[Bug math/13381] New: rounding problem wih sincosl

[Bug math/13381] New: rounding problem wih sincosl

[gastineau at imcce dot fr]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

             Bug #: 13381
           Summary: rounding problem wih sincosl
           Product: glibc
           Version: 2.14
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: aj@suse.de
        ReportedBy: gastineau@imcce.fr
    Classification: Unclassified


With some input values, the sincosl function and sinl returns a different value
for the sin part. 

This problem occurs with glibc 2.14.

The code source is at the end of the message.

The output with these compilers is :
gcc -m64 bugsincos.c -O0 -o bugsincos -lm
./bugsincos
diffC=0.000000e+00 C1=0xf.e8f0776670a18eap-4 C=0xf.e8f0776670a18eap-4
diffS=-6.776264e-21 S1=0xd.903ba52345a81a4p-7 S=0xd.903ba52345a81a5p-7

diffS must be 0 if same algorithm is used inside the math library.

If I compile with "-O3", the problem doesn't occur because it doesn't use the
math library.
I give some system information below and the source code.

Mickaël

xxxxx$ gcc  -m64 bugsincos.c -O0 -o bugsincos -lm
xxxxx$ ./bugsincos
diffC=0.000000e+00 C1=0xf.e8f0776670a18eap-4 C=0xf.e8f0776670a18eap-4
diffS=-6.776264e-21 S1=0xd.903ba52345a81a4p-7 S=0xd.903ba52345a81a5p-7
xxxxx$ nm bugsincos | grep sincosl
                 U sincosl@@GLIBC_2.2.5
xxxxx$ rpm -qa | grep glibc
glibc-static-2.14-5.x86_64
glibc-headers-2.14-5.x86_64
glibc-devel-2.14-5.x86_64
glibc-2.14-5.i686
glibc-common-2.14-5.x86_64
glibc-2.14-5.x86_64
xxxxx$ gcc --version
gcc (GCC) 4.6.1 20110908 (Red Hat 4.6.1-9)
Copyright (C) 2011 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.


-------------- cut here----------------
#include <mathimf.h>
#include <stdio.h>

int main()
{
long double X=0xd.96c3941c1094ed5p-7L;
long double C=cosl(X);
long double S=sinl(X);
long double C1, S1;
sincosl(X, &S1, &C1);
printf("diffC=%Le C1=%La C=%La\n", C1-C, C1, C);
printf("diffS=%Le S1=%La S=%La\n", S1-S, S1, S);
return 0;

}
-------------- cut here----------------

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[Bug math/13381] rounding problem wih sincosl

[gastineau at imcce dot fr]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

gastineau at imcce dot fr changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |gastineau at imcce dot fr

--- Comment #1 from gastineau at imcce dot fr 2011-11-07 16:17:24 UTC ---
The correct source code is :


#define _GNU_SOURCE
#include <math.h>
#include <stdio.h>

int main()
{
long double X=0xd.96c3941c1094ed5p-7L;
long double C=cosl(X);
long double S=sinl(X);
long double C1, S1;
sincosl(X, &S1, &C1);
printf("diffC=%Le C1=%La C=%La\n", C1-C, C1, C);
printf("diffS=%Le S1=%La S=%La\n", S1-S, S1, S);
return 0;

}

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[Bug math/13381] rounding problem wih sincosl

[schwab@linux-m68k.org]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #2 from Andreas Schwab <schwab@linux-m68k.org> 2011-11-08 07:47:15 UTC ---
You'll have to complain to Intel.

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[Bug math/13381] rounding problem wih sincosl

[gastineau at imcce dot fr]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #3 from gastineau at imcce dot fr 2011-11-08 08:36:20 UTC ---
I don't understand. I use the gcc compiler and the glibc. 
You should check the second source code.  The first source code was an error.
 The second source code produce the error.

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[Bug math/13381] rounding problem wih sincosl

[schwab@linux-m68k.org]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #4 from Andreas Schwab <schwab@linux-m68k.org> 2011-11-08 08:58:45 UTC ---
Everything is implemented in hardware.

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[Bug math/13381] rounding problem wih sincosl

[vincent-srcware at vinc17 dot net]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

Vincent Lefèvre <vincent-srcware at vinc17 dot net> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |vincent-srcware at vinc17
                   |                            |dot net

--- Comment #5 from Vincent Lefèvre <vincent-srcware at vinc17 dot net> 2011-11-09 00:48:59 UTC ---
The AMD Opteron doesn't have this "bug".

Now, there's a much more important problem than the rounding, on both Intel and
AMD processors: the fact that their implementation is broken due to the lack of
accurate range reduction. Try with X = 1.0e22 and compare the results obtained
with -O0 (hardware implementation) and -O3 (obtained with MPFR, I suppose, thus
correct).

