internal/trace: use MU slope to optimize MMU

This commit speeds up MMU construction by ~10X (and reduces the number
of windows considered by ~20X) by using an observation about the
maximum slope of the windowed mutator utilization function to advance
the window time in jumps if the window's current mean mutator
utilization is much larger than the current minimum.

Change-Id: If3cba5da0c4adc37b568740f940793e491e96a51
Reviewed-on: https://go-review.googlesource.com/c/60791
Run-TryBot: Austin Clements <austin@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Hyang-Ah Hana Kim <hyangah@gmail.com>

src/internal/traceparser/gc.go

@@ -194,6 +194,12 @@ func (c *MMUCurve) MMU(window time.Duration) (mmu float64) {
 			}
 		}
 
+		// The maximum slope of the windowed mutator
+		// utilization function is 1/window, so we can always
+		// advance the time by at least (mu - mmu) * window
+		// without dropping below mmu.
+		minTime := time + int64((mu-mmu)*float64(window))
+
 		// Advance the window to the next time where either
 		// the left or right edge of the window encounters a
 		// change in the utilization curve.
@@ -202,6 +208,9 @@ func (c *MMUCurve) MMU(window time.Duration) (mmu float64) {
 		} else {
 			time = t2
 		}
+		if time < minTime {
+			time = minTime
+		}
 		if time > util[len(util)-1].Time-int64(window) {
 			break
 		}
@@ -225,9 +234,29 @@ func (in *integrator) advance(time int64) totalUtil {
 	util, pos := in.u.util, in.pos
 	// Advance pos until pos+1 is time's strict successor (making
 	// pos time's non-strict predecessor).
+	//
+	// Very often, this will be nearby, so we optimize that case,
+	// but it may be arbitrarily far away, so we handled that
+	// efficiently, too.
+	const maxSeq = 8
+	if pos+maxSeq < len(util) && util[pos+maxSeq].Time > time {
+		// Nearby. Use a linear scan.
 		for pos+1 < len(util) && util[pos+1].Time <= time {
 			pos++
 		}
+	} else {
+		// Far. Binary search for time's strict successor.
+		l, r := pos, len(util)
+		for l < r {
+			h := int(uint(l+r) >> 1)
+			if util[h].Time <= time {
+				l = h + 1
+			} else {
+				r = h
+			}
+		}
+		pos = l - 1 // Non-strict predecessor.
+	}
 	in.pos = pos
 	var partial totalUtil
 	if time != util[pos].Time {