powerpc/perf_counter: Add generic support for POWER-family PMU hardware

This provides the architecture-specific functions needed to access
PMU hardware on the 64-bit PowerPC processors.  It has been designed
for the IBM POWER family (POWER 4/4+/5/5+/6 and PPC970) but will
hopefully also suit other 64-bit PowerPC machines (although probably
not Cell given how different it is in this area).  This doesn't
include back-ends for any specific processors.

This implements a system which allows back-ends to express the
constraints that their hardware has on what events can be counted
simultaneously.  The constraints are expressed as a 64-bit mask +
64-bit value for each event, and the encoding is capable of
expressing the constraints arising from having a set of multiplexers
feeding an event bus, with some events being available through
multiple multiplexer settings, such as we get on POWER4 and PPC970.
Furthermore, the back-end can supply alternative event codes for
each event, and the constraint checking code will try all possible
combinations of alternative event codes to try to find a combination
that will fit.

Signed-off-by: Paul Mackerras <paulus@samba.org>
This commit is contained in:
Paul Mackerras 2009-01-09 20:21:55 +11:00
parent 93a6d3ce69
commit 4574910e50
3 changed files with 817 additions and 0 deletions

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@ -8,3 +8,65 @@
* as published by the Free Software Foundation; either version
* 2 of the License, or (at your option) any later version.
*/
#include <linux/types.h>
#define MAX_HWCOUNTERS 8
#define MAX_EVENT_ALTERNATIVES 8
/*
* This struct provides the constants and functions needed to
* describe the PMU on a particular POWER-family CPU.
*/
struct power_pmu {
int n_counter;
int max_alternatives;
u64 add_fields;
u64 test_adder;
int (*compute_mmcr)(unsigned int events[], int n_ev,
unsigned int hwc[], u64 mmcr[]);
int (*get_constraint)(unsigned int event, u64 *mskp, u64 *valp);
int (*get_alternatives)(unsigned int event, unsigned int alt[]);
void (*disable_pmc)(unsigned int pmc, u64 mmcr[]);
int n_generic;
int *generic_events;
};
extern struct power_pmu *ppmu;
/*
* The power_pmu.get_constraint function returns a 64-bit value and
* a 64-bit mask that express the constraints between this event and
* other events.
*
* The value and mask are divided up into (non-overlapping) bitfields
* of three different types:
*
* Select field: this expresses the constraint that some set of bits
* in MMCR* needs to be set to a specific value for this event. For a
* select field, the mask contains 1s in every bit of the field, and
* the value contains a unique value for each possible setting of the
* MMCR* bits. The constraint checking code will ensure that two events
* that set the same field in their masks have the same value in their
* value dwords.
*
* Add field: this expresses the constraint that there can be at most
* N events in a particular class. A field of k bits can be used for
* N <= 2^(k-1) - 1. The mask has the most significant bit of the field
* set (and the other bits 0), and the value has only the least significant
* bit of the field set. In addition, the 'add_fields' and 'test_adder'
* in the struct power_pmu for this processor come into play. The
* add_fields value contains 1 in the LSB of the field, and the
* test_adder contains 2^(k-1) - 1 - N in the field.
*
* NAND field: this expresses the constraint that you may not have events
* in all of a set of classes. (For example, on PPC970, you can't select
* events from the FPU, ISU and IDU simultaneously, although any two are
* possible.) For N classes, the field is N+1 bits wide, and each class
* is assigned one bit from the least-significant N bits. The mask has
* only the most-significant bit set, and the value has only the bit
* for the event's class set. The test_adder has the least significant
* bit set in the field.
*
* If an event is not subject to the constraint expressed by a particular
* field, then it will have 0 in both the mask and value for that field.
*/

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@ -94,6 +94,7 @@ obj-$(CONFIG_AUDIT) += audit.o
obj64-$(CONFIG_AUDIT) += compat_audit.o
obj-$(CONFIG_DYNAMIC_FTRACE) += ftrace.o
obj-$(CONFIG_PERF_COUNTERS) += perf_counter.o
obj-$(CONFIG_8XX_MINIMAL_FPEMU) += softemu8xx.o

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@ -0,0 +1,754 @@
/*
* Performance counter support - powerpc architecture code
*
* Copyright 2008-2009 Paul Mackerras, IBM Corporation.
