runtime: fix hard goal calculation

[gostls13.git] / src / runtime / mgcpacer.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

import (
        "internal/cpu"
        "internal/goexperiment"
        "runtime/internal/atomic"
        "unsafe"
)

const (
        // gcGoalUtilization is the goal CPU utilization for
        // marking as a fraction of GOMAXPROCS.
        gcGoalUtilization = goexperiment.PacerRedesignInt*gcBackgroundUtilization +
                (1-goexperiment.PacerRedesignInt)*(gcBackgroundUtilization+0.05)

        // gcBackgroundUtilization is the fixed CPU utilization for background
        // marking. It must be <= gcGoalUtilization. The difference between
        // gcGoalUtilization and gcBackgroundUtilization will be made up by
        // mark assists. The scheduler will aim to use within 50% of this
        // goal.
        //
        // Setting this to < gcGoalUtilization avoids saturating the trigger
        // feedback controller when there are no assists, which allows it to
        // better control CPU and heap growth. However, the larger the gap,
        // the more mutator assists are expected to happen, which impact
        // mutator latency.
        //
        // If goexperiment.PacerRedesign, the trigger feedback controller
        // is replaced with an estimate of the mark/cons ratio that doesn't
        // have the same saturation issues, so this is set equal to
        // gcGoalUtilization.
        gcBackgroundUtilization = 0.25

        // gcCreditSlack is the amount of scan work credit that can
        // accumulate locally before updating gcController.heapScanWork and,
        // optionally, gcController.bgScanCredit. Lower values give a more
        // accurate assist ratio and make it more likely that assists will
        // successfully steal background credit. Higher values reduce memory
        // contention.
        gcCreditSlack = 2000

        // gcAssistTimeSlack is the nanoseconds of mutator assist time that
        // can accumulate on a P before updating gcController.assistTime.
        gcAssistTimeSlack = 5000

        // gcOverAssistWork determines how many extra units of scan work a GC
        // assist does when an assist happens. This amortizes the cost of an
        // assist by pre-paying for this many bytes of future allocations.
        gcOverAssistWork = 64 << 10

        // defaultHeapMinimum is the value of heapMinimum for GOGC==100.
        defaultHeapMinimum = goexperiment.PacerRedesignInt*(512<<10) +
                (1-goexperiment.PacerRedesignInt)*(4<<20)

        // scannableStackSizeSlack is the bytes of stack space allocated or freed
        // that can accumulate on a P before updating gcController.stackSize.
        scannableStackSizeSlack = 8 << 10
)

func init() {
        if offset := unsafe.Offsetof(gcController.heapLive); offset%8 != 0 {
                println(offset)
                throw("gcController.heapLive not aligned to 8 bytes")
        }
}

// gcController implements the GC pacing controller that determines
// when to trigger concurrent garbage collection and how much marking
// work to do in mutator assists and background marking.
//
// It uses a feedback control algorithm to adjust the gcController.trigger
// trigger based on the heap growth and GC CPU utilization each cycle.
// This algorithm optimizes for heap growth to match GOGC and for CPU
// utilization between assist and background marking to be 25% of
// GOMAXPROCS. The high-level design of this algorithm is documented
// at https://golang.org/s/go15gcpacing.
//
// All fields of gcController are used only during a single mark
// cycle.
var gcController gcControllerState

type gcControllerState struct {
        // Initialized from $GOGC. GOGC=off means no GC.
        //
        // Updated atomically with mheap_.lock held or during a STW.
        // Safe to read atomically at any time, or non-atomically with
        // mheap_.lock or STW.
        gcPercent int32

        _ uint32 // padding so following 64-bit values are 8-byte aligned

        // heapMinimum is the minimum heap size at which to trigger GC.
        // For small heaps, this overrides the usual GOGC*live set rule.
        //
        // When there is a very small live set but a lot of allocation, simply
        // collecting when the heap reaches GOGC*live results in many GC
        // cycles and high total per-GC overhead. This minimum amortizes this
        // per-GC overhead while keeping the heap reasonably small.
        //
        // During initialization this is set to 4MB*GOGC/100. In the case of
        // GOGC==0, this will set heapMinimum to 0, resulting in constant
        // collection even when the heap size is small, which is useful for
        // debugging.
        heapMinimum uint64

        // triggerRatio is the heap growth ratio that triggers marking.
        //
        // E.g., if this is 0.6, then GC should start when the live
        // heap has reached 1.6 times the heap size marked by the
        // previous cycle. This should be ≤ GOGC/100 so the trigger
        // heap size is less than the goal heap size. This is set
        // during mark termination for the next cycle's trigger.
        //
        // Protected by mheap_.lock or a STW.
        //
        // Used if !goexperiment.PacerRedesign.
        triggerRatio float64

        // trigger is the heap size that triggers marking.
        //
        // When heapLive ≥ trigger, the mark phase will start.
        // This is also the heap size by which proportional sweeping
        // must be complete.
        //
        // This is computed from triggerRatio during mark termination
        // for the next cycle's trigger.
        //
        // Protected by mheap_.lock or a STW.
        trigger uint64

        // consMark is the estimated per-CPU consMark ratio for the application.
        //
        // It represents the ratio between the application's allocation
        // rate, as bytes allocated per CPU-time, and the GC's scan rate,
        // as bytes scanned per CPU-time.
        // The units of this ratio are (B / cpu-ns) / (B / cpu-ns).
        //
        // At a high level, this value is computed as the bytes of memory
        // allocated (cons) per unit of scan work completed (mark) in a GC
        // cycle, divided by the CPU time spent on each activity.
        //
        // Updated at the end of each GC cycle, in endCycle.
        //
        // For goexperiment.PacerRedesign.
        consMark float64

        // consMarkController holds the state for the mark-cons ratio
        // estimation over time.
        //
        // Its purpose is to smooth out noisiness in the computation of
        // consMark; see consMark for details.
        //
        // For goexperiment.PacerRedesign.
        consMarkController piController

        // heapGoal is the goal heapLive for when next GC ends.
        // Set to ^uint64(0) if disabled.
        //
        // Read and written atomically, unless the world is stopped.
        heapGoal uint64

