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

["carlos at redhat dot com" <sourceware-bugzilla at sourceware dot org>]

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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