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version
* 2 of the License, or (at your option) any later version.
*/
#include <linux/kernel.h>
#include <linux/sched.h>
#include <linux/perf_counter.h>
#include <linux/percpu.h>
#include <linux/hardirq.h>
#include <asm/reg.h>
#include <asm/pmc.h>
struct cpu_hw_counters {
int n_counters;
int n_percpu;
int disabled;
int n_added;
struct perf_counter *counter[MAX_HWCOUNTERS];
unsigned int events[MAX_HWCOUNTERS];
u64 mmcr[3];
};
DEFINE_PER_CPU(struct cpu_hw_counters, cpu_hw_counters);
struct power_pmu *ppmu;
void perf_counter_print_debug(void)
{
}
/*
* Return 1 for a software counter, 0 for a hardware counter
*/
static inline int is_software_counter(struct perf_counter *counter)
{
return !counter->hw_event.raw && counter->hw_event.type < 0;
}
/*
* Read one performance monitor counter (PMC).
*/
static unsigned long read_pmc(int idx)
{
unsigned long val;
switch (idx) {
case 1:
val = mfspr(SPRN_PMC1);
break;
case 2:
val = mfspr(SPRN_PMC2);
break;
case 3:
val = mfspr(SPRN_PMC3);
break;
case 4:
val = mfspr(SPRN_PMC4);
break;
case 5:
val = mfspr(SPRN_PMC5);
break;
case 6:
val = mfspr(SPRN_PMC6);
break;
case 7:
val = mfspr(SPRN_PMC7);
break;
case 8:
val = mfspr(SPRN_PMC8);
break;
default:
printk(KERN_ERR "oops trying to read PMC%d\n", idx);
val = 0;
}
return val;
}
/*
* Write one PMC.
*/
static void write_pmc(int idx, unsigned long val)
{
switch (idx) {
case 1:
mtspr(SPRN_PMC1, val);
break;
case 2:
mtspr(SPRN_PMC2, val);
break;
case 3:
mtspr(SPRN_PMC3, val);
break;
case 4:
mtspr(SPRN_PMC4, val);
break;
case 5:
mtspr(SPRN_PMC5, val);
break;
case 6:
mtspr(SPRN_PMC6, val);
break;
case 7:
mtspr(SPRN_PMC7, val);
break;
case 8:
mtspr(SPRN_PMC8, val);
break;
default:
printk(KERN_ERR "oops trying to write PMC%d\n", idx);
}
}
/*
* Check if a set of events can all go on the PMU at once.
* If they can't, this will look at alternative codes for the events
* and see if any combination of alternative codes is feasible.
* The feasible set is returned in event[].
*/
static int power_check_constraints(unsigned int event[], int n_ev)
{
u64 mask, value, nv;
unsigned int alternatives[MAX_HWCOUNTERS][MAX_EVENT_ALTERNATIVES];
u64 amasks[MAX_HWCOUNTERS][MAX_EVENT_ALTERNATIVES];
u64 avalues[MAX_HWCOUNTERS][MAX_EVENT_ALTERNATIVES];
u64 smasks[MAX_HWCOUNTERS], svalues[MAX_HWCOUNTERS];
int n_alt[MAX_HWCOUNTERS], choice[MAX_HWCOUNTERS];
int i, j;
u64 addf = ppmu->add_fields;
u64 tadd = ppmu->test_adder;
if (n_ev > ppmu->n_counter)
return -1;
/* First see if the events will go on as-is */
for (i = 0; i < n_ev; ++i) {
alternatives[i][0] = event[i];
if (ppmu->get_constraint(event[i], &amasks[i][0],
&avalues[i][0]))
return -1;
choice[i] = 0;
}
value = mask = 0;
for (i = 0; i < n_ev; ++i) {
nv = (value | avalues[i][0]) + (value & avalues[i][0] & addf);
if ((((nv + tadd) ^ value) & mask) != 0 ||
(((nv + tadd) ^ avalues[i][0]) & amasks[i][0]) != 0)
break;
value = nv;
mask |= amasks[i][0];
}
if (i == n_ev)
return 0; /* all OK */
/* doesn't work, gather alternatives... */
if (!ppmu->get_alternatives)
return -1;
for (i = 0; i < n_ev; ++i) {
n_alt[i] = ppmu->get_alternatives(event[i], alternatives[i]);
for (j = 1; j < n_alt[i]; ++j)
ppmu->get_constraint(alternatives[i][j],
&amasks[i][j], &avalues[i][j]);
}
/* enumerate all possibilities and see if any will work */
i = 0;
j = -1;
value = mask = nv = 0;
while (i < n_ev) {
if (j >= 0) {
/* we're backtracking, restore context */
value = svalues[i];
mask = smasks[i];
j = choice[i];
}
/*
* See if any alternative k for event i,
* where k > j, will satisfy the constraints.
