator

I stumbled across a relatively small, vanilla C multi-precision integer library:
http://piumarta.com/software/mpint/

It is distributed under an MIT license, so should be compatible with Maple.

It is by the insanely talented Ian Piumarta of View Points Research http://www.viewpointsresearch.org/html/writings.htm

It isn't Fixed Point arithmetic, but it maybe a simple place to start :-)

Posted 5 years ago #
mabl
Member

Isn't there support for Fixed Point Math in gcc? As far as I know, the only thing one has to do is to implement the hardware specific parts in ASM. I guess this would be the fastest and cleanest solution...

Posted 5 years ago #
gbulmer
Moderator

I didn't know that. Thank you.

Do you mean this http://gcc.gnu.org/wiki/FixedPointArithmetic

How do I get gcc to generate code?

Posted 5 years ago #
poslathian
LeafLabs

hmm both interesting options - if anyone wants to start bringing up a library project to add this sort of functionality, gbulmer started a branch a while back that can be revived. Perhaps we can use it as a foundation for an audio synthesis library. I will make time for this if there is interest in collaboration!

Posted 5 years ago #
gbulmer
Moderator

If fixed point "just works", a friend might become very interested in audio sysnthesis.

(I'm still trying to catch up, so I won't get to this till end of week, or later)

I assume declaring the "_Fract" and "_Accum" and "_Sat" should 'just work'?

Posted 5 years ago #
mabl
Member

I tried finding some more information on fixed point in gcc but there hardly is any. For ATMEL AVRs there is a patch [1] that is now afaik. also in the official ATMEL toolchain.

Maybe this is already implemented for arm? So the only thing you'd need is a gcc with --enable-fixed-point..

[1] http://www.avrfreaks.net/index.php?name=PNphpBB2&file=viewtopic&t=73345

Posted 5 years ago #
gbulmer
Moderator

I looked down the gcc FixedPoint wiki page
http://gcc.gnu.org/wiki/FixedPointArithmetic

and this looks less promising:
"9. Support fixed-point operators using real instructions in the backends (ex, MIPS, Blackfin). (The MIPS backend has added several fixed-point operators.) "

I tried running arm-none-eabi-gcc with a dumb little (Xcode generated) example:
#include <stdio.h>
_Sat _Fract sat_add3 (_Sat _Fract a, _Sat _Fract b) { return a + b; } int main (int argc, const char * argv[]) { // insert code here... _Sat _Fract a, b;
printf("Hello, World!\n"); return 0; }

but got:

main.c:4: error: fixed-point types not supported for this target
main.c:4: error: fixed-point types not supported for this target
main.c:4: error: fixed-point types not supported for this target
main.c: In function 'main':
main.c:12: error: fixed-point types not supported for this target

I tried --enable-fixed-point but got

cc1: error: unrecognized command line option "-fenable-fixed-point"

I am going to pursue it, as audio is one of my interests. But I'm unsure what to try next.

Posted 5 years ago #
mabl
Member

It could be that fixed points are also only supported for C (and not C++) but there seems to be work on it:
http://www.mail-archive.com/gcc@gcc.gnu.org/msg49765.html

Posted 5 years ago #
gbulmer
Moderator

mabl - That was C. The file was main.c, the compiler was the ARM version of gcc that LeafLabs includes in the Maple IDE donload. I believe the .c suffix should cause gcc to treat it as a C source file.

But I will keep chipping away, a few minutes a day :-)

Posted 5 years ago #
poslathian
LeafLabs

gblumer - that is disappointing that gcc shrugged off your efforts so directly. If we can agree on what short of front end to fixed point types seem reasonable I suppose well just have to write our own library.

Posted 5 years ago #
poslathian
LeafLabs

gbulmer thats a good thread on the avr forums. I agree with some of the posters there that we should have saturating types. Rollover is almost always the wrong thing (especially with non integers), but saturation is fairly often the right thing. It does slow things down pretty substantially I would imagine though.

Posted 5 years ago #
gbulmer
Moderator

I found this fixed point library last night:
http://code.google.com/p/fixpointlib/

I haven't downloaded it.
It doesn't seem to have progressed after its initial release last June.

It has saturating operations, multiply, sqrt, sin, cos, tan, ... x^y, etc.

AND, it claims to be tested on Cortex-M3!
It gives execution timings on a Cortex-M3 simulator.
Looks a bit ugly, but that could be wrapped up in C++ if it really mattered.

Posted 5 years ago #

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