[Bug math/29193] New: sincos produces a different output than sin/cos

["dangelog at gmail dot com" <sourceware-bugzilla@sourceware.org>]

https://sourceware.org/bugzilla/show_bug.cgi?id=29193

            Bug ID: 29193
           Summary: sincos produces a different output than sin/cos
           Product: glibc
           Version: 2.31
            Status: UNCONFIRMED
          Severity: normal
          Priority: P2
         Component: math
          Assignee: unassigned at sourceware dot org
          Reporter: dangelog at gmail dot com
  Target Milestone: ---

Hello,

Please consider this reduced testcase:

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

    double degreesToRadians(double degrees)
    {
        return degrees * (M_PI / 180);
    }

    double __attribute__ ((noinline)) a(double rad)
    {
        return sin(rad);
    }

    double __attribute__ ((noinline)) b(double rad)
    {
        double s;
        double c;
        sincos(rad, &s, &c);
        if (c > 100)
            return 0.0;
        return s;
    }

    int main() 
    {
        double d = 297;
        double rad = degreesToRadians(d);

        printf("%a\n%a\n", a(rad), b(rad));
    }


Godbolt: https://c.godbolt.org/z/z45GGWEEK

Under GCC 12.1 -O2 -fno-builtin, the output is:

-0x1.c83201d3d2c6ep-1
-0x1.c83201d3d2c6dp-1


In other words, sincos seems to be introducing ~1ULP of error when compared to
calling sin/cos separately. 

This is annoying, because GCC has a specific optimization where it replaces
nearby sin/cos calls with a call to sincos (slightly modified example here:
https://c.godbolt.org/z/rYEhrcPcx ). However, by doing so, it actually changes
the results. As sincos is not documented to be any different from sin+cos, the
optimization is correct, in principle. (If, on the other hand, sincos could
generate different results than sin/cos, then GCC must stop employing such
optimization without -ffast-math or similar flags).

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