[comp.os.minix] floating point routines

cuccia@ucbarpa.Berkeley.EDU (Nick Cuccia) (07/12/87)

In article <1205@botter.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:

>1) No floats.  I agree, they would be nice, but I haven't personally used
>   a number > 32767 in years.  Is anyone working on floats?

>Andy Tanenbaum (ast@cs.vu.nl)

I'm currently working on versions of /usr/lib/libm.a (math functions)
and /usr/lib/libmp.a (multiple precision integer functions) to be distributed
with GNU, and will post sources when I'm finished.  My development
environments are several VAXen (750 running 4.2BSD, 8600 running 4.3BSD) and
a Sun 3/280 running SunOS v3.2, and will port the routines to MINIX when
final tuning is finished.

This brings me to another question: one of the niceties of the C compiler
for the Sun is the '-f' flag, through which the user can tell the compiler
what kind of acceleration hardware, if any, is installed in the workstation
or server.  For those working on the C compiler: how difficult would it be
to install such a flag, whose args would be the following:

	flag		meaning
	----		-------
	-fsingle	do not promote floats to doubles
	-f8087		compile code to be used with 8087 processor
	-fswitch	generate code that determines whether or not
			an accelerator chip is installed at runtime.

--Nick

tasayco@phoenix.Princeton.EDU (Maria Tasayco) (11/15/90)

Keywords: atari, M68000, floating point

I have received many responses to my offering of a (soon to be)
IEEE-compliant floating point package for the m68000 GNU C compiler,
so I decided to post the sources. Sorry for the length of the article,
but I think there is enough interest to justify its posting ...

Disclaimer: THIS IS A VERY CRUDE PACKAGE! It is evolving, and I
welcome suggestions and/or bug finding-fixing, but can't guarantee,
at the moment, that it is working correctly. But please try it out.

------------------------------------------------------------------------
				   
Here they are! The floating point code is divided in the following files:

	float.s		contains the code for single precision
	double.s	contains the code for double precision
	floatex.s	defines the floating point condition code register,
			which is used, among other things, to signal 
			exceptions (over- and underflow, divide by zero,
			inexact result, invalid operation).

The fp CCR (__fpCCR) looks like:

		struct {
		  short _exception_bits;	
		  short _trap_enable_bits;	
		  short _sticky_bits;
		  short _rounding_mode;
		  short _format;
		} _fpCCR;

and it is globally defined, so you can modify it at run time (if you know
what you are doing!). The different fields are more or less explained in
floatex.s, but here goes a little more detail:

 The exception bits (V Z O U I: invalid operation, divide by zero, overflow,
underflow, inexact result, in this order) are set by each arithmetic routine
(should comparison set them also? I guess so, but haven't done that yet) if
they apply. They are cleared otherwise, so _exception_bits always reflect the
result of the last operation. The _sticky_bits, on the other hand, are set
as _exception_bits but never cleared (unless you do it explicitely). Thus they
can be used after a long calculation to check if something weird happened in
the middle. The _trap_enable_bits are (will be!) checked after each exception
to see whether we have to trap (not yet implemented). The _format field was 
put there to give information to the exception handler as to whether we were
dealing with singles or doubles, or long doubles (not yet implemented, but
probably in the near future). The _rounding_mode should be used to choose one
of the four rounding modes defined by IEEE. For the moment I am doing a very
simple minded rounding. Hopefully this will change soon.

 Note that I am also including dflonum.c and flonum.h (with one change),
as you will need the conversion routines which I haven't yet written.
If you happen to have the code for each routine in a separate file (as is
the case with the Minix library), here is the list of routines which are
to be replaced:

single precision:
		___addsf3
		___subsf3
		___mulsf3
		___divsf3
		___negsf2
		___cmpsf2
double precision:
		___adddf3
		___subdf3
		___muldf3
		___divdf3
		___negdf2
		___cmpdf2

Compile double.s, float.s, floatex.s and, if you need, dflonum.c with MYFLOAT
#defined (which selects only the conversion routines), and pull out dflonum.o 
and sflonum.o from gnu.olb (#if TOS), or the named routines from libc32.a (I
haven't tested the things with short ints, but they should work OK, I guess),
and insert the ones you just compiled. THEN START TESTING, PLEASE!!! I am sure
a lot of bugs crept in (I just finished fixing a bug in the handling of denor-
malized numbers), so I will really appreciate any feeback, even if it is to
tell me that I wrote crap! Also, the routines are (almost certainly!) not 
optimized, so anybody can try his/her hands at it (but please tell me what
changes you make, so we can keep a decent library for all of us). 