*/
while (++j < n_alt[i]) {
nv = (value | avalues[i][j]) +
(value & avalues[i][j] & addf);
if ((((nv + tadd) ^ value) & mask) == 0 &&
(((nv + tadd) ^ avalues[i][j])
& amasks[i][j]) == 0)
break;
}
if (j >= n_alt[i]) {
/*
* No feasible alternative, backtrack
* to event i-1 and continue enumerating its
* alternatives from where we got up to.
*/
if (--i < 0)
return -1;
} else {
/*
* Found a feasible alternative for event i,
* remember where we got up to with this event,
* go on to the next event, and start with
* the first alternative for it.
*/
choice[i] = j;
svalues[i] = value;
smasks[i] = mask;
value = nv;
mask |= amasks[i][j];
++i;
j = -1;
}
}
/* OK, we have a feasible combination, tell the caller the solution */
for (i = 0; i < n_ev; ++i)
event[i] = alternatives[i][choice[i]];
return 0;
}
static void power_perf_read(struct perf_counter *counter)
{
long val, delta, prev;
if (!counter->hw.idx)
return;
/*
* Performance monitor interrupts come even when interrupts
* are soft-disabled, as long as interrupts are hard-enabled.
* Therefore we treat them like NMIs.
*/
do {
prev = atomic64_read(&counter->hw.prev_count);
barrier();
val = read_pmc(counter->hw.idx);
} while (atomic64_cmpxchg(&counter->hw.prev_count, prev, val) != prev);
/* The counters are only 32 bits wide */
delta = (val - prev) & 0xfffffffful;
atomic64_add(delta, &counter->count);
atomic64_sub(delta, &counter->hw.period_left);
}
/*
* Disable all counters to prevent PMU interrupts and to allow
* counters to be added or removed.
*/
u64 hw_perf_save_disable(void)
{
struct cpu_hw_counters *cpuhw;
unsigned long ret;
unsigned long flags;
local_irq_save(flags);
cpuhw = &__get_cpu_var(cpu_hw_counters);
ret = cpuhw->disabled;
if (!ret) {
cpuhw->disabled = 1;
cpuhw->n_added = 0;
/*
* Set the 'freeze counters' bit.
* The barrier is to make sure the mtspr has been
* executed and the PMU has frozen the counters
* before we return.
*/
mtspr(SPRN_MMCR0, mfspr(SPRN_MMCR0) | MMCR0_FC);
mb();
}
local_irq_restore(flags);
return ret;
}
/*
* Re-enable all counters if disable == 0.
* If we were previously disabled and counters were added, then
* put the new config on the PMU.
*/
void hw_perf_restore(u64 disable)
{
struct perf_counter *counter;
struct cpu_hw_counters *cpuhw;
unsigned long flags;
long i;
unsigned long val;
s64 left;
unsigned int hwc_index[MAX_HWCOUNTERS];
if (disable)
return;
local_irq_save(flags);
cpuhw = &__get_cpu_var(cpu_hw_counters);
cpuhw->disabled = 0;
/*
* If we didn't change anything, or only removed counters,
* no need to recalculate MMCR* settings and reset the PMCs.
* Just reenable the PMU with the current MMCR* settings
* (possibly updated for removal of counters).
*/
if (!cpuhw->n_added) {
mtspr(SPRN_MMCRA, cpuhw->mmcr[2]);
mtspr(SPRN_MMCR1, cpuhw->mmcr[1]);
mtspr(SPRN_MMCR0, cpuhw->mmcr[0]);
goto out;
}
/*
* Compute MMCR* values for the new set of counters
*/
if (ppmu->compute_mmcr(cpuhw->events, cpuhw->n_counters, hwc_index,
cpuhw->mmcr)) {
/* shouldn't ever get here */
printk(KERN_ERR "oops compute_mmcr failed\n");
goto out;
}
/*
* Write the new configuration to MMCR* with the freeze
* bit set and set the hardware counters to their initial values.