        // lastHeapGoal is the value of heapGoal for the previous GC.
        // Note that this is distinct from the last value heapGoal had,
        // because it could change if e.g. gcPercent changes.
        //
        // Read and written with the world stopped or with mheap_.lock held.
        lastHeapGoal uint64

        // heapLive is the number of bytes considered live by the GC.
        // That is: retained by the most recent GC plus allocated
        // since then. heapLive ≤ memstats.heapAlloc, since heapAlloc includes
        // unmarked objects that have not yet been swept (and hence goes up as we
        // allocate and down as we sweep) while heapLive excludes these
        // objects (and hence only goes up between GCs).
        //
        // This is updated atomically without locking. To reduce
        // contention, this is updated only when obtaining a span from
        // an mcentral and at this point it counts all of the
        // unallocated slots in that span (which will be allocated
        // before that mcache obtains another span from that
        // mcentral). Hence, it slightly overestimates the "true" live
        // heap size. It's better to overestimate than to
        // underestimate because 1) this triggers the GC earlier than
        // necessary rather than potentially too late and 2) this
        // leads to a conservative GC rate rather than a GC rate that
        // is potentially too low.
        //
        // Reads should likewise be atomic (or during STW).
        //
        // Whenever this is updated, call traceHeapAlloc() and
        // this gcControllerState's revise() method.
        heapLive uint64

        // heapScan is the number of bytes of "scannable" heap. This
        // is the live heap (as counted by heapLive), but omitting
        // no-scan objects and no-scan tails of objects.
        //
        // For !goexperiment.PacerRedesign: Whenever this is updated,
        // call this gcControllerState's revise() method. It is read
        // and written atomically or with the world stopped.
        //
        // For goexperiment.PacerRedesign: This value is fixed at the
        // start of a GC cycle, so during a GC cycle it is safe to
        // read without atomics, and it represents the maximum scannable
        // heap.
        heapScan uint64

        // lastHeapScan is the number of bytes of heap that were scanned
        // last GC cycle. It is the same as heapMarked, but only
        // includes the "scannable" parts of objects.
        //
        // Updated when the world is stopped.
        lastHeapScan uint64

        // stackScan is a snapshot of scannableStackSize taken at each GC
        // STW pause and is used in pacing decisions.
        //
        // Updated only while the world is stopped.
        stackScan uint64

        // scannableStackSize is the amount of allocated goroutine stack space in
        // use by goroutines.
        //
        // This number tracks allocated goroutine stack space rather than used
        // goroutine stack space (i.e. what is actually scanned) because used
        // goroutine stack space is much harder to measure cheaply. By using
        // allocated space, we make an overestimate; this is OK, it's better
        // to conservatively overcount than undercount.
        //
        // Read and updated atomically.
        scannableStackSize uint64

        // globalsScan is the total amount of global variable space
        // that is scannable.
        //
        // Read and updated atomically.
        globalsScan uint64

        // heapMarked is the number of bytes marked by the previous
        // GC. After mark termination, heapLive == heapMarked, but
        // unlike heapLive, heapMarked does not change until the
        // next mark termination.
        heapMarked uint64

        // heapScanWork is the total heap scan work performed this cycle.
        // stackScanWork is the total stack scan work performed this cycle.
        // globalsScanWork is the total globals scan work performed this cycle.
        //
        // These are updated atomically during the cycle. Updates occur in
        // bounded batches, since they are both written and read
        // throughout the cycle. At the end of the cycle, heapScanWork is how
        // much of the retained heap is scannable.
        //
        // Currently these are measured in bytes. For most uses, this is an
        // opaque unit of work, but for estimation the definition is important.
        //
        // Note that stackScanWork includes all allocated space, not just the
        // size of the stack itself, mirroring stackSize.
        //
        // For !goexperiment.PacerRedesign, stackScanWork and globalsScanWork
        // are always zero.
        heapScanWork    atomic.Int64
        stackScanWork   atomic.Int64
        globalsScanWork atomic.Int64

        // bgScanCredit is the scan work credit accumulated by the
        // concurrent background scan. This credit is accumulated by
        // the background scan and stolen by mutator assists. This is
        // updated atomically. Updates occur in bounded batches, since
        // it is both written and read throughout the cycle.
        bgScanCredit int64

        // assistTime is the nanoseconds spent in mutator assists
        // during this cycle. This is updated atomically. Updates
        // occur in bounded batches, since it is both written and read
        // throughout the cycle.
        assistTime int64

        // dedicatedMarkTime is the nanoseconds spent in dedicated
        // mark workers during this cycle. This is updated atomically
        // at the end of the concurrent mark phase.
        dedicatedMarkTime int64

        // fractionalMarkTime is the nanoseconds spent in the
        // fractional mark worker during this cycle. This is updated
        // atomically throughout the cycle and will be up-to-date if
        // the fractional mark worker is not currently running.
        fractionalMarkTime int64

        // idleMarkTime is the nanoseconds spent in idle marking
        // during this cycle. This is updated atomically throughout
        // the cycle.
        idleMarkTime int64

        // markStartTime is the absolute start time in nanoseconds
        // that assists and background mark workers started.
        markStartTime int64

        // dedicatedMarkWorkersNeeded is the number of dedicated mark
        // workers that need to be started. This is computed at the
        // beginning of each cycle and decremented atomically as
        // dedicated mark workers get started.
        dedicatedMarkWorkersNeeded int64

        // assistWorkPerByte is the ratio of scan work to allocated
        // bytes that should be performed by mutator assists. This is
        // computed at the beginning of each cycle and updated every
        // time heapScan is updated.
        assistWorkPerByte atomic.Float64

        // assistBytesPerWork is 1/assistWorkPerByte.
        //
        // Note that because this is read and written independently
        // from assistWorkPerByte users may notice a skew between
        // the two values, and such a state should be safe.
        assistBytesPerWork atomic.Float64

        // fractionalUtilizationGoal is the fraction of wall clock
        // time that should be spent in the fractional mark worker on
        // each P that isn't running a dedicated worker.
        //
        // For example, if the utilization goal is 25% and there are
        // no dedicated workers, this will be 0.25. If the goal is
        // 25%, there is one dedicated worker, and GOMAXPROCS is 5,
        // this will be 0.05 to make up the missing 5%.
        //
        // If this is zero, no fractional workers are needed.
        fractionalUtilizationGoal float64