NOTE: BEWARE OF SCAN AND PRINT FUNCTIONS! The ones which come standard with
gcc do not support denormalized numbers (they print 0.0), and have some
problems with the input of floats. For example, I found that if I input
1.0e-308, or something like that, there is no problem as a double, but 
as a float it gets converted to a number around 18! This is most probably
a problem with the conversion routines, which will be my next task. But 
be prepared for weird things. Also, the printing routines definitely do not
support INFINITY or NaN. If somebody is willing to do the changes, that 
shouldn't be very hard (you have to change in doprnt.c to check whether
the number is finite or not, and while you are at it, change the check for
zero so as to handle denormalized numbers).

 A very simple program to test one routine is the following:

#include <stdio.h>

void main()
{
  float f;
  int index, n = 50;
  union { float f; int i; } f2i;

  f = 10000.0 / 3.0;
  for (index = 1; index < n; index++) {
    f = f / (float)10.0;	/* don't forget the cast! */
    f2i.f = f;
    printf(" %d %08x %e \n", index, f2i.i, f);
  }
}

which should result in something like this

 1 43a6aaaa 3.333333e+02 
 2 42055555 3.333333e+01 
 3 40555555 3.333333e+00 
 /* many more lines ... */
 40 02e2dad6 3.333332e-37 
 41 01357bde 3.333332e-38 
 42 00244bf9 0.000000e+00 
 43 0003a132 0.000000e+00 
 44 00005ceb 0.000000e+00 
 45 0000094a 0.000000e+00 
 46 000000ed 0.000000e+00 
 47 00000017 0.000000e+00 
 48 00000002 0.000000e+00 
 49 00000000 0.000000e+00 

If you forget the cast to float you will see that after number 42 it goes
berserk. This is again, presumably, a problem with the conversion routines, 
since the generated code will attempt to do the calculation in double 
precision and then convert to single.


THINGS I HAVEN'T DONE:

1. As I said before, rounding is done in a very naive way. This should be
   improved.
2. Trapping on exceptions is "almost there", but I haven't yet tried it.
3. In the comparison routine there should be a check for NaN, since they
   are unordered. Since the compiler will only test for 0, positive or 
   negative, it is not clear how to pass this information back (maybe 
   through exception trapping?).
4. Long doubles. Actually, I wrote some code for long doubles some time
   ago, but it is in a slightly different format, so I have to work on
   it a little (should I support denormalized long doubles?).
5. The conversion routines! These need to be redone to check for INFINITY,
   NaN, and the other exceptions. I am working on them, but have to write
   my thesis ...
6. Scanning and printing routines. These will probably not require too 
   much effort. Any volunteers?

 It is my intention to support this code, so if people is interested they
should e-mail me so I can send them bug-fixes and/or improvements. I started
writing this code because (besides my being masochist) sometimes I want to
do numerical calculations on the atari, since I can leave it running for a
long time and nobody will complain, and didn't want to use any other
compiler than gcc (which I think is great, both in size and in scope!), 
but found that their floating point support was lacking quite a bit.

 Finally, any comments you may have, or any questions, please feel free
to send them to me. 

	Francisco Figueirido
	e-mail: tasayco@phoenix.princeton.edu
		figuei@max.physics.sunysb.edu


P.S.: I hope the code is readable ...

What follows is an uuencoded, compressed, shar-ed bunch of files
(if you need them in a different format, please tell me). I am 
including only the sources.

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