Bug?

[Earle R. Horton]

In article <19831 at mimsy.UUCP> steveg at tove.umd.edu (Steve Green) writes:
>
>Why does this program print "no" under AUX and print "yes" on this vax?
>
>main ()
>{
>	double x = .5;
>
>	if (.4 <= x - .1)
>		printf ("Yes\n");
>	else
>		printf ("No\n");
>}
>
>What am I missing?  Is it time for me to re-read my K&R??
>Is it just my AUX that is doing it?  System V?

A/UX gives the seemingly false result because the temporary used to
hold "x - .1" is a 68881 register.  These registers hold two bytes
more of information than a double.  The temporary is not rounded after
the computation of "x - .1," and so the equality test fails.  If you
trace through this code using sdb to single-step machine instructions,
you will see what is happening here.

I don't think K&R says anything about this, because K&R assumes that
"double" is the natural size for a floating point quantity in the
local implementation.  In this case, that is false.  The natural size
is mc68881 96-bit extended.  Note that floating point constants are
stored in 64 bits, not 96.

It is in general bad practice to apply an equality test to the result
of a computation.  Instead of
	( a == b )
use
	( ( a < b + MINDOUBLE ) && ( a > b - MINDOUBLE ) )

MINDOUBLE is in <values.h>.

Furthermore, if the computation is very involved, then the machine
result may diverge from the ideal result by more than this.  All the
gory details may be found in any good textbook on numerical methods.

Earle R. Horton