+static
+double get_slack (double limit, double half_bin_width, int *n_half_bins)
+{
+ double ipart, remainder;
+
+ assert (half_bin_width > 0);
+
+ remainder = modf (limit / half_bin_width, &ipart);
+
+ /* In C modf and % behave in an unexpected (to me at any rate) manner
+ when presented with a negative value
+
+ For example, modf (-7.0 / 3.0) returns -2.0 R -0.3333
+ */
+
+
+ *n_half_bins = ipart;
+
+ return remainder * half_bin_width;
+}
+
+
+/* This functions adjusts the upper and lower range of the histogram to make them fit BIN_WIDTH
+ MIN and MAX are the lowest and highest data to be plotted in the histogram.
+ ADJ_MIN and ADJ_MAX are locations of the adjusted values of MIN and MAX (the range will
+ always be equal or slightly larger).
+ Returns the number of bins.
+
+ The "testing_assert" expressions in this function should be algebraically correct.
+ However, due to floating point rounding they could fail, especially when small numbers
+ are involved. In normal use, therefore, testing_assert does nothing.
+ */
+static int
+adjust_bin_ranges (double bin_width, double min, double max, double *adj_min, double *adj_max)
+{
+ const double half_bin_width = bin_width / 2.0;
+
+ /* The lower and upper limits of the histogram, in units of half
+ bin widths */
+ int lower_limit, upper_limit;
+
+ double lower_slack = get_slack (min, half_bin_width, &lower_limit);
+ double upper_slack = -get_slack (max, half_bin_width, &upper_limit);
+
+ testing_assert (max > min);
+
+ /* If min is negative, then lower_slack may be less than zero.
+ In this case, the lower bound must be extended in the negative direction
+ so that it is less than OR EQUAL to min.
+ */
+ if (lower_slack < 0)
+ {
+ lower_limit--;
+ lower_slack += half_bin_width;
+ }
+ testing_assert (lower_limit * half_bin_width <= min);
+
+ /* However, the upper bound must be extended regardless, because histogram bins
+ span the range [lower, upper). In other words, the upper bound must be
+ greater than max.
+ */
+ upper_limit++;;
+ upper_slack += half_bin_width;
+ testing_assert (upper_limit * half_bin_width > max);
+
+ /* The range must be an EVEN number of half bin_widths */
+ if ( (upper_limit - lower_limit) % 2)
+ {
+ /* Extend the range at the end which gives the least unused space */
+ if (upper_slack > lower_slack)
+ {
+ lower_limit--;
+ lower_slack += half_bin_width;
+ }
+ else
+ {
+ upper_limit++;
+ upper_slack += half_bin_width;
+ }
+ }
+
+ /* But the range should be aligned to an ODD number of
+ half bin widths, so that the labels are aesthetically pleasing ones.
+ Otherwise we are likely to get labels such as -3 -1 1 3 instead of -2 0 2 4
+ */
+ if ( lower_limit % 2 == 0)
+ {
+ /* If there is not enough slack at either end to perform a shift,
+ then we must extend the range so that there is. We must extend
+ by two half bin widths in order to preserve the EVEN condition
+ established above. Also, we extend on the end with the least
+ slack, in order to keep things as balanced as possible. */
+ if ( upper_slack > lower_slack && upper_slack <= half_bin_width)
+ {
+ lower_limit -= 2;
+ lower_slack += 2 * half_bin_width;
+ }
+
+ if (lower_slack > upper_slack && lower_slack < half_bin_width)
+ {
+ upper_limit += 2;
+ upper_slack += 2 * half_bin_width;
+ }
+
+ if (upper_slack > lower_slack)
+ {
+ testing_assert (upper_slack > half_bin_width);
+
+ /* Adjust the range to the left */
+ lower_limit --;
+ upper_limit --;
+ upper_slack -= half_bin_width;
+ lower_slack += half_bin_width;
+ }
+ else
+ {
+ testing_assert (lower_slack >= half_bin_width);
+
+ /* Adjust the range to the right */
+ lower_limit ++;
+ upper_limit ++;
+ lower_slack -= half_bin_width;
+ upper_slack += half_bin_width;
+ }
+ }
+
+ /* If there are any completely empty bins, then remove them,
+ since empty bins don't really add much information to the histogram.
+ */
+ if (upper_slack > 2 * half_bin_width)
+ {
+ upper_slack -= 2 * half_bin_width;
+ upper_limit -=2;
+ }
+
+ if (lower_slack >= 2 * half_bin_width)
+ {
+ lower_slack -= 2 * half_bin_width;
+ lower_limit +=2;
+ }
+
+ *adj_min = lower_limit * half_bin_width;
+ *adj_max = upper_limit * half_bin_width;
+
+ testing_assert (*adj_max > max);
+ testing_assert (*adj_min <= min);
+
+ return (upper_limit - lower_limit) / 2.0;
+}
+
+
+