[goffice] Complex: improve ln near unit circle.

[Morten Welinder <mortenw src gnome org>]

commit ae4a4ec431c7e0790cfb283c23cc400c57ec5e24
Author: Morten Welinder <terra gnome org>
Date:   Sat Mar 5 18:21:43 2016 -0500

    Complex: improve ln near unit circle.
    
    |z| is about 1, so Re(ln(z)) is around 0.  That requires a bit of extra
    care.

 ChangeLog                 |    1 +
 NEWS                      |    1 +
 goffice/math/go-complex.c |   11 ++++++++---
 3 files changed, 10 insertions(+), 3 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index 102d7b5..0d6761c 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -3,6 +3,7 @@
        * goffice/math/go-complex.c (go_complex_sqrt): Fix accuracy of
        real component when argument is very near the negative real axis.
        (go_complex_tan): Improve accuracy.
+       (go_complex_ln): Improve accuracy near unit circle.
 
 2016-02-23  Morten Welinder  <terra gnome org>
 
diff --git a/NEWS b/NEWS
index ac85679..b710a6e 100644
--- a/NEWS
+++ b/NEWS
@@ -5,6 +5,7 @@ Morten:
        * Introspection improvements.
        * Improve go_complex_sqrt.
        * Improve go_complex_tan.
+       * Improve go_complex_ln.
 
 --------------------------------------------------------------------------
 goffice 0.10.27:
diff --git a/goffice/math/go-complex.c b/goffice/math/go-complex.c
index 5f06bb4..32608ea 100644
--- a/goffice/math/go-complex.c
+++ b/goffice/math/go-complex.c
@@ -557,9 +557,14 @@ void SUFFIX(go_complex_exp) (COMPLEX *dst, COMPLEX const *src)
 
 void SUFFIX(go_complex_ln) (COMPLEX *dst, COMPLEX const *src)
 {
-       SUFFIX(go_complex_init) (dst,
-               SUFFIX(log) (SUFFIX(go_complex_mod) (src)),
-               SUFFIX(go_complex_angle) (src));
+       DOUBLE x = SUFFIX(fabs) (src->re);
+       DOUBLE y = SUFFIX(fabs) (src->im);
+       DOUBLE lm = x > y
+               ? SUFFIX(log) (x) + 0.5 * SUFFIX(log1p) ((y / x) * (y / x))
+               : SUFFIX(log) (y) + 0.5 * SUFFIX(log1p) ((x / y) * (x / y));
+       DOUBLE a = SUFFIX(go_complex_angle) (src);
+
+       SUFFIX(go_complex_init) (dst, lm, a);
 }
 
 /* ------------------------------------------------------------------------- */