        // test indicates that this is a test-only copy of gcControllerState.
        test bool

        _ cpu.CacheLinePad
}

func (c *gcControllerState) init(gcPercent int32) {
        c.heapMinimum = defaultHeapMinimum

        if goexperiment.PacerRedesign {
                c.consMarkController = piController{
                        // Tuned first via the Ziegler-Nichols process in simulation,
                        // then the integral time was manually tuned against real-world
                        // applications to deal with noisiness in the measured cons/mark
                        // ratio.
                        kp: 0.9,
                        ti: 4.0,

                        // An update is done once per GC cycle.
                        period: 1,

                        // Set a high reset time in GC cycles.
                        // This is inversely proportional to the rate at which we
                        // accumulate error from clipping. By making this very high
                        // we make the accumulation slow. In general, clipping is
                        // OK in our situation, hence the choice.
                        //
                        // Tune this if we get unintended effects from clipping for
                        // a long time.
                        tt:  1000,
                        min: -1000,
                        max: 1000,
                }
        } else {
                // Set a reasonable initial GC trigger.
                c.triggerRatio = 7 / 8.0

                // Fake a heapMarked value so it looks like a trigger at
                // heapMinimum is the appropriate growth from heapMarked.
                // This will go into computing the initial GC goal.
                c.heapMarked = uint64(float64(c.heapMinimum) / (1 + c.triggerRatio))
        }

        // This will also compute and set the GC trigger and goal.
        c.setGCPercent(gcPercent)
}

// startCycle resets the GC controller's state and computes estimates
// for a new GC cycle. The caller must hold worldsema and the world
// must be stopped.
func (c *gcControllerState) startCycle(markStartTime int64, procs int) {
        c.heapScanWork.Store(0)
        c.stackScanWork.Store(0)
        c.globalsScanWork.Store(0)
        c.bgScanCredit = 0
        c.assistTime = 0
        c.dedicatedMarkTime = 0
        c.fractionalMarkTime = 0
        c.idleMarkTime = 0
        c.markStartTime = markStartTime
        c.stackScan = atomic.Load64(&c.scannableStackSize)

        // Ensure that the heap goal is at least a little larger than
        // the current live heap size. This may not be the case if GC
        // start is delayed or if the allocation that pushed gcController.heapLive
        // over trigger is large or if the trigger is really close to
        // GOGC. Assist is proportional to this distance, so enforce a
        // minimum distance, even if it means going over the GOGC goal
        // by a tiny bit.
        if goexperiment.PacerRedesign {
                if c.heapGoal < c.heapLive+64<<10 {
                        c.heapGoal = c.heapLive + 64<<10
                }
        } else {
                if c.heapGoal < c.heapLive+1<<20 {
                        c.heapGoal = c.heapLive + 1<<20
                }
        }

        // Compute the background mark utilization goal. In general,
        // this may not come out exactly. We round the number of
        // dedicated workers so that the utilization is closest to
        // 25%. For small GOMAXPROCS, this would introduce too much
        // error, so we add fractional workers in that case.
        totalUtilizationGoal := float64(procs) * gcBackgroundUtilization
        c.dedicatedMarkWorkersNeeded = int64(totalUtilizationGoal + 0.5)
        utilError := float64(c.dedicatedMarkWorkersNeeded)/totalUtilizationGoal - 1
        const maxUtilError = 0.3
        if utilError < -maxUtilError || utilError > maxUtilError {
                // Rounding put us more than 30% off our goal. With
                // gcBackgroundUtilization of 25%, this happens for
                // GOMAXPROCS<=3 or GOMAXPROCS=6. Enable fractional
                // workers to compensate.
                if float64(c.dedicatedMarkWorkersNeeded) > totalUtilizationGoal {
                        // Too many dedicated workers.
                        c.dedicatedMarkWorkersNeeded--
                }
                c.fractionalUtilizationGoal = (totalUtilizationGoal - float64(c.dedicatedMarkWorkersNeeded)) / float64(procs)
        } else {
                c.fractionalUtilizationGoal = 0
        }

        // In STW mode, we just want dedicated workers.
        if debug.gcstoptheworld > 0 {
                c.dedicatedMarkWorkersNeeded = int64(procs)
                c.fractionalUtilizationGoal = 0
        }

        // Clear per-P state
        for _, p := range allp {
                p.gcAssistTime = 0
                p.gcFractionalMarkTime = 0
        }

        // Compute initial values for controls that are updated
        // throughout the cycle.
        c.revise()

        if debug.gcpacertrace > 0 {
                assistRatio := c.assistWorkPerByte.Load()
                print("pacer: assist ratio=", assistRatio,
                        " (scan ", gcController.heapScan>>20, " MB in ",
                        work.initialHeapLive>>20, "->",
                        c.heapGoal>>20, " MB)",
                        " workers=", c.dedicatedMarkWorkersNeeded,
                        "+", c.fractionalUtilizationGoal, "\n")
        }
}

// revise updates the assist ratio during the GC cycle to account for
// improved estimates. This should be called whenever gcController.heapScan,
// gcController.heapLive, or gcController.heapGoal is updated. It is safe to
// call concurrently, but it may race with other calls to revise.
//
// The result of this race is that the two assist ratio values may not line
// up or may be stale. In practice this is OK because the assist ratio
// moves slowly throughout a GC cycle, and the assist ratio is a best-effort
// heuristic anyway. Furthermore, no part of the heuristic depends on
// the two assist ratio values being exact reciprocals of one another, since
// the two values are used to convert values from different sources.
//
// The worst case result of this raciness is that we may miss a larger shift
// in the ratio (say, if we decide to pace more aggressively against the
// hard heap goal) but even this "hard goal" is best-effort (see #40460).
// The dedicated GC should ensure we don't exceed the hard goal by too much
// in the rare case we do exceed it.
//
// It should only be called when gcBlackenEnabled != 0 (because this
// is when assists are enabled and the necessary statistics are
// available).
func (c *gcControllerState) revise() {
        gcPercent := atomic.Loadint32(&c.gcPercent)
        if gcPercent < 0 {
                // If GC is disabled but we're running a forced GC,
                // act like GOGC is huge for the below calculations.
                gcPercent = 100000
        }
        live := atomic.Load64(&c.heapLive)
        scan := atomic.Load64(&c.heapScan)
        work := c.heapScanWork.Load() + c.stackScanWork.Load() + c.globalsScanWork.Load()