In short, the hardware implementation must not be used. If the user wants a
fast implementation but incorrect results on large values, he can still use
compiler options like -ffast-math, with which the compiler would generate
hardware instructions directly.

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[Bug math/13381] rounding problem wih sincosl

[drepper.fsp at gmail dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

Ulrich Drepper <drepper.fsp at gmail dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|NEW                         |RESOLVED
                 CC|                            |drepper.fsp at gmail dot
                   |                            |com
         Resolution|                            |INVALID

--- Comment #6 from Ulrich Drepper <drepper.fsp at gmail dot com> 2011-12-22 16:33:15 UTC ---
All the more reason to complain to Intel.

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[Bug math/13381] rounding problem wih sincosl

[gastineau at imcce dot fr]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

gastineau at imcce dot fr changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|RESOLVED                    |REOPENED
         Resolution|INVALID                     |

--- Comment #7 from gastineau at imcce dot fr 2011-12-22 16:49:07 UTC ---
if the user does not specify "-ffast-math", the user wants to get the same
result with a call to sincos as two distincts calls to sin and cos, even if the
hardware gives different results.

if you do not want correct this bug, you must specify in the documentation that
the result of sincos may be not the same as two calls to sin and cos. This is a
very important information for developers who take care about accuracy.

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[Bug math/13381] rounding problem wih sincosl

[drepper.fsp at gmail dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

Ulrich Drepper <drepper.fsp at gmail dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|REOPENED                    |RESOLVED
         Resolution|                            |INVALID

--- Comment #8 from Ulrich Drepper <drepper.fsp at gmail dot com> 2011-12-22 17:45:01 UTC ---
If you don't understand how computers work then don't bother other people.  The
function is implemented by a single instruction.  It's entire Intel's
responsibility to provide the result.

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[Bug math/13381] rounding problem wih sincosl

[gastineau at imcce dot fr]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #9 from gastineau at imcce dot fr 2011-12-22 19:31:39 UTC ---
The current glibc documentation says :

In many applications where sin and cos are used, the sine and cosine of the
same angle are needed at the same time. It is more efficient to compute them
simultaneously, so the library provides a 
function to do that.

— Function: void sincos (double x, double *sinx, double *cosx)
— Function: void sincosf (float x, float *sinx, float *cosx)
— Function: void sincosl (long double x, long double *sinx, long double *cosx)
These functions return the sine of x in *sinx and the cosine of x in *cos,
where x is given in radians. Both values, *sinx and *cosx, are in the range of
-1 to 1.

This function is a GNU extension. Portable programs should be prepared to cope
with its absence.



So, if it's a GNU extension, it's not of the responsability of the user to
check that it gives a different result, as the documentation says no thing
about the implementation.

Mickaël




Le 22/12/11 18:45, drepper.fsp at gmail dot com a écrit :
> http://sourceware.org/bugzilla/show_bug.cgi?id=13381
>
> Ulrich Drepper<drepper.fsp at gmail dot com>  changed:
>
>             What    |Removed                     |Added
> ----------------------------------------------------------------------------
>               Status|REOPENED                    |RESOLVED
>           Resolution|                            |INVALID
>
> --- Comment #8 from Ulrich Drepper<drepper.fsp at gmail dot com>  2011-12-22 17:45:01 UTC ---
> If you don't understand how computers work then don't bother other people.  The
> function is implemented by a single instruction.  It's entire Intel's
> responsibility to provide the result.
>

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[Bug math/13381] rounding problem wih sincosl

[vincent-srcware at vinc17 dot net]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #10 from Vincent Lefèvre <vincent-srcware at vinc17 dot net> 2011-12-23 11:01:30 UTC ---
I agree that this bug here can be seen as invalid, as long as the error is not
greater than the documented error bound. It's even "normal" that sincosl
doesn't return the same result as sinl and cosl, as the algorithm is different
and the goal of such a hardware implementation is to provide a result quickly,
though not highly accurate.

Now, there could be two valid related bugs:

1. As these hardware functions seem to be completely wrong for large arguments
(on both Intel and AMD), the glibc should not use them in such cases. At least,
it should provide an option so that it can be compiled to use a software
implementation. Note: though relatively fast hardware range reduction is
possible, I'm sure that was the intent of these hardware instructions when they
were introduced in the 80's (?). I mean that blindly using these hardware
instructions in a system library (i.e. without knowing the application) could
be seen as a misuse of these instructions.

