[Bug math/13629] New: clog() returns wrong values around z=1

[fxcoudert at gcc dot gnu.org]

http://sourceware.org/bugzilla/show_bug.cgi?id=13629

             Bug #: 13629
           Summary: clog() returns wrong values around z=1
           Product: glibc
           Version: unspecified
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: aj@suse.de
        ReportedBy: fxcoudert@gcc.gnu.org
    Classification: Unclassified


On the example below, clog() is called on value 1+epsilon*I. The result (first
output line) is pretty different from the expected result, calculated in the
second output line as a second-order series expansion.

I could reproduce it with glibc versions 2.5, 2.11.2, and 2.13, on both i686
and x86_64 systems (and many compilers).


$ cat a.c                            
#include <math.h>
#include <complex.h>
#include <stdio.h>

int main ()
{
  complex double z, fz,gz;
  z = 1.0f + 0.00000001f*I;
  fz = clog(z);
  gz = (z-1) - (z-1)*(z-1)/2;
  printf (" %.15e + %.15ei\n", creal(fz), cimag(fz));
  printf (" %.15e + %.15ei\n", creal(gz), cimag(gz));
  return 0;
}
$ gcc a.c -lm -O0 -W -Wall -std=c99 && ./a.out
 0.000000000000000e+00 + 1.000000000000000e-08i
 5.000000000000001e-17 + 1.000000000000000e-08i

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