X-Recipient: archive-cygwin@delorie.com
DomainKey-Signature: a=rsa-sha1; c=nofws; d=sourceware.org; h=list-id
	:list-unsubscribe:list-subscribe:list-archive:list-post
	:list-help:sender:message-id:date:from:mime-version:to:subject
	:content-type:content-transfer-encoding; q=dns; s=default; b=HyC
	GjrPK26J6OT66SapxGNRObGt7h1jy6cMqmhFdML1PrF4SoQ7u39QuG5NKCfChw46
	p5/nbQY2BpiCn9rydF0qfLv9qP29eelKukYHf5S4xqrjKv/g2quMZ+zD/7cnbYCW
	MFrUrLMnQoYY9ruLWyXiwtgXxSzz8ImIr3Pi7ccY=
DKIM-Signature: v=1; a=rsa-sha1; c=relaxed; d=sourceware.org; h=list-id
	:list-unsubscribe:list-subscribe:list-archive:list-post
	:list-help:sender:message-id:date:from:mime-version:to:subject
	:content-type:content-transfer-encoding; s=default; bh=+VmPFGYth
	3m3/TjnIchxDfBLyvA=; b=KKWuMxB8PVqfoEVloYJAe6rFjqCTJ0KRn/+r5Md1q
	H6Vi0aphS1UxsCOtLNKc4uXGS6I3Sd7KlQRzi4I5FuZGRsPKeNKlow2b18WInieZ
	w2xeUUfjGaWDzzldWjR58YTZszsR9UxTgfVuodIi8n0Sst4BWzzDUOYDoI54VXZE
	d8=
Mailing-List: contact cygwin-help@cygwin.com; run by ezmlm
List-Id: <cygwin.cygwin.com>
List-Subscribe: <mailto:cygwin-subscribe@cygwin.com>
List-Archive: <http://sourceware.org/ml/cygwin/>
List-Post: <mailto:cygwin@cygwin.com>
List-Help: <mailto:cygwin-help@cygwin.com>, <http://sourceware.org/ml/#faqs>
Sender: cygwin-owner@cygwin.com
Mail-Followup-To: cygwin@cygwin.com
Delivered-To: mailing list cygwin@cygwin.com
Authentication-Results: sourceware.org; auth=none
X-Virus-Found: No
X-Spam-SWARE-Status: No, score=-1.9 required=5.0 tests=BAYES_00,FREEMAIL_FROM,RCVD_IN_DNSWL_NONE autolearn=ham version=3.3.2
X-HELO: smtp4-g21.free.fr
Message-ID: <53A3715B.8000904@free.fr>
Date: Fri, 20 Jun 2014 01:25:15 +0200
From: =?ISO-8859-15?Q?Falk_Tannh=E4user?= <falk.tannhauser@free.fr>
User-Agent: Mozilla/5.0 (Windows NT 6.3; WOW64; rv:24.0) Gecko/20100101 Thunderbird/24.6.0
MIME-Version: 1.0
To: cygwin@cygwin.com
Subject: log2() function from C standard library is inaccurate
Content-Type: text/plain; charset=ISO-8859-15; format=flowed
Content-Transfer-Encoding: 7bit
X-IsSubscribed: yes

I noticed that the log2() function in GNU Octave returns inaccurate results
for many arguments that are exactly representable integer powers of 2.
After discussion on the Octave mailing list https://savannah.gnu.org/bugs/?42583
it occurs that Octave doesn't have this problem on most other platforms
(Linux, OS X) and that it is due to the fact that Octave usually uses
log2() from the local C library.

The following C++ program exposes the error:
_________________________________________________________________
// Compilation: g++ -Wall -Wextra -O3 -s testlog2.cxx -o testlog2
#include <limits>
#include <iostream>

#if 0 /////////////////////////////////////////////////////////
inline double log2(double x)
{
   double result;
   asm ("fyl2x" : "=t" (result) : "0" (x), "u" (1.0) : "st(1)");
   return result;
}
#else /////////////////////////////////////////////////////////
#include <math.h>
#endif ////////////////////////////////////////////////////////

int main()
{
   int n = std::numeric_limits<double>::min_exponent
         - std::numeric_limits<double>::digits;
   std::cout << "n = " << n << " ... "
             << std::numeric_limits<double>::max_exponent - 1
             << '\n';
   int errcnt = 0;
   for(double x = std::numeric_limits<double>::denorm_min();
       x < std::numeric_limits<double>::infinity();
       x *= 2, ++n)
   {
     if(n != log2(x))
     {
       std::cout << n << '\n';
       ++errcnt;
     }
   }
   std::cout << "Found " << errcnt << " errors.\n";
   return 0;
}
_________________________________________________________________

With GCC 4.9.0 or 4.8.3 for x86_64-pc-cygwin, erroneous results
are found for 441 values. This seems to be due to the fact that
log2 is implemented in terms of log (as something like log(x)/log(2)).
OTOH, when using the assembler version of log2 (just changing '#if 0'
to '#if 1' in above code); accurate results are always returned.

Falk

--
Problem reports:       http://cygwin.com/problems.html
FAQ:                   http://cygwin.com/faq/
Documentation:         http://cygwin.com/docs.html
Unsubscribe info:      http://cygwin.com/ml/#unsubscribe-simple