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-modes (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 check
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 above
"test_cos.c" on 32bit and 64bit Linux environments around me, this phenomenon
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 <>