<,�tEXtComment File Manager

File Manager

Viewing File: mgcpacer_test.go

// Copyright 2021 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package runtime_test

import (
	"fmt"
	"math"
	"math/rand"
	. "runtime"
	"testing"
	"time"
)

func TestGcPacer(t *testing.T) {
	t.Parallel()

	const initialHeapBytes = 256 << 10
	for _, e := range []*gcExecTest{
		{
			// The most basic test case: a steady-state heap.
			// Growth to an O(MiB) heap, then constant heap size, alloc/scan rates.
			name:          "Steady",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n >= 25 {
					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		{
			// Same as the steady-state case, but lots of stacks to scan relative to the heap size.
			name:          "SteadyBigStacks",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(132.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(2048).sum(ramp(128<<20, 8)),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				// Check the same conditions as the steady-state case, except the old pacer can't
				// really handle this well, so don't check the goal ratio for it.
				n := len(c)
				if n >= 25 {
					// For the pacer redesign, assert something even stronger: at this alloc/scan rate,
					// it should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
				}
			},
		},
		{
			// Same as the steady-state case, but lots of globals to scan relative to the heap size.
			name:          "SteadyBigGlobals",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  128 << 20,
			nCores:        8,
			allocRate:     constant(132.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				// Check the same conditions as the steady-state case, except the old pacer can't
				// really handle this well, so don't check the goal ratio for it.
				n := len(c)
				if n >= 25 {
					// For the pacer redesign, assert something even stronger: at this alloc/scan rate,
					// it should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
				}
			},
		},
		{
			// This tests the GC pacer's response to a small change in allocation rate.
			name:          "StepAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0).sum(ramp(66.0, 1).delay(50)),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        100,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if (n >= 25 && n < 50) || n >= 75 {
					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles
					// and then is able to settle again after a significant jump in allocation rate.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		{
			// This tests the GC pacer's response to a large change in allocation rate.
			name:          "HeavyStepAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33).sum(ramp(330, 1).delay(50)),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        100,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if (n >= 25 && n < 50) || n >= 75 {
					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles
					// and then is able to settle again after a significant jump in allocation rate.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		{
			// This tests the GC pacer's response to a change in the fraction of the scannable heap.
			name:          "StepScannableFrac",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(128.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(0.2).sum(unit(0.5).delay(50)),
			stackBytes:    constant(8192),
			length:        100,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if (n >= 25 && n < 50) || n >= 75 {
					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles
					// and then is able to settle again after a significant jump in allocation rate.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		{
			// Tests the pacer for a high GOGC value with a large heap growth happening
			// in the middle. The purpose of the large heap growth is to check if GC
			// utilization ends up sensitive
			name:          "HighGOGC",
			gcPercent:     1500,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     random(7, 0x53).offset(165),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12), random(0.01, 0x1), unit(14).delay(25)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 12 {
					if n == 26 {
						// In the 26th cycle there's a heap growth. Overshoot is expected to maintain
						// a stable utilization, but we should *never* overshoot more than GOGC of
						// the next cycle.
						assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.90, 15)
					} else {
						// Give a wider goal range here. With such a high GOGC value we're going to be
						// forced to undershoot.
						//
						// TODO(mknyszek): Instead of placing a 0.95 limit on the trigger, make the limit
						// based on absolute bytes, that's based somewhat in how the minimum heap size
						// is determined.
						assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.90, 1.05)
					}

					// Ensure utilization remains stable despite a growth in live heap size
					// at GC #25. This test fails prior to the GC pacer redesign.
					//
					// Because GOGC is so large, we should also be really close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, GCGoalUtilization+0.03)
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.03)
				}
			},
		},
		{
			// This test makes sure that in the face of a varying (in this case, oscillating) allocation
			// rate, the pacer does a reasonably good job of staying abreast of the changes.
			name:          "OscAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     oscillate(13, 0, 8).offset(67),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 12 {
					// After the 12th GC, the heap will stop growing. Now, just make sure that:
					// 1. Utilization isn't varying _too_ much, and
					// 2. The pacer is mostly keeping up with the goal.
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
					assertInRange(t, "GC utilization", c[n-1].gcUtilization, 0.25, 0.3)
				}
			},
		},
		{
			// This test is the same as OscAlloc, but instead of oscillating, the allocation rate is jittery.
			name:          "JitterAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     random(13, 0xf).offset(132),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12), random(0.01, 0xe)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 12 {
					// After the 12th GC, the heap will stop growing. Now, just make sure that:
					// 1. Utilization isn't varying _too_ much, and
					// 2. The pacer is mostly keeping up with the goal.
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.025)
					assertInRange(t, "GC utilization", c[n-1].gcUtilization, 0.25, 0.275)
				}
			},
		},
		{
			// This test is the same as JitterAlloc, but with a much higher allocation rate.
			// The jitter is proportionally the same.
			name:          "HeavyJitterAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     random(33.0, 0x0).offset(330),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12), random(0.01, 0x152)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 13 {
					// After the 12th GC, the heap will stop growing. Now, just make sure that:
					// 1. Utilization isn't varying _too_ much, and
					// 2. The pacer is mostly keeping up with the goal.
					// We start at the 13th here because we want to use the 12th as a reference.
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
					// Unlike the other tests, GC utilization here will vary more and tend higher.
					// Just make sure it's not going too crazy.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.05)
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[11].gcUtilization, 0.05)
				}
			},
		},
		{
			// This test sets a slow allocation rate and a small heap (close to the minimum heap size)
			// to try to minimize the difference between the trigger and the goal.
			name:          "SmallHeapSlowAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(1.0),
			scanRate:      constant(2048.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 3)),
			scannableFrac: constant(0.01),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 4 {
					// After the 4th GC, the heap will stop growing.
					// First, let's make sure we're finishing near the goal, with some extra
					// room because we're probably going to be triggering early.
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.925, 1.025)
					// Next, let's make sure there's some minimum distance between the goal
					// and the trigger. It should be proportional to the runway (hence the
					// trigger ratio check, instead of a check against the runway).
					assertInRange(t, "trigger ratio", c[n-1].triggerRatio(), 0.925, 0.975)
				}
				if n > 25 {
					// Double-check that GC utilization looks OK.

