[Bug math/15563] New: sincos() is incorrect for long double and large inputs on x86_64

[Bug math/15563] New: sincos() is incorrect for long double and large inputs on x86_64

[carlos at redhat dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=15563

            Bug ID: 15563
           Summary: sincos() is incorrect for long double and large inputs
                    on x86_64
           Product: glibc
           Version: 2.18
            Status: NEW
          Keywords: glibc_2.15
          Severity: normal
          Priority: P2
         Component: math
          Assignee: unassigned at sourceware dot org
          Reporter: carlos at redhat dot com
                CC: aj at suse dot de, bugdal at aerifal dot cx, carlos at redhat dot com,
                    ppluzhnikov at google dot com, vincent-srcware at vinc17 dot net
        Depends on: 13658
            Blocks: 13851, 13852, 13854

Still broken for long double on x86/x86_64.

Tested with current sources.

+++ This bug was initially created as a clone of Bug #13658 +++

sincos() is inaccurate for large inputs on x86_64: with glibc 2.13,

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

int main (void)
{
  volatile double x = 1.0e22;
  double s1, s2, c1;

  sincos (x, &s1, &c1);
  s2 = sin (x);
  printf ("s1 = %.17g\n", s1);
  printf ("s2 = %.17g\n", s2);
  return 0;
}

outputs:

s1 = 0.46261304076460175
s2 = -0.85220084976718879

(s2 is the correct value). I suppose that contrary to the other trig functions,
glibc uses the hardware sincos instruction, which has never been meant to be
used directly by a C library (the hardware elementary functions of the x86
processors were designed for small inputs, and they must not be used by code
where inputs can be large, like here). The sincos() function can simply be
implemented by a call to sin() and a call to cos() on this target.

Ditto for sincosf() and sincosl().

Note: x86 (32 bits) has the same problem, but it has been claimed that users
don't care about correctness on this target.

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[Bug math/15563] sincos() is incorrect for long double and large inputs on x86_64

[carlos at redhat dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=15563

Carlos O'Donell <carlos at redhat dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
           Keywords|glibc_2.15                  |

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[Bug math/15563] sincos() is incorrect for long double and large inputs on x86_64

[joseph at codesourcery dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=15563

--- Comment #1 from joseph at codesourcery dot com <joseph at codesourcery dot com> ---
I can't tell what you think the bug is here.  You give a testcase for 
double but talk about long double, and with the obvious substitutions

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

int main (void)
{
  volatile long double x = 1.0e22;
  long double s1, s2, c1;

  sincosl (x, &s1, &c1);
  s2 = sinl (x);
  printf ("s1 = %.17Lg\n", s1);
  printf ("s2 = %.17Lg\n", s2);
  return 0;
}

I get on x86_64 (with current glibc)

s1 = -0.8522008497671888
s2 = -0.8522008497671888

which appears to be what you'd expect.  So what program are you building, 
with what options, and running with current glibc, and getting what 
results, and what would you like instead?

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[Bug math/15563] sincos() is incorrect for long double and large inputs on x86_64

[carlos at redhat dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=15563

Carlos O'Donell <carlos at redhat dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|NEW                         |RESOLVED
         Resolution|---                         |FIXED

--- Comment #2 from Carlos O'Donell <carlos at redhat dot com> ---
(In reply to joseph@codesourcery.com from comment #1)
> I can't tell what you think the bug is here.  You give a testcase for 
> double but talk about long double, and with the obvious substitutions

I hadn't seen and could not find any discussion of this fix for long double
(remember at the time ldbl-96 did not correctly do argument reduction).

The additional test case I was using was:

cat >> test.c <<EOF
#include <stdio.h>
#include <math.h>
int main() {
        long double x;

        for (x=1.0;x<1.e38;x*=2.0)
                printf("%Le %Lf\n",x,sinl(x));
        return 0;
}
EOF
gcc -Wall -pedantic
-Wl,-rpath=/home/carlos/build/glibc:/home/carlos/build/glibc/math
-Wl,--dynamic-linker=/home/carlos/build/glibc/elf/ld.so -o test test.c -lm

Producing the following results for long double on x86-64 with master:

