petersen@uicsrd.csrd.uiuc.edu (06/16/88)
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
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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 );
}