					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)
					// Make sure GC utilization has mostly levelled off.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.05)
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[11].gcUtilization, 0.05)
				}
			},
		},
		{
			// This test sets a slow allocation rate and a medium heap (around 10x the min heap size)
			// to try to minimize the difference between the trigger and the goal.
			name:          "MediumHeapSlowAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(1.0),
			scanRate:      constant(2048.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 8)),
			scannableFrac: constant(0.01),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 9 {
					// After the 4th GC, the heap will stop growing.
					// First, let's make sure we're finishing near the goal, with some extra
					// room because we're probably going to be triggering early.
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.925, 1.025)
					// Next, let's make sure there's some minimum distance between the goal
					// and the trigger. It should be proportional to the runway (hence the
					// trigger ratio check, instead of a check against the runway).
					assertInRange(t, "trigger ratio", c[n-1].triggerRatio(), 0.925, 0.975)
				}
				if n > 25 {
					// Double-check that GC utilization looks OK.

					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)
					// Make sure GC utilization has mostly levelled off.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.05)
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[11].gcUtilization, 0.05)
				}
			},
		},
		{
			// This test sets a slow allocation rate and a large heap to try to minimize the
			// difference between the trigger and the goal.
			name:          "LargeHeapSlowAlloc",
			gcPercent:     100,
			memoryLimit:   math.MaxInt64,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(1.0),
			scanRate:      constant(2048.0),
			growthRate:    constant(4.0).sum(ramp(-3.0, 12)),
			scannableFrac: constant(0.01),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 13 {
					// After the 4th GC, the heap will stop growing.
					// First, let's make sure we're finishing near the goal.
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
					// Next, let's make sure there's some minimum distance between the goal
					// and the trigger. It should be around the default minimum heap size.
					assertInRange(t, "runway", c[n-1].runway(), DefaultHeapMinimum-64<<10, DefaultHeapMinimum+64<<10)
				}
				if n > 25 {
					// Double-check that GC utilization looks OK.

					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)
					// Make sure GC utilization has mostly levelled off.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.05)
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[11].gcUtilization, 0.05)
				}
			},
		},
		{
			// The most basic test case with a memory limit: a steady-state heap.
			// Growth to an O(MiB) heap, then constant heap size, alloc/scan rates.
			// Provide a lot of room for the limit. Essentially, this should behave just like
			// the "Steady" test. Note that we don't simulate non-heap overheads, so the
			// memory limit and the heap limit are identical.
			name:          "SteadyMemoryLimit",
			gcPercent:     100,
			memoryLimit:   512 << 20,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if peak := c[n-1].heapPeak; peak >= applyMemoryLimitHeapGoalHeadroom(512<<20) {
					t.Errorf("peak heap size reaches heap limit: %d", peak)
				}
				if n >= 25 {
					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		{
			// This is the same as the previous test, but gcPercent = -1, so the heap *should* grow
			// all the way to the peak.
			name:          "SteadyMemoryLimitNoGCPercent",
			gcPercent:     -1,
			memoryLimit:   512 << 20,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(2.0).sum(ramp(-1.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if goal := c[n-1].heapGoal; goal != applyMemoryLimitHeapGoalHeadroom(512<<20) {
					t.Errorf("heap goal is not the heap limit: %d", goal)
				}
				if n >= 25 {
					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		{
			// This test ensures that the pacer doesn't fall over even when the live heap exceeds
			// the memory limit. It also makes sure GC utilization actually rises to push back.
			name:          "ExceedMemoryLimit",
			gcPercent:     100,
			memoryLimit:   512 << 20,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(3.5).sum(ramp(-2.5, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 12 {
					// We're way over the memory limit, so we want to make sure our goal is set
					// as low as it possibly can be.
					if goal, live := c[n-1].heapGoal, c[n-1].heapLive; goal != live {
						t.Errorf("heap goal is not equal to live heap: %d != %d", goal, live)
					}
				}
				if n >= 25 {
					// Due to memory pressure, we should scale to 100% GC CPU utilization.
					// Note that in practice this won't actually happen because of the CPU limiter,
					// but it's not the pacer's job to limit CPU usage.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, 1.0, 0.005)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles.
					// In this case, that just means it's not wavering around a whole bunch.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
				}
			},
		},
		{
			// Same as the previous test, but with gcPercent = -1.
			name:          "ExceedMemoryLimitNoGCPercent",
			gcPercent:     -1,
			memoryLimit:   512 << 20,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(3.5).sum(ramp(-2.5, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n < 10 {
					if goal := c[n-1].heapGoal; goal != applyMemoryLimitHeapGoalHeadroom(512<<20) {
						t.Errorf("heap goal is not the heap limit: %d", goal)
					}
				}
				if n > 12 {
					// We're way over the memory limit, so we want to make sure our goal is set
					// as low as it possibly can be.
					if goal, live := c[n-1].heapGoal, c[n-1].heapLive; goal != live {
						t.Errorf("heap goal is not equal to live heap: %d != %d", goal, live)
					}
				}
				if n >= 25 {
					// Due to memory pressure, we should scale to 100% GC CPU utilization.
					// Note that in practice this won't actually happen because of the CPU limiter,
					// but it's not the pacer's job to limit CPU usage.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, 1.0, 0.005)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles.
					// In this case, that just means it's not wavering around a whole bunch.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
				}
			},
		},
		{
			// This test ensures that the pacer maintains the memory limit as the heap grows.
			name:          "MaintainMemoryLimit",
			gcPercent:     100,
			memoryLimit:   512 << 20,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(3.0).sum(ramp(-2.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if n > 12 {
					// We're trying to saturate the memory limit.
					if goal := c[n-1].heapGoal; goal != applyMemoryLimitHeapGoalHeadroom(512<<20) {
						t.Errorf("heap goal is not the heap limit: %d", goal)
					}
				}
				if n >= 25 {
					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization,
					// even with the additional memory pressure.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles and
					// that it's meeting its goal.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		{
			// Same as the previous test, but with gcPercent = -1.
			name:          "MaintainMemoryLimitNoGCPercent",
			gcPercent:     -1,
			memoryLimit:   512 << 20,
			globalsBytes:  32 << 10,
			nCores:        8,
			allocRate:     constant(33.0),
			scanRate:      constant(1024.0),
			growthRate:    constant(3.0).sum(ramp(-2.0, 12)),
			scannableFrac: constant(1.0),
			stackBytes:    constant(8192),
			length:        50,
			checker: func(t *testing.T, c []gcCycleResult) {
				n := len(c)
				if goal := c[n-1].heapGoal; goal != applyMemoryLimitHeapGoalHeadroom(512<<20) {
					t.Errorf("heap goal is not the heap limit: %d", goal)
				}
				if n >= 25 {
					// At this alloc/scan rate, the pacer should be extremely close to the goal utilization,
					// even with the additional memory pressure.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, GCGoalUtilization, 0.005)