* Then unfreeze the counters.
*/
mtspr(SPRN_MMCRA, cpuhw->mmcr[2]);
mtspr(SPRN_MMCR1, cpuhw->mmcr[1]);
mtspr(SPRN_MMCR0, (cpuhw->mmcr[0] & ~(MMCR0_PMC1CE | MMCR0_PMCjCE))
| MMCR0_FC);
/*
* Read off any pre-existing counters that need to move
* to another PMC.
*/
for (i = 0; i < cpuhw->n_counters; ++i) {
counter = cpuhw->counter[i];
if (counter->hw.idx && counter->hw.idx != hwc_index[i] + 1) {
power_perf_read(counter);
write_pmc(counter->hw.idx, 0);
counter->hw.idx = 0;
}
}
/*
* Initialize the PMCs for all the new and moved counters.
*/
for (i = 0; i < cpuhw->n_counters; ++i) {
counter = cpuhw->counter[i];
if (counter->hw.idx)
continue;
val = 0;
if (counter->hw_event.irq_period) {
left = atomic64_read(&counter->hw.period_left);
if (left < 0x80000000L)
val = 0x80000000L - left;
}
atomic64_set(&counter->hw.prev_count, val);
counter->hw.idx = hwc_index[i] + 1;
write_pmc(counter->hw.idx, val);
}
mb();
cpuhw->mmcr[0] |= MMCR0_PMXE | MMCR0_FCECE;
mtspr(SPRN_MMCR0, cpuhw->mmcr[0]);
out:
local_irq_restore(flags);
}
static int collect_events(struct perf_counter *group, int max_count,
struct perf_counter *ctrs[], unsigned int *events)
{
int n = 0;
struct perf_counter *counter;
if (!is_software_counter(group)) {
if (n >= max_count)
return -1;
ctrs[n] = group;
events[n++] = group->hw.config;
}
list_for_each_entry(counter, &group->sibling_list, list_entry) {
if (!is_software_counter(counter) &&
counter->state != PERF_COUNTER_STATE_OFF) {
if (n >= max_count)
return -1;
ctrs[n] = counter;
events[n++] = counter->hw.config;
}
}
return n;
}
static void counter_sched_in(struct perf_counter *counter, int cpu)
{
counter->state = PERF_COUNTER_STATE_ACTIVE;
counter->oncpu = cpu;
if (is_software_counter(counter))
counter->hw_ops->enable(counter);
}
/*
* Called to enable a whole group of counters.
* Returns 1 if the group was enabled, or -EAGAIN if it could not be.
* Assumes the caller has disabled interrupts and has
* frozen the PMU with hw_perf_save_disable.
*/
int hw_perf_group_sched_in(struct perf_counter *group_leader,
struct perf_cpu_context *cpuctx,
struct perf_counter_context *ctx, int cpu)
{
struct cpu_hw_counters *cpuhw;
long i, n, n0;
struct perf_counter *sub;
cpuhw = &__get_cpu_var(cpu_hw_counters);
n0 = cpuhw->n_counters;
n = collect_events(group_leader, ppmu->n_counter - n0,
&cpuhw->counter[n0], &cpuhw->events[n0]);
if (n < 0)
return -EAGAIN;
if (power_check_constraints(cpuhw->events, n + n0))
return -EAGAIN;
cpuhw->n_counters = n0 + n;
cpuhw->n_added += n;
/*
* OK, this group can go on; update counter states etc.,
* and enable any software counters
*/
for (i = n0; i < n0 + n; ++i)
cpuhw->counter[i]->hw.config = cpuhw->events[i];
n = 1;
counter_sched_in(group_leader, cpu);
list_for_each_entry(sub, &group_leader->sibling_list, list_entry) {
if (sub->state != PERF_COUNTER_STATE_OFF) {
counter_sched_in(sub, cpu);
++n;
}
}
cpuctx->active_oncpu += n;
ctx->nr_active += n;
return 1;
}
/*
* Add a counter to the PMU.