        // Assume we're under the soft goal. Pace GC to complete at
        // heapGoal assuming the heap is in steady-state.
        heapGoal := int64(atomic.Load64(&c.heapGoal))

        var scanWorkExpected int64
        if goexperiment.PacerRedesign {
                // The expected scan work is computed as the amount of bytes scanned last
                // GC cycle, plus our estimate of stacks and globals work for this cycle.
                scanWorkExpected = int64(c.lastHeapScan + c.stackScan + c.globalsScan)

                // maxScanWork is a worst-case estimate of the amount of scan work that
                // needs to be performed in this GC cycle. Specifically, it represents
                // the case where *all* scannable memory turns out to be live.
                maxScanWork := int64(scan + c.stackScan + c.globalsScan)
                if work > scanWorkExpected {
                        // We've already done more scan work than expected. Because our expectation
                        // is based on a steady-state scannable heap size, we assume this means our
                        // heap is growing. Compute a new heap goal that takes our existing runway
                        // computed for scanWorkExpected and extrapolates it to maxScanWork, the worst-case
                        // scan work. This keeps our assist ratio stable if the heap continues to grow.
                        //
                        // The effect of this mechanism is that assists stay flat in the face of heap
                        // growths. It's OK to use more memory this cycle to scan all the live heap,
                        // because the next GC cycle is inevitably going to use *at least* that much
                        // memory anyway.
                        extHeapGoal := int64(float64(heapGoal-int64(c.trigger))/float64(scanWorkExpected)*float64(maxScanWork)) + int64(c.trigger)
                        scanWorkExpected = maxScanWork

                        // hardGoal is a hard limit on the amount that we're willing to push back the
                        // heap goal, and that's twice the heap goal (i.e. if GOGC=100 and the heap and/or
                        // stacks and/or globals grow to twice their size, this limits the current GC cycle's
                        // growth to 4x the original live heap's size).
                        //
                        // This maintains the invariant that we use no more memory than the next GC cycle
                        // will anyway.
                        hardGoal := int64((1.0 + float64(gcPercent)/100.0) * float64(heapGoal))
                        if extHeapGoal > hardGoal {
                                extHeapGoal = hardGoal
                        }
                        heapGoal = extHeapGoal
                }
                if int64(live) > heapGoal {
                        // We're already past our heap goal, even the extrapolated one.
                        // Leave ourselves some extra runway, so in the worst case we
                        // finish by that point.
                        const maxOvershoot = 1.1
                        heapGoal = int64(float64(heapGoal) * maxOvershoot)

                        // Compute the upper bound on the scan work remaining.
                        scanWorkExpected = maxScanWork
                }
        } else {
                // Compute the expected scan work remaining.
                //
                // This is estimated based on the expected
                // steady-state scannable heap. For example, with
                // GOGC=100, only half of the scannable heap is
                // expected to be live, so that's what we target.
                //
                // (This is a float calculation to avoid overflowing on
                // 100*heapScan.)
                scanWorkExpected = int64(float64(scan) * 100 / float64(100+gcPercent))
                if int64(live) > heapGoal || work > scanWorkExpected {
                        // We're past the soft goal, or we've already done more scan
                        // work than we expected. Pace GC so that in the worst case it
                        // will complete by the hard goal.
                        const maxOvershoot = 1.1
                        heapGoal = int64(float64(heapGoal) * maxOvershoot)

                        // Compute the upper bound on the scan work remaining.
                        scanWorkExpected = int64(scan)
                }
        }

        // Compute the remaining scan work estimate.
        //
        // Note that we currently count allocations during GC as both
        // scannable heap (heapScan) and scan work completed
        // (scanWork), so allocation will change this difference
        // slowly in the soft regime and not at all in the hard
        // regime.
        scanWorkRemaining := scanWorkExpected - work
        if scanWorkRemaining < 1000 {
                // We set a somewhat arbitrary lower bound on
                // remaining scan work since if we aim a little high,
                // we can miss by a little.
                //
                // We *do* need to enforce that this is at least 1,
                // since marking is racy and double-scanning objects
                // may legitimately make the remaining scan work
                // negative, even in the hard goal regime.
                scanWorkRemaining = 1000
        }

        // Compute the heap distance remaining.
        heapRemaining := heapGoal - int64(live)
        if heapRemaining <= 0 {
                // This shouldn't happen, but if it does, avoid
                // dividing by zero or setting the assist negative.
                heapRemaining = 1
        }

        // Compute the mutator assist ratio so by the time the mutator
        // allocates the remaining heap bytes up to heapGoal, it will
        // have done (or stolen) the remaining amount of scan work.
        // Note that the assist ratio values are updated atomically
        // but not together. This means there may be some degree of
        // skew between the two values. This is generally OK as the
        // values shift relatively slowly over the course of a GC
        // cycle.
        assistWorkPerByte := float64(scanWorkRemaining) / float64(heapRemaining)
        assistBytesPerWork := float64(heapRemaining) / float64(scanWorkRemaining)
        c.assistWorkPerByte.Store(assistWorkPerByte)
        c.assistBytesPerWork.Store(assistBytesPerWork)
}

// endCycle computes the trigger ratio (!goexperiment.PacerRedesign)
// or the consMark estimate (goexperiment.PacerRedesign) for the next cycle.
// Returns the trigger ratio if application, or 0 (goexperiment.PacerRedesign).
// userForced indicates whether the current GC cycle was forced
// by the application.
func (c *gcControllerState) endCycle(now int64, procs int, userForced bool) float64 {
        // Record last heap goal for the scavenger.
        // We'll be updating the heap goal soon.
        gcController.lastHeapGoal = gcController.heapGoal

        // Compute the duration of time for which assists were turned on.
        assistDuration := now - c.markStartTime