					// Make sure the pacer settles into a non-degenerate state in at least 25 GC cycles and
					// that it's meeting its goal.
					assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[n-2].gcUtilization, 0.005)
					assertInRange(t, "goal ratio", c[n-1].goalRatio(), 0.95, 1.05)
				}
			},
		},
		// TODO(mknyszek): Write a test that exercises the pacer's hard goal.
		// This is difficult in the idealized model this testing framework places
		// the pacer in, because the calculated overshoot is directly proportional
		// to the runway for the case of the expected work.
		// However, it is still possible to trigger this case if something exceptional
		// happens between calls to revise; the framework just doesn't support this yet.
	} {
		e := e
		t.Run(e.name, func(t *testing.T) {
			t.Parallel()

			c := NewGCController(e.gcPercent, e.memoryLimit)
			var bytesAllocatedBlackLast int64
			results := make([]gcCycleResult, 0, e.length)
			for i := 0; i < e.length; i++ {
				cycle := e.next()
				c.StartCycle(cycle.stackBytes, e.globalsBytes, cycle.scannableFrac, e.nCores)

				// Update pacer incrementally as we complete scan work.
				const (
					revisePeriod = 500 * time.Microsecond
					rateConv     = 1024 * float64(revisePeriod) / float64(time.Millisecond)
				)
				var nextHeapMarked int64
				if i == 0 {
					nextHeapMarked = initialHeapBytes
				} else {
					nextHeapMarked = int64(float64(int64(c.HeapMarked())-bytesAllocatedBlackLast) * cycle.growthRate)
				}
				globalsScanWorkLeft := int64(e.globalsBytes)
				stackScanWorkLeft := int64(cycle.stackBytes)
				heapScanWorkLeft := int64(float64(nextHeapMarked) * cycle.scannableFrac)
				doWork := func(work int64) (int64, int64, int64) {
					var deltas [3]int64

					// Do globals work first, then stacks, then heap.
					for i, workLeft := range []*int64{&globalsScanWorkLeft, &stackScanWorkLeft, &heapScanWorkLeft} {
						if *workLeft == 0 {
							continue
						}
						if *workLeft > work {
							deltas[i] += work
							*workLeft -= work
							work = 0
							break
						} else {
							deltas[i] += *workLeft
							work -= *workLeft
							*workLeft = 0
						}
					}
					return deltas[0], deltas[1], deltas[2]
				}
				var (
					gcDuration          int64
					assistTime          int64
					bytesAllocatedBlack int64
				)
				for heapScanWorkLeft+stackScanWorkLeft+globalsScanWorkLeft > 0 {
					// Simulate GC assist pacing.
					//
					// Note that this is an idealized view of the GC assist pacing
					// mechanism.

					// From the assist ratio and the alloc and scan rates, we can idealize what
					// the GC CPU utilization looks like.
					//
					// We start with assistRatio = (bytes of scan work) / (bytes of runway) (by definition).
					//
					// Over revisePeriod, we can also calculate how many bytes are scanned and
					// allocated, given some GC CPU utilization u:
					//
					//     bytesScanned   = scanRate  * rateConv * nCores * u
					//     bytesAllocated = allocRate * rateConv * nCores * (1 - u)
					//
					// During revisePeriod, assistRatio is kept constant, and GC assists kick in to
					// maintain it. Specifically, they act to prevent too many bytes being allocated
					// compared to how many bytes are scanned. It directly defines the ratio of
					// bytesScanned to bytesAllocated over this period, hence:
					//
					//     assistRatio = bytesScanned / bytesAllocated
					//
					// From this, we can solve for utilization, because everything else has already
					// been determined:
					//
					//     assistRatio = (scanRate * rateConv * nCores * u) / (allocRate * rateConv * nCores * (1 - u))
					//     assistRatio = (scanRate * u) / (allocRate * (1 - u))
					//     assistRatio * allocRate * (1-u) = scanRate * u
					//     assistRatio * allocRate - assistRatio * allocRate * u = scanRate * u
					//     assistRatio * allocRate = assistRatio * allocRate * u + scanRate * u
					//     assistRatio * allocRate = (assistRatio * allocRate + scanRate) * u
					//     u = (assistRatio * allocRate) / (assistRatio * allocRate + scanRate)
					//
					// Note that this may give a utilization that is _less_ than GCBackgroundUtilization,
					// which isn't possible in practice because of dedicated workers. Thus, this case
					// must be interpreted as GC assists not kicking in at all, and just round up. All
					// downstream values will then have this accounted for.
					assistRatio := c.AssistWorkPerByte()
					utilization := assistRatio * cycle.allocRate / (assistRatio*cycle.allocRate + cycle.scanRate)
					if utilization < GCBackgroundUtilization {
						utilization = GCBackgroundUtilization
					}

