I get the NA Digest newsletter, and a recent issue (NA Digest Sunday, February 24, 2008 Volume 08 : Issue 08) has an article about problems with cosine calculations on some 64 bit Linux environments, and I'm wondering if any Monks have seen this sort of behavior in Perl. I've attached a copy of the article:

From: Tomonori Kouya <>
Date: Sun, 17 Feb 2008 20:45:30 -0500
Subject: Strange Phenomenon of Cosine Function on Linux x86_64 env

Dear NA digest subscribers,

I am in trouble about the problem on cosine function in IEEE754 double
precision. On Fedora Core 4/8 or CentOS 4/5 x86_64 + gcc 4 env, I ran 
+the
program which included the functions below in 4 different rounding-mod
+es (RN,
RZ, RP, RM) in order to know amount of round-off error.

    current_rmode = fegetround(); // get current rounding mode
    fesetround(rmode);            // change rounding mode
    ret = cos(x);                 // cosine function
    fesetround(current_rmode);    // restore rounding mode

As a result, very different values of cosine func are obtained like:

cos(  5.04710873550435011e+01) =
    RN, RZ:   9.78937668119415738e-01,   9.78937668119415627e-01
    RP, RM:   5.55012195441045186e-01,   9.78937668119415627e-01
                  ^^^^^^^^^^^^^^^^^^^^^^^ incorrect!
In the RN mode, the cosine function always returns correct values, but
+ often
incorrect and very different values in other 3 modes. If you want to c
+heck
this phenomenon on your env, you can download my sample program from
http://na-inet.jp/weblog/archives/test_cos.c. By trying to run the abo
+ve
"test_cos.c" on 32bit and 64bit Linux environments around me, this phe
+nomenon
could not be found in 32bit env such as Pentium 3/4 and in Mac OS X 10
+.4 +
Xcode + Core2Duo.

I will appreciate your sending the information about this problem.

Sincerely yours, 
Tomonori KOUYA <>
[download]

Note that I am not Tomonori Kouya, which is why I've removed his (her?) email address.

Apparently, this question is spreading far: it's shown up in comp.lang.fortran.