Path: utzoo!attcan!uunet!husc6!mailrus!iuvax!pur-ee!uiucdcs!uxc.cso.uiuc.edu!uicsrd.csrd.uiuc.edu!petersen
From: petersen@uicsrd.csrd.uiuc.edu
Newsgroups: comp.sys.amiga
Subject: PDC math library
Message-ID: <42600024@uicsrd.csrd.uiuc.edu>
Date: 15 Jun 88 20:46:00 GMT
Lines: 39
Nf-ID: #N:uicsrd.csrd.uiuc.edu:42600024:000:1664
Nf-From: uicsrd.csrd.uiuc.edu!petersen    Jun 15 15:46:00 1988


I started out using the portable math library that Fred Fish had posted
to the next a while back, but when I ran the Savage benchmark I found
out that the version I was using was missing quite a bit in the accuracy
department.  I did a little research and found out about the CORDIC algorithms
for the elementry functions and rewrote the basic functions using this
method.  CORDIC functions require a table of atan(), and atanh() values which
Macsyma was happy to provide to the required precision (I think I over-did
this part because all of the table values are accurate to 32 digits).  After
fixing more of the floating point bugs in PDC and compiling the new basic
functions I reran the Savage benchmark.  This time the numbers were getting
closer but are still not as good as the sun math library.  The main problem
is that the CORDIC routines I wrote need a few guard digits to throw away
but I can't get the extra digits using the standard double type.

I was hoping to be able to get closer to the ~16|17 digits of precision
that is capable of the IEEE double format.

the value of 'a' = 2.50000000000993960469E+003

As you can see I'm only getting about ~11|12 digits of precision.

Does any one have any ideas to make the library routines a little more
accurate.  Or is speed more important than accuracy (If so I should go
back to the old routines, not very accurate but fairly fast).

-Paul Petersen
--------------------------------
extern double	tan(), atan(), exp(), log(), sqrt();
main()
{	
	int		i;
	double	a;

		a = 1.0;
		for (i = 0; i < 2499; i++) 
			a = tan(atan(exp(log(sqrt(a*a))))) + 1.0;
		printf( "the value of 'a' = %24.20e\n", a );
}