* If all counters are not already frozen, then we disable and
* re-enable the PMU in order to get hw_perf_restore to do the
* actual work of reconfiguring the PMU.
*/
static int power_perf_enable(struct perf_counter *counter)
{
struct cpu_hw_counters *cpuhw;
unsigned long flags;
u64 pmudis;
int n0;
int ret = -EAGAIN;
local_irq_save(flags);
pmudis = hw_perf_save_disable();
/*
* Add the counter to the list (if there is room)
* and check whether the total set is still feasible.
*/
cpuhw = &__get_cpu_var(cpu_hw_counters);
n0 = cpuhw->n_counters;
if (n0 >= ppmu->n_counter)
goto out;
cpuhw->counter[n0] = counter;
cpuhw->events[n0] = counter->hw.config;
if (power_check_constraints(cpuhw->events, n0 + 1))
goto out;
counter->hw.config = cpuhw->events[n0];
++cpuhw->n_counters;
++cpuhw->n_added;
ret = 0;
out:
hw_perf_restore(pmudis);
local_irq_restore(flags);
return ret;
}
/*
* Remove a counter from the PMU.
*/
static void power_perf_disable(struct perf_counter *counter)
{
struct cpu_hw_counters *cpuhw;
long i;
u64 pmudis;
unsigned long flags;
local_irq_save(flags);
pmudis = hw_perf_save_disable();
power_perf_read(counter);
cpuhw = &__get_cpu_var(cpu_hw_counters);
for (i = 0; i < cpuhw->n_counters; ++i) {
if (counter == cpuhw->counter[i]) {
while (++i < cpuhw->n_counters)
cpuhw->counter[i-1] = cpuhw->counter[i];
--cpuhw->n_counters;
ppmu->disable_pmc(counter->hw.idx - 1, cpuhw->mmcr);
write_pmc(counter->hw.idx, 0);
counter->hw.idx = 0;
break;
}
}
if (cpuhw->n_counters == 0) {
/* disable exceptions if no counters are running */
cpuhw->mmcr[0] &= ~(MMCR0_PMXE | MMCR0_FCECE);
}
hw_perf_restore(pmudis);
local_irq_restore(flags);
}
struct hw_perf_counter_ops power_perf_ops = {
.enable = power_perf_enable,
.disable = power_perf_disable,
.read = power_perf_read
};
const struct hw_perf_counter_ops *
hw_perf_counter_init(struct perf_counter *counter)
{
unsigned long ev;
struct perf_counter *ctrs[MAX_HWCOUNTERS];
unsigned int events[MAX_HWCOUNTERS];
int n;
if (!ppmu)
return NULL;
if ((s64)counter->hw_event.irq_period < 0)
return NULL;
ev = counter->hw_event.type;
if (!counter->hw_event.raw) {
if (ev >= ppmu->n_generic ||
ppmu->generic_events[ev] == 0)
return NULL;
ev = ppmu->generic_events[ev];
}
counter->hw.config_base = ev;
counter->hw.idx = 0;
/*
* If this is in a group, check if it can go on with all the
* other hardware counters in the group. We assume the counter
* hasn't been linked into its leader's sibling list at this point.
*/
n = 0;
if (counter->group_leader != counter) {
n = collect_events(counter->group_leader, ppmu->n_counter - 1,
ctrs, events);
if (n < 0)
return NULL;
}
events[n++] = ev;
if (power_check_constraints(events, n))
return NULL;
counter->hw.config = events[n - 1];
atomic64_set(&counter->hw.period_left, counter->hw_event.irq_period);
return &power_perf_ops;
}
/*
* Handle wakeups.
*/
void perf_counter_do_pending(void)
{
int i;
struct cpu_hw_counters *cpuhw = &__get_cpu_var(cpu_hw_counters);
struct perf_counter *counter;
set_perf_counter_pending(0);
for (i = 0; i < cpuhw->n_counters; ++i) {
counter = cpuhw->counter[i];
if (counter && counter->wakeup_pending) {
counter->wakeup_pending = 0;
wake_up(&counter->waitq);
}
}
}
/*
* Record data for an irq counter.
* This function was lifted from the x86 code; maybe it should
* go in the core?