					// Knowing the utilization, calculate bytesScanned and bytesAllocated.
					bytesScanned := int64(cycle.scanRate * rateConv * float64(e.nCores) * utilization)
					bytesAllocated := int64(cycle.allocRate * rateConv * float64(e.nCores) * (1 - utilization))

					// Subtract work from our model.
					globalsScanned, stackScanned, heapScanned := doWork(bytesScanned)

					// doWork may not use all of bytesScanned.
					// In this case, the GC actually ends sometime in this period.
					// Let's figure out when, exactly, and adjust bytesAllocated too.
					actualElapsed := revisePeriod
					actualAllocated := bytesAllocated
					if actualScanned := globalsScanned + stackScanned + heapScanned; actualScanned < bytesScanned {
						// actualScanned = scanRate * rateConv * (t / revisePeriod) * nCores * u
						// => t = actualScanned * revisePeriod / (scanRate * rateConv * nCores * u)
						actualElapsed = time.Duration(float64(actualScanned) * float64(revisePeriod) / (cycle.scanRate * rateConv * float64(e.nCores) * utilization))
						actualAllocated = int64(cycle.allocRate * rateConv * float64(actualElapsed) / float64(revisePeriod) * float64(e.nCores) * (1 - utilization))
					}

					// Ask the pacer to revise.
					c.Revise(GCControllerReviseDelta{
						HeapLive:        actualAllocated,
						HeapScan:        int64(float64(actualAllocated) * cycle.scannableFrac),
						HeapScanWork:    heapScanned,
						StackScanWork:   stackScanned,
						GlobalsScanWork: globalsScanned,
					})

					// Accumulate variables.
					assistTime += int64(float64(actualElapsed) * float64(e.nCores) * (utilization - GCBackgroundUtilization))
					gcDuration += int64(actualElapsed)
					bytesAllocatedBlack += actualAllocated
				}

				// Put together the results, log them, and concatenate them.
				result := gcCycleResult{
					cycle:         i + 1,
					heapLive:      c.HeapMarked(),
					heapScannable: int64(float64(int64(c.HeapMarked())-bytesAllocatedBlackLast) * cycle.scannableFrac),
					heapTrigger:   c.Triggered(),
					heapPeak:      c.HeapLive(),
					heapGoal:      c.HeapGoal(),
					gcUtilization: float64(assistTime)/(float64(gcDuration)*float64(e.nCores)) + GCBackgroundUtilization,
				}
				t.Log("GC", result.String())
				results = append(results, result)

				// Run the checker for this test.
				e.check(t, results)

				c.EndCycle(uint64(nextHeapMarked+bytesAllocatedBlack), assistTime, gcDuration, e.nCores)

				bytesAllocatedBlackLast = bytesAllocatedBlack
			}
		})
	}
}

type gcExecTest struct {
	name string

	gcPercent    int
	memoryLimit  int64
	globalsBytes uint64
	nCores       int

	allocRate     float64Stream // > 0, KiB / cpu-ms
	scanRate      float64Stream // > 0, KiB / cpu-ms
	growthRate    float64Stream // > 0
	scannableFrac float64Stream // Clamped to [0, 1]
	stackBytes    float64Stream // Multiple of 2048.
	length        int

	checker func(*testing.T, []gcCycleResult)
}

// minRate is an arbitrary minimum for allocRate, scanRate, and growthRate.
// These values just cannot be zero.
const minRate = 0.0001

func (e *gcExecTest) next() gcCycle {
	return gcCycle{
		allocRate:     e.allocRate.min(minRate)(),
		scanRate:      e.scanRate.min(minRate)(),
		growthRate:    e.growthRate.min(minRate)(),
		scannableFrac: e.scannableFrac.limit(0, 1)(),
		stackBytes:    uint64(e.stackBytes.quantize(2048).min(0)()),
	}
}

func (e *gcExecTest) check(t *testing.T, results []gcCycleResult) {
	t.Helper()

	// Do some basic general checks first.
	n := len(results)
	switch n {
	case 0:
		t.Fatal("no results passed to check")
		return
	case 1:
		if results[0].cycle != 1 {
			t.Error("first cycle has incorrect number")
		}
	default:
		if results[n-1].cycle != results[n-2].cycle+1 {
			t.Error("cycle numbers out of order")
		}
	}
	if u := results[n-1].gcUtilization; u < 0 || u > 1 {
		t.Fatal("GC utilization not within acceptable bounds")
	}
	if s := results[n-1].heapScannable; s < 0 {
		t.Fatal("heapScannable is negative")
	}
	if e.checker == nil {
		t.Fatal("test-specific checker is missing")
	}

	// Run the test-specific checker.
	e.checker(t, results)
}

type gcCycle struct {
	allocRate     float64
	scanRate      float64
	growthRate    float64
	scannableFrac float64
	stackBytes    uint64
}

type gcCycleResult struct {
	cycle int

	// These come directly from the pacer, so uint64.
	heapLive    uint64
	heapTrigger uint64
	heapGoal    uint64
	heapPeak    uint64

	// These are produced by the simulation, so int64 and
	// float64 are more appropriate, so that we can check for
	// bad states in the simulation.
	heapScannable int64
	gcUtilization float64
}

func (r *gcCycleResult) goalRatio() float64 {
	return float64(r.heapPeak) / float64(r.heapGoal)
}

func (r *gcCycleResult) runway() float64 {
	return float64(r.heapGoal - r.heapTrigger)
}

func (r *gcCycleResult) triggerRatio() float64 {
	return float64(r.heapTrigger-r.heapLive) / float64(r.heapGoal-r.heapLive)
}

func (r *gcCycleResult) String() string {
	return fmt.Sprintf("%d %2.1f%% %d->%d->%d (goal: %d)", r.cycle, r.gcUtilization*100, r.heapLive, r.heapTrigger, r.heapPeak, r.heapGoal)
}

func assertInEpsilon(t *testing.T, name string, a, b, epsilon float64) {
	t.Helper()
	assertInRange(t, name, a, b-epsilon, b+epsilon)
}

func assertInRange(t *testing.T, name string, a, min, max float64) {
	t.Helper()
	if a < min || a > max {
		t.Errorf("%s not in range (%f, %f): %f", name, min, max, a)
	}
}

