[goffice] Complex: fix corner case for complex sqrt.

[Morten Welinder <mortenw src gnome org>]

commit e5e05ec9f709288ca2f2799438be112972167dfe
Author: Morten Welinder <terra gnome org>
Date:   Sat Mar 5 15:58:05 2016 -0500

    Complex: fix corner case for complex sqrt.
    
    When the argument is near the nagative real axis, we will get a result
    that is near the imaginary axis and thus has a small real part.  Getting
    the small real part right requires a little extra care.

 ChangeLog                 |    5 +++++
 NEWS                      |    1 +
 goffice/math/go-complex.c |   14 ++++++++++++++
 3 files changed, 20 insertions(+), 0 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index 065b038..583ad56 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,8 @@
+2016-03-05  Morten Welinder  <terra gnome org>
+
+       * goffice/math/go-complex.c (go_complex_sqrt): Fix accuracy of
+       real component when argument is very near the negative real axis.
+
 2016-02-23  Morten Welinder  <terra gnome org>
 
        * goffice/math/go-complex.c (go_complex_powx): Expose the power
diff --git a/NEWS b/NEWS
index b8e47f6..ebba682 100644
--- a/NEWS
+++ b/NEWS
@@ -3,6 +3,7 @@ goffice 0.10.28:
 Morten:
        * Configuration fixes.
        * Introspection improvements.
+       * Improve go_complex_sqrt.
 
 --------------------------------------------------------------------------
 goffice 0.10.27:
diff --git a/goffice/math/go-complex.c b/goffice/math/go-complex.c
index c845483..c9a5f89 100644
--- a/goffice/math/go-complex.c
+++ b/goffice/math/go-complex.c
@@ -271,6 +271,20 @@ SUFFIX(go_complex_div) (COMPLEX *dst, COMPLEX const *a, COMPLEX const *b)
 void
 SUFFIX(go_complex_sqrt) (COMPLEX *dst, COMPLEX const *src)
 {
+       if (src->re < 0 && -src->re > SUFFIX(fabs)(src->im)) {
+               // Near the negative axis we do not want to squeeze
+               // angle/pi against +-1.
+               COMPLEX msrc, r;
+               msrc.re = - src->re;
+               msrc.im = - src->im;
+               SUFFIX(go_complex_sqrt) (&r, &msrc);
+               if (src->im >= 0)
+                       SUFFIX(go_complex_init) (dst, 0 - r.im, r.re);
+               else
+                       SUFFIX(go_complex_init) (dst, r.im, 0 - r.re);
+               return;
+       }
+
        SUFFIX(go_complex_from_polar_pi)
                (dst,
                 SUFFIX(sqrt) (SUFFIX(go_complex_mod) (src)),