*/
static void perf_store_irq_data(struct perf_counter *counter, u64 data)
{
struct perf_data *irqdata = counter->irqdata;
if (irqdata->len > PERF_DATA_BUFLEN - sizeof(u64)) {
irqdata->overrun++;
} else {
u64 *p = (u64 *) &irqdata->data[irqdata->len];
*p = data;
irqdata->len += sizeof(u64);
}
}
/*
* Record all the values of the counters in a group
*/
static void perf_handle_group(struct perf_counter *counter)
{
struct perf_counter *leader, *sub;
leader = counter->group_leader;
list_for_each_entry(sub, &leader->sibling_list, list_entry) {
if (sub != counter)
sub->hw_ops->read(sub);
perf_store_irq_data(counter, sub->hw_event.type);
perf_store_irq_data(counter, atomic64_read(&sub->count));
}
}
/*
* A counter has overflowed; update its count and record
* things if requested. Note that interrupts are hard-disabled
* here so there is no possibility of being interrupted.
*/
static void record_and_restart(struct perf_counter *counter, long val,
struct pt_regs *regs)
{
s64 prev, delta, left;
int record = 0;
/* we don't have to worry about interrupts here */
prev = atomic64_read(&counter->hw.prev_count);
delta = (val - prev) & 0xfffffffful;
atomic64_add(delta, &counter->count);
/*
* See if the total period for this counter has expired,
* and update for the next period.
*/
val = 0;
left = atomic64_read(&counter->hw.period_left) - delta;
if (counter->hw_event.irq_period) {
if (left <= 0) {
left += counter->hw_event.irq_period;
if (left <= 0)
left = counter->hw_event.irq_period;
record = 1;
}
if (left < 0x80000000L)
val = 0x80000000L - left;
}
write_pmc(counter->hw.idx, val);
atomic64_set(&counter->hw.prev_count, val);
atomic64_set(&counter->hw.period_left, left);
/*
* Finally record data if requested.
*/
if (record) {
switch (counter->hw_event.record_type) {
case PERF_RECORD_SIMPLE:
break;
case PERF_RECORD_IRQ:
perf_store_irq_data(counter, instruction_pointer(regs));
counter->wakeup_pending = 1;
break;
case PERF_RECORD_GROUP:
perf_handle_group(counter);
counter->wakeup_pending = 1;
break;
}
}
}
/*
* Performance monitor interrupt stuff
*/
static void perf_counter_interrupt(struct pt_regs *regs)
{
int i;
struct cpu_hw_counters *cpuhw = &__get_cpu_var(cpu_hw_counters);
struct perf_counter *counter;
long val;
int need_wakeup = 0, found = 0;
for (i = 0; i < cpuhw->n_counters; ++i) {
counter = cpuhw->counter[i];
val = read_pmc(counter->hw.idx);
if ((int)val < 0) {
/* counter has overflowed */
found = 1;
record_and_restart(counter, val, regs);
if (counter->wakeup_pending)
need_wakeup = 1;
}
}
/*
* In case we didn't find and reset the counter that caused
* the interrupt, scan all counters and reset any that are
* negative, to avoid getting continual interrupts.
* Any that we processed in the previous loop will not be negative.
*/
if (!found) {
for (i = 0; i < ppmu->n_counter; ++i) {
val = read_pmc(i + 1);
if ((int)val < 0)
write_pmc(i + 1, 0);
}
}
/*
* Reset MMCR0 to its normal value. This will set PMXE and
* clear FC (freeze counters) and PMAO (perf mon alert occurred)
* and thus allow interrupts to occur again.
* XXX might want to use MSR.PM to keep the counters frozen until
* we get back out of this interrupt.
*/
mtspr(SPRN_MMCR0, cpuhw->mmcr[0]);
/*
* If we need a wakeup, check whether interrupts were soft-enabled
* when we took the interrupt. If they were, we can wake stuff up
* immediately; otherwise we'll have to set a flag and do the
* wakeup when interrupts get soft-enabled.
*/
if (need_wakeup) {
if (regs->softe) {
irq_enter();
perf_counter_do_pending();
irq_exit();
} else {
set_perf_counter_pending(1);
}
}
}
static int init_perf_counters(void)
{
if (reserve_pmc_hardware(perf_counter_interrupt)) {
printk(KERN_ERR "Couldn't init performance monitor subsystem\n");
return -EBUSY;
}
return 0;
}
arch_initcall(init_perf_counters);