// float64Stream is a function that generates an infinite stream of
// float64 values when called repeatedly.
type float64Stream func() float64

// constant returns a stream that generates the value c.
func constant(c float64) float64Stream {
	return func() float64 {
		return c
	}
}

// unit returns a stream that generates a single peak with
// amplitude amp, followed by zeroes.
//
// In another manner of speaking, this is the Kronecker delta.
func unit(amp float64) float64Stream {
	dropped := false
	return func() float64 {
		if dropped {
			return 0
		}
		dropped = true
		return amp
	}
}

// oscillate returns a stream that oscillates sinusoidally
// with the given amplitude, phase, and period.
func oscillate(amp, phase float64, period int) float64Stream {
	var cycle int
	return func() float64 {
		p := float64(cycle)/float64(period)*2*math.Pi + phase
		cycle++
		if cycle == period {
			cycle = 0
		}
		return math.Sin(p) * amp
	}
}

// ramp returns a stream that moves from zero to height
// over the course of length steps.
func ramp(height float64, length int) float64Stream {
	var cycle int
	return func() float64 {
		h := height * float64(cycle) / float64(length)
		if cycle < length {
			cycle++
		}
		return h
	}
}

// random returns a stream that generates random numbers
// between -amp and amp.
func random(amp float64, seed int64) float64Stream {
	r := rand.New(rand.NewSource(seed))
	return func() float64 {
		return ((r.Float64() - 0.5) * 2) * amp
	}
}

// delay returns a new stream which is a buffered version
// of f: it returns zero for cycles steps, followed by f.
func (f float64Stream) delay(cycles int) float64Stream {
	zeroes := 0
	return func() float64 {
		if zeroes < cycles {
			zeroes++
			return 0
		}
		return f()
	}
}

// scale returns a new stream that is f, but attenuated by a
// constant factor.
func (f float64Stream) scale(amt float64) float64Stream {
	return func() float64 {
		return f() * amt
	}
}

// offset returns a new stream that is f but offset by amt
// at each step.
func (f float64Stream) offset(amt float64) float64Stream {
	return func() float64 {
		old := f()
		return old + amt
	}
}

// sum returns a new stream that is the sum of all input streams
// at each step.
func (f float64Stream) sum(fs ...float64Stream) float64Stream {
	return func() float64 {
		sum := f()
		for _, s := range fs {
			sum += s()
		}
		return sum
	}
}

// quantize returns a new stream that rounds f to a multiple
// of mult at each step.
func (f float64Stream) quantize(mult float64) float64Stream {
	return func() float64 {
		r := f() / mult
		if r < 0 {
			return math.Ceil(r) * mult
		}
		return math.Floor(r) * mult
	}
}

// min returns a new stream that replaces all values produced
// by f lower than min with min.
func (f float64Stream) min(min float64) float64Stream {
	return func() float64 {
		return math.Max(min, f())
	}
}

// max returns a new stream that replaces all values produced
// by f higher than max with max.
func (f float64Stream) max(max float64) float64Stream {
	return func() float64 {
		return math.Min(max, f())
	}
}

// limit returns a new stream that replaces all values produced
// by f lower than min with min and higher than max with max.
func (f float64Stream) limit(min, max float64) float64Stream {
	return func() float64 {
		v := f()
		if v < min {
			v = min
		} else if v > max {
			v = max
		}
		return v
	}
}

func applyMemoryLimitHeapGoalHeadroom(goal uint64) uint64 {
	headroom := goal / 100 * MemoryLimitHeapGoalHeadroomPercent
	if headroom < MemoryLimitMinHeapGoalHeadroom {
		headroom = MemoryLimitMinHeapGoalHeadroom
	}
	if goal < headroom || goal-headroom < headroom {
		goal = headroom
	} else {
		goal -= headroom
	}
	return goal
}

func TestIdleMarkWorkerCount(t *testing.T) {
	const workers = 10
	c := NewGCController(100, math.MaxInt64)
	c.SetMaxIdleMarkWorkers(workers)
	for i := 0; i < workers; i++ {
		if !c.NeedIdleMarkWorker() {
			t.Fatalf("expected to need idle mark workers: i=%d", i)
		}
		if !c.AddIdleMarkWorker() {
			t.Fatalf("expected to be able to add an idle mark worker: i=%d", i)
		}
	}
	if c.NeedIdleMarkWorker() {
		t.Fatalf("expected to not need idle mark workers")
	}
	if c.AddIdleMarkWorker() {
		t.Fatalf("expected to not be able to add an idle mark worker")
	}
	for i := 0; i < workers; i++ {
		c.RemoveIdleMarkWorker()
		if !c.NeedIdleMarkWorker() {
			t.Fatalf("expected to need idle mark workers after removal: i=%d", i)
		}
	}
	for i := 0; i < workers-1; i++ {
		if !c.AddIdleMarkWorker() {
			t.Fatalf("expected to be able to add idle mark workers after adding again: i=%d", i)
		}
	}
	for i := 0; i < 10; i++ {
		if !c.AddIdleMarkWorker() {
			t.Fatalf("expected to be able to add idle mark workers interleaved: i=%d", i)
		}
		if c.AddIdleMarkWorker() {
			t.Fatalf("expected to not be able to add idle mark workers interleaved: i=%d", i)
		}
		c.RemoveIdleMarkWorker()
	}
	// Support the max being below the count.
	c.SetMaxIdleMarkWorkers(0)
	if c.NeedIdleMarkWorker() {
		t.Fatalf("expected to not need idle mark workers after capacity set to 0")
	}
	if c.AddIdleMarkWorker() {
		t.Fatalf("expected to not be able to add idle mark workers after capacity set to 0")
	}
	for i := 0; i < workers-1; i++ {
		c.RemoveIdleMarkWorker()
	}
	if c.NeedIdleMarkWorker() {
		t.Fatalf("expected to not need idle mark workers after capacity set to 0")
	}
	if c.AddIdleMarkWorker() {
		t.Fatalf("expected to not be able to add idle mark workers after capacity set to 0")
	}
	c.SetMaxIdleMarkWorkers(1)
	if !c.NeedIdleMarkWorker() {
		t.Fatalf("expected to need idle mark workers after capacity set to 1")
	}
	if !c.AddIdleMarkWorker() {
		t.Fatalf("expected to be able to add idle mark workers after capacity set to 1")
	}
}

