[goffice] Complex: improve tan.

[Morten Welinder <mortenw src gnome org>]

commit e623ffea22b99336b64e10440480606b64e81e5a
Author: Morten Welinder <terra gnome org>
Date:   Sat Mar 5 18:11:40 2016 -0500

    Complex: improve tan.

 ChangeLog                 |    1 +
 NEWS                      |    1 +
 goffice/math/go-complex.c |   30 ++++++++++++++++++++++++------
 3 files changed, 26 insertions(+), 6 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index 583ad56..102d7b5 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -2,6 +2,7 @@
 
        * 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.
 
 2016-02-23  Morten Welinder  <terra gnome org>
 
diff --git a/NEWS b/NEWS
index ebba682..ac85679 100644
--- a/NEWS
+++ b/NEWS
@@ -4,6 +4,7 @@ Morten:
        * Configuration fixes.
        * Introspection improvements.
        * Improve go_complex_sqrt.
+       * Improve go_complex_tan.
 
 --------------------------------------------------------------------------
 goffice 0.10.27:
diff --git a/goffice/math/go-complex.c b/goffice/math/go-complex.c
index c9a5f89..5f06bb4 100644
--- a/goffice/math/go-complex.c
+++ b/goffice/math/go-complex.c
@@ -564,7 +564,7 @@ void SUFFIX(go_complex_ln) (COMPLEX *dst, COMPLEX const *src)
 
 /* ------------------------------------------------------------------------- */
 
-void SUFFIX(go_complex_sin) ( COMPLEX *dst,  COMPLEX const *src)
+void SUFFIX(go_complex_sin) (COMPLEX *dst, COMPLEX const *src)
 {
        SUFFIX(go_complex_init) (dst,
                SUFFIX(sin) (src->re) * SUFFIX(cosh) (src->im),
@@ -573,7 +573,7 @@ void SUFFIX(go_complex_sin) ( COMPLEX *dst,  COMPLEX const *src)
 
 /* ------------------------------------------------------------------------- */
 
-void SUFFIX(go_complex_cos) (COMPLEX *dst,  COMPLEX const *src)
+void SUFFIX(go_complex_cos) (COMPLEX *dst, COMPLEX const *src)
 {
        SUFFIX(go_complex_init) (dst,
                SUFFIX(cos) (src->re) * SUFFIX(cosh) (src->im),
@@ -584,11 +584,29 @@ void SUFFIX(go_complex_cos) (COMPLEX *dst,  COMPLEX const *src)
 
 void SUFFIX(go_complex_tan) (COMPLEX *dst, COMPLEX const *src)
 {
-       COMPLEX s, c;
+       DOUBLE R = src->re, I = src->im;
+       DOUBLE sr = SUFFIX(sin) (R);
+       DOUBLE cr = SUFFIX(cos) (R);
 
-       SUFFIX(go_complex_sin) (&s, src);
-       SUFFIX(go_complex_cos) (&c, src);
-       SUFFIX(go_complex_div) (dst, &s, &c);
+       // Code here inspired by gsl, but doesn't follow it.
+
+       if (SUFFIX(fabs) (I) < 1) {
+               DOUBLE shi = SUFFIX(sinh) (I);
+               DOUBLE D = cr * cr + shi * shi;
+
+               SUFFIX(go_complex_init) (dst,
+                                        sr * cr / D,
+                                        0.5 * SUFFIX(sinh) (2 * I) / D);
+       } else {
+               DOUBLE u = SUFFIX(exp) (-SUFFIX(fabs)(I));
+               DOUBLE C = 2 * u / (1 - u * u);
+               DOUBLE S = C * C;
+               DOUBLE D = 1 + cr * cr * S;
+               DOUBLE T = 1.0 / SUFFIX(tanh) (SUFFIX(fabs) (I));
+               SUFFIX(go_complex_init) (dst,
+                                        sr * cr * S / D,
+                                        (I < 0 ? -T : T) / D);
+       }
 }
 
 /* ------------------------------------------------------------------------- */