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From: smithw@hamblin.math.byu.edu (Dr. William V. Smith)
Newsgroups: comp.sys.next
Subject: Re: NeXT Mathematica Bug(really 68040 BUG)
Message-ID: <SMITHW.91Mar5103226@hamblin.hamblin.math.byu.edu>
Date: 5 Mar 91 18:32:26 GMT
References: <1991Mar3.053006.2986@math.ucla.edu>
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In-Reply-To: smithw@hamblin.math.byu.edu's message of 5 Mar 91 10:28:21

mcguire@cs.tamu.edu (Tim McGuire): writes:
>The problem is apparently not with the 68040.  Some helpful person on the
>Mathematica mailing list (whose name slips me) reports the problem
>occurs when the #include <math.h> directive is omitted, but disappears

The test was done on an '030 cube (2.0 software, 1.2 mma).  It is true
that when math.h is not included there appears to be a problem on '030
and the "problem" goes away when you insert #include <math.h>.
However, when math.h is included *on the '040 NeXT* there is still a real
discontinuity in tanh().  Since tanh() is trapped and computed in
software, this is a software fix (hope, hope, hope).  There is a code
error which gives the correct asymptotic value of tanh(x) as x-> minus
infinity, but switches formulas for computing tanh at about x=-1.8.
Witness: (this file "test2.c")

#include <math.h>
    main()
{
        printf("%g %g\n", tanh(-1.73287), tanh(-1.73288));
      }


yields the result (this is on *the '040 cube*)
                               ^^^^^^^^^^^^^
Venus%% cc test2.c -o mathtest
Venus%% mathtest
-0.939394 -1.060605

-1.060605 is NOT the correct value for tanh(-1.73288)
which is in fact this is the result of the same program on
an  '030 cube:
     ^^^^^^^^
zuni$ cc test2.c -o mathtest
zuni$ mathtest
-0.939394 -0.939395

-0.939395 *is* (approximately of course) the correct
value of tanh(-1.73288).

This is an '040 specific problem, and has nothing to do
with mathematica except that mathematica does use machine
coded functions to do numerical work with elementary functions.

(If the #include <math.h> is left out, then both platforms yield
errors since this function is called as a double, and the
compiler doesn't know what to do with it without math.h)

So, NeXT, please include the fix in 2.1 ok???

-Bill

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