explain :P

diff --git a/qcsrc/server/g_damage.qc b/qcsrc/server/g_damage.qc
index 621df85a1b76f0415deda05f9bf8e6ef2fe6ec9e..72878430090bef689439128b49d37e5c8c1ea96f 100644 (file)
--- a/qcsrc/server/g_damage.qc
+++ b/qcsrc/server/g_damage.qc
@@ -1292,7 +1292,76 @@ float Fire_AddDamage(entity e, entity o, float d, float t, float dt)
                        // but, try mindps
                        totaltime = min(maxtime, totaldamage / mindps); // always >= mintime
 
-                       // can these two ever differ?
+                       /*
+                       BOTH SAEM (but lower one is numerically more stable as maxtime has potentially less ops behind)
+                       because:
+                       maxtime = max(mintime, t)
+                       maxdps = max(mindps, d/t)
+                       mindamage = mindps * mintime
+                       maxdamage = mindps * mintime + d
+                       totaldamage = min(mindps * mintime + d, max(mintime, t) * max(mindps, d/t))
+                       totaltime1 = max(mintime, min(mindps * mintime + d, max(mintime, t) * max(mindps, d/t)) / max(mindps, d/t))
+                       totaltime2 = min(max(mintime, t), min(mindps * mintime + d, max(mintime, t) * max(mindps, d/t)) / mindps)
+                               
+                       1. max(mintime, t) == t
+                       totaltime1 = max(mintime, min(mindps * mintime + d, t * max(mindps, d/t)) / max(mindps, d/t))
+                       totaltime2 = min(t, min(mindps * mintime + d, t * max(mindps, d/t)) / mindps)
+
+                       1.1. max(mindps, d/t) == mindps
+                       <=> mindps >= d/t
+                       <=>
+                       totaltime1 = max(mintime, min(mindps * mintime + d, t * mindps) / mindps)
+                       totaltime2 = min(t, min(mindps * mintime + d, t * mindps) / mindps)
+
+                       totaltime1 = max(mintime, min(mintime + d / mindps, t))
+                       totaltime2 = min(t, min(mintime + d / mindps, t))
+
+                       totaltime1 = max(mintime, min(mintime + d / mindps, t))
+                       totaltime2 = min(t, mintime + d / mindps)
+
+                       totaltime1 = min(max(mintime, mintime + d / mindps), max(mintime, t))
+                       totaltime2 = min(t, mintime + d / mindps)
+
+                       totaltime1 = min(mintime + d / mindps, t)
+                       totaltime2 = min(t, mintime + d / mindps)
+
+                       YES     
+
+                       1.2. max(mindps, d/t) == d/t
+                       totaltime1 = max(mintime, min(mindps * mintime + d, t * d/t) / d/t)
+                       totaltime2 = min(t, min(mindps * mintime + d, t * d/t) / mindps)
+
+                       totaltime1 = max(mintime, min(mindps * mintime / (d/t) + t, t))
+                       totaltime2 = min(t, min(mintime + d / mindps, d / mindps))
+
+                       totaltime1 = max(mintime, t) == t
+                       totaltime2 = min(t, d / mindps) == t
+
+                       YES
+
+                       2. max(mintime, t) == mintime
+                       totaltime1 = max(mintime, min(mindps * mintime + d, mintime * max(mindps, d/t)) / max(mindps, d/t))
+                       totaltime2 = min(mintime, min(mindps * mintime + d, mintime * max(mindps, d/t)) / mindps)
+
+                       2.1. max(mindps, d/t) == mindps
+                       totaltime1 = max(mintime, min(mindps * mintime + d, mintime * mindps) / mindps)
+                       totaltime2 = min(mintime, min(mindps * mintime + d, mintime * mindps) / mindps)
+
+                       totaltime1 = max(mintime, min(mintime + d / mindps, mintime)) = mintime
+                       totaltime2 = min(mintime, min(mintime + d / mindps, mintime)) = mintime
+
+                       YES
+
+                       2.2. max(mindps, d/t) == d/t
+                       totaltime1 = max(mintime, min(mindps * mintime + d, mintime * d/t) / d/t)
+                       totaltime2 = min(mintime, min(mindps * mintime + d, mintime * d/t) / mindps)
+
+                       totaltime1 = max(mintime, min(mindps * mintime / (d/t) + d / (d/t), mintime)) == mintime
+                       totaltime2 = min(mintime, min(mintime + d / mindps, mintime * d/t / mindps))
+                       //                    bigger!               bigger!
+
+                       YES
+                       */
 
                        e.fire_damagepersec = totaldamage / totaltime;
                        e.fire_endtime = time + totaltime;