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From: Paul Makepeace on 2 Apr 2010 06:21
(Not sure if this has already been posted; sorry if this is old news.)

I recently noticed FixedPointList[Cos, .7] does not complete with
7.0.1 on OS X 10.6.3 -- symptoms are Mathematica is stuck
"Running...".

After some digging it turns out it's oscillating indefinitely. Here's
my edited exchange with WRI support:

---
If I put a limit on the invocation it returns, then "Raw Form" shows
the numbers are oscillating, presumably related to some precision
issue.

FixedPointList[Cos, .7, 500]

0.7390851332151605, 0.7390851332151608, 0.7390851332151605,
0.7390851332151608, 0.7390851332151605

---
WRI support replied,

Hello,

Thank you for the email.

First I think is kernel problem. But it turned out it is not. I can
reproduce this problem on my Mac machine. And I have consulted this
problem with our development group. This is caused by the recent change of
math library of OSX. The workaround might be specifying SameTest function,
see below:

In[1]:= FixedPointList[Cos, .7, SameTest -> (Equal[N[#1], N[#2]] &)]

Out[1]= {0.7, 0.764842, 0.721492, 0.750821, 0.731129, 0.744421, \
0.73548, 0.741509, 0.73745, 0.740185, 0.738344, 0.739584, 0.738749, \
0.739312, 0.738932, 0.739188, 0.739016, 0.739132, 0.739054, 0.739106, \
0.739071, 0.739095, 0.739079, 0.739089, 0.739082, 0.739087, 0.739084, \
0.739086, 0.739085, 0.739086, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
0.739085}

I have forwarded your examples to our development group and have included
your contact information so that you can be notified when this has been
resolved.
---

HTH, Paul

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