[Bug math/14473] Inaccurate CPOW* function on all machines.

["mwelinder at gmail dot com" <sourceware-bugzilla at sourceware dot org>]

https://sourceware.org/bugzilla/show_bug.cgi?id=14473

M Welinder <mwelinder at gmail dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |mwelinder at gmail dot com

--- Comment #5 from M Welinder <mwelinder at gmail dot com> ---
There are at least two classes of accuracy issues with cpow(z,z2):

(1) Insufficient precision in intermediate results, affecting primarily "large"
    arguments

(2) Bad handling of |z1| == 1.  Sample program below.  This is actually
    easy to solve: use atan2pi, sinpi, and cospi instead of atan2, sin, and
    cos.


#include <complex.h>
#include <stdio.h>
#include <math.h>

int dont_optimize = 0;

int
main (int argc, char **argv)
{
  double complex z1, z2, z;

  /*
   * z here should be real.  I see an imaginary part of
   * 2.54571e-17, except when gcc is allowed to optimize
   * the whole thing at compile time.  Exact result should
   * be -exp(-pi/2) =~ -0.20788
   *
   * Surprise: Mathematica gets it wrong too.  I see the
   * same value as gcc for N[I^(I+2)].
   */
  z1 = dont_optimize + I;
  z2 = 2 + I;
  z = cpow (z1, z2);
  printf ("%g + %g i\n", creal (z), cimag (z));

  /*
   * Really scary version.  Exact result is exp(-pi/2)
   * =~ 0.20788.  I see "0.177058 + -0.108924 i".
   */
  z2 = ldexp (1,53) + I;
  z = cpow (z1, z2);
  printf ("%g + %g i\n", creal (z), cimag (z));

  return 0;
}

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