��b IDATx��ytVս��ϓ22 �A@�IR��:�h�CiZ[�v��*E��:�W��ũZA� ^d��QeQ ��@ !��j�Z�'�>g�s��V��仿$�|?g�)&x-E�IE�N�T ��;@x�T.i��%-��X��}S�v�S�5�.��r/UHz^�_$-��W"�w��)�Ɗ�/@Z �&IoX��P�$K��}��JzX��:�;`�� &�, ��ŋu�i��,�e��6��m��X� Ե��rKb1�ԗ��)D�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�AD�A�݀!��I*��]R;I�2$eZ#OR��Z��Sr��r�6m��teff�u��*((P��u�'��v{��DIߔ4^�pI��m�'77WEEE;v�Ǝ��4�-��$]'�RI��{��\�I�&�G�� :I��HJ�� DWBB��=�\��W�R�޽m� o$K�(�V9��ABB�.��}��jѢ��v�`^?IO�ȅ}ڶm�G}T#F��J`�5�6��$-��ھ}�F��I�&��v;0(h;��Б�3�8CӧOWf��!�;A i:��F_m��9s&�|�q%=�#��w��Z�p�rrrl�a A� &��P\\��СC�[A#!� �{��o��l��F�} `��E2��}��M��K/��vV��)i��{4Bff�V�\��|ۭX�`��b�@��k��ɶ�@��%i��$K�z��5z�h�mX�[�I�XZ`� '��b%$��r�5��M��4�º��/�l� ԃ��ߖ�xhʔ)�[@=�} K�6IM}^��5k��㏷݆��z ��Η�ÿO��:gdG��B�m��y�T/��@+��Vɶ�纽z񕏵l�.��y�޴i�t뭷zV��0[�Y^>�Ws�qs}�\/�@$�(�T7�f��.��I�nݺi��R$푔n��.�~?H))\Z�RW'M�o�~v� Ov6o��ԃ��x��z��!�S,&�xm/�y�ɞԟ?�'ua��S�ѽ��b�,8�Gל�K��b��o�i�&��3t7Y,��)JJ��c[�n��z��ӳ�d�E��&K�sZ�Lӄ��I?@��&�%ӟ�۶mSMM�њ0��i�ؐSZ�,�|J+��N�� ~�,��0A0!5%Q-��YQQa��3}$_vV��r�f9f?S8`��zD�AD�AD�AD�AD�AD�AD�AD�AD�A�d��q�P��,ت��m��M��mg��1V?�r�S��I꒟��]�u|�l ��R��CyE�f�٢9�j��URb�zt�Ѱ!m5~tG��j�2�D��h�G�*�{H9�)꒟��ר3:(+3\?�/;TU��ݭ��ʴ~S�6lڧ��U��J*�i�$�d�(#=Yݺd�{�,�p|3��B))��q�:��vN0Y.�jk��ק6��;�SɶVzHJJЀ�-u��tѹ�սk��>�QUU��\��޲��~]fF�n��K?��&��ߡ��5��b��=z9�)��^�|u_�k�-[��y%Z��NU6 ��7M�i��:�]ۦt�k��[�n� ��X��(�e6B�b�.��"�8�cۭ|��~�t�e��u��u��w�|��ή��I-5�"��~��U��k��;��Zi�cE�m��N/��:�]�M��> cQ�^�ui�ƞ��??Ң��p�c#TUU�3�U��a��k��Nw�A`��:��Y_V��-8.KKf�R��itv�޲* 9S�6ֿ��j�,Ճ��NOMߤ��]��z�^��f��O�h��|��<�>@Å5��_��/I��u?{S��Y��4h�K��/2��]��4�%i��t�5��q�]�G�G��e�2�%i�R��| ��W��&f�*^]�??��vq[��Lg��E��_��3f}��F�xu~��}q��d�-��ږF�xu~I N>\��;��͗��O��֊�:�̗��W��J@Bh�W=��y��|��Ggwܷ�H�_NY��?��)T��d��i�'?��խw�h�lm�Qi� �!SUU��sw4kӺ�e4rf��x�u�-[n�Ht��MFj}�H�_��u�~w�>)�o�V}�(�T'��e��bʒ�v��3_�[+v�n@Ȭ\S�}��o��t��}w��=��k�H��F�n�xg��S�� 0eޢm~�l��}��u��q��Z�f��F��oZuu��E��g� ��`z�t~?b�;t�%�>��WTkķ�h��[�2e�G8L��IW�x��,��^\thr�l��^��Ϊ��{��=�ǆ��<}�q��V�@ ��⠨��W��y^��L��F_��>�0��U�k��D�u�ʫu��Cs$)I��v��:�IK��;6ֲ�4{^��6��ե��m+l��3>�݆��uM �9��u��?>�Z��c��}g�~q��h��Kw��ڭ��eFMM�~p�М�uq�ǿz��6T��b@8��@Y�|��jx��]�(^]�gf�}�M�"tG ��-w��.@�vOqh~/�HII��`��S�[l��.��6�nØXL��9�v�U�cOo��B�\�x�o��Ǥ�'�T�&I��Ǎ�Qw��_w�p�v��[�k�m��O�{�w�~�>�#=P1P�ɞ�a�-w��e�:i�Ǐl��H��o�׈��꒟�f9��SzH�?��+s�h�k%F��s:��q��Vh�qY��`��j�vO�'ρ?PyX3�lх��]�˾u��V�{��ݞ]1��,�M�z�YN�W~̈́�joY�n��}��ȚF߾׮mS]��F�� z�+�E��D�xm/��d{�F��{-�W��-�4w�Y��듏:�?