Path: utzoo!news-server.csri.toronto.edu!cs.utexas.edu!swrinde!elroy.jpl.nasa.gov!ucla-cs!ucla-ma!news
From: barry@pico.math.ucla.edu (Barry Merriman)
Newsgroups: comp.sys.next
Subject: Bug in the 68040 chip
Message-ID: <1991Mar4.042515.4740@math.ucla.edu>
Date: 4 Mar 91 04:25:15 GMT
Sender: news@math.ucla.edu
Organization: UCLA Dept. of Math, UCLA Inst. for Fusion and Plasma Research
Lines: 59

Don't be alarmed---but there appears to be a bug in the 68040
chip. It does not compute the hyperbolic tangent function
correctly. 

To see this for yourself, run the following bit of C code
(donated by Steve Wolfram) on a 68040 Next:

printf("%g %g\n", tanh(-1.73287), tanh(-1.73288));

and you will see a clear discontinuity in the values.

At best this would indicate the C math library for the 68040
has a bad tanh(x). But I think (not sure though) that the
68040 itself computes the tanh(x)---in which case the bug
is at a deeper level. 

In the latter case, all is not lost: tanh(x) is not etched
into the 68040 (unlike things like multiply, divide and sqrt),
instead it is done in assembly code.

Background: I originally found this bug in Mathematica on 
my 68040 Next when I plotted Tanh[x] is found it to be 
discontinuos. I thought it was a bug in Mathematica, since I assumed
it computed its own special functions. However, Mathematica has been
cleared by (who else) Steve Wolfram:

>printf("%g %g\n", tanh(-1.73287), tanh(-1.73288));
>in a minimal C program on a NeXT under OS version 2.0 shows a 
>discontinuity.
>Mathematica (apparently mistakenly) relies on built-in math functions.
>Stephen Wolfram

Contributions from other folks on the mathematica mailing list
have shown that the bug occurs only on 68040 NeXTs.


So, this says the problem is not M'ma, but rather either
(1) the C math library for the 68040, or (2) the 68040's builtin
tanh.

*However*, the M'ma I run was originally compiled on a 68030 Next,
and the problem does *not* occur on 030's, so this means the
problem is at a deeper level than the C math library. This seems
to leave only option (2).

The nature of the bug is clear if you plot Tanh[x] in M'ma. Since
Tanh[x] -> -1 as x -> -infinity, at some point you want to 
switch to an approximation of the form Tanh[x] = -1 + Correction[x], where
Correction[x] is a positive correction term. From the plot, its
clear they accidentally switched to Tanh[x] = -1 - Correction[x].
So, a sign error seems to underlie the problem.

Does anyone know if there's a bugs@motorola.com? :-)

--
Barry Merriman
UCLA Dept. of Math
UCLA Inst. for Fusion and Plasma Research
barry@math.ucla.edu (Internet)