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Bug in Tanh[x] (summary and speculation)

  • To: mathgroup at
  • Subject: Bug in Tanh[x] (summary and speculation)
  • From: CAMERON at
  • Date: Sat, 2 Mar 91 15:18 EST


Barry Merriman (barry at said that he had
found a bug with Tanh[x] in Mma version 1.2 on the NeXT.
He said that Plot[Tanh[x],{x,-3,3}] produced an incorrect
plot, but defining tanh[x] := ((Exp[x] - Exp[-x])/(Exp[x] + Exp[-x])
and plotting that produced a correct one.  He also said
that one specific value that was computed incorrectly
was Tanh[-1.8], which his setup (computer+software) computes
as -1.053193987153732 but which ought to be -0.946806.
He didn't say which version of the operating system he
was using, nor did he say which processor ('030 or '040).

Alfred Gray (gray at reported reproducing Barry's
results under NeXT OS version 2.0 with both Mma version 1.2
and beta-test version 2.0.  He didn't say which processor, though.

Dave Seaman (ags at reported that Tanh
worked *correctly* with NeXT Mma version 1.2 running under
OS version 1.0 (necessarily on an '030, since version 1.0
of the OS doesn't run on the '040).

Now I have both Mma version 1.2 and Mma version 2.0 beta on
my NeXT with OS version 2.0, and Tanh works *correctly* under
both versions on my machine.  Tanh[-1.8] gives the right
value, and plots of Tanh[x] and tanh[x] (as defined above)
both give the same (correct) graph.  BUT I have an '030
NeXT (I upgraded the software but not the processor).

My conclusion:

If Alfred and Barry both have '040 boards in their NeXTs,
then the data say that (1) version 1.2 or 2.0beta of Mma
doesn't matter, and (2) version 1.0 or 2.0 of the NeXT
operating system doesn't matter, but (3) '030 or '040 processor
DOES matter.  This leads me to accuse the NeXT '040
board as the culprit in this affair.

Other data:

I have no idea how Ken Yip's (yip-ken at CS.YALE.EDU) report
(that plotting Tanh[x] or Sinh[x] from -3 to 3 caused his
Sparc 330 running Mma 1.2 to crash) or Steve Christensen's
report (that his Sun-4/110 and Sparcstation 1 both work
correctly with Mma 1.2) should be weighed in drawing conclusions.

--Cameron Smith
  Baffled Mathematica consultant
  cameron at

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