From 2d22d698d32575fd883d2be072c041709254c86d Mon Sep 17 00:00:00 2001
From: Carl Worth <cworth@cworth.org>
Date: Thu, 14 Feb 2008 11:50:26 -0800
Subject: [PATCH] Make _cairo_slope_compare return a non-zero result for slopes
 that differ by pi

This was an initial attempt to fix the infinite loop bug
described here:

	Infinite loop when scaling very small values using 24.8
	http://bugs.freedesktop.org/show_bug.cgi?id=14280

This doesn't actually fix that bug, but having a more robust
comparison function can only be a good thing.
---
 src/cairo-slope.c | 30 ++++++++++++++++++++++++++++--
 1 file changed, 28 insertions(+), 2 deletions(-)

diff --git a/src/cairo-slope.c b/src/cairo-slope.c
index e8421fc35..af97a6399 100644
--- a/src/cairo-slope.c
+++ b/src/cairo-slope.c
@@ -47,8 +47,15 @@ _cairo_slope_init (cairo_slope_t *slope, cairo_point_t *a, cairo_point_t *b)
    positive X axis and increase in the direction of the positive Y
    axis.
 
-   WARNING: This function only gives correct results if the angular
-   difference between a and b is less than PI.
+   This function always compares the slope vectors based on the
+   smaller angular difference between them, (that is based on an
+   angular difference that is strictly less than pi). To break ties
+   when comparing slope vectors with an angular difference of exactly
+   pi, the vector with a positive dx (or positive dy if dx's are zero)
+   is considered to be more positive than the other.
+
+   Also, all slope vectors with both dx==0 and dy==0 are considered
+   equal and more positive than any non-zero vector.
 
    <  0 => a less positive than b
    == 0 => a equal to b
@@ -78,6 +85,25 @@ _cairo_slope_compare (cairo_slope_t *a, cairo_slope_t *b)
     if (b->dx == 0 && b->dy ==0)
 	return -1;
 
+    /* Finally, we're looking at two vectors that are either equal or
+     * that differ by exactly pi. We can identify the "differ by pi"
+     * case by looking for a change in sign in either dx or dy between
+     * a and b.
+     *
+     * And in these cases, we eliminate the ambiguity by reducing the angle
+     * of b by an infinitesimally small amount, (that is, 'a' will
+     * always be considered less than 'b').
+     */
+    if (((a->dx > 0) != (b->dx > 0)) ||
+	((a->dy > 0) != (b->dy > 0)))
+    {
+	if (a->dx > 0 || (a->dx == 0 && a->dy > 0))
+	    return +1;
+	else
+	    return -1;
+    }
+
+    /* Finally, for identical slopes, we obviously return 0. */
     return 0;
 }