Subject: improved accuracy for timing

From: Chee Yap <[email-masked]>
Date: Wed, 8 Dec 1999 13:39:50 -0500 (EST)

Dear Class:

I will discuss an issue you should be aware of
if your exponents looks suspicious.  

1)  Remember that it is not the absolute
timing that we are interested in, but the
exponents for Karatsuba and the library's multiplication.

2) The
	System.currentTimeMillis()
is a long integer.  This is 64 bits.

If you perform division, the result is probabily
a double number.  This typically means that the system
will first convert a long integer to a double value.

YOU CAN LOSE PRECISION THIS WAY, because a double
has only 53 bits for the mantissa (and 11 bits for exponent).

In particular, if you try to compute average time (which
my previous emails tell you NOT to do), you may already
have lost all the important bits in your numbers.

If you do not understand this point, come speak to one of
us (or ask your classmates who know).

--Chee