1.000000e+00 0.841471
2.000000e+00 0.909297
4.000000e+00 -0.756802
8.000000e+00 0.989358
1.600000e+01 -0.287903
3.200000e+01 0.551427
6.400000e+01 0.920026
1.280000e+02 0.721038
2.560000e+02 -0.999208
5.120000e+02 0.079518
1.024000e+03 -0.158533
2.048000e+03 -0.313057
4.096000e+03 -0.594642
8.192000e+03 -0.956173
1.638400e+04 -0.559938
3.276800e+04 0.927856
6.553600e+04 0.692065
1.310720e+05 -0.999114
2.621440e+05 -0.084107
5.242880e+05 0.167618
1.048576e+06 0.330493
2.097152e+06 0.623844
4.194304e+06 0.975129
8.388608e+06 0.432248
1.677722e+07 -0.779564
3.355443e+07 -0.976517
6.710886e+07 0.420760
1.342177e+08 -0.763403
2.684355e+08 -0.986198
5.368709e+08 0.326568
1.073742e+09 -0.617326
2.147484e+09 -0.971310
4.294967e+09 -0.461987
8.589935e+09 0.819460
1.717987e+10 0.939325
3.435974e+10 -0.644430
6.871948e+10 0.985544
1.374390e+11 0.333940
2.748779e+11 -0.629540
5.497558e+11 -0.978265
1.099512e+12 -0.405705
2.199023e+12 0.741632
4.398047e+12 0.994984
8.796093e+12 -0.199069
1.759219e+13 0.390169
3.518437e+13 0.718491
7.036874e+13 0.999473
1.407375e+14 -0.064885
2.814750e+14 0.129496
5.629500e+14 0.256811
1.125900e+15 0.496397
2.251800e+15 0.861840
4.503600e+15 0.874217
9.007199e+15 -0.848926
1.801440e+16 0.897335
3.602880e+16 -0.792078
7.205759e+16 0.967000
1.441152e+17 -0.492738
2.882304e+17 0.857539
5.764608e+17 0.882269
1.152922e+18 -0.830649
2.305843e+18 0.925004
4.611686e+18 -0.702922
9.223372e+18 0.999930
1.844674e+19 0.023599
3.689349e+19 -0.047184
7.378698e+19 -0.094263
1.475740e+20 -0.187686
2.951479e+20 -0.368701
5.902958e+20 -0.685451
1.180592e+21 -0.998179
2.361183e+21 -0.120410
4.722366e+21 0.239068
9.444733e+21 0.464271
1.888947e+22 0.822404
3.777893e+22 0.935738
7.555786e+22 -0.660063
1.511157e+23 0.991692
3.022315e+23 0.255132
6.044629e+23 -0.493378
1.208926e+24 -0.858295
2.417852e+24 -0.880879
4.835703e+24 0.833914
9.671407e+24 -0.920465
1.934281e+25 0.719481
3.868563e+25 -0.999377
7.737125e+25 0.070569
1.547425e+26 -0.140786
3.094850e+26 -0.278768
6.189700e+26 -0.535435
1.237940e+27 -0.904431
2.475880e+27 -0.771696
4.951760e+27 0.981584
9.903520e+27 -0.375022
1.980704e+28 0.695303
3.961408e+28 0.999452
7.922816e+28 0.066180
1.584563e+29 -0.132069
3.169127e+29 -0.261824
6.338253e+29 -0.505382
1.267651e+30 -0.872184
2.535301e+30 -0.853307
5.070602e+30 0.889843
1.014120e+31 -0.812011
2.028241e+31 0.947848
4.056482e+31 -0.604204
8.112964e+31 0.962895
1.622593e+32 0.519724
3.245186e+32 -0.888036
6.490371e+32 -0.816591
1.298074e+33 0.942700
2.596148e+33 -0.629050
5.192297e+33 0.978003
1.038459e+34 0.408007
2.076919e+34 -0.745003
4.153837e+34 -0.993925
8.307675e+34 0.218781
1.661535e+35 -0.426961
3.323070e+35 -0.772176
6.646140e+35 -0.981295
1.329228e+36 0.377820
2.658456e+36 -0.699631
5.316912e+36 -0.999779
1.063382e+37 -0.042054
2.126765e+37 0.084034
4.253530e+37 0.167473
8.507059e+37 0.330216

This looks perfectly correct, and therefore it seems I must have made a mistake
in my initial testing.

I will note that this is not fixed in 2.15, but is fixed on master.

I haven't done a thorough check to find which patch fixed this.

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[Bug math/15563] sincos() is incorrect for long double and large inputs on x86_64

[joseph at codesourcery dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=15563

--- Comment #3 from joseph at codesourcery dot com <joseph at codesourcery dot com> ---
commit 8848d99dce1e57168a492d146f5e72195c7665a5
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Fri Mar 16 12:28:25 2012 +0000

    Implement ldbl-96 sinl / cosl / sincosl (bug 13851).

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[Bug math/15563] sincos() is incorrect for long double and large inputs on x86_64

[fweimer at redhat dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=15563

Florian Weimer <fweimer at redhat dot com> changed:

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

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