��?��_�g�P�f� ^3��e��cg ��ҵs��8R��2�מ�z�@T��A��N��Gj�)��}CNi��/�R~��}��c:5�{��!��Z�HӋӾ��6}T�]��G�]�7W�6^��n �9*,��Y��qOZj��:P?�Q�� DF��L�|��?��-�^��.��Ɵ�7��}f�F�h׶��xe��2P�s��c��z�1��&5\cn��[�=�V��n[��ĶE鎀uˌ��d3G�II ��k�;�l�NmشOuuRVf��BE��]ۣ�eӶu :��X�-[��(��e��r�4��~��LH�i�6:��Ѻ@ԅ��r��ST�0��trk%$Č��0ez��"� *��z�"��T�/X9|8��.��C5F�eg}��C�Q%�͞�ˣ��JvL��/��?�j�^��h��&�9x�F��`�њ�Z��(��&�y��F��&Iݻf�g��#��W��;�3^�{Wo^4�'v�V[[�K'��;+��m��Ӎִ�]AC@��W?1^{�එyh��+^]��f��m��~�i��Ե�]AB@��WTk�̏t��uR�?�l�.O�IH�i�Yy�Զ�]A�ˀ7c��:��q}ힽ��a�f�6��Z~�қm(��+sK4{^�6}T��*UUu�]��n��.��:kx{�:��2�� _m��=�sA�ߤ�U��@?��Z��-V�ކ�е��z왍��Nэ��{|5� pڶn��b� �p-@��sPg]0G7�fy��-��M�{GCF��'%�{�4`��=�$-�Ge\��eU:m�+Z�t�'�W��jO�!O�AF@��i�k&t�݆��ϥ_�� e��}��=]"��Wz��_��.��͜�E3�l�e�W��F�i��h|t��-w��Z��ۍ��-�u��w=�6�YN��{��6|��}��|��*={��Ѽ��n.�S�.��z��1z��j�ۻT��H]��흾� �D�u��D��v��mv��K��.`V]yY�~s�I��@��t?/��ϓ.� ��m�&�["�+��P��?M��z�ovV��ЫG3�-�G��RR��[(!!\�_��,��^��%?�v@��ҵ�ő�� m��`�Y)�te�m8��G��Mx.))A�]Y��i`�V��i��W�`�?�^��~!�S#��^+�ѽ��GZj��?V�ģ�0.))A�꨷��l�z�L�*��]��O��X�r��Y�`DBBL�Oj��{��-M�H'�ii�-ϰ��ok�7^�� )쭡�b��]�UX��S�ְ�mռY��|5��*��c�ֽk��0B��7镹%ڽ��P#8n�Ȏ��q}mJr�23��_>��l��E�5��$i��wu��i�+ ��H�~�F`��IjƵ@�q �\ �@#qG�0"��.�0"� l��`��.�0!� ,�AQ�HN6�q��z�k��KJ�#��o;`X�v2��>,tێJ��J��7Z/*��A��.@f�ف�jM��zk��g��@TvZ�H3Z�xu�6Ra��'%��O��?/d�Q��5�x��Yk��U]��R�ֽk�ق@��Da�S^�RS�ּ�5��|��B��e��HNN�͘p �Hvc�Y�c��C5:��y �#��`�οb��;z��2��.��!��k��r��}g��U��Wk��yZ��n�=�f�� Pv��sn��3�p��~�;4p�˚=�ē~�Nm�I] ��¾0lH[��_��L��h�sh��_��ғߤ��c_њ�e��c�)��g�7��V�IZ��5��yr�gk̞W��#��IjӪ�v�>��՞��y睝��M�8�[�|�]��\�շ��8�M��6�%�|@P��Z��ڨ�I-m��>=�k��=�'a��iRo�-x�?>Q��.��}`�Ȏ:�Ws�mu� �u�� > �.@,&��;+!!�˱�tﭧD��Q�w��RW\��vF\~Q7�>�s�p�Y�w$��%A~�;~}��6��¾��g�&if_��=��j�,�v+�U��L�1(tW��a��ke��:@Ș>�j�$�Gq�2�t7S?�vL��|��]u�/�� .�(�0�E��6M��k�6�h��iۺ��z�ښ��O��r��i�f�ޱ�xm/��G�x>�� La�l%%��~�{��l�Bs��R4�*��}{�0Z/��t��N�I��ɚ��p�V^#�L�f�:u@k#�RSu�� =��S^��Zy��uR/��.@n�&��΃z~��B=��0eg뺆��#,��Þ�[�B/?�H� uUf�7�y ��W��y}Bw��eg��ל`��Wh�(|��|��`l`.�;�Ws��?��V�@"��c:i�ɍ��L֯��PG�v�6z�c�tM��̠��'��:w��uW��;d��=�;E�v�e��D��}��9�J@B(��0�iհ�b�v�P�1{�\P��&��G�7��D��޴I��y��_��$-Q�jm�~Yrr�&]�C��Dv%b�h|�Yz�n�i_�R;�k��g�}n��JOII��w��yuL}{�Ќǋ�}�:+3Y�?:��W��J/N+Rz��d=�h��b��;d��j͒su��ݔ��@NKMԄ�j��qz��C��5@��y°�h��L��m;*5�ezᕏ��=�ep�� X��L�n?�מ:��r�`��۵�tŤ�Z�|�1�v`�V�뽧��_c��s�ج'�ߤ%o�Tuum�k%%%h�)�u�y]��N�k��[�n� ��'b�2� �l�.