        // Assume background mark hit its utilization goal.
        utilization := gcBackgroundUtilization
        // Add assist utilization; avoid divide by zero.
        if assistDuration > 0 {
                utilization += float64(c.assistTime) / float64(assistDuration*int64(procs))
        }

        if goexperiment.PacerRedesign {
                if c.heapLive <= c.trigger {
                        // Shouldn't happen, but let's be very safe about this in case the
                        // GC is somehow extremely short.
                        //
                        // In this case though, the only reasonable value for c.heapLive-c.trigger
                        // would be 0, which isn't really all that useful, i.e. the GC was so short
                        // that it didn't matter.
                        //
                        // Ignore this case and don't update anything.
                        return 0
                }
                idleUtilization := 0.0
                if assistDuration > 0 {
                        idleUtilization = float64(c.idleMarkTime) / float64(assistDuration*int64(procs))
                }
                // Determine the cons/mark ratio.
                //
                // The units we want for the numerator and denominator are both B / cpu-ns.
                // We get this by taking the bytes allocated or scanned, and divide by the amount of
                // CPU time it took for those operations. For allocations, that CPU time is
                //
                //    assistDuration * procs * (1 - utilization)
                //
                // Where utilization includes just background GC workers and assists. It does *not*
                // include idle GC work time, because in theory the mutator is free to take that at
                // any point.
                //
                // For scanning, that CPU time is
                //
                //    assistDuration * procs * (utilization + idleUtilization)
                //
                // In this case, we *include* idle utilization, because that is additional CPU time that the
                // the GC had available to it.
                //
                // In effect, idle GC time is sort of double-counted here, but it's very weird compared
                // to other kinds of GC work, because of how fluid it is. Namely, because the mutator is
                // *always* free to take it.
                //
                // So this calculation is really:
                //     (heapLive-trigger) / (assistDuration * procs * (1-utilization)) /
                //         (scanWork) / (assistDuration * procs * (utilization+idleUtilization)
                //
                // Note that because we only care about the ratio, assistDuration and procs cancel out.
                scanWork := c.heapScanWork.Load() + c.stackScanWork.Load() + c.globalsScanWork.Load()
                currentConsMark := (float64(c.heapLive-c.trigger) * (utilization + idleUtilization)) /
                        (float64(scanWork) * (1 - utilization))

                // Update cons/mark controller.
                oldConsMark := c.consMark
                c.consMark = c.consMarkController.next(c.consMark, currentConsMark)

                if debug.gcpacertrace > 0 {
                        printlock()
                        print("pacer: ", int(utilization*100), "% CPU (", int(gcGoalUtilization*100), " exp.) for ")
                        print(c.heapScanWork.Load(), "+", c.stackScanWork.Load(), "+", c.globalsScanWork.Load(), " B work (", c.lastHeapScan+c.stackScan+c.globalsScan, " B exp.) ")
                        print("in ", c.trigger, " B -> ", c.heapLive, " B (∆goal ", int64(c.heapLive)-int64(c.heapGoal), ", cons/mark ", oldConsMark, ")")
                        println()
                        printunlock()
                }
                return 0
        }

        // !goexperiment.PacerRedesign below.

        if userForced {
                // Forced GC means this cycle didn't start at the
                // trigger, so where it finished isn't good
                // information about how to adjust the trigger.
                // Just leave it where it is.
                return c.triggerRatio
        }

        // Proportional response gain for the trigger controller. Must
        // be in [0, 1]. Lower values smooth out transient effects but
        // take longer to respond to phase changes. Higher values
        // react to phase changes quickly, but are more affected by
        // transient changes. Values near 1 may be unstable.
        const triggerGain = 0.5

        // Compute next cycle trigger ratio. First, this computes the
        // "error" for this cycle; that is, how far off the trigger
        // was from what it should have been, accounting for both heap
        // growth and GC CPU utilization. We compute the actual heap
        // growth during this cycle and scale that by how far off from
        // the goal CPU utilization we were (to estimate the heap
        // growth if we had the desired CPU utilization). The
        // difference between this estimate and the GOGC-based goal
        // heap growth is the error.
        goalGrowthRatio := c.effectiveGrowthRatio()
        actualGrowthRatio := float64(c.heapLive)/float64(c.heapMarked) - 1
        triggerError := goalGrowthRatio - c.triggerRatio - utilization/gcGoalUtilization*(actualGrowthRatio-c.triggerRatio)

        // Finally, we adjust the trigger for next time by this error,
        // damped by the proportional gain.
        triggerRatio := c.triggerRatio + triggerGain*triggerError

        if debug.gcpacertrace > 0 {
                // Print controller state in terms of the design
                // document.
                H_m_prev := c.heapMarked
                h_t := c.triggerRatio
                H_T := c.trigger
                h_a := actualGrowthRatio
                H_a := c.heapLive
                h_g := goalGrowthRatio
                H_g := int64(float64(H_m_prev) * (1 + h_g))
                u_a := utilization
                u_g := gcGoalUtilization
                W_a := c.heapScanWork.Load()
                print("pacer: H_m_prev=", H_m_prev,
                        " h_t=", h_t, " H_T=", H_T,
                        " h_a=", h_a, " H_a=", H_a,
                        " h_g=", h_g, " H_g=", H_g,
                        " u_a=", u_a, " u_g=", u_g,
                        " W_a=", W_a,
                        " goalΔ=", goalGrowthRatio-h_t,
                        " actualΔ=", h_a-h_t,
                        " u_a/u_g=", u_a/u_g,
                        "\n")
        }

        return triggerRatio
}

// enlistWorker encourages another dedicated mark worker to start on
// another P if there are spare worker slots. It is used by putfull
// when more work is made available.
//
//go:nowritebarrier
func (c *gcControllerState) enlistWorker() {
        // If there are idle Ps, wake one so it will run an idle worker.
        // NOTE: This is suspected of causing deadlocks. See golang.org/issue/19112.
        //
        //      if atomic.Load(&sched.npidle) != 0 && atomic.Load(&sched.nmspinning) == 0 {
        //              wakep()
        //              return
        //      }

