[gnumeric] R.QCAUCHY: Improve accuracy a bit for p>0.5

[Morten Welinder <mortenw src gnome org>]

commit c78646ec2ad3a21f8b0dcc6afa045ce6df47a5ed
Author: Morten Welinder <terra gnome org>
Date:   Wed Oct 30 21:37:22 2013 -0400

    R.QCAUCHY: Improve accuracy a bit for p>0.5
    
    There are more floating point numbers near 0 than near pi.  Therefore,
    flip tail when p>0.5 so tan(p*pi) gets computed more accurately.

 NEWS                   |    1 +
 plugins/fn-r/ChangeLog |    5 +++++
 plugins/fn-r/extra.c   |    4 ++++
 3 files changed, 10 insertions(+), 0 deletions(-)
---
diff --git a/NEWS b/NEWS
index 435b036..6b32a5e 100644
--- a/NEWS
+++ b/NEWS
@@ -3,6 +3,7 @@ Gnumeric 1.12.9
 Morten:
        * Minor improvement to history dialog.
        * Fix drop-down sizing (gtk+ regression).  [#710749]
+       * Improve accuracy of R.QCAUCHY.
 
 Xabier Rodríguez Calvar:
        * Fix dialog button order. [#710378]
diff --git a/plugins/fn-r/ChangeLog b/plugins/fn-r/ChangeLog
index d5c4635..8bc072a 100644
--- a/plugins/fn-r/ChangeLog
+++ b/plugins/fn-r/ChangeLog
@@ -1,3 +1,8 @@
+2013-10-30  Morten Welinder  <terra gnome org>
+
+       * extra.c (qcauchy): Flip tail if p>0.5.  Improves accuracy when
+       we get really close to 1.
+
 2013-10-07  Morten Welinder <terra gnome org>
 
        * Release 1.12.8
diff --git a/plugins/fn-r/extra.c b/plugins/fn-r/extra.c
index 7b0a88b..1aef7a9 100644
--- a/plugins/fn-r/extra.c
+++ b/plugins/fn-r/extra.c
@@ -34,6 +34,10 @@ qcauchy (gnm_float p, gnm_float location, gnm_float scale,
                else
                        p = gnm_exp (p);
        }
+       if (p > 0.5) {
+               p = 1 - p;
+               lower_tail = !lower_tail;
+       }
        if (lower_tail) scale = -scale;
        return location + scale / gnm_tan(M_PIgnum * p);
 }