Histograms: Ensure that the bins are aligned to an odd number of half bin widths

This has the benefit that the centres of the bins are aligned to integer multiples
of bin widths, and thus the labels are shorter.  For example, instead of labels
-1.5 -0.5 0.5 1.5 2.5 we get -2 -1 0 1 2 which is more aesthetically pleasing.

diff --git a/src/math/histogram.c b/src/math/histogram.c
index 0b2369f63c7b6ecad3329d6c728e2ed5eebf7dcf..9b89df689527996d1d4393f8f21fb56e3bba494f 100644 (file)
--- a/src/math/histogram.c
+++ b/src/math/histogram.c
@@ -60,31 +60,52 @@ histogram_create (double bin_width, double min, double max)
   int bins;
   struct histogram *h = xmalloc (sizeof *h);
   struct statistic *stat = &h->parent;
-
   double upper_limit, lower_limit;
+  const double half_bin_width = bin_width / 2.0;
+
+  /* -1 if the lower end of the range contains more unused space
+     than the upper end.
+     +1 otherwise.  */
+  short sparse_end = 0;
 
   assert (max >= min);
 
   if (max == min)
-     bin_width = 1;
+    bin_width = 1;
 
-  lower_limit = floor (2 * min / bin_width) - 1;
-  upper_limit = floor (2 * max / bin_width) + 1;
+  lower_limit = floor (min / half_bin_width) - 1;
+  upper_limit = floor (max / half_bin_width) + 1;
   
-  /* The range must be an even number of half bin_widths */
+  if (remainder (min, half_bin_width > remainder (max, half_bin_width)))
+    sparse_end = -1;
+  else
+    sparse_end = +1;
+
+  /* The range must be an EVEN number of half bin_widths */
   if ( (int)(upper_limit - lower_limit) % 2)
     {
       /* Extend the range at the end which gives the least unused space */
-      if (remainder (min, bin_width / 2.0) > remainder (max, bin_width / 2.0))
+      if (sparse_end == +1)
        lower_limit --;
       else
        upper_limit ++;
+      
+      /* Now the other end has more space */
+      sparse_end *= -1;
+    }
+
+  /* But the range should be aligned to an ODD number of
+     half bin widths, so that the labels are aesthetically pleasing ones. */
+  if ( (int)lower_limit % 2 == 0)
+    {
+      lower_limit += -sparse_end ;
+      upper_limit += -sparse_end ;
     }
 
   bins = (upper_limit - lower_limit) / 2.0;
 
-  upper_limit *= bin_width / 2;
-  lower_limit *= bin_width / 2;  
+  upper_limit *= half_bin_width;
+  lower_limit *= half_bin_width;
 
   h->gsl_hist = gsl_histogram_alloc (bins);