        // There are no idle Ps. If we need more dedicated workers,
        // try to preempt a running P so it will switch to a worker.
        if c.dedicatedMarkWorkersNeeded <= 0 {
                return
        }
        // Pick a random other P to preempt.
        if gomaxprocs <= 1 {
                return
        }
        gp := getg()
        if gp == nil || gp.m == nil || gp.m.p == 0 {
                return
        }
        myID := gp.m.p.ptr().id
        for tries := 0; tries < 5; tries++ {
                id := int32(fastrandn(uint32(gomaxprocs - 1)))
                if id >= myID {
                        id++
                }
                p := allp[id]
                if p.status != _Prunning {
                        continue
                }
                if preemptone(p) {
                        return
                }
        }
}

// findRunnableGCWorker returns a background mark worker for _p_ if it
// should be run. This must only be called when gcBlackenEnabled != 0.
func (c *gcControllerState) findRunnableGCWorker(_p_ *p) *g {
        if gcBlackenEnabled == 0 {
                throw("gcControllerState.findRunnable: blackening not enabled")
        }

        if !gcMarkWorkAvailable(_p_) {
                // No work to be done right now. This can happen at
                // the end of the mark phase when there are still
                // assists tapering off. Don't bother running a worker
                // now because it'll just return immediately.
                return nil
        }

        // Grab a worker before we commit to running below.
        node := (*gcBgMarkWorkerNode)(gcBgMarkWorkerPool.pop())
        if node == nil {
                // There is at least one worker per P, so normally there are
                // enough workers to run on all Ps, if necessary. However, once
                // a worker enters gcMarkDone it may park without rejoining the
                // pool, thus freeing a P with no corresponding worker.
                // gcMarkDone never depends on another worker doing work, so it
                // is safe to simply do nothing here.
                //
                // If gcMarkDone bails out without completing the mark phase,
                // it will always do so with queued global work. Thus, that P
                // will be immediately eligible to re-run the worker G it was
                // just using, ensuring work can complete.
                return nil
        }

        decIfPositive := func(ptr *int64) bool {
                for {
                        v := atomic.Loadint64(ptr)
                        if v <= 0 {
                                return false
                        }

                        if atomic.Casint64(ptr, v, v-1) {
                                return true
                        }
                }
        }

        if decIfPositive(&c.dedicatedMarkWorkersNeeded) {
                // This P is now dedicated to marking until the end of
                // the concurrent mark phase.
                _p_.gcMarkWorkerMode = gcMarkWorkerDedicatedMode
        } else if c.fractionalUtilizationGoal == 0 {
                // No need for fractional workers.
                gcBgMarkWorkerPool.push(&node.node)
                return nil
        } else {
                // Is this P behind on the fractional utilization
                // goal?
                //
                // This should be kept in sync with pollFractionalWorkerExit.
                delta := nanotime() - c.markStartTime
                if delta > 0 && float64(_p_.gcFractionalMarkTime)/float64(delta) > c.fractionalUtilizationGoal {
                        // Nope. No need to run a fractional worker.
                        gcBgMarkWorkerPool.push(&node.node)
                        return nil
                }
                // Run a fractional worker.
                _p_.gcMarkWorkerMode = gcMarkWorkerFractionalMode
        }

        // Run the background mark worker.
        gp := node.gp.ptr()
        casgstatus(gp, _Gwaiting, _Grunnable)
        if trace.enabled {
                traceGoUnpark(gp, 0)
        }
        return gp
}

// resetLive sets up the controller state for the next mark phase after the end
// of the previous one. Must be called after endCycle and before commit, before
// the world is started.
//
// The world must be stopped.
func (c *gcControllerState) resetLive(bytesMarked uint64) {
        c.heapMarked = bytesMarked
        c.heapLive = bytesMarked
        c.heapScan = uint64(c.heapScanWork.Load())
        c.lastHeapScan = uint64(c.heapScanWork.Load())

        // heapLive was updated, so emit a trace event.
        if trace.enabled {
                traceHeapAlloc()
        }
}

// logWorkTime updates mark work accounting in the controller by a duration of
// work in nanoseconds.
//
// Safe to execute at any time.
func (c *gcControllerState) logWorkTime(mode gcMarkWorkerMode, duration int64) {
        switch mode {
        case gcMarkWorkerDedicatedMode:
                atomic.Xaddint64(&c.dedicatedMarkTime, duration)
                atomic.Xaddint64(&c.dedicatedMarkWorkersNeeded, 1)
        case gcMarkWorkerFractionalMode:
                atomic.Xaddint64(&c.fractionalMarkTime, duration)
        case gcMarkWorkerIdleMode:
                atomic.Xaddint64(&c.idleMarkTime, duration)
        default:
                throw("logWorkTime: unknown mark worker mode")
        }
}

func (c *gcControllerState) update(dHeapLive, dHeapScan int64) {
        if dHeapLive != 0 {
                atomic.Xadd64(&gcController.heapLive, dHeapLive)
                if trace.enabled {
                        // gcController.heapLive changed.
                        traceHeapAlloc()
                }
        }
        // Only update heapScan in the new pacer redesign if we're not
        // currently in a GC.
        if !goexperiment.PacerRedesign || gcBlackenEnabled == 0 {
                if dHeapScan != 0 {
                        atomic.Xadd64(&gcController.heapScan, dHeapScan)
                }
        }
        if gcBlackenEnabled != 0 {
                // gcController.heapLive and heapScan changed.
                c.revise()
        }
}

func (c *gcControllerState) addScannableStack(pp *p, amount int64) {
        if pp == nil {
                atomic.Xadd64(&c.scannableStackSize, amount)
                return
        }
        pp.scannableStackSizeDelta += amount
        if pp.scannableStackSizeDelta >= scannableStackSizeSlack || pp.scannableStackSizeDelta <= -scannableStackSizeSlack {
                atomic.Xadd64(&c.scannableStackSize, pp.scannableStackSizeDelta)
                pp.scannableStackSizeDelta = 0
        }
}

func (c *gcControllerState) addGlobals(amount int64) {
        atomic.Xadd64(&c.globalsScan, amount)
}