2. The IEEE 754-2008 standard recommends correct rounding. So, a RFE to have
correct rounding would be valid, but perhaps wontfix for the extended precision
(not standard, its primary goal being to ease accurate implementations of the
double precision). For the double precision, unless this has been fixed, sincos
is affected by this problem, which affects code using sin and cos compiled by
GCC; see

  http://www.vinc17.net/research/slides/sieste2010.pdf

Slides 11-15 for this point.

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[Bug math/13381] rounding problem wih sincosl

[gastineau at imcce dot fr]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #11 from gastineau at imcce dot fr 2011-12-23 11:20:24 UTC ---
The documentation does not mention that the algorithm is different and that
sincosl could return a different result that cosl and sinl.
So I think that the documentation may be updated to specify that result could
be differents.



Le 23/12/11 12:01, vincent-srcware at vinc17 dot net a écrit :
> http://sourceware.org/bugzilla/show_bug.cgi?id=13381
>
> --- Comment #10 from Vincent Lefèvre<vincent-srcware at vinc17 dot net>  2011-12-23 11:01:30 UTC ---
> I agree that this bug here can be seen as invalid, as long as the error is not
> greater than the documented error bound. It's even "normal" that sincosl
> doesn't return the same result as sinl and cosl, as the algorithm is different
> and the goal of such a hardware implementation is to provide a result quickly,
> though not highly accurate.
>
> Now, there could be two valid related bugs:
>
> 1. As these hardware functions seem to be completely wrong for large arguments
> (on both Intel and AMD), the glibc should not use them in such cases. At least,
> it should provide an option so that it can be compiled to use a software
> implementation. Note: though relatively fast hardware range reduction is
> possible, I'm sure that was the intent of these hardware instructions when they
> were introduced in the 80's (?). I mean that blindly using these hardware
> instructions in a system library (i.e. without knowing the application) could
> be seen as a misuse of these instructions.
>
> 2. The IEEE 754-2008 standard recommends correct rounding. So, a RFE to have
> correct rounding would be valid, but perhaps wontfix for the extended precision
> (not standard, its primary goal being to ease accurate implementations of the
> double precision). For the double precision, unless this has been fixed, sincos
> is affected by this problem, which affects code using sin and cos compiled by
> GCC; see
>
>    http://www.vinc17.net/research/slides/sieste2010.pdf
>
> Slides 11-15 for this point.
>

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[Bug math/13381] rounding problem wih sincosl

[vincent-srcware at vinc17 dot net]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #12 from Vincent Lefèvre <vincent-srcware at vinc17 dot net> 2011-12-23 11:41:46 UTC ---
(In reply to comment #11)
> The documentation does not mention that the algorithm is different and that
> sincosl could return a different result that cosl and sinl.

It doesn't have to. The C standard doesn't even require that the following
program always return true on finite values of c (i.e. x and y can be
different).

int test (double c)
{
  double x, y;
  x = sin(c);
  y = sin(c);
  return x == y;
}

See my SIESTE slides to see how one can easily affect the result returned by
sin().

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[Bug math/13381] rounding problem wih sincosl

[martyn.j.corden at intel dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

martyn.j.corden at intel dot com changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |martyn.j.corden at intel
                   |                            |dot com

--- Comment #13 from martyn.j.corden at intel dot com 2012-01-09 20:02:37 UTC ---
Yes, this is likely an issue of slightly different algorithms in the math
library. The main purpose of a sincos function is to give results more
quickly/efficiently that two separate calls to sin and cos, and that might be
better achieved with a different algorithm.
      The same issue arose in the math library provided with the Intel
compiler, libimf. Following a customer report, a change was made for version
12.1 of the Intel compiler, (in Intel Composer XE 2011 SP1), so that sincosl
would return the same results as calls to sinl and cosl. Presumably, similar
changes could be made to the GNU libm if this is felt to be an important issue,
otherwise the sincos documentation should be updated to warn of the potential
difference.  If you have access to Intel’s libimf, it is also possible to link
to it when compiling with gcc, to work around this issue.

Martyn Corden      (Intel Developer Support)

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[Bug math/13381] rounding problem wih sincosl

[vincent-srcware at vinc17 dot net]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #14 from Vincent Lefèvre <vincent-srcware at vinc17 dot net> 2012-02-03 14:49:31 UTC ---
Note: for the correctness problem on large arguments (which is a much more
important problem than the one reported here), I've reported bug 13658. A
consequence might be that the problem reported here would no longer appear, but
without any guarantee (it is not about correct rounding yet).

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[Bug math/13381] rounding problem wih sincosl

[fweimer at redhat dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=13381

Florian Weimer <fweimer at redhat dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
              Flags|                            |security-

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