=��͜�E%��gf$��[c;�s:�V-�͞W��ߤW�h��-��j�7��]4��=��F-X�]�>��Z�LS�i��[�Y��*�W��e;��Z�a��n(ӇW|e(HNNP��5[= r4tP �&0�<��p�c#��`�v�TNV GFq��v�T�i�*��Ty�a�m�$��ߏWyE�*�V��JKMTfF�w��>'��$-�ؽ�.Ho��.��8��c��"@D�AD�AD�AD�AD�AD�AD�AD�AD�A~�j��*֘,N;Pi�3599�h=��g�o�ضL�g��i��J�5��փy~�}&��Z��d9p֚ e:|��h��L��`��`��b/��d9p�?�fgg+%%�hM��gXo��s�ج��, Ω��Ol0Z��h=x��d��j��L��m��h��ݻ�o��O�[�g_�l�,8a��]�٭+��ӧ��0��$��I�]��c��]:粹:Te��ꢢ"�5a^��K�g�h,&��=��=��՟^��߶�ߢE�ܹS �J}��I%�:8 �IDAT~,�9/ʃPW'M�o�}z��N�ƍ쨓z�Pb��NZ�~�^z�=4m��s��w��g;5�� Y�~��S�VM��RXUյڱ�R��f��?��s�:w �;6�H:�º��i��5��-�maM��&O��3;1I�K�eam�Z�h�͛7+##�v+�c ~u�~ca]�Gn��F'��ټL~��PPP��b��n� v�o��C�4R,ӟ��gg��%�hq}@#M�4IÇ�� O�y^�x�M��Z�x�� )� �yOw@H�k�N˖-Sǎm�b]X@n��+i��͖��!++K3g�d��\�$m�t�$^��Y�f��J��\8PR��F�)77W��א!Cl��$i��:�@@��_o��G�� I{$��#� ��8磌��ŋ9�1A��(�I�m7��֭��>}�ߴ�J�q�7ޗt��^� -[��ԩS�j�*��}��%]&�'� -��ɓ'�ꫯVzz��vB#�;a �7@G��xI��{��j޼�ƌ��.�LÇWBB�7��`O��"I�$/�@R�@eee��@�۷��>}�0��,ɒ2$53Xs��|c��S~��rpTYYY��} kH�c�%��&k��.]��, @��AD�AD�AD�AD�AD�AD�AD�AD�A��@�l��T��<%''�*��L�o�^={��رc5h� %$+CnܸQ3f��ҥK�}�vUVV��s�9G� R,�_{�x��ˇ��3��o߾��;TTTd�}��馛��]uuuG��~��i�ԩ��@4��b��n��v�m�vfϞ�/�Peeeq}}za I~,�誫��{UWW뮻��}��_~Y�ƍSMMM��Yχ֝w��aw\�ď�cxꩧt�E��ƍկ_?�۷��5��@�u�?�1�k�N�ׯWzz�/�w�y�>}z�j��3�� k�(�ٺu��q_�Z�v�f̘��:~�AB�Q&�r��|��!��%K��ҥK��g��Ԟ={<_��X-�z� !��C�y�FUU��z~�AB�QIIIjݺ��W�$UXX��D��ٳ��Z~�AB�Q�ƍ�e��c��W�$<(~<�RSS�v�Zu��jjjԧO�Z��Qu��@4� 8��m�&&&j�ԩ��g�$�ď��1h� ͟?_��{�768��@��g �=@�`)))��5o��6m��3��)��ѣ�ƌ��J�;w��ҿUTT��/��K��ZR�{~a=@��0o�<��*狔��i�F��ɶ[�ˎ;T]]��OX@��?��K�.�ۈ�xN ��pppppppppppppppppP��fl߾],�{ｧ��k۶mڿ��o�5B��TӦMӴiӴ|�r�� DB��2e�|�A��n!D��y�'t��k�Ν�[A� $***t�5��'�� "�!�駟��o�a�Dn�Ν:t�֭[g�D��ШQ��0�6q�D��;��@ ��x� M�6�v�(Pii��z�m��Z�4e��w��"@��̴i�x��f��[��~-F�ٱc��&I�Z�2�|��n��!�?$@��{�[��H�T��ɏ�#��@�h��Ȏ��I#�_�m�(F��/6Z3��z��'�\r�,��r��!��;��w2Z3j��=~�G��Y��7��"I�$��i�I.�p��_"��?�p��N`�y��DD��?: ��_�� G�ÿa��b�7J��!B��x@�0�� B��o ��c��G��@`1��C��[@�0��G ��@`0��C��_�u�V1�� a��CX��>�W�` |��`!<��S�`"<��.��`#�c�`�?c��A��C4 �?��c�� p#��~@�0��?:��0��8&��_��M�Q1��J�h#��?��/`��7��;I��q7�aw�Q��A�1Hp ��!�#��<8��/#@�1��U�l7��=�S�=��K.�4Z�?E��_$i��@��!�1�!E4�?��`��P_� ��@��Bă�1��0�#��:��"��a��U�,�x�b��F��Y1� ��[��n|��n� ��#'��v�E��H:`�x��b� ��#��v��D��4��Y ��h��i.i��&��E�Ζ��v#��O� H��4�I�Ŷ��}�:I�k�h��@t��ZR��F��#��(�tXҙ��zZ �?��I��3l7q��@õ��|ۍ�1,G��p�u��Y� ��Ꮿ@h��J��v#�x��xk$ ��v#�9��5��}��_��$��c �S�#��=+��"K�{F��*m7�`#��%�H:NRS�p�6I?��sIՖ{Ap��$I$I:QR��v�2$�Z�@�UJ*��$�]<��F��O4IEND�B`