// commit recomputes all pacing parameters from scratch, namely
// absolute trigger, the heap goal, mark pacing, and sweep pacing.
//
// If goexperiment.PacerRedesign is true, triggerRatio is ignored.
//
// This can be called any time. If GC is the in the middle of a
// concurrent phase, it will adjust the pacing of that phase.
//
// This depends on gcPercent, gcController.heapMarked, and
// gcController.heapLive. These must be up to date.
//
// mheap_.lock must be held or the world must be stopped.
func (c *gcControllerState) commit(triggerRatio float64) {
        if !c.test {
                assertWorldStoppedOrLockHeld(&mheap_.lock)
        }

        if !goexperiment.PacerRedesign {
                c.oldCommit(triggerRatio)
                return
        }

        // Compute the next GC goal, which is when the allocated heap
        // has grown by GOGC/100 over where it started the last cycle,
        // plus additional runway for non-heap sources of GC work.
        goal := ^uint64(0)
        if c.gcPercent >= 0 {
                goal = c.heapMarked + (c.heapMarked+atomic.Load64(&c.stackScan)+atomic.Load64(&c.globalsScan))*uint64(c.gcPercent)/100
        }

        // Don't trigger below the minimum heap size.
        minTrigger := c.heapMinimum
        if !isSweepDone() {
                // Concurrent sweep happens in the heap growth
                // from gcController.heapLive to trigger, so ensure
                // that concurrent sweep has some heap growth
                // in which to perform sweeping before we
                // start the next GC cycle.
                sweepMin := atomic.Load64(&c.heapLive) + sweepMinHeapDistance
                if sweepMin > minTrigger {
                        minTrigger = sweepMin
                }
        }

        // If we let the trigger go too low, then if the application
        // is allocating very rapidly we might end up in a situation
        // where we're allocating black during a nearly always-on GC.
        // The result of this is a growing heap and ultimately an
        // increase in RSS. By capping us at a point >0, we're essentially
        // saying that we're OK using more CPU during the GC to prevent
        // this growth in RSS.
        //
        // The current constant was chosen empirically: given a sufficiently
        // fast/scalable allocator with 48 Ps that could drive the trigger ratio
        // to <0.05, this constant causes applications to retain the same peak
        // RSS compared to not having this allocator.
        if triggerBound := uint64(0.7*float64(goal-c.heapMarked)) + c.heapMarked; minTrigger < triggerBound {
                minTrigger = triggerBound
        }

        // For small heaps, set the max trigger point at 95% of the heap goal.
        // This ensures we always have *some* headroom when the GC actually starts.
        // For larger heaps, set the max trigger point at the goal, minus the
        // minimum heap size.
        // This choice follows from the fact that the minimum heap size is chosen
        // to reflect the costs of a GC with no work to do. With a large heap but
        // very little scan work to perform, this gives us exactly as much runway
        // as we would need, in the worst case.
        maxRunway := uint64(0.95 * float64(goal-c.heapMarked))
        if largeHeapMaxRunway := goal - c.heapMinimum; goal > c.heapMinimum && maxRunway < largeHeapMaxRunway {
                maxRunway = largeHeapMaxRunway
        }
        maxTrigger := maxRunway + c.heapMarked
        if maxTrigger < minTrigger {
                maxTrigger = minTrigger
        }

        // Compute the trigger by using our estimate of the cons/mark ratio.
        //
        // The idea is to take our expected scan work, and multiply it by
        // the cons/mark ratio to determine how long it'll take to complete
        // that scan work in terms of bytes allocated. This gives us our GC's
        // runway.
        //
        // However, the cons/mark ratio is a ratio of rates per CPU-second, but
        // here we care about the relative rates for some division of CPU
        // resources among the mutator and the GC.
        //
        // To summarize, we have B / cpu-ns, and we want B / ns. We get that
        // by multiplying by our desired division of CPU resources. We choose
        // to express CPU resources as GOMAPROCS*fraction. Note that because
        // we're working with a ratio here, we can omit the number of CPU cores,
        // because they'll appear in the numerator and denominator and cancel out.
        // As a result, this is basically just "weighing" the cons/mark ratio by
        // our desired division of resources.
        //
        // Furthermore, by setting the trigger so that CPU resources are divided
        // this way, assuming that the cons/mark ratio is correct, we make that
        // division a reality.
        var trigger uint64
        runway := uint64((c.consMark * (1 - gcGoalUtilization) / (gcGoalUtilization)) * float64(c.lastHeapScan+c.stackScan+c.globalsScan))
        if runway > goal {
                trigger = minTrigger
        } else {
                trigger = goal - runway
        }
        if trigger < minTrigger {
                trigger = minTrigger
        }
        if trigger > maxTrigger {
                trigger = maxTrigger
        }
        if trigger > goal {
                goal = trigger
        }

        // Commit to the trigger and goal.
        c.trigger = trigger
        atomic.Store64(&c.heapGoal, goal)
        if trace.enabled {
                traceHeapGoal()
        }

        // Update mark pacing.
        if gcphase != _GCoff {
                c.revise()
        }
}

// oldCommit sets the trigger ratio and updates everything
// derived from it: the absolute trigger, the heap goal, mark pacing,
// and sweep pacing.
//
// This can be called any time. If GC is the in the middle of a
// concurrent phase, it will adjust the pacing of that phase.
//
// This depends on gcPercent, gcController.heapMarked, and
// gcController.heapLive. These must be up to date.
//
// For !goexperiment.PacerRedesign.
func (c *gcControllerState) oldCommit(triggerRatio float64) {
        // Compute the next GC goal, which is when the allocated heap
        // has grown by GOGC/100 over the heap marked by the last
        // cycle.
        goal := ^uint64(0)
        if c.gcPercent >= 0 {
                goal = c.heapMarked + c.heapMarked*uint64(c.gcPercent)/100
        }

        // Set the trigger ratio, capped to reasonable bounds.
        if c.gcPercent >= 0 {
                scalingFactor := float64(c.gcPercent) / 100
                // Ensure there's always a little margin so that the
                // mutator assist ratio isn't infinity.
                maxTriggerRatio := 0.95 * scalingFactor
                if triggerRatio > maxTriggerRatio {
                        triggerRatio = maxTriggerRatio
                }

