[Oberon] FPGA  DIY Dialogs
John R. Strohm
strohm at airmail.net
Wed Feb 6 03:03:20 CET 2019
Floatingpoint numbers are not exact.
No matter how closely they may round, no matter how close they look, they
may not be exactly equal.
You formed a number that is "close" to 123.123. You formed another number
that is "close" to 123.123. When you subtracted the two, you saw the
difference between "close" and "exact". Your two numbers were close, but
they were not exactly equal. They differed by 0.0000076395, or thereabouts.
This is probably very close to the lower error limit of your processor's
floatingpoint representation.
When you multiplied the problem by two, you got "close enough" that the
error rounded off.
I remember losing it one night, trying to explain that an error of a mile or
so, on a problem that involved LITERALLY astronomical distances (with a
system that was probably not too wellconditioned to begin with), was not
bad.
I also remember a lecture in the introductory numerical methods class,
something over forty years ago, that asked the question "What is a good
answer?". The example was solving two simultaneous linear equations. One
solution gave an error that was exactly on one of the lines, but not at the
exact intersection. Another gave a point that was a little way off both
lines. However, if you calculated the distance from the calculated solution
to the exact solution, you found that the second method gave a "closer"
answer. Thirty years later, I'd say something about Linfinity norm vs. L2
norm.
Original Message
From: Tomas Kral
Sent: Tuesday, February 5, 2019 3:14 PM
To: oberon at lists.inf.ethz.ch
Subject: Re: [Oberon] FPGA  DIY Dialogs
Hi,
Testing `Calc', shows something I need yet to improve about (yx). While
(y+x) seems alright. So are y*x, y/x.
Sanity check
123.123 Enter
123.123 Enter

0.0 <= good
This has a problem
123 Enter
.123 Enter
+
1.231230+E02 <= top of stack
123.123 Enter

7.629395E06 <= ???
But this works
123 Enter
.123 Enter
+
1.231230+E02 <= top of stack
123.123 Enter
+
2.462460+E02 <= good
246.246 Enter

0.0 <= good

Tomas Kral <thomas.kral at email.cz>

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