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// 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"
"internal/goexperiment"
"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,
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 {
if goexperiment.PacerRedesign {
// 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)
}
// 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,
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 {
if goexperiment.PacerRedesign {
// 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,
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 {
if goexperiment.PacerRedesign {
// 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,
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,
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,
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,
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 goexperiment.PacerRedesign && 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,
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)
if goexperiment.PacerRedesign {
assertInRange(t, "GC utilization", c[n-1].gcUtilization, 0.25, 0.3)
} else {
// The old pacer is messier here, and needs a lot more tolerance.
assertInRange(t, "GC utilization", c[n-1].gcUtilization, 0.25, 0.4)
}
}
},
},
{
// This test is the same as OscAlloc, but instead of oscillating, the allocation rate is jittery.
name: "JitterAlloc",
gcPercent: 100,
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, 1.05)
if goexperiment.PacerRedesign {
assertInRange(t, "GC utilization", c[n-1].gcUtilization, 0.25, 0.3)
} else {
// The old pacer is messier here, and needs a lot more tolerance.
assertInRange(t, "GC utilization", c[n-1].gcUtilization, 0.25, 0.4)
}
}
},
},
{
// This test is the same as JitterAlloc, but with a much higher allocation rate.
// The jitter is proportionally the same.
name: "HeavyJitterAlloc",
gcPercent: 100,
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)
if goexperiment.PacerRedesign {
assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[11].gcUtilization, 0.05)
} else {
// The old pacer is messier here, and needs a little more tolerance.
assertInEpsilon(t, "GC utilization", c[n-1].gcUtilization, c[11].gcUtilization, 0.07)
}
}
},
},
// 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)
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.Trigger(),
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
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) 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
}
}