                // If we let triggerRatio go too low, then if the application
                // is allocating very rapidly we might end up in a situation
                // where we're allocating black during a nearly always-on GC.
                // The result of this is a growing heap and ultimately an
                // increase in RSS. By capping us at a point >0, we're essentially
                // saying that we're OK using more CPU during the GC to prevent
                // this growth in RSS.
                //
                // The current constant was chosen empirically: given a sufficiently
                // fast/scalable allocator with 48 Ps that could drive the trigger ratio
                // to <0.05, this constant causes applications to retain the same peak
                // RSS compared to not having this allocator.
                minTriggerRatio := 0.6 * scalingFactor
                if triggerRatio < minTriggerRatio {
                        triggerRatio = minTriggerRatio
                }
        } else if triggerRatio < 0 {
                // gcPercent < 0, so just make sure we're not getting a negative
                // triggerRatio. This case isn't expected to happen in practice,
                // and doesn't really matter because if gcPercent < 0 then we won't
                // ever consume triggerRatio further on in this function, but let's
                // just be defensive here; the triggerRatio being negative is almost
                // certainly undesirable.
                triggerRatio = 0
        }
        c.triggerRatio = triggerRatio

        // Compute the absolute GC trigger from the trigger ratio.
        //
        // We trigger the next GC cycle when the allocated heap has
        // grown by the trigger ratio over the marked heap size.
        trigger := ^uint64(0)
        if c.gcPercent >= 0 {
                trigger = uint64(float64(c.heapMarked) * (1 + triggerRatio))
                // Don't trigger below the minimum heap size.
                minTrigger := c.heapMinimum
                if !isSweepDone() {
                        // Concurrent sweep happens in the heap growth
                        // from gcController.heapLive to trigger, so ensure
                        // that concurrent sweep has some heap growth
                        // in which to perform sweeping before we
                        // start the next GC cycle.
                        sweepMin := atomic.Load64(&c.heapLive) + sweepMinHeapDistance
                        if sweepMin > minTrigger {
                                minTrigger = sweepMin
                        }
                }
                if trigger < minTrigger {
                        trigger = minTrigger
                }
                if int64(trigger) < 0 {
                        print("runtime: heapGoal=", c.heapGoal, " heapMarked=", c.heapMarked, " gcController.heapLive=", c.heapLive, " initialHeapLive=", work.initialHeapLive, "triggerRatio=", triggerRatio, " minTrigger=", minTrigger, "\n")
                        throw("trigger underflow")
                }
                if trigger > goal {
                        // The trigger ratio is always less than GOGC/100, but
                        // other bounds on the trigger may have raised it.
                        // Push up the goal, too.
                        goal = trigger
                }
        }

        // Commit to the trigger and goal.
        c.trigger = trigger
        atomic.Store64(&c.heapGoal, goal)
        if trace.enabled {
                traceHeapGoal()
        }

        // Update mark pacing.
        if gcphase != _GCoff {
                c.revise()
        }
}

// effectiveGrowthRatio returns the current effective heap growth
// ratio (GOGC/100) based on heapMarked from the previous GC and
// heapGoal for the current GC.
//
// This may differ from gcPercent/100 because of various upper and
// lower bounds on gcPercent. For example, if the heap is smaller than
// heapMinimum, this can be higher than gcPercent/100.
//
// mheap_.lock must be held or the world must be stopped.
func (c *gcControllerState) effectiveGrowthRatio() float64 {
        if !c.test {
                assertWorldStoppedOrLockHeld(&mheap_.lock)
        }

        egogc := float64(atomic.Load64(&c.heapGoal)-c.heapMarked) / float64(c.heapMarked)
        if egogc < 0 {
                // Shouldn't happen, but just in case.
                egogc = 0
        }
        return egogc
}

// setGCPercent updates gcPercent and all related pacer state.
// Returns the old value of gcPercent.
//
// Calls gcControllerState.commit.
//
// The world must be stopped, or mheap_.lock must be held.
func (c *gcControllerState) setGCPercent(in int32) int32 {
        if !c.test {
                assertWorldStoppedOrLockHeld(&mheap_.lock)
        }

        out := c.gcPercent
        if in < 0 {
                in = -1
        }
        // Write it atomically so readers like revise() can read it safely.
        atomic.Storeint32(&c.gcPercent, in)
        c.heapMinimum = defaultHeapMinimum * uint64(c.gcPercent) / 100
        // Update pacing in response to gcPercent change.
        c.commit(c.triggerRatio)

        return out
}

//go:linkname setGCPercent runtime/debug.setGCPercent
func setGCPercent(in int32) (out int32) {
        // Run on the system stack since we grab the heap lock.
        systemstack(func() {
                lock(&mheap_.lock)
                out = gcController.setGCPercent(in)
                gcPaceSweeper(gcController.trigger)
                gcPaceScavenger(gcController.heapGoal, gcController.lastHeapGoal)
                unlock(&mheap_.lock)
        })

        // If we just disabled GC, wait for any concurrent GC mark to
        // finish so we always return with no GC running.
        if in < 0 {
                gcWaitOnMark(atomic.Load(&work.cycles))
        }

        return out
}

func readGOGC() int32 {
        p := gogetenv("GOGC")
        if p == "off" {
                return -1
        }
        if n, ok := atoi32(p); ok {
                return n
        }
        return 100
}

type piController struct {
        kp float64 // Proportional constant.
        ti float64 // Integral time constant.
        tt float64 // Reset time in GC cyles.

        // Period in GC cycles between updates.
        period float64

        min, max float64 // Output boundaries.

        // PI controller state.

        errIntegral float64 // Integral of the error from t=0 to now.
}

func (c *piController) next(input, setpoint float64) float64 {
        // Compute the raw output value.
        prop := c.kp * (setpoint - input)
        rawOutput := prop + c.errIntegral

        // Clamp rawOutput into output.
        output := rawOutput
        if output < c.min {
                output = c.min
        } else if output > c.max {
                output = c.max
        }

        // Update the controller's state.
        if c.ti != 0 && c.tt != 0 {
                c.errIntegral += (c.kp*c.period/c.ti)*(setpoint-input) + (c.period/c.tt)*(output-rawOutput)
        }
        return output
}